Neural synergies for controlling reach and grasp movement in macaques

Accepted Manuscript Neural synergies for controlling reach and grasp movement in macaques Yaoyao Hao, Shaomin Zhang, Qiaosheng Zhang, Guanglin Li, Weidong Chen, Xiaoxiang Zheng PII: DOI: Reference:

S0306-4522(17)30427-X http://dx.doi.org/10.1016/j.neuroscience.2017.06.022 NSC 17834

To appear in:

Neuroscience

Received Date: Accepted Date:

10 November 2016 16 June 2017

Please cite this article as: Y. Hao, S. Zhang, Q. Zhang, G. Li, W. Chen, X. Zheng, Neural synergies for controlling reach and grasp movement in macaques, Neuroscience (2017), doi: http://dx.doi.org/10.1016/j.neuroscience. 2017.06.022

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Title: Neural synergies for controlling reach and grasp movement in macaques Authors and affiliations: Yaoyao Hao1,2, Shaomin Zhang1,2,3,4*, Qiaosheng Zhang1,2, Guanglin Li5, Weidong Chen1, Xiaoxiang Zheng1,2,3,4 1

Qiushi Academy for Advanced Studies, Zhejiang University, Hangzhou, 310027,

China 2

Key Laboratory of Biomedical Engineering of Ministry of Education, Zhejiang

University, Hangzhou, 310027, China 3

Department of Biomedical Engineering, Zhejiang University, Hangzhou, 310027,

China 4

Zhejiang Provincial Key Laboratory of Cardio-Cerebral Vascular Detection

Technology and Medicinal Effectiveness Appraisal, Zhejiang University, Hangzhou, 310027, China 5

Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences,

Shengzhen, 518055, China *Corresponding author: Shaomin Zhang (Address: Mail Box 1536#, 38 Zheda Road, Hangzhou, 310027, China. E-mail: [email protected]) Conflict of Interest: The authors declare no competing financial interests.

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Abstract It has been suggested that the brain adopts a simplified strategy to coordinate a large number of degrees of freedom in motor control. Synergies have been proposed as a strategy to produce movements by recruitment of a small number of fixed modular patterns. However, there is no direct support for a synergistic organization of that brain itself. In this study, we recorded neural activities from the dorsal premotor cortex (PMd) of monkeys trained to reach and grasp differently shaped objects (grasping task) or the same object in different positions (reaching task). Non-negative matrix factorization (NNMF) was applied to the neural data to extract neural synergies, whose functional roles were verified in several ways. We found that motor cortex used similar neural synergies for grasping different objects; combining only a few of the synergies accounted for most of the variance in the original data. When used for single-trial task decoding, the synergy coefficients performed as well and robustly as the original data in both tasks. The synergy amplitudes for each unit were significantly correlated with the corresponding neuron’s firing rate. In addition, we also observed synergies shared between tasks and task-specific synergies, as shown before for muscle synergies. Altogether, we demonstrated that neural synergies are effective in describing neural population activity during reach to grasp movements and provide a new tool for interpreting neural data for movement control. Keywords: Neural synergy, monkey, motor cortex, reach to grasp, non-negative matrix factorization

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Introduction The complexity of the musculoskeletal dynamics derives from the fact that a large number of degrees of freedom must be coordinated to achieve a given motor task (Bernstein, 1967). How the brain overcomes this complexity to control body movement efficiently is one of the fundamental questions in motor neuroscience. It has been proposed that the central nerves system (CNS) might have implemented a simplified strategy to produce various complicated movements (Ting and McKay, 2007; D'Avella and Lacquaniti, 2013). According to one of the possible solutions proposed, the CNS produces desired movement by recruiting of a much smaller number of fixed modular patterns or synergies (Bizzi and Cheung, 2013; Santello et al., 2013). Synergies have been observed and demonstrated at different levels of description, such as kinematics (Santello et al., 1998; Thakur et al., 2008), force kinetics (Latash et al., 2001; Kuo et al., 2013) and muscular activities (D'Avella et al., 2003; Brochier et al., 2004; Overduin et al., 2008). Given the hierarchical organization of the motor control architecture, it is reasonable to ask whether the synergies observed are organized by the CNS. Recent studies have inferred their underlying neural substrates. Recordings in motor cortex and spinal cord showed that the neural signals were more correlated with muscle synergies rather than individual activities (Holdefer and Miller, 2002; Kargo and Nitz, 2003; Hart and Giszter, 2010; Yakovenko et al., 2011). A recent study also showed that population level activity of motor cortex reflects the recruitment of muscle synergies during objects handling 3

