Transcript Document

Response dynamics and
phase oscillators in the brainstem
Eric Brown
Jeff Moehlis
Mark Gilzenrat
Phil Holmes
Jonathan Cohen
Princeton Univ.
Program in Neuroscience
Psychology / Applied and
Computational Mathematics
Ed Clayton
Janusz Rajkowski
Gary Aston-Jones
Univ. of Pennsylvania
Dept. of Psychiatry
Laboratory of Neuromodulation
and Behavior
1
Neuromodulatory nucleus locus coeruleus (LC)
LOCUS COERULEUS:
ROLE IN MODULATION
OF COGNITIVE
PERFORMANCE
(Usher et al. 1999, AstonJones et al. 1994)
LC consists of ~ 30,000 neurons ...
2
OUTLINE … from spikes to speed-accuracy
• Experimental data
• Model of LC dynamics
• Role of LC in cognitive performance
3
Cognitive performance is correlated with LC firing rate (1)
2 distinct modes of LC operation
Tonic (T):
fast baseline firing, poor performance
Phasic (P): slow baseline firing, good performance
Usher et al. (1999)
LC firing rate:
FAST=Tonic mode
SLOW=Phasic mode
T
P
Task errors:
HIGH=Tonic mode
LOW=Phasic Mode
4
Larger LC responses occur at lower baseline firing rates (2)
2 distinct modes of operation
Just saw...
Tonic (T):
fast baseline firing, poor performance
Phasic (P): slow baseline firing, good performance
Also...
Hz.
Tonic
Tonic :
Phasic:
Stim.
rel. weak response to task stimulus
rel. strong response to task stimulus
Hz.
8
8
4
4
0
0
t (ms)
Phasic
Stim.
t (ms)
LINK TO COGNITIVE PERFORMANCE?
NE release (Usher et al. 1999, Servan-Schreiber et al. 1990)
5
• Experimental data:
– PHASIC and TONIC LC modes have differing …
• baseline firing rates
• responses to stimulus
• levels of task performance
• Model of LC dynamics
• Role of LC in cognitive performance
6
Modeling LC neurons
The Hindmarsh-Rose model
includes A current and is
reduced to 2 effective variables:
J.T. Williams measured transient
potassium current (“A
current”) in rat LC neurons,
responsible for slow
“pacemaker” firing
Rose and Hindmarsh,Proc. R. Soc.
Lond. B., 1989.
Solution to HR equations
Data from slice
~80 mV
~100 mV
30
mV
mV
3s
in vivo: additional (noisy) inputs
7
Reduction of neurons to phases
V  ...
;
V
q  ...
t
q
0.3
0.25
0.2
0.15
0.1
V
0.05
0
q
0
2p
q
fire
-50
0
50
V
ALERT: Interesting
methods here!
Winfree ‘74, Guckenheimer ‘75
8
Simple (and accurate) phase description
sensory input
I(t)
coupling
dq
   z (q )   I (t )   (t ) 
dt
 ...
“noise”
natural frequency
phase response curve
 x z(q)
fast
p
q
fire
q0
slow
q
z(q ) 
Movie!
c

1  cos(q )
Ermentrout, Neural Comp., 1996
9
Simple (and accurate) phase description
sensory input
I(t)
coupling
dq
   z (q )   I (t )   (t ) 
dt
natural frequency
 ...
“noise”
phase response curve
 x z(q)
q
z(q ) 
c

1  cos(q )
Ermentrout, Neural Comp., 1996
10
Actually have many oscillators rotating at once

dWt , i
dqi
  i  zi (q )   I (t )  

dt
dt


i  1, ..., N
Phase resetting! Winfree (1964), Tass (1999) ...

 ...

j
11
Actually have many oscillators rotating at once

dWt , i
dqi
  i  zi (q )   I (t )  

dt
dt


i  1, ..., N
f. rate
baseline

 ...

j
f. rate peak
Phase resetting! Winfree (1964), Tass (1999) ...
12
Take continuum limit and discover...
f. rate PEAK  BASELINE ~
(w/o noise, coupling)
1

DESCRIBE LC BY
DENSITY of phases
r(q,t)
cf. Fetz and Gustaffson, 1983 ; Hermann and Gerstner 2002
FIRE
q0
13
Take continuum limit and discover...
f. rate PEAK  BASELINE ~
(w/o noise, coupling)
1

