Short-term and spike-timing-dependent plasticity facilitate the formation of modular neural networks

Abstract The brain has the phenomenal ability to reorganise itself by forming new connections among neurons and by pruning others. The so-called neural or brain plasticity facilitates the modification of brain structure and function over different time scales. Plasticity might occur due to external stimuli received from the environment, during recovery from brain injury, or due to modifications within the body and brain itself. In this paper, we study the combined effect of short-term (STP) and spike-timing-dependent plasticity (STDP) on the synaptic strength of excitatory coupled Hodgkin-Huxley neurons and show that plasticity can facilitate the formation of modular neural networks with complex topologies that resemble those of networks with preferential attachment properties. In particular, we use an STDP rule that alters the synaptic coupling intensity based on time intervals between spikes of postsynaptic and presynaptic neurons. Previous work has shown that STDP may induce the emergence of directed connections from high to low frequency spiking neurons. On the other hand, STP is attributed to the release of neurotransmitters in the synaptic cleft of neurons that alter its synaptic efficiency. Our results suggest that the combined effect of STP and STDP with long recovery times facilitates the formation of connections among neurons with similar spike frequencies only, a kind of preferential attachment. We then pursue this further and show that, when starting with all-to-all neural configurations, depending on the STP recovery time and distribution of neural frequencies, modular neural networks can emerge as a direct result of the combined effect of STP and STDP.

[1]  Y. Dan,et al.  Spike timing-dependent plasticity: a Hebbian learning rule. , 2008, Annual review of neuroscience.

[2]  G. Bi,et al.  Synaptic modification by correlated activity: Hebb's postulate revisited. , 2001, Annual review of neuroscience.

[3]  E. Lameu,et al.  Alterations in brain connectivity due to plasticity and synaptic delay , 2017, The European Physical Journal Special Topics.

[4]  Misha Tsodyks,et al.  Short-Term Facilitation may Stabilize Parametric Working Memory Trace , 2011, Front. Comput. Neurosci..

[5]  Angelo Bifone,et al.  Modular structure of brain functional networks: breaking the resolution limit by Surprise , 2016, Scientific Reports.

[6]  G. Bi,et al.  Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type , 1998, The Journal of Neuroscience.

[7]  Shih-Chii Liu Analog VLSI Circuits for Short-Term Dynamic Synapses , 2003, EURASIP J. Adv. Signal Process..

[8]  Vladimir Parpura,et al.  Mathematical Modeling in Neuroscience: Neuronal Activity and Its Modulation by Astrocytes , 2016, Front. Integr. Neurosci..

[9]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[10]  Jacob G Foster,et al.  Edge direction and the structure of networks , 2009, Proceedings of the National Academy of Sciences.

[11]  L. Abbott,et al.  Synaptic Depression and Cortical Gain Control , 1997, Science.

[12]  Everton J. Agnes,et al.  Diverse synaptic plasticity mechanisms orchestrated to form and retrieve memories in spiking neural networks , 2015, Nature Communications.

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

[14]  Richard F. Betzel,et al.  Modular Brain Networks. , 2016, Annual review of psychology.

[15]  K. Lashley Studies of Cerebral Function in Learning (VI). , 1924 .

[16]  W. Gerstner,et al.  Connectivity reflects coding: a model of voltage-based STDP with homeostasis , 2010, Nature Neuroscience.

[17]  M. Baptista,et al.  Complementary action of chemical and electrical synapses to perception , 2014, 1412.1369.

[18]  Chris G. Antonopoulos,et al.  Chimera-like States in Modular Neural Networks , 2015, Scientific Reports.

[19]  Peter A. Tass,et al.  Unlearning tinnitus-related cerebral synchrony with acoustic coordinated reset stimulation: theoretical concept and modelling , 2012, Biological Cybernetics.

[20]  M. Newman Analysis of weighted networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  E L Lameu,et al.  Inference of topology and the nature of synapses, and the flow of information in neuronal networks. , 2017, Physical review. E.

[22]  C. Stevens,et al.  Facilitation and depression at single central synapses , 1995, Neuron.

[23]  Rubin Wang,et al.  The Energy Coding of a Structural Neural Network Based on the Hodgkin–Huxley Model , 2018, Front. Neurosci..

[24]  W. Gerstner,et al.  Spike-Timing-Dependent Plasticity: A Comprehensive Overview , 2012, Front. Syn. Neurosci..

