A survey on linear relations between main electrical components during action potential in ventricular cell

Abstract

The action potential in a cell is generated as a result of microscopic nonlinear and complex interactions between several components. In our research we found some approximately linear relationships between these components. This finding could lead to better understanding and simpler modeling of the effect of different ionic concentrations on cellular activity.

Introduction

In a ventricular cell, the action potential (AP) is generated as a result of microscopic interactions between several components. These interactions are nonlinear and complex, and hence it can be difficult to determine the relationships between the components. Linear relationship is the simplest kind of similarity. Linear dependency (independency) is a rough measure of the linear relationship between observations. If two observations are linearly dependent (LD); they carry common information and we may generate one from a coefficient of the other. If three observations are LD, we can generate each of them from a combination of others, and so on. In this research we have a macroscopic look at the ventricular cell, i.e. we look at it as a system from which we have made several observations and try to determine how many of these observations carry dependent (independent) information about cell (microscopic) activity i.e. we are looking for some possible linear relationships between observations. We have used COR (Cellular Open Resource) [1] and the Noble et al. [2] guinea-pig ventricular cell model for generating eleven main observations. These observations are: AP, some main ionic concentrations and currents and also contraction. Using a novel and interesting mathematical criteria we investigate the dependency (independency) of every two and every three combinations of observations, finding that {[Na]_i and [K]_i} are two highly dependent observations and {iCaL, ito, and [Ca]_i} are three very dependent ones. We also find that {iKr and iNaCa} are two very independent observations while {AP, iKr and ito} are three highly independent ones. In this paper we have presented tables which can be used for dependency (independency) comparison of observations. This dependency analysis may be used for the prediction of the effects of a parameter, e.g. an ionic concentration, on the different observations.