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Related Concept Videos

¹H NMR of Conformationally Flexible Molecules: Temporal Resolution00:52

¹H NMR of Conformationally Flexible Molecules: Temporal Resolution

At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately 105 times per second. These two chair conformers are in equilibrium. The rapid ring flipping results in the interconversion of the axial proton to an equatorial proton and an equatorial to the axial proton. Such interconversions are too rapid and cannot be detected on the NMR timescale. Hence, the NMR spectrometer cannot distinguish between the...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Newman Projections02:06

Newman Projections

Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as conformers.
¹H NMR of Conformationally Flexible Molecules: Variable-Temperature NMR01:15

¹H NMR of Conformationally Flexible Molecules: Variable-Temperature NMR

The axial and equatorial protons in cyclohexane can be distinguished by performing a variable-temperature NMR experiment. In this process, except for one proton, the remaining eleven protons are replaced by deuterium. The deuterium substitution avoids the possible peak splitting caused by the spin-spin coupling between the adjacent protons. The remaining proton flips between the axial and equatorial positions.
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...
Transition State Theory01:25

Transition 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...

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Related Experiment Video

Updated: May 11, 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

Hierarchical Nyström methods for constructing Markov state models for conformational dynamics.

Yuan Yao1, Raymond Z Cui, Gregory R Bowman

  • 1School of Mathematical Sciences, LMAM-LMEQF-LMPR, Peking University, Beijing 100871, China. yuany@math.pku.edu.cn

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

This study introduces a new method using the Nyström method to improve Markov state models (MSMs) for biomolecular dynamics. It accurately identifies key protein states by focusing on well-sampled regions, overcoming limitations of finite sampling.

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Area of Science:

  • Computational chemistry and biophysics.
  • Molecular dynamics simulations and data analysis.

Background:

  • Markov state models (MSMs) are widely used to study protein conformational dynamics.
  • Building MSMs involves dividing simulations into microstates and coarse-graining them into macrostates.
  • Poorly sampled microstates can lead to inaccuracies in kinetic analysis during coarse-graining.

Purpose of the Study:

  • To develop a novel method for improving Markov state models (MSMs) by addressing issues with poorly sampled microstates.
  • To enhance the accuracy of identifying metastable states in biomolecular systems.
  • To provide a robust approach for coarse-graining molecular dynamics simulation data.

Main Methods:

  • A formalism based on the Nyström method for matrix approximation is proposed.
  • A hierarchical approach is used, building microstate sets from high to low populations.
  • Spectral clustering is progressively applied to microstate sets within each hierarchy level.

Main Results:

  • The proposed method effectively handles poorly sampled microstates in MSMs.
  • It successfully identifies major metastable states by prioritizing highly populated microstates.
  • The algorithm's performance was validated on the alanine dipeptide and trpzip2 peptide systems.

Conclusions:

  • The Nyström method-based approach offers a significant improvement for constructing accurate MSMs.
  • This method mitigates artifacts caused by finite sampling in molecular dynamics data.
  • It provides a more reliable way to understand the essential conformational dynamics of biomolecules.