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Part IV- Single neuron computation A note The problem with theory The problem with practice Models of action potential H&H is a good “conductance model”, but most models are simpler: They use “integrate and fire neurons”• point neurons (no spatial considerations) • every input give small depolarization / hyper-polarization excitatory or inhibitory but of costant size(+1 or -1). • The inputs are summed. The only determining factor is above/below threshold(and the threshold is constant) 1.linearly summing all inputs (conductance is passive) 2.threshold impose non linearity (t is a low pass filter)= AND & OR functions =>McCullough and Pitts(1943)- This is sufficient to allow any computation Integrate and fire models Simple common model- leak integrate and fire: Summing input across time: V(t)=Vm+Rm*Ie(1-exp(-t/t) Time difference (isi) between spike is linear to input amplitude Rm I e EL Vreset 1 risi t m ln tisi R I E V L th m e 1 I&F : What will input integration be dependent upon? integration in time Two stimuli arrive with a time difference. Will they be united to a bigger stimulation or be separated? Dependent on t As t increase, stimuli are less separable Very brief: low firing rate, coincident detection Prolonged: higher rate, lower sensitivity Problems with I&F I & F models are DETERMINISTIC- Same input will necessarily lead to same firing rate, and all the cell can do is add up inputs (not only the AP is “all or none”, the neuron is “all or none”). Theoretically, this played a big part in the bottom up approach to visual processes- basic features are added up to more complex features… In reality input and threshold ARE NEVER CONSTANT Inadequacy of I&F models • Problems: 1. No inactivation (or other conductance references)-can be imposed on the models 2. Regular firing- if input is same on average , I&F model will produce very regular periodic firing rate with constant Inter Spike Interval (ISI) Rm I e EL Vreset 1 risi t m ln tisi R I E V L th m e Tal & Schwartz 1999 1 Tal & Schwartz 1999 3.Nonlinear I-V curve In reality, neurons have near Gaussian firing rate. Rate/Noise: for Gaussian =1, for integrate and fire ∞, for neuron ~1.2). Realistic ISI distribution I&F inadequacy solutions TYPE I-assume that the neurons ARE DETERMINISTIC therefore their only source of variance is the input. Therefore claiming that input is naturally Poisson-like (true). Especially true for high threshold and small t Cannot explain why experiment controlling input give variable results Variable input make variable firing rate Increasing input variance will broder ISI distribution, Stevens & zador 1997 TYPE II- assuming non deterministic response and implementing it by any of the various non linear component of the neuron-voltage gated ion channels, channel is difference kinetics, differential distribution of channels, morphological changes… Strong VS Sometimes give good predictions weaker negative feedback, softky & koch 1993 Conductance models Adding to H&H specific channels known to be found in various cells, or known geometry… Multitude of voltage activated channels: • 4 subtypes of voltage activated Ca2+ channels • Voltage activated Cl- channels • Voltage activated non-selective cation channels • Activation in hyperpolarization (h type) • Ca2+ activated voltage dependent K+ channel • Rapid, inactivating K+ channel (A type) “Allows complex information processing” Example: Epilepsy in mutant mice lacking Ka channels Example of other channels’ importance- Action potential is not the only spiking mechanism Burst firing due to Ca firing: • Exist cells with 2 additional type of channels: 1. T type voltage activated Ca channels (T for transient)- open at very low threshold, inactivate fast. 2. L type voltage activated Ca channels (L for long)- open only at higher threshold, very very slow de-activation (not inactivation-what is the difference?) =>T open at low threshold (Vm)->inward current->depolarization-> action potential (T close)->higher depolarization->L open for long period- chain of action potential (what stops it?) Burst firing due to Ca firing: =>T open at low threshold (Vm)->inward current>depolarization-> action potential (T close)->higher depolarization->L open for long period- chain of action potential what stops it? When will it start again? How are the action potential effected? • Burst firing due to Ca firing: what will happen at these cells if held depolarized? Conclusion- Action potential isn’t everything! • The integrate and fire and conductance models assumes single compartmental model (since everything is summed linearly everywhere), described in various levels of detailed. • However, not all effects are linear (none are linear…) and they aren’t similar everywhere across neurons. Requires: 1.Understanding the non-linear functions 2. Finding the relevant compartments Important terms EPSP- Excitatory post synaptic potential- a depolarizing input whose Ex >Ethreshold IPSP- Inhibitatory post synaptic potential- an input whose Ex <Ethreshold (depolarizing or