Related Experiment Video
Updated: Jun 4, 2026
11:23
A Multilayer Microfluidic Platform for the Conduction of Prolonged Cell-Free Gene Expression
Published on: October 6, 2019
Renewal theory for single-molecule systems with multiple reaction channels
1Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA. berezh@mail.nih.gov
The Journal of Chemical Physics
|February 24, 2011
Summary
This study applies renewal theory to analyze cyclical single-molecule systems, providing simple formulas for event distribution functions. These findings aid in understanding molecular motors and enzymatic reactions.
Area of Science:
- Physical Chemistry
- Biophysics
- Statistical Mechanics
Background:
- Many single-molecule systems exhibit cyclical behavior, returning to their initial state after completing a cycle.
- These systems, including enzymatic reactions and molecular motors, can be modeled as renewal processes.
- Understanding the dynamics of these systems is crucial in various scientific fields.
Purpose of the Study:
- To analyze single-molecule systems exhibiting cyclical behavior using renewal theory.
- To derive simple formulas for multivariate distribution functions of event numbers within observation times.
- To provide a theoretical framework for studying systems like molecular motors and enzymatic reactions.
Main Methods:
- Application of renewal theory to model cyclical single-molecule systems.
- Analysis of multivariate distribution functions for event counts.
- Derivation of formulas for Laplace transforms of these distribution functions.
Main Results:
- Development of simple formulas for the Laplace transforms of distribution functions in renewal processes.
- Quantitative analysis of event distributions in cyclical single-molecule systems.
- Demonstration of the applicability of renewal theory to diverse molecular systems.
Conclusions:
- Renewal theory offers a powerful framework for analyzing cyclical single-molecule systems.
- The derived formulas simplify the study of event distributions in these systems.
- This work provides valuable insights for research in biophysics and physical chemistry.
Related Concept Videos
01:27Fast Reactions
Fast reactions occurring in times shorter than the time needed to mix reactants pose a unique challenge for investigation. In a liquid-phase continuous-flow system, reactants A and B are swiftly pushed into the mixing chamber, where mixing occurs within 1 ms. The reaction mixture then flows through an observation tube, and one measures light absorption to determine species concentrations at various points of the tube. This method is most appropriate when relatively large volumes of reactants...
02:31Multi-Step Reactions
Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...
01:25Transition State Theory
Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
03:06Reaction Mechanisms
Chemical reactions often occur in a stepwise fashion, involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs.
For instance, the decomposition of ozone appears to follow a mechanism with two steps:
For instance, the decomposition of ozone appears to follow a mechanism with two steps:
01:29Chain Reactions
Chain reactions involve highly reactive transient species, such as atoms or free radicals, as intermediates. These intermediates facilitate rapid reactions over an extended period. The process includes a series of steps: a reactive intermediate is consumed, reactants are converted to products, and the intermediate is regenerated. This cycle enables continuous repetition, amplifying the production of products with a small amount of intermediate. Chain reactions often utilize free radicals as...
01:26Reaction Mechanisms: The Steady-State Approximation
The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...