(Overduin et al., 2015). Transcranial magnetic stimulation on human (Gentner and Classen, 2006) and intracortical microstimulation on monkey (Overduin et al., 2012) evoked similar synergies used in natural movements, possibly indicating a modular representation of muscle groups in the brain. An anatomical study found that cortico-motoneuronal cells for different muscles overlap extensively in the brain, which may provide a neural substrate for muscle synergies (Rathelot and Strick, 2006). However, direct support for neural synergy, i.e., whether the brain adopts a functional synergy strategy to generate movements, has not been addressed yet (but see Berger et al. 2013). Here, we hypothesize that a similar synergistic organization is working in the brain during movement control. To this end, we tried to extract synergies from neural activities in motor cortex while monkeys reached to grasp different objects. Then, we investigated whether the synergies were effective in input (i.e., whether the original neural data could be reconstructed by combining the synergies) and functional task (i.e., whether the synergies had the same task discrimination property as the original data) spaces (Alessandro et al., 2013). We found that the synergies extracted from different objects are similar to each other. When using the same set of synergies to represent the neural data, a large fraction of the variation could be accounted for by only a small number of synergies. Functionally, the synergy amplitude was significantly correlated with neuronal firing rate and the remaining coefficients can be robustly classified as the original data. When comparing the synergies extracted from grasping and reaching tasks, we found about two-thirds of them are similar, 4

indicating that different motor tasks not only have their specific synergies to generate various movements, but also share some of the synergies to simplify movement control.

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Experimental Procedures Two rhesus monkeys (Macaca mulatta, male, named as B03 and B04) were trained to perform reaching and grasping tasks, during which neural activities were recorded through multielectrode arrays chronically implanted in motor cortex. All procedures conformed to the Guide for the Care and Use of Laboratory Animals (China Ministry of Health) and had been approved by Zhejiang University Committee on animal usage. Part of the data had been reported previously (Hao et al., 2014). Behavioral tasks Monkeys were trained to reach and grasp differently shaped objects attached to a panel in front of them, one at a time. Four objects used in this study (Cylinder, Plate, Ring and Cone) and their corresponding grasping postures (power grip, side grip, two-finger hook and precision grip) are shown on the right side of Fig. 1A. The dimension of the panel containing the objects was around 35 cm × 35 cm and the distance between the panel and the eyes of the animal was approximately 30 cm. The monkey maintained his hand on the starting position for at least 1 s before the object was lit on (Light ON). Following the Light ON event, the monkey was required to reach and grasp the object using the proper grip pattern and hold it for 1.5–2 s until the light was off (Light OFF). The monkey released the object and returned the hand to the rest position after Light OFF. Completion of a successful trial resulted in water reward. Hand and arm movements were recorded using an infrared video camera (25 fps) during the experiment. The trial-by-trial behavioral timings (including

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initiation of movement, object grasping and releasing) were obtained from the video recordings by calculating the time relative to the Light ON event. There are two types of paradigms performed by the subjects, named ‘grasping’ and ‘reaching’ tasks respectively. In the grasping task (Hao et al., 2014), only one object was mounted on the panel for each trial (as shown in Fig. 1A). In each session, four objects, each for a block of ∼50 trials, were presented in the same position to the monkey in a randomized order. In this way, the monkey performed different grasp movements with the same reaching direction. In the reaching task (Cao et al., 2013), four identical objects (either cylinder or cone) were mounted on the panel in a two-by-two matrix (as shown in Fig.4A). The distance between two neighbor objects is about 15 cm. The subject reached to grasp one of them at a time according to which object was lit on. In some of the sessions, either grasping or reaching task was performed, and in other sessions, both tasks were performed one after another. Array implantation and data acquisition Each monkey was implanted with a 100-electrode Utah array (Blackrock Microsystem, USA) in the dorsal premotor cortex (PMd) of the hemisphere contralateral to the hand performing the task (Fig. 1B). The array (4.2 mm × 4.2 mm) was arranged in a 10 × 10 matrix, each with a 1.5 mm length shank, spaced by 400 μm. The surgery for implantation (Zhang et al., 2012; Chhatbar et al., 2010) was performed under general anesthesia (10 mg/kg ketamine and 1 mg/kg diazepam, followed by endotracheal administration of 1%–2% isoflurane). A craniotomy was performed over motor cortex

