# American Institute of Mathematical Sciences

2016, 13(3): 521-535. doi: 10.3934/mbe.2016005

## Integrator or coincidence detector --- what shapes the relation of stimulus synchrony and the operational mode of a neuron?

 1 Department of Computer Science, University of Cyprus, 1678 Nicosia, Cyprus, Cyprus, Cyprus 2 Department of Electrical Engineering and Computer Science, Technische Universitat Berlin, 10587 Berlin, Germany

Received  March 2015 Revised  November 2015 Published  January 2016

The operational mode of a neuron (i.e., whether a neuron is an integrator or a coincidence detector) is in part determined by the degree of synchrony in the firing of its pre-synaptic neural population. More specifically, it is determined by the degree of synchrony that causes the neuron to fire. In this paper, we investigate the relationship between the input and the operational mode. We compare the response-relevant input synchrony, which measures the operational mode and can be determined using a membrane potential slope-based measure [7], with the spike time distance of the spike trains driving the neuron, which measures spike train synchrony and can be determined using the multivariate SPIKE-distance metric [10]. We discover that the relationship between the two measures changes substantially based on the values of the parameters of the input (firing rate and number of spike trains) and the parameters of the post-synaptic neuron (synaptic weight, membrane leak time constant and spike threshold). More importantly, we determine how the parameters interact to shape the synchrony-operational mode relationship. Our results indicate that the amount of depolarisation caused by a highly synchronous volley of input spikes, is the most influential factor in defining the relationship between input synchrony and operational mode. This is defined by the number of input spikes and the membrane potential depolarisation caused per spike, compared to the spike threshold.
Citation: Achilleas Koutsou, Jacob Kanev, Maria Economidou, Chris Christodoulou. Integrator or coincidence detector --- what shapes the relation of stimulus synchrony and the operational mode of a neuron?. Mathematical Biosciences & Engineering, 2016, 13 (3) : 521-535. doi: 10.3934/mbe.2016005
##### References:

show all references

##### References:
 [1] Xiangying Meng, Gemma Huguet, John Rinzel. Type III excitability, slope sensitivity and coincidence detection. Discrete & Continuous Dynamical Systems - A, 2012, 32 (8) : 2729-2757. doi: 10.3934/dcds.2012.32.2729 [2] Aldana M. González Montoro, Ricardo Cao, Christel Faes, Geert Molenberghs, Nelson Espinosa, Javier Cudeiro, Jorge Mariño. Cross nearest-spike interval based method to measure synchrony dynamics. Mathematical Biosciences & Engineering, 2014, 11 (1) : 27-48. doi: 10.3934/mbe.2014.11.27 [3] Moisey Guysinsky, Serge Yaskolko. Coincidence of various dimensions associated with metrics and measures on metric spaces. Discrete & Continuous Dynamical Systems - A, 1997, 3 (4) : 591-603. doi: 10.3934/dcds.1997.3.591 [4] Giuseppe D'Onofrio, Enrica Pirozzi. Successive spike times predicted by a stochastic neuronal model with a variable input signal. Mathematical Biosciences & Engineering, 2016, 13 (3) : 495-507. doi: 10.3934/mbe.2016003 [5] Shigeki Akiyama. Strong coincidence and overlap coincidence. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5223-5230. doi: 10.3934/dcds.2016027 [6] Maide Bucolo, Federica Di Grazia, Luigi Fortuna, Mattia Frasca, Francesca Sapuppo. An environment for complex behaviour detection in bio-potential experiments. Mathematical Biosciences & Engineering, 2008, 5 (2) : 261-276. doi: 10.3934/mbe.2008.5.261 [7] Yuan Li, Ruxia Zhang, Yi Zhang, Bo Yang. Sliding mode control for uncertain T-S fuzzy systems with input and state delays. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2020006 [8] Lluís Alsedà, Michał Misiurewicz. Semiconjugacy to a map of a constant slope. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3403-3413. doi: 10.3934/dcdsb.2015.20.3403 [9] Chol-Ung Choe, Thomas Dahms, Philipp Hövel, Eckehard Schöll. Control of synchrony by delay coupling in complex networks. Conference Publications, 2011, 2011 (Special) : 292-301. doi: 10.3934/proc.2011.2011.292 [10] Samuel Roth. Constant slope models for finitely generated maps. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2541-2554. doi: 10.3934/dcds.2018106 [11] Antonio Tribuzio. Perturbations of minimizing movements and curves of maximal slope. Networks & Heterogeneous Media, 2018, 13 (3) : 423-448. doi: 10.3934/nhm.2018019 [12] David Li-Bland, Pavol Ševera. Integration of exact Courant algebroids. Electronic Research Announcements, 2012, 19: 58-76. doi: 10.3934/era.2012.19.58 [13] M. M. Rao. Integration with vector valued measures. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5429-5440. doi: 10.3934/dcds.2013.33.5429 [14] Louis Tebou. Simultaneous stabilization of a system of interacting plate and membrane. Evolution Equations & Control Theory, 2013, 2 (1) : 153-172. doi: 10.3934/eect.2013.2.153 [15] Giovanni Alessandrini, Elio Cabib. Determining the anisotropic traction state in a membrane by boundary measurements. Inverse Problems & Imaging, 2007, 1 (3) : 437-442. doi: 10.3934/ipi.2007.1.437 [16] Gerard Thompson. Invariant metrics on Lie groups. Journal of Geometric Mechanics, 2015, 7 (4) : 517-526. doi: 10.3934/jgm.2015.7.517 [17] Nathan Albin, Nethali Fernando, Pietro Poggi-Corradini. Modulus metrics on networks. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 1-17. doi: 10.3934/dcdsb.2018161 [18] Siwei Yu, Jianwei Ma, Stanley Osher. Geometric mode decomposition. Inverse Problems & Imaging, 2018, 12 (4) : 831-852. doi: 10.3934/ipi.2018035 [19] José M. Arrieta, Esperanza Santamaría. Estimates on the distance of inertial manifolds. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 3921-3944. doi: 10.3934/dcds.2014.34.3921 [20] Liliana Trejo-Valencia, Edgardo Ugalde. Projective distance and $g$-measures. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3565-3579. doi: 10.3934/dcdsb.2015.20.3565

2018 Impact Factor: 1.313