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The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes…

The response of cells during spreading and motility is dictated by several multi-physics events, which are triggered by extracellular cues and occur at different time-scales. For this sake, it is not completely appropriate to provide a cell…

Macro-economic models describe the dynamics of economic quantities. The estimations and forecasts produced by such models play a substantial role for financial and political decisions. In this contribution we describe an approach based on…

The nonlinearity of dynamics in systems biology makes it hard to infer them from experimental data. Simple linear models are computationally efficient, but cannot incorporate these important nonlinearities. An adaptive method based on the…

Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…

The migratory dynamics of cells in physiological processes, ranging from wound healing to cancer metastasis, rely on contact-mediated cell-cell interactions. These interactions play a key role in shaping the stochastic trajectories of…

The importance of molecular-scale forces in sculpting biological form and function has been acknowledged for more than a century. Accounting for forces in biology is a problem that lies at the intersection of soft condensed matter physics,…

This paper concerns a model for tumor cell migration through the surrounding extracellular matrix by considering mass balance phenomena involving the chemical interactions produced on the cell surface. The well-posedness of this model is…

Social interaction between microbes can be described at many levels of details, ranging from the biochemistry of cell-cell interactions to the ecological dynamics of populations. Choosing the best level to model microbial communities…

Biological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several…

Inhibiting a signalling pathway concerns controlling the cellular processes of a cancer cell's viability, cell division, and death. Assay protocols created to see if the molecular structures of the drugs being tested have the desired…

We present a model for cell growth, division and packing under soft constraints that arise from the deformability of the cells as well as of a membrane that encloses them. Our treatment falls within the framework of diffuse interface…

Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's…

Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…

Epigenetic Tracking is a mathematical model of biological cells, originally conceived to study embryonic development. Computer simulations proved the capacity of the model to generate complex 3-dimensional cellular structures, and the…

Mathematical models are increasingly being used to understand complex biochemical systems, to analyze experimental data and make predictions about unobserved quantities. However, we rarely know how robust our conclusions are with respect to…

Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops.…

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…

Most models of biological pattern formation are simulated on continuous domains even though cells are discrete objects that provide internal boundaries to the diffusion of regulatory components. In our previous papers on simulating…

Mounting evidence shows that oscillatory activity is widespread in cell signaling. Here we review some of this recent evidence, focusing on both the molecular mechanisms that potentially underlie such dynamical behavior, and the potential…