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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
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 2 / 18
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
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 3 / 18
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
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 3 / 18
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
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 3 / 18
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
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 3 / 18
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
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 3 / 18
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
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 3 / 18
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.”
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 4 / 18
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.”
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 4 / 18
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.”
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 4 / 18
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.”
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 4 / 18
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.”
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 4 / 18
cellular noise
Overview
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 5 / 18
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?
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 6 / 18
cellular noise action potentials
Recall: Neuronal transmission
Hodgkin–Huxley model:
−Cm · ∂V
∂t= leakage + gNa · m3 · h · (V − ENa) + gK · n4 · (V − EK )
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cellular noise action potentials
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
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 8 / 18
cellular noise action potentials
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!
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 8 / 18
cellular noise action potentials
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):
Johannes Bill (IGI, TU Graz) Noise in the Nervous System 9 / 18
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.
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noise in neural networks
Overview
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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.
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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
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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)
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noise in neural networks benefits
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!
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noise in neural networks benefits
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
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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?
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conclusion
The end.
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