Models and properties of power-law adaptation in neural systems.

Many biological systems exhibit complex temporal behavior that cannot be adequately characterized by a single time constant. This dynamics, observed from single channels up to the level of human psychophysics, is often better described by power-law rather than exponential dependences on time. We develop and study the properties of neural models with scale-invariant, power-law adaptation and contrast them with the more commonly studied exponential case. Responses of an adapting firing-rate model to constant, pulsed, and oscillating inputs in both the power-law and exponential cases are considered. We construct a spiking model with power-law adaptation based on a nested cascade of processes and show that it can be "programmed" to produce a wide range of time delays. Finally, within a network model, we use power-law adaptation to reproduce long-term features of the tilt aftereffect.

[1]  D. Gilden.  Cognitive emissions of 1/f noise. , 2001, Psychological review.

[2]  Rudd,et al.  Doubly differential cross sections of low-energy electrons emitted in the ionization of molecular hydrogen by bare carbon ions. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[3]  Alon Fishbach,et al.  Primary auditory cortex of cats: feature detection or something else? , 2003, Biological Cybernetics.

[4]  L S Liebovitch,et al.  Fractal model of ion-channel kinetics. , 1987, Biochimica et biophysica acta.

[5]  J. Thorson,et al.  Distributed Relaxation Processes in Sensory Adaptation , 1974, Science.

[6]  Thomas J. Anastasio,et al.  The fractional-order dynamics of brainstem vestibulo-oculomotor neurons , 1994, Biological Cybernetics.

[7]  N. Logothetis,et al.  Very slow activity fluctuations in monkey visual cortex: implications for functional brain imaging. , 2003, Cerebral cortex.

[8]  H. Seung,et al.  Tilt aftereffect and adaptation-induced changes in orientation tuning in visual cortex. , 2005, Journal of neurophysiology.

[9]  Stephen T. Neely,et al.  Signals, Sound, and Sensation , 1997 .

[10]  Jouin,et al.  Energy dependence of cross sections for double-electron capture in 48-132-keV C6++He collisions. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[11]  E. Salpeter,et al.  Diffusion models of ion-channel gating and the origin of power-law distributions from single-channel recording. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Jeffrey M. Hausdorff,et al.  Long-range anticorrelations and non-Gaussian behavior of the heartbeat. , 1993, Physical review letters.

[13]  G. Ermentrout,et al.  Modelling of intersegmental coordination in the lamprey central pattern generator for locomotion , 1992, Trends in Neurosciences.

[14]  M. Greenlee,et al.  Marathon adaptation to spatial contrast: Saturation in sight , 1985, Vision Research.

[15]  Shimon Marom,et al.  Interaction between Duration of Activity and Time Course of Recovery from Slow Inactivation in Mammalian Brain Na+Channels , 1998, The Journal of Neuroscience.

[16]  P. Schwindt,et al.  Calcium-dependent potassium currents in neurons from cat sensorimotor cortex. , 1992, Journal of neurophysiology.

[17]  Mark W. Greenlee,et al.  Saturation of the tilt aftereffect , 1987, Vision Research.

[18]  M. Meister,et al.  Fast and Slow Contrast Adaptation in Retinal Circuitry , 2002, Neuron.

[19]  P. Lennie,et al.  Rapid adaptation in visual cortex to the structure of images. , 1999, Science.

[20]  Walter Senn,et al.  Minimal Models of Adapted Neuronal Response to In VivoLike Input Currents , 2004, Neural Computation.

[21]  J. Wixted,et al.  Genuine power curves in forgetting: A quantitative analysis of individual subject forgetting functions , 1997, Memory & cognition.

[22]  Dora E. Angelaki,et al.  Response properties of pigeon otolith afferents to linear acceleration , 1997, Experimental Brain Research.

[23]  D L Gilden,et al.  1/f noise in human cognition. , 1995, Science.

[24]  N. Qian,et al.  Learning and adaptation in a recurrent model of V1 orientation selectivity. , 2003, Journal of neurophysiology.

[25]  P. Schwindt,et al.  Long-lasting reduction of excitability by a sodium-dependent potassium current in cat neocortical neurons. , 1989, Journal of neurophysiology.

[26]  D. Anderson,et al.  Transfer characteristics of first and second order lateral canal vestibular neurons in gerbil , 1976, Brain Research.

[27]  M. Nelson,et al.  Logarithmic time course of sensory adaptation in electrosensory afferent nerve fibers in a weakly electric fish. , 1996, Journal of neurophysiology.

[28]  P. Schwindt,et al.  Two transient potassium currents in layer V pyramidal neurones from cat sensorimotor cortex. , 1991, The Journal of physiology.

[29]  H. Sompolinsky,et al.  Theory of orientation tuning in visual cortex. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[30]  M. Sur,et al.  Adaptation-Induced Plasticity of Orientation Tuning in Adult Visual Cortex , 2000, Neuron.

[31]  Jeffrey M. Hausdorff,et al.  Multiscaled randomness: A possible source of 1/f noise in biology. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  J. Movshon,et al.  Adaptation changes the direction tuning of macaque MT neurons , 2004, Nature Neuroscience.

[33]  J. Doyle,et al.  Robust perfect adaptation in bacterial chemotaxis through integral feedback control. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[34]  W. Regehr,et al.  Short-term synaptic plasticity. , 2002, Annual review of physiology.

[35]  D Rose,et al.  Dynamics of Adaptation to Contrast , 1982, Perception.

[36]  I. Nelken,et al.  Processing of low-probability sounds by cortical neurons , 2003, Nature Neuroscience.

[37]  Eve Marder,et al.  Oscillating Networks: Control of Burst Duration by Electrically Coupled Neurons , 1991, Neural Computation.

[38]  I. Nelken,et al.  Multiple Time Scales of Adaptation in Auditory Cortex Neurons , 2004, The Journal of Neuroscience.

[39]  Vulpiani,et al.  Predictability in systems with many characteristic times: The case of turbulence. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[40]  L. Abbott,et al.  Cascade Models of Synaptically Stored Memories , 2005, Neuron.

[41]  Adrienne L. Fairhall,et al.  Multiple Timescales of Adaptation in a Neural Code , 2000, NIPS.

[42]  Naama Brenner,et al.  History-Dependent Multiple-Time-Scale Dynamics in a Single-Neuron Model , 2005, The Journal of Neuroscience.

[43]  P. Schwindt,et al.  Post‐inhibitory excitation and inhibition in layer V pyramidal neurones from cat sensorimotor cortex. , 1991, The Journal of physiology.

[44]  Richard B. Anderson.  The power law as an emergent property , 2001, Memory & cognition.

[45]  Adrienne L. Fairhall,et al.  Efficiency and ambiguity in an adaptive neural code , 2001, Nature.

[46]  S. Wearne,et al.  Fractional Reaction-Diffusion , 2000 .