Reconstruction of vector fields: the case of calcium release fluxes

ALEJANDRA C VENTURA; LUCIANA BRUNO; SILVINA PONCE DAWSON

Salvador, Brasil

Conferencia; VIII Latin American Workshop on Nonlinear Phenomena; 2003

Statistical and nonlinear physics community in Latin-America

In this work we propose a model-independent algorithm to reconstruct intracellular calcium release fluxes from fluorescense data. The liberation of calcium ions from intracellular stores into the cytosol is used as a signaling mechanism by virtually all cell types to regulate functions as diverse as secretion, contraction, proliferation, and cell death. The method implemented here is based on ideas of the theory of dynamical systems that have been used to analyze chaotic experimental records. In the 80´s a flurry of activity blossomed in the area of time series analysis together with the increasing interest in chaotic systems. These studies were aided by Whytney´s and Ruelle-Takens theorems, which are of help in order to obtain information on the dynamical systems that generates an experimentally measured time series. Roughly speaking, the Ruelle-Takens theorem states that given a scalar time series (like the one that is obtained when a single variable is measured in an experiment) it is possible to construct a multi-dimensional time series (as if several variables had been measured from the same system instead of only one) using "delay coordinates". If the (embedding) dimension of the multi-dimensional phase space constructed in this way is large enough, then the space is in a one-to-one correspondence with the actual phase space of the system under study. Even if such an abstract approach  does not provide information on the physical processes that are working in order to produce the obvervable evolution, it is still useful in order to predict the future time dependence of the measured variable.In this case we have spatio-temporal series of a single variable (fluorescence records from line-scan imaging) with which we reconstruct a set of evolution equations that allows us to infer the Ca2+ release flux by contrasting the prediction of the equations in the absence of Ca2+ current to the actual observation of the experiment in the presence of the current. No assumptions are necessary about the processes that affect the spatio-temporal dynamics. Rather, we build up the method using the information that is already contained in the experimentally obtained image. In order to probe the accuracy of the method we have applied it to various numerically generated "images". We have seen that the method is linear (the reconstructed release flux is proportional to the simulated one) and that it reproduces the time evolution of the current quite accurately.