102 research outputs found
Chirality and Protein Folding
There are several simple criteria of folding to a native state in model
proteins. One of them involves crossing of a threshold value of the RMSD
distance away from the native state. Another checks whether all native contacts
are established, i.e. whether the interacting amino acids come closer than some
characteristic distance. We use Go-like models of proteins and show that such
simple criteria may prompt one to declare folding even though fragments of the
resulting conformations have a wrong sense of chirality. We propose that a
better condition of folding should augment the simple criteria with the
requirement that most of the local values of the chirality should be nearly
native. The kinetic discrepancy between the simple and compound criteria can be
substantially reduced in the Go-like models by providing the Hamiltonian with a
term which favors native values of the local chirality. We study the effects of
this term as a function of its amplitude and compare it to other models such as
with the side groups and with the angle-dependent potentials.Comment: To be published in a special issue of J. Phys.: Cond. Mat. (Bedlewo
Workshop
Delineation of the Native Basin in Continuum Models of Proteins
We propose two approaches for determining the native basins in off-lattice
models of proteins. The first of them is based on exploring the saddle points
on selected trajectories emerging from the native state. In the second
approach, the basin size can be determined by monitoring random distortions in
the shape of the protein around the native state. Both techniques yield the
similar results. As a byproduct, a simple method to determine the folding
temperature is obtained.Comment: REVTeX, 6 pages, 5 EPS figure
Mechanical Stretching of Proteins: Calmodulin and Titin
Mechanical unfolding of several domains of calmodulin and titin is studied
using a Go-like model with a realistic contact map and Lennard-Jones contact
interactions. It is shown that this simple model captures the experimentally
observed difference between the two proteins: titin is a spring that is tough
and strong whereas calmodulin acts like a weak spring with featureless
force-displacement curves. The difference is related to the dominance of the
alpha secondary structures in the native structure of calmodulin. The tandem
arrangements of calmodulin unwind simultaneously in each domain whereas the
domains in titin unravel in a serial fashion. The sequences of contact events
during unraveling are correlated with the contact order, i.e. with the
separation between contact making amino acids along the backbone in the native
state. Temperature is found to affect stretching in a profound way.Comment: To be published in a special bio-issue of Physica A; 14 figure
Viscosity Dependence of the Folding Rates of Proteins
The viscosity dependence of the folding rates for four sequences (the native
state of three sequences is a beta-sheet, while the fourth forms an
alpha-helix) is calculated for off-lattice models of proteins. Assuming that
the dynamics is given by the Langevin equation we show that the folding rates
increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and
have a maximum at intermediate values. The Kramers theory of barrier crossing
provides a quantitative fit of the numerical results. By mapping the simulation
results to real proteins we estimate that for optimized sequences the time
scale for forming a four turn \alpha-helix topology is about 500 nanoseconds,
whereas the time scale for forming a beta-sheet topology is about 10
microseconds.Comment: 14 pages, Latex, 3 figures. One figure is also available at
http://www.glue.umd.edu/~klimov/seq_I_H.html, to be published in Physical
Review Letter
Investigation of routes and funnels in protein folding by free energy functional methods
We use a free energy functional theory to elucidate general properties of
heterogeneously ordering, fast folding proteins, and we test our conclusions
with lattice simulations. We find that both structural and energetic
heterogeneity can lower the free energy barrier to folding. Correlating
stronger contact energies with entropically likely contacts of a given native
structure lowers the barrier, and anticorrelating the energies has the reverse
effect. Designing in relatively mild energetic heterogeneity can eliminate the
barrier completely at the transition temperature. Sequences with native
energies tuned to fold uniformly, as well as sequences tuned to fold by a
single or a few routes, are rare. Sequences with weak native energetic
heterogeneity are more common; their folding kinetics is more strongly
determined by properties of the native structure. Sequences with different
distributions of stability throughout the protein may still be good folders to
the same structure. A measure of folding route narrowness is introduced which
