Mean-field analysis of two-species totally asymmetric simple exclusion process (TASEP) with attachment and detachment

In the field of statistical physics, unidirectional motion of a large number of particles along a single track can be described by totally asymmetric simple exclusion process (TASEP), from which many meaningful properties, such as the appearance of domain wall (defined as the borderline of high particle density and low particle density along the motion track) and boundary layers, can be obtained. However, it is biologically general that a single track may be occupied by different particle species. For example, in cells each microtubule protofilament is usually occupied by different species of motor protein. So previous studies about TASEP that included only one particle species may not be reasonable enough to describe more detailed properties of particle motion processes in a real cell environment. To address this problem, TASEP including two particle species is discussed in this study. Theoretical methods to get particle densities of each species are provided. By which, phase transition related properties of particle densities are obtained. Our analysis shows that domain wall and boundary layers of single species densities always appear simultaneously with those of the total particle density. The height of the domain wall of total particle density is equal to the summation of those of single particle species. Phase diagrams for typical model parameters are also presented. The methods presented in this study can be generalized to analyze TASEP with more particle species. Key words: two-species TASEP, domain wall, boundary layer, molecular motor, phase transition. En physique statistique, le mouvement unidirectionnel d'un grand nombre de particules le long d'une seule trajectoire peut etre decrit par un processus d'exclusion simple totalement asymetrique (PESTA/TASEP). A partir de la nous pouvons obtenir plusieurs proprietes significatives, comme le mur de domaine (defini comme la frontiere entre la haute densite de particules et la basse densite le long de la trajectoire du mouvement) et les couches limites. Cependant, on trouve generalement en biologie qu'une trajectoire simple peut etre occupes par differentes especes de particules. Par exemple, dans les cellules, chaque proto-filament de microtubule est generalement occupe par differents types de proteines moteurs. C'est pourquoi certaines etudes anterieures sur PESTA incluant une seule espece de particules peuvent etre mal adaptees aux proprietes detaillees des mouvements des particules dans l'environnement d'une vraie cellule. Pour corriger ce probleme, nous etudions ici un procede PESTA qui inclut deux especes de particules. Nous donnons les methodes pour les densites de particules des deux especes, a partir desquelles on obtient les proprietes reliees aux transitions de phase des densites des particules de chaque espece. Notre analyse montre que le mur de domaine et les couches limites des densites d'une seule espece apparaissent simultanement avec ceux de la densite totale. Nous presentons les diagrammes de phase pour des parametres de modele typiques. Les methodes presentees ici peuvent etre generalisees pour analyser PESTA avec plus d'especes de particules. [Traduit par la Redaction] Mots-cles : PESTA a deux especes, mur de domaine, couche limite, moteur moleculaire, transition de phase.
1. Introduction In the last decades, several theoretical models have been developed to describe the unidirectional motion of a large number of particles, including the motion of motor proteins along [...]