Time-Dependent Markov State Models for Single Molecule Force Spectroscopy

Ghosh, Susmita; Chatterjee, Abhijit; Bhattacharya, Swati

doi:10.1021/acs.jctc.6b01094

Cited by 11 publications

(13 citation statements)

References 26 publications

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“…The stitching algorithm provides a computational strategy for synthesizing waiting times from MD for a target environment. Equation assumes first-order dynamics therefore ascertaining exponential distribution for the waiting times becomes necessary . The stitching procedure presented here is a variation of the one presented originally in refs and while adapting it to the calculation of waiting times for specific local environments.…”

Section: Methodsmentioning

confidence: 99%

Relative Occurrence of Oxygen-Vacancy Pairs in Yttrium-Containing Environments of Y₂O₃-Doped ZrO₂ Can Be Crucial to Ionic Conductivity

Jaipal

Chatterjee

2017

J. Phys. Chem. C

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Yttria-stabilized zirconia (YSZ) is widely used as an electrolyte in solid oxide fuel cells. Much of current research on ionic conductivity in YSZ has focused on understanding migration barriers for O2– ion movement and vacancy trapping behavior in an attempt to understand why dopant cation edges result in fewer vacancy hopping transitions. We show that the free energy of finding O2–-vacancy (O2–-vac) pairs in a local environment can also be crucial to the hopping transitions. Higher probability of O2–-vac pairs can result in a greater number of transitions. O2– ion movement in bulk YSZ is studied here using multiple independent short molecular dynamics (MD) trajectories. Analysis of the MD trajectories yields free energy of O2–-vac pairs in 42 different local cation (Y3+/Zr4+) environments, to our knowledge calculated for the first time, as well as coarse-grained O2– hopping rates and Arrhenius parameters. On the basis of the free energies we conclude that it is possible that ionic movement is hindered in some environments not only because of high migration barriers or vacancy trapping as believed earlier but also because O2–-vac pairs are destabilized by these environments. Increasing the temperature and/or decreasing the dopant composition stabilizes O2–-vac pairs in these environments, which in turn affects the YSZ conductivity. Another newly found aspect is the connection between the kinetic rate constants for different environments; namely, the rates of interconversion between two environments depend on their O2–-vac free energy differences.

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Section: Methodsmentioning

confidence: 99%

Relative Occurrence of Oxygen-Vacancy Pairs in Yttrium-Containing Environments of Y₂O₃-Doped ZrO₂ Can Be Crucial to Ionic Conductivity

Jaipal

Chatterjee

2017

J. Phys. Chem. C

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“…Consider a MD trajectory of a duration τ MD . Analysis of the trajectory using a combination of distance metrics [38][39][40][41][42][43] and clustering methods, 4,44 and tests for the Markovian approximation (e.g., implied time scales for discrete-time MSMs 23 and tests for first-order behavior for continuous time MSMs 36,45 ) can yield information about the states of the system and the associated kinetic rates. Although states are randomly visited in the trajectory, the occupation π S (t) for a Markov state S at time t is deterministic and is given by the master equation…”

Section: Validity Time For a Markov State Modelmentioning

confidence: 99%

A new class of enhanced kinetic sampling methods for building Markov state models

Bhoutekar

Ghosh

Bhattacharya

et al. 2017

The Journal of Chemical Physics

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Markov state models (MSMs) and other related kinetic network models are frequently used to study the long-timescale dynamical behavior of biomolecular and materials systems. MSMs are often constructed bottom-up using brute-force molecular dynamics (MD) simulations when the model contains a large number of states and kinetic pathways that are not known a priori. However, the resulting network generally encompasses only parts of the configurational space, and regardless of any additional MD performed, several states and pathways will still remain missing. This implies that the duration for which the MSM can faithfully capture the true dynamics, which we term as the validity time for the MSM, is always finite and unfortunately much shorter than the MD time invested to construct the model. A general framework that relates the kinetic uncertainty in the model to the validity time, missing states and pathways, network topology, and statistical sampling is presented. Performing additional calculations for frequently-sampled states/pathways may not alter the MSM validity time. A new class of enhanced kinetic sampling techniques is introduced that aims at targeting rare states/pathways that contribute most to the uncertainty so that the validity time is boosted in an effective manner. Examples including straightforward 1D energy landscapes, lattice models, and biomolecular systems are provided to illustrate the application of the method. Developments presented here will be of interest to the kinetic Monte Carlo community as well.