correlates with rate, and which can give information about the intrinsic biases
in ordering due to native topology. This theoretical framework allows us to
systematically investigate the coupled effects of energy and topology in
protein folding, and to interpret recent experiments which investigate these
effects.Comment: 12 pages, 1 figure, to appear in Proc. Natl. Acad. Sc
Thermodynamic stability of folded proteins against mutations
By balancing the average energy gap with its typical change due to mutations
for protein-like heteropolymers with M residues, we show that native states are
unstable to mutations on a scale M* ~ (lambda/sigma_mu)^(1/zeta_s), where
lambda is the dispersion in the interaction free energies and sigma_mu their
typical change. Theoretical bounds and numerical estimates (based on complete
enumeration on four lattices) of the instability exponent zeta_s are given. Our
analysis suggests that a limiting size of single-domain proteins should exist,
and leads to the prediction that small proteins are insensitive to random
mutations.Comment: 5 pages, 3 figures, to be published in Physical Review Letter
Mechanical unfolding of RNA: From hairpins to structures with internal multiloops
Mechanical unfolding of RNA structures, ranging from hairpins to ribozymes,
using laser optical tweezer (LOT) experiments have begun to reveal the features
of the energy landscape that cannot be easily explored using conventional
experiments. Upon application of constant force (), RNA hairpins undergo
cooperative transitions from folded to unfolded states whereas subdomains of
ribozymes unravel one at a time. Here, we use a self-organized polymer (SOP)
model and Brownian dynamics simulations to probe mechanical unfolding at
constant force and constant-loading rate of four RNA structures of varying
complexity. Our work shows (i) the response of RNA to force is largely
determined by the native structure; (ii) only by probing mechanical unfolding
over a wide range of forces can the underlying energy landscape be fully
explored.Comment: 26 pages, 6 figures, Biophys. J. (in press
Folding in two-dimenensional off-lattice models of proteins
Model off-lattice sequences in two dimensions are constructed so that their
native states are close to an on-lattice target. The Hamiltonian involves the
Lennard-Jones and harmonic interactions. The native states of these sequences
are determined with a high degree of certainty through Monte Carlo processes.
The sequences are characterized thermodynamically and kinetically. It is shown
that the rank-ordering-based scheme of the assignment of contact energies
typically fails in off-lattice models even though it generates high stability
of on-lattice sequences. Similar to the on-lattice case, Go-like modeling, in
which the interaction potentials are restricted to the native contacts in a
target shape, gives rise to good folding properties. Involving other contacts
deteriorates these properties.Comment: REVTeX, 9 pages, 8 EPS figure
Forced-unfolding and force-quench refolding of RNA hairpins
Using coarse-grained model we have explored forced-unfolding of RNA hairpin
as a function of and the loading rate (). The simulations and
theoretical analysis have been done without and with the handles that are
explicitly modeled by semiflexible polymer chains. The mechanisms and time
scales for denaturation by temperature jump and mechanical unfolding are vastly
different. The directed perturbation of the native state by results in a
sequential unfolding of the hairpin starting from their ends whereas thermal
denaturation occurs stochastically. From the dependence of the unfolding rates
on and we show that the position of the unfolding transition state
(TS) is not a constant but moves dramatically as either or is
changed. The TS movements are interpreted by adopting the Hammond postulate for
forced-unfolding. Forced-unfolding simulations of RNA, with handles attached to
the two ends, show that the value of the unfolding force increases (especially
at high pulling speeds) as the length of the handles increases. The pathways
for refolding of RNA from stretched initial conformation, upon quenching
to the quench force , are highly heterogeneous. The refolding times, upon
force quench, are at least an order of magnitude greater than those obtained by
temperature quench. The long -dependent refolding times starting from
fully stretched states are analyzed using a model that accounts for the
microscopic steps in the rate limiting step which involves the trans to gauche
transitions of the dihedral angles in the GAAA tetraloop. The simulations with
explicit molecular model for the handles show that the dynamics of force-quench
refolding is strongly dependent on the interplay of their contour length and
the persistence length, and the RNA persistence length.Comment: 42 pages, 15 figures, Biophys. J. (in press
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