Dynamics of motor cortex Matt Kaufman Cold Spring Harbor Laboratory - - PowerPoint PPT Presentation

Dynamics of motor cortex

Matt Kaufman Cold Spring Harbor Laboratory Stanford CS379C

CIS jPC1 jPC2 jPC1

Basics of neurophysiology

Time Voltage

Basics of neurophysiology

Basics of neurophysiology

Time Firing rate Time Voltage

Average over similar trials

What are we trying to do here?

What more do we want?

How does the computation proceed? i.e., how do inputs get transformed into outputs?

“Classic” systems neuroscience

How does activity in neurons relate to behavior? (what areas, what signals)

What are we trying to do here?

“Classic” systems neuroscience

How does activity in neurons relate to behavior? (what areas, what signals)

What are we trying to do here?

How does the computation proceed? i.e., how do inputs get transformed into outputs?

Motor cortex is likely an engine, not a representation

How does the brain control movement?

• How is activity in motor cortex translated

into activity in the muscles?

• How does the activity get to be that way?
• Why is the activity what it is?

➡ Dimensionality reduction and state space analysis

time firing rate

4 fictional neurons’ responses

Dimensionality reduction

Dimensionality reduction

+ Neural responses made up

• f these components

Dimensionality reduction

Components are also readouts

• f the neural responses

How to choose readouts?

Preparation and movement

delay period

Preparation and movement

go cue

Preparation and movement

Preparation and movement

TARGET GO MOVE

75

cell J114

spikes / second

r = -0.55

Preparation and movement

• PMd

PMd M1

The dynamical systems model

• f (monkey) motor cortex
• Motor cortex activity translates into

muscle activity in a functionally simple way.

• Motor cortex is a pattern generator.
• A large, condition-independent input is

probably what starts the pattern going.

1 2

monkey J-array

TARGET GO MOVE

75

cell J114

spikes / second

r = -0.55

Preparation and movement

How is activity during movement related to muscle activity? How do we keep still during the delay period?

preferred non-preferred preparatory activity peri- movement activity

TARGET MOVE GO

An imaginary ‘canonical’ neuron

(what most of us probably expect to see)

For real neurons, preparatory activity is not a sub-threshold version of movement activity

preferred non-preferred preparatory activity peri- movement activity

TARGET MOVE GO

Response of an actual neuron

TARGET GO MOVE

75

cell J114

spikes / second

r = -0.55

Churchland, Cunningham, Kaufman et al, Neuron 2010 Kaufman et al, J Neurophys 2010

TARGET GO MOVE

75

cell J114

spikes / second

r = -0.55

For real neurons, preparatory activity is not a sub-threshold version of movement activity

Churchland, Cunningham, Kaufman et al, Neuron 2010 Kaufman et al, J Neurophys 2010

For real neurons, preparatory activity is not a sub-threshold version of movement activity

TARGET GO MOVE

75

cell J114

spikes / second

r = -0.55

Churchland, Cunningham, Kaufman et al, Neuron 2010 Kaufman et al, J Neurophys 2010

TARGET GO MOVE

75

cell J114

spikes / second

r = -0.55

The correlation of preparatory and movement-period tuning is essentially zero

r ≈ 0!

Churchland, Cunningham, Kaufman et al, Neuron 2010 Kaufman et al, J Neurophys 2010

TARGET GO MOVE

75

cell J114

spikes / second

r = -0.55

Movement-period activity is itself complex, multiphasic, and exhibits no consistent preferred direction

Churchland and Shenoy, J Neurophys 2007 Churchland, Cunningham, Kaufman et al, Neuron 2010

There is a strong but hidden relationship between these epochs. That relationship is consistent with a dynamical interpretation.

TARGET GO MOVE

75

cell J114

spikes / second

r = -0.55

Churchland, Cunningham, Kaufman et al, Neuron 2010

Preparation and movement

How do we keep still during the delay period?

Nonlinear threshold?

preferred non-preferred peri- movement activity

TARGET MOVE GO

threshold preparatory activity

target on move! starts go

A ‘gate’ or ‘switch’?

