Behavioral/Systems/CognitiveCentral and Sensory Contributions to the Activation andOrganization of Muscle Synergies during NaturalMotor BehaviorsVincent C. K. Cheung,1,2Andrea dAvella,3MatthewC. Tresch,4and Emilio Bizzi2,51Division of Health Sciences and Technology, Harvard Medical School and Massachusetts Institute of Technology, and 2Department of Brain and CognitiveSciences and McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, 3Department ofNeuromotor Physiology, Istituto di Ricovero e Cura a Carattere Scientifico, Fondazione Santa Lucia, 00179 Rome, Italy, 4Department of BiomedicalEngineering, Northwestern University and Rehabilitation Institute of Chicago, Chicago, Illinois 60208, and 5European Brain Research Institute, 00143Rome, ItalyPrevious studies have suggested that the motor system may simplify control by combining a small number of muscle synergies repre-sented as activation profiles across a set of muscles. The role of sensory feedback in the activation and organization of synergies hasremained an open question. Here, we assess to what extent the motor system relies on centrally organized synergies activated by spinaland/or supraspinal commands to generate motor outputs by analyzing electromyographic (EMG) signals collected from 13 hindlimbmuscles of the bullfrog during swimming andjumping, before andafter deafferentation. We first establishedthat, for bothbehaviors, theintact 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 anddeafferented data sets. Most muscle synergies were identified as shared synergies, suggesting that EMGs of locomotor behaviors aregenerated primarily by centrally organized synergies. Both the amplitude and temporal patterns of the activation coefficients of mostshared synergies, however, were altered by deafferentation, suggesting that sensory inflow modulates activation of those centrallyorganized synergies. For most synergies, effects of deafferentation on the activation coefficients were not consistent across frogs, indi-cating substantial interanimal variability of feedback actions. We speculate that sensory feedback might adapt recruitment of musclesynergies to behavioral constraints, and the few synergies specific to the intact or deafferented states might represent afferent-specificmodules or feedback reorganization of spinal neuronal networks.Key words: deafferentation; locomotion; frog; feedback; afferent; non-negative matrix factorization; central patterngenerators; jumping;swimmingIntroductionMotorcoordinationcanbeunderstoodasthemechanismbywhichtheCNScontrolsthemanydegreesof freedomintheredundant musculoskeletal system to achieve purposeful behav-iors (Bernstein, 1967). Previous experiments have suggested thatthe CNS may simplify control by activating a small number ofmodules (Grillner, 1985; Bizzi et al., 1991; Stein and Smith, 1997;Tresch et al., 2002), formulated as muscle synergies, or activationprofiles across a set of muscles, the linear combination of whichcan generate diverse motor patterns (Tresch et al., 2002; Hart andGiszter, 2004; Ting and Macpherson, 2005). Previous studies ex-amining this hypothesis have relied on animals with intact affer-ents(Saltiel etal., 2001)orhavecharacterizedpredominantlyfeedforward, ballistic movements, suchas cutaneous reflexes(Tresch et al., 1999) and kicking (dAvella et al., 2003). The role ofsensory feedback in synergy organization and activation has thusremained an open question.The simplest role of feedback in such a modular motor systemwould be to modulate activation of centrally organized synergies(seeFig. 1A1). Spinal and/or supraspinal neuronal networkswouldspecifytheparticularmuscleactivationbalanceofeachsynergy, withsensory feedback playing no role inits specification.It is well established that complex electromyographic (EMG) pat-terns during many behaviors can be generated without afferents(Grillner, 1975; Delcomyn, 1980). Force field primitives of thespinalizedfrogbeforeandafterdeafferentationwerealsoverysimilar (Loeb et al., 1993), suggesting the presence of modulesdirectly activated by central commands.Received July 29, 2004; revised May 19, 2005; accepted May 20, 2005.This work was supported by the Chyn Doug Shiah Memorial Fellowship and the Schoemaker Foundation Fellow-ship (V.C.K.C) and by National Institutes of Health/National Institute of Neurological Disorders and Stroke GrantsNS09343andNS39865(E.B.). Wegivespecial thanks toEmeryN. Brownfor his encouragement andconstant supportof this work. We also thank Steve G. Massaquoi andPhilippe Saltiel for many helpful discussions, SimonOverduinforcommentsonthismanuscript, MargoCantor for technical support, andCharlottePotakfor administrativeassistance.Correspondence should be addressed to Andrea dAvella, Department of Neuromotor Physiology, Istituto diRicovero e Cura a Carattere Scientifico, Fondazione Santa Lucia, Via Ardeatina 306, 00179 Rome, Italy. E-mail:a.davella@hsantalucia.it.DOI:10.1523/JNEUROSCI.4904-04.2005Copyright 2005 Society for Neuroscience 0270-6474/05/256419-16$15.00/0The Journal of Neuroscience, July 6, 2005 25(27):6419 6434 6419In addition, there may be synergies organized within the CNSbut specifically accessible only by feedback signals (see Fig. 1A2).This possibility is suggested by the corrective responses observedduring limb perturbations in the cat (Forssberg, 1979) and frog(KargoandGiszter, 2000a). Alternatively, sensoryinflowmaymodifyactivationsofindividualmuscleswithinasynergy(seeFig. 1A3) or contribute to specification of synergies by reorganiz-ing interneuronal networks (Pearson, 2004) (see Fig. 1A4). Yetanother possibility is that synergies arise as emergent propertiesof the entire neural network comprising both central circuits andfeedbackloops. Whether differences betweenafferentedanddeafferented EMGs (Grillner and Zangger, 1984; Kargo and Gisz-ter, 2000b) reflect afferent modulationof centrally organizedsyn-ergies, recruitment of afferent-specific synergies, feedback reor-ganizationofexistingsynergies, oremergentpropertiesofthemotor circuitry has remained unclear.In this study, we assess to what extent the CNS relies on cen-trallyorganizedsynergiesaccessiblebycentralcommands(seeFig.1A1)togeneratemotoroutputsforlocomotorbehaviors.We collectedhindlimb EMGs fromintact frogs during swimmingand jumping, before and after ipsilateral deafferentation. Then,weexploitedanon-negativefactorizationalgorithm(LeeandSeung, 1999) to identify synergies shared by, and synergies spe-cific to, the intact and deafferented data sets. Our analyses indi-cate that, to a large degree, both data sets can be explained by a setof shared synergies. We conclude that a small number of centrallyorganized synergies, activated by central commands but modu-lated by sensory feedback, plays a predominant role in generatingcomplex motor patterns for locomotor behaviors.Materials and MethodsSurgeries and experimental procedure. Four adult bullfrogs (Rana cates-beiana, 270590g)werestudied. Oneachfrog, threesurgerieswereperformed on separate days. In all surgeries, the frog was anesthetizedwithice andtricaine (ethyl 3-aminobenzoate methanesulfonate, 0.1mg/g; Sigma, St. Louis, MO) injected into the left iliac lymph sac. In thefirst surgery, the dorsal nerve roots were exposedby rongeuring vertebrae56 and cauterizing the dura mater. In the second surgery, bipolar EMGelectrodes were implanted into 13 muscles in the right hindlimb, includ-ing the following (according to the nomenclature of Ecker, 1971): rectusinternus major (RI), adductor magnus (AD), semimembranosus (SM),semitendinosus (ST), iliopsoas (IP), vastus internus (VI), rectus femorisanticus (RA), gastrocnemius (GA), tibialis anticus (TA), peroneus (PE),biceps (or iliofibularis) (BI), sartorius (SA), and vastus externus (VE). Allwires were passedsubcutaneously to a 37-pind-subconnector, securedtothe back skin with a custom-made plastic platform and Nexaband glue(VeterinaryProductsLaboratories,Phoenix,AZ).Thecrimpcontactswere insulated by epoxy. The third surgery was a deafferentation proce-dure: dorsal roots 79 on the right side were severed at the level of thesixth vertebra. After some of the surgeries, antibiotic (enrofloxacin, 103mg/g; Bayer, Shawnee Mission, KS) was also administered subcutane-ously for prophylaxis.Patterns of EMG during unrestrained swimming and jumping, per-formed in a specially designed tank and cage, respectively, were collectedafterelectrodeimplantationandbeforedeafferentationduringonetotwo experimental sessions conducted over 13 d. After deafferentation,anotheronetotwosessionsofEMGdatawerecollectedover13d.Betweensurgeries andexperimental sessions, the frog was allowedat least18 h for recovery. Episodes of both in-phase and out-of-phase swimming(NauwelaertsandAerts,2002)wereeitherspontaneousorelicitedbylightly touching the hindlimbs with a plastic rod. During all swimmingtrials, removable light-bodied Permlastic (Kerr USA, Romulus, MI) wasalso used to provide additional insulation of the EMG-electrode connec-tor against water. For the jumping responses, a few of them were spon-taneous, but most of them were elicited by lightly scratching the skin ofeither hindlimb with a pair of sharp forceps. All swimming and jumpingexperimental trials were also videotaped, and the EMGand video record-ings wereapproximatelysynchronizedbyadigital counter. Correctplacement of electrodeswasconfirmedinpostmortemexaminationsafter all experimental procedures. All procedures were approved by theMassachusetts Institute of Technology Committee on Animal Care be-fore experimentation.Data collection and preprocessing. Continuous EMG signals, both in-tact and deafferented, were amplified (gain of 10,000), bandpass filtered(101000Hz)throughdifferentialalternatingcurrentamplifiers,anddigitized (1000 Hz). Using custom software written in Matlab (Math-Works,Natick,MA),theEMGtracesweremanuallyparsedintoseg-ments, each containing a single jump or consecutive swimming cycles.The parsed data were then high-pass filtered [window-based finite im-pulse response (FIR); 50th order; cutoff of 50 Hz] to remove any motionartifacts.Subsequently,thedatawererectified,low-passfiltered(FIR;50th order; 20 Hz) to remove noise, and integrated over 10 ms intervals.The EMGs were not normalized before further analyses.AnalysisstageI: extractingmusclesynergiesseparately. WemodeledEMGsofeachbehaviorasthelinearcombinationofasetofmusclesynergies, each represented as anactivationprofile across the 13 recordedmuscles, and activated by a time-varying activation coefficient. We hy-pothesized that the synergies and their activations are non-negative andare identifiable by applying the non-negative matrix factorization(NMF)algorithm(Lee and Seung, 1999) to the EMGdata. The NMF algorithmisa reasonable method for extracting synergies because, as a result of itsnon-negativity constraint imposed on both the synergies and their acti-vations, the synergies extracted tend to