Cortical activity in the null space: permitting preparation without - - PowerPoint PPT Presentation

Kaufman, Churchland, Ryu, & Shenoy Nature Neuroscience 2014

NEU 560, Lecture 6 part I (PCA and regression applications) Jonathan Pillow

Cortical activity in the null space: permitting preparation without movement

but first: subspaces!

Figure1. Illustrationoftheoptimal-subspacehypothesis.Theconfigurationoffiringratesis representedinastatespace,withthefiringrateofeachneuroncontributinganaxis,onlythree

• f which are drawn. For each possible movement, we hypothesize that there exists a subspace
• f states that are optimal in the sense that they will produce the desired result when the

movement is triggered. Different movements will have different optimal subspaces (shaded areas). The goal of motor preparation would be to optimize the configuration of firing rates so thatitlieswithintheoptimalsubspaceforthedesiredmovement.Fordifferenttrials(arrows), thisprocessmaytakeplaceatdifferentrates,alongdifferentpaths,andfromdifferentstarting points.

Neural Variability in Premotor Cortex Provides a Signature

• f Motor Preparation

Mark M. Churchland,1,2 Byron M. Yu,2 Stephen I. Ryu,2,3 Gopal Santhanam,2 and Krishna V. Shenoy1,2

J Neurosci 2006

Motivation:

• how can we plan a course of action, while still

waiting for the right moment to act?

• preparatory activity occurs in motor cortex

prior to a movement; why doesn’t it cause movement? (sub-threshold? gating?)

no

• new proposed mechanism: linear algebra!

Fig 1

10 cm 1 a.u. 110 spikes per s 200 ms

b a

Vertical target position Vertical cursor position Central spot Firing rate of one PMd neuron Deltoid EMG Target Go Move

Methods:

• multi-electrode recordings:

• dorsal premotor cortex (PMd)

• primary motor cortex (M1)
• behavior: monkey cued about upcoming

movement

• preparatory activity: predicts aspects of

movement (reaction time, variability, etc)

task and typical data

M

WN

• muscles

time

1 T 1 m

=

1 m 1 n

neuron neurons …

1 n

neuron- muscle weights time

1 T

Model: regression!

• basic idea: neural activity patterns orthogonal to

the row space of W won’t affect the muscles

Fig 2

Firing rate neuron 1 Firing rate neuron 2 Preparation Baseline Reach right Go cue FR neuron 1 FR neuron 2 Output-potent projection Output-null projection Time T G Time T G Time T G Time T G Reach left

toy example: muscle force proportional to sum

• f two neural inputs

(If you understand this, you understand the entire paper)

n u l l s p a c e M = N1 + N2

Fig 3:

Movement Preparation Go cue –0.5 0.5 Projection onto dim1 –0.5 0.5 Projection onto dim1 –0.5 0.5 Projection onto dim2 –0.5 0.5 Projection onto dim2 Monkey J, array Monkey N, array 115 Firing rate – 4 T a r g 4 – 2 M

• v

e 6 – 4 T a r g 4 – 2 M

• v

e 6 – 4 T a r g 4 – 2 M

• v

e 6 85 Firing rate 95 Firing rate

+ c × =

Prep tuning / move tuning: 25% Prep tuning / move tuning: 150% Prep tuning / move tuning: 16%

a b

illustrative pair: population analysis (axes from PCA):

Approach: estimate output-potent (and output-null) dimensions from movement period activity only via principal components regression (PCR) then look at row space of W^T

(each column of W has weights for a single muscle) 6PCs for N, 3PCs for M, 
 ⟹ W is 6 x 3 
 ⟹ 3D “potent” and 3D null space

=

• • • • • •
• • • • • •

• • • • • •

ˆ W = arg min

W ||M − WN||2

M W N

fig 4:

e s f e , . t

• a

.

• J

N J Array N Array 1 Fraction of preparatory tuning 3.0× 8.2× 2.8× 5.6×

a b c

Output-null Output-potent Output-potent Output- null Data set NA –400 Targ 400 –300 Move 0.32 Tuning

* * * *

Output- potent Output- null

d

−400 Targ 400 −300 Move 600 −1 1 Projection (a.u.) Targ 400 −300 Move −400 600 −1 1 Projection (a.u.) Test epoch Regression epoch From data set JA

tuning ratio:

Accords nicely with observation that preparatory tuning often uncorrelated with peri-movement tuning

“Trial-averaged data were used except where noted: the primary goal of these analyses was to explain how there can be preparatory tuning without movement, not to explain trial-by-trial variability.”

caveat: trial-averaged activity only!

summary

• null spaces: simple reason preparatory neural

activity fails to generate movement


(i.e., muscles add it up in a way that cancels out)

• preparatory PMd activity also lies in null space
• f weights driving M1 from PMd