• PMd

target on 200 ms upwards! reach downwards! reach move starts go

Movement is not triggered by firing rates crossing a threshold

Churchland et al., J. Neurophys., 2007 Churchland, Cunningham, Kaufman et al., Neuron, 2010 Kaufman et al, J Neurophys 2010 Churchland, Cunningham, Kaufman et al., Nature, 2012

Output-null hypothesis

M = f(N, t)

Muscle activity is a function of Neural activity and time

M = WN

Muscle activity is a linear function of Neural activity muscle

Output-null hypothesis

M = WN

muscle If there are more neurons than muscles, W has a null space

Output-null model

1 2

firing rate neuron 1 firing rate neuron 2

Output-null axis Output-potent axis

1 2

firing rate neuron 1 firing rate neuron 2

Preparation Reach right Go cue Baseline Reach left

Output-null model

1 2

firing rate neuron 1 firing rate neuron 2

Preparation Reach right Go cue Baseline Reach left

Output-null model

5

• projection onto dim1
• projection onto dim2

Baseline

5

• projection onto dim1
• projection onto dim2

Preparation

5

• projection onto dim1
• projection onto dim2

Move

Output-null model

Output-potent axis Output-null axis (activity along axis should resemble muscle activity) (activity along axis should not especially resemble muscle activity)

Output-null model

Output-potent axis Output-null axis (activity along axis should resemble muscle activity) (activity along axis should not especially resemble muscle activity)

During movement

Output-null model

Output-potent axis Output-null axis

During preparation

Small variance on

• utput-potent axes

Large variance on

• utput-null axes

Output-null model

Output-potent axis Output-null axis

J N J Array N Array 1 Fraction of prep tuning 3.0x 5.6x 8.2x 2.8x Output- null Output-
 potent Kaufman et al, 2014 Nat Neuro

Output-null model

Output-potent axis Output-null axis

Generalization of output-null

PMd + M1 PMd M1

? ✓

Kaufman et al, 2014 Nat Neuro

Generalization of output-null

PMd M1

Output-potent axis Output-null axis

J Array N Array 1 Fraction of prep tuning 2.4x 2.2x

Output- null Output-
 potent Kaufman et al, 2014 Nat Neuro

The dynamical systems model

• f (monkey) motor cortex
• Motor cortex activity translates into

muscle activity in a functionally simple way.

• Motor cortex is a pattern generator.
• A large, condition-independent input is

probably what starts the pattern going.

1 2

monkey J-array

There is a strong but hidden relationship between these epochs. That relationship is consistent with a dynamical interpretation.

TARGET GO MOVE

75

cell J114

spikes / second

r = -0.55

Churchland, Cunningham, Kaufman et al, Neuron 2010

5

• projection onto dim1
• projection onto dim2

There is a strong but hidden relationship between these epochs. That relationship is consistent with a dynamical interpretation.

What kind of dynamics?

Dynamical systems

Dynamics are rules for how a system behaves over time.

x(t+1) = f( x(t) )

state a moment from now is a function of the current state

Dynamical systems

dx/dt = f(x)

where the state is going is a function of the current state Dynamics are rules for how a system behaves over time.

Dynamical systems

dx/dt = f(x)

in any small neighborhood, approximately:

dx/dt = Mx

cell 114 monkey J

target move onset

200 ms

cell 112 monkey J cell 15 monkey N cell 12 monkey B cell 59 monkey J cell 30 monkey N

Individual neuron responses appear very complex

Rotational patterns are seen for all available datasets

monkey B monkey N monkey J-array monkey A

Churchland, Cunningham, Kaufman et al, 2012 Nature

Neural population

Projection onto jPC

2 (a.u.)

state space rates versus time

=

What these spirals mean

400 ms

Rotational patterns are seen for all available datasets

monkey J-array

Churchland, Cunningham, Kaufman et al, 2012 Nature

The dynamical systems model

• f (monkey) motor cortex
• Motor cortex activity translates into

muscle activity in a functionally simple way.

• Motor cortex is a pattern generator.
• A large, condition-independent input is

probably what starts the pattern going.

1 2

monkey J-array

PC2 PC1 PC3

jPC

2

jPC 1

cross-condition mean jPC

How are dynamics activated?