be sparse rather than holistic and,thus, morephysiologicallyinterpretable(LeeandSeung, 1999). Also,unlike methods such as the independent component analysis (Bell andSejnowski, 1995; Hyvarinen and Oja, 2000), NMF does not rely on theassumption that synergy activations are statistically independent; hence,NMF is more compatible with the previous finding that activations ofmultiple synergies might be correlated (Saltiel et al., 2001).Our synergy analyses were divided into two stages. In stage I, our goalsweretoestimatethenumberofintactanddeafferentedsynergies,thenumber of synergies shared by the two data sets, as well as the amount ofvariance representing systematic variation within each data set. We con-sideredtheintactanddeafferenteddatasetsseparatelyandextractedsynergies fromeach of them. Stated formally, our model in stage I has thefollowing mathematical form:dt a1Ncatwa, (1)where, for the 13 recorded muscles, d(t) represents the EMGdata at timet,waisa13-dimensionalvectordenotingtheathsynergy,ca(t)isthetime-varying scalar activation coefficient for wa, and N is the total num-berofsynergiesextracted.NotethatEquation1canalsobestatedinmatrix notation as DWC, where D, W, and Care the data, synergy, andcoefficient matrices, respectively. In stage I, the above model was appliedseparately to each of the intact and deafferented data sets, for each of theswimming and jumping behaviors.The intact and deafferented synergies and their activation coefficientswereextractedbyimplementingtheNMFmultiplicativeupdaterules(LeeandSeung, 2001)inMatlab. Undertheseupdaterules, at eachiteration, new estimates of W and C were calculated by multiplying thecurrent estimates by factors depending on D and current estimates of WandC. This iterative estimationprocedure was stoppedafter convergenceof the reconstruction error DWC, defined here as having 20 consec-utive iterations with a change of EMG reconstruction error 0.01%.The NMF algorithm requires the number of synergies extracted to bespecified before application of the algorithm. Because such informationwas not known a priori, for each behavior, we extracted 110 synergiesfromsubsets of the intact and deafferented data sets, respectively. At eachnumber of synergies, we performed cross-validation (Browne, 2000) as astep for estimating the correct number of synergies (see also next section,Estimating the numbers of intact and deafferented synergies for stage I).In our cross-validation procedure, the jumping or swimming EMG seg-6420 J. Neurosci., July 6, 2005 25(27):6419 6434 Cheung et al. Central/Sensory Contributions to Muscle Synergiesmentswerefirstdividedintofourequalpartitions. Threeofthefourpartitions were pooled together, and synergies were extracted from thispooled data set. These synergies were thenvalidated by fitting themto theremaining unused partition (using NMF with W held fixed and C up-dated across iterations), and the quality of fit was quantified as an R2value. Thiscross-validationprocedurewasrepeated20timesateachnumber of synergy, eachtime withdifferent randomWandC(uniformlydistributedbetween0and1)initiatingNMF, andwithdifferentran-domly selected data partitions for cross-validation.For each number of synergies, a baseline cross-validation R2was alsocomputedbyrepeatingtheextraction-validationproceduredescribedaboveonthesametrainingandtestingEMGsegmentsbutwiththesamplesofeachmuscleineachdatasetindependentlyandrandomlyshuffled. An actual cross-validation R2higher than this baseline cross-validation R2suggests that systematic variation in the data set is capturedby the synergies.Estimating the numbers of intact and deafferented synergies for stage I. Incross-validation, whenmore synergies are extractedthannecessary,some synergies may capture random fluctuations rather than systematicvariation within the extraction data set. In such a case, the quality of fit ofthe synergies to the validation data is expected to be reduced. Thus, thecorrect number of intact or deafferented synergies (denoted by Nin* andNde* for the intact and deafferented data sets, respectively) can be esti-mated by plotting the cross-validation R2against the number of syner-gies extracted. A point beyond which additional increase in the numberof synergiesdecreasestheR2, oratwhichtheslopeof theR2curvechanges sharply, indicates that anyadditional synergies beyondthatpoint capture only noise and/or a small additional fraction of data vari-ation. Thispointshouldthen, inprinciple, bethecorrectnumberofsynergies.However, ourpreviousexperiencewithcross-validationR2curvesfromfrog EMGs during natural behaviors has shown that the slope of thecurve usually decreases gradually as the number of synergies extractedincreases, making it difficult to determine the number of synergies byvisual inspection of the R2curve. To estimate Nin* and Nde* objectively,wefitportionsoftheR2curvetostraightlinesusingstandardleast-squares technique, first including all data points on the curve in the fit,and then the 2nd to 10th points, and so on until only the 9th and 10thpoints were included. As the range of the fit moves toward the right sideofthecurve, themeansquarederror(MSE)ofthefitisexpectedtodecrease because the R2curve approaches a straight line as the number ofsynergies extracted increases. The correct number of synergies can thenbe estimated as the first point on the R2curve at which the linear fit of allpoints from that point to the 10th point produces a small MSE. In otherwords, thischosenpointrepresentsthepointatwhichtheR2curveplateaus to a straight line. In our analyses, the first point on the R2curvefor which the corresponding MSE falls below 105was selected as thecorrectnumberofsynergiesforstageI(seeFig. 3A, B, arrows). Thiscriterion resulted in numbers of synergies corresponding to qualitativeinspection of the R2curves but performed this identification objectively.Two approaches of assessing synergy similarity for stage I. After estimat-ing the correct numbers of synergies, we proceeded to assess similaritybetween the intact and deafferented synergy sets. The intact and deaffer-ented synergy sets each define a lower-dimensional subspace within the13-dimensional EMGspace. The intact and deafferented synergies canbesimilar in the weaker sense that their subspaces overlap each other or inthe stronger sense that the actual synergy bases of the two synergy sets aresimilar. Thus, it is possible that the intact and deafferented synergy setsare similar only in their subspaces but not in their actual synergies. Forexample, in Figure 1B, the two sets of synergies, represented by solid anddashedarrows,respectively,aredifferentintheirstructures(i.e.,theypointtodifferentdirectionsintheEMGspace),buttheynonethelessspan the same two-dimensional subspace within the three-dimensionalEMG space. Comparing the intact and deafferented subspaces as well asthestructures of thesynergies underlyingthem, wecanthenassesswhether the NMF algorithm is capable of finding only the shared sub-space or the actual synergy bases spanning the shared subspace as well.For the first approachof similarity assessment, we evaluated the degreeof overlap between the two subspaces spanned by the intact and deaffer-ented synergies, respectively, by computing a set of principal angles usingan algorithm described by Golub and Van Loan (1983, pp 428430). If,for instance, the intact and deafferented subspaces share a three-dimensional common subspace, the cosines of the first three principalangles should be close to one. We refer to the number of principal angleswith cosines 0.90 as the shared subspace dimensionality (ssd) betweentwosynergysets. Iftheintactanddeafferentedsubspacescompletelyoverlapeachother, thenssdisthenumberof intact ordeafferentedsynergies, whichever number is smaller.The second, more stringent method of assessing similarity betweentheintact and deafferented synergies evaluates the degree of similarity be-tweentheactualsynergyvectorsusingscalarproducts.Wefirstcom-puted the best-matching scalar products between the intact and deaffer-ented synergy sets. The vector normof each synergy was first normalizedto one. Each synergy in the intact set was then matched to the synergy inthe deafferented set giving the maximumscalar product between them. Iftwo or more synergies from one set were matched to the same synergy inthe other set, we isolated all multiply-matched and unmatched synergies,andthetotal scalarproductofeverypossiblematchingcombinationbetween those two sets of remaining synergies was calculated; the com-binationgiving the maximumtotal scalar product was thenconsideredtobe the best match. We refer to the number of best-matching scalar prod-ucts0.90asthenumberofsharedsynergies(nss), representingthenumber of synergies that are similar between the intact and deafferentedsynergy sets.Because extraction of synergies was repeated 20 times, there were 20 20 400 intact and deafferented synergy sets for comparison, and thus,400 ssd and 400 nss values. The average ssd and nss values were calculatedfor each animal and each behavior.Baseline synergy similarity for stage I. The procedures described aboveestimatethenumberof shareddimensions(ssd)andthenumberofshared synergies (nss) between intact and deafferented data sets. To as-sess the significance of these values, we computed baseline ssd and nssvaluesusingarandomizationprocedure.Foreachofthe400pairsofintact-deafferented synergy sets, two sets of random synergies compris-ing Nin* and Nde* vectors were generated by random shuffling of theFigure 1. Hypotheses and concepts invoked in this study. A, Different possible roles of sen-sory feedback ina modular motor system. Eachblack square represents a CNS neuronal networkspecifyingthe muscle activationbalance withina muscle synergy, andeachcircle represents themotoneuron pool for a muscle. A1, In this scheme, synergies are organized centrally and acti-vated by spinal and/or supraspinal commands. Sensory feedback can modulate their activationbut plays no role in specifying the activation balances within the synergies. A2, Centrally orga-nizedsynergies specifically accessible by sensory inflow. These synergies may be responsible forthe 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, Feedbackreorganization of CNS neuronal assemblies, resulting in altered synergy structures after deaf-ferentation. It is possible that, when feedback is available, some interneurons capable of gen-eratingmotor patterns under the deafferentedconditionare not activated, whereas some otherinterneurons requiringsensorysignals for activationarerecruitedinstead. This schemeis similarto the model put forthby 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. TheEMG data are described by two different sets of synergy bases, indicated by solid and dashedarrows, respectively. Despite having different structures, these two synergy sets span the same2 d subspace within the 3 d EMG space and can describe the EMG data