Noise induced processes in neural systems

Real neurons, and their networks, are far too complex to be described exactly by simple deterministic equations. Any description of their dynamics must therefore incorporate noise to some degree. It is my thesis that the nervous system is organized in such a way that its performance is optimal, subject to this constraint. I further contend that neuronal dynamics may even be enhanced by noise, when compared with their deterministic counter-parts. To support my thesis I will present and analyze three case studies. I will show how noise might (i) extend the dynamic range of mammalian cold-receptors and other cells that exhibit a temperature-dependent discharge; (ii) feature in the perception of ambiguous figures such as the Necker cube; (iii) alter the discharge pattern of single cells.

[1]  K. Schäfer,et al.  Oscillation and noise determine signal transduction in shark multimodal sensory cells , 1994, Nature.

[2]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[3]  L. Chua,et al.  Symbolic dynamics of piecewise-linear maps , 1994 .

[4]  Fabio Marchesoni,et al.  Resonant trapping: A failure mechanism in switch transitions , 1997 .

[5]  A. Gorman,et al.  Ionic requirements for membrane oscillations and their dependence on the calcium concentration in a molluscan pace‐maker neurone , 1982, The Journal of physiology.

[6]  Bulsara,et al.  Array enhanced stochastic resonance and spatiotemporal synchronization. , 1995, Physical review letters.

[7]  W. Freeman.  The physiology of perception. , 1991, Scientific American.

[8]  Frank Moss,et al.  5. Stochastic Resonance: From the Ice Ages to the Monkey's Ear , 1994 .

[9]  G. Milstein.  Numerical Integration of Stochastic Differential Equations , 1994 .

[10]  Pierre Peretto.  An Introduction to the Modeling of Neutral Networks: Introduction , 1992 .

[11]  A. Longtin.  AUTONOMOUS STOCHASTIC RESONANCE IN BURSTING NEURONS , 1997 .

[12]  R. Plant,et al.  Bifurcation and resonance in a model for bursting nerve cells , 1981, Journal of mathematical biology.

[13]  H. E. Derksen,et al.  Fluctuation phenomena in nerve membrane , 1968 .

[14]  Paul C. Bressloff,et al.  A Phase Model of Temperature-Dependent Mammalian Cold Receptors , 2000, Neural Computation.

[15]  K Schäfer,et al.  Classification of a calcium conductance in cold receptors. , 1988, Progress in brain research.

[16]  P. Bressloff,et al.  PHYSICS OF THE EXTENDED NEURON , 1997 .

[17]  S. Rice.  Mathematical analysis of random noise , 1944 .

[18]  Richard W. Hamming,et al.  Numerical Methods for Scientists and Engineers , 1963 .

[19]  Frank Moss,et al.  STOCHASTIC RESONANCE: TUTORIAL AND UPDATE , 1994 .

[20]  Paul C. Bressloff,et al.  A self-organizing network in the weak-coupling limit , 1997 .

[21]  Daniel T. Gillespie,et al.  The multivariate Langevin and Fokker–Planck equations , 1996 .

[22]  R. Shepard,et al.  Toward a universal law of generalization for psychological science. , 1987, Science.

[23]  Bressloff.  Analysis of quantal synaptic noise in neural networks using iterated function systems. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[24]  M. Stadler,et al.  The Function of Meaning in Cognitive Order Formation , 1995 .

[25]  Karin Hinzer,et al.  Encoding with Bursting, Subthreshold Oscillations, and Noise in Mammalian Cold Receptors , 1996, Neural Computation.

[26]  F. Attneave.  Multistability in perception. , 1971, Scientific American.

[27]  D. Carpenter,et al.  The role of the electrogenic sodium pump in modulation of pacemaker discharge of Aplysia neurons , 1974, Journal of cellular physiology.

[28]  R. Llinás,et al.  Electrophysiological analysis of synaptic transmission , 1969 .

