Illia Horenko

Hierarchical analysis of conformational dynamics in biomolecules: Transition networks of metastable states

Molecular dynamics simulation generates large quantities of data that must be interpreted using physically meaningful analysis. A common approach is to describe the system dynamics in terms of transitions between coarse partitions of conformational space. In contrast to previous work that partitions the space according to geometric proximity, the authors examine here clustering based on kinetics, merging configurational microstates together so as to identify long-lived, i.e., dynamically metastable, states. As test systems microsecond molecular dynamics simulations of the polyalanines Ala(8) and Ala(12) are analyzed. Both systems clearly exhibit metastability, with some kinetically distinct metastable states being geometrically very similar. Using the backbone torsion rotamer pattern to define the microstates, a definition is obtained of metastable states whose lifetimes considerably exceed the memory associated with interstate dynamics, thus allowing the kinetics to be described by a Markov model. This model is shown to be valid by comparison of its predictions with the kinetics obtained directly from the molecular dynamics simulations. In contrast, clustering based on the hydrogen-bonding pattern fails to identify long-lived metastable states or a reliable Markov model. Finally, an approach is proposed to generate a hierarchical model of networks, each having a different number of metastable states. The model hierarchy yields a qualitative understanding of the multiple time and length scales in the dynamics of biomolecules.

Quantum-classical Liouville approach to molecular dynamics: Surface hopping Gaussian phase-space packets

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a molecular system are modeled quantum-mechanically while the remaining degrees of freedom are treated within the classical approximation. Such models can be systematically derived as a first order approximation to the partial Wigner transform of the quantum Liouville-von Neumann equation. The resulting adiabatic quantum-classical Liouville equation (QCLE) can be decomposed into three individual propagators by means of a Trotter splitting: Phase oscillations of the coherences resulting from the time evolution of the quantum-mechanical subsystem. Exchange of densities and coherences reflecting non-adiabatic effects in quantum-classical dynamics. Classical Liouvillian transport of densities and coherences along adiabatic potential energy surfaces or arithmetic means thereof. A novel stochastic implementation of the QCLE is proposed in the present work. In order to substantially improve the traditional algorithm based on surface hopping trajectories [J. C. Tully, J. Chem. Phys. 93 (2), 1061 (1990)], we model the evolution of densities and coherences by a set of surface hopping Gaussian phase-space packets (GPPs) with variable width and with adjustable real or complex amplitudes, respectively. The dense sampling of phase-space offers two main advantages over other numerical schemes to solve the QCLE. First, it allows to perform a quantum-classical simulation employing a constant number of particles, i. e. the generation of new trajectories at each surface hop is avoided. Second, the effect of non-local operators in the exchange of densities and coherences can be treated without having to invoke the momentum jump approximation. For the example of a single avoided crossing we demonstrate that convergence towards fully quantum-mechanical dynamics is much faster for surface hopping GPPs than for trajectory-based methods. For dual avoided crossings the Gaussian-based dynamics correctly reproduces the quantum-mechanical result even when trajectory-based methods not accounting for the transport of coherences fail qualitatively.

On the Identification of Nonstationary Factor Models and Their Application to Atmospheric Data Analysis

Abstract A numerical framework for data-based identification of nonstationary linear factor models is presented. The approach is based on the extension of the recently developed method for identification of persistent dynamical phases in multidimensional time series, permitting the identification of discontinuous temporal changes in underlying model parameters. The finite element method (FEM) discretization of the resulting variational functional is applied to reduce the dimensionality of the resulting problem and to construct the numerical iterative algorithm. The presented method results in the sparse sequential linear minimization problem with linear constrains. The performance of the framework is demonstrated for the following two application examples: (i) in the context of subgrid-scale parameterization for the Lorenz model with external forcing and (ii) in an analysis of climate impact factors acting on the blocking events in the upper troposphere. The importance of accounting for the nonstationarit...

Systematic Metastable Atmospheric Regime Identification in an AGCM

In this study we apply a recently developed clustering method for the systematic identification of metastable atmospheric regimes in high-dimensional data sets generated by atmospheric models. The novelty of this approach is that it decomposes the phase space in, possibly, over-lapping clusters and simultaneously estimates the most likely switching sequence amongst the clusters. The parameters of the clustering and switching are estimated by a Finite Element approach. The switching amongst the clusters can be described by a Markov transition matrix. Possible metastable regime behavior is assessed by inspecting the eigenspectrum of the associated transition probability matrix. Here we apply the recently introduced metastable data-analysis method to high-dimensional data sets produced by a barotropic model and a comprehensive atmospheric General Circulation Model (GCM). We are able to successfully identify significant and dynamically relevant metastable regimes in both models. The metastable regimes in the barotropic model correspond to blocked and zonal states. Similar regime states were already previously identified in highly reduced phase spaces of just one- and two-dimensions in the same model. Next the clustering method is applied to a comprehensive atmospheric GCM where 7 significant flow regimes are identified. The spatial structures of the regimes correspond amongst others to both phases of the Northern Annular Mode and Pacific blocking. The regimes are maintained predominantly by transient eddy fluxes of low-pass filtered anomalies. It is demonstrated how the dynamical description of the slow process switching between the regimes can be acquired from the analysis results and an investigation of the resulting simplified dynamical model with respect to predictability is performed. A predictability study shows that a simple Markov model is able to predict the regimes up to 6 days ahead, which is comparable to the ability of high resolution state-of-the-art numerical weather prediction models to accurately predict the onset and decay of blockings. The implications of our results for the derivation of reduced models for extended-range predictability are discussed.

Finite Element Approach to Clustering of Multidimensional Time Series

We present a new approach to clustering of time series based on a minimization of the averaged clustering functional. The proposed functional describes the mean distance between observation data and its representation in terms of

Automated Model Reduction for Complex Systems exhibiting Metastability

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Changes in the Metastability of the Midlatitude Southern Hemisphere Circulation and the Utility of Nonstationary Cluster Analysis and Split-Flow Blocking Indices as Diagnostic Tools

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Fully adaptive propagation of the quantum-classical Liouville equation

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On Simultaneous Data-Based Dimension Reduction and Hidden Phase Identification

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Automated Generation of Reduced Stochastic Weather Models I: Simultaneous Dimension and Model reduction for Time Series Analysis

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