Central and sensory contributions to the activation and organization of muscle synergies during natural motor behaviors

Abstract

Previous studies have suggested that the motor system may simplify control by combining a small number of muscle synergies represented as activation profiles across a set of muscles. The role of sensory feedback in the activation and organization of synergies has remained an open question. Here, we assess to what extent the motor system relies on centrally organized synergies activated by spinal and/or supraspinal commands to generate motor outputs by analyzing electromyographic (EMG) signals collected from 13 hindlimb muscles of the bullfrog during swimming and jumping, before and after deafferentation. We first established that, for both behaviors, the intact and deafferented data sets possess low and similar dimensionalities. Subsequently, we used a novel reformulation of the non-negative matrix factorization algorithm to simultaneously search for synergies shared by, and synergies specific to, the intact and deafferented data sets. Most muscle synergies were identified as shared synergies, suggesting that EMGs of locomotor behaviors are generated primarily by centrally organized synergies. Both the amplitude and temporal patterns of the activation coefficients of most shared synergies, however, were altered by deafferentation, suggesting that sensory inflow modulates activation of those centrally organized synergies. For most synergies, effects of deafferentation on the activation coefficients were not consistent across frogs, indicating substantial interanimal variability of feedback actions. We speculate that sensory feedback might adapt recruitment of muscle synergies to behavioral constraints, and the few synergies specific to the intact or deafferented states might represent afferent-specific modules or feedback reorganization of spinal neuronal networks.

Figures

Figure 1.

Hypotheses and concepts invoked in this study. A, Different possible roles of sensory feedback in a modular motor system. Each black square represents a CNS neuronal network specifying the muscle activation balance with in a muscle synergy, and each circle represents the motoneuron pool for a muscle. A1, In this scheme, synergies are organized centrally and activated by spinal and/or supraspinal commands. Sensory feedback can modulate their activation but plays no role in specifying the activation balances within the synergies. A2, Centrally organized synergies specifically accessible by sensory inflow. These synergies may be responsible for the corrective responses seen during limb perturbations (Forssberg, 1979; Kargo and Giszter, 2000a). A3, Centrally organized synergies acting as templates for motor output generation. Each muscle within each synergy is independently regulated by afferent signals. A4, Feedback reorganization of CNS neuronal assemblies, resulting in altered synergy structures after deafferentation. It is possible that, when feedback is available, some interneurons capable of generating motor patterns under the deafferented condition are not activated, whereas some other interneurons requiring sensory signals for activation are recruited instead. This scheme is similar to the model put forth by Pearson (2004). B, The concept of synergy bases spanning a subspace. Shown in the diagram is a hypothetical case with EMG data collected from three muscles. The EMG data are described by two different sets of synergy bases, indicated by solid and dashed arrows, respectively. Despite having different structures, these two synergy sets span the same 2 d subspace within the 3 d EMG space and can describe the EMG data equally well.

Figure 2.

Examples of EMG data collected from intact and deafferented locomotor behaviors. Shown are EMG data collected from 13 hindlimb muscles of frog 1, high-pass filtered (50th-order FIR; cutoff of 50 Hz) to remove motion artifacts, and subsequently rectified. A, EMGs of five consecutive swimming cycles before dorsal root transection. B, Two different swimming episodes after deafferentation, each of which comprises three consecutive cycles. C, EMGs of a representative jump before deafferentation. D, EMGs of a deafferented jump. C and D are divided into three phases for ease of visual inspection. Notice that the deafferented EMGs appear to involve the same muscle groups embedded within the intact EMGs. Comparison of the onset times of AD, ST, IP, and PE in phase a of C with those in phase a′ of D suggests that there may be synergies specific to the intact or deafferented state. For more detailed descriptions, see Results.

Figure 3.

