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Membrane potential fluctuations in a neural integrator Zhao Huang A DISSERTATION PRESENTED TO THE FACULTY OF PRINCETON UNIVERSITY IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY RECOMMENDED FOR ACCEPTANCE BY THE DEPARTMENT OF PHYSICS Advisor: David W. Tank JUNE 2009 Copyright 2009 by Zhao Huang. All rights reserved. . Abstract How the brain is able to maintain short-term memory is an unanswered question. The neural correlate of short-term memory is persistent discharge in the absence of continued stimulus. This thesis describes the study of one model system of persistent activity, the goldfish oculomotor neural integrator that integrates (in the calculus sense) transient saccadic and vestibular signals into permanent changes in eye position. We use in vivo whole-cell intracellular recordings of integrator neurons in awake goldfish to temporally resolve individual excitatory postsynaptic potentials (EPSPs). We discovered that the EPSP rate increases with average membrane potential and eye position. The EPSPs also form a frothy fluctuation that constitutes a significant fraction of the total membrane voltage. This suggests that network mechanisms play a substantial if not dominant role in the operation of these neurons. But contrary to predictions of existing neural integration network models, individual EPSPs do not appear to possess long time constants that were critical to network stability and tuning. We present numeric models that show how under some regimes, neurons may be more responsive to fast fluctuation inputs than slow constant inputs. These results motivate the theoretical studies of a new class of neural integrator models that are characterized by fluctuation dominated spike dynamics. iii Acknowledgements This work would not have been possible without building on top of the experiences of many others. I would like to thank Tom Adelman for his support and many innovative suggestions such as the brain clamp. I would like to thank Guy Major for his invaluable tutelage with intracellular recordings and endless passion for fish brains. Anton Khabbaz helped me hone my meager electronics skills and without his help, the data would have been infinitely noisier. Thanks to Santanu Chakraborty for teaching me electrophysiology and the art of goldfish surgery. I am grateful to Emry Aksay for initiating me into the mysteries of Area I anatomy I would like to thank Forrest Collman for providing many stimulating discussions and Andrew Miri and David Markowitz who were always generous with their time and advice. Mark Goldman also provided many helpful comments. And most of all, I would like to thank David Tank for his endless patience and support. iv Table of Contents Abstract .................................................................................................................. iii Acknowledgements................................................................................................ iv Table of Contents.....................................................................................................v List of Figures ....................................................................................................... vii Appendix A: Summary plot for all eight cells .......................................................96 Bibliography ..........................................................................................................97 1 Introduction 1.0 Persistent neural activity and the oculomotor neural integrator ..................1 1.1 Biophysics of a neuron.................................................................................5 2 Models of persistent activity 2.0.0 Network models ......................................................................................13 2.0.1 Anatomical evidence for feedback in cortex and MVN, NPH .........16 2.0.2 In vitro analogue of cortical persistent activity.................................18 2.1.0 Intrinsic cellular mechanisms .................................................................19 2.1.1 Short term synaptic potentiation .......................................................19 2.1.2 Calcium wave model.........................................................................20 2.1.3 Plateau potentials ..............................................................................21 3 Goldfish Area I 3.0 Area I physiology.......................................................................................24 v 3.1 Correlations between paired Area I cells ...................................................26 3.2 Partial inactivation experiments.................................................................26 3.3 Sharp intracellular recordings ....................................................................27 4 Experimental setup 4.0 Whole-cell patch recoding .........................................................................31 4.1 Surgical preparations .................................................................................34 4.2 Vibration isolation .....................................................................................35 4.3 Electrophysiology ......................................................................................39 4.4 Eye tracking system ...................................................................................45 5 Results of whole-cell patch recordings 5.0 Comparison of whole-cell patch recordings with sharp recordings...........46 5.1 Resolved EPSPs have a short time duration ..............................................49 5.2 EPSPs increase with membrane potential and eye position.......................51 5.3 Are integrator cells driven by fluctuations in synaptic input or by the average increase in synaptic input?............................................................65 5.4 Discussion ..................................................................................................70 6 How neurons may operate in a fluctuation dominated regime 6.0 Influences of a distal action potential initiation site on neural discharge ..74 6.1 Origin of voltage/current threshold in the Hodgkin-Huxley model...........75 6.2 Influences of cable geometry on the site of action potential initiation ......83 6.3 Numeric modeling of the properties of different locations of action potential initiation ......................................................................................84 6.4 Discussion ..................................................................................................93 vi List of Figures 1.1 Discharge characteristics of an integrator neuron ............................................3 1.2 Schematic of a neuron........................................................................................6 1.3 Electrical compartment model ...........................................................................7 1.4 Differences between extracellular and intracellular recordings ......................10 3.1 Membrane potential increases with eye position .............................................28 4.1 Different electrode geometries.........................................................................33 4.2 Schematic of experimental setup .....................................................................36 4.3 Picture of a brain clamp ...................................................................................40 5.1 Comparison of sharp vs. whole-cell intracellular recordings ..........................47 5.2 Expanded views of intracellular waveforms....................................................47 5.3 Different shapes of EPSPs ...............................................................................50 5.4 Simulated periodic EPSPs integration in a RC model .....................................54 5.5 Simulated EPSPs integration with 1 ms jitter ..................................................54 5.6 Simulated EPSPs integration with random arrival times.................................55 5.7 Simulated counting of EPSPs with random arrival times................................55 5.8 EPSP frequency increases with eye position ...................................................58 5.9 EPSP frequency increases with average membrane voltage........................... 59 5.10 EPSP frequency necessary to create fluctuations ..........................................59 5.11 Illustration of fluctuations..............................................................................60 vii 5.12 EPSP frequency necessary to construct entire membrane waveform............61 5.13 Dependence of frequency estimation on EPSP shape....................................61 5.14 Different EPSPs used to illustrate the shape dependence of the frequency estimation......................................................................................62 5.15 Ratios of counted EPSPs to estimated number of EPSPs ..............................62 5.16 EPSPs cause large fluctuations in the membrane voltage .............................63 5.17 Peak-to-peak fluctuations increases with membrane voltage ........................64 5.18 Ratio of peak to peak fluctuations to the waveform ......................................64 5.19 Integrator cell operating in its normal regime................................................66 5.20 Expanded view of single action potentials.....................................................67 5.21 Moderately expanded view of single action potentials..................................67 5.22 Action potentials are initiated in the upper part of the preceding voltage range...............................................................................................................68 5.23 Action potential threshold increases with the average membrane potential..70 6.1 Steady-state Hodgkin-Huxley gating variables as a function of membrane voltage..............................................................................................................77 6.2 Voltage dependent time constants of the gating variables...............................78 6.3 Time course of GK and GNa after a sudden membrane change from Vrest to Vrest + 40 mV........................................................................................78 6.4 Instantaneous I-V curve around the resting membrane potential ....................80 6.5 Slightly slower than instantaneous I-V curve around the resting membrane potential...........................................................................................................80 6.6 Example ramp current injections into a hypothetical space clamped squid axon..................................................................................................................82 viii 6.7 Relationship between the threshold current and the ramp duration necessary to elicit an action potential in a model squid axon...............................................82 6.8 Measured somatic voltage threshold of ramp current injections to elicit an action potential in a model squid axon ............................................................83 6.9 Current threshold vs. ramp duration for a ramp injection in a model Area I neuron with and without dendrites...................................................................85 6.10 Somatic voltage threshold vs. ramp duration for a ramp injection in a model Area I neuron with and without dendrites......................................................85 6.11 Frequency dependence of transferring somatic voltages to the distal axonal compartment in the model Area I neuron ......................................................88 6.12 Influence of the location of the action potential initiation site on threshold current ............................................................................................................89 6.13 Influence of the location of the action potential initiation site on threshold voltage............................................................................................................89 6.14 Increasing the conductance of the action potential initiation site lowers the current threshold ......................................................................................91 6.15 Increasing the conductance of the action potential initiation site lowers the voltage threshold ......................................................................................91 6.16 Effects of the diameter of the axon on the current threshold.........................92 6.17 Effects of the diameter of the axon on the voltage threshold ........................92 ix 1 Introduction 1.0 Persistent neural activity and the oculomotor neural integrator One basic function that all nervous systems have to accomplish is to store information. It is hard to imagine how any computation engine with even a modicum of complexity could operate without some form of memory storage. In the brain, long-term memory is thought to be encoded through long-term physical alteration of synapses and the synthesis of new proteins. The synthesis of proteins is a slow process and would not be adequate for the storage of short-term information. In many working memory experiments, the ability to store short-term information is correlated with persistent neural activities [1]. In a typical experiment [2, 42, 46, 49], the animal is presented with a transient stimulus (a visual pattern) and an estimation of the initial stimulus (matching previous pattern to a new pattern) is elicited after some time delay. During the delay period, patterns of neural activities can be found in wide spread regions of the cortex (and even subcortical regions [47, 48, 61]) that persist during the delay period (in the absence of any stimulus), and terminates upon the behavioral response, (choosing matching pattern). Perturbations to the persistent neural activity through either lesions or electrical stimulations have adverse effects on the animal's ability to hold information. Thus persistent neural activity is a necessary component of short-term memory and might the basis for information storage in the brain. 