hyperpolarizing) Dendrite- the place where integration take place. Sometime stabbed with “Spines” If Ex=Vm (like Cl)=>Shunting Inhibition I-V curve showing Shunting inhibition- lower g will decrease both depolarization and hyper-polarization Synaptic integration-the neuron as a decision maker Sub- threshold signals added across the dendriteThe common view- linear summation EPSP excitatory IPSP inhibitory Dependent on t & l The common viewlinear summation Notice the even in this simplified view COINCIDENCE IS CRUCIAL, allowing added signal to reach beyond threshold (meaning- allowing AND and OR functions) Also it is an important Signal for associative learning, Showing temporal proximity of Two events in an indication for causality Computations with coincidence detection Recognition through coincidence of features, auditory localization through temporal mismatch between the two ears… But EPSP and IPSP are NOT summed linearly. First of all, they decay across the dendrite (dendrite as high frequency filter) Vx = Vo X exp(-x/λ) Vλ ≒ 0.37 (Vo) length constant, λ internal resistance (ri) membrane resistance (rm) The reality is never linear… Non linear dendritic elements are divided to 1. Passive dendritic properties 2. Active ones. Passive dendritic non linear properties Morphology related: 1. Distal dendrite sites are thinner than the proximal sites- Rm smaller, attenuated signal, more decrease in space. (might be valuable for for distinguishing the source of the signal- for example a soma specifically sensitive to fast signals will favor proximal ones) 2. Spine morphology (large “head” with low Rm and then very thin highly resistive “neck”) is amplifying the signal-more back and forward propagation Smaller “neck:= higher EPSP amplitude • Morphology effect propagation: for example, the cortex has less branching then cerebellum and therefore more back and forward propagation Back propagation Forward propagation cortex cerebellum Vetter 2001 Dendrite amputation leads to sharper AP at lower threshold Bekkers & Hausser 2007 Passive dendritic non linear properties II Temporal integration related: 1. Sub linear summation of temporally clustered inputs due to shunting inhibition- opening a channel (by the first input current) decreases Rm, therefore (since V=IR), any further current will cause smaller voltage changes. An example GABAB channel are Cl channels having little effect on Vm, but decrease any following inputs • Shunting inhibition decreases Rm and therefore also l and more importantly, t smaller, more sensitive to coincidence/synchrony Rm (ZD 7288 , K(A) antagonist leads to increase in both excitation and inhibition. Why? Shunting inhibition) Magee & Johnston 2005 2. The effects of Back propagation (increasing concurrent EPSP, less distally) more in spines with big head… MOSTLY for control- tells the dendrite that it just transmitted a spike, make related signals more favorable for creating a second spike Back propagation decrease in space Notice the dialectics- Back propagation also shunts future EPSP Hausser, Major & Stuart 2001 Active dendritic non linear properties I Active= due to presence of voltage gated ion channels Supra linear summation Caused by signal amplification through local voltage gated ion channel (mostly Na, Ca and NMDA receptor) Supra linear summation of back propagation and EPSP London and Hausser 2005 Blocked by TTX –due to Na voltage gated channels Stuart & hausser 2001 Supra linear summation occurs preferably at distal sites (logic: this is where signals requires most amplification) Usually required coincidence (in order to reach the channels’ threshold- amplifies coincidence detections Amplification of EPSP+ back propagation coincidence in distal dendrite Stuart & hausser 2001 • Example I-Na channel amplifying a Simultaneous input • Example II- K(a) channel CLOSES at depolarization (less shunting inhibition) and future input is amplified. • Simulation show large effect to the smallest changes in voltage sensitive channel distribution Morphology and channel distribution interact-an example Few branches Many branches, very attenuated The more branches, the more the signal is attenuated and effected by the presents of voltage sensitive channels Vetter 2003 Computations so far Addition/subtraction: summation+ shunting inhibition Multiplication/division: supra/sublinear summation high pass filter- the membrane Coincidence-AND, OR, learning Amplification Delay- AND-NOT Dendritic computation: Filter, logic, coincidence, amplification London and Hausser 2005 Single neuron computations (for example) • • • • • Sound localization and feature combination-AND Motion detection- AND and AND-NOT “working memory”- on-going amplification Novelty detection- low pass filter Phase detection (through well places voltage sensitive channels; this neuron will be a “resonator”) • Adaptation-high pass filter through shunting inhibition Herz 2006 Extreme case of supra linear summationlocation irrelevance in the hippocampal CA1 Since distal inputs decays on the way to soma we expect higher amplitude of proximal EPSP at soma recording In