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Effects of noisy adaptation on neural spiking statistics Tilo Schwalger,Benjamin Lindner, Karin Fisch, Jan Benda Max-Planck Institute for the Physics of.

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Presentation on theme: "Effects of noisy adaptation on neural spiking statistics Tilo Schwalger,Benjamin Lindner, Karin Fisch, Jan Benda Max-Planck Institute for the Physics of."— Presentation transcript:

1 Effects of noisy adaptation on neural spiking statistics Tilo Schwalger,Benjamin Lindner, Karin Fisch, Jan Benda Max-Planck Institute for the Physics of Complex Systems, Dresden Stochastic Models in Neuroscience, Marseille 2010 LMU, Munich

2 Neurons show spike-frequency adaptation Gabbiani & Krapp, J Neurophysiol 2006 Intrinsic negative feedback

3 Outline What is the source of noise? ● Stratagy and introduction of the model ● ISI statistics for two cases i.“deterministic adaptation” + stochastic receptor current ii.“Stochastic adaptation” + deterministic receptor current ● “mixed case”

4 What is the source of variability? – The strategy ● Introduce variability by stochastic ion currents (channel noise), e.g. ● Modelling signal transduction of auditory receptor cells ● Receptor current ● Sodium current ● Potassium (delayed rectifier) current ● Adaptation current (M-type)

5 What is the source of variability? – The strategy ● Introduce variability by stochastic ion currents (channel noise), e.g. ● Modelling signal transduction of auditory receptor cells ● Receptor current ● Sodium current ● Potassium (delayed rectifier) current ● Adaptation current (M-type) ● Study separately the effect of a specific channel noise ● on the interspike interval (ISI) statistics ● ISI density, firing rate, coefficient of variation (CV), skewness, excess, … ● ISI serial correlation coefficient ● Compare different predictions with experimental data Interspike interval [ms ] Probability density

6 What is the source of variability? – The strategy ● Introduce variability by stochastic ion currents (channel noise), e.g. ● Modelling signal transduction of auditory receptor cells ● Receptor current ● Sodium current ● Potassium (delayed rectifier) current ● Adaptation current (M-type) ● Study separately the effect of a specific channel noise ● on the interspike interval (ISI) statistics ● ISI density, firing rate, coefficient of variation (CV), skewness, excess, … ● ISI serial correlation coefficient ● Compare different predictions with experimental data ● Here: stochastic adaptation current vs. Stochastic receptor current in a simplified model Interspike interval [ms ] Probability density

7 M-type adaptation current ● Two-state channel model ● (voltage-gated) ● Adaptation current with finite number of channels ● voltage-gated potassium current ● Slow kinetics # M-channels open # M- channels

8 Perfect integrate-and-fire model Stochastic adaption current White noise: fast receptor channels

9 Perfect integrate-and-fire model membrane Potential V M-channel activation fraction of open M-channels W Time [ms] Stochastic adaption current White noise: fast receptor channels threshold reset

10 Perfect integrate-and-fire model membrane Potential V M-channel activation fraction of open M-channels W Time [ms] Stochastic adaption current White noise: fast receptor channels threshold reset Firing rate Time [ms]

11 Diffusion approximation of channel noise ● adaptation split up in deterministic and noise part ● Additive noise approximation:

12 Two limit cases Deterministic adaptation

13 Two limit cases Stochastic adaptation Deterministic adaptation

14 Deterministic adaptation (N a →∞) ● Mean adaptation approximation reduced input current much larger than mean ISI

15 Deterministic adaptation (N a →∞) Inverse Gaussian ISI density Negative ISI correlations Gerstein & Mandelbrot, 1964

16 Stochastic adaptation current acts as a colored noise ● Slow modulation of instantaneous firing rate ● due to slow noise process η(t) ● average over fast dynamics of

17 Stochastic adaptation current acts as a colored noise ● Slow modulation of instantaneous firing rate ● due to slow noise process η(t) ● average over fast dynamics of → Colored noise-driven PIF neuron

18 Colored noise model captures ISI density

19 ISI density: B. Lindner, Phys Rev E 2004 small noise

20 Stochastic adaptation yields positive ISI correlations Positive ISI correlations B. Lindner, Phys Rev E 2004

21 ISI density – comparison Determistic adaptation Stochastic adaptation Same CV Inverse Gaussian fails!

22 ISI density – comparison Determistic adaptation Stochastic adaptation

23 How to discriminate from an inverse Gaussian density? skewnes s Inverse Gaussian

24 How to discriminate from an inverse Gaussian density? skewnes s excess (kurtosis) Inverse Gaussian

25 How to discriminate from an inverse Gaussian density? skewnes s excess (kurtosis) Inverse Gaussian Defin e inverse Gaussian distribution:

26 Separation of deterministic and stochastic adaptation Rescaled skewness Rescaled excess

27 Dependence on the adaptation time- scale Rescaled excess Serial correlation coefficient at lag 1

28 Skewness and excess of ISIs – theory ● PIF model driven by colored noise ● Fokker-Planck equation for p(v,η,t) ● Initial condition + fire&reset rule

29 Skewness and excess of ISIs – theory ● PIF model driven by colored noise ● Fokker-Planck equation for p(v,η,t) ● Initial condition ● ISI density + fire&reset rule

30 Skewness and excess of ISIs – theory ● PIF model driven by colored noise ● Fokker-Planck equation for p(v,η,t) ● Initial condition ● ISI density ● Variable transformation ● Fokker-Planck equation + fire&reset rule

31 Skewness and excess of ISIs – theory ● Small noise expansion

32 Mixed case – fast and slow fluctuations D>0 fixed, vary number of channels

33 Simulation of Hodgkin-Huxley type model with M-current Modified Traub-Miles model (Ermentrout, 2000) Mixed case Serial correlations

34 Summary ● Introduced an integrate-and-fire-model with stochastic adaptation current ● (channel noise) ● Case of deterministic adaptation current and white current noise: ● inverse Gaussian ISI distribution and negative serial correlations ● Case of stochastic adaptation current and no white noise: ● peaked ISI distribution and positive serial correlations ● Results might be useful to determine the dominant source of noise

35 Acknowledgements Karin Fisch LMU, Munich Benjamin Lindner MPIPKS, Dresden Jan Benda LMU, Munich

36 Variability depends on sound intensity Karin Fisch & Jan Benda, LMU

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