Related papers: Modeling a simple enzyme reaction with delay and d…
New advances in nano sciences open the door for scientists to study biological processes on a microscopic molecule-by-molecule basis. Recent single-molecule biophysical experiments on enzyme systems, in particular, reveal that enzyme…
Enzyme catalysis in reactors for industrial applications usually require an external intervention of the species involved in the chemical reactions. We analyze the most elementary open enzyme catalysis with competitive inhibition where a…
Biological molecular machines are proteins that operate under isothermal conditions hence are referred to as free energy transducers. They can be formally considered as enzymes that simultaneously catalyze two chemical reactions: the free…
The statistical analysis of enzyme kinetic reactions usually involves models of the response functions which are well defined on the basis of Michaelis-Menten type equations. The error structure however is often without good reason assumed…
We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization…
Micro-Electro Mechanical Systems (MEMS) are defined as very small structures that combine electrical and mechanical components on a common substrate. Here, the electrostatic-elastic case is considered, where an elastic membrane is allowed…
Delayed processes are ubiquitous throughout biology. These delays may arise through maturation processes or as the result of complex multi-step networks, and mathematical models with distributed delays are increasingly used to capture the…
The exciton dynamics in a molecular heterodimer is studied as a function of differences in excitation and reorganization energies, asymmetry in transition dipole moments and excited state lifetimes. The heterodimer is composed of two…
We develop a formal model of the emergence of self-constructing objects (e.g. heteropolymers with autocatalytic capability) in an open system, which don't contain such objects initially. The objects are constructed from subunits (e.g.…
The efficient calculation of rare-event kinetics in complex dynamical systems, such as the rate and pathways of ligand dissociation from a protein, is a generally unsolved problem. Markov state models can systematically integrate ensembles…
Molecular dynamics simulations are used to study structure formation in simple model polymer chains that are subject to excluded volume and torsional interactions. The changing conformations exhibited by chains of different lengths under…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical…
Michaelis--Menten analysis is often conducted by nonlinear least squares under a constant-variance assumption, even though enzyme-kinetic data frequently display concentration-dependent heteroscedasticity and often include repeated or…
During the eukaryotic cell cycle, chromatin undergoes several conformational changes, which are believed to play key roles in gene expression regulation during interphase, and in genome replication and division during mitosis. In this…
Inspired by the need for effective stochastic models to describe the complex behavior of biological motor proteins that move on linear tracks exact results are derived for the velocity and dispersion of simple linear sequential models (or…
Protein function often involves changes between different conformations. Central questions are how these conformational changes are coupled to the binding or catalytic processes during which they occur, and how they affect the catalytic…
The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
Theoretical analysis, which maps single molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and…