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Low-dimensional spike rate dynamics of coupled adaptive model neurons

Low-dimensional spike rate dynamics of coupled adaptive model neurons Augustin et al. BMC Neuroscience 2015, 16(Suppl 1):P183 http://www.biomedcentral.com/1471-2202/16/S1/P183 POSTER PRESENTATION Open Access Low-dimensional spike rate dynamics of coupled adaptive model neurons 1,2* 1,2 1,2 Moritz Augustin , Josef Ladenbauer , Klaus Obermayer From 24th Annual Computational Neuroscience Meeting: CNS*2015 Prague, Czech Republic. 18-23 July 2015 The spiking activity of single neurons can be well approximated by a low-dimensional ordinary differential described by a two-dimensional integrate-and-fire model equation in different ways [4,6,7]. Although these approx- that includes neuronal adaptation [1] caused by slowly imation techniques are interrelated it is not clear which decaying potassium currents [2]. For fluctuating inputs reduced model best reproduces the spike rate of the ori- sparsely coupled spiking model neurons exhibit stochas- ginal spiking network, depending on the statistics of the tic population dynamics which can be effectively charac- input. Here we first extend each of these reduction meth- ods to account for neuronal adaptation and then evaluate terized using the Fokker-Planck equation (see, e.g., [3-5]). This approach leads to a model with an infinite- the reduced models in terms of spike rate reproduction dimensional state space and non-standard boundary accuracy for a range of biologically plausible input statistics, conditions. However, the spike rate dynamics can be computational demand and implementation complexity Figure 1 Simulation of a large population of adaptive exponential integrate-and-fire (aEIF) neurons driven by a stochastic current with time-varying moments. Instantaneous spike rate and adaptation current averaged over 200,000 neurons are shown in gray. Overlaid are mean spike rate and adaptation current of two derived low-dimensional models receiving input with the same time-dependent moments as the population of aEIF neurons. * Correspondence: augustin@ni.tu-berlin.de Neural Information Processing Group, Berlin Institute of Technology, Berlin, Germany Full list of author information is available at the end of the article © 2015 Augustin et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http:// creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/ zero/1.0/) applies to the data made available in this article, unless otherwise stated. Augustin et al. BMC Neuroscience 2015, 16(Suppl 1):P183 Page 2 of 2 http://www.biomedcentral.com/1471-2202/16/S1/P183 (see, e.g., Figure 1). These reduced descriptions are well suited for (i) application in neural mass/mean-field based brain network models, having a link to single neuron prop- erties retained and being computationally efficient, and (ii) mathematical analyses of, e.g., asynchronous and rhythmic network states. Acknowledgements This work was supported by the DFG Collaborative Research Center SFB910. Authors’ details Neural Information Processing Group, Berlin Institute of Technology, Berlin, Germany. Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany. Published: 18 December 2015 References 1. Brette R, Gerstner W: Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. J Neurophysiol 2005, 94:3637-3642. 2. Ladenbauer J, Augustin M, Obermayer K: How adaptation currents change threshold, gain, and variability of neuronal spiking. J Neurophysiol 2014, 111:939-953. 3. Brunel N: Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 2000, 8:183-208. 4. Mattia M, Del Giudice P: Population dynamics of interacting spiking neurons. Phys Rev E 2002, 66:051917. 5. Augustin M, Ladenbauer J, Obermayer K: How adaptation shapes spike rate oscillations in recurrent neuronal networks. Front Comput Neurosci 2013, 7:9. 6. Schaffer E, Ostojic S, Abbott L: A complex-valued firing-rate model that approximates the dynamics of spiking networks. PLOS Comput Biol 2013, 9:e1003301. 7. Ostojic S, Brunel N: From spiking neuron models to linear-nonlinear models. PLOS Comput Biol 2011, 7:e1001056. doi:10.1186/1471-2202-16-S1-P183 Cite this article as: Augustin et al.: Low-dimensional spike rate dynamics of coupled adaptive model neurons. BMC Neuroscience 2015 16(Suppl 1): P183. Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color figure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution Submit your manuscript at www.biomedcentral.com/submit http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png BMC Neuroscience Springer Journals

