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COMPUTING AND MOVEMENT COORDINATING CELL GROUPS

MULTI-ELECTRODE MOTOR CORTEX DATA In our final project we would like to further explore the data from the laboratory of Dr John Donoghue which consists

of electrophysiology measurements from the primary motor cortex (M1) of monkeys that performed center-out

reaching task. The neural spikes were recorded using a 96- channel array that was chronically implanted into the

primary motor cortex (Figure 1).

The center- out reaching task the monkeys performed

consisted of three subtasks. Firstly, the subject had to

touch the center of the screen and hold its hand there.

Once the center was acquired, the monkey had to wait for

the onset of the target. This target then appeared in one of

the eight directions [0, 45, 90, 135, 180, 225, 270, or 315

degrees]. This direction is stored in the trial_angle

variable for each trial. Once another cue, the go cue onset

has appeared, the monkey had to move its hand to reach

the target in order to get a reward. The time of go cue

onset, as well as the time of starting the movement, and

the time of reaching the target (target acquired) have been

recorded and stored respectively in trial_go, trial_move

and trial_acq for each trial. The whole process is shown

on Figure 2 in the context of a similar experiment (Rao

& Donoghue 2014).

Figure 1 Placement of multi-electrode array (MEA), and location of M1 (Rao & Donoghue 2014)

Figure 2 The process of the cue-reaching task as described by Rao et al (Rao & Donoghue 2014). On this figure, the target is purple when not acquired, but

changes to yellow when the hand is in the acceptable (acquired) zone.

The data set includes 17 correctly executed trials for each

direction.

The electrophysiology data obtained from the MEA

includes the neural spike data of 62 neurons, some of

which are obtained from the same electrode. The actual

channel placement (channel_map) is also provided in a

10*10 array. Within the electrophysiology data set, a list

of arrays (spk_times) of spike times for the 62 neurons is

stored. In addition to that, the spk_channels variable

contains the actual channel from which the spike data

were taken from for each neuron. The average spike

waveform is also given for each channel in

spk_templates, but the individual spike waves are not

provided.

OUR EXPERIMENT

PART I: DECODING DIRECTION

In our project, the approach we took that was new to us

was to use a machine learning algorithm in Python to

learn to decode direction of movement from the neuron

activity patterns. A machine learning algorithm allows us

to make no assumptions about the manner in which

neurons in the motor cortex represent information about

movement. In other words, we seek to predict direction,

but do not specify how such direction is represented by

the neurons in the form of firing rates. As will be

described later, we look at firing rates during 2 different

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temporal phases (before AND after movement). This

makes using machine learning particularly relevant

because although it is understood that populations of

neurons encode movement direction by vectorial

summation of firing rates, the way primary motor cortical

neurons represent direction before movement (in a

possible cue-to-action processing stage) is not as well

described (Rao & Donoghue, 2014); thus, machine

learning allows us to make no assumptions on that end.

With that, we allow the algorithm to discover the rules for

such classification — in machine learning terms, this is

called “feature detection”, extracted from noisy data

which can contain irrelevant information that does not

contribute to the classification. These features are then

used as rules for subsequent prediction.

We implemented a machine learning classification

method from scikit-learn using a simple randomised

decision tree algorithm (Pedregosa et al., 2011). First, we

took the firing rates of neurons across trials of all

directions from the moment of cue presentation (trial_go)

to target acquisition (trial_acq). The goal for the

algorithm is to learn to predict direction of movement

when only information on the firing rates of neurons is

provided. Prediction accuracy determines how good the

classification is and this is measured by the “leave-one-

out” cross-validation method. Figure 3 depicts an

example (with made-up values) of how this works. Since

we have 136 trials/experiments, we train the algorithm

with data from 135 (136 - 1; N-1) trials, and leave one out

(trial 3, in the case depicted in Figure 3) to serve as a test

set. In this “unknown” test set, we provide the trained

algorithm with only the firing rates of all neurons, but

conceal the direction of movement that they were

originally recorded for. Based on its training on the other

135 trials, it predicts the direction associated with trial 3

(in our example). We do this 136 (N) times, once for

every trial and obtain a prediction accuracy determined

by the percentage of correct predictions over total

experiments (136). This method was chosen as we have a

small data-set and the method will provide us with greater

accuracy and stability. Using this method, we found that

using overall firing rates (from cue presentation to target

acquisition) gives 83% decoding accuracy.

Figure 3: Illustration of the leave-one-out cross-validation method. Given N trials in our data set, we perform N experiments. In each, N-1 examples

were used for training and 1 remaining left out to use for testing. In the test case, when provided only the firing rates of neurons, the algorithm predicts

the direction originally associated with the firing. The prediction is cross-validated with the known direction. This leave-one-out cross-validation is

performed N times and the total number of correct predictions out of N experiments is taken as a percentage to give prediction accuracy.

