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Muscles: Non-linear Transformers of Motor Neuron Activity

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Neuromechanical Modeling of Posture and Locomotion

Abstract

Predicting movement from neural activity requires quantitative understanding of muscle response to motor neuron input. Muscles are sufficiently complicated that fulfilling this goal requires computer simulation. We therefore first explain in considerable detail one approach to modeling muscle. We then provide multiple examples of how muscle intrinsic properties and muscle diversity make straightforward predictions of how muscles transform neural input into movement impossible, including the dependence of muscle velocity on sarcomere number, the inadequacy of mean data in muscle modeling, the effects of muscle low-pass filtering, spike-number vs. spike frequency coding for contraction amplitude, how the role of passive muscle force in movement generation varies as a function of limb size, how muscles produce forces greater than their ‘maximum force’, energy conserving mechanisms, muscles that brake rather than produce movement, and how muscles can generate restoring responses (preflexes) to perturbing input in the absence of sensory feedback.

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References

  • Ache JM, Matheson R (2012) Passive joint forces are tuned to limb use in insects and drive movements without motor activity. Curr Biol 23:1418–1426

    Article  Google Scholar 

  • Ahn AN, Full RJ (2002) A motor and a brake: two leg extensor muscles acting at the same joint manage energy differently in a running insect. J Exp Biol 205:379–389

    CAS  PubMed  Google Scholar 

  • Arendt D (2008) The evolution of cell types in animals: emerging principles from molecular studies. Nat Rev Genet 9:868–882

    Article  CAS  PubMed  Google Scholar 

  • Atwood HL (1967) Crustacean neuromuscular mechanisms. Am Zool 7:527–551

    Article  Google Scholar 

  • Atwood HL (1971) Z and T tubules in stomach muscles of the spiny lobster. J Cell Biol 50:264–268

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Atwood HL (1972) Crustacean muscle. In: Bourne GH (ed) Structure and function of muscle. Academic Press, New York, pp 421–489

    Chapter  Google Scholar 

  • Atwood HL (1973) An attempt to account for the diversity of crustacean muscles. Am Zool 13:257–378

    Article  Google Scholar 

  • Atwood HL (1976) Organization and synaptic physiology of crustacean neuromuscular systems. Prog Neurobiol 7:291–391

    Article  CAS  PubMed  Google Scholar 

  • Biewener AA, Blickhan R, Perry AK, Heglund NC, Taylor CR (1988) Muscle forces during locomotion in kangaroo rats: force platform and tendon buckle measurements compared. J Exp Biol 137:191–205

    CAS  PubMed  Google Scholar 

  • Blümel M, Guschlbauer C, Daun-Gruhn S, Hooper SL, Buschges A (2012a) Hill-type muscle model parameters determined from experiments on single muscles show large animal-to-animal variation. Biol Cybern 106:559–571

    Article  PubMed  PubMed Central  Google Scholar 

  • Blümel M, Guschlbauer C, Hooper SL, Buschges A (2012b) Using individual-muscle specific instead of across-muscle mean data halves muscle simulation error. Biol Cybern 106:573–585

    Article  PubMed  Google Scholar 

  • Blümel M, Hooper SL, Guschlbauer C, White WE, Buschges A (2012c) Determining all parameters necessary to build Hill-type muscle models from experiments on single muscles. Biol Cybern 106:543–558

    Article  PubMed  PubMed Central  Google Scholar 

  • Bosboom EMH, Hesselink MKC, Oomens CWJ, Bouten CVC, Drost MR, Baaijens FPT (2001) Passive transverse mechanical properties of skeletal muscle under in vivo compression. J Biomech 34:1365–1368

    Article  CAS  PubMed  Google Scholar 

  • Bottinelli R, Canepari M, Pellegrino MA, Reggiani C (1996) Force-velocity properties of human skeletal muscle fibres: myosin heavy chain isoform and temperature dependence. J Physiol 495:573–586

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Brown IE, Loeb GE (2000) A reductionist approach to creating and using neuromusculoskeletal models. In: Winters JM, Crago PE (ed) Biomechanics and neural control of posture and movement. Springer, New York, pp 148–163