Stage I analysis of swimming EMGs before and after deafferentation. A, B, In analysis stage I, we extracted and cross-validated 1-10 synergies from the intact and deafferented data sets, respectively, and the quality of fit of the synergies to the validation data was quantified as R2 values. To assess the R2 expected by chance, we also repeated the extraction and validation procedures on the same training and testing data sets but with the samples of each muscle in both independently and randomly shuffled. We then estimated the correct number of intact and deafferented synergies by fitting decreasing portions of the actual R2 curve to straight lines, and the first point on the curve for which the portion approximates a straight line (as indicated by a small mean squared error in the linear fit) was selected as the correct number of synergies. A, Cross-validation R2 curves for the intact swimming data set of frog 3. Solid curve, R2 curve from original data (mean ± SD; n = 20). Dashed curve, R2 curve from shuffled data (mean ± SD; n = 20). The black arrow indicates the correct number of intact synergies estimated by our procedure, and the dashed straight line is its corresponding linear fit. B, Cross-validation R2 curves for the deafferented swimming data set of frog 3. Same key as A. C, D, Assessing similarity between the intact and deafferented synergies using two approaches. C, The degree of overlap between the subspaces spanned by the intact and deafferented synergy sets, respectively, is indicated by the average ssd values (▪; n = 20 × 20 = 400). The average ssd values expected by chance were computed by calculating principal angles between shuffled synergy sets (×; mean ± 5 × SD after 20 trials of shuffling). D, The number of stage I intact synergies for which the actual structures were preserved after deafferentation was indicated by the average nss values (▪; n = 20 × 20 = 400). The average nss values expected by chance were computed by calculating scalar products between shuffled synergy sets (×; mean ± 5 × SD after 20 trials of shuffling).

Figure 4.

Examples of swimming synergies from analysis stage I. A, B, A pair of intact and deafferented swimming synergy sets of frog 2.Each of the six intact synergies was matched to the deafferented synergy giving the best-matching scalar product, its actual value shown between the two panels. C, The cosines of the six principal angles between the intact and deafferented subspaces defined by the synergies shown in A and B. Notice that, whereas only three of six best-matching scalar products are >0.90 in A and B, the cosines of four of six principal angles are >0.90. This indicates that, although only three synergies are apparently similar to one another, the two subspaces actually share a four-dimensional common subspace. Therefore, the nss by itself potentially underestimates the degree of similarity between the intact and deafferented synergies. For additional discussion, see Results.

Figure 5.

Determining the numbers of synergies in analysis stage II. In our stage II model, three numbers of synergies, Nin*, Nde*, and Nsh*, need to be specified. Our strategy for estimating the correct values of these three parameters was to extract synergies with Nin, Nde = 3... 8 (i.e., 6 × 6 = 36 combinations of Nin and Nde), and, at each of these combinations, estimate Nsh* for that particular combination of Nin and Nde. We then proceeded to estimate Nin* and Nde* by examining the difference between the stage II and stage I R2 values. A, Estimating the correct number of shared synergies in frog 2 swimming given Nin, Nde = 6. As Nsh was progressively increased, the dimensionality of the subspace shared between the specific synergies decreased. The correct number of shared synergies can be estimated by noting the point at which the specific synergies do not share a common subspace. Shown in A is the mean shared dimensionality between the specific synergies (mean ± SD; n = 20). The shared dimensionality at the maximum Nsh was defined to be zero, because at this point there are no specific synergies to be compared. The smallest Nsh with a shared dimensionality falling below 0.25 was selected to be Nsh*. B, Estimating the correct total numbers of intact and deafferented synergies (frog 2 swimming). For each of the intact and deafferented data sets, wecomputed an R2 value for the stage II solution at each combination ofNin and Nde and calculated the absolute difference between the stage I cross-validation R2 and the stage II R2. The intact and deafferented differences were then summed together. We reason that the correct stage II estimates of Nin* and Nde* are the combination for which the R2 values come closest to the stage I values. In B, this R2 difference across the 36 combinations of Nin and Nde is depicted as a grayscale map: the darker the color, the more R2 difference at a combination. The combination with the minimum R2 difference is marked with an asterisk.

Figure 6.

Swimming synergies of all frogs (analysis stage II). Shown in this figure are the stage II synergies of the extraction repetition with the highest R2 of the four frogs. The synergies shared between the intact and deafferented data sets are labeled Sh, synergies specific to the intact data set are labeled Insp, and synergies specific to the deafferented data set are labeled Desp. Synergies active only during the extension phase of the swimming cycle are marked with e on their right sides, and those active in both the extension and flexion phases are marked e+f. All synergies shown in this figure were clustered into six classes (S1-S6), and the class of each synergy is marked on its left side. The sign of the moment arms (MA) around the hip, knee, and ankle joints of the 13 muscles included in this study are listed below the synergies of frog 3 and frog 4 (e, extensor action; f, flexor action). Moment arm signs are based on results of Kargo and Rome (2002) and González (2003).

Figure 7.

