P110 What is membrane electrical excitability?
Lionardo Truqui2, Hector Chaparro-Reza1, Vania Victoria Villegas1, Marco Arieli Herrera-Valdez1*
1Dinamics, Biophysics, and Systems Physiology Laboratory, Universidad Nacional Autónoma de México.
2Graduate Program in Mathematics, Universidad Nacional Autónoma de México
*Email: marcoh@ciencias.unam.mx
Neuronal excitability is a phenomenon that is understood in different ways. A neuron may be regarded as more excitable than another if it responds to a stimulus with more action potentials within a fixed period of time. Another way to think about how excitable a neuron is could be to consider the delay with which it starts to respond to a given stimulus. We use the simplest, 2-dimensional, biophysical model of neuronal membrane potential based on two transmembrane currents carried by sodium and potassium ions similar to the Morris-Lecar model[4], but without leak current [1], to study conditions that should be satisfied by an excitable system, and provide a formal definition of electrical excitability. The model consist only on two currents, a Na and a K current, as small currents are not necessary to generate action potentials [3]. We first establish the notion that a model based on autonomous evolution rules is associated with a family of dynamical systems. For instance, if the parameter representing the input current in the equation for the membrane potential is varied todescribe experimental data in current-clamp experiments, the family is defined at least by the input current, and its members can be associated to different sets of trajectories in phase space. We then proceed to analyse the properties of single dynamical systems by examination of their underlying vector fields. In a similar way as originally proposed by Fitz-Hugh [2], we define a region from which all trajectories are action potentials, and call it the Excitability Region. We also propose a measure to quantify the extent to which a single dynamical system is excitable, and then proceed to compare different degrees of excitability. Since the membrane potential of a neuron is represented by a family of dynamical systems, we then examine which of those systems are excitable under the above definition, and assess which ones are more excitable, as a function of the input current. While doing so, we explore the bifurcation structure of the model taking the input current as the bifurcation parameter, and characterize the changes in excitability induced by varying the sizes of the population of ion channels. Having done so, we define neuronal excitability by extending our definition for a single dynamical system to the whole family in the model. We discuss how our measure of excitability behaves around attractor nodes and attractor foci, and also use our definitions to describe the I-F relations of types I, II, and III, that have been used previously to characterize excitability.
Acknowledgements
Universidad Nacional Autónoma de México
References
[1] Av-Ron, E., Parnas, H., and Segel, L. A. (1991). A minimal biophysical model for an excitable and oscillatory neuron. Biological Cybernetics, 65(6):487–500.
[2] FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysical journal, 1(6):445–466.
[3] Herrera-Valdez, M. A. and Lega, J. (2011). Reduced models for the pacemaker dynamics of cardiac cells. Journal of Theoretical Biology, 270(1):164–176.
[4] Morris, C. and Lecar, H. (1981). Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 35:193–213.