1 In contrast to the vast literature [41] documenting working memory paradigms and the cellular circuitry of the cortex, how the brain maintains persistent neural activity is still a very open question. [7] Part of the difficulty in answering the question arises from the paucity of empirical data. While it is relatively easy to characterize the output of a neuron, it is very difficult to measure the input that it receives. The technical difficulty of this task is particularly accentuated in working memory paradigms, where the animal subject is awake and is a persistent source of mechanical instabilities. In order to ameliorate the mechanical difficulties, we have chosen to focus our efforts on a special non-cognitive class of persistent activity known as oculomotor neural integrators [3]. In particular, we will discuss recent progress on recording intracellular activities in the goldfish velocity-to-position oculomotor integrator [4]. The oculomotor integrator translates brief saccadic and vestibular inputs (from the semicircular canals) into sustained changes in eye positions. (The general concept of neural integrators has more applications than just the oculomotor systems [43, 44], and it is highly probable that our work here will applicable to other systems.) Goldfish spontaneously move their eyes in a horizontal scanning pattern in the dark. Their eyes fixate in one stable position for 0.5s to 5s before making quick saccades to a different stable position. The stability of the eye is achieved in the absence of visual and proprioceptive feedback. This necessitates some internal persistent signal to sustain ocular muscle activity that would otherwise relax the eye to a neutral position. The neural basis for such a persistent signal (Fig. 1) has been 2 Fig 1.1 a) Eye position b) Measured extracellular action potentials of an integrator cell c) Instantaneous spike frequency (ISF) d) Eye position vs. average action potential frequency 3 located in the hindbrain in a region named Area I [4]. The outputs of these integrator cells generally possess a linear relationship between firing output and eye position [5] with a heterogeneous mixture of slopes and thresholds. The oculomotor system is also sensitive to rotations of the head and counter rotates the eye to form a stable image on the retina. This is known as the vestibuloocular reflex (VOR). The semicircular canal that senses head rotation outputs velocity and acceleration signals through vestibular neurons. These transient signals have to be integrated into position signals by a neural integrator. Lesion experiment and analysis of neural activity patterns suggest that the fixation and VOR subsystems share the same integrator [45]. As angular rotation is an analog process, the ocular motor integrator must possess graded persistence. This is an important distinction between integrators and simpler bi-stable flip-flop behaviors. Area I integrators possess both VOR sensitivity and graded activity patterns. Other examples of neural integrators exist. For example, the head direction system [6] in rats is thought to integrate vestibular (and other cues) to produce a persistent signal head direction signal. In general, the mechanisms by which persistent activity are generated are unknown [7]. Mechanisms generally fall into one of two camps: network mechanisms such as positive feedback that boot-strap intrinsic cellular decay constants to long time durations or cellular mechanisms that rely on internal biochemical dynamics to generate long lasting output. Our work presents experimental evidence that network mechanisms play an important role in generating persistence in the goldfish oculomotor integrator. 4 1.1 Biophysics of a neuron Before we continue with our presentation, we will briefly describe the anatomy of a neuron for the physicist who is unfamiliar with neuroscience terminology. An extended overview can be found in [50]. A neuron is the ‘atom’ of the brain and in most cases can be separated into three distinct anatomical regions. The soma (cell body) contains the major cellular organelles and is in general the thickest part of the neuron, ranging from ~ 5 m to 10s of m in diameter in the central nervous system. While inputs from other neurons can directly connect to the soma, the majority of inputs are received by a neuron at the dendritic tree. The arborization of the dendritic tree can span several hundred microns in reach and is made up of thin branches that are generally much smaller in diameter than the soma. The output of the neuron is carried by another thin tube, the axon, in a regenerative fashion over a distance of millimeters. Some neurons have branching axon segments called collaterals and a single neuron can provide input for multiple target neurons. While information generally flows from the dendrite to the soma to the axon to the target dendrite, examples exist for direct dendro-dendritic [51] or dendro-axonal connections [52]. Information flows into neurons through synapses. Neurotransmitter diffuse through the synaptic cleft and gate specific ion channels with different temporal dynamics. Some receptors like AMPA receptors [55] have short ~5 ms kinetics while others such as NMDA [56] receptors can have long ~100 ms durations. Short and long are referred in comparison to the membrane time constant, which is usually about ~ 10 ms. 5 Fig 1.2 Schematic of a neuron As the intracellular medium of a neuron is resistive, a typical neural membrane is not an isopotential surface. Passive membranes with simplified geometries can be described with explicit analytical solutions using Green's functions and cable theory [57]. However, biological neurons generally show a diversified geometry with non-linear active and passive conductances embedded non-uniformly in the membrane. The morphology of real neurons cannot be over trivialized as simulations suggest the physical geometry of a neuron can a large impact on its behavior [87]. 6 Fig 1.3 Electrical compartment model In order to model realistic neurons, they are generally segmented into compartments and modeled discreetly. For a single compartment with voltage Vm, Kirkhoff's law gives C (V Em ) (V V0 ) (V1 V ) dV I channels (1.1) dt rT rL rL I channels k g k (t , V )(V Ek ) RL rL dx RT1 rT1dx (1.2) C cdx Typical values: c = membrane capacitance, 1F/cm2 rT = membrane resistance 30 k cm2 rL = intracellular resistance 150 cm Many terms in Eq. 1.1 are familiar to physicists from simple cable theory. The new terms, Vm, gk, Ek arise from the active and passive conductances of protein channels that are embedded in the membrane. These protein channels show a rich 7 repertoire of behaviors such as voltage sensitivity, ion specific selectivity, and nonlinear temporal dynamics [53, 54]. A subgroup of these protein channels actively pumps select ions in and out of the cell to maintain an active gradient across the membrane for several common ion species. Taking the permeability of the membrane to each ion into account, the resting membrane potential of a neuron can be calculated using the GoldmanHodgkin-Katz Vm P [ K ] PNa [ Na ]out PCl [Cl ]in ... RT ln( k out ) (1.3) F Pk [ K ]in PNa [ Na ]in PCl [Cl ]out ... equation. The chemical gradient and permeability of the two dominant ions Na+, K+, are mostly responsible for setting the resting potential across the cell membrane Vm to ~ -70 mV. (The permeability of the membrane to potassium ions is much higher than that for sodium ions and so sets the membrane closer to the potassium reversal potential/chemical potential.) When a synapse is activated, select ion species are permitted to move across the membrane in accordance their reversal potential Ek. The temporal and voltage dynamics of the permeability of the channel is embedded in gk(t,v). We can consider synaptic input to be charge injection if it is excitatory input or charge extraction if it is inhibitory input. (Although inhibition can also occur through the shunting of excitatory current.) From Eq. 1.1 it's clear that inputs can sum temporally and spatially in an RC-circuit type fashion for passive membranes. Membranes with active channels can produce non-linear summation. 8 In almost all neurons, there exists a special region with a particularly high density of voltage sensitive sodium and potassium channels. Classically, this region is associated with the axon hillock, the junction between the soma and the axon. When the membrane voltage crosses a threshold at the axon hillock, a cascade of voltage sensitive sodium channels is opened, resulting in a sudden depolarization of the membrane. (The cell membrane is re-polarized by the opening of potassium channels.) This non-linear event is known as the action potential and is the output signal of the neuron. (The action potential travels down the axon and activates neural-transmitters at the axon terminus, signaling other neurons.) We will present a more detailed discussion of action potential generation in later chapters. The large voltage swing of an action potential, ~ 100 mV, can be detected with electrodes placed in the extracellular medium. These extracellular recordings are sensitive to the composition of the extracellular matrix that affects the current flow associated with the action potential. Free aqueous ions move quickly to shield stray charges. Empirically, we can measure a 1 mV signal associated with the 100 mV action potential in the goldfish hindbrain if the extracellular electrode is within a micron or so of the neuron for a 4" to 6" fish. The strength of the signal quickly falls off as a function of distance, and the measurement of the AP discharge falls to about ~100 V when the electrode is 50 m+ away. For small goldfish fish, ~1", it is hard to detect extracellular signals greater than 100 V regardless of the proximity of the electrode to the neuron. Electrodes used in extracellular recordings can be fabricated from a wide range of materials. But regardless of their construction, they generally are 9 composed of some insulated material with an exposed conductive core at the very tip ~ 1-5 ms. Their resistances are generally on order of ~1-5 M. For the 2 M saline-filled, 2 m open tip, glass electrode that we typically use, the rms Johnson noise is approximately 15 V (0-10 kHz), or ~40 V peak-to-peak. This is adequate for the detection of extracellular signals associated with action potentials. However, such electrodes are insensitive to synaptic signals that are roughly 100 smaller in amplitude than an action potential. Aside from being smaller in absolute voltage, synaptic signals are also hard to measure because the extracellular waveform is a distorted/filtered version of the true waveform (that exists across the neural membrane) [59] and is more representative of a capacitive discharge of the membrane. Fig 1.4 Differences between extracellular and intracellular recordings To obtain an electrical measurement of the sub-threshold waveform that represents the synaptic input, the recording electrode has to be inserted through the insulating membrane layer and into the cell. For small cells in the central nervous 10 system, this is typically done with a very fine 100 nm tip glass needle. Accordingly, this method is known as the sharp intracellular recording technique. Alternatively, the membrane of the neuron can be fused to the tip of a glass electrode before penetration using a technique called whole-cell patch-clamp [60]. In the patchclamp technique, the glass electrode tip is gently pressed against the outer surface of a neuron. A very gentle negative suction is applied to seal the neural membrane to the inner lip of the glass electrode. If the electrode tip and neural surface are very 'clean', the two materials will fuse together to form a high resistance contact G+ contact. A more vigorous suction is made to rupture the inner membrane of the seal. If done correctly, a hole will be made in the seal, but the outer edges of the membrane will still be tightly coupled to the glass surface. This creates a direct contact between the intracellular medium and the inner saline of the electrode. However, to form a stable junction, the tip of a patch electrode should still be small (~1 m) in comparison to the size of the neuron (~10 m) being patched. While the relevant physical scale of extracellular recordings is on the order of tens of microns due to the propagation of currents in the extracellular medium, the physical scale of intracellular recordings is on order of ~1 m as set by the tip size. Correspondingly, extracellular recordings are much less demanding in terms of mechanical stability than intracellular recordings. The differences in difficulty are magnified when recordings have to be made in awake behaving animals to study short-term memory. For this reason, most measurements of short-term memory paradigms are made using extracellular recording techniques. Thus, while we know 11 much about how the output of neurons is correlated with information storage, we do not know much about how such output is generated. Even without having to invoke special dynamics, a single neuron can be said to possess a memory of its past stimulus on the time scale of its membrane time constant ~10 ms. However, this is several orders of magnitude shorter than the time courses of cognitive or eye fixation events that can last seconds. How then, does the brain boost 10 ms to one second? 12 2 Models of persistent activity 2.0.0 Network models Due to the paucity of empirical evidence, many mechanisms have been proposed to explain how persistent activity is maintained in the brain. They generally fall into one of two camps: positive feedback through network dynamics or intrinsic cellular mechanisms that possess long dynamics. It has been hypothesized for a long time [18, 19] that persistent neural activity is maintained by positive feedback through recurrent excitatory connections. (It is also possible to generate net positive feedback through mutual inhibitory connections, a phenomenon known as disinhibition.) However, positive feedback is notorious for suffering from tuning and stability problems. We can illustrate the problems with a simple toy model. As the firing rate of a neuron is set by its membrane potential, the decay in firing rate is also set by the membrane time constant. Let v(t) be the firing and , the time constant set by the decay of the membrane potential. Then v(t ) dv dt (2.1) If positive feedback was added to the system v(t ) dv kv(t ) dt 13 (2.2) then the apparent time constant is T 1 k and dT T dk . Given a membrane T constant of 10 ms and an apparent time constant of ~10 s for eye fixation events, a very small change in the feedback would cause a 1,000 fold change in the apparent time constant. Still, many models based on recurrent connections have been proposed to explain persistent activity in the cortex [62, 63, 64] and in the oculomotor system [12, 13, 14, 15, 83]. Most are based on linear elements that take on the general mathematical form cell N dvi vi Wij v j f i (2.3) dt j 1 where vi is the instantaneous rate of action potentials of the ith neuron in the network. cell sets the timescale of an individual neuron and is thought to correspond to an intrinsic cellular constant such as a synaptic time constant or membrane time constant. fi represents a basal tonic input. Wij sets the connection strength between individual neurons. Feedback does not imply the existence of a multi-stable or continuously stable solution that is required for graded persistent memory systems such as the ocular motor system. If we set dv 0 in Eq. 2.3, we have a system of N linear dt equations with N variables that in general produces one fixed solution. Thus to produce the graded persistence seen in nature, a special topology/tuning of Wij and fi is required. 