equally well.Cheung et al. Central/Sensory Contributions to Muscle Synergies J. Neurosci., July 6, 2005 25(27):6419 6434 6421vector components in the original intact and deafferented synergy sets,respectively. The ssd and nss values between these two sets of randomsynergies were then determined. Calculation of baseline ssd or nss, be-tweeneveryintact-deafferentedpairof synergysets, wasrepeated20times, each time with the vector components shuffled anew. For eachrepetition, the average baseline ssd and nss across the 400 pairs of synergysets were also calculated.Analysis stage II: simultaneous extraction of shared and data set-specificsynergies. In the stage I procedures described above, synergies were ex-tracted separately from the intact and deafferented data sets. The sub-spaces spanned by these synergies were then compared with one another,and the similarity between the synergies themselves was assessed. How-ever, thereareanumberof potential shortcomingswiththestageIanalysis.First, although the stage I intact and deafferented subspaces may sharea common subspace, the synergies extracted fromeither data set may notactuallyspanthiscommonsubspace, becausethiscommonsubspacedoes not necessarily coincide with the subspace defined by any subset ofthe extracted synergies. To see this, consider a three-dimensional spacedefined by three synergies, represented as vectors along the x-, y-, andz-axes, respectively. Suppose further that the common subspace is a two-dimensional tilted plane within this three-dimensional space. Obviously,this plane is not spanned by any two of the three synergies. In such a case,thecompositionsofthetwosynergiespreservedafterdeafferentationremain unclear from the stage I extraction results.Second, separate extraction of synergies performed in stage I might beexpected to underestimate the number of intact or deafferented synergies(Nin* or Nde*). If the activation of two synergies tended to covary withinone of the two data sets, NMF would tend to combine these synergiestogether into a single synergy. If in the other data set these two synergieswere activated independently, NMF would identify them correctly forthis data set. Thus, if, for instance, two of five intact synergies tended tocovary in the deafferented data set, the stage I estimates of Nin* and Nde*would be 5 and 4, respectively, whereas the correct estimates should be 5and 5. Therefore, the stage I estimates of data set dimensionalities areexpected to underestimate the true number of intact and deafferentedsynergies.Beyond this problem in identifying the correct numbers of synergies,such covariation of synergies might also result in an underestimation ofthenumberofsynergiespreservedafterdeafferentation.Again,if,forinstance, twosynergies tendedtocovary inthe deafferentedbut not intheintact data set, the combined deafferented synergy uncovered by NMFwouldbeseenasdissimilartoitstwocorrespondingintactsynergies.Thus, if there were five synergies in fact shared between the two data sets,the nss value would indicate that only three synergies were shared.Toaccountforsuchpossibilities,wethereforeperformedasecondstageofanalysis, usinganovel reformulationoftheNMFalgorithm.Information from both data sets is used simultaneously in this reformu-lation, allowing both for synergies shared between the data sets and forsynergies observed specifically within one data set or another. We let theNMF algorithm search, by itself, for synergies common to both data setswhile at the same time allowing the algorithmto isolate synergies relevantonly to each data set. Our model in stage II can be stated formally asfollows:dint a1Nshcash_intwash a1Ninspcainsptwainsp;(2)ddet a1Nshcash_detwash a1Ndespcadesptwadesp,where the superscripts in and de stand for intact and deafferented,respectively, and sh, insp, and desp stand for synergies shared bythe two data sets, synergies specific to the intact data set, and synergiesspecific to the deafferented data set, respectively. Note that the coeffi-cients, cash_in(t) and cash_de(t), although activating the same synergy wash, infactcontributetotheintactanddeafferentedEMGdata,respectively.The number of intact or deafferented synergies in the stage II model isthenthesumof thenumberof sharedsynergiesandthenumberofsynergies specific to each data set (i.e., N for intact data set NshNinsp; and Nfor deafferented data set NshNdesp). Converting Equa-tions 2 into their matrix forms, we haveDallDinDde Wall Call;WallWshWinspWdesp,CallCsh_inCsh_deCinsp00 Cdesp . (3)Intheaboveequations,forthecolumnsinCallcorrespondingtotherange of the deafferented data, the rows for the intact-specific synergiesweresettozero, becausebydefinitiontheydonotcontributetothegeneration of the deafferented data. Similarly, in the Callcolumns usedfor reconstructing the intact data, the rows for the deafferented-specificsynergies were set to zero.We extracted shared and specific synergies simultaneously from equalnumbers of intact and deafferented EMG segments using the NMF algo-rithm. As a result of its multiplicative update rules, if the initial conditionof any matrix component is zero, the estimate of that matrix componentafter any number of iterations remains zero. Thus, the only manipulationnecessaryforstageIIistosettherelevantmatrixcomponentsoftheinitial Callto zero (as indicated in Eq. 3) while choosing random values(uniformlydistributedbetween0and1)forall thenonzeroentries.TheseinitialconditionsensurethatthespecificsynergiesinWallwillexplain only one of the two data sets.Estimating the numbers of intact and deafferented synergies for stage II.As in stage I, the stage II procedure we described requires the number ofsynergies to be specified before application of the algorithm. To estimatethe number of shared synergies (Nsh*), stage II synergies were extractedwith Nshprogressively increasing from 1 to the smaller of Ninor Nde. AsNshincreases, the degree of overlap between the subspaces defined by theintact-specific anddeafferented-specific synergies is expectedtode-crease, because every time Nshis increased by one, another feature sharedbetween the intact and deafferented EMGs is taken up as a shared syn-ergy. Thus, Nsh* is indicated by the Nshat which there is minimal overlapbetween the subspaces spanned by the intact- and deafferented-specificsynergies. The degree of this overlap between the specific synergies wasquantified as a dimensionality value by finding the number of principalangles with cosines 0.90. The smallest Nshwith a mean shared dimen-sionalitybetweenthespecificsynergies(averagedacross20extractionrepetitions)below0.25wastakentobethecorrectnumberofsharedsynergies. This threshold of 0.25 ensures that, at the chosen Nsh*, sharingbetweenthespecificsynergiesisobservedinlessthanfiveof the20extraction runs.The above procedure estimates the correct number of shared synergiesgiven particular total numbers of intact and deafferented synergies, com-prising shared synergies and synergies specific to each data set. To esti-mate the correct total numbers of synergies, we used the results of thestage I analysis, choosing the total numbers of intact and deafferentedsynergies to be those numbers that gave an R2in the stage II analysisclosest to the R2obtained in the stage I analysis (see Fig. 5B). This R2criterion guarantees that the stage II solution explains the intact anddeafferenteddatasetsaswell asthestageIsolution, whiledirectlyidentifying the synergies that are shared between intact and deaffer-ented data sets.Clustering synergies of different frogs. After selecting the stage II num-bers of synergies, for each frog and behavior, the synergy solution for theextraction repetition giving the highest overall R2was selected for addi-tional analyses. For each behavior, the shared and data set-specific syn-ergies from the four frogs were pooled together and grouped into classesby cluster analysis. The Matlab statistics-toolbox functions pdist(Minkowski option; p3), linkage(wardoption), andclusterwereapplied sequentially to the pooled synergy matrix. The number of clus-ters was determined by selecting the minimum number of clusters par-titioningthesynergiessuchthatnotwosynergieswithineachclusterwere from the same frog.Analyzing the coefficients of the stage II shared synergies. For each frogand each behavior, the activation coefficients of the stage II shared syn-6422 J. Neurosci., July 6, 2005 25(27):6419 6434 Cheung et al. Central/Sensory Contributions to Muscle Synergiesergies before and after deafferentation were analyzed. The coefficients ofeachsharedsynergyweremultipliedbythemagnitudeof that synergyvector,so that the coefficients represent activation of unit vectors. AMatlab graph-ical user interface was then built for manual parsing of the coefficient timetraces into extension and flexion phases, so that the extension phase of eachcycle would correspond to a burst of activation of the extension synergies.The peakcoefficient amplitudes of eachphase andof eachsharedsynergy, before andafter deafferen-tation, were compared (t test, 0.05).Effects of deafferentation on the duration ofsynergyactivationwerecharacterizedbyfirstfitting the coefficient time trace of each phase toa Gaussian function using standard nonlinearleast-squaresmethod(BatesandWatts,1988,pp 3242). The time points corresponding tomean 2 SD of the Gaussian function weredefined to be the offset and onset of the activa-tion burst, respectively. For the extensionphases, if the burst offset as defined above laywithintheflexionphaseafterthat extensionphase, the burst offset was redefined to be thelasttimepointofthatextensionphase. Like-wise, for the flexion phases, if the burst onset asdefinedabovelaywithintheadjoiningexten-sionphase, theonsetwasredefinedtobethefirst time point of that flexion phase. The coef-ficient burst duration of each phase and of eachsharedsynergy, beforeandafterdeafferenta-tion, werethencompared(ttest, 0.05).Only the phases in which the Gaussian fit ex-plained the original coefficient time trace withR260%wereincludedinourstatisticsofburst duration.Patternsofcorrelationbetweensynergies. Toinvestigate whether the activationof twoormore synergies are coordinated by centralmechanisms or sensory feedback, we computedthe Pearsons correlation coefficient (r) be-tween the peak coefficient amplitudes of everypair of sharedsynergies for eachof thetwophases, for each of the intact and deafferentedconditions, andforeachbehavior. Statisticalsignificance of the difference between the intactr andthedeafferentedr was determinedbyFishers r-to-Ztransformationmethod[0.01 (Hays, 1994, pp 647651)].ResultsFromfour frogs, we collected and analyzedEMGsignalsfrom13hindlimbmusclesduring intact swimming (91, 315, 311, and200cyclesfromfrogs14, respectively),deafferented swimming (56, 205, 169, and140), intactjumping(97, 47, 76, and50jumps), anddeafferentedjumping(172,60, 22, and 56).Synergies underlying intact anddeafferented behaviors: visualinspection of EMG dataFigure 2 shows representative examples ofEMG segments, all collected from frog 1,during intact and deafferented swimmingand jumping. In Figure 2A, there are fiveconsecutive swimming cycles. Notice that,in this episode, the muscles SM, GA, andVE tend to be coactivated as a group andthattheirpeakcycleamplitudesstayrelativelyconstantacrossthese five cycles. The muscles RI, AD, and IP tend to be coactivewith the SM-GA-VE group, but their peak cycle amplitudes fromthe first to last cycles decrease gradually. More importantly, thesame two muscle groups seemto underlie the deafferented swim-Figure 2. Examples of EMG data collected from intact and deafferented locomotor behaviors. Shown are EMG data collectedfrom 13 hindlimb muscles of frog 1, high-pass filtered (50th-order FIR; cutoff of 50 Hz) to remove motion artifacts, and subse-quently rectified. A, EMGs of fiveconsecutiveswimmingcycles beforedorsal root transection. B, Twodifferent swimmingepisodesafter 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 deafferentedEMGs 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 Dsuggests that there may be synergies specific to the intact or deafferented state.For more detailed descriptions, see Results.Cheung et al. Central/Sensory Contributions to Muscle Synergies J. Neurosci., July 6, 2005 25(27):6419 6434 6423ming EMG patterns in Figure 2B as well. Both the SM-GA-VEand RI-AD-IP groups are present in the two episodes of Figure2B, but the amplitude of the latter group appears to be signifi-cantlysmallerinthesecondepisodethaninthefirstepisode.Thus, visual inspection of EMG data suggests that some of theswimming muscle synergies may be preserved after deafferenta-tionandthattheiractivationacrosstimemaybedifferentiallymodulated.Shown in Figure 2C is an EMG segment collected during anintact jump. It is divided into three phases, labeled a, b, and c, forease of visual inspection. Phase a is characterized by activation ofall 13 muscles. In phase b, we notice EMG bursts in SM, IP, BI,and SA. Phase c, however, features a prominent ST with someactivity in TA and PE. A similar tripartite structure is also seen indeafferentedjumpingEMGs, exemplifiedbyFigure2D. Thethree phases in Figure 2D, labeled a, b, and c, are analogous tophases a, b, and c of Figure 2C, respectively. Despite the fact thatb has a longer duration than b, the SM-IP-BI-SA group activein phase b is also noticeable in the deafferented episode but inboth b and c. Note also that the TA and PE bursts in c havelarger peakamplitudes andlonger durations thanthoseinphase c. It appears therefore that, in jumping, at least some ofthe synergy structures remain invariant after deafferentation,although the amplitudes and time courses of their activationmay be affected.A more detailed comparison between phase a (Fig. 2C) andphase a (Fig. 2D) shows that the relative onset times of somemuscles were altered after dorsal root transection. In phase a, STactivity precedes that of all other muscles; in phase a, however,the onset times of ST, AD, IP, and PE seem to be the same. Thus,itispossiblethatthestructuresofsomemusclesynergiesarechanged after deafferentation.The above observations motivatedus tohypothesize thatswimming and jumping EMGs can be generated by linear com-bination of muscle synergies represented as time-invariant acti-vation profiles across the 13 muscles and to expect that most ofthese synergies are preserved after feedback deprivation. We fur-ther hypothesized that the structures of the muscle synergies, aswell as their corresponding time-varying activation coefficients,can be identified by applying the NMF algorithm(Lee and Seung,1999; Tresch et al., 1999) to the EMG data. As explained in Ma-terials and Methods, for each of the swimming and jumping be-haviors, we systematically assessed the number of synergies pre-served after deafferentation and identified the structures of thepreserved synergies in two stages of analyses. In stage I, we ex-tracted synergies from the intact and deafferented data sets sepa-ratelyandassessedsimilaritybetweenthetwosynergysets.Our comparison in stage I led us to realize some limitations ofextracting synergies fromindividual data sets separately,prompting us to analyze our data in a second analytical stagein which we extracted synergies from pooled intact and deaf-ferenteddata. Wewill first illustrateourtwo-stagemethodusingtheswimmingEMGs as anexample. Theswimmingsynergieswill thenbepresented, followedbytheanalyticalresults of the jumping EMGs.Muscle synergies underlying swimming before andafter deafferentationAnalysis stage I: intact and deafferented swimming EMGs havelow and similar dimensionalitiesWefirst estimatedthenumberof synergiesintheintact anddeafferented data sets by extracting 110 synergies from each ofthem. Extraction results at each number of synergies were cross-validated (see Materials and Methods). The quality of fit in thevalidation step was quantified as an R2value.Figure 3, A and B, shows plots of R2against the number ofswimmingsynergiesextractedforboththeintactanddeaffer-ented data sets of frog 3 (solid curve; mean SD; n 20), alongwith the R2levels expected if the data sets were not generated bymuscle synergies (shuffled data, dashed curve; mean SD; n 20). It is clear that, inboth the intact and deafferented conditions,90% of variance in the original swimming EMGs is explainedby five to six synergies (i.e., R2 90%), whereas by chance, thesame amount of variance is explained only when 10 synergies areused. This result indicates that both the intact and deafferentedswimmingdatasetspossesslowandsimilardimensionalities.Similar results were obtained from the other three frogs.To systematically compare synergies of intact swimming withthose of deafferented swimming, the numbers of synergiespresent in the intact and deafferented data sets (denoted by Nin*and Nde*, respectively) need to be determined. Ideally, the pointon the R2curve at which the slope changes sharply indicates sucha number. As exemplified by the R2curve of Figure 3A, however,theslopesofmostofourR2curvesdecreasegraduallyasthenumberofsynergiesextractedincreases,makingestimationofNin* and Nde* by visual inspection of the R2curves difficult.Nonetheless, all of our R2curves doseemtoapproachastraight line as the number of synergies extracted increases (Fig.Figure 3. Stage I analysis of swimming EMGs before and after deafferentation. A, B, Inanalysis stage I, we extracted and cross-validated 110 synergies from the intact and deaffer-ented data sets, respectively, and the quality of fit of the synergies to the validation data wasquantified as R2values. To assess the R2expected by chance, we also repeated the extractionand validation procedures on the same training and testing data sets but with the samples ofeach muscle in both independently and randomly shuffled. We then estimated the correctnumber of intact and deafferented synergies by fitting decreasing portions of the actual R2curve to straight lines, and the first point on the curve for which the portion approximates astraight line (as indicated by a small mean squared error in the linear fit) was selected as thecorrect number of synergies. A, Cross-validation R2curves for the intact swimming data set offrog 3. Solid curve, R2curve from original data (mean SD; n 20). Dashed curve, R2curvefromshuffleddata(meanSD; n20). Theblackarrowindicates thecorrect number of intactsynergies estimatedbyour procedure, andthedashedstraight lineis its correspondinglinear fit.B, Cross-validation R2curves 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 syn-ergy sets, respectively, is indicated by the average ssd values (f; n 20 20 400). Theaverage ssd values expected by chance were computed by calculating principal angles betweenshuffled synergy sets (; mean 5 SD after 20 trials of shuffling). D, The number of stageI intact synergies for which the actual structures were preserved after deafferentation wasindicatedby the average nss values (f; n 20 20 400). The average nss values expectedby chance were computed by calculating scalar products between shuffled synergy sets (;mean 5 SD after 20 trials of shuffling).6424 J. Neurosci., July 6, 2005 25(27):6419 6434 Cheung et al. Central/Sensory Contributions to Muscle Synergies3A, B). ThisobservationpromptedustoestimatethecorrectnumberofsynergiesbyfittingdecreasingportionsofeachR2curvetostraightlinesandchoosingthefirstpointatwhichastraight line fits the portion of the R2curve well (for more details,see Materials and Methods). In Figure 3, Aand B, the point of thebest estimate of the number of synergies on the R2curve is indi-catedbyanarrow;itscorrespondinglinearfitisshownasadashedstraightline.Forfrog3swimming(Fig.3A, B),thenNin* and Nde* are 5 and 6, respectively, confirming that theintact anddeafferenteddimensionalitiesaresimilarfortheswimming EMGs.Table 1 summarizes our estimates of the numbers of synergiesin frogs 14. With the exception of frog 1 (the frog with the leastamount of swimming data collected), in all frogs, Nin* and Nde*are either the same or differ only by one, further suggesting thatthe number of synergies underlying intact swimming is similar tothatunderlyingdeafferentedswimming. NotealsoinTable1that, in all frogs, a high percentage of data variance (90%) isexplainedby the chosennumbers of synergies, indicating that ourestimatesofNin*andNde*provideagooddescriptionoftheobserved data.Analysis stage I: assessing similarity between the intact anddeafferented swimming synergiesTo assess whether the intact and deafferented swimming syner-gies are similar, we first assessedthe degree of overlapbetweenthesubspaces spanned by the sets of Nin* intact synergies and theNde*deafferentedsynergies (ssd), respectively, bycomputingprincipal angles (Golub and Van Loan, 1983).Figure 3C shows the mean ssd between the intact and deaffer-ented swimming synergies of each frog (f; n 20 20 400)and the corresponding mean baseline ssd between random syn-ergies (; mean 5 SD after 20 trials of shuffling). It is clearthat, in all four frogs, the actual ssd lies well above the baseline ssd( p 0.01), suggesting that there is a nontrivial degree of inter-section between the intact and deafferented synergy subspaces.Rounding the mean ssd values, we see that, on average, three ofsix, four of six, four of five, and two of four dimensions of theintact synergy subspaces of frogs 1 through 4, respectively, aresharedwiththeir correspondingdeafferentedsynergysub-spaces. Our analyses thus far indicate that NMF succeeded inidentifying swimming synergies before and after deaf-ferentationsharingacommonsubspace, althoughthetwosubspaces do not completely overlap each other.We then directly compared intact and deafferented synergiesbycalculatingscalarproductsbetweentheintactanddeaffer-entedsynergysets, estimatingthenssbetweentheintact anddeafferented synergy sets.Figure 3D shows the mean nss values of