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“…However, by using these techniques that employ simplified interaction potentials and reduced numbers of particles the details of the formation and rupture of noncovalent bonds cannot be studied with atomistic resolution. Markov State Models (MSMs) allow to study the kinetics of conformational transitions on long time scales using dynamical information from short atomistic simulation runs [15,16] and they have successfully been applied to extent the dynamical range of FPMD simulations [17,18]. Also methods that are developed directly to increase the efficiency of FPMD simulations are available [19,20].…”

Section: Introductionmentioning

confidence: 99%

Force probe simulations using an adaptive resolution scheme

Oestereich,

Gauss,

Diezemann

2021

Preprint

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Molecular simulations of the forced unfolding and refolding of biomolecules or molecular complexes allow to gain important kinetic, structural and thermodynamic information about the folding process and the underlying energy landscape. In force probe molecular dynamics (FPMD) simulations, one pulls one end of the molecule with a constant velocity in order to induce the relevant conformational transitions. Since the extended configuration of the system has to fit into the simulation box together with the solvent such simulations are very time consuming. Here, we apply a hybrid scheme in which the solute is treated with atomistic resolution and the solvent molecules far away from the solute are described in a coarse-grained manner. We use the adaptive resolution scheme (AdResS) that has very successfully been applied to various examples of equilibrium simulations. We perform FPMD simulations using AdResS on a well studied system, a dimer formed from mechanically interlocked calixarene capsules. The results of the multiscale simulations are compared to all-atom simulations of the identical system and we observe that the size of the region in which atomistic resolution is required depends on the pulling velocity, i.e. the particular non-equilibrium situation. For large pulling velocities a larger all atom region is required. Our results show that multiscale simulations can be applied also in the strong non-equilibrium situations that the system experiences in FPMD simulations.

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Time-Dependent Markov State Models for Single Molecule Force Spectroscopy

Cited by 11 publications

References 26 publications

Relative Occurrence of Oxygen-Vacancy Pairs in Yttrium-Containing Environments of Y₂O₃-Doped ZrO₂ Can Be Crucial to Ionic Conductivity

Relative Occurrence of Oxygen-Vacancy Pairs in Yttrium-Containing Environments of Y₂O₃-Doped ZrO₂ Can Be Crucial to Ionic Conductivity

A new class of enhanced kinetic sampling methods for building Markov state models

Force probe simulations using an adaptive resolution scheme

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Time-Dependent Markov State Models for Single Molecule Force Spectroscopy

Cited by 11 publications

References 26 publications

Relative Occurrence of Oxygen-Vacancy Pairs in Yttrium-Containing Environments of Y2O3-Doped ZrO2 Can Be Crucial to Ionic Conductivity

Relative Occurrence of Oxygen-Vacancy Pairs in Yttrium-Containing Environments of Y2O3-Doped ZrO2 Can Be Crucial to Ionic Conductivity

A new class of enhanced kinetic sampling methods for building Markov state models

Force probe simulations using an adaptive resolution scheme

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Relative Occurrence of Oxygen-Vacancy Pairs in Yttrium-Containing Environments of Y₂O₃-Doped ZrO₂ Can Be Crucial to Ionic Conductivity

Relative Occurrence of Oxygen-Vacancy Pairs in Yttrium-Containing Environments of Y₂O₃-Doped ZrO₂ Can Be Crucial to Ionic Conductivity