    Chapter  Google Scholar 

  • Brown IE, Scott SH, Loeb GE (1996) Mechanics of feline soleus: II. Design and validation of a mathematical model. J Muscle Res Cell Motil 17:221–233

    Article  CAS  PubMed  Google Scholar 

  • Brown IE, Cheng EJ, Loeb GE (1999) Measured and modeled properties of mammalian skeletal muscle. II. The effects of stimulus frequency on force-length and force-velocity relationships. J Muscle Res Cell Motil 20:627–643

    Article  CAS  PubMed  Google Scholar 

  • Cavagna GA, Saibene FP, Margaria R (1964) Mechanical work in running. J Appl Physiol 19:249–256

    CAS  PubMed  Google Scholar 

  • Cavagna GA, Saibene FP, Margaria R (1965) Effect of negative work on the amount of positive work performed by an isolated muscle. J Appl Physiol 20:157–158

    CAS  PubMed  Google Scholar 

  • Cavagna GA, Heglund N, Taylor R (1977) Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure. Am J Physiol 233:243–261

    Google Scholar 

  • Cheng EJ, Brown IE, Loeb GE (2000) Virtual muscle: a computational approach to understanding the effects of muscle properties on motor control. J Neurosci Methods 101:117–130

    Article  CAS  PubMed  Google Scholar 

  • Chiel H, Beer R (1997) The brain has a body: adaptive behavior emerges from interactions of nervous system, body and environment. Trends Neurosci 20:553–557

    Article  CAS  PubMed  Google Scholar 

  • Costello WJ, Govind CK (1983) Contractile responses of single fibers in lobster claw closer muscles: correlation with structure, histochemistry, and innervation. J Exp Zool 227:381–393

    Article  Google Scholar 

  • Edman KAP (1979) The velocity of unloaded shortening and its relation to sarcomere length and isometric force in vertebrate muscle fibers. J Physiol 291:143–159

    Article  CAS  Google Scholar 

  • Farahat WA, Herr HM (2010) Optimal workloop energetics of muscle-actuated systems: an impedance matching view. PLoS Comput Biol 6:e1000795. doi:10.1371/journal.pcbi.1000795

    Article  PubMed  PubMed Central  Google Scholar 

  • Full RJ, Koditschek DE (1999) Templates and anchors: neuromechanical hypotheses of legged locomotion on land. J Exp Biol 202:3325–3332

    CAS  PubMed  Google Scholar 

  • Full RJ, Stokes D, Ahn A, Josephson R (1998) Energy absorption during running by leg muscles in a cockroach. J Exp Biol 201:997–1012

    PubMed  Google Scholar 

  • Gilliver SF, Degens H, Rittweger J, Sargeant AJ, Jones DA (2009) Variation in the determinants of power of chemically skinned human muscle fibres. Exp Physiol 94:1070–1078

    Article  CAS  PubMed  Google Scholar 

  • Gilliver SF, Jones DA, Rittweger J, Degens H (2011) Variation in the determinants of power of chemically skinned type I rat soleus muscle fibres. J Comp Physiol [A] 197:311–319

    Article  Google Scholar 

  • Goslow GE Jr, Reinking RM, Stuart DG (1973) The cat step cycle: hind limb joint angles and muscle lengths during unrestrained locomotion. J Morphol 141:1–42

    Article  PubMed  Google Scholar 

  • Goslow GE Jr, Seeherman HJ, Taylor CR, McCuthin MN, Heglund NC (1981) Electrical activity and relative length changes of dog limb muscles as a function of speed and gait. J Exp Biol 94:15–42

    PubMed  Google Scholar 

  • Govind CK, Atwood HL, Maynard DM (1975) Innervation and neuromuscular physiology of intrinsic foregut muscles in the blue crab and spiny lobster. J Comp Physiol [A] 96:185–204

    Article  Google Scholar 

  • Grottel K, Celichowski J (1990) Division of motor units in medial gastrocnemius muscle of the rat in the light of variability of their principal properties. Acta Neurobiol Exp (Warsz) 50:571–588

    CAS  Google Scholar 

  • Guschlbauer C, Scharstein H, Büschges A (2007) The extensor tibiae muscle of the stick insect: biomechanical properties of an insect walking leg muscle. J Exp Biol 210:1092–1108