frogs 14 (f; n 20 20 400) together with their baseline nss values computedby matching randomly shuffled synergies (; mean 5 SDafter 20 trials of shuffling). In all frogs, the nss value is clearlyabove its baseline ( p 0.01), indicating that the sharing of syn-ergies is well above that expected by chance. Rounding the meannss of each frog, we see that, on average, two of six, three of six,two of five, and two of four synergies extracted from the intactdata sets of frogs 14, respectively, are similar to those extractedfrom deafferented data sets. Note that, in all frogs except frog 4,the mean nss is smaller than the mean ssd. Therefore, extractingintact anddeafferentedswimmingsynergies separately, NMFfound synergies sharing a common subspace, but the shared syn-ergies themselves do not span the entire shared subspace, as illus-trated in the following example.The shared stage I synergies do not span the entire sharedsubspace: illustrative examplesShown in Figure 4, A and B, is an example of intact and deaffer-ented synergy sets identified for frog 2 swimming. The topmostsynergy pair, In.1/De.1, is the pair with the highest scalar product(value shown between panels), and the bottommost pair, In.6/De.6, is the pair with the smallest. As can be seen, synergies In.1and In.2 are almost identical in structure to De.1 and De.2, re-spectively. Synergy In.6, with its prominent STcomponent, is notfound in the deafferented synergy set, although both De.3 andDe.5havemoreSTactivationthanIn.3andIn.5, respectively.Similarly, although synergy De.6 (SMand VE) is not found in theintact synergy set, In.4 has more prominent SM and VE than itscorresponding De.4. These observations already suggest that, al-though only three of the six scalar products are 0.90, the degreeof similarity between the two sets of synergies shown in Figure 4,Aand B, may well be more than three. Examination of the cosinesof the six principal angles between the two synergy sets of Figure4, A and B, is consistent with such a possibility. As illustrated inFigure 4C, the cosines of the first four angles are close to one,suggesting that the intact and deafferented synergy subspaces de-finedby the synergies inFigure 4, AandB, share a four-dimensional common subspace. In other words, although In.1In.3(or De.1De.3) are three of the synergies spanningthiscommon subspace, there is at least one more common synergyembedded within the subspace defined by In.4In.6, or that de-fined by De.4De.6.Together, the results in Figure 3, Cand D, and the examples inTable 1. Estimating the number of synergies shared between the intact and deafferented synergy sets in two stages of analysesFrog/ behaviorStage I Stage IINin* Nde* ssd nssCV R2(%)Nin* Nde* Nsh* Ninsp* Ndesp*R2(%)Intact Deaff Intact DeaffFrog 1, swim 6 4 3.46 2.43 89.0 91.3 6 4 4 2 0 88.4 91.5Frog 2, swim 6 6 4.13 3.44 91.2 89.7 6 6 6 0 0 91.1 90.2Frog 3, swim 5 6 3.83 1.66 88.3 92.0 5 6 5 0 1 87.4 91.5Frog 4, swim 4 4 2.43 1.56 86.3 91.7 5 4 4 1 0 87.0 92.4Frog 1, jump 4 4 2.18 1.45 91.3 90.4 4 5 4 0 1 90.6 90.0Frog 2, jump 4 4 2.10 1.01 90.3 90.6 4 5 4 0 1 89.6 89.9Frog 3, jump 4 5 2.06 1.01 90.1 91.1 4 5 3 1 2 89.2 90.9Frog 4, jump 5 4 2.00 0.95 90.9 89.7 6 4 4 2 0 91.1 88.8In analysis stage I, we compared the intact and deafferented (Deaff) synergies using two approaches: by assessing the degree of overlap between the subspaces spanned by the intact and deafferented synergies (ssd), respectively, and bycalculating scalar products to estimate the nss before and after deafferentation. In analysis stage II, the number of synergies preserved after deafferentation is reflected by the Nsh* value at our estimates of the correct total numbers of intactand deafferented synergies (Nin* and Nde*). The R2values listed refer to the percentage of data variance explained by the listed numbers of synergies (averaged across 20 extraction repetitions). CV, Cross-validation.Cheung et al. Central/Sensory Contributions to Muscle Synergies J. Neurosci., July 6, 2005 25(27):6419 6434 6425Figure 4 suggest strongly that (1) there aresharedsynergiesunderlyingboththein-tact and deafferented swimming data setsand (2) at this analytical stage, NMF un-coverssynergiessharingacommonsub-space but is unable to find an explicit set ofnon-negative synergies spanning thissharedspace. Moreover, asdescribedinMaterialsandMethods,combinationsofsynergies within one data set would be ex-pected to result in stage I underestimatingthe number of intact or deafferented syn-ergies, as well as the number of synergiespreserved across deafferentation. This un-derestimation is a consequence of the factthat stage I identifies muscle synergies byextractingthemseparatelyforeachdataset. Inthe stage II analysis describedbelow,weattemptedtoovercometheselimita-tions to better assess the number of sharedsynergiesunderlyingboththeintactanddeafferented EMG data sets.Analysis stage II: extracting shared anddata set-specific swimming synergiesInthesecondstageof our analyses, weused a different synergy extraction method to obtain an explicitset of synergies spanning the subspace shared by intact and deaf-ferented EMGs. In stage II, we pooled these two data sets togetherand exploited the NMF update rules to search for synergies com-mon to both data sets while simultaneously allowing the algo-rithm to isolate any synergies specific to either data set.In stage II, three parameters, the number of intact, deaffer-ented, and shared synergies, have to be specified before applica-tion of the NMF algorithm. Figure 5A is an example from frog 2swimming, illustratingour methodof estimatingthecorrectnumber of shared synergies (Nsh*) given particular numbers ofintact and deafferented synergies (both of which were set to be sixin this example). As the number of shared synergies (Nsh) wasprogressively increased, the dimensionality of the subspaceshared between the specific synergies also decreased as expected.Ascanbeseen, theshareddimensionalityfell belowourpre-definedthresholdof0.25onlywhensixsharedsynergieswereextracted. Thus, in this example, if there were six intact and sixdeafferentedswimmingsynergies, all sixintactsynergieswerepreserved after deafferentation.On the other hand, the correct total numbers of intact (Nin*)anddeafferented(Nde*) synergies for stage II, eachof whichcom-prises both shared and specific synergies, were estimated by com-paring the stage II R2values at different combinations of totalnumbers of intact and deafferented synergies with the R2valuesobtained in stage I (see Materials and Methods and legend to Fig.5).Figure5BillustratesthedifferencebetweenthestageIandstage II R2values as the total numbers of intact and deafferentedsynergies were, respectively, varied fromthree to eight. At each ofthese 36 (6 6) combinations, the number of shared synergieswas estimated using the method illustrated in Figure 5A. For frog2 swimming (Fig. 5B), the stage II R2values came closest to thestage I R2values when six intact synergies and six deafferentedsynergies were extracted. Together, results of Figure 5, A and B,thus suggest that, for frog 2 swimming, the stage II estimates ofNin*, Nde*, and Nsh* are 6, 6, and 6, respectively; that is, there aresix synergies underlying both the intact and deafferented swim-mingdatasets, all sixof whicharepreservedafter feedbackdeprivation.We applied the above methods to all frogs to determine thenumber of total and shared synergies, and our results are shownFigure4. Examplesof swimmingsynergiesfromanalysisstageI. A, B, Apair of intact anddeafferentedswimmingsynergysetsof frog2. Eachof thesixintact synergieswasmatchedtothedeafferentedsynergygivingthebest-matchingscalar product, itsactual valueshownbetweenthetwopanels. C, Thecosines of thesixprincipal angles betweentheintact anddeafferentedsubspaces definedbythesynergiesshown 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 sixprincipal angles are 0.90. This indicates that, although only three synergies are apparently similar to one another, the two subspacesactually share a four-dimensional common subspace. Therefore, the nss by itself potentially underestimates the degree of similaritybetweenthe intact anddeafferentedsynergies. 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 esti-mating the correct values of these three parameters was to extract synergies with Nin, Nde3. . . 8 (i.e., 6 6 36 combinations of Ninand Nde), and, at each of these combinations,estimate Nsh* for that particular combination of Ninand Nde. We then proceeded to estimateNin* and Nde* by examining the difference between the stage II and stage I R2values. A,Estimating the correct number of shared synergies in frog 2 swimming given Nin, Nde6. AsNshwas progressively increased, the dimensionality of the subspace shared between the spe-cific synergies decreased. The correct number of shared synergies can be estimated by notingthe point at which the specific synergies do not share a common subspace. Shown in A is themean shared dimensionality between the specific synergies (mean SD; n 20). The shareddimensionality at the maximum Nshwas defined to be zero, because at this point there are nospecific synergies to be compared. The smallest Nshwith a shared dimensionality falling below0.25was selectedto be Nsh*. B, Estimatingthe correct total numbers of intact anddeafferentedsynergies (frog2swimming). For eachof theintact anddeafferenteddatasets, wecomputedanR2value for the stage II solutionat eachcombinationof NinandNdeandcalculatedthe absolutedifference between the stage I cross-validation R2and the stage II R2. The intact and deaffer-ented differences were then summed together. We reason that the correct stage II estimates ofNin* and Nde* are the combinationfor whichthe R2values come closest to the stage I values. InB, this R2difference across the 36 combinations of Ninand Ndeis depicted as a grayscale map:the darker the color, the more R2difference at a combination. The combination with the min-imum R2difference is marked with an asterisk.6426 J. Neurosci., July 6, 2005 25(27):6419 6434 Cheung et al. Central/Sensory Contributions to Muscle Synergiesin the right column of Table 1. In all frogs, the degree of sharingbetweentheintactanddeafferentedsynergysetssuggestedbystage II (as indicated by Nsh*) is greater than that suggested bystage I (as indicated by ssd) by one to two synergies. More impor-tantly, if we compare the total numbers of intact and deafferentedsynergies (Nin* and Nde*) determined in stage I with those esti-mated in stage II (Table 1), we see that the stage I numbers are thesame as the stage II numbers in all but one instance (Nin* of frog4swimming). Therefore, theincreasedsharingdiscoveredinstage II is not a consequence of explainingthe data sets with more synergies. This ob-servation further supports that the sharedsynergiesidentifiedinstageII representunderlying structures shared by the intactand deafferented data sets rather than be-ing just