Stage I analysis of jumping EMGs before and after deafferentation. A, B, We applied the same stage I procedure as applied to the swimming EMGs (described in the legend for Fig. 3 A, B) to our jumping EMGs. A, Cross-validation R2 curves for the intact jumping data set of frog 4. Solid curve, R2 curve from original data (mean ± SD; n = 20). Dashed curve, R2 curve from shuffled data (mean ± SD; n = 20). The black arrow indicates the correct number of intact synergies estimated by our procedure, and the dashed straight line is its corresponding linear fit. B, Cross-validation R2 curves for the deafferented jumping data set of frog 4. Same key as A. C, D, Assessing similarity between the intact and deafferented synergies using two approaches. C, The degree of overlap between the subspaces spanned by the intact and deafferented synergy sets, respectively, is indicated by the average ssd values (▪; n = 20 × 20 = 400). The average ssd values expected by chance were computed by calculating principal angles between shuffled synergy sets (×; mean ± 5 × SD after 20 trials of shuffling). In all frogs, the actual mean ssd is well above its corresponding baseline value (p < 0.01). D, The number of stage I intact synergies with actual structures that were preserved after deafferentation was indicated by the average nss values (▪; n = 20 × 20 = 400). The average nss values expected by chance were computed by calculating scalar products between shuffled synergy sets (×; mean ± 5 × SD after 20 trials of shuffling). In all frogs, the actual mean nss is higher than its corresponding baseline value (p < 0.01).

Figure 8.

Jumping synergies of all frogs (analysis stage II). Shown in this figure are the stage II synergies of the extraction repetition with the highest R2 of the four frogs. The synergies shared between the intact and deafferented data sets are labeled Sh, synergies specific to the intact data set are labeled Insp, and synergies specific to the deafferented data set are labeled Desp. Synergies active only during the extension phase of jumping are marked with e on their right sides; those active only during the flexion phase are marked with f, and those active in both phases are marked e+f. All synergies shown in this figure were clustered into six classes (J1-J6), and the class of each synergy is marked on its left side. The sign of the moment arms (MA) around the hip, knee, and ankle joints of the 13 muscles included in this study are listed below the synergies of frog 3 and frog 4 (e, extensor action; f, flexor action). Moment arm signs are based on results of Kargo and Rome (2002) and González (2003).

Figure 9.

Reconstructing the original EMGs with synergies and their coefficients. The intact and deafferented EMG examples shown in Figure 2, C and D, are reconstructed using the stage II synergies extracted from the jumping EMGs of frog 1 (Fig. 8). The original EMG data, filtered and integrated (for filtering and integration parameters, see Materials and Methods), is indicated by thick black lines, and the time-varying coefficients of the synergies are shown below the EMGs. The reconstruction of the motor pattern is superimposed onto the original EMGs. The colors composing the reconstruction match the colors of the coefficients such that the colors reflect the respective contribution of each synergy to the reconstruction at each time point. Note that synergy Desp1 (yellow) is deafferented specific; thus, by definition, it contributes to the reconstruction of only the deafferented EMG episode. For more discussion, see Results.

Figure 10.

Sensory feedback can uncouple or couple the activation of synergies. We calculated the Pearson's correlation coefficient (r) peak coefficient amplitudes of every pair of shared synergies, for each behavior, each of the extension and flexion phases, and each of the intact and deafferented conditions. A, The flexion-phase peak coefficient amplitudes of synergies J3 and J6 (frog 1). The intact samples are shown as crosses (+), and the deafferented samples are shown as circles (○). This is an example of a pair of synergies showing an increase in correlation after deafferentation (intact r = 0.3156; deafferented r = 0.6736). The straight line represents the least-squares fit to the deafferented samples. B, Interpretation of the results shown in A. Each black square represents a central neuronal network coding for a muscle synergy or a network coordinating the activation of multiple synergies; each black circle represents the motoneuronal pool of a particular muscle. The finding that the deafferented samples are highly correlated suggests that J3 and J6 (frog 1) are coordinated by central mechanisms upstream of the synergies. However, the smaller correlation with afferents intact suggests that one or both synergies might be modulated by sensory feedback. For more discussion, see Results. C, The extension-phase peak coefficient amplitudes of synergies S1 and S2 (frog 3). Again, the intact samples are shown as crosses (+), and the deafferented samples are shown as circles (○). This is an example of a pair of synergies showing a decrease in correlation after deafferentation (intact r = 0.7065; deafferented r = 0.5011). The straight line represents the least-squares fit to the intact samples. D, Interpretation of the results shown in C. That the deafferented r is relatively small suggests that S1 and S2 are controlled as two relatively independent modules by feedforward commands, but the high correlation observed under the intact state implies that sensory afferents might help to couple the activation of these two synergies during swimming extension.