Mathematical modeling of bacterial cell cycle: The problem of coordinating genome replication with cell growth

Abstract

In this paper, we perform an analysis of bacterial cell-cycle models implementing different strategies to coordinately regulate genome replication and cell growth dynamics. It has been shown that the problem of coupling these processes does not depend directly on the dynamics of cell volume expansion, but does depend on the type of cell growth law. Our analysis has distinguished two types of cell growth laws, "exponential" and "linear", each of which may include both exponential and linear patterns of cell growth. If a cell grows following a law of the "exponential" type, including the exponential V(t) = V0exp (kt) and linear V(t) = V0(1 + kt) dynamic patterns, then the cell encounters the problem of coupling growth rates and replication. It has been demonstrated that to solve the problem, it is sufficient for a cell to have a repressor mechanism to regulate DNA replication initiation. For a cell expanding its volume by a law of the "linear" type, including exponential V(t) = V0+ V1exp (kt) and linear V(t) = V0+ kt dynamic patterns, the problem of coupling growth rates and replication does not exist. In other words, in the context of the coupling problem, a repressor mechanism to regulate DNA replication, and cell growth laws of the "linear" type displays the attributes of universality. The repressor-type mechanism allows a cell to follow any growth dynamic pattern, while the "linear" type growth law allows a cell to use any mechanism to regulate DNA replication.