representation of time in cortico-basal ganglia circuits

8/9/2019 Representation of Time in Cortico-Basal Ganglia Circuits

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Dan OShea

Neuroscience Journal Club

27 April 2010

Neural representation of time in cortico-basal

ganglia circuitsDezhe Z. Jina,1, Naotaka Fujiib,1, and Ann M. Graybielc,2aDepartment of Physics, Pennsylvania State University, 104 Davey Laboratory, PMB 206, University Park, PA 16802; bLaboratory for Adaptive Intelligence,Brain Science Institute, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan; and cDepartment of Brain and Cognitive Sciences and the McGovern Institutefor Brain Research, Massachusetts Institute of Technology, 43 Vassar Street, 46-6133, Cambridge, MA 02139

Contributed by Ann M. Graybiel, September 4, 2009 (sent for review July 27, 2009)


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Timing

What are the neural mechanisms that enable us

to process the order, interval, and duration ofcomplex sensory and motor events?

Mauk and Buonomano, 2004


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Timing Centers

Ivry 1996


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Timing Centers

Cerebellum: focus on variability for short intervals < 1s

Lesions lead to impaired timing of coordinated movements [Hore et al. 1991]

Variability in repetitive nger tapping [Ivry et al. 1988]

Locus of eyeblink conditioning (100 ms - 3 s) [Thompson 1990]

Selective impairment on short interval (


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Timing Centers







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Timing Centers







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Timing Models

Centralized or Distributed?

Clock, Spectral, Network?

Striatal Beat Frequency Model

Two mechanisms for representingtemporal information. (a) Clock-countermodels postulate a pacemaker thatproduces output to a counter. Longerintervals are represented b y increasesin the number of pacemaker outputsthat accumulate in the counter.(b) Interval-based models assume thatdifferent intervals are represented b ydistinct elements, each correspondingto a specific duration.

( a ) ~ U

(b) Interval model

300ms 400ms

~ : 4 0 0 m e

Counter

5 0 0m s 1996 Current Opinion in Neurobiology

have conv erged o n a value of approximate ly 49 Hz [33,34] .This value i s of interes t given recent ne urophysio logicalevidence suggest ing that osci l la tory brain act ivi ty near40 Hz migh t serve as a mech anism for integrat ing act ivi tyacross di f ferent neural regions [35,36,37] . By al lowingfor f lexibi li ty in the cal ibrat ion uni t , pa cema ker modelscan accoun t for why the subuni t s of an act ion retainthei r propor t ional t iming when that act ion i s per formed atdifferent overall rates [38,39].Distr ibuted t im ing mechanismsPa c e m a ke r m ode l s a s s i gn t he o r i g in o f t e m por a l i n f o r m a -t ion to a s ingle mechani sm (Figure la) . This n eed no tmean that there i s a s ingle osci l la tor ; a set of s imi lar lyent rained osci l la tors can provide rel iabi l i ty and robustness[21 ] . Al ternat ive t iming models emphasize a dis t r ibutedrepresentat ion in which temporal informat ion i s encodedacross a set of processors tuned wi th di f ferent ia l sensi t ivi tyfunct ions . An analogy can be drawn here to the waycel l s in the visual cor tex are tuned to edges at di f ferentor ientat ions . The dis t r ibut ion of temporal informa t ion,however , may be funct ional ra ther than s t ructural . To date ,physiologis t s have not observed chronotopic maps in anybrain area.N e ur a l ne t w or k m ode l s ha ve be e n us e d t o e xp lo r ethe viabi l i ty of dis t r ibuted mo dels of t iming. Some of

