Abstract
Muscle spindle discharge during active movement is a function of mechanical and neural parameters. Muscle length changes (and their derivatives) represent its primary mechanical, fusimotor drive its neural component. However, neither the action nor the function of fusimotor and in particular of γ-drive, have been clearly established, since γ-motor activity during voluntary, non-locomotor movements remains largely unknown. Here, using a computational approach, we explored whether γ-drive emerges in an artificial neural network model of the corticospinal system linked to a biomechanical antagonist wrist simulator. The wrist simulator included length-sensitive and γ-drive-dependent type Ia and type II muscle spindle activity. Network activity and connectivity were derived by a gradient descent algorithm to generate reciprocal, known target α-motor unit activity during wrist flexion-extension (F/E) movements. Two tasks were simulated: an alternating F/E task and a slow F/E tracking task. Emergence of γ-motor activity in the alternating F/E network was a function of α-motor unit drive: if muscle afferent (together with supraspinal) input was required for driving α-motor units, then γ-drive emerged in the form of α-γ coactivation, as predicted by empirical studies. In the slow F/E tracking network, γ-drive emerged in the form of α-γ dissociation and provided critical, bidirectional muscle afferent activity to the cortical network, containing known bidirectional target units. The model thus demonstrates the complementary aspects of spindle output and hence γ-drive: i) muscle spindle activity as a driving force of α-motor unit activity, and ii) afferent activity providing continuous sensory information, both of which crucially depend on γ-drive.
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References
Appelberg, B., Jeneskog, T., & Johansson, H. (1975). Rubrospinal control of static and dynamic fusimotor neurones. Acta Physiologica Scandinavica, 95(4), 431–440.
Bashor, D. P. (1998). A large-scale model of some spinal reflex circuits. Biological Cybernetics, 78(2), 147–157.
Buchanan, T. S., Lloyd, D. G., Manal, K., & Besier, T. F. (2004). Neuromusculoskeletal modeling: estimation of muscle forces and joint moments and movements from measurements of neural command. Journal of Applied Biomechanics, 20(4), 367–395.
Clough, J. F., Kernell, D., & Phillips, C. G. (1968). The distribution of monosynaptic excitation from the pyramidal tract and from primary spindle afferents to motoneurones of the baboon's hand and forearm. Journal of Physiology, 198(1), 145–166.
Clough, J. F., Phillips, C. G., & Sheridan, J. D. (1971). The short-latency projection from the baboon's motor cortex to fusimotor neurones of the forearm and hand. Journal of Physiology, 216(2), 257–279.
Colebatch, J. G., & Gandevia, S. C. (1989). The distribution of muscular weakness in upper motor neuron lesions affecting the arm. Brain, 112(Pt 3), 749–763.
Dimitriou, M. (2014). Human muscle spindle sensitivity reflects the balance of activity between antagonistic muscles. Journal of Neuroscience, 34(41), 13644–13655. doi:10.1523/JNEUROSCI.2611-14.2014.
Dimitriou, M., & Edin, B. B. (2008). Discharges in human muscle spindle afferents during a key-pressing task. Journal of Physiology, 586(Pt 22), 5455–5470.
Dimitriou, M., & Edin, B. B. (2010). Human muscle spindles act as forward sensory models. Current Biology, 20(19), 1763–1767. doi:10.1016/j.cub.2010.08.049.
Edin, B. B., & Vallbo, A. B. (1990a). Dynamic response of human muscle spindle afferents to stretch. Journal of Neurophysiology, 63(6), 1297–1206.
Edin, B. B., & Vallbo, A. B. (1990b). Muscle afferent responses to isometric contractions and relaxations in humans. Journal of Neurophysiology, 63(6), 1307–1313.
Ellaway, P. H., Taylor, A., & Durbaba, R. (2015). Muscle spindle and fusimotor activity in locomotion. Journal of Anatomy, 227(2), 157–166. doi:10.1111/joa.12299.
