Browsing by Author "Yang, Haw"

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Analysis of Trajectory Entropy for Continuous Stochastic Processes at Equilibrium
(2014-07-17)
Haas, Kevin R.
;
Yang, Haw
;
Chu, Jhih-Wei
;
生物科技學系
;
生物資訊及系統生物研究所
The analytical expression for the trajectory entropy of the overdamped Langevin equation is derived via two approaches. The first route goes through the Fokker-Planck equation that governs the propagation of the conditional probability density, while the second method goes through the path integral of the Onsager-Machlup action. The agreement of these two approaches in the continuum limit underscores the equivalence between the partial differential equation and the path integral formulations for stochastic processes in the context of trajectory entropy. The values obtained using the analytical expression are also compared with those calculated with numerical solutions for arbitrary time resolutions of the trajectory. Quantitative agreement is clearly observed consistently across different models as the time interval between snapshots in the trajectories decreases. Furthermore, analysis of different scenarios illustrates how the deterministic and stochastic forces in the Langevin equation contribute to the variation in dynamics measured by the trajectory entropy.
Analysis of Trajectory Entropy for Continuous Stochastic Processes at Equilibrium
(2014-07-17)
Haas, Kevin R.
;
Yang, Haw
;
Chu, Jhih-Wei
;
生物科技學系
;
生物資訊及系統生物研究所
The analytical expression for the trajectory entropy of the overdamped Langevin equation is derived via two approaches. The first route goes through the Fokker-Planck equation that governs the propagation of the conditional probability density, while the second method goes through the path integral of the Onsager-Machlup action. The agreement of these two approaches in the continuum limit underscores the equivalence between the partial differential equation and the path integral formulations for stochastic processes in the context of trajectory entropy. The values obtained using the analytical expression are also compared with those calculated with numerical solutions for arbitrary time resolutions of the trajectory. Quantitative agreement is clearly observed consistently across different models as the time interval between snapshots in the trajectories decreases. Furthermore, analysis of different scenarios illustrates how the deterministic and stochastic forces in the Langevin equation contribute to the variation in dynamics measured by the trajectory entropy.
Compound Molecular Logic in Accessing the Active Site of Mycobacterium tuberculosis Protein Tyrosine Phosphatase B
(2018-11-07)
Morrell, Thomas E.
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Rafalska-Metcalf, Ilona U.
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Yang, Haw
;
Chu, Jhih-Wei
;
生物資訊及系統生物研究所
Protein tyrosine phosphatase B (PtpB) from Mycobacterium tuberculosis (Mtb) extends the bacteria's survival in hosts and hence is a potential target for Mtb-specific drugs. To study how Mtb-specific sequence insertions in PtpB may regulate access to its active site through large-amplitude conformational changes, we performed free-energy calculations using an all-atom explicit solvent model. Corroborated by biochemical assays, the results show that PtpB's active site is controlled via an "either/or" compound conformational gating mechanism, an unexpected discovery that Mtb has evolved to bestow a single enzyme with such intricate logical operations. In addition to providing unprecedented insights for its active-site surroundings, the findings also suggest new ways of inactivating PtpB.
Coupling between Protein Conformation and Local Unfolding Highlights the Role of Disorder in Protein Function and Suggests a New Target for Tuberculosis Treatment
(2014-01-28)
Morrell, Thomas E.
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Rafalska-Metcalf, Ilona U.
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Chu, Jhih-Wei
;
Yang, Haw
;
交大名義發表
Expectation-Maximization of the Potential of Mean Force and Diffusion Coefficient in Langevin Dynamics from Single Molecule FRET Data Photon by Photon
(2013-12-12)
Haas, Kevin R.
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Yang, Haw
;
Chu, Jhih-Wei
;
生物科技學系
;
生物資訊及系統生物研究所
The dynamics of a protein along a well-defined coordinate can be formally projected onto the form of an overdamped Lagevin equation. Here, we present a comprehensive statistical-learning framework for simultaneously quantifying the deterministic force (the potential of mean force, PMF) and the stochastic force (characterized by the diffusion coefficient, D) from single-molecule Forster-type resonance energy transfer (smFRET) experiments. The likelihood functional of the Langevin parameters, PMF and D, is expressed by a path integral of the latent smFRET distance that follows Langevin dynamics and realized by the donor and the acceptor photon emissions. The solution is made possible by an eigen decomposition of the time-symmetrized form of the corresponding Fokker-Planck equation coupled with photon statistics. To extract the Langevin parameters from photon arrival time data, we advance the expectation-maximization algorithm in statistical learning, originally developed for and mostly used in discrete-state systems, to a general form in the continuous space that allows for a variational calculus on the continuous PMF function. We also introduce the regularization of the solution space in this Bayesian inference based on a maximum trajectory-entropy principle. We use a highly nontrivial example with realistically simulated smFRET data to illustrate the application of this new method.
Fisher information metric for the Langevin equation and least informative models of continuous stochastic dynamics
(2013-09-28)
Haas, Kevin R.