Low-dimensional spike rate dynamics of coupled adaptive model neurons

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Springer Journals
Copyright
Copyright © 2015 by Augustin et al.
Subject
Biomedicine; Neurosciences; Neurobiology; Animal Models
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1471-2202
DOI
10.1186/1471-2202-16-S1-P183
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Abstract

Augustin et al. BMC Neuroscience 2015, 16(Suppl 1):P183 http://www.biomedcentral.com/1471-2202/16/S1/P183 POSTER PRESENTATION Open Access Low-dimensional spike rate dynamics of coupled adaptive model neurons 1,2* 1,2 1,2 Moritz Augustin , Josef Ladenbauer , Klaus Obermayer From 24th Annual Computational Neuroscience Meeting: CNS*2015 Prague, Czech Republic. 18-23 July 2015 The spiking activity of single neurons can be well approximated by a low-dimensional ordinary differential described by a two-dimensional integrate-and-fire model equation in different ways [4,6,7]. Although these approx- that includes neuronal adaptation [1] caused by slowly imation techniques are interrelated it is not clear which decaying potassium currents [2]. For fluctuating inputs reduced model best reproduces the spike rate of the ori- sparsely coupled spiking model neurons exhibit stochas- ginal spiking network, depending on the statistics of the tic population dynamics which can be effectively charac- input. Here we first extend each of these reduction meth- ods to account for neuronal adaptation and then evaluate terized using the Fokker-Planck equation (see, e.g., [3-5]). This approach leads to a model with an infinite- the reduced models in terms of spike rate reproduction dimensional state space and non-standard boundary accuracy for a range of biologically plausible input statistics, conditions. However, the spike rate dynamics can be computational demand and implementation complexity Figure 1 Simulation of a large population of adaptive exponential integrate-and-fire (aEIF) neurons driven by a stochastic current with time-varying moments. Instantaneous spike rate and adaptation current averaged over 200,000 neurons are shown in gray. Overlaid are mean spike rate and adaptation current of two derived low-dimensional models receiving input with the same time-dependent moments as the population of aEIF neurons. * Correspondence: augustin@ni.tu-berlin.de Neural Information Processing Group, Berlin Institute of Technology, Berlin, Germany Full list of author information is available at the end of the article © 2015 Augustin et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http:// creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/ zero/1.0/) applies to the data made available in this article, unless otherwise stated. Augustin et al. BMC Neuroscience 2015, 16(Suppl 1):P183 Page 2 of 2 http://www.biomedcentral.com/1471-2202/16/S1/P183 (see, e.g., Figure 1). These reduced descriptions are well suited for (i) application in neural mass/mean-field based brain network models, having a link to single neuron prop- erties retained and being computationally efficient, and (ii) mathematical analyses of, e.g., asynchronous and rhythmic network states. Acknowledgements This work was supported by the DFG Collaborative Research Center SFB910. Authors’ details Neural Information Processing Group, Berlin Institute of Technology, Berlin, Germany. Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany. Published: 18 December 2015 References 1. Brette R, Gerstner W: Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. J Neurophysiol 2005, 94:3637-3642. 2. Ladenbauer J, Augustin M, Obermayer K: How adaptation currents change threshold, gain, and variability of neuronal spiking. J Neurophysiol 2014, 111:939-953. 3. Brunel N: Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 2000, 8:183-208. 4. Mattia M, Del Giudice P: Population dynamics of interacting spiking neurons. Phys Rev E 2002, 66:051917. 5. Augustin M, Ladenbauer J, Obermayer K: How adaptation shapes spike rate oscillations in recurrent neuronal networks. Front Comput Neurosci 2013, 7:9. 6. Schaffer E, Ostojic S, Abbott L: A complex-valued firing-rate model that approximates the dynamics of spiking networks. PLOS Comput Biol 2013, 9:e1003301. 7. Ostojic S, Brunel N: From spiking neuron models to linear-nonlinear models. PLOS Comput Biol 2011, 7:e1001056. doi:10.1186/1471-2202-16-S1-P183 Cite this article as: Augustin et al.: Low-dimensional spike rate dynamics of coupled adaptive model neurons. BMC Neuroscience 2015 16(Suppl 1): P183. Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color figure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution Submit your manuscript at www.biomedcentral.com/submit

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BMC Neuroscience – Springer Journals

Published: Dec 18, 2015

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