Fetz, E. E., Perlmutter, S. I., Maier, M. A., Flament, D., & Fortier, P. A. (1996). Response patterns and post-spike effects of premotor neurons in cervical spinal cord of behaving monkeys. Canadian Journal of Physiology and Pharmacology, 74, 531–546.
Flament, D., Fortier, P. A., & Fetz, E. E. (1992). Response patterns and postspike effects of peripheral afferents in dorsal root ganglia of behaving monkeys. Journal of Neurophysiology, 67(4), 875–889.
Freund, P., Schmidlin, E., Wannier, T., Bloch, J., Mir, A., Schwab, M. E., & Rouiller, E. M. (2006). Nogo-A-specific antibody treatment enhances sprouting and functional recovery after cervical lesion in adult primates. Nature Medicine, 12(7), 790–792.
Grandjean, B., & Maier, M. A. (2014). Model-based prediction of fusimotor activity and its effect on muscle spindle activity during voluntary wrist movements. Journal of Computational Neuroscience, 37(1), 49–63. doi:10.1007/s10827-013-0491-3.
Grigg, P., & Preston, J. B. (1971). Baboon flexor and extensor fusimotor neurons and their modulation by motor cortex. Journal of Neurophysiology, 34(3), 428–436.
Houk, J., & Simon, W. (1967). Responses of Golgi tendon organs to forces applied to muscle tendon. Journal of Neurophysiology, 30, 1466–1481.
Hulliger, M. (1984). The mammalian muscle spindle and its central control. Reviews of Physiology, Biochemistry and Pharmacology, 101, 1–110.
Hultborn, H., Lindström, S., & Wigström, H. (1979). On the function of recurrent inhibition in the spinal cord. Experimental Brain Research, 37(2), 399–403.
Jones, K. E., Wessberg, J., & Vallbo, A. B. (2001). Directional tuning of human forearm muscle afferents during voluntary wrist movements. Journal of Physiology, 536(Pt 2), 635–647.
Kakuda, N., & Nagaoka, M. (1998). Dynamic response of human muscle spindle afferents to stretch during voluntary contraction. Journal of Physiology, 513(Pt 2), 621–628.
Kakuda, N., Vallbo, A. B., & Wessberg, J. (1996). Fusimotor and skeletomotor activities are increased with precision finger movement in man. Journal of Physiology, 492(Pt 3), 921–929.
Koeze, T. H., Afshar, F., & Watkins, E. S. (1974). Fusimotor activation - effect of stimulation of the primate red nucleus. Confins de la Neurologie, 36(4–6), 341–346.
Lafargue, G., Paillard, J., Lamarre, Y., & Sirigu, A. (2003). Production and perception of grip force without proprioception: is there a sense of effort in deafferented subjects? European Journal of Neuroscience, 17(12), 2741–2749.
Lan, N., & He, X. (2012). Fusimotor control of spindle sensitivity regulates central and peripheral coding of joint angles. Frontiers in Computational Neuroscience, 6, 66. doi:10.3389/fncom.2012.00066.
Lawrence, D. G., & Kuypers, H. G. (1968a). The functional organization of the motor system in the monkey. I. The effects of bilateral pyramidal lesions. Brain, 91(1), 1–14.
Lawrence, D. G., & Kuypers, H. G. (1968b). The functional organization of the motor system in the monkey. II. The effects of lesions of the descending brain-stem pathways. Brain, 91(1), 15–36.
Lemon, R. N. (2008). Descending pathways in motor control. Annual Review of Neuroscience, 31, 195–218.
Lindberg, P. G., Skejø, P. H., Rounis, E., Nagy, Z., Schmitz, C., Wernegren, H., Bring, A., Engardt, M., Forssberg, H., & Borg, J. (2007). Wallerian degeneration of the corticofugal tracts in chronic stroke: a pilot study relating diffusion tensor imaging, transcranial magnetic stimulation, and hand function. Neurorehabilitation and Neural Repair, 21(6), 551–560.
Loeb, G. E., Levine, W. S., & He, J. (1990). Understanding sensorimotor feedback through optimal control. Cold Spring Harbor Symposia on Quantitative Biology, 55, 791–803.