ARE ALL 62 NEURONS NECESSARY FOR DECODING

ACCURACY?

Next, we asked whether all 62 neurons in this data-set

were necessary to obtain this accuracy or was there some

level of redundancy. To address this question, we aimed

to reduce dimensions — that is, to estimate the

importance of neurons in providing classification

accuracy and reduce the set to include just the most

important neurons for classification. We estimated the

importance of neurons using the randomized decision

trees in scikit-learn as above (Pedregosa et al., 2011), and

identified neurons that contain the most information

necessary to predict direction (and for the classifier to

distinguish between directions). We found that training

the algorithm with a set of reduced dimensions — only 23

of the highest ranked neurons — was sufficient to achieve

83% accuracy. If every neuron contributes equally to

specifying direction, one would expect a steep drop in

predictive value with the loss of as many as 64% (23/62)

of the neuronal population! This suggests that these 23

neurons had firing rate patterns that were sufficient to

decode direction.

Interestingly, when 23 units were randomly chosen to

train the algorithm, it achieved a predictive score of 63 ±

8% (mean ± standard deviation, 10 runs). This implies

that not just any 23 neurons are sufficient for prediction

— the neurons identified to have strong predictive power

are indeed very likely to contain important features to

decode direction. Do neurons other than the 23

“important” ones contain information that is 1) redundant

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2) not important for direction specification or 3) do they

encode other information related to direction but are not

represented in the form of firing rates?

ARE THE 23 HIGHEST RANKED NEURONS PREDICTIVE

BECAUSE THEY CONTAIN UNIQUE, NON-REDUNDANT

FEATURES? To understand if the population contains neurons that

specified for directions with redundancy, we did a

correlation analysis. This is achieved by taking the first

37 seconds of recording with neither visual stimulus nor

motor activity, which can be regarded as the baseline, and

then performing a spike cross-correlation. This allowed

us to identify neurons with correlated activity (without

the influence of any stimulus), following the Hebbian

principle that neurons that wire together, fire together --

and may thus represent redundant directional tuning, such

that loss of redundant neurons do not affect the predictive

power of the population, as described above.

We then asked if these 23 neurons were sufficiently

predictive of direction because they contained unique &

non-redundant direction-specific information. If so,

extracting 23 unique neurons with the least mean

correlation coefficients - that is, “most unlike” other

neurons recorded in that array - and testing the directional

decoding accuracy of this subset should yield comparable

predictive score (83%) as the 23 “most direction-

predictive” neurons. Surprisingly, taking 23 most

uncorrelated neurons instead yielded a predictive score of

71%, less than expected. This suggests that amongst the

23 sufficiently direction-predictive neurons described

earlier, there are also neurons that contain partially

redundant information. As such, whether a neuron

contributes largely to direction specification is not

strongly associated with whether it contains unique, non-

redundant directional information.

PART 2: Following these preliminary & exploratory findings, we

hypothesized that the response properties of neurons in

the motor cortex are heterogeneous. As such, although

the firing rate of all neurons in general contains some

direction-specific information, it is possible that its

overall activity also contains information that contributes

to generating movement direction in different ways. For

example, the activity can also specify responses

associated with the visual cue and/or movement planning

prior to the movement. Although such functions are

conventionally thought to be subserved by the premotor

cortex and supplementary motor cortex, there is

increasing evidence that neurons in the primary motor

cortex can also carry information more than direction of

movement (eg. Rao & Donoghue, 2014). There is also

evidence that the directional tuning of neurons is context-

dependent, with factors such as somatosensory input

about limb position and visual cues modulating the

directional tuning (eg. Churchland & Shenoy, 2007).

Interestingly, motor cortical neurons have also been

shown to respond with directional preference with respect

to different reference frames (some with “intrinsic-space”

preferred direction with reference to subject’s arm, and

some with an “extrinsic-space” preferred direction with

external space as a reference) (Kakei, Hoffman & Strick,

1999). In the case of our data set, the directions for the

trials are all specified in “extrinsic space”.

CAN NEURONS BE CLASSIFIED BASED ON DIFFERENT

RESPONSE PROPERTIES BEFORE AND DURING

MOVEMENT? This question motivated us to explore the data and

attempt to classify neurons based on their response

properties. We noticed that neurons fired not only during

movement but also before the actual movement,

suggesting a processing phase. To understand how these

different time periods of firing contribute to movement

direction, we considered 1) firing between go cue onset

(trial_go, in dataset) and the start of movement

(trial_move) as activity that may be associated with

motor planning or cue-to-action processing; and 2) firing

between movement (trial_move) and target acquisition

(trial_acq) as activity associated with the generation of

motor output.