these models s t i l l re ta in the basic osci l la tory idea, butenvis ion ei the r a ser ies of harmonical ly related osci l la tors[40] or a populat ion of oscil la tors dis t r ibuted arounda m e a n f r e que nc y [ 41 ] . B y s e l e c t i ng c om bi na t i ons o fthese osci l la tors or exploi t ing b eat f requen cies (pha seinteract ions) such networks can encode intervals over arange of durat ions .A n a l t e rna t i ve m e t a ph or f o r a t i m ing m e c ha n i s m i sgiven by the hour-glass (see Figure lb) . Whi le there i ss t i l l per iodici ty a t a microscopic level (e .g. the fal l inggrains of sand) , the system as a whole represents apar t icular interval . Th e represe ntat ion o f t ime may then bedis t r ibuted across a set of such interval t imers , each wi tha par t icular process ing cycle . In such models , intervals of300 ms and 400 ms are represented by dis t inct mechan isms(Figure lb) ; in c lock-counter models , shor t and longintervals are const ructed f rom the same mechanisms,wi th the counter threshold increased in the la t ter case(Figure la) .I n t e r va l - bas e d m ode l s ha ve b e e n us e d t o e xp l o r e howthe cerebel lar cor tex might encode the precise t imingbe t w e e n t he c ond i t i one d s t i m u lus ( C S) a nd unc ond i t i one ds t i m u l us ( U S) i n e ye b l i nk c ond i t i on i ng . I n c om pu t e rs imulat ions , a populat ion of di f ferent intervals can becreated by incorporat ing neuronal processes that operate

Liquid State MachineMaas et al. 2002

Clock-counter vs. IntervalIvry 1996

Meck et al. 2008


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Timing and Reinforcement Learning

Reward predicted

Reward occurs

No prediction

Reward occurs

Reward predicted

No reward occurs

(No CS)

(No R)CS-1 0 1 2 s

CS

R

R

Do dopamine neurons report an error

in the prediction of reward?

Spectral timing theory, complete compound stimulus, and time stamp event encoding

Shultz et al. 1997


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A

400 msec

400 msec

400 msec

400 msec

400-800 msec

Fixation

Reward

1 sec

Go4

Go2

Go3

Go1

Task Description


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Peri-event Time Histograms

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

5

10

15

20

25

30

35

FiringRate(Hz)

Time (msec)

0 500 1000 1500 2000 2500 3000 3500 4000 4500 500010

5

0

5

10

Time (msec)

Residual(Hz)

A

B

C

-

Fixation Go 1 Go 2 Go 3 Go 4

A

400 msec

400 msec

400 msec

400 msec

400-800 msec

Fixation

Reward

1 sec

Go4

Go2

Go3

Go1

5,699 Single-Units over 3 years!

Selection Criteria: Maximum Firing Rate > 2 Hz

Low trial-to-trial drift

Resembles smoothed PETH

Not previously recorded

1613 / 2496 in DLPFC2035 / 3203 in Caudate (CN)


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66 DLPFC Clusters (609 unclassied)c1 n72 c2 n59 c3 n58 c4 n50 c5 n42 c6 n39 c7 n33 c8 n31

c9 n30 c10 n29 c11 n23 c12 n22 c13 n19 c14 n18 c15 n17 c16 n17







c65 n3 c66 n2

1 sec

Fixation

1000 ms

Go 1

400 ms

Go 2

400 ms

Go 3

400 ms

Go 4

400 ms

ExtraPeak

400 ms

Reward / Inter-trial Interval

2000 ms


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35 CN Clusters (965 unclassied)





c33 n7 c34 n5 c35 n3

1 sec

Fixation

1000 ms

Go 1

400 ms

Go 2

400 ms

Go 3

400 ms

Go 4

400 ms

ExtraPeak

400 ms


2000 ms


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A c1 n72 c2 n59 c4 n50 c7 n33 c11 n23 c14 n18 c24 n14

DLPFC

c1 c2 c4 c7 c11 c14 c24

c26 n13 c28 n13 c35 n10 c36 n9 c43 n7 c45 n7 c46 n7

c26 c28 c35 c36 c43 c45 c46

1 sec

DLPFC/CN Comparison

B CNc1 n188 c2 n135 c3 n69 c5 n55 c7 n44 c9 n36 c10 n30

c1 c2 c3 c5 c7 c9 c10

c13 n26 c14 n23 c15 n21 c19 n16 c27 n10 c32 n7 c35 n3

c13 c14 c15 c19 c27 c32 c35


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Identifying Visual Neurons

A

400 msec

400 msec

400 msec

400 msec

400-800 msec

Fixation

Reward

1 sec

Go4

Go2

Go3

Go1

Saccade Latency (msec)

Numberof

Saccades

4000

2000

0100 150 200 250 300 350 400

Peak in ring rate related to visual signal (sensory) or saccade (motor)?