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and the array was inserted into the flat gyrus dorsal to the spur of arcuate sulcus using a pneumatic inserter. The cranial defect was closed by suturing back the dura, fixing back the bone flap and closing the skin. The monkey was allowed to recover from surgery for at least one week, during which, antibiotics (ceftriaxone sodium, 50 mg/kg) were administered. Raw signals from each channel of the array were buffered (1× gain), amplified (~600 gain), filtered (Butterworth bandpass, 0.3–7500 Hz), and digitized (14 bit resolution, 30 kHz sample) using Cerebus system (Blackrock Microsystem, USA). The signals were further digitally filtered (Butterworth bandpass, 250-5000 Hz), and a threshold (-5.5 times the root mean square value) was set to detect spikes. Single units were isolated offline using Offline Sorter (Plexon, USA) and only the units with a signal to noise ratio larger than 3.0 and 1% of interspike intervals (ISIs) less than 1 ms were used in this study. An average of 35 and 57 units per session were isolated from subject B03 and B04, respectively. Each unit’s spikes were counted and summed over each contiguous 100-ms bin to obtain its firing rates along the time course of movement. Synergy extraction and analysis We used nonnegative matrix factorization (NNMF) algorithm (Lee and Seung, 1999) to extract synergies from neural firing activities in each separated session. Neural data are decomposed into a linear combination of a set of time-invariant activations (synergies) with time-dependent coefficients:

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 =   ∙ + 



where F(t) is neural firing rate of all units (m-dimensional vector, m is the total number of units in the session) at sample time t; Si is the i-th synergy (m-dimensional vector); ci(t) is the scalar coefficient for the i-th synergy at time t; N, the input to the algorithm, is the total number of synergies; and σ(t) is the m-dimensional residual errors. Given the number of synergies, the factorization uses an iterative method starting with random initial values of the synergies and coefficients to minimize the root-mean-squared residual errors. In order to avoid finding local minima, the algorithm ran 10,000 times using different random initializations and selected the solution with the lowest reconstruction error. The synergies and coefficients were then normalized to the range [0, 1] after extraction. The validity of the decomposition was assessed first by a measure of the goodness of the reconstruction, i.e., from the perspective of input space (D'Avella et al., 2006; Delis et al., 2013), defined as variance accounted for (VAF): 





 VAF = 1 −      −    ∙  !    −   



 

where s and t index the trials and time samples, respectively; Ts is the number of time  is the mean firing rate vector across time samples. The VAF, samples in trial s;  measuring the ratio between sum of squared residuals and sum of total variations (i.e., the squared residual from the mean activation), thus quantifies how well the actual firing patterns are fitted with a given set of synergies. The VAF increases as 9

more synergies are added. The number of synergies to be extracted was chosen as the minimum number for which the VAF value exceeded 90%. Neural synergies extracted from different object conditions (i.e., either different objects in grasping task or different reach positions in reaching task) were compared to determine if they used the similar neural basis. Because the one-second neural data after visual cue on (during which monkey is reaching to grasp and hold the object) is found important for reaching to grasp movement (Hao et al., 2014), they are employed to extract synergies. First, the firing rate bins were aligned at Light ON event and averaged across all the trials under each object condition; synergies were then extracted separately from each of these object conditions (Note that the data averaging was only used for synergy extraction, not for the data reconstruction, which is based on single-trial resolution). Second, the similarity between pairs of synergies was quantified by their dot product. The best-matched pair was defined as the one with highest dot product among all possible pairs. The second-best matched pair was the one with the highest dot product among remaining pairs. The process continued until there was no more synergy left in one of the object conditions. The significance of each matched pair was determined by Monte Carlo simulation (Overduin et al., 2012), in which, the dot products were computed using synergies with randomly shuffling units identity for 10,000 times. The actual dot product was then compared with the 99th percentile of the distribution of the shuffled products to determine if the matched pair was similarly significant (p < 0.01). It is important to note that all the synergy-related analyses were done in each separated session. 10

Task decoding with neural synergies The validity of the decomposition was additionally assessed by a measure of single-trial decoding analysis to quantify how well the single-trial coefficients obtained under different object conditions can be separated from each other, i.e., from the perspective of task space (Delis et al., 2013). In order to achieve this end, the binned neural firing rates were first averaged across all trials under each object condition and concatenated together to form a big matrix; one set of synergies was then extracted from the big matrix in the session. Then, the neural data of each single trial were fitted by the same set of synergies and the derived coefficients at each time samples (i.e., bins) were used for decoding evaluation. We employed a classifier of support vector machine (SVM) to decode different object conditions. The percentage of correct decoding of individual trials was defined as the metric of decoding performance. The SVM worked in a bin-wise mode, i.e., the classifier gave out one result for each bin. The final accuracy, however, was computed in a trial-wise mode. To be consistent with a previous study (Hao et al., 2014), a majority voting strategy was used to output the final decoding result, in which, each bin contributed one vote and the majority within a trial determined the classification. The decoding performance using synergy coefficients was compared with the decoding results with raw neural firing data. All the decoding accuracies were cross-validated using the leaving-one-out method. The decoding accuracies varied with the number of synergies and the minimum number of synergies that captured all the task-discriminating variance is determined when the increase of synergies does not 11