Within each of these two different time windows, we ran

the same algorithm (as in part 1) to identify the neurons,

based on their characteristic firing rate, which are most

important for conveying directional information. This

gives us the neurons whose firing, between go cue onset

to start of movement AND movement onset to target

acquisition, made them likely to be involved in specifying

direction through cue-to-action processing and motor

output respectively. With that, we are also able to identify

neurons which are important for specifying direction in

both of these temporal categories. This gives us 3

classifications of neurons, as illustrated in the form of

the Utah array in Figure 4: neurons important for

specifying direction during 1) cue-to-action processing

(red), 2) motor output (blue) and 3) both of these

functions (purple shades between red & blue showing

relative importance).

From Figure 4, we can make a few broad observations.

Firstly, cue-to-action processing neurons (red) were not

specifically clustered at a particular area in the electrode

array, which could suggest potential encroachment of the

premotor cortex, which carries cue-related information.

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Instead, there is no clear pattern, with these neurons

seemingly interspersed across the array.

Figure 4: Spatial organization of neurons important for specifying

direction during cue-to-action processing (red), motor output (blue) and

both of these functions (purple shades between red & blue showing

relative importance of the phase). The size of each circle represents the

neuron’s importance in decoding directions through its overall activity

from cue presentation (trial_go) to target acquisition (trial_acq).

In addition, there was no clear spatial cluster of neurons,

which appear to represent directions through both

functions (purple). This was likewise observed by Rao &

Donoghue (2014) with a slightly different methodology.

The neuron’s relative importance (size of circles) also

does not appear to have a defined spatial organization.

Secondly, the largest proportion of neurons is active

through both of these processes (purple), although to

varying extents. Thirdly, there is no correlation between a

neuron’s importance in decoding direction during the

whole duration (cue to target acquisition; depicted as size

of circles) and whether it is specifically important in

either functions (cue-to-action processing or motor

generation). As such, neurons whose activity is important

for decoding direction with overall activity from cue to

target acquisition spread across the 3 categories of

neurons that we identified earlier.

Next, we decided to explore if activity during only cue-

to-action processing or only motor output was sufficient

to give the prediction accuracy obtained with overall

activity. When we trained the algorithm using firing rates

of all neurons before movement (cue-to-action

processing), we found that it was sufficient to predict

direction with 67% accuracy, while training only with

the highest ranked 23 neurons achieved marginal

increase to 68%. It is worth noting that this accuracy is

slightly higher than when considering overall activity of

23 randomly chosen neurons! This suggests that even

considering activity only before movement can achieve

reasonable accuracy to decode direction, suggesting that

this phase likely contains some important direction-

specific information, possibly planning processes.

Training the algorithm using firing rates of all neurons

during the motor output led to a prediction accuracy of

72% while considering only the 23 highest ranked

neurons for motor output achieved greater accuracy of

76%. Taken together, neither activity during cue-to-action

processing nor during movement were sufficient on their

own to achieve the 83% accuracy obtained from overall

activity, implying that activity during both phases

make important contributions to improving the

accuracy of decoding direction. These results are

summarized in Figure 5.

Finally, in Figure 6, we provide tuning curves for 6

representative neurons to illustrate the types of neurons

we have observed in this data-set. We found some

neurons (Figures 6a & 6b) that have rather different

tuning curves during the cue-to-processing & movement

phases, with only partial overlap during these phases. In

these neurons, both breadth of tuning and levels of

activity appear to be different during cue-to-action

processing and active movement. For example, the

neuron shown in Figure 6b has a sharper tuning,

particularly for the 315° direction during active

movement (blue - - -). In contrast, Figures 6c to 6f show

neurons that have comparable tuning curves across

directions during cue-to-action processing and motor

generation. However, whereas neurons shown in Figure

6c and 6d have different levels of activity during the two

phases, neurons shown in Figures 6e & 6f have similar

levels of activity. In the case of the neuron shown in

Figure 6d, there is greater activity and it also appears to

be more broadly tuned during the cue-to-action

processing phase.

Figure 5: Percentage prediction accuracy of neurons in the dataset when overall activity, only cue-to-action processing activity or only motor output-

associated activity were considered.

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PROBLEM THAT REMAINS TO BE SOLVED

IS THE MONKEY GETTING ANY BETTER? According to the study by Kargo & Nitz (Kargo & Nitz

2003) performed on rats trained to do a reach-to-grasp

task, learning has at least two phases. They have shown

that in the early phase, on the first day of training, the

performance of the subject animals showed fast, within

day improvements. In another study by Xiao (Xiao 2005),

monkeys performed a visually guided reaching task using

a robot arm. The main conclusion of this paper was that

premotor cortex neurons show learning-related plasticity.

It has also been pointed out that memory can be displayed

by cell activity properties, such as average firing rate,

dynamic range or preferred direction.