the result of the algorithm averag-ing out structures specific to each data set.Most swimming synergies are preservedafter deafferentationFigure 6 shows all the shared and data set-specific synergies from the extraction rep-etition with the highest overall R2in eachfrog. As can be seen, for frogs 14, respec-tively, four of six, six of six, five of six, andfour of five synergies appear as shared syn-ergies, suggesting that most synergies un-derlyingintact swimmingare preservedafter deafferentation. Therefore, the swim-ming EMGs are predominantly generatedbycentrallyencodedsynergiesaccessibleby spinal and/or supraspinal commands.Inspection of synergies in Figure 6 fur-ther suggests that many of the swimmingsynergies are similar across frogs. For in-stance, in both frog 1 and frog 2, a sharedsynergy with TA and PE activation can beseen, and all frogs possess a shared synergywithaprominent STcomponent. Somesynergies appear to be frog specific, how-ever. For instance, synergy Sh.4 of frog 4,withitsprominentVEcomponent, doesnot resemble any synergy from the otherthree frogs.Inlightofthesimilarityoftheswim-ming synergies across frogs, we proceededto group them into classes by cluster anal-ysis. We progressively increased the num-berofclustersuntil notwosynergiesineach cluster were from the same frog. Sixclusters of shared swimming synergies(denotedbyS1S6)wereidentified;fourof them(S1S4) werefoundinat leastthree of the four frogs. The principal mus-cles involved in these six groups of syner-gies are summarizedbelow. Refer toFigure6 for a summary of the functions of eachmuscle listed (as reflected by the signs ofthe moment arms).Synergy S1 is an extension synergycomprising the ankle extensor GA(allfrogs)andthehipextensorsRIandAD(frogs 3 and 4). Synergy S2 is another ex-tension synergy comprising SM, VE, andGA, extensors of the hip, knee, and ankle, respectively (frogs 1, 3,and 4). Synergy S3 includes the hip extensor/knee flexor, ST (allfrogs)andthehip-kneeflexorBI(frogs3and4). SynergyS4includes two knee extensors/ankle flexors, TA and PE (frogs 1, 2,and4), aswell asthehip-kneeflexorSA(frog2). SynergyS5features the hip flexor IP and the hip-knee flexor BI (frogs 1 and2). Synergy S6 features twohipflexors/knee extensors, RAandVE(frogs 2 and 3).Figure 6. Swimming synergies of all frogs (analysis stage II). Shown in this figure are the stage II synergies of the extractionrepetitionwiththehighest R2of thefour frogs. Thesynergies sharedbetweentheintact anddeafferenteddatasets arelabeledSh,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 inboth the extension and flexion phases are marked ef. All synergies shown in this figure were clustered into six classes (S1S6),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 jointsof 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 Gonzalez (2003).Cheung et al. Central/Sensory Contributions to Muscle Synergies J. Neurosci., July 6, 2005 25(27):6419 6434 6427Both S1 and S2 were active only during the extension phase ofthe swimming cycle. All the rest of the synergies, except the S4 offrog 4, were active in both the extension and flexion phases of theswimming cycle.To summarize our analyses of the swimming EMGs, in ourstage I analysis, we established that both the intact and deaffer-ented swimming data sets possess similar and low dimensionali-ties (Fig. 3A, B; Table 1). The intact and deafferented synergy setsidentifiedinstageIshareacommonsubspace(Figs. 3C, 4C),indicating that at least some synergies are preserved after deaffer-entation. To tackle some potential limitations of stage I (see Ma-terials and Methods), we proceeded to our stage II analysis (Fig.5). The degree of sharing was found to be higher in stage II (Table1), suggesting that our stage II analysis canbetter assess the degreeof sharing through combining information from different datasets.MostofthestageIIsynergieswereidentifiedassynergiessharedbetweentheintactanddeafferenteddatasets(Fig. 6),suggesting that most synergies underlying the swimming behav-ior are centrally encoded modules activated by spinal and/or su-praspinal commands. Sixclassesof swimmingsynergieswereidentified(Fig. 6), two of which(S1 andS2) were activatedduringthe extension phase only.Muscle synergies underlying jumping before andafter deafferentationWeappliedthesametwo-stagemethodillustratedaboveforswimming EMGs to the data collected during jumping to assesswhether the same conclusions hold for the jumping behavior.Stage I analysis of jumping EMGs: the intact and deafferenteddata sets possess similar low dimensionalitiesOurstageIanalysesofthejumpingEMGsshowthat,liketheswimming data sets, the intact anddeafferentedjumping data setspossess low and similar dimensionalities. Shown in Figure 7, Aand B, are the stage I cross-validation R2curves for frog 4 jump-inganalogoustothoseshowninFigure3,AandB,forfrog3swimming. We see that, in both the intact and deafferented datasets, four to five synergies are sufficient to explain 90% of datavariance. The R2curves resulting from extracting synergies fromthe unshuffled data sets (solid curve; mean SD; n 20) also liewell above those expected by chance (shuffled data, dashed curve;meanSD; n20), confirmingthat actual datastructureswithin the data sets are captured by our synergies. By fitting theR2curves to straight lines, Nin* and Nde* for frog 4 jumping weredetermined to be 5 and 4, respectively (Fig. 7A, B, arrows). Sim-ilar results were obtained from the other three frogs (Table 1).We also compared the similarity between the subspaces de-fined by each synergy set (ssd), and between the actual synergiesin each set (nss). Although the nss values indicate that, for all fourfrogs, on average only one intact jumping synergy also appears asa deafferented synergy (Fig. 7D), our subspace analysis suggeststhat the intact and deafferented synergy subspaces share a two-dimensional subspace (Fig. 7C). As in swimming, the differencebetween the ssd and nss values implies that, in stage I, NMF findsonly a common subspace shared between the intact and deaffer-ented jumping synergies but not all of the synergies spanning thisshared subspace.Stage II analysis of jumping EMGs: most jumping synergies arepreserved after deafferentationWe then proceeded to stage II and determined Nin*, Nde*, andNsh* for eachfrog by pooling the intact anddeafferentedjumpingdata sets together. As summarized in Table 1, our stage II analysessuggest that four of four, four of four, three of four, andfour of sixintact jumping synergies for frogs 14, respectively, are preservedafter deafferentation, and reconstruction of the original EMGsusingthesenumbers of synergies yields R2values of 90%.Therefore, the hypothesis that most synergies underlying the in-tactEMGsarepreservedafterfeedbackdeprivationholdsnotonly for swimming but for jumping as well. All of the shared anddata set-specific jumping synergies of each frog from the extrac-tionrepetitionwiththehighestoverall R2aresummarizedinFigure 8.For frog 3, if we compare its intact-specific synergy (Insp.1)withoneofitsdeafferented-specificsynergies(Desp.1),weseethat both contain activation of similar muscles (RI, SM, VI, RA,GA, and VE) but indifferent balances betweenthese muscles. Theintact-specificsynergy(Insp.1)hasrelativelymoreGAandVEthan its deafferented counterpart (Desp.1) but less RI and SM.One interpretation of this observation is that sensory feedbackmay fine-tune the activation of individual muscles within a syn-ergy, thereby altering the muscle activation balance profile of thesynergy (Fig. 1A3). A similar interpretation may account for thesimilarity and difference between frog 4s Sh.1 and Insp.1 (Fig. 8).As in our analysis of the swimming synergies, we grouped ourjumping synergies into classes by cluster analysis. We found sixclasses of shared jumping synergies (denoted by J1J6), four ofwhich (J1J4) were found in at least three of the four frogs. Theirprincipal muscles are summarized below. Refer to Figure 8 for asummary of the functions of each muscle listed (as reflected bythe signs of the moment arms).Synergy J1 is an extension synergy found in all frogs compris-ingallmajorextensorsofthehindlimb,RI,AD,andSM(hipextensors), VI, RA, VE, TA, and PE (knee extensors), as well asFigure 7. Stage I analysis of jumping EMGs before and after deafferentation. A, B, We ap-plied the same stage I procedure as applied to the swimming EMGs (described in the legend forFig. 3 A, B) to our jumping EMGs. A, Cross-validation R2curves for the intact jumping data set offrog 4. Solid curve, R2curve from original data (mean SD; n 20). Dashed curve, R2curvefromshuffleddata(meanSD; n20). Theblackarrowindicates thecorrect number of intactsynergies estimatedbyour procedure, andthedashedstraight lineis its correspondinglinear fit.B, Cross-validation R2curves 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 synergysets, respectively, is indicatedby the average ssdvalues (f; n 20 20 400). The averagessd values expected by chance were computed by calculating principal angles betweenshuffledsynergy sets (; mean 5 SD after 20 trials of shuffling). In all frogs, the actual mean ssdis well above its corresponding baseline value ( p 0.01). D, The number of stage I intactsynergies with actual structures that were preserved after deafferentation was indicated by theaverage nss values (f; n 20 20 400). The average nss values expected by chance werecomputed by calculating scalar products between shuffled synergy sets (; mean 5 SDafter 20 trials of shuffling). In all frogs, the actual mean nss is higher than its correspondingbaseline value ( p 0.01).6428 J. Neurosci., July 6, 2005 25(27):6419 6434 Cheung et al. Central/Sensory Contributions to Muscle SynergiesGA (ankle extensor). Synergy J2 is an extension synergy foundonly in frogs 3 and 4. It includes RI (frog 3), SM (frog 4), and theextensors VI, RA, GA, and VE. Synergy J3 includes the hip exten-sor/knee flexor ST(all frogs), the knee extensors/ankle flexors TAand PE(frogs 1, 2, and 3), and the hip flexor/knee flexor SA(frogs2 and 3). Synergy J4 includes the hip flexor IP and the hip-kneeflexor BI, with more BI than IP (frogs 1, 2, and 4), the hip exten-sor/knee flexor SM is found in frogs 1 and 4, and the hip-kneeflexor, SA, is foundinfrogs 1 and2. Synergy J5 features mostly thehip flexor IP (frogs 2, 3, and 4), and also RA (frogs 2 and 3), SA(frogs 2 and 4), and ST (frog 4). Synergy J6contains activation in the two knee exten-sors/ankle flexors TAand PE, as well as SA,BI, and VE (frogs 1 and 2).Inall frogs, synergiesJ1andJ2wereactive only during the extension phase ofjumping. Most of the rest of the synergieswere active in both the extension and flex-ion phases of jumping.Although a detailed analysis of the sim-ilarities and differences between the swim-ming and jumping synergies is beyond thescopeofthisstudy(butseedAvellaandBizzi, 2005), it is evident from our results(Figs. 6, 8) that some synergies