firing rates & spike time precisionbard/bardware/code.pdf · 2002. 7. 18. · the...
TRANSCRIPT
Firing rates & spike time precisionThe link to membrane characteristics
Bard Ermentrout
University of Pittsburgh
July 2002
Firing rates & spike time precision – p.1/17
Outline
Many results on spike time precision:theoretical, in vitro, and in vivo
With constant stimuli & noise, precision islow;
Rapidly varying stimuli can be very precise
Precision is tied to background level ofexcitation
This can be related to the PRC by treating theneuron as a generalized oscillator
Firing rates & spike time precision – p.2/17
Outline
Many results on spike time precision:theoretical, in vitro, and in vivo
With constant stimuli & noise, precision islow;
Rapidly varying stimuli can be very precise
Precision is tied to background level ofexcitation
This can be related to the PRC by treating theneuron as a generalized oscillator
Firing rates & spike time precision – p.2/17
Outline
Many results on spike time precision:theoretical, in vitro, and in vivo
With constant stimuli & noise, precision is low;
Rapidly varying stimuli can be very precise
Precision is tied to background level ofexcitation
This can be related to the PRC by treating theneuron as a generalized oscillator
Firing rates & spike time precision – p.2/17
Outline
Many results on spike time precision:theoretical, in vitro, and in vivo
With constant stimuli & noise, precision is low;
Rapidly varying stimuli can be very precise
Precision is tied to background level ofexcitation
This can be related to the PRC by treating theneuron as a generalized oscillator
Firing rates & spike time precision – p.2/17
Outline
Many results on spike time precision:theoretical, in vitro, and in vivo
With constant stimuli & noise, precision is low;
Rapidly varying stimuli can be very precise
Precision is tied to background level ofexcitation
This can be related to the PRC by treating theneuron as a generalized oscillator
Firing rates & spike time precision – p.2/17
Neurons code via rate & timing
What is the relationship between rate andtiming?
Rate seems to matter at high spike rates
Timing may be more important at low rates
Firing rates & spike time precision – p.3/17
Neurons code via rate & timing
What is the relationship between rate andtiming?
Rate seems to matter at high spike rates
Timing may be more important at low rates
Firing rates & spike time precision – p.3/17
Neurons code via rate & timing
What is the relationship between rate andtiming?
Rate seems to matter at high spike rates
Timing may be more important at low rates
Firing rates & spike time precision – p.3/17
Theoretical results
Shadlen et al elegantly show that presence ofinput correlations destroys rate codes at lowfrequencies
Many have shown timing carries informationde Ruyter et al work on fly lobular plate
Reich et al Primary visual cortex
In vitro Mainen & Sejnowski show corticalneurons respond reliably to fast stimuli
Firing rates & spike time precision – p.4/17
Theoretical results
Shadlen et al elegantly show that presence ofinput correlations destroys rate codes at lowfrequencies
Many have shown timing carries informationde Ruyter et al work on fly lobular plate
Reich et al Primary visual cortex
In vitro Mainen & Sejnowski show corticalneurons respond reliably to fast stimuli
Firing rates & spike time precision – p.4/17
Theoretical results
Shadlen et al elegantly show that presence ofinput correlations destroys rate codes at lowfrequencies
Many have shown timing carries informationde Ruyter et al work on fly lobular plate
Reich et al Primary visual cortex
In vitro Mainen & Sejnowski show corticalneurons respond reliably to fast stimuli
Firing rates & spike time precision – p.4/17
How does the neuron multiplex?
Slowly changing inputs are coded with ratecode and fast inputs with spike timing
The two cannot be separate
Can we quantify this interaction?
Strategy: Use dynamics of action potentialinitiation to study the role of frequency onspike timing
Firing rates & spike time precision – p.5/17
How does the neuron multiplex?
Slowly changing inputs are coded with ratecode and fast inputs with spike timing
The two cannot be separate
Can we quantify this interaction?
Strategy: Use dynamics of action potentialinitiation to study the role of frequency onspike timing
Firing rates & spike time precision – p.5/17
How does the neuron multiplex?
Slowly changing inputs are coded with ratecode and fast inputs with spike timing
The two cannot be separate
Can we quantify this interaction?
Strategy: Use dynamics of action potentialinitiation to study the role of frequency onspike timing
Firing rates & spike time precision – p.5/17
How does the neuron multiplex?
Slowly changing inputs are coded with ratecode and fast inputs with spike timing
The two cannot be separate
Can we quantify this interaction?
