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Population vector code: a geometric universal as actuator

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Abstract

The population vector code relates directional tuning of single cells and global, directional motion incited by an assembly of neurons. In this paper three things are done. First, we analyze the population vector code as a purely geometric construct, focusing attention on its universality. Second, we generalize the algorithm on the basis of its geometrical realization so that the same construct that responds to sensation can function as an actuator for behavioral output. Third, we suggest at least a partial answer to the question of what many maps, neuronal representations of the outside sensory world in space–time, are good for: encoding vectorial input they enable a direct realization of the population vector code.

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References

  • Abbott LF (1994) Decoding neuronal firing and modelling neural networks. Q Rev Biophys 27: 291–31

    Article  CAS  PubMed  Google Scholar 

  • Averbeck BB, Latham PE, Pouget A (2006) Neural correlations, population coding, and computation. Nat Neurosci 6: 358–66

    Article  CAS  Google Scholar 

  • Barth FG (ed) (1985) Neurobiology of arachnids. Springer, Berlin

    Google Scholar 

  • Bergenheim M, Ribot-Ciscar E, Roll JP (2000) Proprioceptive population coding of two-dimensional limb movements in humans: I. Muscle spindle feedback during spatially oriented movements. Exp Brain Res 134: 301–10

    Article  CAS  PubMed  Google Scholar 

  • Bosco G, Poppele RE (1993) Broad directional tuning in spinal projections to the cerebellum. J Neurophysiol 70: 863–66

    CAS  PubMed  Google Scholar 

  • Brand A, Behrend O, Marquardt T, McAlpine D, Grothe B (2002) Precise inhibition is essential for microsecond interaural time difference coding. Nature 417: 543–47

    Article  CAS  PubMed  Google Scholar 

  • Brownell PH (1977) Compressional and surface waves in sand: used by desert scorpions to locate prey. Science 1977: 479–82

    Article  Google Scholar 

  • Brownell PH (1984) Prey detection by the sand scorpion. Sci Am 251(6): 94–05

    Article  Google Scholar 

  • Brownell PH, Farley RD (1979) Detection of vibrations in sand by tarsal sense organs of the nocturnal scorpion Paruroctonus mesaensis. J Comp Physiol 131:23–0; Orientation to vibrations in sand by the nocturnal scorpion Paruroctonus mesaensis: mechanism of target localization. J Comp Physiol 131:31–8

    Google Scholar 

  • Brownell PH, van Hemmen JL (2001) Vibration sensitivity and a computational theory for prey-localizing behavior in sand scorpions. Am Zool 41(5): 1229–240

    Article  Google Scholar 

  • Brownell PH, Polis G (eds) (2001) Scorpion biology and research. Oxford University Press, Oxford

    Google Scholar 

  • Georgopoulos AP, Kalaska JF, Caminiti R, Massey JT (1982) On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex. J Neurosci 2: 1527–537

    CAS  PubMed  Google Scholar 

  • Georgopoulos AP, Caminiti R, Kalaska JF, Massey JT (1983) Spatial coding of movement: a hypothesis concerning the coding of movement direction by motor cortical populations. Exp Brain Res Suppl 7: 327–36

    Google Scholar 

  • Georgopoulos AP, Kalaska JF, Crutcher MD, Caminiti R, Massey JT (1984) The representation of movement direction in the motor cortex: single cell and population studies. In: Edelman GM, Goll WE, Cowan WM(eds) Dynamic aspects of neocortical function. Neurosciences Research Foundation, New York, pp 501–24

    Google Scholar 

  • Georgopoulos AP, Kettner RE, Schwartz AB (1988) Primate motor cortex and free arm movements to visual targets in three-dimensional space. II. Coding of the direction of movement by a neuronal population. J Neurosci 8: 2928–937

    CAS  PubMed  Google Scholar 

  • Georgopoulos AP, Schwartz AB, Kettner RE (1986) Neuronal population coding of movement direction. Science 233: 1416–419

    Article  CAS  PubMed  Google Scholar 

  • Gerstner W, Kempter R, van Hemmen JL, Wagner H (1996) A neuronal learning rule for sub-millisecond temporal coding. Nature 383: 76–8

