Download Dynamical systems view

Alex Cayco Gajic
Journal Club 10/29/13
How does motor cortex
generate muscle activity?
Representational perspective:
• Muscle activity or abstract
trajectory parameters?
(e.g. hand velocity)
• Focus on ‘code’ in single
neurons
Criticism of the representational approach
An epic, twenty-year battle was fought over the cortical
representation of movement. Do motor cortex neurons represent
the direction of the hand during reaching, or do they represent
other features of movement such as joint rotation or muscle
output?
Graziano 2011
The role of the motor system is to produce movement, not to
describe it.
Cisek 2006
How does motor cortex
generate muscle activity?
Representational perspective:
• Muscle activity or abstract
trajectory parameters?
(e.g. hand velocity)
• Focus on ‘code’ in single
neurons
Dynamical systems perspective:
• How can cortex flexibly generate
such a large repertoire of movements?
• Focus on basis sets/ mixed signals, network properties
A few equations
• Representational view:
rn(t) = fn(param1(t),param2(t),…)
• Dynamical systems perspective:
• Neural responses  muscle movement:
m(t) = G[r(t)]
But dimensionality of m << dimensionality of r, so G is
probably not invertible
• Dynamical system for population activity:
τ r’(t) = h(r(t)) + u(t)
• Dimensionality reduction techniques will be important to find
robust, redundant activity patterns
Voluntary movements are “prepared”
Churchland et al. 2006
Random delay period
Voluntary movements are “prepared”
• RT decreases with delay period, indicating “preparation”
Churchland et al. 2006
Voluntary movements are “prepared”
• RT decreases with delay period, indicating “preparation”
• Variety of complex single-neuron responses
Churchland et al. 2006
What is preparatory activity?
Representational view
• Hypothesis: preparatory activity is the subthreshold form of
movement activity
Churchland et al. 2010a
What is preparatory activity?
Representational view
• Hypothesis: preparatory activity is the subthreshold form of
movement activity
Churchland et al. 2010a
What is preparatory activity?
Representational view
• Hypothesis: preparatory activity is the subthreshold form of
movement activity
Churchland et al. 2010a
What is preparatory activity?
Representational view
• Hypothesis: preparatory activity is the subthreshold form of
movement activity
• Reality: preparatory & movement tuning are uncorrelated on
average
Churchland et al. 2010a
What is preparatory activity tuned for?
Leave out one condition (direction), use linear regression to
predict left-out preparatory firing rate from a set of “preferred
directions”.
PCA analysis:
•
Perimovement: activity of
other neurons
•
Kinematic: position, velocity,
acceleration
•
EMG: activity for multiple
muscles
dimensionality
Best performance: from whole population dynamics.
Churchland et al. 2010a
What is preparatory activity?
Dynamical systems view
• Hypothesis: preparatory activity brings population dynamical
state to an initial value that produces correct motion with
minimal reaction time.
• Reduction in variability
across different trials as
states converge to muscle
activation (FF)
Churchland et al. 2010b
What is preparatory activity?
Dynamical systems view
• Hypothesis: preparatory activity brings population dynamical
state to an initial value that produces correct motion with
minimal reaction time.
Churchland et al. 2010b
What is preparatory activity?
Dynamical systems view
• Hypothesis: preparatory activity brings population dynamical
state to an initial value that produces correct motion with
minimal reaction time.
Churchland et al. 2010b
What is preparatory activity?
Dynamical systems view
• Hypothesis: preparatory activity brings population dynamical
state to an initial value that produces correct motion with
minimal reaction time.
Churchland et al. 2010b
Convergence of trajectories
• Reduction in variance comes from convergence of
trajectories during motor preparation
10-D PCA
Covariance ellipses
Outlier (monkey hesitated)
Churchland et al. 2010b
Convergence of trajectories
• Reduction in variance comes from convergence of
trajectories during motor preparation
10-D PCA
Covariance ellipses
Outlier (monkey hesitated)
• Prediction: perturbing initial states near go cue should
increase RT
Churchland et al. 2010b
Preparation & response time
• Use subthreshold microstimulation to perturb prepatory
activity
• No change in wave profile, change in RT only when
perturbation occurs at go cue
Churchland & Shenoy 2007a
Preparation & response time
• Use subthreshold microstimulation to perturb prepatory
activity
• No change in wave profile, change in RT only when
perturbation occurs at go cue
• Change in RT due to preparatory state – less dramatic in
M1, doesn’t exist in saccadic RT
Churchland & Shenoy 2007a
Preparation & response time
• corr(alpha,RT) ?
Afshar et al 2011
Preparation & response time
• corr(alpha,RT) < 0
• Farther along mean neural trajectory
 smaller RT
Afshar et al 2011
PMd neural responses are bizarre
•
•
•
•
Tuning differs between preparatory & perimovement periods
Response are complex and multiphasic
Responses of different neurons are heterogeneous
Activity fluctuates longer than movement scale
Churchland et al. 2010a
Low-dimensional activity is rotational
• In low-dimensionality projections,
trajectories rotate with phase set by
preparatory state (captures ~28%
variance)
• However, the reaches were not
overtly rhythmic
• Brief sinusoidal oscillations form a
basis set for more complex patterns
Churchland et al. 2012
Neural population responses are rotational
Churchland et al. 2012
Kinematic/EMG data are not
Churchland et al. 2012
What is jPCA?
• X = (n)x(ct) matrix
• PCA to reduce to Xred = (k)x(ct)
• Fit Xred’ = MXred, Xred’ = MskewXred
using linear regression
• V1, V2 conjugate eigenvectors of
Mskew
• jPC1 = V1+V2
• jPC2 = j(V1-V2)
• Project Xred onto jPC1, jPC2
Churchland et al. 2012
Conclusions
• Dynamical systems approach gives insight into movement
without making assumptions about single-neuron tuning.
• “Preparation” funnels neural trajectories to achieve fast
movement without minimal variation.
• Preparatory state predicts both RT and trial-to-trial variability.
• Rotational PMd firing rate dynamics form a basis for more
complex muscular activity.