    Article  PubMed  Google Scholar 

  • Haeufle DFB, Grimmer S, Seyfarth A (2010) The role of intrinsic muscle properties for stable hopping–stability is achieved by the force-velocity relation. Bioinspir Biomim 5:016004 doi:10.1088/1748-3182/5/1/016004

    Article  CAS  Google Scholar 

  • Hawkins D, Bey M (1997) Muscle and tendon force-length properties and their interactions in vivo. J Biomech 30:63–70

    Article  CAS  PubMed  Google Scholar 

  • Heglund NC, Cavagna GA (1987) Mechanical work, oxygen consumption, and efficiency in isolated frog and rat muscle. Am J Physiol 253:C22–C29

    CAS  PubMed  Google Scholar 

  • Herzog W, Leonard TR, Renaud JM, Wallace J, Chaki G, Bornemisza S (1992) Force-length properties and functional demands of cat gastrocnemius, soleus and plantaris muscles. J Biomech 25:1329–1335

    Article  CAS  PubMed  Google Scholar 

  • Hill AV (1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Biol Sci 126:136–195

    Article  Google Scholar 

  • Hill AV (1950) The series elastic component of muscle. Proc R Soc Lond B Biol Sci 141:104–117

    Article  Google Scholar 

  • Hooper SL, Guschlbauer C, von Uckermann G, Büschges A (2006) Natural neural output that produces highly variable locomotory movements. J Neurophysiol 96:2072–2088

    Article  PubMed  Google Scholar 

  • Hooper SL, Guschlbauer C, von Uckermann G, Büschges A (2007a) Different motor neuron spike patterns produce contractions with very similar rises in graded slow muscles. J Neurophysiol 97:1428–1444

    Article  PubMed  Google Scholar 

  • Hooper SL, Guschlbauer C, von Uckermann G, Büschges A (2007b) Slow temporal filtering may largely explain the transformation of stick insect (Carausius morosus) extensor motor neuron activity into muscle movement. J Neurophysiol 98:1718–1732

    Article  PubMed  Google Scholar 

  • Hooper SL, Guschlbauer C, Blümel M, Rosenbaum P, Gruhn M, Akay T, Büschges A (2009) Neural control of unloaded leg posture and of leg swing in stick insect, cockroach, and mouse differs from that in larger animals. J Neurosci 29:4109–4119

    Article  CAS  PubMed  Google Scholar 

  • Hoyle G (1967) Specificity of muscle. In: Wiersma CAG (ed) Invertebrate muscle systems. University of Chicago Press, Chicago, pp 151–167

    Google Scholar 

  • Hoyle G (1969) Comparative aspects of muscle. Annu Rev Physiol 31:43–84

    Article  CAS  PubMed  Google Scholar 

  • Huxley AF, Niedergerke R (1954) Structural changes in muscle during contraction. Nature 173:971–973

    Article  CAS  PubMed  Google Scholar 

  • Jahromi SS, Atwood HL (1969a) Correlation of structure, speed of contraction, and total tension in the fast and slow abdominal muscle fibers of the lobster (Homarus americanus). J Exp Zool 171:25–38

    Article  CAS  PubMed  Google Scholar 

  • Jahromi SS, Atwood HL (1969b) Structural features of muscle fibres in the cockroach leg. J Insect Physiol 15:2255–2262

    Article  Google Scholar 

  • Jahromi SS, Atwood HL (1971) Structural and contractile properties of lobster leg-muscle fibers. J Exp Zool 176:475–486

    Article  CAS  PubMed  Google Scholar 

  • Jewell BR, Wilkie DR (1958) An analysis of the mechanical components in frog’s striated muscle. J Physiol 143:515–540

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Komuro T (1981) Fine structural study of the abdominal muscle receptor organs of the crayfish (Procambuarus clarkii). Fast and slow receptor muscles. Tissue Cell 13:79–92

    Article  CAS  PubMed  Google Scholar 

  • Lang F, Costello WJ, Govind CK (1977) Development of the dimorphic claw closer muscles of the lobster Homarus americanus. I Regional distribution of muscle fiber types in adults. Biol Bull 152:75–83

