American Institute of Mathematical Sciences

Advanced
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?

Achilleas Koutsou 1, , Jacob Kanev 2, , Maria Economidou 1, and  Chris Christodoulou 1,

1. 

Department of Computer Science, University of Cyprus, 1678 Nicosia, Cyprus, Cyprus, Cyprus
2. 

Department of Electrical Engineering and Computer Science, Technische Universitat 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.
Keywords: Operational mode, membrane potential slope, coincidence detection, temporal integration., spike distance metrics, input synchrony.
Mathematics Subject Classification: 92B25, 92C20, 92-0.
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:
[1]

M. Abeles, Role of the cortical neuron: integrator or coincidence detector?, Israel Journal of Medical Sciences, 18 (1982), 83-92.

[2]

A. Aertsen, M. Diesmann and M.-O. Gewaltig, Propagation of synchronous spiking activity in feedforward neural networks, Journal of Physiology Paris, 90 (1996), 243-247. doi: 10.1016/S0928-4257(97)81432-5.

[3]

G. Bugmann, C. Christodoulou and J. G. Taylor, Role of temporal integration and fluctuation detection in the highly irregular firing of a leaky integrator neuron model with partial reset, Neural Computation, 9 (1997), 985-1000. doi: 10.1162/neco.1997.9.5.985.

[4]

F. Hausdorff, Grundzüge der Mengenlehre, Verlag von Veit & Comp., Leipzig, 1914.

[5]

M. A. Kisley and G. L. Gerstein, The continuum of operating modes for a passive model neuron, Neural Computation, 11 (1999), 1139-1154. doi: 10.1162/089976699300016386.

[6]

P. König, A. K. Engel and W. Singer, Integrator or coincidence detector? The role of the cortical neuron revisited, Trends in Neurosciences, 19 (1996), 130-137.

[7]

A. Koutsou, C. Christodoulou, G. Bugmann and J. Kanev, Distinguishing the causes of firing with the membrane potential slope, Neural Computation, 24 (2012), 2318-2345. doi: 10.1162/NECO_a_00323.

[8]

T. Kreuz, D. Chicharro, R. G. Andrzejak, J. S. Haas and H. D. I. Abarbanel, Measuring multiple spike train synchrony, Journal of Neuroscience Methods, 183 (2009), 287-299. doi: 10.1016/j.jneumeth.2009.06.039.

[9]

T. Kreuz, D. Chicharro, M. Greschner and R. G. Andrzejak, Time-resolved and time-scale adaptive measures of spike train synchrony, Journal of Neuroscience Methods, 195 (2011), 92-106. doi: 10.1016/j.jneumeth.2010.11.020.

[10]

T. Kreuz, D. Chicharro, C. Houghton, R. G. Andrzejak and F. Mormann, Monitoring spike train synchrony, Journal of Neurophysiology, 109 (2013), 1457-1472. doi: 10.1152/jn.00873.2012.

[11]

T. Kreuz, J. S. Haas, A. Morelli, H. D. I. Abarbanel and A. Politi, Measuring spike train synchrony, Journal of Neuroscience Methods, 165 (2007), 151-161. doi: 10.1016/j.jneumeth.2007.05.031.

[12]

D. Pompeiu, Sur la continuité des fonctions de variables complexes, Annales de la Faculté des Sciences de Toulouse, 7 (1905), 265-315. doi: 10.5802/afst.226.

[13]

S. Ratté, M. Lankarany, Y.-A. Rho, A. Patterson and S. A. Prescott, Subthreshold membrane currents confer distinct tuning properties that enable neurons to encode the integral or derivative of their input, Frontiers in Cellular Neuroscience, 8 (2014), 452.

[14]

M. Rudolph and A. Destexhe, Tuning neocortical pyramidal neurons between integrators and coincidence detectors, Journal of Computational Neuroscience, 14 (2003), 239-251.

[15]

C. V. Rusu and R. V. Florian, A new class of metrics for spike trains, Neural Computation, 26 (2014), 306-348. doi: 10.1162/NECO_a_00545.

[16]

M. N. Shadlen and W. T. Newsome, Noise, neural codes and cortical organization, Current Opinion in Neurobiology, 4 (1994), 569-579. doi: 10.1016/0959-4388(94)90059-0.

[17]

M. N. Shadlen and W. T. Newsome, The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding, Journal of Neuroscience, 18 (1998), 3870-3896.

[18]

W. R. Softky and C. Koch, Cortical cells should fire regularly, but do not, Neural Computation, 4 (1992), 643-646. doi: 10.1162/neco.1992.4.5.643.

[19]

W. R. Softky and C. Koch, The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs, Journal of Neuroscience, 13 (1993), 334-350.

[20]

J. D. Victor, Spike train metrics, Current Opinion in Neurobiology, 15 (2005), 585-592. doi: 10.1016/j.conb.2005.08.002.

[21]

J. D. Victor and K. P. Purpura, Metric-space analysis of spike trains: Theory, algorithms and application, Network: Computation in Neural Systems, 8 (1997), 127-164. doi: 10.1088/0954-898X_8_2_003.

