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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
=>McCullough and Pitts(1943)- This is sufficient to allow any
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 
th  
 m e
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
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 
th  
 m e
Tal & Schwartz 1999
Tal & Schwartz 1999
3.Nonlinear I-V curve
In reality, neurons have near Gaussian firing
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…
Sometimes give good
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
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
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
Vetter 2001
Dendrite amputation leads to sharper
AP at lower threshold
Bekkers & Hausser 2007
Passive dendritic non linear properties
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
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
summation+ shunting inhibition
supra/sublinear summation
high pass filter- the membrane
Coincidence-AND, OR, learning
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
Magee 2000
There is amplification of distal input
EXACTLY enough to compensate for
their propagation decay- Homeostatic
Magee 2000
Not purely due to morphology- when
blocking voltage gated channels signals
• Distal EPSP are also more narrow
to compensate for smearing through
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”
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 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
-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
“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
Williams & stuart 2003
So how should we model the neuron
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
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
Hausser & mel 2003