14 Using an eigenmode analysis, Seung [11] showed that all of the published linear models reduce to this common framework. That is, the linear models all constrain Wij and bi in such a way to produce a solution where a continuous line of fixed points (line attractor) represents the persistent activity observed in the neural network. Seung identified the general mathematical requirements necessary for a stable solution. Wij must have a single unity eigenvalue and the left eigenvector corresponding to the unity eigenvalue must be orthogonal to fi. A large energy gap should also exist between the unity eigenvalue and the other N-1 eigenvalues (whose real parts are less than one) so that the system relaxes to the line attractor state after some small perturbation. Put together, these conditions impose stringent precision requirements on the parameters. The precision that is required to tune the network is on the order of ~ cell network . In the first liner models proposed by Cannon and Robinson [13, 14], cell was identified with the membrane constant of ~5 ms. This would require a biologically implausible tuning requirement of 0.05%. Seung proposed to identify cell with a long NMDA N-methyl-D-aspartate receptor (NMDAR) synaptic time constant ~100 ms [11, 12]. (Or effectively gk(t,v) has a 100 ms long time dynamic.) NMDA has also been hypothesized to play important roles in persistent activity in cortical models [65, 66]. The diversity and function of different NMDA receptor subtypes has been reviewed in [67]. NMDA receptors typically exist as heteromers composed of different subunits. Diheteromeric receptors that involve 15 the NR2D subunit can have second long deactivation time constants. Interestingly, the NR2D subunit is moderately expressed in both the prefrontal cortex (in mammals) and the brainstem regions (mammals and zebrafish) [68, 69, 70] and could potentially play a role in mediating persistent activity in those areas. 2.0.1 Anatomical evidence for feedback in cortex and MVN, NPH Feedback models are popular not only because of their mathematical elegance, but also because there exists abundant anatomical evidence to support their existence. Strong feed-forward and feedback connections exist within and between cortical areas. There also exist many reciprocal cortex-subcortex loops such as cortico-thalamic connections that could mediate recurrent feedback. Feedback loops also appear to exist in mammalian integrator regions. We'll discuss the physiology of those brain regions in some detail as it has the most direct relevance to our study. The study of ocular motor integrators originated in studies of mammalian preparations [8]. In mammals, integration in the vertical plane involves the interstitial nucleus of Cajal [26]. Similarly the nucleus prepositus hypoglossi (NPH) and the medial vestibular nucleus (MVN) are important parts of the horizontal integrator. Extracellular recording of the three regions show a heterogeneous mixture of neurons with position and velocity sensitivities. Micro-lesions [32,34], chemical in-activation [33, 35, 38, 40] and micro-stimulation [23] experiments show that disruptions to those regions impair VOR and gaze-holding ability, dropping the apparent time constant of gaze fixation from ~10 s to ~100's ms. 16 Extensive tracing studies show that the purported mammalian integration regions contain the connectivity patterns appropriate for an integrator. Burst and vestibular neurons project into the NIC and NPH [27, 28] that in turn project to abducen motorneurons that directly innervate the muscle. The bilateral MVN and PH nuclei are fully connected by internuclear projections. In addition, neurons in the MVN and PH have recurrent collaterals that could potentially mediate intranuclear feedback loops The feedback loops within the integrator region appear to have important functions as damage to the commissural connections of the MVN and PH causes gaze-evoked nystagmus [92]. Moreover, transient micro-stimulation of the regions can induce persistent changes in eye position [37, 39]. This effect would only be possible if memory storage of the eye position was located in the MVN/PH or in a downstream target. Empirical evidence suggest however that the motor nuclei downstream of MVN/PH themselves do not store eye position memory. While there is some anatomical evidence to support the existence of feedback loops, in vitro studies of the guinea pig and avian MVNs have not found any evidence for membrane bistability or other intrinsic long cellular dynamics that could explain persistent neural activity. However, in vitro studies cannot replicate the full physiological environment that a neuron experiences in vivo, and there might exist some overlooked neuromodulatory mechanism that is only apparent in vivo. It is also possible that the incorrect subset of neurons were examined as there is no behavioral correlate in in vitro preparations to ascertain that the experiment is truly assaying an integrator neuron. 17 2.0.2 In vitro analogue of cortical persistent activity is mediated by balanced inhibition and excitation While no in vitro preparation for persistent activities has been developed for integrator brain regions, an in vitro analogue for persistent cortical activity has been developed by the McCormick lab [73, 74]. They showed that in vitro slices of ferret prefrontal and occipital cortex can generate recurring periods of sustained activity that lasts between 0.5 to 3 s. These states were bistable, and undergo rhythmic oscillations between the active (UP) and quiescent states (DOWN). Using intracellular recording [75], it was shown that the driving current for the neural activity came from a balance of excitatory and inhibitory current. Potential feedback loops that could mediate such activities were also physiologically inferred. Blocking either AMPA or NMDA receptors abolished the UP states but no actual measurements of individual synaptic events were made and thus it's unclear if long synaptic time constants were involved. However, in this cortical model, finetuning may not be a necessary requirement as the activity pattern appeared to be bistable and resembled a flip-flop circuit. It's not clear whether the in vitro bistable activity patterns accurately reflect in vivo behavior. But it still shows that the appropriate circuitry exists and that network dynamics can be used to generate persistence. In general however, the network fine-tuning required to generate persistent activity is a problem. Even if a ~100 ms NMDA-like time constant was used for synaptic events, the network parameters would still have to be tuned within ~1% for linear models that rely on long synaptic time constants. This stringent requirement 18 may be too difficult to achieve in noisy in vivo biological settings. In order to address the fine-tuning problem, some researchers have introduced bi-stable or hysteric elements to improve the robustness of the feedback model [16, 17]. The problem of robustness or t he need for positive feedback can be completely sidestepped if there exist intrinsic cellular dynamics that can generate persistent current. While not ubiquitous, examples of such persistent intrinsic mechanisms exist. 2.1.0 Intrinsic cellular mechanisms The membrane time constant of a neuron sets the rate at which synaptic information is lost for a passive membrane. This in some sense sets the lower temporal bound for information storage in a single neuron. While the membrane time constant represents one intrinsic time constant for neurons, there exist other intrinsic mechanisms that possess time constants much longer than that of the membrane. Accordingly, these intrinsic mechanisms have been proposed to underlie persistent activity. 2.1.1 Short term synaptic potentiation One of the earliest models that use intrinsic cellular mechanisms was proposed by Shen in 1989 [9]. He proposed to achieve robust integration of synaptic input using a basic property of synapses known as short term potentiation [71]. Short term potentiation refers to the phenomenon where repetitive stimulation of a synapse results in increased neurotransmitter release per action potential from the presynaptic terminal. (The mechanism for this behavior involves 19 the gradual accumulation of calcium ions in the presynaptic terminal with every action potential. Calcium gates neurotransmitter release.) Increased presynaptic transmitter release implies that the action potentials that come later in an input train are more effective in eliciting a prolonged response. If the first action potential occurred at time t=0 and increased the efficacy of the presynaptic terminal by an amount p(t). A second stimulus increases the amount of transmitter released by a factor of 1+ p(t). From experimental observations, p(t) was found to assume the form e t p . Shen showed that if the inter-spike interval of the input train and the membrane constant are significantly smaller than p, then the potentiation can effect an integration of the input. p have been experimentally observed to range from the tens of milliseconds to seconds. By itself, a long p may also serve as a basis for boosting stability in feedback models. Recently NMDA receptor dependent short term potentiation has been observed in the NPH of in-vitro rat brainstem slices [72]. Such short term potentiation could serve as the basis for neural integration or for boosting stability for feedback models. 2.1.2 Loewenstein's calcium wave model Loewenstein and Sompolinsky [40] implemented a novel mechanism for integration using calcium bi-stability. They segmented each dendrite into compartments. In each compartment, calcium-induced calcium release and calcium clearance are tuned to generate local bistability of intracellular calcium concentration. Calcium can diffuse from one compartment to the next and divides 20 the dendritic segment into zones of high and law calcium. With careful tuning of parameters, the boundary between the two zones is stationary. Synaptic input induces increases in intracellular calcium concentration and shifts the 'wavefront' along the dendrite. Inhibitory input moves the wavefront in the opposite direction. The intracellular calcium level is converted into current that triggers neural discharge via a calcium-activated channel. It is not clear if the parameters used in this model are robust. As calcium can diffuse between compartments, the position of the wavefront is subject to drift. While some robustness is gained from branching dendritic arbors that cancel out random drift, the parameters of the model still has to be finely tuned between calcium extrusion and release. However, it does highlight a single cell mechanism in which integration maybe achieved. 2.1.3 Plateau potentials While calcium bistability in the way suggested by Loewenstein and Sompolinsky is untested, voltage bistability in the form of voltage sensitive channels has a long track record. Various motorneurons and reticulo-spinal neurons show intrinsic membrane bi-stability in the form of a prolonged depolarization known as plateau potentials. These mechanisms generally involve calcium in some fashion (although persistent sodium currents may be involved in mammals [80].) In vitro motorneurons can produce a plateau potential that is largely mediated by L-type Ca channels [78,79]. After an initial depolarization, these low threshold voltage sensitive channels activate to allow calcium to flow into the neuron, forming a self-sustaining dynamic. 21 Aside from being a source of positive current, calcium can also activate other channels to produce a net positive current. For example, in the ‘semi-intact’ lamprey preparation [34, 35], successive stimuli to brain stem reticulospinal neurons will activate NMDA receptors that mediate the entry of calcium into the neuron. The calcium then activates non-specific cation channels (CAN) that produce a long duration depolarization of the membrane. CAN current in conjunction with various forms of neuromodulatory activation such as serotonin or muscarinic activation can produce plateau potentials in higher brain areas such as hippocampul CA1 cell as well [81]. More recently, a promising in vitro preparation involving the entorhinal cortex [24] has been induced to shown graded persistence under muscarinic activation. CAN currents provide the depolarizing drive. Moderate 0.5 s+ long depolarization pulses can evoke transitions in firing rate of up to 40 Hz. However, very long 5-10 s hyperpolarizations up to 80 mV are necessary to stop firing completely. It is speculated that the persistent activity arises from a compartmentalized model of calcium bistability. [25] However, while the machinery for bi-stability appears to exist in many parts of the brain, it has not been demonstrated that plateau potentials play any role in an intact physiological setting except perhaps for the fictitious swimming behavior induced in the semi-intact lamprey preparation. Part of the difficulty in studying the origins of persistent activity lies with the fact that it requires the animal subject to be awake and behaving. The awake behavior necessarily generates mechanical vibrations that render intracellular 22 recordings difficult. Moreover, many higher forms of persistent activity are observed during working memory tasks of primates, animals that are expensive to perform invasive and deleterious experiments. For all of these reasons, we were led to study the ocular motor integrator in the goldfish. 23 3 Goldfish Area I 3.0 Anatomy The goldfish is particularly well suited for electro-physiological experiments. A large part of its usefulness lies with its innate good nature. Unlike common mammal preparations like mice, cats, or even other fish species such as zebrafish, goldfish are content to be restrained in a body harness with their head fixed for long periods of time. This makes this species particularly useful for intracellular recordings where the pertinent characteristic size of the experiment is on order of a micron, but endogenous behaviors produce motions on the order of ~cm. Goldfish oculomotor behavior is also less complex and the underlying circuit is fewer in cell numbers and localizations than mammals. Unlike mammals that scan in both the vertical and horizontal axis, spontaneous scanning behavior in the goldfish occurs primarily in the horizontal plane. Thus there is only one primary integrator locus for gaze holding behavior active in a head restrained animal. This locus has been located in the brainstem [4] and is analogous to the NPH region in mammals. Another locus, that is insensitive to position but sensitive to velocity has also been found, called Area II. While the mammalian integrator regions contain thousands of cells, the goldfish integrator nucleus is purported to contain 30-40 neurons as identified by biocytin staining [4]. The discharge of Area I neurons is correlated with eye position and its inactivation affects both gaze holding and VOR. The discharge of Area II neurons 24 is related to eye velocity and its inactivation affects VOR without affecting gaze holding. Thus Area I is thought to be responsible for position storage while Area II neurons is thought to responsible for ‘velocity storage.’ Area I is located within a small region in the hindbrain between rhombomere 7 and 8. The region is a rostral-caudal column roughly 300 m long, 100 m wide, centered about 350 m from the midline. Integrator neurons in Area I appear to be similar to the medium size neurons in the rostral NPH. In mammals, these “principal” neurons project unilaterally and arborize within the nucleus as well as sending projections to motorneurons in the abducen. Area I neurons receive projections from vestibular neurons and send projections to motor neurons [30, 31]. Some Area I neurons send bilateral projections to the contralateral Area I nucleus setting up a potential recurrent feedback loop. Correlation studies suggest that the contralateral projections are inhibitory and therefore may be a source of net recurrent feedback through disinhibition [21]. However experiments in the goldfish that either inactivate Area I unilaterally or attempt to cut the projections across the midline only produce small integrator deficits. This is in contradiction to experiments [22, 23] in primates where midline lesions produce severe deficits in integrator performance. This suggests that contra-lateral inhibition that has been postulated to be important in some models, is not a critical source of feedback in the goldfish integrator. It is unclear if the axons of Area I position neurons arborize within the ipsilateral nucleus. Although clearly labeled axon collaterals were not detected in the intracellular neurobiotin injections, this may be attributed to incomplete labeling 25 and transport barriers. The axons appear to be constricted in the region where it emanates from the soma. This in conjunction with the natural small size of axon collaterals, suggest that insufficient dye may have diffused to visualize their connections. In addition, it is possible that gap junctions occur between the dendrites of Area I neurons as this structure has been characterized in other goldfish oculomotor nuclei [117]. 3.1 Correlations between paired Area I cells Paired and triplet recordings of position sensitive neurons [21] show that positive correlations exist between ipsilateral pairs of neurons and negative or no correlations exist between contra-lateral pairs. The timescale of the positive correlations are very brief (5-10 ms) and exist in almost all ipsilateral paired recordings. Interestingly, the correlations are pronounced at low firing rates but are absent at higher firing rates. It is unlikely that such correlations can exist if the driving force for discharge only came from intrinsic cellular mechanisms as the temporal dynamics of different cells would be independent and unlikely to produce any correlation. While positive correlation would be a consistent signature of recurrent feedback, it is also possible that the correlations arise from common input. (This common input could arise from vestibular neurons discharge at a constant rate under experimental conditions. It is possible that this could produce the observed correlations at low rates.) 3.2 Partial inactivation experiments 26 Dual electrode drug injection and electrophysiological recording [82] experiments show that precise partial inactivation of Area I using extracellular application of drugs (muscimol or lidocaine) produce a sharp loss of persistence in the remaining position sensitive neurons on the ipsilateral side. After carefully mapping out the anatomical extent of the Area I region, one recording electrode was positioned at the rostral periphery of the region while a drug injection electrode was placed at a distal caudal region. As the dendrites of Area I tend to run caudally, there should be minimal interference of the rostral neurons by the caudal injections. Silencing one portion of the neuron population apparently induces a loss of persistence in the remaining neurons. This suggest that some network connectivity might exist between the neurons because if single neurons were capable to maintaining persistence (through plateau potentials), then knocking out a subpopulation of the network should not affect the remaining neurons. However, the loss in persistence was not as dramatic as predicted by line attractor models, which suggest the system possesses some intrinsic stability. 3.3 Sharp intracellular recordings The most important experiments that had been performed on Area I examined the intracellular physiology of position sensitive cells using sharp intracellular electrodes [20]. (Some attempts at whole-cell recordings were made, but the recordings were too short to provide additional information.) Sharp electrodes are very fine, narrow glass electrodes with tips on order of 100 nm. They physically pierce the cell membrane to measure the intracellular voltages. 27 These experiments showed that a sustained membrane depolarization is elicited in the integrator neurons after a saccade. Artificial membrane depolarizations elicited by current injection through the electrode suggest that the membrane steps are of sufficient strength to produce the natural action potential discharge. Hyperpolarizing the membrane (with injection of negative current) did not remove the voltage steps and implied that back propagating action potentials (into the soma and dendrite) are unnecessary for the generation of the membrane steps. Fig 3.1 Membrane potentials Vm increases with eye position. (Cell is hyperpolarized to prevent spiking.) However, transient current injections were unable to elicit permanent changes in membrane potential or intrinsic firing rate. This is in stark contrast to every reported example of plateau potential or membrane bistability where transient current injections were able to elicit permanent changes in cellular activity. In 28 addition, the step changes in membrane potential remained even as the neurons were hyperpolarized below action potential threshold, suggesting that they were caused by steps in membrane current (or conductance.) Along with the absence of somatic or proxi-somatic plateau potentials, no intrinsic oscillatory pace maker currents were found either. Triangular injections of current showed no hysteresis in current-firing rate relationship. In about a quarter of the recordings, there was an increase in rms fluctuations of the membrane potential as it became progressively depolarized. This increased fluctuation amplitude could arise from an increase in EPSP rate, input synchrony, or amplitude of the EPSPs. (In two unpublished recordings, individual EPSPs were resolved and provided some preliminary evidence for increased EPSP rate.) In general, the exact origin of the fluctuations was un-resolvable from the sharp intracellular recordings. The technical explanations for this originally was not clear. While a sharp electrode’s impedance is very high ~100 M due to small size of its tip, ~100nm, it doesn’t seem to be sufficiently high enough in parallel with the electrode and amplifier capacitance ~5-10 pFs, to produce an RC time constant that would entirely filter way individual EPSPs. (100 M x 10 pFs = 1 ms). (It is possible that the 5-10 pFs capacitance is an underestimate as solution creep up the shank of the electrode could have rendered a much larger portion of the electrode to be capacitively coupled.) Sharp electrodes in general introduce a leak [86] in the cellular membrane through the physical impalement of the cell and this may have shunted current. The physics of salt solutions is complex and exhibits many 29 frequency dependent dielectric and conduction properties. These may be accentuated at small scales ~100 nm by surface effects such as the Debye layer and may produce low-pass filtering effect. All these properties of sharp recordings could act in conjunction in reducing its temporal resolution. 30 4 Experimental Setup 4.0 Whole-cell Patching Recording In order to increase the temporal resolution of the recording, we turned to the whole-cell patch technique. The patch clamp technique was originally developed to study the kinetics of ion channels [85]. Later the technique was extended to recordings from entire cells [60]. As mentioned previously, the whole-cell patch technique consists of fusing a relatively large pore glass pipette ~ 1.2 m to the cell membrane through an unknown mechanism. As long as the glass surface and cell surface are relatively clean, such seals can form spontaneously upon contact (though in practice they are encouraged with some negative pressure.) Seal quality is assayed by measuring the resistance of the electrode tip. Good seals measure G The tightness of the seal confers a substantial mechanical bond between the glass tip and cell membrane. It's not uncommon in (brain) slice preparations to see the attached cell pulled along with the tip of the pipette during retraction of the electrode. In the goldfish in vivo preparation however, the mechanical stability of the seal is counteracted by instabilities associated with a large pipette tip penetrating through the tough brain stem tissue (see Fig 4.1) The compressed brain eventually relaxes and moves away from the pipette. Thus, virtually all recordings are lost because of a slow (~1 min) sealing of the tip (resistance reaching G rather than a sudden change in membrane potential and loss of apparent cell resistance (which would be indicative of vibration problems.) 31 Electrodes were fabricated with either the P-2000 or P-87 puller (Sutter Instruments.) Tips were drawn by the puller by heating a small uniform 1mm/1.2mm capillary tube and separating the two halves apart with tension. The visco-elastic properties of liquid glass are such that the size of the final tip is highly correlated with the width of the electrode shank. Sharp intracellular microelectrodes have very tiny tips and very slender shanks. In contrast, patch electrodes are relatively stubby. It is difficult to produce a relatively large tip opening ~ 1 m but still slender patch pipette. Penetrating tissue with thick patch electrodes causes a tremendous amount of built-up tension as the brain is compressed and sheared with electrode advancement. In practice, recording from patch electrode last shorter than that of sharp electrodes after external vibrations issues are resolved. Empirically, sharp recordings last over 40 minutes while patch recordings last between 5-10 minutes. It is possible to pull thicker sharp electrodes than that depicted in Fig 4.1 to reduce capacitive coupling, but thicker shanks also increase the stiffness of the pipette which lessens the ability of the pipette to vibrate with the tissue. Patch electrodes convey a considerable increase in temporal sensitivity over sharp electrodes. Unlike the small 100 nm diameter of the sharp electrodes, the patch electrodes that we used have relatively large ~1-1.2 m openings assayed using the bubble number test [88]. This in conjunction with the relatively stubby taper, produces a low resistance electrode. If the internal electrode solution (~2-3M KAc) for sharp electrodes were used for patch electrodes, the resistance of the patch electrode would be a few hundred K. However, diffusion between the intracellular 32 Fig 4.1 Different electrode geometries a) extracellular electrode b) patch pipette c) sharp intracellular electrode Resistance Tip size extracellular electrode: 2 M 1m patch pipette: 6 M 1 m sharp intracellular electrode: 100 M .1 m Table 4.1 Dimensions and resistance of different types of electrodes 33 space and the patch electrode medium occurs rapidly (due to the large opening at the tip), and so the electrode solution has to be matched to the intracellular medium. The patch electrodes used in this experiment were typically between 5-6 M and correspondingly have a much higher temporal resolution than sharp electrodes. Capacitive coupling is also less of a problem for patch electrodes due to low resistance tip 10 M * 10-12 pF = 0.1 ms and thicker shank. (The wall thickness of the drawn glass is roughly proportional to the shank diameter.) 4.1 Surgical preparations All experiments were performed in strict compliance with the Guide for the Care and Use of Laboratory Animals. The Princeton IACUC committee approved specific protocols. Goldfish (Carassius auratus, 4-6”, Hunting Creek Fisheries, Thurmond MD) were stored at 20-22 C in 75 gallon aquariums with daily exposure to light. Prior to the experiment, a stabilizing metal bolt was attached to the exposed skull with self-tapping screws (R-TX002, Small Parts, Miami Lakes, FL), followed by two layers of superglue, and dental acrylic. During the experiment, the stabilizing metal bolt was clamped with two locking nuts to fix the goldfish head position. Two soft sponges were pressed against the fish body to supply additional restraint. A small plastic tube was inserted into the mouth to circulate water and to improve respiration. Unlike previous experimenters, the operculum (bony plate over the gills) was removed to help 34 release bubbles (spontaneous cavitations) that irritate the fish. Removal of the operculum also reduced vibration coupling between the cranium and the rest of the body. Supersaturated levels of oxygen appeared to pacify the animal and so carbogen (95% O2 / 5% CO2) was directly infused into the tank. Lidocaine was used as a local anesthetic to open a small window (~1 cm) in the cranium to allow access to the hindbrain. A small metal spatula (see next section) was gently inserted ~500-700 ms underneath the hindbrain and fixed to a post using fast drying hot glue. The hindbrain surface was kept free of debris and protein buildup (from surgical wounds) using a perfusion of ACSF (in mM, 140 NaCl, 2.55 KCl, 5 NaHCO3, 0.42 Na2HPO4, 5 HEPES, 1.16 CaCl2, 1 MgCl2, pH 7.2, 270 mOsm). Excess ACSF was vacuumed using a small syringe tip. The perfusion system was turned off during the final approach to the cell body layer to minimize vibrations. Fish tank water was continuously interchanged with an external five-gallon tank. 4.2 Vibration isolation The physical scale of the experiment is determined by the tip of the recording electrode, ~1 m, which forms the junction with the cell. This small size implies that excess vibration is directly detrimental to the neural recording. Excess vibration can also introduce spurious artifacts that are difficult to interpret and fix. 35 Fig 4.2 Schematic of experimental setup Some previous experimenters have reported that Gseals are hard to obtain with integrator cells. Other experimenters have reported recordings only from ‘cells’ that lack synaptic activity or membrane fluctuations but still demonstrate robust resting membrane potentials. Taken together, the two experiences suggest the integrator cells are tightly covered with glia (support) cells that impede the access of the recording electrode. Recent experience, however, suggest that the problems are not caused by glia cells, though they may exist, but rather are artifacts of vibration related problems. The aforementioned problems disappear once efforts have been made to eliminate the different sources of vibration in the system. (In light of this, it is suspected that excess vibration can impede the formation of the Gseal between the glass electrode and the cell membrane by 36 either damaging the glass tip in transit to the recording site or by destabilizing the junction between the glass surface and cell membrane during the seal process. (The seal process takes a few seconds to occur.) Even after a successful seal has been made, excess vibration may