Neuronal Transmission of Subthreshold Periodic Stimuli Via Symbolic Spike Patterns

We study how sensory neurons detect and transmit a weak external stimulus. We use the FitzHugh–Nagumo model to simulate the neuronal activity. We consider a sub-threshold stimulus, i.e., the stimulus is below the threshold needed for triggering action potentials (spikes). However, in the presence of noise the neuron that perceives the stimulus fires a sequence of action potentials (a spike train) that carries the stimulus’ information. To yield light on how the stimulus’ information can be encoded and transmitted, we consider the simplest case of two coupled neurons, such that one neuron (referred to as neuron 1) perceives a subthreshold periodic signal but the second neuron (neuron 2) does not perceive the signal. We show that, for appropriate coupling and noise strengths, both neurons fire spike trains that have symbolic patterns (defined by the temporal structure of the inter-spike intervals), whose frequencies of occurrence depend on the signal’s amplitude and period, and are similar for both neurons. In this way, the signal information encoded in the spike train of neuron 1 propagates to the spike train of neuron 2. Our results suggest that sensory neurons can exploit the presence of neural noise to fire spike trains where the information of a subthreshold stimulus is encoded in over expressed and/or in less expressed symbolic patterns.

[1]  Mark D. McDonnell,et al.  The benefits of noise in neural systems: bridging theory and experiment , 2011, Nature Reviews Neuroscience.

[2]  Christoph Bandt,et al.  Small Order Patterns in Big Time Series: A Practical Guide , 2019, Entropy.

[3]  John O'Keefe,et al.  Independent rate and temporal coding in hippocampal pyramidal cells , 2003, Nature.

[4]  S. R. Lopes,et al.  Symbolic analysis of bursting dynamical regimes of Rulkov neural networks , 2020, Neurocomputing.

[5]  J. García-Ojalvo,et al.  Effects of noise in excitable systems , 2004 .

[6]  Cristina Masoller,et al.  Characterizing signal encoding and transmission in class I and class II neurons via ordinal time-series analysis. , 2019, Chaos.

[7]  F. Varela,et al.  Measuring phase synchrony in brain signals , 1999, Human brain mapping.

[8]  Cristina Masoller,et al.  Sub-threshold signal encoding in coupled FitzHugh-Nagumo neurons , 2017, Scientific Reports.

[9]  Luciano Zunino,et al.  Permutation entropy based time series analysis: Equalities in the input signal can lead to false conclusions , 2017 .

[10]  Chun-I Yeh,et al.  Temporal precision in the neural code and the timescales of natural vision , 2007, Nature.

[11]  Cristina Masoller,et al.  Emergence of spike correlations in periodically forced excitable systems. , 2015, Physical review. E.

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

[13]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[14]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[15]  Niels Wessel,et al.  Classifying cardiac biosignals using ordinal pattern statistics and symbolic dynamics , 2012, Comput. Biol. Medicine.

[16]  Ricardo Sevilla-Escoboza,et al.  Ordinal synchronization: Using ordinal patterns to capture interdependencies between time series , 2018, Chaos, Solitons & Fractals.

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

[18]  Massimiliano Zanin,et al.  Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review , 2012, Entropy.

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

[20]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[21]  Cristina Masoller,et al.  Neuronal coupling benefits the encoding of weak periodic signals in symbolic spike patterns , 2019, Commun. Nonlinear Sci. Numer. Simul..

[22]  Kelvin E. Jones,et al.  Neuronal variability: noise or part of the signal? , 2005, Nature Reviews Neuroscience.