[29]  John P. Miller,et al.  Broadband neural encoding in the cricket cereal sensory system enhanced by stochastic resonance , 1996, Nature.

[30]  G. Parisi,et al.  Stochastic resonance in climatic change , 1982 .

[31]  Teuvo Kohonen,et al.  Self-Organization and Associative Memory, Third Edition , 1989, Springer Series in Information Sciences.

[32]  J. Kaas,et al.  Multiple representations of the body within the primary somatosensory cortex of primates. , 1979, Science.

[33]  Petr Lánský,et al.  Sources of periodical force in noisy integrate-and-fire models of neuronal dynamics , 1997 .

[34]  Frank Moss,et al.  Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance , 1993, Nature.

[35]  J. Rinzel,et al.  Oscillatory and bursting properties of neurons , 1998 .

[36]  Bulsara,et al.  Time-interval sequences in bistable systems and the noise-induced transmission of information by sensory neurons. , 1991, Physical review letters.

[37]  Leon Glass.  Chaos in neural systems , 1998 .

[38]  Taylor,et al.  Random iterative networks. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[39]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[40]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[41]  H Wachtel,et al.  Negative Resistance Characteristic Essential for the Maintenance of Slow Oscillations in Bursting Neurons , 1974, Science.

[42]  C. Gardiner.  Handbook of Stochastic Methods , 1983 .

[43]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[44]  T. Lubensky,et al.  Principles of condensed matter physics , 1995 .

[45]  S. Neely,et al.  A model for active elements in cochlear biomechanics. , 1986, The Journal of the Acoustical Society of America.

[46]  Chapeau-Blondeau,et al.  Stochastic resonance in a neuron model that transmits spike trains. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[47]  Schmutz,et al.  Robust competitive networks. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[48]  J. Jack,et al.  Electric current flow in excitable cells , 1975 .

[49]  B. Mandelbrot,et al.  RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. , 1964, Biophysical journal.

[50]  E. Izhikevich,et al.  Weakly connected neural networks , 1997 .

[51]  W. Little.  The existence of persistent states in the brain , 1974 .

[52]  S. Aubry.  Anti-integrability in dynamic and variational problems , 1995 .

[53]  Charles Pecher,et al.  La Fluctuation D'excitabilité de la Fibre Nerveuse , 1939 .

[54]  N. Mclachlan.  Theory and Application of Mathieu Functions , 1965 .

[55]  Professor Dr. Dr. h.c. Hermann Haken,et al.  Synergetic Computers and Cognition , 1991, Springer Series in Synergetics.

[56]  I Lundström,et al.  A proposed 1-f noise mechanism in nerve cell membranes. , 1974, Journal of theoretical biology.

[57]  Luigi M. Ricciardi,et al.  Diffusion models of neuron activity , 1998 .

[58]  G. Schöner,et al.  Concepts for a Dynamic Theory of Perceptual Organization: An Example from Apparent Movement , 1995 .

[59]  Henry C. Tuckwell,et al.  Introduction to theoretical neurobiology , 1988 .

[60]  H. A. Braun,et al.  Theories and Models of Temperature Transduction , 1990 .

[61]  Paul C. Bressloff,et al.  Neuronal dynamics based on discontinuous circle maps , 1990 .

[62]  H. Haken,et al.  Synergetic Computers for Pattern Recognition and Associative Memory , 1987 .

[63]  R. Tsien,et al.  Multiple types of neuronal calcium channels and their selective modulation , 1988, Trends in Neurosciences.

[64]  Kurt Wiesenfeld,et al.  Minireview of stochastic resonance. , 1998, Chaos.

[65]  J. Byrne,et al.  Simulation of the bursting activity of neuron R15 in Aplysia: role of ionic currents, calcium balance, and modulatory transmitters. , 1991, Journal of neurophysiology.

[66]  Zhou,et al.  Escape-time distributions of a periodically modulated bistable system with noise. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[67]  A. Bulsara,et al.  Stochastic resonance in a single neuron model: theory and analog simulation. , 1991, Journal of theoretical biology.