cause the membrane surrounding the seal to rip off of the cell and reform into a self-stabilized membrane that has no synaptic activity but still possess a voltage gradient across the membrane.) Excess vibration will manifest itself as excess voltage/current fluctuations when an electrode approaches a cell surface. This can be assessed by applying a small 5 mV voltage step to the electrode while monitoring the current. As the electrodes is advanced, decreases in current indicates blockage of the electrode tip because of the approach of cellular mass. In stable recordings, there is no obvious increase in the noise of the current when approaching a neuron aside from what is expected from inherent electrical noise sources (Johnson noise.) Some sources of vibration are intrinsic to the organic nature of the goldfish. Undue stress from surgery or low oxygen levels will cause the goldfish to rapidly ‘gill’ and flex its jaw and forehead muscles. This effect is reduced by supersaturating the fish tank with oxygen as well as removing the operculum. Over the course of several hours, ammonia levels can also rise in the tank from defecation. The best course to solve this problem is to continuously replace the water with an external tank that contains ammonia-fixating bacteria. On a good day, the fish should be free of all visible movements (including gilling motions) for at least 12 hrs post surgery. (Except for the months April-Sept, 37 where innate mating behaviors cause the fish to be frisky and troublesome. During those months, Fish also develop a spongy tissue above the hindbrain) Aside from internally generated goldfish vibrations, the experiment is also susceptible to several external mechanical sources. One large source of mechanical vibration comes from the motorized pump that drives water through the mouth tube. Previous tank designs had directly connected the output of the pump to the mouth tube using a semi-rigid plastic (Tygon) tubing. Although the strength of the motordriven vibration was not quantified, its effects could easily be felt by touching the vibrating tubing just outside the mouth tube. Once identified, this problem was easily solved by first pumping the water into an open top reservoir before letting gravity smoothly feed the water down the mouth tube. This dissipated the motor driven momentum that was most likely the greatest source of vibration in the system. In order to isolate the fish tank from floor vibrations, some care was also made to suspend the fish tank inside the Helmholtz coil with a series of bungee cords (weak springs.) The net effect of the bungee cords compare favorably with that of a conventional air table as measured by an accelerometer (Wilcoxon P31). Peak to peak rms Floor 30-40 mm/s2 7-9 mm/s2 Newport air table 4-5 mm/s2 .7-1 mm/s2 Base of goldfish tank 1.2 mm/s2 .2 mm/s2 Table 4.2 Vibration measurements of different surfaces 0-450 Hz 38 In order to stabilize the goldfish brain with respect to the animal's internally generated motion, we inserted a 'brain clamp' underneath the hindbrain. Tom Adelman invented this very useful device. The brain clamp is essentially a very small hollow metal spatula, with a fine mesh grid on top. It slides underneath the hindbrain and upon application of vacuum (~0.5 psi), holds the ventral surface of the hindbrain lightly in place. The exact construction of the device has evolved over time, but the most recent model was formed by 1) grinding a 1 mm stainless hollow tube flat, 2) constructing a support well using Torr-Seal (Varian), 3) gluing on a 25x25 m nickel grid (TEM grid, samples from Imaging Facilities, Depart. of Molecular Biology, Princeton), and 4) overlaying a very thin layer of superglue (Loctite 4212) to waterproof the Torr-Seal. Aside from its ability to vacuum-hold the brain in place, the brain clamp also plays an important role as structural support. Careful post-mortem dissection of the cranium shows that the hindbrain does not rest flat on the skull, but rather is offset from the skeletal bone by a few hundred microns. Thus, contrary to the naked eye, the hindbrain is not in a stable position, but is in an unstable one much like a floating zeppelin tethered loosely by cranial nerves and the spinal cord. In such a situation, advancement of pipettes in tissue introduces significant stresses and instabilities. 4.3 Electrophysiology Electrodes holders are advanced by a MP-285 manipulator (Sutter Instruments.) The advancement was made in units of 1 m at the maximum 39 Fig 4.3 Brain clamp advancement velocity, 2.9 mm/sec. While the MP-285 is a motor/gear driven system, its maximal speed is comparable to piezo-driven devices. This is useful for making quick jabs in the brain to reduce tissue-glass adhesion. If the tissue adheres too strongly to the glass, then the brain will tend to be dragged in unison with electrode advancement until some maximal stress is reached and a backlash occurs. Before intracellular recordings are attempted, a gross location of the integrator region is first mapped using thin, slender extracellular electrodes. These electrodes are filled with 2M NaCl, ~ 1 m beveled (and sharpened) diameter tips, and can detect extracellular currents associated with action potential discharge. The sensitivity of the extracellular electrodes are typically ~50 V peak to peak. However, strong signatures of extracellular activity do not correspond to high probabilities of intracellular recordings. This is a somewhat curious discrepancy as strong extracellular signatures are commonly associated with somatic regions that produce the largest capacitive discharge during action potential 40 generation. In tandem, the cell soma is virtually the only region of the cell that possesses the physical dimensions to be patched by a 1.2 m tip. Perhaps, the action potential initiation zones for integrator cells lie far away from the soma? Thus, in general extracellular mapping can only help determine a very rough location of the integrator region and is most useful towards determining the rostral-caudal coordinate of the region. The medial-lateral coordinate of integrator cells can be precisely determined by finding the lateral edge of the medial lateral fiber (MLF) tract which forms the medial bound of the reticulo-column of cell bodies in the hindbrain. The edge of the MLF is measured by monitoring the resistance of a flat 1.2 m tip electrode (patch electrode) as a function of back pressure as it advances in tissue. Small rectangular current/voltage pulses are used to monitor the resistance of the electrode tip. As the tissue progressively blocks the electrode tip, the measured resistance will increase. Pneumatic pressure (N2) can be added to the back open end of the electrode to generate a hydrodynamic spray that dislodges the closed tip. The MLF is characterized by the inability for a 2 psi back pressure to separate the tissue from the tip. (In contrast, a backpressure of 0.5 psi is sufficient to push away all normal cell surface membranes in the cell body column.) A similar procedure can be used to determine the precise depth of the start of the cell body column. The upper fiber tracts on the dorsal surface of the hindbrain require 5+ psi to penetrate cleanly. After the mapping procedure is completed, a rough sense of the lateral edge of the integrator region, its approximate depth, and approximate medial-lateral 41 coordinate has been obtained. At this point, patch-type electrodes are inserted into the general region with large backpressures 1-5 psi until the appropriate cell depth has been reached. Backpressure is reduced to 0.25-0.3 psi and the electrode is carefully advanced. When stable contact has been made with a surface that produces a 0.3-4 M increase in electrode resistance, a small 100 ms, 0.75 psi pressure blast is applied, before the back pressure is reduced to –0.2 psi. This generally results in a G seal within a few seconds. Then shorts bursts of suction is applied using a mouth tube and is used to break the electrode/membrane seal to achieve whole-cell recording. Capacitance transients are minimized using the capacitance compensation knob prior to break in. Series resistance compensation is maximized by increasing the bridge balance until the measurement circuit is verge of oscillation in voltage clamp mode or by minimizing the transient associated with a voltage step. Small deviations exist between the optimized in vivo protocol for patching brainstem neurons and standard patching protocols for other preparations (e.g. cortical slices.) Namely, the backpressures used in the in vivo experiments are much higher. Through trial and error it has been found that advancing with smaller standard backpressures like 0.1 psi in the cell body region, invariably results in poor seals, quite possibly from contaminated tips. If the resistance of the electrode ever rises to 1 M+ beyond the base resistance and is advanced in tissue for more than 50 m at that elevated resistance, the resultant seal is invariably poor. The differences in procedure may arise from physical differences between the in vivo brain and sliced brain. In the in vivo environment, there is a considerable 42 backpressure against the tip of the electrode because it has to push through a considerable amount of tissue before reaching the target area. In the slice environment, the top of the hindbrain has been removed and so there is little tissue to create the backpressure. Thus, a large hydrodynamic pressure has to be maintained for the in vivo recording to keep the tip clean. The osmolarity of the optimal in vivo patch solution was also higher than expected. Conventionally, the patch solution is kept at a lower osmolarity, -20 mOsm, than the surrounding ACSF (272 mOsm). However, it was empirically found that solutions with ~250 mOsm did not seal well, but solutions with osmolarities between 260 and 300 mOsm were able to make seals. The neural tissue is quite tough in the in-vivo hindbrain, and even though the ventral surface of the brain is gripped by the brain clamp, a ~ 45 angle exists between the incident electrode and the brain/brain clamp. This in effect generates a large and unavoidable shearing force in the brain. (The 45 arises from the curvature of the bone that curves into the skull from the spinal cord, approximately where the hindbrain begins.) Thus, brain tissue is always pushing back on the tip with a relatively large force. The eventual relaxation of the brain is suspected of limiting the recording times of each neuron. Extracellular electrodes were pulled from 0.5mm/1.00 ID/OD (Sutter Calif.) capillary tubes using a P-2000 electrode puller and beveled to 3M (using a 2M NaCl internal solution.) Patch/sharp intracellular electrodes were pulled from either 0.6mm/1.2mm ID/OD or 0.9/1.2mm ID/OD capillary tubes (FHC) using either the P2000 or the P87 electrode puller (Sutter Instruments) respectively. Before pulling, 43 glass for intracellular electrodes were first sonicated in 100% ethanol for 1hr. DI water was then flowed through the capillary tubes fitted in a custom holder for another hr. Capillary tubes were individually blown dry using nitrogen gas and baked overnight at 80 C. The intracellular solution used for whole-cell recording was in mM: 125 KCH3SO4, 9.6 K-Hepes, 3 Na2-ATP, 0.3MgCl2, 0.1 K2-EGTA, pH 7.3, 262 mOsm. (Sealing difficulties occurred with 250 mOsm solution.) For sharp intracellular recordings, the internal solution was 3M K-Acetate. Goldfish sharp electrodes were pulled thinner and longer than conventional sharp electrodes to allow the shank to flex with excess vibration. This however, made penetration of the upper fiber tracts difficult especially during the spring-fall months. Patch electrodes were pulled to a tip size of 1-1.2 m (bubble number 66.4), resistance 5-7 M. This tip size is larger than what was tried before (0.60-0.70 m bubble number 4.5-5), as it was found that small tips became easily contaminated and resulted in few good seals. Small tip electrodes generated insufficient hydrodynamic spray at the tip to cleanly penetrate the upper fiber tracts (regardless of the backpressure used) for 4”-6” sized goldfish. Extracellular voltage waveforms were band pass filtered at 100 Hz - 10 kHz using an 8-pole bessel filter (Cygnus). Current monitor signals were band pass filtered between 0 and 5 kHz or 0 and 2 kHz. Intracellular voltage waveforms were filtered between 0-30 kHz as set internally by the AxoClamp 2B (Axon Instruments). All signals were sampled at 25 kHz and recorded using a Digidata 1322A (Molecular devices, Axon Instruments) 44 4.4 Eye tracking system Eye position was measured using the sclera search-coil technique [84]. Small copper coils (5.4 mm, 40 turns, Sokymat) were sewn onto goldfish sclera prior to the experiment using TG-100 sutures (Ethicon). Eye movements induced an angle difference between the Helmholtz coil system (CNC Engineering, Seattle WA) surrounding the fish tank and the eye coil. The induced coil current is amplified by phase sensitive detectors before sampled (25 kHz) and recorded (Digidata 1322A). The resolution of the eye tracking system is between 0.05 and 0.1. As the MP-285 introduced a substantial amount of metal into the Helmholtz coil, the system was recalibrated using an eye coil mounted on a protractor where the left and right goldfish eyes would normally be located 45 5 Results of intracellular measurements using whole-cell patch recordings 5.0 Comparison of whole patch recordings with sharp recordings We recorded eight Area I integrator cells using whole-cell patch recordings. As seen in Fig 5.1, the whole-cell patch technique demonstrates considerable improvement in temporal resolution over the sharp recordings. The patch recordings reveal the existence of small 0.2-3 mV excitatory postsynaptic potentials (EPSPs) that last ~ 5 - 10 ms. In the sharp recordings, the EPSPs are obscured. Partly, this is because the EPSPs generally have a prominent sharp peak (~ 1 ms) that would be highly attenuated by the RC filter of the high resistance tip. The f3db for an RC filter is 1/2RC or about 1/2(100 )(10 pF) ~ 159 Hz. The f3db point corresponds roughly to a reduction in voltage by ~30%. For a 1 ms, 1 kHz signal, the voltage reduction is close to ~84%. Thus the initial peak would be nearly abolished in sharp recordings. Without the sharp initial peak it is difficult to separate the EPSPs at high frequencies. For 7/8 Area I integrator cells recorded using the patch technique, the input resistance Rcell is 6626 Mmean +/- std) (This was assessed using small voltage pulses in voltage clamp mode immediately after breaking the seal.) The eighth cell recorded had an unusually high input resistance of 400 M It's unclear whether or not the high input resistance was an artifact or reflected a very small cell 46 Fig 5.1 a) Intracellular waveform from a sharp recording b) Intracellular recording from a whole-cell patch recording Fig 5.2 a) Eye position b) Hyperpolarized intracellular waveform reveals steps in membrane potential c), d) Expanded view of membrane potential 47 geometry. In comparison, previous sharp experiments [20] reported an Rm of 30 M The apparent resting membrane for the 8 cells was -69 +/- 5 mV (after correcting for the liquid junction potential.) Previous sharp recordings reported -61 +/- 7 mV. The difference in membrane resistance and resting membrane potential between the patch recordings and the sharp recordings are consistent with the literature [86]. Sharp recordings puncture the cell and introduce a leak resistance that lowers the apparent cell resistance as well as depolarizes the membraneComparisons between the two cell resistances suggest that sharp recordings introduce a 60 M leak resistance in goldfish integrator cells The apparent membrane time constant as assessed by negative squarepulsed current injections was 12.0 +/- 1.9 ms for n=4 cells. This is a little bit lower than the previously reported values of 16.3 +/- 3.9 ms. Hyperpolarizing the membrane with negative current injections (up to -0.3 nA) reveals the existence of membrane steps that are tightly correlated with eye position for all eight cells as expected from previous reports (Fig 5.2). For the 8 eight cells recorded, the average range for the membrane steps was 7.7 +/- 2.8 mV over a complete left-right scanning cycle. Previously using sharp recordings, the recorded range was 3.7 +/- 2.2 mV. The origins of the differences between the membrane time constants and the ranges of the membrane steps between the two techniques are unclear. (The latter perhaps can be attributed to an increase in apparent cell resistance.) The goldfish hindbrain is opaque, and it is not possible to target specific cell types/morphology. 