DESCRIBE LC BY
DENSITY of phases
r(q,t)
cf. Fetz and Gustaffson, 1983 ; Hermann and Gerstner 2002
FIRE
q0
(3 Hz base)
snap
(1 Hz base)
14
Possible mechanism for different tonic vs. phasic LC responses
12
Stim.
Hz.
12
Tonic
Phasic
Hz.
DATA
0
THEORY/
SIMS.
0
(3 Hz base)
12
Hz.
0
t (s)
0
(2 Hz base)
12
Hz.
1
0
t (s)
0
BUT: data returns to base w/o periodic ringing. Add:
15
Possible mechanism for different tonic vs. phasic LC responses
12
Stim.
12
Tonic
Hz.
Phasic
Hz.
DATA
0
THEORY/
SIMS.
0
(3 Hz base)
12
Hz.
0
t (s)
1
0
(2 Hz base)
12
Hz.
0
t (s)
0
BUT: data returns to base w/o periodic ringing. Add:
LC
Baseline Activity Over
Time
FREQUENCY
DRIFT
LC Activity (Hz)
Hz 3.5
3
2.5
2
1.5
1
0.5
0
Overall Baseline Activity = 2.930
Number of Trials per 10 min bin ˜ 82
600
1200
1800
Time (sec)
2400
16
Possible mechanism for different tonic vs. phasic LC responses
12
Stim.
12
Tonic
Hz.
Phasic
Hz.
DATA
0
THEORY/
SIMS.
0
(3 Hz base)
12
Hz.
0
(2 Hz base)
12
Hz.
t (s)
0
t (s)
0
1
0
BUT: data returns to base w/o periodic ringing. Add:
FREQUENCY DRIFT
LC Baseline Activity Over Time
+
Hz 3.5
LC Activity (Hz)
NOISE
P(ISI)
curve: model
bars: data
3
2.5
2
1.5
1
0.5
0
Overall Baseline Activity = 2.930
Number of Trials per 10 min bin ˜ 82
600
1200
1800
Time (sec)
ISI(sec.)
2400
0
1
2
3
17
Possible mechanism for different tonic vs. phasic LC responses
12
Stim.
Hz.
12
Tonic
Phasic
Hz.
DATA
0
THEORY/
SIMS.
0
(3 Hz base)
12
Hz.
0
t (s)
0
(2 Hz base)
12
Hz.
1
0
0
t (s)
BUT: data returns to base w/o periodic ringing. Add:
FREQUENCY DRIFT
NOISE
18
Possible mechanism for different tonic vs. phasic LC responses
12
Stim.
Hz.
12
Tonic
Phasic
Hz.
DATA
0
THEORY/
SIMS.
0
(3 Hz base)
12
Hz.
0
t (s)
0
(2 Hz base)
12
Hz.
1
0
t (s)
0
BUT: data returns to base w/o periodic ringing. Add:
FREQUENCY DRIFT
NOISE
(
~ exp a t  b t 2