[68]  L Stark,et al.  Eye Movements during the Viewing of Necker Cubes , 1978, Perception.

[69]  Rappel,et al.  Stochastic resonance in an autonomous system with a nonuniform limit cycle. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[70]  M. Riani,et al.  Periodic perturbation of ambiguous figure: A neural-network model and a non-simulated experiment , 1995 .

[71]  G. Ermentrout,et al.  Parabolic bursting in an excitable system coupled with a slow oscillation , 1986 .

[72]  Daniel J. Amit,et al.  Modeling brain function: the world of attractor neural networks, 1st Edition , 1989 .

[73]  John G. Taylor,et al.  Discrete time leaky integrator network with synaptic noise , 1991, Neural Networks.

[74]  B. Katz,et al.  Some Observations on Biological Noise , 1950, Nature.

[75]  H Lecar,et al.  Theory of threshold fluctuations in nerves. II. Analysis of various sources of membrane noise. , 1971, Biophysical journal.

[76]  J. Rinzel,et al.  Dissection of a model for neuronal parabolic bursting , 1987, Journal of mathematical biology.

[77]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[78]  S. K. Park,et al.  Random number generators: good ones are hard to find , 1988, CACM.

[79]  John Rinzel,et al.  A Formal Classification of Bursting Mechanisms in Excitable Systems , 1987 .

[80]  Noise effects in a nonlinear dynamic system: The rf superconducting quantum interference device. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[81]  Louis J. DeFelice,et al.  Introduction to membrane noise , 1981 .

[82]  Martin Tobias Huber,et al.  Computer Simulations of Neuronal Signal Transduction: The Role of Nonlinear Dynamics and Noise , 1998 .

[83]  D. Gillespie.  The mathematics of Brownian motion and Johnson noise , 1996 .

[84]  J. Rothwell.  Principles of Neural Science , 1982 .

[85]  Y. Kuramoto,et al.  Phase transitions in active rotator systems , 1986 .

[86]  Mantegna,et al.  Noise enhanced stability in an unstable system. , 1996, Physical review letters.

[87]  H. Haken,et al.  Stochastic resonance without external periodic force. , 1993, Physical review letters.

[88]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

[89]  J. Lisman.  Bursts as a unit of neural information: making unreliable synapses reliable , 1997, Trends in Neurosciences.

[90]  Paul Glendinning,et al.  Stability, instability and chaos , by Paul Glendinning. Pp. 402. £45. 1994. ISBN 0 521 41553 5 (hardback); £17.95 ISBN 0 521 42566 2 (paperback) (Cambridge). , 1997, The Mathematical Gazette.

[91]  B Katz,et al.  The statistical nature of the acetylcholine potential and its molecular components , 1972, The Journal of physiology.

[92]  Wiesenfeld,et al.  Theory of stochastic resonance. , 1989, Physical review. A, General physics.

[93]  Robert M. Westervelt,et al.  Stability and dynamics of simple electronic neural networks with added inertia , 1986 .

[94]  H Lecar,et al.  Theory of threshold fluctuations in nerves. I. Relationships between electrical noise and fluctuations in axon firing. , 1971, Biophysical journal.

[95]  E. Kandel.  Small systems of neurons. , 1979, Scientific American.

[96]  Jack D. Cowan,et al.  Stochastic Single Neurons , 1995, Neural Computation.

[97]  R. Westervelt,et al.  Dynamics of simple electronic neural networks , 1987 .

[98]  Santucci,et al.  Stochastic resonance as a bona fide resonance. , 1995, Physical review letters.

[99]  P. Hänggi,et al.  Reaction-rate theory: fifty years after Kramers , 1990 .

[100]  Peter Földiák,et al.  SPARSE CODING IN THE PRIMATE CORTEX , 2002 .