48 Sharp electrodes and whole-cell patch electrodes used "blindly" may have different biases in targeting cell types. Sharp electrodes, with their fine point, may potentially record from all structures while patch electrode with their large ~1 um tip would generally only record uncovered somatic regions. 5.1 Resolved EPSPs have a short time duration The increased temporal resolution of the patch recordings revealed that the visible portion of the waveform is composed of EPSPs. Unlike predictions made by recurrent network models, the observed EPSPs have short time scales ~5-10 ms. Example EPSPs waveforms are shown in Fig 5.3. Most EPSPs possess a sharp initial peak followed by a slower phase. Some EPSPs do not possess the fast phase, but it is possible that travel down passive portions of the dendritic cable had smoothed out high frequency components. Standard electrophysiology amplifiers offer two recording modes: current clamp mode and voltage clamp mode. In current clamp mode, current is injected into the electrode such that the total current flowing into the electrode is set to zero. This nullifies the voltage offset that arises from the resistance of the tip. In voltage clamp mode, current is injected into the electrode such that the voltage at the tip is set to a constant value. This creates a uniform potential at a local region inside the cell surrounding the tip and reduces capacitive charging of the membrane as well as axial resistance. (In a realistic cellular morphology, the field set by the tip is not uniform. Nor does the field extend far down the dendrite in an active cell as the opening of local conductances from synaptic inputs shunt currents. [110]) 49 Fig 5.3 Shapes of EPSPs recorded under current clamp Nevertheless the voltage clamp mode offers some improvement in temporal resolution over the current clamp mode. To analyze the shape of EPSP waveforms, we chose the largest EPSPs (that are isolated n=17) under the assumption that they represent inputs most proximal to the recording site and fitted the falling phase with double exponentials Table 5.1. ae a b c d t b ce t d Mean Std. Deviation 0.060 nA 0.30 ms 0.061 nA 3 ms 0.023 nA 0.17 ms 0.023 nA 2.2 ms Table 5.1 Double exponential fit of EPSP waveform in voltage clamp mode In contrast, under current clamp mode, the fast time constant of the falling portion of waveform averaged 0.73 +/- 0.50 ms. The rising phase of the EPSPs 50 recorded were similar under both modes, 0.63 +/- 0.12 ms for current clamp and 0.53 +/- 0.16 ms for voltage clamp. (Unfortunately, the voltage clamp method is not compatible with the eye tracking system as EMF from the Helmholtz coils saturates and overloads the voltage clamp circuit.) The peculiar sharp rise of the EPSPs suggests that mixed conductances underlie their generation. The shape of the EPSP is similar to dendritic spikes observed in CA1 hippocampal neurons that possess mixed NMDA, AMPA conductances [112, 113]. Synaptic junctions of goldfish Mauthner cells that posses mixed NMDA, AMPA components in conjunction with a gap junction also exhibits this basic shape. 5.2 EPSPs increase with membrane potential and eye position Network models of persistent firing predict that the number of EPSPs increases with eye position while models of persistent firing based on intrinsic mechanisms suggest that variations in EPSP frequency do not play a prominent role. Thus accurately counting the EPSPs in the waveform is an important problem. However, counting small EPSPs with short time durations is a troublesome procedure at the high rates that are required to construct the waveform. We will illustrate the problems with a simple model. Suppose a neuron is a perfect single compartment RC circuit and each EPSP represents a stereotyped current injection at t0. Then Cm dV V I (t ) dt Rm (5.1) I (t ) (t t k ) I 0 k 51 As we observe V, we can recover the times of each input using a simple Fourier transformation. F V iwC m 1 Rm 1 ( ' ) t t F k (5.2) F I 0 In reality, a wide variety of EPSPs can be found and the exact distribution is unknown. There exist many 2-3 mV EPSPs, but it is unclear whether or not they are the dominant sources of input during the elevated membrane potentials. Moreover, as EPSPs travel down the dendritic tree, their shapes flatten and easily blend together. I0 is thus essentially unknown. The most serious problem with the Fourier transform method is that it assumes an implicit mechanism, that is I (t ) (t t k ) I 0 . However if there exist hidden regenerative mechanisms k with the form of I (t ) (t t k ) I 0 H (t t ' ) , where H is the Heaviside k function, then the Fourier transform would yield an answer but it would be incorrect. In general regenerative plateau potentials that underlie the fast fluctuations would empirically be unobservable and presents a "hidden problem." The fact that we can only observe the top of the waveform is a fundamental problem and, as we have shown, a great many unknown factors affect the construction of the whole waveform. While it is possible to attempt to brute force a 52 reconstruction of the waveform, the great number of variables that can be manipulated to fit the waveform would make such reconstructions of dubious value. To some extent the counting problem is alleviated by the sharp initial rise of the EPSP that provides a prominent feature with which to count. However, at high enough rates, even sharp peaks will tend blend together. We can see this by simulating the integration of a realistic 1 mV EPSP using a RC model with a 12 ms time constant. At 300 Hz and perfect periodicity, individual EPSPs are clearly discernable. (Fig 5.4 The green crosses denote the apex of an EPSP.) However, at 3000 Hz, the tops of the EPSPs make a ripple that would barely be observable above the background noise. If we add a small amount of noise, a 1 ms jitter, the top of the waveform develops a frothy top Fig 5.5. A single sharp rise and fall of the fluctuations can be composed of multiple EPSPs. If the arrival times are random, Fig 5.6, then the waveform develops a significant amount of fluctuations that is exaggerated by the asymmetric aspect ratio of the base EPSP. If we try to count the sharp rises as indicators of EPSP frequency, then we will significantly under count the true frequency as shown in Fig 5.7. Furthermore, in realistic cell morphologies, the majority of EPSPs will arrive at the dendritic tree and micro-inflections that indicate the arrival of an EPSP will be smoothed by cable properties. Thus counting the number of EPSPs by sharp rises in the voltage membrane will always undercount the true number of EPSPs at high frequencies. In reality, only a fraction of the EPSPs arrive near the soma. The rest arrive further distal in the dendritic tree and become submerged as part of the 53 Fig 5.4 Simulated periodic EPSP integration in a simple RC model at a) 300 Hz b) 3000 Hz c) expanded view of b) Fig 5.5 Simulate periodic EPSP integration with random 1 ms jitter at a) 3000 Hz b) zoomed in view of a) c) further expanded zoom of a) 54 Fig 5.6 Simulate EPSP integration with random arrival times a) 3000 Hz b) zoomed in view of a) c) further expanded zoom of a) Fig 5.7 a) Measured number of sharp rises as a function of membrane potential in a simulated model RC circuit b) ratio of measured frequency to the true frequency 55 'unobservable' portion of the waveform. For the EPSPs that ride on top of the waveform, we can count them using their initial sharp rises. The criterion for their selection is a minimum rise rate of 2.5 mV/ms. As the sizes of the EPSPs change with eye position, a better metric to judge the rate of EPSPs would be to weight it by its size to produce a weighted frequency. Fig 5.8 shows the results of the counting procedure for one cell. The frequency of the observable EPSPs oscillates in synchrony with the average membrane voltage. Fig 5.9 shows a plot between the EPSP frequency and average membrane voltage (over a 100 ms period.) We see in Fig 5.9 c), d) that EPSP rate generally rises with average membrane potential but that a leveling of the counted EPSP frequency occurs after Vm is ~ 8 mV above the baseline voltage. The origin of this leveling can most readily be explained by the blending of the peaks as predicted by the RC circuit model explained earlier. That the leveling voltage occurs much later than predicted is most likely due to smoothing of the distally arriving EPSPs via cable properties that forms the submerged uncountable portion. Regardless of the origins of the leveling in the apparent count of EPSP rate, the counted EPSPs are linear over a substantial portion of the range of the membrane voltage. This is important as the integrator has to maintain eye stability at low rates, (low average membrane potentials), as well as it maintains stability at high rates (high average membrane potentials). This issue will be discussed further in the later discussion section. Summary plots for the other 7 cells are located in the appendix A. 56 As mentioned before, many assumptions have to be made to estimate the number of EPSPs necessary to make up the whole waveform. Nevertheless, we will attempt to estimate this number using some conservative assumptions. To start, while the nature of the membrane waveform underneath the frothy fluctuations is unobservable, the fluctuations on top are clearly of synaptic origin Fig 5.11. If we segment the waveform into 100 ms bins and attribute the waveform above the minimum voltages of each individual segment to barrages of EPSPs, we can estimate the number of EPSPs required to make the fluctuations using the RC model. I epsp t C m dV V Vm VL Vm dt Rm Rm I t dt N I t dt (5.3) epsp 0 VL is the minimum voltage of the 100 ms segment and I0 is a stereotypical 1mv EPSP, shape a) in Fig 5.14. Rm is the input resistance of the cell and Cm is inferred from the measured time constant of the cell. Results are shown in Fig 5.10. We can also attempt the same procedure for the total waveform to estimate the number of EPSPs necessary to generate the full range of membrane voltage steps in Fig 5.12. While the peak frequency of the counted EPSPs was between 700-800 Hz, the estimated peak frequency of the EPSPs necessary to make the fluctuations and the total waveform was roughly between 1300 Hz and 5500 Hz respectively. 57 Fig 5.8 a) Intracellular membrane voltage b) Counted freq. of visible EPSPs c) Weighted freq. of visible EPSPs 58 Fig 5.9 a) Freq. of EPSPs vs. average membrane voltage (100 ms) b) Weighted freq. of EPSPs vs average membrane voltage (100 ms) Small variations in the shape of the stereotyped EPSPs have a large impact Fig 5.10 Frequency of EPSPs necessary to create the fluctuations (100 ms) of the waveform. The red line denotes the lower bound of the fluctuation. 59 on the estimation of the required EPSP frequency Fig 5.13, 5.14. The shapes of the distal EPSPs are unknown and may possess sizes larger than the observable proximal EPSPs. However, even when a moderate sized EPSP is used as the stereotyped EPSP for frequency calculations, the observable (counted) EPSPs is a significant fraction of the estimated fluctuation EPSPs (~60%) and estimated total number of EPSPs (~15%-20%) Fig 5.15. Thus, a substantial fraction of the synaptic input increases with the average membrane potential and eye position as predicted by network theories of persistent firing. Moreover, the estimated fluctuation EPSPs themselves while not completely counted, constitutes a formidable fraction, ~35%, of the estimated total number of EPSPs at the most depolarized membrane levels. Fig 5.11 Expanded view of 5.10 to illustrate the construction of the lower voltage bound used to outline the fluctuations. 60 Fig 5.12 Frequency of EPSPs necessary to construct entire waveform Fig 5.13 Frequency of EPSPs necessary to construct entire waveform if different EPSP shapes are used 61 Fig 5.14 Different shapes of EPSPs used in Fig 5.13 Fig 5.15 Ratio of counted EPSPs to the total estimated number of EPSPs and the ratio of the number of estimated fluctuation EPSPs to the total estimated number of EPSPs. EPSP shape a) in Fig 5.14 are used for the calculation. 