2000 character limit reached
A robust balancing mechanism for spiking neural networks
Published 23 Jan 2024 in cond-mat.dis-nn and q-bio.NC | (2401.12559v1)
Abstract: Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works also in absence of strong external currents. Biologically, the mechanism exploits the plasticity of excitatory-excitatory synapses induced by short-term depression. Mathematically, the nonlinear response of the synaptic activity is the key ingredient responsible for the emergence of a stable balanced regime. Our claim is supported by a simple self-consistent analysis accompanied by extensive simulations performed for increasing network sizes. The observed regime is essentially fluctuation driven and characterized by highly irregular spiking dynamics of all neurons.
- C. van Vreeswijk and H. Sompolinsky, Science 274, 1724 (1996).
- D. Sherrington and S. Kirkpatrick, Physical review letters 35, 1792 (1975).
- S. Kirkpatrick and D. Sherrington, Physical Review B 17, 4384 (1978).
- M. Antoni and S. Ruffo, Physical Review E 52, 2361 (1995).
- T. Konishi and K. Kaneko, Journal of Physics A: Mathematical and General 23, L715 (1990).
- A. T. Winfree, The Geometry of Biological Time, 2nd ed., Interdisciplinary Applied Mathematics, Vol. 12 (Springer-Verlag New York, 2001).
- S. H. Strogatz and I. Stewart, Scientific american 269, 102 (1993).
- A. Pikovsky and M. Rosenblum, Chaos: An Interdisciplinary Journal of Nonlinear Science 25, 097616 (2015).
- L. F. Abbott and C. Van Vreeswijk, Physical Review E 48, 1483 (1993).
- C. van Vreeswijk, Physical Review E 54, 5522 (1996).
- H. Haken, Brain dynamics: synchronization and activity patterns in pulse-coupled neural nets with delays and noise (Springer Science & Business Media, 2006).
- X.-J. Wang and G. Buzsáki, Journal of neuroscience 16, 6402 (1996).
- S. Luccioli and A. Politi, Phys. Rev. Lett. 105, 158104 (2010).
- E. Ullner and A. Politi, Physical Review X 6, 011015 (2016).
- W. R. Softky and C. Koch, Journal of neuroscience 13, 334 (1993).
- A. Destexhe and D. Paré, Journal of neurophysiology 81, 1531 (1999).
- R. M. Bruno and B. Sakmann, Science 312, 1622 (2006).
- M. N. Shadlen and W. T. Newsome, Current opinion in neurobiology 4, 569 (1994).
- N. Brunel and V. Hakim, Neural computation 11, 1621 (1999).
- J. Barral and A. D. Reyes, Nature neuroscience 19, 1690 (2016).
- M. Monteforte and F. Wolf, Phys. Rev. Lett. 105, 268104 (2010).
- A. Litwin-Kumar and B. Doiron, Nat Neurosci 15, 1498 (2012).
- J. Kadmon and H. Sompolinsky, Phys. Rev. X 5, 041030 (2015).
- R. Rosenbaum and B. Doiron, Physical Review X 4, 021039 (2014).
- R. Pyle and R. Rosenbaum, Physical Review E 93, 040302 (2016).
- M. di Volo and A. Torcini, Phys. Rev. Lett. 121, 128301 (2018).
- Y. Ahmadian and K. D. Miller, Neuron 109, 3373 (2021).
- S. Chung and D. Ferster, Neuron 20, 1177 (1998).
- A. D. Lien and M. Scanziani, Nature neuroscience 16, 1315 (2013).
- M. Tsodyks and S. Wu, Scholarpedia 8, 3153 (2013).
- M. V. Tsodyks and H. Markram, Proceedings of the national academy of sciences 94, 719 (1997).
- R. E. Mirollo and S. H. Strogatz, SIAM Journal on Applied Mathematics 50, 1645 (1990).
- A. N. Burkitt, Biological cybernetics 95, 1 (2006).
- B. Ermentrout, Neural computation 8, 979 (1996).
- The parameters are set as follows. Each neuron has a probability of 10% to be connected to any other neuron, to guarantee that 80% (20%) of these connections are excitatory (inhibitory) as in the cortex we set pe=0.08superscript𝑝𝑒0.08p^{e}=0.08italic_p start_POSTSUPERSCRIPT italic_e end_POSTSUPERSCRIPT = 0.08 (pi=0.02superscript𝑝𝑖0.02p^{i}=0.02italic_p start_POSTSUPERSCRIPT italic_i end_POSTSUPERSCRIPT = 0.02). For the STD parameters we set u=0.5𝑢0.5u=0.5italic_u = 0.5 (a single spike emission halves the synaptic resources) and τd=1subscript𝜏𝑑1\tau_{d}=1italic_τ start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT = 1 s. The overall coupling strength has been fixed to G=1𝐺1G=1italic_G = 1. For the ZI(ϕ)subscript𝑍Iitalic-ϕZ_{\rm I}(\phi)italic_Z start_POSTSUBSCRIPT roman_I end_POSTSUBSCRIPT ( italic_ϕ ) (ZLIF(ϕ)subscript𝑍LIFitalic-ϕZ_{\rm LIF}(\phi)italic_Z start_POSTSUBSCRIPT roman_LIF end_POSTSUBSCRIPT ( italic_ϕ )) PRC we considered synapses with α−1=0.2superscript𝛼10.2\alpha^{-1}=0.2italic_α start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT = 0.2 ms (α−1=0.04superscript𝛼10.04\alpha^{-1}=0.04italic_α start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT = 0.04 ms).
- In our case, the inhibitory field is equal to the excitatory field.
- G. Buzsáki and K. Mizuseki, Nature Reviews Neuroscience 15, 264 (2014).
- S. Romani and M. Tsodyks, Hippocampus 25, 94 (2015).
- D. Hansel and G. Mato, Journal of Neuroscience 33, 133 (2013).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.