Related papers: A discrete inhomogeneous model for the yeast cell …
In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the…
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…
In Dictyostelium discoideum the proportion of cell types is known to be actively regulated, recovering, for example, after the removal of a given cell type. However, we have recently shown that regulation is intrinsically imprecise: it…
To understand the sophisticated control mechanisms of the human's endocrine system is a challenging task that is a crucial step towards precise medical treatment of many disfunctions and diseases. Although mathematical models describing the…
A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…
The more we learn about the cytoplasm of cells, the more we realise that the cytoplasm is not uniform but instead is highly inhomogeneous. In any inhomogeneous solution, there are concentration gradients, and particles move either up or…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
Time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current…
We investigate the stability properties of two different classes of metabolic cycles using a combination of analytical and computational methods. Using principles from structural kinetic modeling (SKM), we show that the stability of…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
The invariant ellipsoid method is aimed at minimization of the smallest invariant and attractive set of a linear control system operating under bounded external disturbances. This paper extends this technique to a class of the so-called…
Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability…
Phage lambda is one of the most studied biological models in modern molecular biology. Over the past 50 years quantitative experimental knowledge on this biological model has been accumulated at all levels: physics, chemistry, genomics,…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary timescales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of…
Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and…