Related papers: Single molecule enzymology a la Michaelis-Menten
We analyze the standard model of enzyme-catalyzed reactions at various substrate-enzyme ratios to identify the regions of validity of the quasi-steady-state approximation. Certain prevalent conditions are checked and compared against the…
We show how one may analytically compute the stationary density of the distribution of molecular constituents in populations of cells in the presence of noise arising from either bursting transcription or translation, or noise in…
Catalysts speed up chemical reactions with no energy input and without being transformed in the process, therefore leaving equilibrium constants unchanged. Some catalysts, however, are much more efficient at accelerating one direction of a…
Causal ordering of key events in the cell cycle is essential for proper functioning of an organism. Yet, it remains a mystery how a specific temporal program of events is maintained despite ineluctable stochasticity in the biochemical…
Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…
To develop and investigate detailed mathematical models of cellular metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, explicit…
Single molecule time trajectories of biomolecules provide glimpses into complex folding landscapes that are difficult to visualize using conventional ensemble measurements. Recent experiments and theoretical analyses have highlighted…
Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics…
This dissertation explores the application of machine learning in molecular biology, focusing on gene expression regulation and cellular behavior at the single-cell level. Using modern neural networks, the research addresses key challenges…
The existing literature on stochastic simulation of chemical reaction networks has a tendency to move as quickly as possible to the abstract formulation of the stochastic dynamics in terms of probabilities based on the concept of the…
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with…
In this paper I show that, for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the…
Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the…
Ensemble averaging of molecular states is fundamental for the experimental determination of thermodynamic quantities. A special case occurs for single-molecule investigations under equilibrium conditions, for which free energy, entropy and…
How stochastic, microscopic events generate deterministic, macroscopic properties is a fundamental question in physics. We address this question by developing a quantum master equation model for concentrated radical solutions, where random…
Single-molecule stretching experiments are widely utilized within the fields of physics and chemistry to characterize the mechanics of individual bonds or molecules, as well as chemical reactions. Analytic relations describing these…
The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially…
Heterogeneous gas and solid catalyst reactions occur at the atomic level, and understanding and controlling complex catalytic reactions at this level is crucial for the development of improved processes and materials. There are postulations…
Molecular machines are stochastic systems that catalyze the energetic processes keeping living cells alive and structured. Inspired by the examples of F1-ATP synthase and the bacterial flagellum, we present a minimal model of an externally…
In this paper we derive several quasi steady-state approximations (QSSAs) to the stochastic reaction network describing the Michaelis-Menten enzyme kinetics. We show how the different assumptions about chemical species abundance and…