gain any further statistically significant increase of decoding performance (Delis et al., 2013). Meanwhile, the decoding analyses, both using original neural data and synergy data, were further also evaluated by dropping a number of neurons in each separated session. For each iteration, a random set of neurons was dropped from the neural ensemble and the synergies were recomputed with the remained subsets of the neurons. This procedure was repeated 1,000 times and the averaged decoding accuracies were deemed as the accuracy of the current number of neurons. To further investigate the functional role of the synergy, we try to relate the individual synergy component with the neuronal importance to specific task, i.e., whether important neurons to a task have larger synergy amplitudes. The neuronal importance was evaluated by an information theoretical method, mutual information, which has been introduced to measure the information amount between the neural firing rate and the task (Wang et al., 2009; Cao et al., 2013). Each unit’s spikes were first binned using 10 ms bins, so that there will be only 0 or 1 in each bin. Then the mutual information between binned neural activity f and task y is defined as I#; % =  &%  &#|%log %

#

&#|% &#

where y = [y1, y2, y3, y4] are different directions in reaching task or different objects in grasping task and p(y) represents the probability of corresponding action (which is assumed as 1/4 because of the same trial numbers in each condition). The neural firing activity f is 0 or 1 and p(f) is the probability of the firing rate for the whole task. Whereas p(f|y) is conditional probability of firing rate (0 or 1) for a certain condition. 12

The synergy amplitude for each neuron was calculated as the sum of the corresponding components in all synergies extracted (under the criteria of VAF > 90%). The calculated mutual information for each neuron was then linearly regressed with the corresponding synergy amplitude. All the algorithms were implemented using MATLAB (Mathworks Inc.) and the SVM was developed with open source library LIBSVM (Chang and Lin, 2011).

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Results Each monkey performed the grasping task for a total of 8 sessions. In some of the sessions (6/8 and 5/8 for Monkey B03 and B04, respectively), the monkeys also performed the reaching task. The average reaction time between Light ON and movement onset measured based on the video recordings was 385 ms (SD, 100 ms) and 235 ms (SD, 93 ms) for monkey B03 and B04, respectively. The movement time between movement onset and stable object contact was 504 ms (SD, 115 ms) and 412 ms (SD, 87 ms) for monkey B03 and B04, respectively. Synergies extracted from different objects are similar To extract synergies, we applied NNMF method separately to the neuronal activities recorded when the monkeys were grasping different objects. In each row of Fig. 1C, the first four synergies, each of which comprises a time-invariant pattern of neuronal activity, are illustrated for each object in a representative session. The decomposition also extracts four time-dependent coefficients along the time course of reaching to grasp movement. The high VAF values of reconstruction (> 95%) indicate a good reconstruction of the neural activity by combining the four synergies and corresponding coefficients. Most prominently, the synergies extracted for each object are significantly similar to each other (Monte Carlo simulation, p < 0.01), although the neural activities are distinct and highly classifiable for each object as shown before (Hao et al., 2014). Each of the synergies in one object can find the significantly matched one in another object, and the case is true for all the sessions

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in both monkeys. Thus the similarity may indicate that motor cortex shares a similar pattern of neural bias when grasping different objects. Grasping task decoding with neural synergy coefficients As motor cortex uses similar neural synergies for grasping different objects, we tried to use the same set of synergies to represent the neural data and see how the remaining coefficients can be discriminated for each of the task conditions (i.e., task decoding). In each session, the same set of synergies is extracted from the concatenated averaged neural activities for each object condition and the coefficients for each trial are solved from this set of synergies (see methods). To determine how many synergies are enough for task decoding, we first examined the relationship between number of synergies and reconstruction VAF. Figure 2A illustrates the averaged (and individual) VAF curves which monotonically increase as the number of synergies increases for both monkeys. The reconstruction VAF increases rapidly using the first 2 or 3 synergies and saturates gradually beyond that. An averaged dimensionality of 4.6 (± 0.74) and 7.4 (± 1.41) is needed to capture over 90% of the variation of the neural data for Monkey B03 and B04, respectively. We next investigate whether the remaining coefficients can be classified as different objects given the high VAF values of reconstruction. The coefficients of one sample session are reduced into 3D space (from 6 in this example) for visualization (Fig. 2B). Each dot represents the coefficient of a single bin (the 5th of the 10 bins) of a grasping trial. The coefficients for each object can be clearly separated even in the reduced