are sharedbetween the two behaviors (e.g., comparefrog 2s S5, J4 and frog 3s S1, J1), whereassome other synergies appear to be specifictoswimming(e.g., S2)orjumping(e.g.,frog 2s J5). Our results thus support theidea that there are pattern-generating cir-cuitries shared between behaviors so thatcontrol is simplified (Grillner, 1985; Soffe,1993; Stein, 2005), as well as behavior-specificmodules adaptedtothespecificdemandsofeachtask(Prattetal., 1996;Jing et al., 2004).To summarize our analyses of thejumping EMGs, in stage I, we found thatboth the intact and deafferented jumpingdatasetspossesslowandsimilardimen-sionalities (Fig. 7A, B). In stage II, most ofthesynergieswereextractedassynergiessharedbetweenthe intact anddeaffer-ented data sets (Fig. 8), allowing us to con-cludethatmostsynergiesunderlyingthejumping behavior are centrally organizedmodules activated by spinal and/or su-praspinal commands. Six classes of jumpingsynergies wereidentified(Fig. 8), twoofwhich (J1 and J2) were activated during theextensionphase only. We note alsothatmanyjumpingsynergies appear tobe similarto our swimming synergies (Figs. 6, 8).Effects of deafferentation on theactivation of synergiesReconstructing EMG data with synergiesand their coefficientsTheresultsof theprevioustwosectionsshow, that for both swimming and jump-ing, there is a large degree of sharing be-tweensynergies before andafter deafferen-tation. However, as canbe seeninFigure 2,there were also substantial changes in the EMGs observed afterdeafferentation. We therefore investigated how such EMG alter-ations were produced by examining patterns of synergy activa-tion coefficients used to reconstruct the observed EMGs beforeand after deafferentation. In Figure 9, the jumping EMG exam-ples shown in Figure 2 are reconstructed from the jumping syn-ergies of frog 1 (Fig. 8). We see that activation of SM, IP, BI, andSAinphasec,asnotedpreviously,isexplainedbyprolongedactivation of synergy J4 (light blue) in the deafferented example.Figure 8. Jumping synergies of all frogs (analysis stage II). Shown in this figure are the stage II synergies of the extractionrepetitionwiththehighest R2of thefour frogs. Thesynergies sharedbetweentheintact anddeafferenteddatasets arelabeledSh,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 theflexionphase are markedwithf, andthose active inbothphases are markedef. All synergies showninthis figure were clusteredinto six classes (J1J6), and the class of each synergy is marked on its left side. The sign of the moment arms (MA) around the hip,knee, andankle joints of the 13muscles includedinthis study are listedbelowthe synergies of frog3andfrog4(e, extensor action;f, flexor action). Moment arm signs are based on results of Kargo and Rome (2002) and Gonzalez (2003).Cheung et al. Central/Sensory Contributions to Muscle Synergies J. Neurosci., July 6, 2005 25(27):6419 6434 6429The increased amplitude and duration ofTA and PE after deafferentation, however,are explained by a prolonged and in-creased activation of synergy J6 (green) inphase c compared with phase c. Also, thealtered relative onset times of AD, ST, IP,and PE in phase a is accounted for by thedeafferented-specific synergy (yellow).The examples in Figure 9 therefore suggestthat the altered EMG patterns after deaf-ferentation can be characterized bychanges intheamplitudeandtemporalpatterns of the shared synergy coefficientsand, toalesser extent, bythedataset-specific synergies.Deafferentation alters both the amplitudeand temporal patterns of synergy activationWe proceeded to systematically analyze ef-fects of deafferentation on both the ampli-tude and temporal patterns of the synergycoefficients.Thepercentagechangesoftheexten-sionandflexionpeakamplitudesof thedifferent classes of synergies after deaffer-entation are summarized in the left half ofTable2.Fortheextensionsynergies(S1,S2, J1, and J2), deafferentation had a muchmorepronouncedeffectonthejumpingsynergies(J1, J2)thanontheswimmingsynergies (S1, S2). As summarized inTable2, for three of the four frogs, there was a2544%decreaseintheextensionpeakamplitudeof J1afterdeafferentation. Incontrast, the extension peak amplitude ofS1 for frogs 1 and 2, as well as that of S2 forfrogs 1, 3, and 4, was not altered by deaf-ferentation. One explanation for this dif-ferenceis that sensoryfeedbackplays amuch more important role in reinforcingtheactivationofjumpingextensionsynergiesthanthatoftheswimmingextensionsynergies.Althoughotherinterpretations(suchasmusclefatigue)arepossible, wethinkthattheaboveinterpretation is likely because it makes biomechanical sense (seeDiscussion). Wespeculatethat theexceptional increaseinS1extension amplitude for frog 4 (Table 2) might be attributable toa more-than-usual denervation supersensitivity to inputs in thespinal interneuronsormotoneuronsinducedbyoursurgicalprocedure.For the non-extension synergies (S3-S6, J3-J6), except S5 andJ3, the effects of deafferentationonthe peak coefficient amplitudewere much less consistent across animals. For instance, whereasinfrog 2 there was a 59%decrease inflexionpeak amplitude of J5,in frog 3, this synergy increased by 36%, and in frog 4, the differ-ence between the intact and deafferented means of the same syn-ergy are not statistically significant ( p 0.05).The right half of Table 2 summarizes the percentage change ofcoefficient burst durationforboththeextensionandflexionphases. Again, results across animals tend not to be very consis-tent. For example, we have seen in Figure 9 that, in frog 1, acti-vation of J4 (SM, IP, BI, SA) during the flexion phase was pro-longedafterdeafferentation. Consistentwiththisobservation,our burst duration analysis indicates that, on average, there was a2.8-fold increase in the flexion burst duration for synergy J4 infrog 1. However, for frog 2, a 58% decrease in flexion burst du-ration was noted for the same synergy, and, for frog 4, no changeinflexionburst durationwas indicatedinstead. We thus concludethat deafferentation alters the temporal patterns of the synergycoefficients, but, for each synergy, individual frogs might rely onsensory feedback differently to sculpt the temporal profile of syn-ergy activation.Sensory feedback can uncouple or couple the activation of synergiesToinvestigatethepossiblerolesoffeedbackincorrelatingordecorrelating the activations of two synergies, we calculated thePearsons correlation coefficient (r) between the peak coefficientamplitudes of every pair of shared synergies, for each frog, eachbehavior, each of the extension and flexion phases, and each ofthe intact and deafferented data sets. We then compared the in-tact and deafferented r values to assess whether deafferentationcausesanincreasedordecreasedcorrelationbetweenthepeakamplitudes of the synergies. An increase in correlation after deaf-ferentation between two synergies would indicate that, althoughactivation of each synergy may be modulated by sensory feed-back, activation of both may be correlated and coordinated bycentral mechanisms. Conversely, a decrease in correlation afterFigure 9. Reconstructing the original EMGs with synergies and their coefficients. The intact and deafferented EMG examplesshown in Figure 2, C and D, are reconstructed using the stage II synergies extracted fromthe jumping EMGs of frog 1 (Fig. 8). Theoriginal EMG data, filtered and integrated (for filtering and integration parameters, see Materials and Methods), is indicated bythick black lines, and the time-varying coefficients of the synergies are shown below the EMGs. The reconstruction of the motorpatternis superimposedonto the original EMGs. The colors composingthe reconstructionmatchthe colors of the coefficients suchthat thecolors reflect therespectivecontributionof eachsynergy tothereconstructionat eachtimepoint. Notethat synergy Desp1(yellow) is deafferentedspecific; thus, by definition, it contributes to the reconstructionof only the deafferentedEMGepisode. Formore discussion, see Results.6430 J. Neurosci., July 6, 2005 25(27):6419 6434 Cheung et al. Central/Sensory Contributions to Muscle Synergiesdeafferentation would indicate that feedback signals play a role incorrelating their activation.Among all pairs of swimming or jumping synergies, we iden-tified 10 pairs with extension or flexion peak coefficient ampli-tudes that are well correlated under either the intact or deaffer-ented condition (r 0.6; p 0.01) and with an intact r that issmaller than the deafferented r ( p 0.01). One such pair, J3 andJ6 of frog 1 (flexion peak), is shown in Figure 10A as an example.We see that, although the intact flexion peak coefficient ampli-tudes () between the two synergies are not well correlated (r 0.3156; p0.01), thedeafferentedpeakamplitudes (E)arestronglycorrelated(r0.6736;p0.01).Thedifferencebe-tweentheintactanddeafferentedrvaluesinthiscaseisalsostatistically significant ( p 0.01). Thus, sensory feedback mayfunction to uncouple two centrally coupled synergies by modu-lating activation of each synergy independently (Fig. 10B). Notethat, in Figure 10A, there are 15 intact jumps () for which the J3and J6 activation patterns overlap with those of the deafferentedjumpsandappeartobecorrelatedmuchlikethedeafferentedsamples. It is possible that, in those jumps, feedback signals weregated (Burke, 1999) or were less effective, thereby causing thosejump flexion phases to be similar to the deafferented cases.The other pairs of shared synergies showing a similar increaseincorrelationcoefficient after deafferentationareas follows:S1/S4 (frog 1, extension); S2/S4 (frog 1, extension); S1/Sh.4 (frog1, extension); J1/J3(frog1, extension); J3/J4(frog1; flexion);S1/Sh.6(frog2, extension); S1/S3(frog3, extension); S3/Sh.4(frog 4, extension); andS2/S3 (frog 4, extension). It is noteworthythat, among these 10 pairs of synergies showing an increase incorrelation after feedback deprivation, six of them involve J3 orS3, both of which possess a prominent STcomponent (Figs. 6, 8).It therefore appears that the two STsynergies are more likely to beuncoupled from other synergies by sensory inflow.In addition, we found another four pairs of shared synergiesforwhichtheextensionpeakcoefficientamplitudesarecorre-Table 2. Effects of deafferentation on the amplitude and temporal patterns ofsynergy coefficientsSynergy FrogExt. peak amp.(% change)Flex. peak amp.