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We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
We advocate the use of qualitative models in the analysis of large biological systems. We show how qualitative models are linked to theoretical differential models and practical graphical models of biological networks. A new technique for…
Most available tools propose simulation frameworks to study models of biological systems, but simulation only explores a few of the most probable behaviours of the system. On the contrary, techniques such as model checking, coming from…
We present a method for logical specification of the behavior of a system based on the specification of its components and for representing and specifying the effect of a class of communication "signaling pathways" among them. Variations in…
The cell is arguably the most fundamental unit of life and is central to understanding biology. Accurate modeling of cells is important for this understanding as well as for determining the root causes of disease. Recent advances in…
The goal of this paper is to advance an extensible theory of living systems using an approach to biomathematics and biocomputation that suitably addresses self-organized, self-referential and anticipatory systems with multi-temporal…
The complexity of biological systems and processes, spanning molecular to macroscopic scales, necessitates the use of multiscale simulations to get a comprehensive understanding. Quantum mechanics/molecular mechanics (QM/MM) molecular…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
Recently, symbolic computation and computer algebra systems have been successfully applied in systems biology, especially in chemical reaction network theory. One advantage of symbolic computation is its potential for qualitative answers to…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
Experimental approaches have been applied to address questions in understanding three-dimensional chromatin organisation and function. As datasets increase in size and complexity, it becomes a challenge to reach a mechanistic interpretation…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
The fundamental understanding of how cells physically interact with each other and their environment is key to understanding their organisation in living tissues. Over the past decades several computational methods have been developed to…
The biomolecules in and around a living cell -- proteins, nucleic acids, lipids, carbohydrates -- continuously sample myriad conformational states that are thermally accessible at physiological temperatures. Simultaneously, a given…
The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices…
Rule-based modeling is a powerful way to model kinetic interactions in biochemical systems. Rules enable a precise encoding of biochemical interactions at the resolution of sites within molecules, but obtaining an integrated global view…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of Ordinary Differential Equations. Alternative approaches based on formal calculi, often derived from process algebras or term…
Living systems continuously transform matter and energy through the chemical processes that constitute their metabolism. The overall metabolic rate of an organism correlates positively with its body mass, however both the exact scaling…
Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential-equation approach by generating typical system histories instead of just statistical measures such as the mean and…
Examining individual components of cellular systems has been successful in uncovering molecular reactions and interactions. However, the challenge lies in integrating these components into a comprehensive system-scale map. This difficulty…