[25]  Chris G. Antonopoulos,et al.  Spike timing-dependent plasticity induces non-trivial topology in the brain , 2016, Neural Networks.

[26]  E L Lameu,et al.  Recurrence quantification analysis for the identification of burst phase synchronisation. , 2018, Chaos.

[27]  E. Bennett,et al.  Chemical and Anatomical Plasticity of Brain Changes in brain through experience, demanded by learning theories, are found in experiments with rats , 1964 .

[28]  Leonhard Lücken,et al.  Noise-enhanced coupling between two oscillators with long-term plasticity. , 2015, Physical review. E.

[29]  Mark D. McDonnell,et al.  Phase changes in neuronal postsynaptic spiking due to short term plasticity , 2017, PLoS Comput. Biol..

[30]  E. Schuman,et al.  Spatially Stable Mitochondrial Compartments Fuel Local Translation during Plasticity , 2019, Cell.

[31]  Chris G Antonopoulos,et al.  Dynamic range in the C. elegans brain network. , 2015, Chaos.

[32]  E L Lameu,et al.  Synchronous behaviour in network model based on human cortico-cortical connections. , 2018, Physiological measurement.

[33]  L. Abbott,et al.  Synaptic plasticity: taming the beast , 2000, Nature Neuroscience.

[34]  M E J Newman Assortative mixing in networks. , 2002, Physical review letters.

[35]  Chris G. Antonopoulos,et al.  Do Brain Networks Evolve by Maximizing Their Information Flow Capacity? , 2015, PLoS Comput. Biol..

[36]  Raoul Borges,et al.  Effects of the spike timing-dependent plasticity on the synchronisation in a random Hodgkin-Huxley neuronal network , 2015, Commun. Nonlinear Sci. Numer. Simul..

[37]  J. Konorski Conditioned reflexes and neuron organization. , 1948 .

[38]  G. Fagiolo Clustering in complex directed networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Frank W. Stahnisch,et al.  Santiago Ramón y Cajal's concept of neuronal plasticity: the ambiguity lives on , 2002, Trends in Neurosciences.

[40]  W. James,et al.  The Principles of Psychology. , 1983 .

[41]  Antonio M. Batista,et al.  Dynamic range in a neuron network with electrical and chemical synapses , 2014, Commun. Nonlinear Sci. Numer. Simul..

[42]  Albert-Lszl Barabsi,et al.  Network Science , 2016, Encyclopedia of Big Data.

[43]  C. Barnes,et al.  Neural plasticity in the ageing brain , 2006, Nature Reviews Neuroscience.

[44]  Peter A. Tass,et al.  Delay-Induced Multistability and Loop Formation in Neuronal Networks with Spike-Timing-Dependent Plasticity , 2018, Scientific Reports.

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

[46]  S. R. Lopes,et al.  Dynamic range in small-world networks of Hodgkin-Huxley neurons with chemical synapses , 2014 .

[47]  Peter A. Tass,et al.  Self-organized noise resistance of oscillatory neural networks with spike timing-dependent plasticity , 2013, Scientific Reports.

[48]  Chris G. Antonopoulos,et al.  Evaluating performance of neural codes in model neural communication networks , 2019, Neural Networks.

[49]  Murilo S. Baptista,et al.  Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model , 2016, Neural Networks.

[50]  H. Buchtel,et al.  Neuronal plasticity: historical roots and evolution of meaning , 2008, Experimental Brain Research.

[51]  Jürgen Kurths,et al.  Bistable Firing Pattern in a Neural Network Model , 2018, Front. Comput. Neurosci..

[52]  Chris G. Antonopoulos,et al.  Dynamical complexity in the C.elegans neural network , 2015, 1510.07260.

[53]  R. Zucker Short-term synaptic plasticity. , 1989 .

[54]  S. Romani,et al.  Short‐term plasticity based network model of place cells dynamics , 2015, Hippocampus.

[55]  Celso Grebogi,et al.  Synaptic Plasticity and Spike Synchronisation in Neuronal Networks , 2017, 1709.00455.

[56]  Wulfram Gerstner,et al.  A neuronal learning rule for sub-millisecond temporal coding , 1996, Nature.

[57]  Mark C. W. van Rossum,et al.  Recurrent networks with short term synaptic depression , 2009, Journal of Computational Neuroscience.