Transition from Thermokinetic to Chemical Instabilities in a Modified Sal’nikov Model

Abstract

Traditionally, thermokinetic and chemical oscillations have been studied independently, but in cellular media recent studies have shown that cell's temperature is not uniform. Thus, on this context it is possible to inquire about the influence of thermal effects on chemical oscillatory behavior and vice versa. To this end, in this paper we propose a dynamical model based on a modified Sal'nikov oscillator that can address both kinds of oscillatory behavior (thermokinetic and chemical). We found that the system modeled can jump from thermal oscillations to mixed chemical-thermal oscillations through a transition or bifurcation parameter. Thermokinetic oscillations are well defined in a limit cycle, while chemical-thermal oscillations appear in the form of a burst. The model could be useful in explaining biochemical energy recovery under cellular stress conditions.

Temperature influence on a linear array of coupled Sal'nikov oscillators: the muscle fiber scenario

“…These ideas were developed in a previous paper [2], where a chemical energy inlet was modeled for a single sarcomere. In such cases, it showed the relevance of chemical oscillations coupled with the local thermal gradient in stressing conditions to replenish levels of a chemical specie of interest, i.e., ATP.…”

“…Sal'nikov's modified model proposed before [2] was based upon three differential equations (eq. 1-3), including two chemical (𝑌 and 𝑍) species and heat conduction.…”

“…Theoretically, all that is needed is a model reaction capable of producing thermal and chemical oscillations. A Sal'nikov-modified model, including a third autocatalytic reaction, fulfills this requirement [2]. In that case, shifting from chemical oscillations (using autocatalytic reaction) to mixed thermal-chemical oscillations is possible.…”

“…We show how a thermal gradient or a thermal pulse influences the dynamics of biochemical oscillations in a simplified biochemical model of muscle fiber and discuss the consequences in a living muscle. For this purpose, each simplified sarcomere behavior is governed according to a modified Sal'nikov model, as proposed in a previous paper [2].…”