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space and single bin resolution. We further quantify the relationship between the classification accuracies and the number of synergies using a SVM decoder. Figure 2C shows the averaged (and individual) decoding accuracies as a function of synergy numbers for both monkeys. The trends are similar to the VAF ones in Fig. 2A and the decoding accuracy exceeds the chance level with only 2 synergies for both monkeys. The accuracy increases moderately after a dimensionality of 3 and finally gets to an accuracy of 0.93 and 0.90 for Monkey B03 and B04, respectively. These accuracies for each session are compared with the decoding accuracies using the original data for both monkeys, as shown in Fig. 2D. Although the averaged accuracies are lower for decoding using synergy coefficients than the one using the original data, neither of them is significantly different in both monkeys (p = 0.1129 and 0.1119 for Monkey B03 and B04, respectively). Note that the accuracies of synergy decoding are achieved by only a dimensionality of 4.6 and 7.5, rather than the original ones of 35 and 57 for Monkey B03 and B04, respectively. This indicates that a smaller number of synergies (comparing with the original number of neurons) modulated by different weights might be employed by the brain to generate a variety of distinct movements. If motor cortex really adopts a synergetic strategy to coordinate neural activity for controlling the reaching to grasp movement, the results obtained above should be irrelevant to the recording sets, i.e., arbitrarily reducing a number of neurons (simulation of the situation that with a different recording ensemble) would result in similar synergy patterns. To test this hypothesis, we extracted synergy patterns from the neural ensemble with a reduced number of neurons and compared them with 16

synergies extracted from the original whole neural ensemble (with the same identity of synergies removed). One representative result in Fig. 3A shows the significant similarity between the original and dropped synergies, suggesting that the synergy patterns remains stable despite different recording ensembles with neurons loss. As expected, the correlation between original and reduced neuron synergies decreases as the amplitudes of the dropped synergies increase (Fig. 3B). When the number of neurons is dropped systematically from 10% to 80%, the percentage of similarity between original and dropped synergies decreases monotonically (Fig. 3C). However, 85% of the original synergies are still similar to the dropped ones even when the neurons are dropped to 50% of the original. This indicates that the synergy decomposition is not necessarily recomputed after neuron loss; removing the corresponding synergy components would be feasible. We then test if these reduced synergies are still effective in task decoding or as effective as the original neuronal counterpart. As shown in Fig. 3D for one sample session of Monkey B03, both the decoding accuracies using original neuronal data (neuron decoding) and the synergy coefficients (synergy decoding) decrease as the number of dropped neurons increases. When the two types of decoding accuracies of all the sessions are plotted against each other (Fig. 3E), they are perfectly aligned along the right diagonal, indicating the same decoding performance. The same situation is true for Monkey B04 as shown in Fig. 3F and 3G. For Monkey B04, the neuron decoding is a little higher than synergy one at the beginning in Fig. 3F, but this effect is not significant. Reaching task decoding with individual synergy coefficients 17

In some of the sessions, the monkeys were also employed to do a reaching task as shown in Fig. 4A (also see method). Similar to the grasping task, the synergy decomposition works well with the reaching data and the synergies are also similar across the four reach locations (data not shown). Both VAF and decoding accuracies increase as the number of synergies increases (Fig. 4B). A dimensionality of 6.3 (± 2.3) and 6.6 (± 1.5) is enough for capturing over 90% of the total variance and the synergy coefficients are used for evaluating the decoding performance of each session. The decoding accuracies for synergy are still comparable with the original ones (Fig. 4C). To our surprise, the synergy decoding is even higher than the original ones in some sessions (especially for B03), considering that the dimensionality is much lower. Note that the decoding results were highly cross-validated using the leaving-one-out method. As the synergy coefficients achieve a classification accuracy comparable with that of all the neurons in both tasks, we wonder if the performance of individual synergy coefficients is higher than that of individual neurons. A similar decoding method but with individual coefficients or neurons involved was used to assess the performance (cross-validated using leaving one out method). The decoding accuracies of all the coefficients and neurons in one representative session are shown in Fig. 4D, where we found that the performance for individual coefficients is actually comparable with most of the individual neurons. The best accuracies that can be achieved show no significant difference between each other for both tasks and both monkeys (Fig. 4E). However, the average performance of synergy 18