Maier, M. A., Illert, M., Kirkwood, P. A., Nielsen, J., & Lemon, R. N. (1998a). Does a C3-C4 propriospinal system transmit corticospinal excitation in the primate? An investigation in the macaque monkey. Journal of Physiology, 511(Pt 1), 191–212.
Maier, M. A., Perlmutter, S. I., & Fetz, E. E. (1998b). Response patterns and force relations of monkey spinal interneurons during active wrist movement. Journal of Neurophysiology, 80(5), 2495–2513.
Maier, M. A., Shupe, L. E., & Fetz, E. E. (2005). Dynamic neural network models of the premotoneuronal circuitry controlling wrist movements in primates. Journal of Computational Neuroscience, 19(2), 125–146.
Manuel, M., & Zytnicki, D. (2011). Alpha, beta and gamma motoneurons: functional diversity in the motor system's final pathway. Journal of Integrative Neuroscience, 10(3), 243–276.
Nafati, G., Rossi-Durand, C., & Schmied, A. (2004). Proprioceptive control of human wrist extensor motor units during an attention-demanding task. Brain Research, 1018(2), 208–220.
Nathan, P. W., & Smith, M. C. (1982). The rubrospinal and central tegmental tracts in man. Brain, 105(Pt 2), 223–269.
Polit, A., & Bizzi, E. (1979). Characteristics of motor programs underlying arm movements in monkeys. Journal of Neurophysiology, 42, 183–194.
Prochazka, A. (1996). Proprioceptive feedback and movement regulation. In: Handbook of Physiology. Exercise: Regulation and Integration of Multiple Systems, sect. 12, part I, 1996. pp. 89–127, Bethesda, MD: Am Physiol Soc.
Prochazka, A., & Ellaway, P. (2012). Sensory systems in the control of movement. Comprehensive Physiology, 2(4), 2615–2627. doi:10.1002/cphy.c100086.
Prochazka, A., Hulliger, M., Zangger, P., & Appenteng, K. (1985). Fusimotor set’: new evidence for alpha-independent control of gamma-motoneurones during movement in the awake cat. Brain Research, 339, 136–140.
Raphael, G., Tsianos, G. A., & Loeb, G. E. (2010). Spinal-like regulator facilitates control of a two-degree-of-freedom wrist. Journal of Neuroscience, 30(28), 9431–9444. doi:10.1523/JNEUROSCI.5537-09.2010.
Rathelot, J. A., & Strick, P. L. (2006). Muscle representation in the macaque motor cortex: an anatomical perspective. Proceedings of the National Academy of Sciences USA, 103(21), 8257–8262.
Ribot-Ciscar, E., Hospod, V., Roll, J. P., & Aimonetti, J. M. (2009). Fusimotor drive may adjust muscle spindle feedback to task requirements in humans. Journal of Neurophysiology, 101, 633–640.
Riddle, C. N., Edgley, S. A., & Baker, S. N. (2009). Direct and indirect connections with upper limb motoneurons from the primate reticulospinal tract. Journal of Neuroscience, 29(15), 4993–4999.
Rothwell, J. C., Gandevia, S. C., & Burke, D. (1990). Activation of fusimotor neurones by motor cortical stimulation in human subjects. Journal of Physiology (London), 431, 743–756.
Sanes, J. N., Mauritz, K. H., Evarts, E. V., Dalakas, M. C., & Chu, A. (1984). Motor deficits in patients with large-fiber sensory neuropathy. Proceedings of the National Academy of Sciences USA, 81(3), 979–982.
Sasaki, S., Isa, T., Pettersson, L. G., Alstermark, B., Naito, K., Yoshimura, K., Seki, K., & Ohki, Y. (2004). Dexterous finger movements in primate without monosynaptic corticomotoneuronal excitation. Journal of Neurophysiology, 92(5), 3142–3147.
