Related papers: From Discrete Protein Kinetics to Continuous Brown…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…
In spite of decades of research, much remains to be discovered about folding: the detailed structure of the initial (unfolded) state, vestigial folding instructions remaining only in the unfolded state, the interaction of the molecule with…
Molecular Dynamics (MD) simulations are fundamental computational tools for the study of proteins and their free energy landscapes. However, sampling protein conformational changes through MD simulations is challenging due to the relatively…
We provide a detailed multiscale analysis of a system of particles interacting through a dynamical network of links. Starting from a microscopic model, via the mean field limit, we formally derive coupled kinetic equations for the particle…
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…
Proteins, by virtue of their central role in most biological processes, represent one of the key subjects of the study of molecular evolution. Inherent to the indispensability of proteins for living cells is the fact that a given protein…
Recent advances in coarse-grained lattice and off-lattice protein models are reviewed. The sequence dependence of thermodynamical folding properties are investigated and evidence for non-randomness of the binary sequences of good folders…
Basing on main principles of statistical mechanics only, an exact virial expansion for path probability distribution of molecular Brownian particle in a fluid is derived which connects response of the distribution to perturbations of the…
Proteins play crucial roles in every cellular process by interacting with each other, with nucleic acids, metabolites, and other molecules. The resulting assemblies can be very large and intricate and pose challenges to experimental…
The macroscopic continuous approach of the mechanics of granular media assumes that the whole system of discrete variables (contact locations, contact forces,...) can be replaced by continuous field equations relating stress and strain on…
Many cell functions are accomplished thanks to intracellular transport mechanisms of macromolecules along filaments. Molecular motors such as dynein or kinesin are proteins playing a primary role in these processes. The behavior of such…
Protein-DNA interactions are vital for many processes in living cells, especially transcriptional regulation and DNA modification. To further our understanding of these important processes on the microscopic level, it is necessary that…
Brownian dynamics is a popular fine-grained method for simulating systems of interacting particles, such as chemical reactions. Though the method is simple to simulate, it is generally assumed that the dynamics is impossible to solve…
Natural protein sequences somehow encode the structural forms that these molecules adopt. Recent developments in structure-prediction are agnostic to the mechanisms by which proteins fold and represent them as static objects. However, the…
As an example of topic where biology and physics meet, we present the issue of protein folding and stability, and the development of thermodynamics-based bioinformatics tools that predict the stability and thermal resistance of proteins and…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
Biofilms are complex structures which are inhabited by numerous amount of different species of microorganisms. Due to their ubiquity, they influence human life on an everyday basis. It is therefore important to understand the interactions…
The theory of biochemical processes needs simple but realistic models of phenomena underlying microscopic dynamics of proteins. Many experiments performed in the 1980s have demonstrated that within the protein native state, apart from usual…
The Kinesin family of motor proteins are involved in a variety of cellular processes that transport materials and generate force. With recent advances in experimental techniques, such as optical tweezers which can probe individual…