685 research outputs found
Optimal Reaction Coordinates
The dynamic behavior of complex systems with many degrees of freedom is often analyzed by projection onto one or a few reaction coordinates. The dynamics is then described in a simple and intuitive way as diffusion on the associated free energy pro le. In order to use such a picture for a quantitative description of the dynamics one needs to select the coordinate in an optimal way so as to minimize non-Markovian effects due to the projection. For equilibrium dynamics between two boundary states (e.g., a reaction) the optimal coordinate is known as the committor or the pfold coordinate in protein folding studies. While the dynamics projected on the committor is not Markovian, many important quantities of the original multidimensional dynamics on an arbitrarily complex landscape can be computed exactly. Here we summarize the derivation of this result, discuss different approaches to determine and validate the committor coordinate and present three illustrative applications: protein folding, the game of chess, and patient recovery dynamics after kidney transplant
Modellierung der freien Energiefläche von Biomolekülen durch Torsionswinkel-Principal-Component-Analysis von Molekulardynamiksimulationen
This work presents a contribution to the literature on methods in search of lowdimensional models that yield insight into the equilibrium and kinetic behavior of peptides and small proteins. A deep understanding of various methods for projecting the sampled configurations of molecular dynamics simulations to obtain a low-dimensional free energy landscape is acquired. Furthermore low-dimensional dynamic models for the conformational dynamics of biomolecules in reduced dimensionality are presented. As exemplary systems, mainly short alanine chains are studied. Due to their size they allow for performing long simulations. They are simple, yet nontrivial systems, as due to their flexibility they are rapidly interconverting conformers. Understanding these polypeptide chains in great detail is of considerable interest for getting insight in the process of protein folding. For example, K. Dill et al. conclude in their review [28] about the protein folding problem that "the once intractable Levinthal puzzle now seems to have a very simple answer: a protein can fold quickly and solve its large global optimization puzzle simply through piecewise solutions of smaller component puzzles".Das Ziel der vorliegenden Arbeit ist es, einen Beitrag zur Entwicklung von Methoden zur Modellierung von freien Energieflächen von Biomolekülen zu leisten. Ausgehend von Molekulardynamik-Simulationen geht es insbesondere darum, niedrig-dimensionale Modelle für die Beschreibung von Konformationen und der Kinetik von Peptiden und kleinen Proteinen zu erhalten
Topological Methods for Exploring Low-density States in Biomolecular Folding Pathways
Characterization of transient intermediate or transition states is crucial
for the description of biomolecular folding pathways, which is however
difficult in both experiments and computer simulations. Such transient states
are typically of low population in simulation samples. Even for simple systems
such as RNA hairpins, recently there are mounting debates over the existence of
multiple intermediate states. In this paper, we develop a computational
approach to explore the relatively low populated transition or intermediate
states in biomolecular folding pathways, based on a topological data analysis
tool, Mapper, with simulation data from large-scale distributed computing. The
method is inspired by the classical Morse theory in mathematics which
characterizes the topology of high dimensional shapes via some functional level
sets. In this paper we exploit a conditional density filter which enables us to
focus on the structures on pathways, followed by clustering analysis on its
level sets, which helps separate low populated intermediates from high
populated uninteresting structures. A successful application of this method is
given on a motivating example, a RNA hairpin with GCAA tetraloop, where we are
able to provide structural evidence from computer simulations on the multiple
intermediate states and exhibit different pictures about unfolding and
refolding pathways. The method is effective in dealing with high degree of
heterogeneity in distribution, capturing structural features in multiple
pathways, and being less sensitive to the distance metric than nonlinear
dimensionality reduction or geometric embedding methods. It provides us a
systematic tool to explore the low density intermediate states in complex
biomolecular folding systems.Comment: 23 pages, 6 figure
Manifold Learning in Atomistic Simulations: A Conceptual Review
Analyzing large volumes of high-dimensional data requires dimensionality
reduction: finding meaningful low-dimensional structures hidden in their
high-dimensional observations. Such practice is needed in atomistic simulations
of complex systems where even thousands of degrees of freedom are sampled. An
abundance of such data makes gaining insight into a specific physical problem
strenuous. Our primary aim in this review is to focus on unsupervised machine
learning methods that can be used on simulation data to find a low-dimensional
manifold providing a collective and informative characterization of the studied
process. Such manifolds can be used for sampling long-timescale processes and
free-energy estimation. We describe methods that can work on datasets from
standard and enhanced sampling atomistic simulations. Unlike recent reviews on
manifold learning for atomistic simulations, we consider only methods that
construct low-dimensional manifolds based on Markov transition probabilities
between high-dimensional samples. We discuss these techniques from a conceptual
point of view, including their underlying theoretical frameworks and possible
limitations
A self-learning algorithm for biased molecular dynamics
A new self-learning algorithm for accelerated dynamics, reconnaissance
metadynamics, is proposed that is able to work with a very large number of
collective coordinates. Acceleration of the dynamics is achieved by
constructing a bias potential in terms of a patchwork of one-dimensional,
locally valid collective coordinates. These collective coordinates are obtained
from trajectory analyses so that they adapt to any new features encountered
during the simulation. We show how this methodology can be used to enhance
sampling in real chemical systems citing examples both from the physics of
clusters and from the biological sciences.Comment: 6 pages, 5 figures + 9 pages of supplementary informatio
Protein folding tames chaos
Protein folding produces characteristic and functional three-dimensional
structures from unfolded polypeptides or disordered coils. The emergence of
extraordinary complexity in the protein folding process poses astonishing
challenges to theoretical modeling and computer simulations. The present work
introduces molecular nonlinear dynamics (MND), or molecular chaotic dynamics,
as a theoretical framework for describing and analyzing protein folding. We
unveil the existence of intrinsically low dimensional manifolds (ILDMs) in the
chaotic dynamics of folded proteins. Additionally, we reveal that the
transition from disordered to ordered conformations in protein folding
increases the transverse stability of the ILDM. Stated differently, protein
folding reduces the chaoticity of the nonlinear dynamical system, and a folded
protein has the best ability to tame chaos. Additionally, we bring to light the
connection between the ILDM stability and the thermodynamic stability, which
enables us to quantify the disorderliness and relative energies of folded,
misfolded and unfolded protein states. Finally, we exploit chaos for protein
flexibility analysis and develop a robust chaotic algorithm for the prediction
of Debye-Waller factors, or temperature factors, of protein structures
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