Although in the provided dataset we have no information

about the duration of the breaks between the successful

trials, nor do we know whether the full experiment was

performed on a single day, but it is reasonable to assume

that the trials are given in the order they were performed.

Based on these assumptions, our second question was to

determine whether the monkey is getting better at the

task. In order to quantify that process, we considered the

changes in reaction time. We also hypothesized a

correlation between the average firing rate, supported by

Xiao’s findings (Xiao 2005), and we aimed to determine

and whether this change of activity if there’s any is

different for the previously identified cell groups.

Preliminary exploration of the provided data did not show

any of the hypothesized correlations, but the amount of

data analyzed is not sufficient to draw any conclusions.

We have concluded that there must have been a

preliminary training period before the experiments that

we have the data from. Improvement in performing the

task could not have been observed, inasmuch as the main

learning period was over. In order to address the proposed

question, more extensive analyses on data from the

training period should be carried out separating different

directions.

FUTURE QUESTIONS We used a machine learning algorithm for our

classification. However, this algorithm is limited by its

ability to only predict directions in the 45 degree intervals

(0, 45, 90 etc) as in this dataset and cannot predict

intermediate directions, as would be achievable by an

algorithm which implements vector summation. Thus, it

may not be generalizable to other data-sets where

directions of movement tested are different from that used

in our data. Our method is a fast and simple way to

understand whether activity after cue presentation and

prior to movement could have important implications on

predicting direction. Following our results, it will be interesting to implement an algorithm capable of

decoding intermediate directions of movement. However,

in order to do so and obtain a reasonable accuracy, a

larger data-set containing more neurons will be necessary

to train the algorithm to decode directions.

As it has previously been proposed, the primary motor

cortex is not only involved in action generation, but

neuronal networks may also perform cue-to-action

processing related computations. Multielectrode array

recordings in awake Macaca monkeys have shown that

MI activity is partially related to visual target processing,

i.e. certain cells of the motor cortex are relevant in this

process. These results suggest that MI is an integral part

of a cue-to action network that responds to stimuli (Rao

& Donoghue 2014). In their analysis, Rao et al have used

cue or movement alignment to determine whether

responses were related more to cues or movements. The

task performed by the monkeys consisted of manual step

tracking and pursuit tracking. The step tracking

enabled the authors to separate the relationship between

cues and movements, while the pursuit tracking

investigated the influence of the target.

During the manual step tracking task, the monkeys had to

acquire the center of the screen and hold for 1000-2000

ms. Afterwards, for the pursuit tracking task, a C1 target

has appeared at the periphery indicating the direction for

an impending movement. When C1 and the first center

target have simultaneously disappeared, a new target, C2

has appeared at the same location as C1 did previously. In

this second part of the experiment the monkeys were

required to reach C2 and hold for 1000-1500 ms, and then

they were rewarded. By distinguishing between C1 with

no movement and C2 with movement, the authors were

able to separate the activity that is cue related only from

movement-related only activity.

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Figure 6a-f: Tuning curves for representative neurons during cue-to-action processing and move phases. See description in text.

In our case, we identified cue-to-action processing

activity as all activity before a movement, which is a

rough approximation — indeed we cannot exclude the

possibility that we may not have isolated purely cue-to-

action processing activity using such a method. In future

explorations of potential roles for cue-to-action

processing activity, it will be important to rigorously

isolate such activity using experimental paradigms like

that applied by Rao & Donoghue (2014). By isolating

purely cue-to-action processing activity, we may then be

able to more rigorously examine how neurons represent

direction of movement through such activity.

Bibliography

Churchland, M.M. & Shenoy, K.V., 2007. Temporal complexity and heterogeneity of single-neuron activity in premotor and motor cortex. Journal of Neurophysiology, 97, pp.4235-57.

Kakei, S., Hoffman, D.S., Strick, P.L., 1999. Muscle and movement representations in the primary motor cortex. Science, 285, pp. 2136-9.

Kargo, W.J. & Nitz, D.A., 2003. Early Skill Learning Is Expressed through Selection and Tuning of

Cortically Represented Muscle Synergies. , 23(35), pp.11255–11269.

Pedregosa et al., 2011. Scikit-learn: Machine Learning in Python. JMLR, 12, pp. 2825-30.

Rao, N.G. & Donoghue, J.P., 2014. Cue to action processing in motor cortex populations. Journal of

neurophysiology, 111(2), pp.441–53. Available at: http://www.ncbi.nlm.nih.gov/pubmed/24174650 [Accessed December 3, 2014].

Xiao, J., 2005. Premotor neuronal plasticity in monkeys adapting to a new dynamic environment. The

European journal of neuroscience, 22(12), pp.3266–80. Available at: http://www.ncbi.nlm.nih.gov/pubmed/16367792 [Accessed December 5, 2014].