Schieber, M. H., & Thach, W. T. (1985). Trained slow tracking. II. Bidirectional discharge patterns of cerebellar nuclear, motor cortex, and spindle afferent neurons. Journal of Neurophysiology, 54(5), 1228–1270.
Scott, S. H. (2004). Optimal feedback control and the neural basis of volitional motor control. Nature review. Neuroscience, 5(7), 532–546.
Shapovalov, A. I., Karamjan, O. A., Kurchavyi, G. G., & Repina, Z. A. (1971). Synaptic actions evoked from the red nucleus on the spinal alpha-motorneurons in the rhesus monkey. Brain Research, 32(2), 325–348.
Taylor, A., Durbaba, R., Ellaway, P. H., & Rawlinson, S. (2006). Static and dynamic gamma-motor output to ankle flexor muscles during locomotion in the decerebrate cat. Journal of Physiology, 571(Pt 3), 711–723.
Vallbo, A. B. (1970). Discharge patterns in human muscle spindle afferents during isometric voluntary contractions. Acta Physiologica Scandinavica, 80(4), 552–566.
Vallbo, A. B., & Hulliger, M. (1981). Independence of skeletomotor and fusimotor activity in man? Brain Research, 223(1), 176–180.
Williams, R. J., & Zipser, D. (1989). A learning algorithm for continually running recurrent neural networks. Neural Computation, 1(2), 270–280.
Windhorst, U. (2008). Muscle spindles are multi-functional. Brain Research Bulletin, 75(5), 507–508. doi:10.1016/j.brainresbull.2007.11.009.
Zajac, F. E. (1989). Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Critical Reviews in Biomedical Engineering, 17(4), 359–411.
Acknowledgments
This work was in part supported by the CNRS (Centre National de la Recherche Scientifique, France). The neural network simulator was initially developed by LE Shupe in the Laboratory of EE Fetz, under ONR contract N00018-89-J-1240, at the Department of Physiology and Biophysics and the Washington National Primate Research Center, University of Washington, Seattle, WA 98195, USA.
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Supplementary Figure 1
Weight space of the alternating F/E network, default condition. Names and (flexion/extension) activity of units are shown at the left and along the top. The connection strength from row unit to column unit is symbolized by the area of the intersecting square in the range {−2,2}. The divergence of connections of a particular unit to other units is given by its row of output weights, and the convergence to any unit is given by the column of its input weights. Excitatory and inhibitory connections are represented by red and green squares respectively. Weights to be limited under the constrained condition are indicated by blue rounded rectangles (CM=> MUf,e; RM=> MUf,e). Sought after emerging weights from muscle afferents (AF) are encircled in purple (AFf,e=> MUf,e; as well as AFf,e=> CM and AFf,e=> CL). AF subsumes primary and secondary afferents, pSA and sSA respectively. Weights from muscle afferents (AF) onto their homonymous spinal interneurons were limited identically under all three conditions and are indicated by blue arrows (pSA,sSA=> IaIN, Golgi=> IbIN). (GIF 395 kb)
Supplementary Figure 2
Learning curves. Learning curves over 300 training cycles corresponding to the default (red) and constrained conditions (blue), respectively. In each case, a network with identical initial seed was used. The average percentage error decreases quickly during the first 100 cycles, then slows down and stabilizes for >200 cycles. A. Alternating F/E task (against auxotonic load). Initial error was 35.4 % and decreased to 4.7 % and 7.3 % for the default and constrained network, respectively. B. Slow F/E tracking task (full network version). For the default and constrained network the initial errors decreased from 32.4 % to 3.7 % and 3.6 %, respectively. Stippled lines: learning curves of the reduced network versions. The final error in the severely constrained network was typically somewhat higher than in the default conditions. (GIF 28 kb)
Supplementary Figure 3