[101]  Kurt Wiesenfeld,et al.  Noisy precursors of nonlinear instabilities , 1985 .

[102]  D. Polan,et al.  Noise: The Political Economy of Music , 1989 .

[103]  K. Aihara,et al.  Chaotic neural networks , 1990 .

[104]  B. Katz.  Nerve, Muscle and Synapse , 1966 .

[105]  A. Holden.  Models of the stochastic activity of neurones , 1976 .

[106]  R. Fox,et al.  QUANTIFYING STOCHASTIC RESONANCE IN BISTABLE SYSTEMS : RESPONSE VS RESIDENCE-TIME DISTRIBUTION FUNCTIONS , 1998 .

[107]  Robert S. MacKay,et al.  Multistability in networks of weakly coupled bistable units , 1995, patt-sol/9501003.

[108]  Alexander B. Neiman,et al.  COHERENCE RESONANCE AT NOISY PRECURSORS OF BIFURCATIONS IN NONLINEAR DYNAMICAL SYSTEMS , 1997 .

[109]  Robert S. Maier,et al.  The Weak-Noise Characteristic Boundary Exit Problem: Old and New Results , 1996 .

[110]  D. Carpenter,et al.  Temperature Effects on Pacemaker Generation, Membrane Potential, and Critical Firing Threshold in Aplysia Neurons , 1967, The Journal of general physiology.

[111]  Massimo Riani,et al.  Effects of Visual Angle on Perspective Reversal for Ambiguous Patterns , 1982, Perception.

[112]  Roman Bek,et al.  Discourse on one way in which a quantum-mechanics language on the classical logical base can be built up , 1978, Kybernetika.

[113]  Morillo,et al.  Distribution of escape times in a driven stochastic model. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[114]  Thomas T. Imhoff,et al.  Noise-enhanced tactile sensation , 1996, Nature.

[115]  B. O. Alving,et al.  A Contribution of an Electrogenic Na+ Pump to Membrane Potential in Aplysia Neurons , 1968, The Journal of general physiology.

[116]  E. Coddington,et al.  Theory of Ordinary Differential Equations , 1955 .

[117]  Paul C. Bressloff,et al.  Stochastic dynamics of the diffusive Haken model with subthreshold periodic forcing , 1998 .

[118]  K. Schäfer,et al.  Static and dynamic activity of cold receptors at various calcium levels. , 1982, Journal of neurophysiology.

[119]  Riani,et al.  Stochastic resonance in the perceptual interpretation of ambiguous figures: A neural network model. , 1994, Physical review letters.

[120]  Ohira,et al.  Master-equation approach to stochastic neurodynamics. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[121]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[122]  Takashi Kunisawa,et al.  Critical Slowing-Down near the Transition Region from the Resting to Time-Ordered States in Squid Giant Axons , 1978 .

[123]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[124]  William Bialek,et al.  Spikes: Exploring the Neural Code , 1996 .

[125]  N. Swindale.  The development of topography in the visual cortex: a review of models. , 1996 .

[126]  Bressloff.  Neural networks, lattice instantons, and the anti-integrable limit. , 1995, Physical review letters.

[127]  Peter M. B. Walker.  Chambers science and technology dictionary , 1988 .

[128]  Bartlett W. Mel,et al.  Information Processing in Dendritic Trees , 1994, Neural Computation.

[129]  B. Katz,et al.  Spontaneous subthreshold activity at motor nerve endings , 1952, The Journal of physiology.

[130]  L. Reichl.  A modern course in statistical physics , 1980 .

[131]  Schieve,et al.  Single effective neuron. , 1991, Physical Review A. Atomic, Molecular, and Optical Physics.

[132]  Dante R. Chialvo,et al.  Modulated noisy biological dynamics: Three examples , 1993 .

[133]  Adi R. Bulsara,et al.  Tuning in to Noise , 1996 .

[134]  Teich,et al.  Information measures quantifying aperiodic stochastic resonance. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.