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