cf. Tass (1999)
19
Possible mechanism for different tonic vs. phasic LC responses
12
Stim.
12
Tonic
Hz.
Phasic
Hz.
DATA
0
THEORY/
SIMS.
0
(3 Hz base)
12
Hz.
0
(2 Hz base)
12
Hz.
t (s)
0
t (s)
0
1
0
BUT: data returns to base w/o periodic ringing. Add:
LC
Baseline Activity Over
Time
FREQUENCY
DRIFT
NOISE
Hz 3.5
LC Activity (Hz)
COUPLING
P(ISI)
cross-cor.
curve: model
bars: data
3
2.5
2
1.5
1
0.5
0
Overall Baseline Activity = 2.930
Number of Trials per 10 min bin ˜ 82
600
1200
1800
Time (sec)
ISI(sec.)
2400
0
1
2
3
data
model
20
Possible mechanism for different tonic vs. phasic LC responses
12
Stim.
Hz.
12
Tonic
Phasic
Hz.
DATA
0
0
15
(3 Hz base)
12
Hz.
(2 Hz base)
12
Hz.
10
10
counts/s
counts/s
SIMS:
freq. drift,
noise,
coupling
15
5
0
0
-200
5
0
0
200
400
t (ms)
600
800
t (s)
1000
1
0
0
-200
0
0
200
400
t (ms)
600
800
1
1000
t (s)
Baseline frequency contributes to the different
responses in tonic vs. phasic modes
cf. Alvarez and Chow (2001), Usher et al. (1999)
21
• Experimental data
• Model of LC dynamics
• Role of LC in cognitive performance
22
LC emits norepinephrine, which can enhance
responsivity (gain) in cortex
Devilbiss and Waterhouse, Synapse (2000)
Responses of single neurons in rat cortex to glutamate
# spikes
(percent of
control)
23
Two-alternative choice task
Firing rates (y1, y2) of
competing neural pops...
[Usher + McClelland, 1999]
inhibn.
y1
y2
inhibn.
noise
noise
s1
s2
stimuli
y1, y2 approach fg(input).
f(input)
fg(input)
g
g gain
input
input
24
Two-alternative choice task
Firing rates (y1, y2) of
competing neural pops...
Decision 1 or 2 made when firing rate y1
or y2 crosses threshold
inhibn.
y1
thresh. 2
y2
inhibn.
noise
noise
s1
s2
stimuli
y1, y2 approach fg(input).
fg
f(input)
(input)
g
thresh. 1
g gain
g
g
input
input
25
Two-alternative choice task
Firing rates (y1, y2) of
competing neural pops...
FEF spike rates vs. time-neural evidence for crossing fixed
threshold prior to response
inhibn.
y1
y2
inhibn.
noise
noise
s1
s2
stimuli
y1, y2 approach fg(input).
f(input)
fg(input)
g
g gain
input
input
J. Schall, V. Stuphorn, J. Brown, Neuron, 2002
26
LC sets gain in decision network
Firing rates (y1, y2) of
competing neural pops...
(Servan-Schreiber, Printz, Cohen
1990, Usher et al., 1999, Usher +
McClelland, 1999)
inhibn.
y1
y2
inhibn.
noise
noise
s1
s2
stimuli
approach values
fg(input), modulated by
gain.
f(input)
gg
fg(input)
g
12
Hz.
input
input
0
27
Expect speed-accuracy tradeoff between
Avg. Reaction Time (<RT>) and Error Rate (ER)
“in general”
28
Observe speed-accuracy tradeoff between
Avg. Reaction Time (<RT>) and Error Rate (ER)
as gain is increased
Mean RT vs gb
25
20
<RT>
15
10
5
0
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1.4
1.6
1.8
2
g
ER vs gb
0.12
0.1
ER
0.08
0.06
0.04
0.02
0
0.6
0.8
1
g
1.2
g
t
g
g
t
t
29
In computational model, Gilzenrat et al. (2002) beat the speedaccuracy tradeoff via the LC and TRANSIENT gain
30
In computational model, Gilzenrat et al. (2002) beat the speedaccuracy tradeoff via the LC: TRANSIENT gain
<RT>
ER
LC becomes
more “phasic”
g
g
t
g
t
t
General trend agrees with Aston-Jones et al. (1994,1999)
behavioral + physiological data
31
SUMMARY
• 1) Have developed biophysical model of LC population:
– Phase density formulation shows 1/ scaling of response
– Helps explain phasic vs. tonic LC modes
– CURRENT WORK:
• Study coupling effects
• Study population responses of other neuron types (nonintuitive results!)
• 2) Decision model shows that LC (in phasic mode) can beat
speed accuracy tradeoff
– CURRENT WORK:
• Study dynamic gain effects
32
Jeff Moehlis
Mark Gilzenrat
Phil Holmes
Jonathan Cohen
Princeton Univ.
Prog. Neurosci./Dept. of Psychology
Prog. in Applied and Computational
Mathematics
Ed Clayton
Janusz Rajkowski
Gary Aston-Jones
Univ. of Pennsylvania
Dept. of Psychiatry
Laboratory of Neuromodulation and
Behavior
33
• Extend results to non-LC neurons:
HH
90
Hz.
80
70
60
s
t
i
m
50
FIRING
RATE
PEAK
~1

~ 1
  b
~ 1
40
0
  b
20
40
60
80
100
t (ms)
– Scaling of PRC encodes sensitivity of population response
– Form of PRC encodes time-course of population response
• e.g. “population rebound excitation” that (always) exceeds stimulus
excitation for HH
34
Coupling
LC has gap junctions,
as well as slow inhibitory
synapses.
35
Both gap junctions and inhibitory synapses (partially) synchronize
fe, fs contain:
mostly just first Fourier
harmonics...
so only in-phase state is
stable (e.g. Okuda 1992)
1
f e, s (q  
2p

2p
0
z (  I coup
e , s (q    d
N
N
X
X
36