Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Probability Histograms

Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.

Entropy

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

Entropy

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...

Probability Laws

Probability Laws

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

Standard Entropy Change for a Reaction

Standard Entropy Change for a Reaction

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Machine learning can be used to distinguish protein families and generate new proteins belonging to those families.

The Journal of chemical physics·2019

Same author

Generating intrinsically disordered protein conformational ensembles from a Markov chain.

The Journal of chemical physics·2018

Same author

Molecular dynamics of apo-adenylate kinase: a distance replica exchange method for the free energy of conformational fluctuations.

The journal of physical chemistry. B·2006

Same author

Molecular dynamics of apo-adenylate kinase: a principal component analysis.

The journal of physical chemistry. B·2006

Same author

Associative mechanism for phosphoryl transfer: a molecular dynamics simulation of Escherichia coli adenylate kinase complexed with its substrates.

Proteins·2004

Search research articles

Related Experiment Video

Updated: Jan 31, 2026

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

Reweighting ensemble probabilities with experimental histogram data constraints using a maximum entropy principle.

Hongfeng Lou¹, Robert I Cukier¹

¹Department of Chemistry, Michigan State University, East Lansing, Michigan 48824-1322, USA.

The Journal of Chemical Physics

|December 24, 2018

Summary

This study introduces a new indicator function method for Maximum Entropy Procedure (MEP) problems when standard methods fail. The approach provides an analytic solution for updating probability distributions with external constraints, demonstrated on peptide conformation ensembles.

More Related Videos

Inverse Probability of Treatment Weighting Propensity Score using the Military Health System Data Repository and National Death Index

Inverse Probability of Treatment Weighting Propensity Score using the Military Health System Data Repository and National Death Index

Published on: January 8, 2020

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Published on: September 12, 2014

Related Experiment Videos

Last Updated: Jan 31, 2026

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

Inverse Probability of Treatment Weighting Propensity Score using the Military Health System Data Repository and National Death Index

Inverse Probability of Treatment Weighting Propensity Score using the Military Health System Data Repository and National Death Index

Published on: January 8, 2020

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Published on: September 12, 2014

Area of Science:

Computational Biology
Statistical Mechanics
Biophysics

Background:

Entropy maximization methods update probability distributions using known constraints.
Jaynes' Maximum Entropy Procedure (MEP) is a standard objective approach for incorporating external data.
Conventional MEP methods using Lagrange multipliers fail when covariance matrices are not invertible.

Purpose of the Study:

To address limitations of conventional MEP when external data is provided as a probability distribution.
To develop a new method for Maximum Entropy Procedure (MEP) that circumvents non-invertible covariance matrices.
To analyze the impact of external constraints on ensemble observables for intrinsically disordered proteins.

Main Methods:

Introduced an indicator function method to solve MEP problems with probability distribution constraints.
Derived an analytic solution for this specific MEP challenge, avoiding iterative Lagrange multiplier methods.
Applied the method to an ensemble of peptide conformations and analyzed resulting ensemble observables.

Main Results:

The indicator function method successfully provides an analytic solution for MEP with probability distribution constraints.
Analysis of peptide ensembles revealed varying sensitivity of different observables (geometric, shape, NMR couplings) to external radius of gyration constraints.
Demonstrated the method's applicability using histatin 5, a peptide with experimentally derived radius of gyration distribution.

Conclusions:

The indicator function method offers a robust alternative for Maximum Entropy Procedure (MEP) when dealing with probability distribution constraints.
The study highlights the importance of selecting appropriate observables when integrating external data into molecular simulations.
This work advances the application of MEP in biophysical studies, particularly for intrinsically disordered proteins.