Strategy: Use dynamics of action potentialinitiation to study the role of frequency onspike timing
Firing rates & spike time precision – p.5/17
Canonical models
Most cortical neurons are type 1
All or none action potentials
Arbitrarily low frequencies
Square root (instantaneous) or linear (steady state) F-I curve
E & K, I & H show the form:
dθ
dt= 1 − cos θ + (1 + cos θ)(β + I(t))
Ermentrout et al extended to include SFA:
I(t) = I0(t) − gmzdz
dt= f(θ)(1 − z) − z/γ
Firing rates & spike time precision – p.6/17
Canonical models
Most cortical neurons are type 1
All or none action potentials
Arbitrarily low frequencies
Square root (instantaneous) or linear (steady state) F-I curve
E & K, I & H show the form:
dθ
dt= 1 − cos θ + (1 + cos θ)(β + I(t))
Ermentrout et al extended to include SFA:
I(t) = I0(t) − gmzdz
dt= f(θ)(1 − z) − z/γ
Firing rates & spike time precision – p.6/17
Canonical models
Most cortical neurons are type 1
All or none action potentials
Arbitrarily low frequencies
Square root (instantaneous) or linear (steady state) F-I curve
E & K, I & H show the form:
dθ
dt= 1 − cos θ + (1 + cos θ)(β + I(t))
Ermentrout et al extended to include SFA:
I(t) = I0(t) − gmzdz
dt= f(θ)(1 − z) − z/γ
Firing rates & spike time precision – p.6/17
Intuitive picture
Firing rates & spike time precision – p.7/17
With adaptation
Low SFA High SFA
Firing rates & spike time precision – p.8/17
Precision
Background noise plus baseline deploarization plus stimulus.
Measure spike time histogram over many repeated trials
Firing rates & spike time precision – p.9/17
Jitter
... is a diffusion process when the cell is oscillating
... but not when bias is low
Firing rates & spike time precision – p.10/17
Generic behavior
What determines the temporal sensitivity?
Can we understand this precision from thedynamics of excitability?
Use the theta model with adaptation – allclass I models are equivalent.
Firing rates & spike time precision – p.11/17
Generic behavior
What determines the temporal sensitivity?
Can we understand this precision from thedynamics of excitability?
Use the theta model with adaptation – allclass I models are equivalent.
Firing rates & spike time precision – p.11/17
Generic behavior
What determines the temporal sensitivity?
Can we understand this precision from thedynamics of excitability?
Use the theta model with adaptation – allclass I models are equivalent.
Firing rates & spike time precision – p.11/17
The Phase-response curve
A convenient measure of neural response foroscillators
Tells how timing of inputs affect the time ofnext spike
Easily computed for models and forexperiments
Firing rates & spike time precision – p.12/17
The Phase-response curve
A convenient measure of neural response foroscillators
Tells how timing of inputs affect the time ofnext spike
Easily computed for models and forexperiments
Firing rates & spike time precision – p.12/17
The Phase-response curve
A convenient measure of neural response foroscillators
Tells how timing of inputs affect the time ofnext spike
Easily computed for models and forexperiments
Firing rates & spike time precision – p.12/17
Application to coding
Stimulus consists of a slow DC bias
plus phasic terms from inputs (fast andsynchronous)
Thus PRC informs us when the neuron will fire
Firing rates & spike time precision – p.13/17
Application to coding
Stimulus consists of a slow DC bias
plus phasic terms from inputs (fast andsynchronous)
Thus PRC informs us when the neuron will fire
Firing rates & spike time precision – p.13/17
Application to coding
Stimulus consists of a slow DC bias
plus phasic terms from inputs (fast andsynchronous)
Thus PRC informs us when the neuron will fire
Firing rates & spike time precision – p.13/17
Experiment & theory
first spike
secondspike
theta+adapt
Firing rates & spike time precision – p.14/17
Firing rate & sensitivity
Low adapt High adapt
At low frequencies - very sensitive
With mauch adaptation, a coincidence detector
At high frequencies - low sensitivity; “integrator”
Firing rates & spike time precision – p.15/17
Firing rate & sensitivity
Low adapt High adapt
At low frequencies - very sensitive
With mauch adaptation, a coincidence detector
At high frequencies - low sensitivity; “integrator”
Firing rates & spike time precision – p.15/17
Consequences
At low firing rates, inputs have a greater effecton spike timing than they do at high rates
The effect of SFA on the PRC can enhancethe ability of coupled cells to synchronize
Many neuromodulators affect SFADopamine & ACh decrease Km
Should decrease synchrony at lowerfrequencies by decreasing skew of PRC
Firing rates & spike time precision – p.16/17
Consequences
At low firing rates, inputs have a greater effecton spike timing than they do at high rates
The effect of SFA on the PRC can enhancethe ability of coupled cells to synchronize
Many neuromodulators affect SFADopamine & ACh decrease Km
Should decrease synchrony at lowerfrequencies by decreasing skew of PRC
Firing rates & spike time precision – p.16/17
Consequences
At low firing rates, inputs have a greater effecton spike timing than they do at high rates
The effect of SFA on the PRC can enhancethe ability of coupled cells to synchronize
Many neuromodulators affect SFADopamine & ACh decrease Km
Should decrease synchrony at lowerfrequencies by decreasing skew of PRC
Firing rates & spike time precision – p.16/17
Acknowledgments
Boris Gutkin
Alex Reyes
National Science Foundation
National Institutes of Health
Firing rates & spike time precision – p.17/17