62 The importance of the fluctuation EPSPs can be illustrated in another way. As can be seen in Fig 5.16, the peak-to-peak voltages that are generated by the fluctuations can become quite large in comparison to the total range of the membrane steps. We segment the waveform into 25 ms segments and plot the peakto-peak voltages of each segment as a function of the lower bound of the membrane voltage of each segment Fig. 5.17 and as a function of time Fig. 5.18. The size of the fluctuation is fairly large relative to the membrane step itself and forms ~30-40% of the total waveform at the peak membrane step positions Fig 5.18 b). The size of the fluctuations/synaptic barrages increase with the size of the membrane step. This can be explained in a natural way as increases in EPSP Fig 5.16 EPSPs cause large fluctuations in the membrane voltage 63 Fig 5.17 Peak-to-peak fluctuation increases with membrane voltage Fig 5.18 a) Peak-to-peak fluctuation oscillates with time b) Ratio of peak-topeak to VLowerBound 64 frequency will increase the probabilities that multiple EPSPs are coincident over the time-scale of a single EPSP. 5.3 Are integrator cells driven by fluctuations in synaptic input or by the average increase in synaptic input? One old but still unresolved question in neuroscience is whether neurons encode and utilize information through the average firing rate or whether or not a time code is utilized where each action potential is individually meaningful. Similarly, we can ask whether or not the firing of a goldfish integrator cell is driven primarily by fluctuations in the synaptic input or by changes in the average membrane potential. As the two variables are intimately correlated, it is hard to distinguish the effects through purely observational measurements. But we will offer some circumstantial experimental evidence that fluctuations may play a large role in driving the firing of integrator cells. In the next chapter, we will present numeric simulations using a conductance based model neuron to show how such sensitivities may arise. Fig 5.19 shows an example of an integrator cell operating in its normal regime (non-hyperpolarized.) The apparent threshold of the action potential is denoted by a green circle and exhibits a sharp kink at its onset. The membrane voltage preceding the apparent threshold of the action potential shows a nonstereotyped behavior suggesting that it is not part of the action potential itself Fig 5.20. Every action potential is preceded by a sharp rise in the membrane voltage (Fig 5.21) suggesting that it is preceded by a fluctuation event. Occasionally it is 65 possible to observe small inflections that are indicative of multiple EPSPs. Fig 5.22 shows that the average threshold (n=377) of action potentials always occur near the top of the voltage range preceding it, suggesting that something must drive the membrane above the local average to elicit the action potential Fig 5.22. Fig 5.19 a) Integrator cell operating in its normal regime b) Expanded view of a single action potential The apparent threshold of the action potentials increases with the average membrane potential Fig 5.23. This is interesting because it suggests that increases in the average membrane potential do not reduce the threshold necessary to elicit an action potential. The more likely explanation for this curious phenomenon is that the action potential initiation zone is located distal from the pipette tip. As mentioned previously, the only region that is amenable to blind patching with our tip size ~ 1 m is the soma. Some neurons such as peripheral motor neurons and 66 Fig 5.20 Expanded view of single action potentials from Fig 5.19 Fig 5.21 Moderately expanded view of Fig 5.19 67 Fig 5.22 a) Action potential are initiated at the top of the preceding voltage range b) Average action potentials initiation is in the upper percentile of the voltage range c) Average action potential threshold is above the preceding average membrane potential 68 retinal ganglion cells obey the classical picture of the action potential initiation zone being localized in the axon hillock adjacent to the soma. However, experimental evidence shows that many other neurons contain a distal initiation zone 40-70 ms down the axon. The relatively narrow diameter of the axon electrically uncouples the initiation zone from the soma. Thus charge, (in the form of a traveling action potential), will flow from the initiation zone and will be injected on top of the somatic waveform. This would give rise to an apparent increase in the threshold. The sharp kink of the threshold itself is also an indication that the initiation zone is distal of the soma. The voltage sensitive sodium and potassium channels discovered by Hodgkin and Huxley give rise to a smoother rise for the action potential initiation than what is found in vivo in cortical cells and here in goldfish integrator cells. Using experimental recordings and numeric simulations McCormick et al., showed [114] that the discrepancy arises from cable properties of the axon. Axonal recordings showed that at the initiation site, the rise of the action potential is smooth, but the threshold is sharpened after propagation to the soma. We will show in the next chapter that having a distal initiation zone lowers the threshold for action potential generation and makes the cell highly susceptible to fluctuations in the input. 69 Fig 5.23 Action potential threshold increases with the average (100 ms) membrane potential 5.4 Discussion Through direct measurements, we observe increases in synaptic activity for 7/8 cells with increases in average membrane potential and eye position (see appendix A.) For all eight cells, we observe an increase in membrane fluctuations (that are composed of EPSPs) with increases in average membrane potential and eye position. At the most elevated eye positions, the membrane fluctuations still constituted a significant fraction of the total wave form, 31 % +/- 11%, (pop. range 15%-46%) Our measurements are consistent with network theories of persistent firing that predict an increase in synaptic rate. The sizable contribution that the fluctuations make to the average waveform suggest that even if long lasting plateau potentials underlie the voltage waveform, network mechanisms play an important function in the operation of these cells. 70 The importance of coincident EPSPs in forming fluctuations can explain some puzzling observations from previous work. Previous [21] pair recording experiments discovered that ipsilateral Area I - Area I firing rates are correlated over very short time scales (~ 10ms) at low firing rates, but lose their correlation as the firing rate increases. The tight correlation times as well as the loss of correlation at high firing rates is consistent with fast fluctuations playing an important role in generating the output of the cells. First, if long lasting synaptic events (~100 ms) dominate the system, then the correlation times would be expected to be on order of the synaptic event itself ~100 ms. The observed EPSP timescale is on the order of 5-10 ms and agrees more readily with the observed correlation times of ~ 10 ms. At low firing rates (and low synaptic input rates), highly coincident EPSPs are necessary to push the membrane voltage across threshold and thus produce a correlated firing rate between pairs of Area I cells. In general, it's interesting to note that naturally occurring volatility at high EPSP frequencies introduces a significant non-linearity into the system. Perhaps, this is the system's method of adding robustness to network dynamics that all theoretical models lack? We can toy with this idea in two simple ways. If a neuron is triggered by the average membrane potential, then the output N , where N is the number of inputs over a unit time. However, if a neuron is triggered by fluctuations that are caused by coincident EPSPs, then the output N , (where the square root comes from the standard deviation of a poisson process.) For a stationary output, the expected change in output for the former case is dN , while for the latter the output 71 ~ 1 N dN . At high N, the non-linear neuron would buffer the system from synaptic noise. Earlier, we showed how a simple mathematical model v(t ) dv kv(t ) , dt of positive feed back using a linear term produces a solution that decays exponentially to zero with a time constant T feedback to a sublinear one, such that v(t ) two stable states 1 k . If we change the linear dv k v(t ) , then the solution has dt dv v k v . The concept of memory of course is a little bit dt different in the two models. In the former, there is only one stable state, the zero firing rate, and the quality of the memory is associated with the time constant of the exponential. In the later case, both zero and k2 are stable states, with k being an attractor. Thus the quality of memory is perfect in the non linear case and we have a basic flip-flop model. It's not clear how to extend this one dimensional model into a network model that shows arbitrary tuning or very fine discrete steps. Nor do integrator cells show preferred firing rates that this toy model would predict. However, after 'training' the goldfish eyes to leak using a moving environment, and presumably altering the synaptic weights of the network, the goldfish eyes decay to shifting null positions. (That is the eyes do not always decay to the same neutral position after a saccade.) Similar experiments that inactivate partial areas of the primate integrator regions also suggest the existence of null positions [115]. These 72 suggest that the system possess inherent preferred modes that are masked while the network is fully tuned. Regardless of how fluctuations of synaptic input are directly impacting the integrator circuit, the importance of fluctuations on neuronal behavior is gaining wider acceptance in the field. Recently it was discovered that discrete synaptic barrages are responsible for preserving contrast selectivity in orientation tuning in the visual cortex rather than the (low) average membrane potential [116]. As integrator neurons must maintain eye stability at both nasal (low firing rates) and temporal positions (high firing rates), network theories for persistent activity show also explain how coincident EPSPSs that form fluctuations are utilized.. In the next chapter, we will examine using numerical simulations how neurons may be physiologically biased towards fluctuating inputs rather towards a slow averaged input. 73 6 How neurons may operate in a fluctuation dominated regime 6.0 Influences of a distal action potential initiation site In this chapter, we will discuss how a distal action potential initiation site in the axon may enhance a neuron's sensitivities to fluctuations. In the classical model of a neuron, the action potential initiation site is located in the axon hillock/initial segment adjacent to the cell body. This model is true for peripheral motor neurons and retinal ganglion cells. However, recent advances in electro-physiology and imaging techniques suggest that not all neurons initiate their action potentials in peri-somatic regions. Dual patch recordings of the soma and the initial axon fiber by Stuart et al [93], suggest that the initiation zone in cortical pyramidal cells is located at least 30 m distal in the axon. Later imaging studies using voltage sensitive dyes confirm that the axon initiation zone is between 35-40 m distal from the soma [94]. In Purkinje cells, the initiation zone is located even further down the axon, ~75 m near the first node of Ranvier. These and other other examples [90, 91, 92, 95-98, 103], suggest that a peri-somatic initiation zone is not necessarily a common feature of all neurons. As suggested in earlier chapters, certain features of Area I cells hint that the action potentials are initiated distally as well. 1) There is little correlation between the location of large extracellular signals and the ease of making patch recordings in 74 the region (which would be indicative of somatic surfaces) 2) The apparent increase in action potential threshold with average membrane potential can most parsimoniously be explained by charge injection via a distal initiation site 3) Sharp kink at the threshold of action potential initiation suggest that the action potential had traveled from elsewhere. The available evidence is so far speculative, but it is informative to probe the consequences of a distal initiation site. We will show that under certain conditions, a distal initiation site will increase the cell's sensitivity to fast fluctuating signals. 6.1 Hodgkin Huxley Channels To understand how neurons transform their synaptic input into action potential discharges, we must first discuss the origin of action potential initiation in depth. The mechanism was originally elucidated by Hodgkin and Huxley in 1952 [53]. In the Hodgkin-Huxley (HH) model, the total membrane current is the sum of the capacitive current, the two voltage sensitive ion channels, INa and IK and a leak current that is voltage insensitive. I (t ) C m dV g Na m 3 h(V E Na ) g K n 4 (V Ek ) g leak (V E Leak ) dt (6.1) In HH's original formulation, m, h, n refer to gating particles that independently activate/inactivate the ion channels. Each gating particle can be in 75 one of two states, permissive or nonpermissive, and the transition between the two was hypothesized to be governed by first-order kinetics. n m n 1 n n h m 1 m h 1 h m (6.2) h Mathematically, this corresponds to three first-order differential equations, dn n (V )(1 n) n (V )n dt dm m (V )(1 m) m (V )m dt dh h (V )(1 h) h (V )h dt (6.3) Using the voltage clamp method, HH were able to experimentally determine the values of the rate constants. Plotting the steady state values for n, m, h in Fig 6.1, we see that n and m can more properly be termed channel activation variables while h is a channel inactivation variable. The initial exponential rise in n, and m describes a very striking relationship between the conductances of the channels and the membrane potential. At higher depolarization voltages, the currents saturate and the overall level of the sodium current is reduced by the inactivation variable h. To gain a better understanding of the temporal dynamics of the model, the 's and's of Eq. 6.3 can be transformed to a voltage dependent time constant n(V) and a steady state value nV). Then we have dn n n dt n n 1 n n n n n n (6.4) While the steady state values nV), mV), hV) are monotonically increasing and decreasing functions respectively, the voltage dependent time 76 constants have a bell shaped dependence (Fig 6.2). There is a striking discrepancy between m (sodium activation) with h (sodium inactivation) and n (potassium inactivation). Fig 6.1 Steady state Hodgkin-Huxley gating variables as a function of membrane voltage Across all membrane voltages, n and h are approximately the same, but m is almost an order of magnitude smaller. The consequences of this effect can be explicitly shown if we integrate Eq. 6.4. Experimentally, this would represent voltage clamping the neuron and very quickly bringing it from the resting state to some voltage V'. (n0 represents the value of the gating variable at resting membrane potential. Typically, this value is very small, ~1% for potassium.) n(t ) n (n n0 )e t / n (V ') 77 (6.5) Fig 6.2 Voltage dependent time constants of the gating variables Fig 6.3 Time course of GK and GNa after a sudden membrane change from Vrest to Vrest + 40 mV. 78 The sodium current quickly rises due to the small activation time constant m but will gradually decline as the longer inactivation time constant h sets in. The potassium current rises more gradually than the sodium current (Fig 6.3) We can now understand how action potentials are initiated in the HH framework. Transient synaptic current elevates the membrane potential. This activates sodium channels that will further depolarize the membrane. If the initial current is strong enough, it will initiate a positive feedback between sodium channel activation and membrane depolarization. This will create a fast sharp depolarization of the membrane. On a longer time scale, the membrane depolarization will activate potassium channels and inactivate sodium channels. This will eventually bring the membrane voltage back to the resting state. In order for the initial current to start the fast sodium cycle, it must first cross a threshold. The origin of the threshold can be understood by considering an instantaneous injection of current. As n and h activate fairly slowly compared to m, we