Abstract
We take an adaptive leaky integrate-and-fire neuron model to explore the effect of non-Poisson neurotransmitter on stochastic resonance and its signal-to-noise ratio (SNR) gain. Event triggered algorithm is adopted to speed up the simulating process. It is revealed that both the output SNR and the SNR gain can be monotonically improved when increasing the shape parameter for Gamma distribution. Particularly, for large signal coupling strength, the 1:1 stochastic phase locking induced by Gamma noise is responsible for the frequency matching stochastic resonance, and the output signal-to-noise ratio can surpass the input signal-to-noise ratio, which is significantly different with Poisson case, while for extremely weak signal coupling strength, the SNR gain peak, which is far larger than unity, is due to noise induced resonance. The observations are meaningful in understanding the neural processing mechanisms from a more realistic viewpoint of synaptic modeling.
摘要
我们采用自适应漏电积分-放电模型来研究非泊松递质对随机共振及其信噪比增益的影响, 并运用事件驱动算法加速模拟过 程. 研究结果表明, 输出信噪比和信噪比增益都会随着伽马分布的形状参数的增加而增加. 特别地, 当输入信号幅值较大时, 由 Gamma噪声诱导的1:1随机锁像揭示出此时发生的是满足频率匹配关系的随机共振现象, 并且输出信噪比可以超过输入信噪比, 这 与Poisson情形显著不同; 而当输入信号幅值极弱时, 信噪比增益会远远大于1, 这是由于发生了噪声诱导的随机共振现象. 这些观察 结果对于从更现实的突触建模角度理解神经信息处理机制是有意义的.
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References
L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Stochastic resonance, Rev. Mod. Phys. 70, 223 (1998).
L. Q. Uddin, Bring the noise: reconceptualizing spontaneous neural activity, Trends Cogn. Sci. 24, 734 (2020).
Y. Xu, Y. Guo, G. Ren, and J. Ma, Dynamics and stochastic resonance in a thermosensitive neuron, Appl. Math. Comput. 385, 125427 (2020).
G. Winterer, M. Ziller, H. Dorn, K. Frick, C. Mulert, N. Dahhan, W. M. Herrmann, and R. Coppola, Cortical activation, signal-to-noise ratio and stochastic resonance during information processing in man, Clin. Neurophysiol. 110, 1193 (1999).
Z. Gingl, P. Makra, and R. Vajtai, High signal-to-noise ratio gain by stochastic resonance in a double well, Fluct. Noise Lett. 01, L181 (2001).
P. Makra, and Z. Gingl, A dynamical system exhibits high signal-to-noise ratio gain by stochastic resonance, Am. Inst. Phys. 7, 100 (2003).
L. Zhangcai, and Q. Youguo, Stochastic resonance driven by time-modulated neurotransmitter random point trains, Phys. Rev. Lett. 91, 208103 (2003).
J. D. Touboul, C. Piette, L. Venance, and G. B. Ermentrout, Noise-induced synchronization and antiresonance in interacting excitable systems: applications to deep brain stimulation in parkinson’s disease, Phys. Rev. X 10, 011073 (2020).
A. N. Burkitt, A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biol. Cybern. 95, 1 (2006).
A. N. Burkitt, A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties, Biol. Cybern. 95, 97 (2006).
Y. M. Kang, J. X. Xu, and Y. Xie, Signal-to-noise ratio gain of a noisy neuron that transmits subthreshold periodic spike trains, Phys. Rev. E 72, 021902 (2005).
A. Amarasingham, T. L. Chen, S. Geman, M. T. Harrison, and D. L. Sheinberg, Spike count reliability and the poisson hypothesis, J. Neurosci. 26, 801 (2006).
A. A. Faisal, L. P. J. Selen, and D. M. Wolpert, Noise in the nervous system, Nat. Rev. Neurosci. 9, 292 (2008).
P. Kara, P. Reinagel, and R. C. Reid, Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons, Neuron 27, 635 (2000).
G. Maimon, and J. A. Assad, Beyond poisson: increased spike-time regularity across primate parietal cortex, Neuron 62, 426 (2009).
K. Rajdl, and P. Lansky, Stein’s neuronal model with pooled renewal input, Biol. Cybern. 109, 389 (2015).
H. Cĝteau, and A. D. Reyes, Relation between single neuron and population spiking statistics and effects on network activity, Phys. Rev. Lett. 96, 058101 (2006).
B. Lindner, Superposition of many independent spike trains is generally not a Poisson process, Phys. Rev. E 73, 022901 (2006).