[22]

J. D. Victor and K. P. Purpura, Spike metrics, in Analysis of Parallel Spike Trains (eds. S. Grün and S. Rotter), Springer Series in Computational Neuroscience, 7, Springer US, Boston, MA, 2010, 129-156. doi: 10.1007/978-1-4419-5675-0_7.

show all references

References:
[1]

M. Abeles, Role of the cortical neuron: integrator or coincidence detector?, Israel Journal of Medical Sciences, 18 (1982), 83-92.

[2]

A. Aertsen, M. Diesmann and M.-O. Gewaltig, Propagation of synchronous spiking activity in feedforward neural networks, Journal of Physiology Paris, 90 (1996), 243-247. doi: 10.1016/S0928-4257(97)81432-5.

[3]

G. Bugmann, C. Christodoulou and J. G. Taylor, Role of temporal integration and fluctuation detection in the highly irregular firing of a leaky integrator neuron model with partial reset, Neural Computation, 9 (1997), 985-1000. doi: 10.1162/neco.1997.9.5.985.

[4]

F. Hausdorff, Grundzüge der Mengenlehre, Verlag von Veit & Comp., Leipzig, 1914.

[5]

M. A. Kisley and G. L. Gerstein, The continuum of operating modes for a passive model neuron, Neural Computation, 11 (1999), 1139-1154. doi: 10.1162/089976699300016386.

[6]

P. König, A. K. Engel and W. Singer, Integrator or coincidence detector? The role of the cortical neuron revisited, Trends in Neurosciences, 19 (1996), 130-137.

[7]

A. Koutsou, C. Christodoulou, G. Bugmann and J. Kanev, Distinguishing the causes of firing with the membrane potential slope, Neural Computation, 24 (2012), 2318-2345. doi: 10.1162/NECO_a_00323.

[8]

T. Kreuz, D. Chicharro, R. G. Andrzejak, J. S. Haas and H. D. I. Abarbanel, Measuring multiple spike train synchrony, Journal of Neuroscience Methods, 183 (2009), 287-299. doi: 10.1016/j.jneumeth.2009.06.039.

[9]

T. Kreuz, D. Chicharro, M. Greschner and R. G. Andrzejak, Time-resolved and time-scale adaptive measures of spike train synchrony, Journal of Neuroscience Methods, 195 (2011), 92-106. doi: 10.1016/j.jneumeth.2010.11.020.

[10]

T. Kreuz, D. Chicharro, C. Houghton, R. G. Andrzejak and F. Mormann, Monitoring spike train synchrony, Journal of Neurophysiology, 109 (2013), 1457-1472. doi: 10.1152/jn.00873.2012.

[11]

T. Kreuz, J. S. Haas, A. Morelli, H. D. I. Abarbanel and A. Politi, Measuring spike train synchrony, Journal of Neuroscience Methods, 165 (2007), 151-161. doi: 10.1016/j.jneumeth.2007.05.031.

[12]

D. Pompeiu, Sur la continuité des fonctions de variables complexes, Annales de la Faculté des Sciences de Toulouse, 7 (1905), 265-315. doi: 10.5802/afst.226.

[13]

S. Ratté, M. Lankarany, Y.-A. Rho, A. Patterson and S. A. Prescott, Subthreshold membrane currents confer distinct tuning properties that enable neurons to encode the integral or derivative of their input, Frontiers in Cellular Neuroscience, 8 (2014), 452.

[14]

M. Rudolph and A. Destexhe, Tuning neocortical pyramidal neurons between integrators and coincidence detectors, Journal of Computational Neuroscience, 14 (2003), 239-251.

[15]

C. V. Rusu and R. V. Florian, A new class of metrics for spike trains, Neural Computation, 26 (2014), 306-348. doi: 10.1162/NECO_a_00545.

[16]

M. N. Shadlen and W. T. Newsome, Noise, neural codes and cortical organization, Current Opinion in Neurobiology, 4 (1994), 569-579. doi: 10.1016/0959-4388(94)90059-0.

[17]

M. N. Shadlen and W. T. Newsome, The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding, Journal of Neuroscience, 18 (1998), 3870-3896.

[18]

W. R. Softky and C. Koch, Cortical cells should fire regularly, but do not, Neural Computation, 4 (1992), 643-646. doi: 10.1162/neco.1992.4.5.643.

[19]

W. R. Softky and C. Koch, The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs, Journal of Neuroscience, 13 (1993), 334-350.

[20]

J. D. Victor, Spike train metrics, Current Opinion in Neurobiology, 15 (2005), 585-592. doi: 10.1016/j.conb.2005.08.002.

[21]

J. D. Victor and K. P. Purpura, Metric-space analysis of spike trains: Theory, algorithms and application, Network: Computation in Neural Systems, 8 (1997), 127-164. doi: 10.1088/0954-898X_8_2_003.

[22]

J. D. Victor and K. P. Purpura, Spike metrics, in Analysis of Parallel Spike Trains (eds. S. Grün and S. Rotter), Springer Series in Computational Neuroscience, 7, Springer US, Boston, MA, 2010, 129-156. doi: 10.1007/978-1-4419-5675-0_7.

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