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Related Concept Videos

Predicting Reaction Outcomes02:24

Predicting Reaction Outcomes

Kinetics describes the rate and path by which a reaction occurs. In contrast, thermodynamics deals with state functions and describes the properties, behavior, and components of a system. It is not concerned with the path taken by the process and cannot address the rate at which a reaction occurs. Although it does provide information about what can happen during a reaction process, it does not describe the detailed steps of what appears on an atomic or a molecular level. On the other hand,...
Reaction Mechanisms: The Steady-State Approximation01:26

Reaction 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...
Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction01:15

Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction

In pharmacokinetics, the rates and order of reactions play a crucial role in understanding how the body processes drugs and help us comprehend drug absorption, distribution, metabolism, and elimination. A critical concept in pharmacokinetics is the rate constant, which quantifies the speed of a reaction. It provides valuable information about the kinetics of drug elimination. The rate constant allows us to determine the rate at which drugs are eliminated from the body.
Pharmacokinetic reactions...
Chemical Equilibria: Systematic Approach to Equilibrium Calculations01:21

Chemical Equilibria: Systematic Approach to Equilibrium Calculations

Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
The first step is to identify all the chemical reactions involved, The...
Reaction Mechanisms: Rate-limiting Step Approximation01:29

Reaction Mechanisms: Rate-limiting Step Approximation

The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
Introduction to Enzyme Kinetics01:19

Introduction to Enzyme Kinetics

Enzyme kinetics studies the rates of biochemical reactions. Scientists monitor the reaction rates for a particular enzymatic reaction at various substrate concentrations. Additional trials with inhibitors or other molecules that affect the reaction rate may also be performed.
The experimenter can then plot the initial reaction rate or velocity (Vo) of a given trial against the substrate concentration ([S]) to obtain a graph of the reaction properties. For many enzymatic reactions involving a...

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Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
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Published on: January 31, 2020

Perspective: Stochastic algorithms for chemical kinetics.

Daniel T Gillespie1, Andreas Hellander, Linda R Petzold

  • 1Dan T Gillespie Consulting, 30504 Cordoba Pl., Castaic, California 91384, USA. gillespiedt@mailaps.org

The Journal of Chemical Physics
|May 10, 2013
PubMed
Summary
This summary is machine-generated.

This study explores stochastic chemical kinetics and numerical simulation algorithms. It details discrete-stochastic methods for well-mixed systems and discusses extensions for non-well-mixed environments, advancing computational chemistry.

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Area of Science:

  • Computational Chemistry
  • Chemical Physics
  • Biophysics

Background:

  • Traditional chemical kinetics relies on continuous-deterministic models (ordinary differential equations) for dilute, well-mixed systems.
  • A discrete-stochastic approach offers a more physically realistic description of chemical kinetics at the molecular level.
  • Bridging deterministic and stochastic models requires understanding necessary approximations.

Purpose of the Study:

  • To provide a comprehensive perspective on stochastic chemical kinetics, emphasizing numerical simulation algorithms.
  • To review the rationale and methods for discrete-stochastic simulations in well-mixed systems.
  • To explore advanced stochastic simulation strategies for complex systems and non-well-mixed environments.

Main Methods:

  • Review of physical and mathematical foundations for discrete-stochastic modeling.
  • Analysis of approximations to reconcile discrete-stochastic and continuous-deterministic descriptions.
  • Examination of simulation strategies for stiff systems, rare events, and sensitivity analysis.
  • Discussion of spatial discretization methods for non-well-mixed systems, including subvolume simulation and molecular diffusion modeling.

Main Results:

  • The discrete-stochastic approach provides a robust framework for simulating chemical kinetics, particularly when molecular discreteness is important.
  • Approximations allow for efficient computation while retaining key stochastic features.
  • Strategies for handling stiff systems, rare events, and sensitivity analysis enhance the applicability of stochastic methods.
  • Subvolume simulation effectively models spatial effects in non-well-mixed systems.

Conclusions:

  • Stochastic chemical kinetics offers a powerful alternative to traditional deterministic models, especially for systems exhibiting significant molecular fluctuations.
  • Numerical simulation algorithms are crucial for implementing stochastic models, with ongoing developments addressing complex scenarios.
  • The discrete-stochastic approach, particularly with spatial extensions, is a promising direction for simulating complex chemical and biological systems.