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This chapter provides a brief introduction to the theory and practice of spatial stochastic simulations. It begins with an overview of different methods available for biochemical simulations highlighting their strengths and limitations.…
Biological systems, unlike physical or chemical systems, are characterized by the very inhomogeneous distribution of their components. The immune system, in particular, is notable for self-organizing its structure. Classically, the dynamics…
Biomolecular condensates constitute a newly recognized form of spatial organization in living cells. Although many condensates are believed to form as a result of phase separation, the physicochemical properties that determine the phase…
Cancer is a complex disease that is characterized by uncontrolled growth and division of cells. It involves a complex interplay between genetic and environmental factors that lead to the initiation and progression of tumors. Recent advances…
Understanding the behaviour of biological systems requires a complex setting of in vitro and in vivo experiments, which attracts high costs in terms of time and resources. The use of mathematical models allows researchers to perform…
Quantum computing is viewed as a promising technology because of its potential for polynomial growth in complexity, in contrast to the exponential growth observed in its classical counterparts. In the current Noisy Intermediate-Scale…
The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single molecule and single cell level can add…
Brownian Dynamics algorithms are widely used for simulating soft-matter and biochemical systems. In recent times, their application has been extended to the simulation of coarse-grained models of cellular networks in simple organisms. In…
Life is characterized by a myriad of complex dynamic processes allowing organisms to grow, reproduce, and evolve. Physical approaches for describing systems out of thermodynamic equilibrium have been increasingly applied to living systems,…
Biology offers many examples of large-scale, complex, concurrent systems: many processes take place in parallel, compete on resources and influence each other's behavior. The scalable modeling of biological systems continues to be a very…
Computer-based modelling and simulation have become useful tools to facilitate humans to understand systems in different domains, such as physics, astrophysics, chemistry, biology, economics, engineering and social science. A complex system…
Accurate simulation of dynamical processes in molecules and reactions is among the most challenging problems in quantum chemistry. Quantum computers promise efficient chemical simulation, but the existing quantum algorithms require many…
Computer simulations have become a very powerful tool for scientific research. Given the vast complexity that comes with many open scientific questions, a purely analytical or experimental approach is often not viable. For example,…
The evolution, regulation and sustenance of biological complexity is determined by protein-protein interaction network that is filled with dynamic events. Recent experimental evidences point out that clustering of proteins has a vital role…
Brownian dynamics simulations are an increasingly popular tool for understanding spatially-distributed biochemical reaction systems. Recent improvements in our understanding of the cellular environment show that volume exclusion effects are…
We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of…
We study a system of diffusing point particles in which any triplet of particles reacts and is removed from the system when the relative proximity of the constituent particles satisfies a predefined condition. Proximity-based reaction…
Using bioimaging technology, biologists have attempted to identify and document analytical interpretations that underlie biological phenomena in biological cells. Theoretical biology aims at distilling those interpretations into knowledge…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterise all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the…