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Through extensive studies of dynamical system modeling cellular growth and reproduction, we find evidence that complexity arises in multicellular organisms naturally through evolution. Without any elaborate control mechanism, these systems…
Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible…
We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as…
We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…
Cells with the same genome can exist in different phenotypes. and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation rate, and small effect of single mutations…
Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how…
A tumor can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, a…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and…
Cell type (e.g. pluripotent cell, fibroblast) is the end result of many complex processes that unfold due to evolutionary, developmental, and transformational stimuli. A cell's phenotype and the discrete, a priori states that define various…
We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring…
In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response.…
A major goal of modern computational biology is to simulate the collective behaviour of large cell populations starting from the intricate web of molecular interactions occurring at the microscopic level. In this paper we describe a…
Feedback in cellular processes is typically inferred through cellular responses to experimental perturbations. Modular response analysis provides a theoretical framework for translating specific perturbations into feedback sensitivities…
Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relationship with the plasticity of cellular states. By adopting a simple theoretical framework for intra-cellular chemical reaction dynamics with…
Biological tools such as genetic lineage tracing, three dimensional confocal microscopy and next generation DNA sequencing are providing new ways to quantify the distribution of clones of normal and mutated cells. Population-wide clone size…