Null hypothesis: PETH peak height for trials aligned to actual saccade times is drawn from same

distribution as peak heights for trials aligned to shuffled saccade times. Expected for visual neuron.

Reject null hypothesis: neuron is saccade aligned, actual peak height is signicantly higher.

: ::


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Identifying Visual NeuronsPeak in ring rate related to visual signal (sensory) or saccade (motor)?




0 200 400 600

Time (msec)

TrialNumber

Spikes: Go Align

200 0 200

Time (msec)

TrialNumber

Spikes: Saccade Align

0 100 200 300 400 5000

5

10

Time (msec)

Rate

(Hz)

PETH: Go Align

200 100 0 100 2000

5

10

Time (msec)

Rate

(Hz)

PETH: Saccade Align

A B

C D

: :

: :

300 200 100 0 100 200 3000

5

10

Time (msec)

Rate(Hz)

.

F Comparison Fitted Curves

-

:

4 5 6 7 80

5

10

15

20

P=0.87004

Peak Height (Hz)

Numb

er

G

-

Visual neuron: null hypothesis not rejected


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Identifying Visual NeuronsPeak in ring rate related to visual signal (sensory) or saccade (motor)?




Saccade associated neuron: null hypothesis rejected

0 200 400 600

Time (msec)

TrialNumber

Spikes: Go Align

200 0 200 400

Time (msec)

TrialNumber

Spikes: Saccade Align

0 100 200 300 400 500 6000

1

2

3

4

Time (msec)

Rate

(Hz)

PETH: Go Align

200 0 200 4000

1

2

3

4

Time (msec)

Rate

(Hz)

PETH: Saccade Align

A B

C D

300 200 100 0 100 200 3000

1

2

3

4

Time (msec)

Rate(Hz)

Comparison Fitted Curves

F

-

-

2 2.5 3 3.5 40

5

10

15

20

P=0.0001866

Number

G


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Time-Stamp Responses in DLPFC

Fixation

1000 msGo 1

400 ms

Go 2

400 ms

Go 3

400 ms

Go 4

400 ms

ExtraPeak

400 msReward / Inter-trial Interval

2000 ms

Task Start First Go Target Off

165 msec 185 msec 205 msec 265 msec 305 msec 415 msec



A DLPFC

FirstGo

TaskStart

TargetOff

0

100

200

300

Time (msec)

0

10

20

30

Time (msec)

Count

100 300 500

100 300 500

FirstPeak

HalfWidth(msec)

16.7Hz 8.3Hz 5.1Hz 3.4Hz 6.3Hz 5.6Hz

1.4Hz 5.2Hz 4.1Hz 6.1Hz 3.7Hz 9.2Hz

10.5Hz 8.8Hz 6.4Hz 4.6Hz 1.6Hz 1.6Hz

B

500 msec

500 msec

500 msec

55

(145-435 ms)

37

(145-355 ms)

33

(145-415 ms)


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Time-Stamp Responses in CN

Fixation

1000 msGo 1

400 ms

Go 2

400 ms

Go 3

400 ms

Go 4

400 ms

ExtraPeak

400 msReward / Inter-trial Interval

2000 ms

Task Start First Go Target Off

10

(165-485 ms)

3

(315-335 ms)

14

(235-415 ms)


315 msec 335 msec


C CN

FirstGo

TaskStart

TargetOff

0

100

200

Time (msec)100 300 500

100 300 500

2

0

4

6

Time (msec)

Count

FirstPeak

HalfWidth(msec)

16.3Hz 10.2Hz 12.6Hz 4.5Hz 5.3Hz 6.1Hz

19.8Hz

325 msec

11.8Hz 19.8Hz

61.9Hz 16.4Hz 21.5Hz 13.8Hz 6.4Hz 12.1Hz

D

500 msec

500 msec

500 msec


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Decoding Time from Population Activity

w1n1(t)

w2n2(t)

b

+ Time Stamp OutputFiring Rate Inputs

Parameters

.

