From the discrete kinetic theory to modelling open systems of active particles

Abstract

This work deals with a methodological development of the kinetic theory for open systems of active particles with discrete states. It essentially refers to the derivation of mathematical tools which provide the guidelines for modelling open systems in different fields of applied sciences. After a description of closed systems, mathematical frameworks suitable for depicting the evolution of open systems are proposed. Finally, some research perspectives towards modelling are outlined.

A novel framework for modeling Tumor Radiotherapy mechanism based on Gene-Environment Network (GEN) and Kinetic Theory

“…Under acute perturbation from outer environment, a cell can start a series of inner activities in response to genome stress [12,13]. As a novel mathematical framework, KTAP can be used in modeling the overall system by evolution equations corresponding to the dynamics of all their elements [14,15]. Recently, the methodology of kinetic theory to model complex biological system is capturing more and more attention on applied mathematicians, and Gene-Environment Network (GEN) model has been widely investigated by using the KTAP methods [15][16][17].…”

“…As a novel mathematical framework, KTAP can be used in modeling the overall system by evolution equations corresponding to the dynamics of all their elements [14,15]. Recently, the methodology of kinetic theory to model complex biological system is capturing more and more attention on applied mathematicians, and Gene-Environment Network (GEN) model has been widely investigated by using the KTAP methods [15][16][17]. GEN can describe not only the stochastic interactions between genes and environmental cofactors at molecular level, but also the systematic dynamics of the integrated system in response to external environment perturbations [18,19].…”

A Hybrid Model for Tumor Radiotherapy Based on Kinetic Theory and Gene-Environment Network

“…Some theoretical methods have been proposed to investigate cellular self-defensive mechanism under genome stress, such as Gene Regulatory Network (GRN) models [6]. In addition, Gene-Environment Network (GEN) model, a novel mathematical framework, has been widely investigated by using the kinetic theory of active particle (KTAP) [7]- [9]. KTAP can model the overall bio-system by evolution equations corresponding to the dynamics of all elements within different subsystems [9].…”

“…In addition, Gene-Environment Network (GEN) model, a novel mathematical framework, has been widely investigated by using the kinetic theory of active particle (KTAP) [7]- [9]. KTAP can model the overall bio-system by evolution equations corresponding to the dynamics of all elements within different subsystems [9]. GEN can describe not only the stochastic interactions between genes and environmental cofactors at molecular level, but also the systematic dynamics of integrated system in response to environmental perturbations [9], [10].…”

“…KTAP can model the overall bio-system by evolution equations corresponding to the dynamics of all elements within different subsystems [9]. GEN can describe not only the stochastic interactions between genes and environmental cofactors at molecular level, but also the systematic dynamics of integrated system in response to environmental perturbations [9], [10]. GEN model is widely used in different research areas, e.g., cellular self-repair kinetics under acute IR [11], as well as cellular fate decision by gene cofactors [12], [13].…”