Slow flexion/extension tracking with external flexion load. Flexion/extension movements with a constant external flexion load were simulated (as in Schieber and Thach 1985). Under this condition a constant flexion load is applied, opposing active flexion and assisting active extension. Compared to the no load condition, the monkey performed similar flexion/extension tracking movements, however, with higher flexor EMG activity during flexion (against the load), while extension (assisted by the load) was achieved by controlled relaxation of the flexor muscle. No active extensor EMG was observed during extension movements. This was simulated by implementing a constant flexor load and by corresponding flexor target α-motor unit activity, which increased gradually during flexion and then decreased in a non-linear fashion during extension. Extensor target α-motor unit activity remained at zero during the entire cycle. After learning the network produced the required flexion and extension movement in the presence of only active flexor EMG activity. This and the corresponding emergent γ-drive and afferent activity is shown in A. From top to bottom: flexor EMG (EMGf), dynamic (GADf) and static (GASf) γ-drive, primary (pSAf) and secondary (sSAf) muscle afferents, and wrist angle (θ, in °). Same for extensor units (below). Emergence of γ-drive: flexor γ-drive is predominant during flexion, in particular for the static drive (GASf ). This produces a brisk, increased activity of the secondary spindle afferent unit (sSAf) at movement onset (during shortening of the parent muscle), followed by a gradual decrease, close to what was expected from recordings (red stippled). Extensor γ-drive (GASe) is tonic and bidirectional, indicative of α-γ dissociation, since this occurs in the complete absence of homonymous (extensor) α-motor unit activity (EMGe). This produces a bidirectional secondary spindle response (sSAe), as was found empirically (even though the expected profile (red stippled) was better approximated during extension than during flexion). Primary muscle spindle afferents (pSAf, pSAe) show weak or length-sensitive responses. The expected profiles (red stippled) were approximated from empirical data (Schieber and Thach 1985; sSAf from Fig. 20, sSAe from Fig. 23). B. Same as in A but with abolished γ-drive. The network in A was run for an additional cycle, but the normally present γ-drive was abolished (GADf, GASf, GADe, GASe set to zero), while the original EMGf (and absent EMGe) was imposed. This produced the same movement, however, in the absence of any γ-drive the primary and secondary afferents are reduced to weak, length-sensitive responses (for muscle length > spindle rest-length; note: spindle rest-length indicated by vertical stippled lines). This demonstrates that muscle afferent feedback without any γ-drive is residual in the slow F/E task. (GIF 47 kb)
Supplementary Figure 4
Divergence of supraspinal input to γ-motor units. Names and (flexion/extension) activity of cortical units are shown at the left. Along the top are shown names and activity of γ-and and of α-motor units, grouped into flexor and extensor units. The excitatory connection strength from cortical (row) unit to column unit is symbolized by the area of the intersecting square in the range {−2,2}. A. Alternating flexion/extension network. Weights emerged such that (unilateral) CM units (CMt1–4) project in parallel to α-and to γ-motor units, strongly onto agonist, weakly onto antagonist α-and γ-motor units. This indicates divergence of CM units onto α-and γ-motor units. Note: CM=> MU weights were limited to a range of {0,0.4} under the constrained condition. B. Slow flexion/extension tracking network. Same organization as in A, but for all 7 cortical target units. Cortical unidirectional target units (CMt1–2, class_I) project preferentially onto agonist, in-phase α-motor units. They project, however, onto flexor as well as extensor γ-motor units. Bidirectional target units (CMt3–7, class_II) project not only to γ-motor units, but also to α-motor units. In particular, whenever a cortical activity pattern was coherent and in-phase with an α-motor unit, the projection emerged preferentially onto this α-motor unit, but not (or weakly) to out-of-phase α-motor units (e.g. CMt4 with a coherent pattern during extension projects onto extensor α-motor units, but not to the flexor α-motor units). Thus, bidirectional (class_II) cortical units diverge and participate in driving α- as well as γ-motor units. (GIF 93 kb)
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Grandjean, B., Maier, M.A. Emergence of gamma motor activity in an artificial neural network model of the corticospinal system. J Comput Neurosci 42, 53–70 (2017). https://doi.org/10.1007/s10827-016-0627-3
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DOI: https://doi.org/10.1007/s10827-016-0627-3