can replace them with basal constants in this thought experiment. The HH currents can then be written as I V g K n0 (V E K ) g Na m(V ) 3 h0(V E Na ) g m (V E Leak ) I Inj (t ) (6.6) 4 The total current ITotal makes a U-shaped bend around the x-axis. (Fig 6.4) The point around V = 0 is an attractor. Small injections of positive currents will shift the voltage up but the small change in INa will be balanced by larger changes in IK and ILeak. This will generate a net outward current that will bring the membrane voltage down. Similarly, an initial hyper-polarization of the membrane will 79 Fig 6.4 Instantaneous I-V curve near the resting membrane potential Fig 6.5 Slightly slower than instantaneous I-V curve near the resting membrane potential 80 generate a net inward current that will increase the membrane voltage and restore the membrane voltage to its resting value. However, if the initial current injection was able to bring the system pass ~2.6 mV, then the system will generate a net inward current that will continue to increase the membrane potential, leading to runaway positive feedback. If the initial current injection was a little bit slower, then INa will be reduced by the inactivation variable h and this would in effect shift the threshold to the right to a higher voltage (Fig 6.5). The generation of the action potential is not only dependent on the initial current being strong enough to stimulate the cell above a certain threshold, but the threshold is also dependent on how quickly the current is injected as sodium channels will inactivate and potassium channels will increasingly open. The full time dependent solution is a little more complicated than the instantaneous model as the potassium current and sodium inactivation variable h are not constant on long time scales. To illustrate the effect fully, we used the simulation software Neuron developed by Hines and Carnevale [99] to numerically compute the relationship between the threshold current and the rate of change in current to evoke an action potential (Fig 6.6). We modeled a single compartment space clamped giant squid axon, 500 m wide, 100 m long, with the conductance values as originally obtained by HH. (The time step of the simulation is 5 s and the temperature is 6.3. We simulated injections of different linear ramp currents and obtained the relationship between the threshold current and the ramp duration that is necessary to 81 Fig 6.6 Example ramp current injections into a hypothetical space clamped squid axon. The difference between the peaks of the two ramp injections is 0.1 nA. Fig 6.7 Relationship between the threshold current and the ramp duration necessary to generate an action potential in a model squid axon 82 evoke an action potential. We also recorded the membrane voltage of a just-subthreshold ramp injection as the voltage threshold of that ramp duration. In Fig 6.7, we see that a ~10 ms ramp requires the lowest peak current to elicit an action potential. Below 10 ms, the threshold increases due to the extra current necessary to charge the membrane in a small amount of time. Above 10 ms, the threshold increases for the reasons we have previously mentioned. Fig 6.8 Measured somatic voltage threshold of ramp current injections to elicit an action potential in a model squid axon. The threshold voltage decreases as the ramp duration is decreased, eventually leading to the minimum instantaneous threshold. 6.2 Cable geometry on site of initiation So far we have discussed action potential generation in a single compartment. In a real neuron, finite cable geometries introduce complexities to the 83 problem [107, 108]. This is because a significant portion of the current that is either injected or arise from the activation of channels flows longitudinally away from the site of initiation. Thus less current is available for polarizing the membrane and the effective voltage threshold is higher. Compartments such as the cell body and dendrites are large effective current sinks. For Area I neurons, we estimate its total capacitance to be over 150 pF from the measured membrane time constant and cell resistance. This is reflective of the extensive dendritic tree that was revealed in previous labeling experiments. 6.3 Numeric modeling with neuron Our model Area I neuron is based on a simple model for cortical cells developed by Yuguo et al, [118]. Their model is adapted for our purposes by the addition of a tapered axon hillock and the segmentation of the axon into two parts to study distance related effects. We used the suggested conductances values. In Yuguo's model, the entire axon is uniformly covered with a HH conductance that is ten times higher than the somatic conductance. We follow his example and set the compartment with the initiation site to have ten times higher conductance than the other compartments which otherwise have the same conductances. The dendrite used by Yuguo provides a capacitance load of ~76pF and is an underestimate of the dendritic capacitance. Our model neuron is simulated at 20C with 5 s time steps. To illustrate the effects of varying the action potential initiation site, we injected current ramps into the somatic compartment as reflective of the soma's geometric role as the site for current integration and recorded the current threshold and voltage thresholds necessary to elicit an action potential. 84 Fig 6.9 Current threshold vs. ramp duration for ramp injections in a model Area I neuron with and without dendrites. Fig 6.10 Peak somatic voltage threshold vs. ramp duration for ramp injections in a model Area I neuron with and without dendrites. 85 The action potential initiation compartment is set by increasing its conductance to a value ten times higher than the other compartments. Length (m) Diameter (m) Segments gNa (ps/m2 ) gK (ps/m2 ) gLeak Dendrite 3000 5 60 800 150 0.33 Soma 16 10 4 800 150 0.33 Hillock 10 1-10 10 800 150 0.33 Axon near 30 1 15 800 150 0.33 Axon far 30 1 15 800 150 0.33 Table 6.1 Parameters of model Area I cell. The compartment with the action potential initiation zone is set by increasing its conductance by a factor of 10. As a large current sink, the dendrite has a tremendous capacity to influence neural discharge properties [87]. It also enhances differences between different locations of the action potential initiation site. In Fig 6.9b, and Fig 6.10, we see that without a dendrite, there is little difference <~3% between having the initiation site located in the proximal (Near) axon segment and the distal (Far) axonal segment. However, with the addition of a 76 pF dendrite, an 11% difference in the current threshold and a 32% difference in somatic voltage threshold are created. The dendrite accentuates inherent geometric differences between the two initiation sites. The overall threshold is increased for both sites with the addition of a dendrite as the dendrite acts as a large current sink. At short time scales the voltage and current threshold increases less for the distal section because the relatively large axial resistance of the proximal axonal segment uncouples the distal 86 segment from the dendrite. Thus, it is easier to generate an action potential in the distal segment. On a longer time scale, the advantage of rapidly raising the voltage of a low capacitance distal segment with fast sodium channels is lost and the distal segment also has to contend with the potassium current from the proximal axonal segment. Moreover, just as the proximal axonal segment acts as a barrier to dendritic influences, it also acts a voltage divider to lessen the impact of the current stimulus. This voltage divider is also frequency dependent. Intuitively (for a neuroscientist), this must be true as axons can propagate high frequency action potentials but do not so readily propagate slow waveforms. By using a perturbation scheme developed by Chandler [101], Mauro [102] showed that the HH equations can be thought to contain an inductive component for small subthreshold voltages. For the potassium channel he derived Eq. 6.8 (and a similar set of equations for the sodium channel.) dI g n L I V dt a gn n n 1 L a (6.8) d d an n a 4 g k n 3 (V Ek ) n n dV dV Tithe association of an inductance with the membrane is at first a little bit strange as ostensibly there does not appear to exist any common forms of inductances such as coils of wires or loops of magnetism that can be associated with 87 the neural membrane. However if we return to the basic definition of inductance V L dI , we can imagine how the neural system with its time and voltage dt dependent conductances can readily produce such a phenomenon. And it is well known that RLC circuits will bandpass filter signals. Fig 6.11 shows the frequency dependence of transferring a 1 mV somatic sine wave to the distal axon segment for our model neuron. Fig 6.11 Frequency dependence of somatic voltage transfer to the distal axonal compartment in the model Area I neuron Fig 6.12 and Fig 6.13 show comparisons between a hillock initiation zone with proximal and distal axonal initiation sites for ramp injections. The more distal the initiation zone is from the dendrites, the larger the effective threshold gap between slow and fast injections. The absolute threshold for the fast currents also diminishes as distance from the initiation zone. 88 Figure 6.12 Influence of the location of the action potential initiation site on the current threshold Fig 6.13 Influence of the location of the action potential initiation site on the somatic voltage threshold 89 Aside from the aforementioned consequences that arise from basic circuit theory, a distal initiation site allows the neuron two other ways to increase its sensitivity to fluctuations. The first is a distal initiation site would allow the neuron to increase the conductance of the initiation zone without undue perturbation to the cell's overall conductance. This would lower the overall threshold. We simulated this by increasing the distal axonal conductance by a factor of fifty (instead of a factor of ten. (Fig 6.14, Fig 6.15) The exact density of sodium channels in the initial segment is unknown although some studies suggest that it may be as high as that at the node of Ranvier ~20-30 ns/m2 [119, 120]. A recent experiment that utilized direct patch-clamp recordings from axon initial segments of cortical pyramidal cells suggested that the density of sodium channels is fifty times that of the soma [120]. While the axonal channel densities of Area I neurons are unknown, it is known from previous labeling experiments that they possess a very thin (sub micron) initial segment. This is somewhat puzzling as Area I must project their neurons several millimeters to the abducen nucleus and the transfer of an action potential would be facilitated by a wider axon. A thin axon however, will increase the isolation of an axonal initiation site and would also enhance the neurons sensitivity to fluctuations. We examined the difference by changing the axon diameter (for both segments) from 1 m to 0.5 m (thin) and 1.5 m (wide). (Fig 6. 16, Fig 6.17) 90 Fig 6.14 Increasing the conductance of the action potential initiation zone lowers the current threshold Fig 6.15 Increasing the conductance of the action potential initiation zone lowers the somatic voltage threshold 91 Fig 6.16 Effects of axon diameter on the current threshold Fig 6.17 Effects of axon diameter on the somatic voltage threshold 92 6.4 Discussion The model that we have used is highly speculative as very little is known about the parameters of actual Area I integrators. However, it is not with merit as a recent study of the avian nucleus laminaris showed that the location of the action potential initiation site for NL neurons is positively correlated with the ability of the NL neuron to detect high frequency coincidence synaptic inputs [103]. This is consistent with our model as a distal initiation site would lower the threshold voltage/current for coincident synaptic events to trigger an action potential. Area I neurons possess large dendritic arbors which act as significant current sinks. This almost forces the initiation zone to be located in the axon. We have suggested several mechanisms by which the cell's sensitivity to fluctuations may be enhanced if this is true. (Coincidently, the observed EPSPs possess aspect ratios which makes them more useful for forming fluctuations rather than smooth averages.) In the cortical in vitro analogue of persistent firing [74], it is possible to observe transitions between up states and down states that are on the order of 20 mV. This large dynamic range however is not observed in Area I cells. Moreover, while the cortical oscillators appear to be bistable and function in either one of two states, Area I cells operate in many intermediate states and the neural discharge at low rates are more easily explained by fluctuations rather than a low average membrane potential. That fluctuations are important beyond their average contribution to the waveform is currently hypothetical. Future experiments can test this theory by 93 injecting current at resting/low membrane potentials (low firing rite, nasal eye positions) in a similar fashion to what we have done for the numerical neurons. Alternatively, as the discharge of Area I cells cannot be voltage clamped, (consistent with the initiation site located away from the electrode tip), an exact waveform can be imposed on the cell using voltage clamp mode to elicit action potentials. (This would avoid the hassle of comparing current and voltages waveform for a charging capacitor and somewhat reduce naturally occurring fluctuations as the potential around the tip would be clamped.) Companion experiments should also be performed to probe the sensitivity of neural discharge with respect to changes in DC membrane voltages. Previously this latter experiment was performed with sharp recordings, but sharp recordings introduce an effective depolarization of the membrane potential and bias the result. If the difference, 10 mV, between the average resting membrane potential of sharp recordings and the patch recordings is an accurate indication of this leak-induced depolarization, then the sharp recordings may have severely biased this sensitivity test. While a single neuron may exhibit similar behavior post-impalement as compared to preimpalement albeit at a higher frequency, it is unlikely that any network architecture would be able to preserve its proper dynamics if every neuron in that network was depolarized by 10 mV. The answer to whether or not Area I is operating in a fluctuation dominated regime is important as Area I cells must still possess stability in the form of persistent firing at low firing rates. This suggests that network mechanisms that attempt to explain the function of the integration must utilize the fluctuations in 94 some manner at low rates - if not at all rates. This motivates further theoretical searches for networks that utilized fluctuation based spike time dynamics. 95 96 Bibliography 1. Goldman-Rakic, PS (1995) “Cellular basis of working memory.” Neuron 14, 477-485 2. 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