coefficients is significantly higher than that of neurons (Fig. 4F), indicating a more concentrated information represented in synergy coefficients. These results have shown that the synergic decomposition extracts essential information while reducing the redundancies, thus demonstrating the functional feasibility of synergy coefficients. Shared and specific synergies between grasping and reaching tasks As the reaching task and grasping task are performed in the same session, we can compare the two tasks on the same set of neuronal ensembles in the perspective of neural synergy. We hypothesize that the two tasks share some of the synergies because they are both reaching to grasp movements in general. However, they also should have some specific synergies because different dominant parameters are encoded (i.e., grip types and reaching directions for grasping and reaching task, respectively). In Fig. 5A, a criterion of VAF > 90% is set and a number of 7 and 6 synergies are extracted for the grasping and reaching task from one sample session of Monkey B04, respectively. We found that 4 pairs of synergies are significantly similar, indicating they are shared across the two tasks, It suggested that these synergies might encode of the general reaching to grasp movement. However, the remaining synergies cannot be matched into significantly similar pairs and deemed as synergies specific to the task. Inspection of the unmatched synergies reveals some specific neuronal components or patterns (e.g., the two red arrows in Fig. 5A indicate two specific synergy components in the reaching task), which may be related to the dominant parameters encoded. The situation is the same for all the sessions tested, 19

which leads to a percentage of 64.9% and 75.8% of the grasping synergies being shared with the reaching ones for Monkey B03 and B04, respectively. As the same neuron identity would have very distinct synergy component in reaching and grasping task, we further investigated whether there are any functional meanings represented by the amplitude of synergy. The synergy amplitude of each neuron is computed by summing up all the synergies of that neuron before they are normalized. The un-normalized synergy will not be scaled arbitrarily as the synergy coefficients have already been normalized in NNMF to ensure the rows of the coefficient matrix have unit length. We first tried to correlate each neuron’s synergy amplitudes with the corresponding firing rates. As shown in Fig. 5B, the synergy amplitude is linearly correlated with the neuron’s average firing rate during the both tasks (r = 0.96 and 0.83 for monkey B03; r = 0.93 and 0.88 for monkey B04, p < 0.01). We then ask whether the synergy amplitude also represents the neuronal importance for a specific task. The importance of each neuron is evaluated by mutual information between the neuronal activities and the grasping or reaching categories in two tasks (see methods). The synergy amplitudes of each neuron are significantly correlated with the corresponding mutual information in both tasks, with small but significant R-values (r = 0.52 and 0.33 for monkey B03; r = 0.32 and 0.30 for monkey B04, p < 0.01). However, this linear relationship might be due to the fact that neurons with higher firing rate tend to have higher importance. Therefore, in order to analyze the relationship between synergy amplitude and neuronal importance, we used a partial correlation measure to remove the factor of firing rate. The partial linear 20

relationship between synergy amplitude and neuronal importance, controlling for the fact of firing rate, were not significant anymore for both tasks and both monkeys (p > 0.01), indicating that the amplitude of synergy is merely an indicator of the neuron’s average firing rate. The shared and specific synergy patterns, but not the sum of synergy amplitudes, revealed different neuronal involvement in two tasks, which is further supported by the distinct neural activities of individual neurons. As shown in Fig. 5C, the neural activity of the same neuron is differently tuned in the two tasks. The neural ensemble can be subdivided into groups of tuning to reaching (e.g., Neuron1), grasping (e.g., Neuron2) or both (e.g., Neuron3), which was further quantified by higher values of mutual information in reaching, grasping and both tasks, respectively. For some neurons (e.g., Neruon1 and Neuron2), they have similar transient after Go cue in two tasks. These activities might be encoding the reaching to grasp movement in general, which might be the basis of the shared synergies. For other neurons (e.g., Neuron3), even the general activities are dissimilar (i.e., Neuron3 goes more excitation in reaching task, but goes more inhibition in grasping task). The distinct activities in two tasks might have been the basis of specific synergies. These results suggested that the functional role of the synergies is related to their neuronal activity basis.

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Discussion A few neural synergies have been extracted from monkey premotor cortex during reaching and grasping tasks. Our results first confirmed that a similar set of neural synergies were used for grasping different objects, indicating that these synergies might be the neural basis for controlling different grasping movements. Then the validity of these synergies was assessed in several ways. Firstly, combining a very small number of synergies could give a good reconstruction of the raw neural activity, accounting for more than 90% of the variance. Secondly, the decoding performance of synergies is comparable or even better than that of original neural activity in both tasks, despite that the dimensionality of the synergies is much smaller. Meanwhile, the synergy patterns and decoding performance remained even when dropping neurons. Thirdly, the synergy amplitude is a good representation of the neuronal firing rate. Lastly, synergies shared between tasks and task-specific synergies were uncovered, similarly to what observed for muscle synergies (D'Avella and Bizzi, 2005). Overall, although synergy decomposition has been applied to neural data before (Overduin et al., 2015), our findings in this study demonstrated that these neural synergies are effective both in input and task spaces, supporting the idea that neural activities during reaching to grasp movements could be interpreted using synergies. The functional role of the synergy was usually assessed by relating the synergy coefficients and the task conditions, e.g., the muscle synergies were directly correlated with reaching directions (D'Avella et al., 2008), grasping object masses (Overduin et al., 2008) and endpoint force fluctuations (Hagio and Kouzaki, 2015). 22

