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  • Book
    Gregory R. Bowman, Frank Noé, Vijay S. Pande, editors.
    Summary: The aim of this book volume is to explain the importance of Markov state models to molecular simulation, how they work, and how they can be applied to a range of problems. The Markov state model (MSM) approach aims to address two key challenges of molecular simulation: 1) How to reach long timescales using short simulations of detailed molecular models 2) How to systematically gain insight from the resulting sea of data MSMs do this by providing a compact representation of the vast conformational space available to biomolecules by decomposing it into states sets of rapidly interconverting conformations and the rates of transitioning between states.This kinetic definition allows one to easily vary the temporal and spatial resolution of an MSM from high-resolution models capable of quantitative agreement with (or prediction of) experiment to low-resolution models that facilitate understanding. Additionally, MSMs facilitate the calculation of quantities that are difficult to obtain from more direct MD analyses, such as the ensemble of transition pathways. This book introduces the mathematical foundations of Markov models, how they can be used to analyze simulations and drive efficient simulations, and some of the insights these models have yielded in a variety of applications of molecular simulation.

    Contents:
    An overview and practical guide to building Markov state models
    Markov model theory
    Estimation and Validation of Markov models
    Uncertainty estimation
    Analysis of Markov models
    Transition Path Theory
    Understanding Protein Folding using Markov state models
    Understanding Molecular Recognition by Kinetic Network Models Constructed from Molecular Dynamics Simulations
    Markov State and Diffusive Stochastic Models in Electron Spin Resonance
    Software for building Markov state models.
    Digital Access Springer 2014
    Access via Advances in experimental medicine and biology ; 2014 ; 797
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    Advances in experimental medicine and biology ; 2014 ; 797
    2014
  • Article
    Flitney FW, Hirst DG.
    J Physiol. 1978 Mar;276:449-65.
    1. A study has been made of the tension responses and sarcomere length changes produced by servo-controlled stretches applied to isometrically contracting frog muscle. Sarcomere lengths were monitored by cine-photography of diffiraction spectra obtained by illuminating a small area of muscle with a laser. 2. The tension increment produced by a ramp-and-hold stretch of approximately 1 mm (ca. 4% of the muscle length) comprises three phases whose limits are defined by two points, S1 and S2, where the slope of the response decreases abruptly. S1 and S2 correspond to extensions of 0.13 and 1.2% of the muscle length. 3. Movements of the first order spectra relative to the zero order recorded during stretch reveal that S2 coincides with an abrupt elongation of the sarcomeres. This is termed sarcomere 'give' and it occurs when the filaments are displaced by 11-12 nm from their steady-state (isometric) position. 4. The stiffness of the sarcomeres, Es, up to S2 decreases with increasing sarcomere length. The maximum force sustained by the muscle at S2, PS2, also shows an inverse dependence on sarcomere length. Both Es and PS2 fall to zero at an extrapolated sarcomere spacing of 3.6-3.7 micrometer, coinciding with the length at which the actin and myosin filaments no longer overlap. 5. The ratio PS2/P0 (where P0 = maximum isometric tension) varies with temperature and speed of stretch. It increases with increasing speeds of stretch until a certain critical velocity, Vc, is reached, beyond which it is almost independent of any further increase. Vc has a positive temperature coefficient, increasing 5-6 in the range 0-30 degrees C (Q10 = 1.8). There is a positive correlation between the maximum speed of isotonic shortening (Vmax.) and Vc in different muscles. 6. Sarcomere 'give' during stretch is considered to be due to forcible detachment of cross-bridges between the actin and myosin filaments. This results in recoil of the extended series elastic elements in the muscle at the expense of the sarcomers. The amount of filament displacement required to induce sarcomere 'give' (11-12 nm) is thought to represent the range of movement over which a cross-bridge can remain attached to actin during a stretch.
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