J. Feng, Y. Deng, and E. Rossoni, Dynamics of moment neuronal networks, Phys. Rev. E 73, 1 (2006).
P. Lansky, L. Sacerdote, and C. Zucca, The Gamma renewal process as an output of the diffusion leaky integrate-and-fire neuronal model, Biol. Cybern. 110, 193 (2016).
J. Bauermann, and B. Lindner, Multiplicative noise is beneficial for the transmission of sensory signals in simple neuron models, Biosystems 178, 25 (2019).
M. Tamborrino, and P. Lansky, Shot noise, weak convergence and diffusion approximations, Phys. D-Nonlinear Phenom. 418, 132845 (2021).
I. Eliazar, and J. Klafter, On the nonlinear modeling of shot noise, Proc. Natl. Acad. Sci. USA 102, 13779 (2005).
Q. Chen, and N. Xu, Shot noise in superconducting wires applied with a periodic electric field, J Nanosci. Nanotechnol. 18, 3729 (2017).
H. X. Lü, and Z. W. Xie, The shot noise in quasi one-dimensional magnetic tunnel junctions, Sci. Sin.-Phys. Mech. Astron. 48, 057501 (2018).
T. Marc, When less is more: Non-monotonic spike sequence processing in neurons, Front. Comput. Neurosci. 5, (2011).
S. R. Seydnejad, Reconstruction of the input signal of the leaky integrate-and-fire neuronal model from its interspike intervals, Biol. Cybern. 110, 3 (2016).
Y. Kang, Y. Chen, Y. Fu, Z. Wang, and G. Chen, Formation of spiral wave in Hodgkin-Huxley neuron networks with Gamma-distributed synaptic input, Commun. Nonlinear Sci. Numer. Simul. 83, 105112 (2020).
J. Benda, L. Maler, and A. Longtin, Linear versus nonlinear signal transmission in neuron models with adaptation currents or dynamic thresholds, J. Neurophysiol. 104, 2806 (2010).
C. Yuan, and J. Wang, Comparison of firing mechanisms of neuron model adaptability under external alternating electric field, J. Northeast. Univ. 35, 1229 (2014).
M. Levakova, L. Kostal, C. Monsempès, P. Lucas, and R. Kobayashi, Adaptive integrate-and-fire model reproduces the dynamics of olfactory receptor neuron responses in a moth, J. R. Soc. Interface. 16, 20190246 (2019).
F. B. Vialatte, M. Maurice, J. Dauwels, and A. Cichocki, Steady-state visually evoked potentials: Focus on essential paradigms and future perspectives, Prog. Neurobiol. 90, 418 (2010).
U. Will, and E. Berg, Brain wave synchronization and entrainment to periodic acoustic stimuli, Neurosci. Lett. 424, 55 (2007).
A. Schilling, K. Tziridis, H. Schulze, and P. Krauss, The stochastic resonance model of auditory perception: A unified explanation of tinnitus development, Zwicker tone illusion, and residual inhibition, Prog. Brain Res. 262, 139 (2021).
H. Markram, J. Lübke, M. Frotscher, A. Roth, and B. Sakmann, Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex, J. Physiol. 500, 409 (1997).
M. J. E. Richardson, and R. Swarbrick, Firing-rate response of a neuron receiving excitatory and inhibitory synaptic shot noise, Phys. Rev. Lett. 105, 178102 (2010).
W. Gerstner, W. M. Kistler, R. Naud, and L. Paninski, Neuronal dynamics: From single neurons to networks and models of cognition (Cambridge University Press, Cambridge, 2014).
S. B. Laughlin, and T. J. Sejnowski, Communication in neuronal networks, Science 301, 1870 (2003).
F. Zhu, R. Wang, X. Pan, and Z. Zhu, Energy expenditure computation of a single bursting neuron, Cogn. Neurodyn. 13, 75 (2019).
Y. M. Kang, J. X. Xu, and Y. Xie, A further insight into stochastic resonance in an integrate-and-fire neuron with noisy periodic input, Chaos Solitons Fractals 25, 165 (2005).
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This work was supported by the Non-Poisson Modeling of Neuron Synaptic Input and Critical Dynamics for Cortical Networks (Grant No. 11772241).
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Kang, Y., Fu, Y. & Chen, Y. Signal-to-noise ratio gain of an adaptive neuron model with Gamma renewal synaptic input. Acta Mech. Sin. 38, 521347 (2022). https://doi.org/10.1007/s10409-021-09029-6
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DOI: https://doi.org/10.1007/s10409-021-09029-6