(% change)Ext. burstduration(% change)Flex. burstduration(% change)S1 Frog 1 NC NA NC NAFrog 2 NC NA 14.9 NAFrog 3 42.4 NA 38.3 NAFrog 4 266.7 NA NC NAS2 Frog 1 NC NA 29.0 NAFrog 3 NC NA NC NAFrog 4 NC NA 27.6 NAS3 Frog 1 Insp Insp Insp InspFrog 2 42.3 65.2 NC NCFrog 3 79.4 NC 15.8 19.4Frog 4 68.9 NC 61.4 50.1S4 Frog 1 NC 115.1 NC NCFrog 2 28.6 NC 17.7 NCFrog 4 Insp NA Insp NAS5 Frog 1 Insp Insp Insp InspFrog 2 24.1 29.6 NC NCS6 Frog 2 26.3 25.9 16.3 57.2Frog 3 90.6 128.0 65.2 NCJ1 Frog 1 25.1 NA 23.8 NAFrog 2 39.7 NA 19.1 NAFrog 3 43.7 NA 25.1 NAFrog 4 Insp NA Insp NAJ2 Frog 3 Insp NA Insp NAFrog 4 50.2 NA 20.2 NAJ3 Frog 1 33.6 51.4 14.5 24.6Frog 2 57.9 59.4 34.6 60.4Frog 3 NC NC NC NCFrog 4 Insp Insp Insp InspJ4 Frog 1 33.8 26.3 NC 276.9Frog 2 NA 37.1 NA 50.3Frog 4 32.2 44.0 25.8 NCJ5 Frog 2 37.4 58.5 27.5 64.5Frog 3 NA 35.7 NA 57.9Frog 4 NC NC NC NCJ6 Frog 1 22.3 22.2 NC 69.6Frog 2 Desp Desp Desp DespChanges in coefficient peak amplitude (amp.) and coefficient burst duration after deafferentation for both theextension (Ext.) and flexion (Flex.) phases were quantified as percentage changes. Instances for which the nullhypothesis that the intact and deafferented means are the same cannot be rejected (t test; p 0.05) are markedwith NC, standing for no change. The abbreviation NA, standing for not available, means that the synergy was notactivated during that particular phase. Insp and Desp stand for intact- and deafferented-specific synergies, respec-tively. For an explanation of how burst duration was determined, see Materials and Methods.Figure 10. Sensory feedback can uncouple or couple the activation of synergies. We calcu-latedthe Pearsons correlationcoefficient ( r) peak coefficient amplitudes of every pair of sharedsynergies, for each behavior, each of the extension and flexion phases, and each of the intactand deafferented conditions. A, The flexion-phase peak coefficient amplitudes of synergies J3and J6 (frog 1). The intact samples are shown as crosses (), and the deafferented samples areshownas circles (E). This is anexample of a pair of synergies showinganincrease incorrelationafter deafferentation(intact r 0.3156; deafferentedr 0.6736). The straight line representsthe 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 anetwork coordinating the activation of multiple synergies; each black circle represents themotoneuronal pool of a particular muscle. The finding that the deafferented samples are highlycorrelated suggests that J3 and J6 (frog 1) are coordinated by central mechanisms upstreamofthe synergies. However, the smaller correlation with afferents intact suggests that one or bothsynergies might be modulated by sensory feedback. For more discussion, see Results. C, Theextension-phase peak coefficient amplitudes of synergies S1 and S2 (frog 3). Again, the intactsamples are shown as crosses (), and the deafferented samples are shown as circles (E). Thisis 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 fitto the intact samples. D, Interpretation of the results shown in C. That the deafferented r isrelatively small suggests that S1andS2arecontrolledas tworelatively independent modules byfeedforward commands, but the high correlation observed under the intact state implies thatsensory afferents might help to couple the activation of these two synergies during swimmingextension.Cheung et al. Central/Sensory Contributions to Muscle Synergies J. Neurosci., July 6, 2005 25(27):6419 6434 6431lated under either the intact or deafferented condition (r 0.6;p 0.01) and for which the intact r is greater than the deaffer-ented r ( p 0.01). Frog 3s S1 and S2 (extension peak) belong tooneof thesepairs(Fig. 10C). Inthisexample, theintactanddeafferentedrvaluesare0.7065( p0.01)and0.5011( p0.01), respectively, and the null hypothesis that the two r valuesare the same can be rejected ( p 0.01). That the deafferented r isrelativelysmall suggeststhat S1andS2arecontrolledastworelatively independent modules by feedforward commands (Fig.10D),butthehighcorrelationobservedundertheintactstateimplies that sensory afferents might help to couple the activationof these two synergies during swimming extension (Fig. 10D).Hence, sensory feedback might function to couple two indepen-dently organized synergies.The other three pairs of shared synergies showing a similardecrease in correlation coefficient after deafferentation are as fol-lows: S1/S6 (frog 2, extension); J3/J5 (frog 2, extension); andJ2/J4(frog 4, extension).Finally, we did not observe consistent coupling and uncou-plingactionsoffeedbackbetweenthesamepairsofsynergiesacross frogs, once again suggesting that the roles of sensory feed-back in modifying synergy activation patterns show substantialinteranimal variability.In summary, the results of this section suggest that the differ-ences between the intact and deafferented EMG patterns can becharacterized as changes in the amplitude and temporal patternsof the synergy coefficients (Fig. 9). Our coefficient analyses fur-thersuggestthatsensoryfeedbackplaysanimportantroleinreinforcing the jumping extension synergy but not the swimmingextensionsynergies(Table2). Fortheamplitudesofthenon-extension synergies and for the burst duration of the coefficients,effects of deafferentationwerenot consistent across animals,however (Table 2). Finally, our correlation analysis reveals thatfeedback can either uncouple or couple two centrally organizedmodules (Fig. 10).DiscussionIn this study, we assess to what extent locomotor EMGs are gen-erated by centrally organized muscle synergies. For both swim-ming and jumping, we established that EMGs before and afterdeafferentation possess similar lowdimensionalities (stage I) andthatmostsynergieswerepreservedafterfeedbackdeprivation(stage II). Deafferentation also altered the amplitude and tempo-ral patterns of activation of the shared synergies.Muscle synergies as centrally organized modulesThe mainfinding of this study is that bothintact anddeafferentedbehaviors are primarily generated by the same set of synergies.Therefore, most, but not all, of the muscle synergies underlyingfrog locomotor behaviors are centrally organized modules acti-vated by spinal and/or supraspinal commands. Such a result issimilar toprevious observations of invariant structures afterdeafferentation in the newt (Szekely et al., 1969), frog (Loeb et al.,1993; Kargo and Giszter, 2000b), and cat (Grillner and Zangger,1984; Giuliani and Smith, 1987; Koshland and Smith, 1989).The present study extends these previous results. By recordingEMGs from intact, freely moving animals, we have obtained re-sultsthatmightreflectstrategiesusedbytheCNStoproducenatural behaviors, not just features of the isolated spinal cord orof constrained tasks. By systematic and quantitative analyses ofEMGs from a large number of muscles, we have established thesufficiency of a small number of synergies to describe both theintact and deafferented data sets well. Thus, our results supportthe hypothesis that the CNS simplifies the daunting task of deriv-ing appropriate muscle patterns for many behaviors by flexiblecombination of a small number of synergies (Tresch et al., 1999;Hart and Giszter, 2004; Ting and Macpherson, 2005). Our find-ings also validate our means of identifying the synergies: the NMFalgorithm would have failed to uncover any shared synergies ifthere had been a gross mismatch between the assumptions of thealgorithm (such as linearity) and our conceptual model of syn-ergy combination.The observation of invariant synergies also suggests that oursynergies may reflect what are commonly referred to as centralpattern generators (CPGs), circuitries capable of generating mo-torpatternswithoutsensoryinput(Grillner, 1981; Rossignol,1996; Marder and Bucher, 2001). The finding that combinationofsynergiescanexplainourdatawell andtheobservationofsynergies shared between behaviors (see Results) further suggestthat our synergies maycorrespondtobuildingblocks of theCPGs, sometimes formulated as a mosaic of unit burst genera-tors (Grillner, 1985). Our linear combination model of syner-gies provides not only an explicit formulation of howthese build-ing blocks can be combined but also a means of identifying them.Our model can then be seen as a more general formulation of theunit burst generator hypothesis, in which each unit can consistof muscles acting across different joints, and the interconnectedunits need not be activated in strict alternation with one another.Such a formulation can include experimentally observed syner-gies such as the mixed knee extensor-ankle flexor synergy of catpaw shaking (Smith et al., 1985).We further speculate that each synergy subserves some basicbiomechanical functions(RaaschandZajac, 1999; Tingetal.,1999; Ting and Macpherson, 2005), such as powering jump ex-tension (Olson and Marsh, 1998) or compensating for interac-tion torque (Zernicke and Smith, 1996; Gribble and Ostry, 1999).An understanding of the principles guiding the composition oflocomotorsynergies will requireadditional experimental andmodeling studies.Afferent roles in synergy activation and organizationAlthoughwe found that most synergies were preserved after deaf-ferentation, the EMGs themselves were changed (Fig. 2), similarto some previous findings that the intact and deafferented musclepatternscouldbequitedifferent(GrillnerandZangger, 1984;Hiebert andPearson, 1999). Ourcoefficient analysesindicatethat such changes could be characterized primarily as alterationsin the amplitude and temporal patterns of activation of sharedsynergies (Fig. 9; Table 2). Therefore, one important role of feed-back might be to shape behaviors by modulating recruitment ofcentrallyorganizedsynergies (Fig. 1A1), consistent withthelong-standing hypothesis that motor outputs depend on interac-tions betweenthe coordinative structures withinCPGs, supraspi-nal commands, and sensory inflow (Grillner, 1981; Clarac, 1991;Prochazka, 1996; Rossignol, 1996; McCrea, 2001).Morespecifically, sensoryinflowduringabehaviormightadapt recruitment of synergies to the constraints imposed by thetask. Forinstance, wefoundthat, duringextension, feedbackplays a prominent role in enhancing the activation amplitude ofthejumpingbut not theswimmingsynergies(Table2). Thisdifference in the importance of feedback might be attributable tothe different biomechanical demands of the two behaviors. Dur-ing jump extension, the frog needs to generate more power toaccelerate the body against gravity within the shortest possibletime. Power generation might be enhanced by an increased acti-vation of the Golgi tendon organs and Ib interneurons [attribut-6432 J. Neurosci., July 6, 2005 25(27):6419 6434 Cheung et al. Central/Sensory Contributions to Muscle Synergiesabletoincreasedextensortensioncausedbythefrogsweightbeing borne solely by the hindlimbs (Roberts and Marsh, 2003,their Fig. 5)], assisting in maximal activation of the extensor syn-ergies through a positive feedback loop after Ib input onto theextensor motoneurons is reversed from inhibitory to excitatory(Pearson and Collins, 1993). A similar reflex reversal mechanismisbelievedtocontributetostance-phasereinforcementoftheextensors in the walking cat (Whelan, 1996).Our analysis of coefficient amplitudes also reveals that feed-backuncouplesmultiplesynergiesthatarecentrallyorganized(Fig. 10); therefore, afferents might allow for more individuatedcontrolofeachsynergy.Thesynergiesuncoupledbyfeedbackmayhavedistinctand/oropposingfunctions.Forexample,inFigure 10A, whereas J3 includes