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 jPC 1 jPC 2 CIS jPC 1

Basics of neurophysiology

Basics of neurophysiology Voltage Time

Basics of neurophysiology Voltage Time Average over similar trials Firing rate Time

What are we trying to do here? “Classic” systems neuroscience How does activity in neurons relate to behavior? (what areas, what signals) What more do we want? How does the computation proceed? i.e., how do inputs get transformed into outputs?

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

Dimensionality reduction 4 fictional neurons’ responses firing rate time

Dimensionality reduction Neural responses made up of these components +

Dimensionality reduction Components are also readouts of the neural responses How to choose readouts?

Preparation and movement

Preparation and movement delay period

Preparation and movement go cue

Preparation and movement

� Preparation and movement M1 PMd PMd 75 spikes / second cell J114 r = -0.55 0 TARGET GO MOVE

The dynamical systems model of (monkey) motor cortex • Motor cortex activity translates into 1 2 muscle activity in a functionally simple way. monkey J-array • Motor cortex is a pattern generator. • A large, condition-independent input is PC 2 probably what starts the pattern going. jPC 1 jPC 2 PC 1 cross-condition jPC mean PC 3

Preparation and movement How is activity during movement related to muscle activity? How do we keep still during the delay period? 75 spikes / second cell J114 r = -0.55 0 TARGET GO MOVE

An imaginary ‘canonical’ neuron (what most of us probably expect to see) preferred non-preferred peri- movement preparatory activity activity TARGET GO MOVE

For real neurons, preparatory activity is not a sub-threshold version of movement activity 75 spikes / second cell J114 preferred r = -0.55 non-preferred peri- movement preparatory activity 0 activity TARGET GO MOVE TARGET GO MOVE Response of an actual neuron Kaufman et al, J Neurophys 2010 Churchland, Cunningham, Kaufman et al, Neuron 2010

For real neurons, preparatory activity is not a sub-threshold version of movement activity 75 spikes / second cell J114 r = -0.55 0 TARGET GO MOVE Kaufman et al, J Neurophys 2010 Churchland, Cunningham, Kaufman et al, Neuron 2010

For real neurons, preparatory activity is not a sub-threshold version of movement activity 75 spikes / second cell J114 r = -0.55 0 TARGET GO MOVE Kaufman et al, J Neurophys 2010 Churchland, Cunningham, Kaufman et al, Neuron 2010

The correlation of preparatory and movement-period tuning is essentially zero 75 r ≈ 0 ! spikes / second cell J114 r = -0.55 0 TARGET GO MOVE Kaufman et al, J Neurophys 2010 Churchland, Cunningham, Kaufman et al, Neuron 2010

Movement-period activity is itself complex, multiphasic, and exhibits no consistent preferred direction 75 spikes / second cell J114 r = -0.55 0 TARGET GO MOVE 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. 75 spikes / second cell J114 r = -0.55 0 TARGET GO MOVE Churchland, Cunningham, Kaufman et al, Neuron 2010

� Preparation and movement How do we keep still during the delay period? Nonlinear threshold? A ‘gate’ or ‘switch’? PMd threshold preferred non-preferred peri- movement preparatory activity activity TARGET GO MOVE move ! target on go starts

Movement is not triggered by firing rates crossing a threshold upwards ! reach downwards ! reach target on go move starts 200 ms 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 is a function of Neural activity activity and time M = WN Muscle is a linear function of activity Neural activity muscle

Output-null hypothesis M = WN If there are more neurons than muscles, W has a null space muscle

Output-null model Output-potent axis 1 firing rate neuron 2 2 Output-null axis firing rate neuron 1

Output-null model 1 firing rate neuron 2 2 Reach right Baseline Preparation Reach left Go cue firing rate neuron 1

Output-null model 1 firing rate neuron 2 2 Reach right Baseline Preparation Reach left Go cue firing rate neuron 1

Output-null model projection onto dim 2 ������� projection onto dim 2 ������� projection onto dim 2 ������� ��� ��� ��� � � � ���� ���� ���� ��� 5 � ��� ��� 5 � ��� ��� 5 � ��� projection onto dim 1 ������� projection onto dim 1 ������� projection onto dim 1 ������� Baseline Preparation Move

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

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

Output-null model Output-null axis Output-potent axis During preparation Small variance on Large variance on output-potent axes output-null axes

Output-null model Output-null axis Output-potent axis 3.0x 8.2x 2.8x 5.6x 1 Output- Fraction of prep tuning null Output- 
 potent 0 J N J Array N Array Kaufman et al, 2014 Nat Neuro

Generalization of output-null PMd PMd + M1 M1 ✓ ? Output-potent axis Output-null axis Kaufman et al, 2014 Nat Neuro

Generalization of output-null PMd M1 Output-null axis Output-potent axis 1 2.4x 2.2x Fraction of prep tuning Output- null Output- 
 potent 0 J Array N Array Kaufman et al, 2014 Nat Neuro

The dynamical systems model of (monkey) motor cortex • Motor cortex activity translates into 1 2 muscle activity in a functionally simple way. monkey J-array • Motor cortex is a pattern generator. • A large, condition-independent input is PC 2 probably what starts the pattern going. jPC 1 jPC 2 PC 1 cross-condition jPC mean PC 3

There is a strong but hidden relationship between these epochs. That relationship is consistent with a dynamical interpretation. 75 spikes / second cell J114 r = -0.55 0 TARGET GO MOVE 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. projection onto dim 2 ������� ��� � ���� ��� 5 � ��� projection onto dim 1 ������� 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 is a function of from now the current state

Dynamical systems Dynamics are rules for how a system behaves over time. d x /dt = f( x ) where the is a function of state is going the current state

Dynamical systems d x /dt = f( x ) in any small neighborhood, approximately: d x /dt = M x

Individual neuron responses appear very complex cell 112 cell 114 cell 59 monkey J monkey J monkey J target move onset 200 ms cell 30 cell 15 monkey N monkey N cell 12 monkey B

Rotational patterns are seen for all available datasets monkey B monkey A monkey N monkey J-array Churchland, Cunningham, Kaufman et al, 2012 Nature

What these spirals mean state space rates versus time Neural population 2 (a.u.) Projection onto jPC = 0 400 ms

Rotational patterns are seen for all available datasets monkey J-array Churchland, Cunningham, Kaufman et al, 2012 Nature

The dynamical systems model of (monkey) motor cortex • Motor cortex activity translates into 1 2 muscle activity in a functionally simple way. monkey J-array • Motor cortex is a pattern generator. • A large, condition-independent input is PC 2 probably what starts the pattern going. jPC 1 jPC 2 PC 1 cross-condition jPC mean PC 3

How are dynamics activated? Idea suggested in: PC 2 ! Churchland, Cunningham, Kaufman et al., Nature, 2012 jPC 1 jPC 2 Models showing this is a natural way for a network to generate brief patterns: PC 1 ! Sussillo, Churchland, Kaufman & Shenoy, in review cross-condition jPC Hennequin, Vogels & Gerstner 2014 mean PC 3