    Article  CAS  PubMed  Google Scholar 

  • Maughan RJ, Watson JS, Weir J (1983) Strength and cross-sectional area of human skeletal muscle. J Physiol 338:37–49

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Morris LG, Hooper SL (1997) Muscle response to changing neuronal input in the lobster (Panulirus interruptus) stomatogastric system: spike number- versus spike frequency-dependent domains. J Neurosci 17:5956–5971

    CAS  PubMed  Google Scholar 

  • Morris LG, Thuma JB, Hooper SL (2000) Muscles express motor patterns of non-innervating neural networks by filtering broad-band input. Nat Neurosci 3:245–250

    Article  CAS  PubMed  Google Scholar 

  • Parnas I, Atwood HL (1966) Phasic and tonic neuromuscular systems in the abdominal extensor muscles of the crayfish and rock lobster. Comp Biochem Physiol 18:701–723

    Article  CAS  PubMed  Google Scholar 

  • Royuela M, Meyer-Rochow VB, Fraile B, Paniagua R (1998) Ultrastructure of muscle cells in Acetabulostoma (Crustacea, Ostracoda)—mussel shrimp from the Ross Sea (Antarctica). Polar Biol 20:77–84

    Article  Google Scholar 

  • Royuela M, Fraile B, Arenas MI, Paniagua R (2000) Characterization of several invertebrate muscle cell types: a comparison with vertebrate muscles. Microsc Res Tech 48:107–115

    Article  CAS  PubMed  Google Scholar 

  • Rubenson J, Pires NJ, Loi HO, Pinniger GJ, Shannon DG (2012) On the ascent: the soleus operating length is conserved to the ascending limb of the force-length curve across gait mechanics in humans. J Exp Biol 215:3539–3551

    Article  PubMed  Google Scholar 

  • Scott SH, Brown IE, Loeb GE (1996) Mechanics of feline soleus: I. Effect of fascicle length and velocity on force output. J Muscle Res Cell Motil 17:207–219

    Article  CAS  PubMed  Google Scholar 

  • Selverston AI, Russell DF, Miller JP, King DG (1976) The stomatogastric nervous system: structure and function of a small neural network. Prog Neurobiol 7:215–290

    Article  CAS  PubMed  Google Scholar 

  • Siebert T, Weihmann T, Rode C, Blickhan R (2010) Cupiennius salei: biomechanical properties of the tibia-metatarsus joint and its flexing muscles. J Comp Physiol 180:199–209

    Article  Google Scholar 

  • Thuma JB, Hooper SL (2010) Direct evidence that stomatogastric (Panulirus interruptus) muscle passive responses are not due to background actomyosin cross-bridges. J Comp Physiol [A] 196:649–657

    Article  Google Scholar 

  • Thuma JB, Harness PI, Koehnle TJ, Morris LG, Hooper SL (2007) Muscle anatomy is a primary determinant of muscle relaxation dynamics in the lobster (Panulirus interruptus) stomatogastric system. J Comp Physiol [A] 193:1101–1113

    Article  Google Scholar 

  • Wickiewicz TL, Roy RR, Powell PL, Perrine JJ, Edgerton VR (1984) Muscle architecture and force-velocity relationships in humans. J Appl Physiol Respirat Environ Exercise Physiol 57:435–443

    CAS  Google Scholar 

  • Wilkie DR (1950) The relationship between force and velocity in human muscle. J Physiol 110:249–280

    Article  Google Scholar 

  • Wilkie DR (1956) The mechanical properties of muscle. Br Med Bull 12:177–182

    Article  CAS  PubMed  Google Scholar 

  • Wilson E, Rustighi E, Mace BR, Newland PL (2010) Isometric force generated by locust skeletal muscle: responses to single stimuli. Biol Cybern 102:503–511

    Article  PubMed  Google Scholar 

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Correspondence to Scott L. Hooper PhD .

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Hooper, S. et al. (2016). Muscles: Non-linear Transformers of Motor Neuron Activity. In: Prilutsky, B., Edwards, D. (eds) Neuromechanical Modeling of Posture and Locomotion. Springer Series in Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3267-2_6

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