    Article  CAS  PubMed  Google Scholar 

  • Hebb DO (1949) The organization of behavior. Wiley, New York

    Google Scholar 

  • Helms Tillery SI, Flanders M, Soechting JF (1991) A coordinate system for the synthesis of visual and kinesthetic information. J Neurosci 11: 770–78

    Google Scholar 

  • van Hemmen JL (2001) Theory of synaptic plasticity. In: Moss F, Gielen S(eds) Handbook of biological physics, vol 4: neuro-informatics, neural modelling. Elsevier, Amsterdam, pp 771–23

    Google Scholar 

  • van Hemmen JL (2006) What is a neuronal map, how does it arise, and what is it good for? In: van Hemmen and Sejnowski (2006), pp 83–02

  • van Hemmen JL (2007) Biology and mathematics: a fruitful merger of two cultures. Biol Cybern 97: 1–

    Article  PubMed  Google Scholar 

  • van Hemmen JL (2006) What is a neuronal map, how does it arise, and what is it good for? In: van Hemmen and Sejnowski (2006), pp 83–02

    Google Scholar 

  • Johnson MT, Ebner TJ (2000) Processing of multiple kinematic signals in the cerebellum and motor cortices. Brain Res Rev 33: 155–68

    Article  CAS  PubMed  Google Scholar 

  • Kalaska JF, Caminiti R, Georgopoulos AP (1983) Cortical mechanisms related to the direction of two-dimensional arm movements: relations in parietal area 5 and comparison with motor cortex. Exp Brain Res 51: 247–60

    Article  CAS  PubMed  Google Scholar 

  • Kapfer C, Seidl AH, Schweizer H, Grothe B (2002) Experience-dependent refinement of inhibitory inputs to auditory coincidence-detector neurons. Nat Neurosci 5: 247–53

    Article  CAS  PubMed  Google Scholar 

  • Kempter R, Leibold C, Wagner H, van Hemmen JL (2001) Formation of temporal feature maps by axonal propagation of synaptic learning. Proc Natl Acad Sci USA 98: 4166–171

    Article  CAS  PubMed  Google Scholar 

  • Konishi M (1993) Listening with two ears. Sci Am 268(4): 34–1

    Article  Google Scholar 

  • Konishi M (2003) Coding of auditory space. Annu Rev Neurosci 26: 31–5

    Article  CAS  PubMed  Google Scholar 

  • Kristan WB Jr, Shaw BK (1997) Population coding and behavioral choice. Curr Opin Neurobiol 7: 826–31

    Article  PubMed  Google Scholar 

  • Kutz DF, Dannenberg W, Werner W, Hoffmann K-P (1997) Population coding of arm-movement-related neurons in and below the superior colliculus of Macaca mulatta. Biol Cybern 76: 331–37

    Article  CAS  PubMed  Google Scholar 

  • Lang HH (1980) Surface wave sensitivity of the back swimmer Notonecta glauca. Naturw 67: 204–05

    Article  Google Scholar 

  • Leibold C, van Hemmen JL (2002) Mapping time. Biol Cybern 87: 428–39

    Article  CAS  PubMed  Google Scholar 

  • Leibold C, van Hemmen JL (2005) Spiking neurons learning phase delays: how mammals may develop auditory time-difference sensitivity. Phys Rev Lett 94: 168102

    Article  PubMed  CAS  Google Scholar 

  • Lewis JE (1999) Sensory processing and the network mechanisms for reading neuronal population codes. J Comp Physiol A 185: 373–78

    Article  CAS  PubMed  Google Scholar 

  • McAlpine D, Grothe B (2003) Sound localization and delay lines—do mammals fit the model?. Trends Neurosci 26: 347–50

    Article  CAS  PubMed  Google Scholar 

  • Murphey RK, Mendenhall B (1973) Localization of receptors controlling orientation to prey by the back swimmer Notonecta undulata. J Comp Physiol A 84: 19–0

    Article  Google Scholar 

  • Murphey RK (1973) Mutual inhibition and the organization of a non-visual orientation in Notonecta. J Comp Physiol A 84: 31–0

    Article  Google Scholar 

  • Motter BC, Steinmetz MA, Duffy CJ, Mountcastle VB (1987) Functional properties of parietal visual neurons: mechanisms of directionality along a single axis. J Neurosci 7: 154–76

