55 research outputs found
Thermodynamically Important Contacts in Folding of Model Proteins
We introduce a quantity, the entropic susceptibility, that measures the
thermodynamic importance-for the folding transition-of the contacts between
amino acids in model proteins. Using this quantity, we find that only one
equilibrium run of a computer simulation of a model protein is sufficient to
select a subset of contacts that give rise to the peak in the specific heat
observed at the folding transition. To illustrate the method, we identify
thermodynamically important contacts in a model 46-mer. We show that only about
50% of all contacts present in the protein native state are responsible for the
sharp peak in the specific heat at the folding transition temperature, while
the remaining 50% of contacts do not affect the specific heat.Comment: 5 pages, 5 figures; to be published in PR
Optimization and evaluation of a coarse-grained model of protein motion using X-ray crystal data
Simple coarse-grained models, such as the Gaussian Network Model, have been
shown to capture some of the features of equilibrium protein dynamics. We
extend this model by using atomic contacts to define residue interactions and
introducing more than one interaction parameter between residues. We use
B-factors from 98 ultra-high resolution X-ray crystal structures to optimize
the interaction parameters. The average correlation between GNM fluctuation
predictions and the B-factors is 0.64 for the data set, consistent with a
previous large-scale study. By separating residue interactions into covalent
and noncovalent, we achieve an average correlation of 0.74, and addition of
ligands and cofactors further improves the correlation to 0.75. However,
further separating the noncovalent interactions into nonpolar, polar, and mixed
yields no significant improvement. The addition of simple chemical information
results in better prediction quality without increasing the size of the
coarse-grained model.Comment: 18 pages, 4 figures, 1 supplemental file (cnm_si.tex
Nonlinearity of Mechanochemical Motions in Motor Proteins
The assumption of linear response of protein molecules to thermal noise or
structural perturbations, such as ligand binding or detachment, is broadly used
in the studies of protein dynamics. Conformational motions in proteins are
traditionally analyzed in terms of normal modes and experimental data on
thermal fluctuations in such macromolecules is also usually interpreted in
terms of the excitation of normal modes. We have chosen two important protein
motors - myosin V and kinesin KIF1A - and performed numerical investigations of
their conformational relaxation properties within the coarse-grained elastic
network approximation. We have found that the linearity assumption is deficient
for ligand-induced conformational motions and can even be violated for
characteristic thermal fluctuations. The deficiency is particularly pronounced
in KIF1A where the normal mode description fails completely in describing
functional mechanochemical motions. These results indicate that important
assumptions of the theory of protein dynamics may need to be reconsidered.
Neither a single normal mode, nor a superposition of such modes yield an
approximation of strongly nonlinear dynamics.Comment: 10 pages, 6 figure
Protein dynamics with off-lattice Monte Carlo moves
A Monte Carlo method for dynamics simulation of all-atom protein models is
introduced, to reach long times not accessible to conventional molecular
dynamics. The considered degrees of freedom are the dihedrals at
C-atoms. Two Monte Carlo moves are used: single rotations about
torsion axes, and cooperative rotations in windows of amide planes, changing
the conformation globally and locally, respectively. For local moves Jacobians
are used to obtain an unbiased distribution of dihedrals. A molecular dynamics
energy function adapted to the protein model is employed. A polypeptide is
folded into native-like structures by local but not by global moves.Comment: 10 pages, 4 Postscript figures, uses epsf.sty and a4.sty; scheduled
tentatively for Phys.Rev.E issue of 1 March 199
An exact expression to calculate the derivatives of position-dependent observables in molecular simulations with flexible constraints
In this work, we introduce an algorithm to compute the derivatives of
physical observables along the constrained subspace when flexible constraints
are imposed on the system (i.e., constraints in which the hard coordinates are
fixed to configuration-dependent values). The presented scheme is exact, it
does not contain any tunable parameter, and it only requires the calculation
and inversion of a sub-block of the Hessian matrix of second derivatives of the
function through which the constraints are defined. We also present a practical
application to the case in which the sought observables are the Euclidean
coordinates of complex molecular systems, and the function whose minimization
defines the constraints is the potential energy. Finally, and in order to
validate the method, which, as far as we are aware, is the first of its kind in
the literature, we compare it to the natural and straightforward
finite-differences approach in three molecules of biological relevance:
methanol, N-methyl-acetamide and a tri-glycine peptideComment: 13 pages, 8 figures, published versio
The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein
The folding pathway and rate coefficients of the folding of a knotted protein
