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Related Concept Videos

State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
Sampling Plans01:23

Sampling Plans

Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
Sampling Methods: Overview01:06

Sampling Methods: Overview

A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of sampling...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Rigid Body Equilibrium Problems - II01:21

Rigid Body Equilibrium Problems - II

A rigid body is in static equilibrium when the net force and the net torque acting on the system are equal to zero.
Consider two children sitting on a seesaw, which has negligible mass. The first child has a mass (m1) of 26 kg and sits at point A, which is 1.6 meters (r1) from the pivot point B; the second child has a mass (m2) of 32 kg and sits at point C. How far from the pivot point B should the second child sit (r2) to balance the seesaw?

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Related Experiment Video

Updated: Jun 19, 2026

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
09:17

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

Structuring and sampling complex conformation space: Weighted ensemble dynamics simulations.

Linchen Gong1, Xin Zhou

  • 1Asia Pacific Center for Theoretical Physics and Department of Physics, Pohang University of Science and Technology, Pohang, Gyeongbuk 790-784, Korea and Center for Advanced Study, Tsinghua University, Beijing 100084, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 2, 2009
PubMed
Summary
This summary is machine-generated.

The weighted ensemble dynamics method robustly explores complex conformational spaces using spectral analysis. This approach accurately reconstructs equilibrium properties and identifies metastable states from simulation data.

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Investigating Protein Sequence-structure-dynamics Relationships with Bio3D-web
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Investigating Protein Sequence-structure-dynamics Relationships with Bio3D-web

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Related Experiment Videos

Last Updated: Jun 19, 2026

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
09:17

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

Investigating Protein Sequence-structure-dynamics Relationships with Bio3D-web
09:51

Investigating Protein Sequence-structure-dynamics Relationships with Bio3D-web

Published on: July 16, 2017

Area of Science:

  • Computational Chemistry
  • Statistical Mechanics
  • Molecular Dynamics

Background:

  • Exploring complex conformational landscapes is crucial for understanding molecular behavior.
  • Traditional simulation methods often struggle with efficiently sampling diverse states.
  • Hierarchical structures within conformational space require advanced analytical techniques.

Purpose of the Study:

  • To introduce a robust method for systematically exploring complex conformational spaces.
  • To enable accurate reconstruction of equilibrium properties from partial trajectory data.
  • To identify and classify metastable and transition states without prior system knowledge.

Main Methods:

  • Weighted ensemble dynamics simulations initiated from diverse conformations.
  • Spectral analysis of the variance-covariance matrix of trajectory-mapped vectors.
  • Utilizing the nondegenerate ground state for statistical weighting and ergodicity assessment.

Main Results:

  • The method successfully predicts system ergodicity via the ground state of the variance-covariance matrix.
  • Equilibrium properties are accurately reconstructed using ground state-derived statistical weights.
  • The degree of degeneracy directly correlates with the number of metastable states observed.

Conclusions:

  • The weighted ensemble dynamics method provides a powerful framework for conformational space exploration.
  • This approach facilitates the identification of metastable and transition states, enhancing molecular simulations.
  • The method's efficacy is demonstrated on both model potentials and biomolecular systems like alanine dipeptide.