    CAS  PubMed  Google Scholar 

  • Mountcastle VB (1998) The cerebral cortex. Harvard University Press, Cambridge

    Google Scholar 

  • Pellionisz A (1988) Tensorial aspects of the multidimensional massively parallel sensorimotor function of neuronal networks. In: Pompeiano O, Allum JHJ(eds) Progress in brain research, vol 76. Elsevier, Amsterdam, pp 341–54

    Google Scholar 

  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes, 3rd edn. Cambridge University Press, Cambridge

    Google Scholar 

  • Reina GA, Moran DW, Schwartz AB (2001) On the relationship between joint angular velocity and motor cortical discharge during reaching. J Neurophysiol 85: 2576–589

    CAS  PubMed  Google Scholar 

  • Salinas E, Abbott LF (1994) Vector reconstruction from firing rates. J Comput Neurosci 1: 89ndash;107

    Article  CAS  PubMed  Google Scholar 

  • Schwartz AB (1992) Motor cortical activity during drawing movements: single-unit activity during sinusoid tracing. J Neurophysiol 68: 528–41

    CAS  PubMed  Google Scholar 

  • Schwartz AB (1994) Direct cortical representation of drawing. Science 265: 540–42

    Article  CAS  PubMed  Google Scholar 

  • Schwartz AB (2007) Useful signals from motor cortex. J Physiol 579: 581–01

    Article  CAS  PubMed  Google Scholar 

  • Schwartz AB, Kettner RE, Georgopoulos AP (1988) Primate motor cortex and free arm movements to visual targets in three-dimensional space. I. Relations between single cell discharge and direction of movement. J Neurosci 8: 2913–927

    CAS  PubMed  Google Scholar 

  • Seung HS, Sompolinsky H (1993) Simple models for reading neuronal population codes. Proc Natl Acad Sci USA 90: 10749–0753

    Article  CAS  PubMed  Google Scholar 

  • Soechting JF (1989) Elements of coordinated arm movements in three-dimensional space. In: Wallace SA(eds) Perspectives on the coordination of Movement. North-Holland, Amsterdam, pp 47–3

    Chapter  Google Scholar 

  • Soechting JF, Flanders M (1991a) Arm movements in 3-dimensional space: Computation, theory, and observation. Exerc Sports Sci Rev 19: 389–18

    Article  CAS  Google Scholar 

  • Soechting JF, Flanders M (1991b) Deducing central algorithms of arm movement control from kinematics. In: Humphrey DR, Freund H-J(eds) Motor control: concepts and issues. Wiley, New York, pp 293–06

    Google Scholar 

  • Stürzl W, Kempter R, van Hemmen JL (2000) Theory of arachnid prey localization. Phys Rev Lett 84: 5668–671

    Article  PubMed  Google Scholar 

  • Taylor DM, Helms Tillery SI, Schwartz AB (2002) Direct cortical control of 3D neuroprosthetic devices. Science 296: 1829–832

    Article  CAS  PubMed  Google Scholar 

  • Turner RS, Anderson ME (1997) Pallidal discharge related to the kinematics of reaching movements in two dimensions. J Neurophysiol 77: 1051–074

    CAS  PubMed  Google Scholar 

  • Weber DJ, Stein RB, Everaert DG, Prochazka A (2006) Decoding sensory feedback from firing rates of afferent ensembles recorded in cat dorsal root ganglia in normal locomotion. IEEE Trans Neural Syst Rehabil Eng 14: 240–43

    Article  PubMed  Google Scholar 

  • Zhang K, Sejnowski TJ (1999) Neuronal tuning: to sharpen or broaden?. Neural Comp NC 11: 75–4

    Article  CAS  Google Scholar 

Download references

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Authors and Affiliations

  1. Physik Department, TU München, 85747, Garching bei München, Germany

    J. Leo van Hemmen

  2. Motor Lab, School of Medicine, University of Pittsburgh, Pittsburgh, PA, 15261, USA

    Andrew B. Schwartz

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  1. J. Leo van Hemmen
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  2. Andrew B. Schwartz
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Correspondence to J. Leo van Hemmen.

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van Hemmen, J.L., Schwartz, A.B. Population vector code: a geometric universal as actuator. Biol Cybern 98, 509–518 (2008). https://doi.org/10.1007/s00422-008-0215-3

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  • DOI: https://doi.org/10.1007/s00422-008-0215-3

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