are calculated for a potential energy function with minimal energetic
frustration. A kinetic transition network is constructed using the discrete
path sampling approach, and the resulting potential energy surface is
visualized by constructing disconnectivity graphs. Owing to topological
constraints, the low-lying portion of the landscape consists of three distinct
regions, corresponding to the native knotted state and to configurations where
either the N- or C-terminus is not yet folded into the knot. The fastest
folding pathways from denatured states exhibit early formation of the
N-terminus portion of the knot and a rate-determining step where the C-terminus
is incorporated. The low-lying minima with the N-terminus knotted and the
C-terminus free therefore constitute an off-pathway intermediate for this
model. The insertion of both the N- and C-termini into the knot occur late in
the folding process, creating large energy barriers that are the rate limiting
steps in the folding process. When compared to other protein folding proteins
of a similar length, this system folds over six orders of magnitude more
slowly.Comment: 19 page
Static and dynamic characteristics of protein contact networks
The principles underlying protein folding remains one of Nature's puzzles
with important practical consequences for Life. An approach that has gathered
momentum since the late 1990's, looks at protein hetero-polymers and their
folding process through the lens of complex network analysis. Consequently,
there is now a body of empirical studies describing topological characteristics
of protein macro-molecules through their contact networks and linking these
topological characteristics to protein folding. The present paper is primarily
a review of this rich area. But it delves deeper into certain aspects by
emphasizing short-range and long-range links, and suggests unconventional
places where "power-laws" may be lurking within protein contact networks.
Further, it considers the dynamical view of protein contact networks. This
closer scrutiny of protein contact networks raises new questions for further
research, and identifies new regularities which may be useful to parameterize a
network approach to protein folding. Preliminary experiments with such a model
confirm that the regularities we identified cannot be easily reproduced through
random effects. Indeed, the grand challenge of protein folding is to elucidate
the process(es) which not only generates the specific and diverse linkage
patterns of protein contact networks, but also reproduces the dynamic behavior
of proteins as they fold. Keywords: network analysis, protein contact networks,
protein foldingComment: Added Appendix
Manipulating Biopolymer Dynamics by Anisotropic Nanoconfinement
How the geometry of nano-sized confinement affects dynamics of biomaterials
is interesting yet poorly understood. An elucidation of structural details upon
nano-sized confinement may benefit manufacturing pharmaceuticals in biomaterial
sciences and medicine. The behavior of biopolymers in nano-sized confinement is
investigated using coarse-grained models and molecular simulations.
Particularly, we address the effects of shapes of a confinement on protein
folding dynamics by measuring folding rates and dissecting structural
properties of the transition states in nano-sized spheres and ellipsoids. We
find that when the form of a confinement resembles the geometrical properties
of the transition states, the rates of folding kinetics are most enhanced. This
knowledge of shape selectivity in identifying optimal conditions for reactions
will have a broad impact in nanotechnology and pharmaceutical sciences.Comment: to appear in Nano Letter
Exploring the Conformational Transitions of Biomolecular Systems Using a Simple Two-State Anisotropic Network Model
Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results. © 2014 Das et al
Detection of Functional Modes in Protein Dynamics
Proteins frequently accomplish their biological function by collective atomic motions. Yet the identification of collective motions related to a specific protein function from, e.g., a molecular dynamics trajectory is often non-trivial. Here, we propose a novel technique termed “functional mode analysis” that aims to detect the collective motion that is directly related to a particular protein function. Based on an ensemble of structures, together with an arbitrary “functional quantity” that quantifies the functional state of the protein, the technique detects the collective motion that is maximally correlated to the functional quantity. The functional quantity could, e.g., correspond to a geometric, electrostatic, or chemical observable, or any other variable that is relevant to the function of the protein. In addition, the motion that displays the largest likelihood to induce a substantial change in the functional quantity is estimated from the given protein ensemble. Two different correlation measures are applied: first, the Pearson correlation coefficient that measures linear correlation only; and second, the mutual information that can assess any kind of interdependence. Detecting the maximally correlated motion allows one to derive a model for the functional state in terms of a single collective coordinate. The new approach is illustrated using a number of biomolecules, including a polyalanine-helix, T4 lysozyme, Trp-cage, and leucine-binding protein
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