CA1: soma input arrives at exactly same size How? Magee 2000 There is amplification of distal input EXACTLY enough to compensate for their propagation decay- Homeostatic balance Magee 2000 Not purely due to morphology- when blocking voltage gated channels signals decays • Distal EPSP are also more narrow to compensate for smearing through propagation What is it good for? less propagation failures…, but no location information? Specific to CA1-not in cortex Williams & stuart 2003 Active dendrite cause Many types of back propagations (as for “forward” propagation) Hausser M 2001 Dependent upon cell type probably because: Very slight changes in voltage gated channel distribution cause great conductance changes Meaning: through selective amplification with active dendrites we can basically induce firing rate to be depend upon very specific inputs: • only temporally clustered inputs • Only inputs from a particular dendritic site (or specific combination of sites…) • Variable effect of back propagation (weak or high and also opposite in direction- shunting if passive, amplification if active) Active dendrites II: Dendrites can also have an action potential Dendritic spike generation: at lower intensity of stimulating a dendrite, a distal signal (dashed) follows somatic signal. At higher- it precedes the somatic signal Hausser & mel 2003 Chen, midtgaard & shepherd 1997 - Only in dendrite with enough channels (example-cortex) -specific for strong synchronous stimulus! Hausser & mel 2003 -specific for distal sites Williams & stuart 2003 Occurs naturally For most neurons (except in CA1) transmission for distal synapses is unreliable and decays entirely until soma, so dendritic spike is the only transmission for distal sites, making then solely coincidence detectors An example: distal sites will only respond during synchronous state such as sleep, making the neuron responding non linearly specifically during sleep and linearly during wakefulness Hausser & mel 2003 Notice the difference between EPSP and an action potential • Action potential will erase momentary information, • EPSP will enhance it ->the logic? once we have action potential, we have all we need…any other suggestions? A note- dendritic spikes might replace back propagation for plasticity • Coincidence lead to strengthening of response (plasticity changes) and we call this the correlate of memory. • Therefore, most models regard the case of coincidence between an input and back propagation. • However, the occurrence of dendritic spike can serve as a back propagating signal though out the dendrite, even due it might never even reach the soma • Meaning: plasticity changes might not have to pass through the soma or axon(it doesn’t have to effect the next cell in the network in order to be considered connected to the previous!) “hand shake” between distal and proximal sites Massive depolarization and hyper-polarization during a dendritic spike will eliminate all other inputs at that time point (they will cause “reset” by shunting), so a distal spike will shunt a proximal region. On the other hand, proximal region is the only region to benefit from back propagation… Supports a distinction between “proximal processing”-less amplified, with back propagation, no dendritic spikes and, “distal Processing” Williams & stuart 2003 So how should we model the neuron now? Modeling neurons with many compartments within each there is non-linear summation1. The distal VS. proximal 2. Each dendritic branch 3. Each spine head Herz 2006 Possible compartments- Hausser & mel 2003 An example for the possibility of “separated branches model” Pirazi, Brannon & Mel 2003 treated dendritic branches is separate compartments: Y is firing rate, m is # of compartments, n is number of inputs. The n inputs are summed non linearly by the S function (in their case-sigmoid). Each compartment is weighed by a measure of her effect on the soma, a. The linear sum of all compartments is passes through the soma and a g filter transforming depolarization into firing rate (threshold function) Poiazi, Brannon & Mel 2003 This is a description of the neuron as a two layers network the first being comprised of each branch/compartment and the second- the somatic sum of branches. This allows predicting firing rate fairly well by knowing only n,m,s and a (all can be found experimentally) without knowing specific channels Poiazi, Brannon & Mel 2003 Polsky, Mel and Schiller (2004) check for compartments in cortical layer 5 neurons (the thin branches as separate compartments). They too found description of two layered network appropriate: Between branches summation was linear Within branches summation was supra linear until a dendritic spike appeared Polsky, Mel & schiller 2004 Summed together, the branches served as good candidate for signal compartment. Moreso, they found they average compartment size was 60mm, with the strength of non linearity decreasing continuously with distance even within a compartment Polsky, Mel & schiller 2004 This suggest that two layers might again be only a simplification… Hausser & mel 2003