;
Yang, Haw
;
Chu, Jhih-Wei
;
生物科技學系
;
生物資訊及系統生物研究所
The evaluation of the Fisher information matrix for the probability density of trajectories generated by the over-damped Langevin dynamics at equilibrium is presented. The framework we developed is general and applicable to any arbitrary potential of mean force where the parameter set is now the full space dependent function. Leveraging an innovative Hermitian form of the corresponding Fokker-Planck equation allows for an eigenbasis decomposition of the time propagation probability density. This formulation motivates the use of the square root of the equilibrium probability density as the basis for evaluating the Fisher information of trajectories with the essential advantage that the Fisher information matrix in the specified parameter space is constant. This outcome greatly eases the calculation of information content in the parameter space via a line integral. In the continuum limit, a simple analytical form can be derived to explicitly reveal the physical origin of the information content in equilibrium trajectories. This methodology also allows deduction of least informative dynamics models from known or available observables that are either dynamical or static in nature. The minimum information optimization of dynamics is performed for a set of different constraints to illustrate the generality of the proposed methodology. (C) 2013 AIP Publishing LLC.
Identifying the structural and kinetic elements in protein large-amplitude conformational motions
(2017-01-01)
Chu, Jhih-Wei
;
Yang, Haw
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生物科技學系
;
生物資訊及系統生物研究所
;
分子醫學與生物工程研究所
The importance of how a protein reconfigures its structure to achieve its function has long been appreciated; yet, the progress in our fundamental understanding of protein dynamics does not seem to be commensurate with the rapid advances in experimental techniques and ever increasing computational prowess. In this review, we attempt to look at this issue based on quantitative characterisations that go beyond simply determining the kinetics rates or only allowing qualitative statements about conformational states. We summarise the theoretical basis for determining from experimental data the kinetics and the structural elements of protein conformational dynamics. The two kinetics elements include the apparent potential of mean force and the intra-molecular diffusion coefficient along a coordinate defined by the pair of single-molecule Forster-type resonance energy transfer reporters that are chemically attached to the protein. We show that it is now possible to resolve the relative contributions of these two kinetics elements when discussing the physical origin of the protein's conformation-reconfiguration rate changes due to mutation or interaction with chemical effectors or with other proteins. The structural element refers to the orthogonal conformational modes that give rise to the intrinsic conformational motions of the protein, and could allow a comparative study among proteins from different families. To achieve these, it is essential that experimental data be rigorously analysed and integrated with molecular simulations - which include molecular dynamics simulations, coarse-grained modelling, and enhanced sampling. In turn, the close interplay between computation and experiment through this new direction could accelerate the discovery of predictive models.
Molecular simulations in conjunction with experimental studies illustrate internal protein logic controlled by conformation and dynamic structural change
(2015-03-22)
Morrell, Thomas
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Rafalska-Metcalf, Ilona
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Chu, Jhih-Wei
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Yang, Haw
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生物科技學系
Structure-mechanics statistical learning unravels the linkage between local rigidity and global flexibility in nucleic acids
(2020-05-21)
Chen, Yi-Tsao
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Yang, Haw
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Chu, Jhih-Wei
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交大名義發表
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生物資訊及系統生物研究所
The mechanical properties of nucleic acids underlie biological processes ranging from genome packaging to gene expression, but tracing their molecular origin has been difficult due to the structural and chemical complexity. We posit that concepts from machine learning can help to tackle this long-standing challenge. Here, we demonstrate the feasibility and advantage of this strategy through developing a structure-mechanics statistical learning scheme to elucidate how local rigidity in double-stranded (ds)DNA and dsRNA may lead to their global flexibility in bend, stretch, and twist. Specifically, the mechanical parameters in a heavy-atom elastic network model are computed from the trajectory data of all-atom molecular dynamics simulation. The results show that the inter-atomic springs for backbone and ribose puckering in dsRNA are stronger than those in dsDNA, but are similar in strengths for base-stacking and base-pairing. Our analysis shows that the experimental observation of dsDNA being easier to bend but harder to stretch than dsRNA comes mostly from the respective B- and A-form topologies. The computationally resolved composition of local rigidity indicates that the flexibility of both nucleic acids is mostly due to base-stacking. But for properties like twist-stretch coupling, backbone springs are shown to play a major role instead. The quantitative connection between local rigidity and global flexibility sets foundation for understanding how local binding and chemical modification of genetic materials effectuate longer-ranged regulatory signals.
Trajectory Entropy of Continuous Stochastic Processes at Equilibrium
(2014-03-20)
Haas, Kevin R.
;
Yang, Haw
;
Chu, Jhih-Wei
;
生物科技學系
;
生物資訊及系統生物研究所
We propose to quantify the trajectory entropy of a dynamic system as the information content in excess of a free-diffusion reference model. The space time trajectory is now the dynamic variable, and its path probability is given by the Onsager-Machlup action. For the time propagation of the overdamped Langevin equation, we solved the action path integral in the continuum limit and arrived at an exact analytical expression that emerged as a simple functional of the deterministic mean force and the stochastic diffusion. This work may have direct implications in chemical and phase equilibria, bond isomerization, and conformational changes in biological macromolecules as well transport problems in general.