Related papers: Predicting the kinetics of RNA oligonucleotides us…

Self-positioned nanomembranes such as rolled-up tubes and wrinkled thin films have been potential systems for a variety of applications and basic studies on elastic properties of nanometer-thick systems. Although there is a clear driving…

Binding and unbinding of ligands to specific sites of a macromolecule are one of the most elementary molecular interactions inside the cell that embody the computational processes of biological regulations. The interaction between…

Single-molecule force spectroscopy has proven to be a powerful tool for studying the kinetic behavior of biomolecules. Through application of an external force, conformational states with small or transient populations can be stabilized,…

RNA secondary structure is modeled with the novel arbitrary-order hidden Markov model ({\alpha}-HMM). The {\alpha}-HMM extends over the traditional HMM with capability to model stochastic events that may be in influenced by historically…

For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…

We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…

Markov processes serve as foundational models in many scientific disciplines, such as molecular dynamics, and their simulation forms a common basis for analysis. While simulations produce useful trajectories, obtaining macroscopic…

Computing reaction rates in biomolecular systems is a common goal of molecular dynamics simulations. The reactions considered often involve conformational changes in the molecule, either changes in the structure of a protein or the relative…

Elastic network models (ENMs) are valuable and efficient tools for characterizing the collective internal dynamics of proteins based on the knowledge of their native structures. The increasing evidence that the biological functionality of…

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…

A chemical kinetic model of the elongation dynamics of RNA polymerase along a DNA sequence is introduced. The proposed model governs the discrete movement of the RNA polymerase along a DNA template, with no consideration given to elastic…

Markov State Models (MSMs) are a powerful framework to reproduce the long-time conformational dynamics of biomolecules using a set of short Molecular Dynamics (MD) simulations. However, precise kinetics predictions of MSMs heavily rely on…

Simulated nucleotide sequences are widely used in theoretical and empirical molecular evolution studies. Conventional simulators generally use fixed parameter time-homogeneous Markov model for sequence evolution. In this work, we use the…

This article is devoted to a prediction of gait kinematics based on the Markov chains in the delay space. We use hypercubic grid in the delay space of angles in the sagittal plane in the knee and hip joints to construct Markov states. Our…

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…

The conformational kinetics of enzymes can be reliably revealed when they are governed by Markovian dynamics. Hidden Markov Models (HMMs) are appropriate especially in the case of conformational states that are hardly distinguishable.…

Many chemical reactions and molecular processes occur on timescales that are significantly longer than those accessible by direct simulation. One successful approach to estimating dynamical statistics for such processes is to use many short…

We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension…

We study networks of biochemical reactions modelled by continuous-time Markov processes. Such networks typically contain many molecular species and reactions and are hard to study analytically as well as by simulation. Particularly, we are…

Asymptotic properties of Markov Processes, such as steady state probabilities or hazard rate for absorbing states can be efficiently calculated by means of linear algebra even for large-scale problems. This paper discusses the methods for…