Single-trial task decoding method was recently developed to evaluate the functional role of synergy and verified in muscle synergies (Delis et al., 2013). The decoding method focuses on task discrimination capabilities of the synergies and provides a more quantitative metric to validate the synergies extracted (Alessandro et al., 2013). In this study, we utilized this metric to evaluate the neural synergy extracted from the motor cortex and showed that the single-trial decoding accuracy of the synergy was as good as the original neural data in both tasks. Moreover, we also demonstrated that the synergy amplitudes are also functionally related to the neuronal firing rate. Therefore, the neural synergy constitutes not only a low dimensional but also a functional representation of the original neural dynamics. In addition, the advantage of a task decoding metric is also revealed in the dropping neuron test, in which, the decoding performance of the synergy decreased as the number of neurons decreased, but the VAF still remained the same. This indicates that the synergies do not always account for task-related variations even when the VAF is above 90%: task-decoding metric assesses the capability of synergy complementary to VAF. In total, the single-trial task decoding metric is a quantitative way of evaluating the functional role of synergy, using which we have demonstrated the validity of the neural synergy extracted from the monkey brain. Behavior-independent and behavior-specific muscle synergies have been observed previously in frogs within a large behavioral repertoire - swimming, jumping and walking (D'Avella and Bizzi, 2005). Here similar shared and specific structures were also found in neural synergies of the monkey motor cortex. The 23

interpretation of the results is straightforward in the perspective of the undergoing neuronal activities. In Fig. 5B and previous study (Cao et al., 2013), we found that some neurons could be tuned to the parameters of both tasks, while other neurons only encoded one of the two. The dual/triple-encoding property of single neuron was also observed in other tasks in primates (Pearce and Moran, 2012) and invertebrates (Jing et al., 2004), and was summarized as ‘multitasking’ principle of neural ensemble physiology (Nicolelis and Lebedev, 2009). Therefore, the neuronal activity itself has the similar (shared) and dissimilar (specific) firing patterns between two tasks, which might be one of the basis for shared and specific synergies. On the other hand, the neural activities underlying different tasks can be viewed as different cell assemblies in the network level, i.e., a small set of connected neurons formed by learning (Harris, 2005; Buzsaki, 2010; Huyck and Passmore, 2013). As the reaching and grasping movements are highly coupled in daily life, the two cell assemblies controlling reaching and grasping movements should largely overlap with each other, which might be the neural basis of the shared and specific synergies. In sum, there are two ways to generate various movements in the perspective of synergies. For movements in the same task (i.e., different locations in reaching task or different objects in grasping task), although the synergies extracted are similar to each other (Fig. 1C), the coefficients are distinct and highly classifiable (Fig. 2D and 4C). The same synergy modulated by different coefficients would also generate various movements. For movements between tasks, even the synergies themselves are not shared completely (Fig. 4A); combining the specific ones would also generate distinct movements. 24

Since the organization of synergies has been observed in behavioral, muscular and now neural level, it is reasonable to wonder about the relationship between synergies in the brain and in the peripheral system. We know that the activation of kinematic synergy would give functional movement (Thakur et al., 2008), the activation of muscle synergy would result in kinematic or kinetic goal (D'Avella et al., 2003; Ting and Macpherson, 2005), and the activation of the neural system would evoke muscle synergies (Overduin et al., 2012). However, the relationship between neural and muscle synergies has rarely been addressed so far. One of the barriers might be that the mapping between brain and muscle and/or muscle and kinematic are more nonlinear and dynamic even after synergy reduction, given the distributed hierarchical organization in the motor control system (Hamilton and Grafton, 2007). One recent study applied synergy decomposition method on neural data and muscular data simultaneously and found some resemblance between neural and muscle synergy (Overduin et al., 2015). They found that the dimensionalities of the neural and muscle synergy are similar and the activation synergy coefficients are correlated with each other. Most importantly, the onset latency of the neural synergy is leading around 70 ms than muscle synergies, indicating a possible causal relationship between two types of synergies (Overduin et al., 2015). The synergy technique reduces the dimensionality of both neural and muscular data, but the relationship between them is still not apparent, which might need a more complicated model or cooperation with other neural control mechanisms (Bizzi and Cheung, 2013). 25

Acknowledgements This work is supported by National Basic Research Program of China (No. 2013CB329506), International Science & Technology Cooperation Program of China (NO. 2014DFG32580), Natural Science Foundation of China (NO. 31371001, 61473261, 61572433, 31627802), and the Fundamental Research Funds for the Central Universities. The authors thank Mr. Yimin Shen and Mr. Shenglong Xiong for assistance in the animal experiments. The authors also thank Prof. Anna W. Roe for manuscript reading.

