13,243 research outputs found
Ratcheted molecular-dynamics simulations identify efficiently the transition state of protein folding
The atomistic characterization of the transition state is a fundamental step
to improve the understanding of the folding mechanism and the function of
proteins. From a computational point of view, the identification of the
conformations that build out the transition state is particularly cumbersome,
mainly because of the large computational cost of generating a
statistically-sound set of folding trajectories. Here we show that a biasing
algorithm, based on the physics of the ratchet-and-pawl, can be used to
identify efficiently the transition state. The basic idea is that the
algorithmic ratchet exerts a force on the protein when it is climbing the
free-energy barrier, while it is inactive when it is descending. The transition
state can be identified as the point of the trajectory where the ratchet
changes regime. Besides discussing this strategy in general terms, we test it
within a protein model whose transition state can be studied independently by
plain molecular dynamics simulations. Finally, we show its power in
explicit-solvent simulations, obtaining and characterizing a set of
transition--state conformations for ACBP and CI2
A correspondence between solution-state dynamics of an individual protein and the sequence and conformational diversity of its family.
Conformational ensembles are increasingly recognized as a useful representation to describe fundamental relationships between protein structure, dynamics and function. Here we present an ensemble of ubiquitin in solution that is created by sampling conformational space without experimental information using "Backrub" motions inspired by alternative conformations observed in sub-Angstrom resolution crystal structures. Backrub-generated structures are then selected to produce an ensemble that optimizes agreement with nuclear magnetic resonance (NMR) Residual Dipolar Couplings (RDCs). Using this ensemble, we probe two proposed relationships between properties of protein ensembles: (i) a link between native-state dynamics and the conformational heterogeneity observed in crystal structures, and (ii) a relation between dynamics of an individual protein and the conformational variability explored by its natural family. We show that the Backrub motional mechanism can simultaneously explore protein native-state dynamics measured by RDCs, encompass the conformational variability present in ubiquitin complex structures and facilitate sampling of conformational and sequence variability matching those occurring in the ubiquitin protein family. Our results thus support an overall relation between protein dynamics and conformational changes enabling sequence changes in evolution. More practically, the presented method can be applied to improve protein design predictions by accounting for intrinsic native-state dynamics
A model for the force stretching double-stranded chain molecules
We modify and extend the recently developed statistical mechanical model for
predicting the thermodynamic properties of chain molecules having noncovalent
double-stranded conformations, as in RNA or ssDNA, and sheets in
protein, by including the constant force stretching at one end of molecules as
in a typical single-molecule experiment. The conformations of double-stranded
regions of the chain are calculated based on polymer graph-theoretic approach
[S-J. Chen and K. A. Dill, J. Chem. Phys. {\bf109}, 4602(1998)], while the
unpaired single-stranded regions are treated as self-avoiding walks. Sequence
dependence and excluded volume interaction are taken into account explicitly.
Two classes of conformations, hairpin and RNA secondary structure are explored.
For the hairpin conformations, all possible end-to-end distances corresponding
to the different types of double-stranded regions are enumerated exactly. For
the RNA secondary structure conformations, a new recursive formula
incorporating the secondary structure and end-to-end distribution has been
derived. Using the model, we investigate the extension-force curves, contact
and population distributions and re-entering phenomena, respectively. we find
that the force stretching homogeneous chains of hairpin and secondary structure
conformations are very different: the unfolding of hairpins is two-state, while
unfolding the latter is one-state. In addition, re-entering transitions only
present in hairpin conformations, but are not observed in secondary structure
conformations.Comment: 19 pages, 28 figure
Estimation of the infinitesimal generator by square-root approximation
For the analysis of molecular processes, the estimation of time-scales, i.e.,
transition rates, is very important. Estimating the transition rates between
molecular conformations is -- from a mathematical point of view -- an invariant
subspace projection problem. A certain infinitesimal generator acting on
function space is projected to a low-dimensional rate matrix. This projection
can be performed in two steps. First, the infinitesimal generator is
discretized, then the invariant subspace is approxi-mated and used for the
subspace projection. In our approach, the discretization will be based on a
Voronoi tessellation of the conformational space. We will show that the
discretized infinitesimal generator can simply be approximated by the geometric
average of the Boltzmann weights of the Voronoi cells. Thus, there is a direct
correla-tion between the potential energy surface of molecular structures and
the transition rates of conformational changes. We present results for a
2d-diffusion process and Alanine dipeptide
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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