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

Cortical activity in the null space: permitting preparation without movement Kaufman, Churchland, Ryu, & Shenoy Nature Neuroscience 2014 NEU 560, Lecture 6 part I (PCA and regression applications) Jonathan Pillow

but first: subspaces! Neural Variability in Premotor Cortex Provides a Signature of Motor Preparation Mark M. Churchland, 1,2 Byron M. Yu, 2 Stephen I. Ryu, 2,3 Gopal Santhanam, 2 and Krishna V. Shenoy 1,2 1 Neurosciences Program and Departments of 2 Electrical Engineering and 3 Neurosurgery, Stanford University, Stanford, California 94305 J Neurosci 2006 Figure1. Illustrationoftheoptimal-subspacehypothesis.Theconfigurationoffiringratesis representedinastatespace,withthefiringrateofeachneuroncontributinganaxis,onlythree of which are drawn. For each possible movement, we hypothesize that there exists a subspace of 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.

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!

• multi-electrode recordings: 
 Methods: - dorsal premotor cortex (PMd) 
 - primary motor cortex (M1) • behavior: monkey cued about upcoming movement • preparatory activity: predicts aspects of movement (reaction time, variability, etc) a b 10 Vertical target position cm Vertical cursor position Central spot Fig 1 0 1 a.u. Deltoid EMG task and 0 typical data Firing rate of one 110 spikes per s PMd neuron 0 Target Go Move 200 ms

� Model: regression! M WN time neuron time 1 T 1 n 1 T 1 1 1 neuron- muscles = muscle neurons weights m m … n • basic idea: neural activity patterns orthogonal to the row space of W won’t affect the muscles

Fig 2 toy example : muscle force proportional to sum of two neural inputs M = N 1 + N 2 Output-null projection FR neuron 2 Output-potent projection T G Time T G Time T G Time Firing rate neuron 2 Go cue Preparation Baseline n Reach right u l l s p a c Reach left e FR neuron 1 Firing rate neuron 1 (If you understand this, you T G Time understand the entire paper)

Fig 3: a Prep tuning / Prep tuning / Prep tuning / 85 115 95 move tuning: move tuning: move tuning: illustrative 25% 150% 16% Firing rate Firing rate Firing rate pair: + c × = 0 0 0 0 g 0 0 e 0 0 g 0 0 e 0 0 g 0 0 e 0 0 r 0 0 v 0 0 r 0 0 v 0 0 r 0 0 v 0 a a a 4 4 2 o 6 4 4 2 o 6 4 4 2 o 6 T T T – – M – – M – – M b Monkey J, array Monkey N, array 0.5 0.5 population Projection onto dim 2 Projection onto dim 2 analysis 0 0 (axes from PCA): –0.5 Movement –0.5 Preparation Go cue –0.5 0 0.5 –0.5 0 0.5 Projection onto dim 1 Projection onto dim 1

<latexit sha1_base64="2g1Cn1+E1VgH4Ux7bm5Y6gkTdk=">AB7XicbVBNS8NAEJ3Ur1q/qh69LBbBiyURQb0VvXhRKhTaEPZbDft0s1u2N0IJfRHePGg4tX/481/47bNQVsfDzem2FmXpRypo3rfjulpeWV1bXyemVjc2t7p7q796hlpgj1ieRStSKsKWeC+oYZTlupojiJOA2i4fXED56o0kyKBzNKaZjgvmAxI9hYKbhFJ+gOBd1qza27U6BF4hWkBgWa3epXpydJlBhCMdatz03NWGOlWGE03Glk2maYjLEfdq2VOCE6jCfnjtGR1bpoVgqW8Kgqfp7IseJ1qMksp0JNgM9703E/7x2ZuKLMGcizQwVZLYozjgyEk1+Rz2mKDF8ZAkmitlbERlghYmxCVsCN78y4vEP61f1t37s1rjqkijDAdwCMfgwTk04Aa4AOBITzDK7w5qfPivDsfs9aSU8zswx84nz/Dro4S</latexit> Approach : estimate output-potent (and output-null) dimensions from movement period activity only ˆ W || M − WN || 2 W = arg min via principal components regression (each column of W has (PCR) then look at row space of W^T weights for a single muscle) W M N 6PCs for N, 3PCs for M, 
 • • • • • • • • • • • • 
 • • • • • • ⟹ W is 6 x 3 
 = ⟹ 3D “potent” and 3D null space

� � � � � � � � � � � � � � � � a fig 4: Output-null 1 Projection (a.u.) 0 Test epoch Regression epoch − 1 − 400 Targ 400 − 300 Move 600 b 1 Output-potent Projection (a.u.) 0 e s From f data set JA − 1 e − 400 Targ 400 − 300 Move 600 c d , tuning ratio: 3.0 × 8.2 × 2.8 × 5.6 × 1 0.32 Fraction of preparatory tuning * * * * Output- . null Output- null t Tuning Output- Output-potent potent Data set NA 0 0 a J N J Array N Array –400 Targ 400 –300 Move .

Accords nicely with observation that preparatory tuning often uncorrelated with peri-movement tuning caveat: trial-averaged activity only! “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.”

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 of weights driving M1 from PMd