noise in the nervous system - semantic scholar€¦ · noise in the nervous system a. aldo faisal,...

Noise in the Nervous SystemA. Aldo Faisal, Luc P. J. Selen, Daniel M. Wolpert

Nature Reviews Neuroscience, 2008

Johannes Bill

Institute for Theoretical Computer ScienceGraz University of Technology

Johannes Bill (IGI, TU Graz) Noise in the Nervous System 1 / 18

overview

Overview


general considerations behavioral loop

The behavioral loop

Noise sources

physical: quantum mechanics, thermodynamics → physical limit

sensory: chemical or mechanical signal transformed to electrical signal

cellular: ion channels, synapses, network feedback, . . .

motor: motor neurons, twitches, contraction of muscle fibers

→ trial-to-trial variability in behavior


general considerations behavioral loop

The behavioral loop

Noise sources

physical: quantum mechanics, thermodynamics → physical limit

sensory: chemical or mechanical signal transformed to electrical signal

cellular: ion channels, synapses, . . .→ focus of this talk

motor: motor neurons, twitches, contraction of muscle fibers

→ trial-to-trial variability in behavior


general considerations definition of noise

The definition of noise

input → encoder → (noisy) channel → received signal

Oxford English Dictionary (as quoted in the paper)

“[. . . ] or more generally any distortions or additions which interfere withthe transfer of information.”→ What about noise in digital systems in which it does not invoke adifferent interpretation of the signal?→ What about sub-theshold signals in threshold systems which invoke nooutput without noise?

Wikipedia, the free encyclopedia

“A disturbance that affects a signal and that may distort the informationcarried by the signal.”


general considerations definition of noise

The definition of noise

input → encoder → (noisy) channel → received signal

Oxford English Dictionary (as quoted in the paper)

“[. . . ] or more generally any distortions or additions which interfere withthe transfer of information.”→ What about noise in digital systems in which it does not invoke adifferent interpretation of the signal?→ What about sub-theshold signals in threshold systems which invoke nooutput without noise?

Noise might be necessary for propagation of information!

Wikipedia, the free encyclopedia

“A disturbance that affects a signal and that may distort the informationcarried by the signal.”


cellular noise

Overview


cellular noise action potentials

AP timing is behaviorally relevant

This information must be encoded as spikes.

Reliability of spike initiation in the axon hill and axonal propagation?

Jitter of spike timing during initiation and axonal propagation?



Recall: Neuronal transmission

Hodgkin–Huxley model:

−Cm · ∂V

∂t= leakage + gNa · m3 · h · (V − ENa) + gK · n4 · (V − EK )



Reliablity of AP initiation and propagation

Initiated spikes travel reliably due to strong AP-peak

For V ≈ Vth, only few Na+-channels open

Channels open and close stochastically (thermodynamic equilibrium)

∆U = Rm ·∆I → small neurons more affected by single channel noise◮ False spike initiation for V ≈ Vth

◮ “Rogue” spikes in axons if ∅ < 0.1 µm◮ “Rogue” spikes in cell body if ∅ < 3 µm



Reliablity of AP initiation and propagation

Initiated spikes travel reliably due to strong AP-peak

For V ≈ Vth, only few Na+-channels open

Channels open and close stochastically (thermodynamic equilibrium)

∆U = Rm ·∆I → small neurons more affected by single channel noise◮ False spike initiation for V ≈ Vth

◮ “Rogue” spikes in axons if ∅ < 0.1 µm◮ “Rogue” spikes in cell body if ∅ < 3 µm

Electrical properties impose a limit to the wiring density of the whole brain!



Variability in AP-timing

Channel noise affects timing of both spike initiation and propagation.

Jitter increases for long and thin axons

Simulation results (Fellous et al, 2004):


cellular noise synapses

Synaptic noise

Kleppe et al, 2006

Vesicle release (maybe meaningful):

Multiple active zones per synapse

Each AZ holds releasable vesicles (STP)

Release probability (e.g. AP width)

Sources of true noise for single vesicle release:

Vesicle size (58%)

Diffusion across synapstic cleft

Location of vesicle release (36%)

Synaptic-receptor channel noise

Total variability of PSC (CV > 20%) can be fullyaccounted for by noise.


noise in neural networks

Overview


noise in neural networks averaging and prior knowledge

Averaging

Basic idea: Combine signals carrying redundant information which aredistorted by independent sources of noise.

Convergence

For N incoming signals: noise-level ∼√

N , while signal ∼ N.

Population coding

Kalaska, 1983

If the same information is encoded by multiple neurons, thepopulation mean is less affected by noise.

Temporal integration

Robust against jitter of spike timingbut: ISI information ignored.


noise in neural networks averaging and prior knowledge

Prior knowledge

Basic idea: Structure of signal known → separate signal from noise.

Example: matched filter

Perfect signal:f (t)

Noisy signal:s(t) = f (t) + σ(t)

Optimal kernel:h(t) = f (−t)

Filter output:f (t) =

∫s(t−τ)·h(τ)dτ


noise in neural networks benefits

Benefits of noise:

Information propagation in threshold-like systems

A simple example:

Threshold system with binary output: f (s) = (signal > threshold)

Sinusoidal input signal + Gaussian noise

Compare:◮ different noise levels◮ orignal signal below / above threshold

General framework: stochastic resonance

Occurs in all threshold-like systems (Kosko and Mitaim, 2003)

Measured in biological neurons (Collins, 1996)



Results: threshold detectorsub-threshold, low noise:

sub-threshold, medium noise:

supra-threshold, low noise:

supra-threshold, medium noise:

Rule of thumb: Noise is useful if positiv detection of sub-threshold signalsis more important than failure to detect supra-threshold input!



Some more benefits

Stochastic resonance:◮ System performs best at finite noise level◮ Biologically realistic: high-conductance states (Ho and Destexhe, 2000)

Asychronous population firing:◮ Fast reaction to changes in input◮ Stability improved by noise (Gerstner, 1999)

Learning:◮ Functional network reorganization in motor cortex can be explained by

reward-modulated Hebbian learning (Legenstein, 2009)◮ Adaptation to dynamic environment◮ Higher robustness


conclusion

Conclusion

Summary

Sources of noise in the behavioral loop

Definition of noise regarding neural networks

Celluar Noise:◮ Initiation and propagation of action potentials◮ Variability in synaptic transmission

Noise in neural networks: reduction and benefits

Discussion

Relationship noisy signal ↔ transmitted informationif the encoder is (partly) given?

Should we consider trial-to-trial variability of AP timingand synaptic weights in PCSIM?


conclusion

The end.


noise in the nervous system - semantic scholar€¦ · noise in the nervous system a. aldo faisal,...

Documents