Models showing this is a natural way for a network to generate brief patterns:

!

Sussillo, Churchland, Kaufman & Shenoy, in review Hennequin, Vogels & Gerstner 2014 Idea suggested in:

!

Churchland, Cunningham, Kaufman et al., Nature, 2012

Predictions

• The trigger signal should be large and unified

across movements.

PC2 PC1 PC3

jPC

2

jPC 1

cross-condition mean jPC

monkey J monkey N

The strongest pattern cares when movement occurs (but is otherwise untuned)

target on move! starts Using dPCA: Brendel, Machens, Brody

We could not find such a pattern in the population of muscles This is not a non-directional representation of speed

Kaufman et al., submitted

Predictions

• The trigger signal should be large and unified

across movements.

• The trigger signal should be orthogonal to the
• ther patterns.

PC2 PC1 PC3

jPC

2

jPC 1

cross-condition mean jPC

Monkey N Monkey J

Kaufman et al., submitted

The trigger signal is orthogonal to the rotations

Go and Movement Delay Baseline

Kaufman et al., submitted

The trigger signal is orthogonal to the rotations

Monkey N Monkey J

Baseline Go and Movement Delay

Kaufman et al., submitted

The trigger signal is orthogonal to the rotations

Monkey N Monkey J

Go and Movement Delay Baseline

Kaufman et al., submitted

Monkey N Monkey J

Go and Movement Delay Baseline

Predictions

• The trigger signal should be large and unified

across movements.

• The trigger signal should be orthogonal to the
• ther patterns.
• The trigger signal should predict movement
• nset on a trial-by-trial basis.

PC2 PC1 PC3

jPC

2

jPC 1

cross-condition mean jPC

r = 0.739 200 400 Crossing time (ms) 200 500 RT (ms)

The ‘trigger signal’ predicts! reaction time very well

Monkey J

Kaufman et al., submitted

Time trajectory breaks plane (ms)

Delayed reaches

The ‘trigger signal’ predicts! reaction time very well

Monkey J

r = 0.739 200 400 Crossing time (ms) 200 500 RT (ms) r = 0.766

Kaufman et al., submitted

Time trajectory breaks plane (ms)

Delayed reaches Non-delayed reaches (generalization)

r = 0.786 200 400 Crossing time (ms) 200 500 RT (ms) r = 0.878 dPC1

b d e c

The ‘trigger signal’ predicts! reaction time very well

Monkey N

Kaufman et al., submitted

Time trajectory breaks plane (ms)

Delayed reaches Non-delayed reaches (generalization)

500 r = 0.471 500 Crossing time (ms) 200 500 RT (ms) r = 0.474 Mean of all neurons

e

Mean overall firing rate predicts! reaction less well

Kaufman et al., submitted

Time trajectory breaks plane (ms)

Delayed reaches Non-delayed reaches (generalization)

How do we keep still during the delay period? By avoiding output-potent dimensions

200 ms

move

• nset

muscle activity

Output-potent axis Output-null axis

Summary

How do we keep still during the delay period? By avoiding output-potent dimensions

200 ms

move

• nset

muscle activity Perhaps the condition-independent change helps ‘turn on’ dynamics How do we trigger activity that drives movement?

Summary

How do we keep still during the delay period? By avoiding output-potent dimensions

200 ms

move

• nset

muscle activity Perhaps the condition-independent change helps ‘turn on’ dynamics How do we trigger activity that drives movement? Simple rotations What are the movement dynamics?

Summary

Acknowledgements

Krishna Shenoy Mark Churchland Jeff Seely Stephen Ryu Wieland Brendel John Cunningham David Sussillo Mackenzie Mazariegos

Funding:

NSF graduate fellowship Swartz Fellowship NIH-NINDS-CRCNS-R01 NIH Director’s Pioneer Award DARPA REPAIR Burroughs-Wellcome Fellowship

The dynamical systems model

• f (monkey) motor cortex
• Motor cortex activity translates into

muscle activity in a functionally simple way.

• Motor cortex is a pattern generator.
• A large, condition-independent input is

probably what starts the pattern going.

1 2

monkey J-array