Related papers: Computational Modelling of Nonlinear Calcium Waves
Cells sense environmental signals and transmit information intracellularly through changes in the abundance of molecular components. Such molecular abundances can be measured in single cells and exhibit significant heterogeneity in clonal…
Self-generated gradients have atttracted a lot of attention in the recent biological literature. It is considered as a robust strategy for a group of cells to find its way during a long journey. This note is intended to discuss various…
Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the…
Electrical waves in the heart form rotating spiral or scroll waves during life-threatening arrhythmias such as atrial or ventricular fibrillation. The wave dynamics are typically modeled using coupled partial differential equations, which…
We present a method based on a time domain simulation of wave propagation that allows studying the optical response of a broad range of dielectric photonic structures. This method is particularly suitable for dealing with complex biological…
Cellular behavior is governed by gene regulatory processes that are intrinsically dynamic and nonlinear, and are subject to non-negligible amounts of random fluctuations. Such conditions are ubiquitous in physical systems, where they have…
A cellular automata model that describes as limit cases of his parameters the spread of contagious diseases modeled by systems of ordinary or partial differential equations is developed. Periodic features of the behavior of human settlement…
Many cells use calcium signalling to carry information from the extracellular side of the plasma membrane to targets in their interior. Since virtually all cells employ a network of biochemical reactions for Ca2+ signalling, much effort has…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special…
A simulation approach to the stochastic growth of bacterial towers is presented, in which a non-uniform and finite nutrient supply essentially determines the emerging structure through elementary chemotaxis. The method is based on cellular…
Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a…
We show that active transport processes in biological systems can be understood through a local equilibrium description formulated at the mesoscale, the scale to describe stochastic processes. This new approach uses the method established…
Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
We describe how to treat the interaction of travelling electrons with localised vibrational modes in nanojunctions. We present a multichannel scattering technique which can be applied to calculate the transport properties for realistic…
This study explores the use of fractional calculus as a possible tool to model wave propagation in complex, heterogeneous media. We illustrate the methodology by focusing on elastic wave propagation in a one-dimensional periodic rod. The…
Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…
Stochastic agent-based models can account for millions of cells with spatiotemporal movement that can be a function of different factors. However, these simulations can be computationally expensive. In this work, we develop a novel…
Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of…