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Figure Legend Fig.1 Synergies extracted from neural activity when grasping four objects. A, Diagram for grasping task. One object was fixed in the center of the panel vertically placed in front of the monkey. The four objects used in grasping task and their corresponding grip type were showed on the right. B, The positions of the arrays implanted were illustrated for monkey B03 (filled square) and B04 (open square). AS, arcuate sulcus; CS, central sulcus. C, Each row represents the first four synergies extracted from the neural activities (number of neurons, 44) when grasping the corresponding objects showing on the leftmost. The VAF values of reconstruction are also displayed for each object on the left. The number on the top of each subplot in the second to fourth row indicates the correlation coefficient with the synergies of the first row in the same column. Double asterisk indicates significant level (p < 0.01). Fig.2 Grasping task decoding with neural synergies. A, VAF values as a function of the number of synergies extracted for both monkey. Light traces show the VAFs for individual sessions and the thick ones indicate the average. B, The remaining coefficients after synergy extraction in one representative session was reduced into 3-dimension space (from 6 in this example) using PCA method to visualization. Each dot shows one grasping trial and different colors are for different object grasping. C, Decoding accuracy of the coefficients after synergy extraction is plotted as a function of the number of synergies. The convention is the same with A. The horizontal line indicates the chance level of 25%. D, The decoding accuracies with synergy or original data are comparable each other for both monkeys. Each dot represents individual 32

session and the bar plots indicate the mean values. The number of synergies used was the same as in A and C, i.e., the least number when VAF exceeds 90%. Fig.3 Decoding with dropping neuron numbers. A, The gray synergies are extracted from neural ensemble with a number of neurons dropped (10 in this example). The dark synergies are extracted from the original completely neural ensemble. The same 10 synergies that was removed are highlighted in orange at the bottom. The comparison of them shows significant similarity (** p < 0.01). B, Averaged correlation between original synergy and dropping synergy as a function of the amplitude of dropped synergies (a.u.). The error bars show the 95% confidence level. C, The percentage of significant similar pairs was plotted as a function of the percentage of dropped neurons. The error bars show the 95% confidence level. D, The decoding accuracies with synergy and original neural data are plotted as a function of decreasing number of neurons for one session of Monkey B03. The shade shows the 95% confidence level. E, The decoding accuracies with synergy for all the sessions are plotted against decoding accuracies with original neural data. The right diagonal is showed in blue. The red dots show the data used in D. F, G, The same with D and E, but for monkey B04. Fig.4 Reaching task decoding with individual synergies. A, Diagram for reaching task. The four same objects are fixed in the four corner positions on the board vertically placed in front of the monkey. The monkey is trained to grasp one of them according to the light cue. B, Averaged VAF values and decoding accuracies as a function of the number of synergies in reaching task. C, The decoding accuracy using synergy and 33

original data is compared in reaching task for both monkeys. The dots indicate individual sessions and the bar plot represents the mean. D, The decoding accuracies of all individual coefficients (n = 4, VAF > 90%) and neurons (n = 31) in one example session of monkey B03. E, The maximum (best) decoding accuracy achieved by synergy coefficient and individual neurons in all the grasping and reaching sessions. F, The average decoding accuracy achieved by synergy coefficient and individual neurons in all the sessions. ** indicates significant difference (p < 0.01). Fig.5 Shared and specific synergies and corresponding neuronal activity. A, Four pairs of synergies are shared (significant similar, ** P < 0.01) between grasping and reaching tasks in one representative session. The remaining 5 synergies (right) cannot find a matched pairs between each other, which are specific to each task. The two red arrows indicate two specific synergy components in reaching task. The data are from one sample session of Monkey B04. B, The synergy amplitudes for each neuron are linearly correlated with their average firing rates in both reaching and grasping tasks. Each dot represents one neuron and the data from all the sessions are plotted for both Monkey B03 and B04. The r values show the significant linear fits (**p < 0.01). C, The neural firing rates of three representative neurons (Neuron1, Neuron2 and Neuron3 in each row) are plotted along the time course of movement (aligned to Light ON and OFF event) in both reaching and grasping tasks (each column). Different colors represent different reaching directions and target objects in reaching and grasping tasks, respectively. The data are averaged across all the trials in one representative session of B03. The mutual information values between each neuron 34

and the task are also indicated in each subplot.

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Highlights Synergies are extracted from neural data during reaching to grasp movement. Different reaching or grasping movements share similar neural basis, i.e., neural synergies. The validity of neural synergy is demonstrated for its functional role in the tasks. Shared and specific synergies are identified between reaching and grasping tasks.

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