Related papers: Comparison of Perron and Floquet eigenvalues in ag…
For monotone linear differential systems with periodic coefficients, the (first) Floquet eigenvalue measures the growth rate of the system. We define an appropriate arithmetico-geometric time average of the coefficients for which we can…
We consider a cell population described by an age-structured partial differential equation with time periodic coefficients. We assume that division only occurs after a minimal age (majority) and within certain time intervals. We study the…
We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive…
Molecular circadian clocks, that are found in all nucleated cells of mammals, are known to dictate rhythms of approximately 24 hours (circa diem) to many physiological processes. This includes metabolism (e.g., temperature, hormonal blood…
The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate…
Periodic forcing of nonlinear oscillators leads to a large number of dynamic behaviors. The coupling of the cell-cycle to the circadian clock provides a biological realization of such forcing. Using high throughput single-cell microscopy,…
We analyze a multi-type age dependent model for cell populations subject to unidirectional motion, in both a stochastic and deterministic framework. Cells are distributed into successive layers; they may divide and move irreversibly from…
Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated…
How are granular details of stochastic growth and division of individual cells reflected in smooth deterministic growth of population numbers? We provide an integrated, multiscale perspective of microbial growth dynamics by formulating a…
We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional Model H for macrophase separations by considering a logistic growth of cancer…
We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer"…
Recent studies at individual cell resolution have revealed phenotypic heterogeneity in nominally clonal tumor cell populations. The heterogeneity affects cell growth behaviors, which can result in departure from the idealized uniform…
In this paper we present a study of local dynamics of the growth of cancer tumor and healthy cells considering the presence of nutrients in the system. We also analyze the evolution of system if we take indirectly into account the level of…
Cells grown in culture act as a model system for analyzing the effects of anticancer compounds, which may affect cell behavior in a cell cycle position-dependent manner. Cell synchronization techniques have been generally employed to…
The rules governing cell division and differentiation are central to understanding the mechanisms of development, aging and cancer. By utilising inducible genetic labelling, recent studies have shown that the clonal population in transgenic…
It is well known that the different cell-division models, such as Timer, Sizer, and Adder, can be distinguished based on the correlations between different single-cell-level quantities such as birth-size, division-time, division-size, and…
Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms…
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the…
We study the effect of correlations in generation times on the dynamics of population growth of microorganisms. We show that any non-zero correlation that is due to cell-size regulation, no matter how small, induces long-term oscillations…