.

.

.

.

.

wMnM(t)

Perceptron Model:

Simple and entirely plausible for a neural circuit

Tests for linear separability

Time stamp encoding:

Can we generate a perceptron that responds only at one point

in time from the instantaneous ring rate of many neurons?


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Perceptron Decoding Example

0 50 100 150 200 250 300 350 400 450 500

Time (ms)

Activity

Individual Neuron Activity

Neuron 1

Neuron 2

Neuron 1 Activity

Ne

uron2Activity

Population Activity Vector


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0 50 100 150 200 250 300 350 400 450 500

Time (ms)

Activity


Neuron 1

Neuron 2


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0 50 100 150 200 250 300 350 400 450 500

Time (ms)

Activity


Neuron 1

Neuron 2

Neuron 1 Activity

N

euron2

Activity

Population Activity Vector


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0 50 100 150 200 250 300 350 400 450 500

Time (ms)

Activity


Neuron 1

Neuron 2


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0 50 100 150 200 250 300 350 400 450 500Time (ms)

Activity


Neuron 1

Neuron 2


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Decoding Time from Population Activity

A DLPFC B

E CN F

0 2000 40000

10

5

20

15

30

25

35Res=50msec

Res=50msec

MaximumMar

gin

Decoded Time (msec) 1 sec

0 2000 40000

5

10

15

20

Decoded Time (msec)

M

aximumMargin

1 sec

Selected Input Proles

Fixation

1000 msGo 1

400 ms

Go 2

400 ms

Go 3

400 ms

Go 4

400 ms

ExtraPeak

400 ms


2000 ms

50 ms Resolution

DLPFC

CN


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Dependence on Resolution and Cell Count

0 20 40 60 80 100 120

0

5

10

15

20

25

30

35

40

Resolution (msec)

Max.

Margin

Prefrontal

0 20 40 60 80 100 120

0

5

10

15

20

25

30

35

40

Resolution (msec)

Max.

Margin

CaudateC D

200 300 400 500 600 700

Number of Neurons

Prefrontal

250200 300 350 400 450 5000

5

10

15

20

25

30

35

Number of Neurons

Max.

Margin

0

5

10

15

20

25

30

35

Max.

Margin

CaudateE F


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Online vs. Offline DecodingOffline Decoding:

Train: trial-averagedring rates for each neuron recorded

Test: same

Online Decoding with articial spiking neurons drawn from a distribution:


Test: articial spike rasters generated from trial-averaged rates

C D

G H

0 50002500

D1

D2

D3

Time (msec)

Freq 15 Freq 12 Freq 12


1 sec

0 2500 5000

D1

D2

D3

Time (msec)


Freq 5Freq 7 Freq 6

1 sec


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Online vs. Offline DecodingOffline Decoding:


Test: same

Online Decoding with articial spiking neurons drawn from a distribution:


Test: articial spike rasters generated from trial-averaged rates

Online Decoding with actual recorded spikes

Train: cluster averaged

ring rates for clusters with >10 neuronsTest: single trial spike rasters from all neurons in those clusters


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Online vs. Offline Decoding

0 20001000 40003000 50000

1

2

3

4

5

6

Resolution=50msec

0 2000 4000 5000300010000

0.5

1

1.5

2

Decoded Time (msec) Time (msec)

Time (msec)0 20001000 4000 50003000

D1

D2

D3

0 20001000 40003000 5000

D1

D2

D3

BA C

D E F

1 sec

1 sec

MaximumM

argin

MaximumM

a

rgin


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Conclusions and Issues

Neurons in CN and DLPFC show phasic responses to external

events that form a time-stamp representation of short-time

Measured during a behavioral paradigm that did not

demand precise timing.

TD learning, spectral timing theory, complete compound

stimulus, and temporal credit assignment problem?

Times longer than 500 ms? Do timing representations require

external triggers?

Mechanisms? Cortical interactions? Striatal beat frequency

model?

representation of time in cortico-basal ganglia circuits

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