37 research outputs found
Dynamics of polymer chain collapse into compact states
Molecular dynamics simulation methods are used to study the folding of
polymer chains into packed cubic states. The polymer model, based on a chain of
linked sites moving in the continuum, includes both excluded volume and
torsional interactions. Different native-state packing arrangements and chain
lengths are explored; the organization of the native state is found to affect
both the ability of the chain to fold successfully and the nature of the
folding pathway as the system is gradually cooled. An order parameter based on
contact counts is used to provide information about the folding process, with
contacts additionally classified according to criteria such as core and surface
sites or local and distant site pairs. Fully detailed contact maps and their
evolution are also examined.Comment: 11 pages, 11 figures (some low resolution
Emergence of glass-like behavior in markov state models of protein folding dynamics
The extent to which glass-like kinetics govern dynamics in protein folding has been heavily debated. Here, we address the subject with an application of space-time perturbation theory to the dynamics of protein folding Markov State Models (MSMs). Borrowing techniques from the s-ensemble method, we argue that distinct active and inactive phases exist for protein folding dynamics, and that kinetics for specific systems can fall into either dynamical regime. We do not, however, observe a true glass transition in any system studied. We go on to discuss how these inactive and active phases might relate to general protein folding properties
Primary Sequences of Protein-Like Copolymers: Levy Flight Type Long Range Correlations
We consider the statistical properties of primary sequences of two-letter HP
copolymers (H for hydrophobic and P for polar) designed to have water soluble
globular conformations with H monomers shielded from water inside the shell of
P monomers. We show, both by computer simulations and by exact analytical
calculation, that for large globules and flexible polymers such sequences
exhibit long-range correlations which can be described by Levy-flight
statistics.Comment: 4 pages, including 2 figures; several references added, some
formulations improve
Interacting Growth Walk - a model for hyperquenched homopolymer glass?
We show that the compact self avoiding walk configurations, kinetically
generated by the recently introduced Interacting Growth Walk (IGW) model, can
be considered as members of a canonical ensemble if they are assigned random
values of energy. Such a mapping is necessary for studying the thermodynamic
behaviour of this system. We have presented the specific heat data for the IGW,
obtained from extensive simulations on a square lattice; we observe a broad
hump in the specific heat above the -point, contrary to expectation.Comment: 4 figures; Submitted to PR
Embedding a Native State into a Random Heteropolymer Model: The Dynamic Approach
We study a random heteropolymer model with Langevin dynamics, in the
supersymmetric formulation. Employing a procedure similar to one that has been
used in static calculations, we construct an ensemble in which the affinity of
the system for a native state is controlled by a "selection temperature" T0. In
the limit of high T0, the model reduces to a random heteropolymer, while for
T0-->0 the system is forced into the native state. Within the Gaussian
variational approach that we employed previously for the random heteropolymer,
we explore the phases of the system for large and small T0. For large T0, the
system exhibits a (dynamical) spin glass phase, like that found for the random
heteropolymer, below a temperature Tg. For small T0, we find an ordered phase,
characterized by a nonzero overlap with the native state, below a temperature
Tn \propto 1/T0 > Tg. However, the random-globule phase remains locally stable
below Tn, down to the dynamical glass transition at Tg. Thus, in this model,
folding is rapid for temperatures between Tg and Tn, but below Tg the system
can get trapped in conformations uncorrelated with the native state. At a lower
temperature, the ordered phase can also undergo a dynamical glass transition,
splitting into substates separated by large barriers.Comment: 19 pages, revtex, 6 figure
Fluctuating Filaments I: Statistical Mechanics of Helices
We examine the effects of thermal fluctuations on thin elastic filaments with
non-circular cross-section and arbitrary spontaneous curvature and torsion.
Analytical expressions for orientational correlation functions and for the
persistence length of helices are derived, and it is found that this length
varies non-monotonically with the strength of thermal fluctuations. In the weak
fluctuation regime, the local helical structure is preserved and the
statistical properties are dominated by long wavelength bending and torsion
modes. As the amplitude of fluctuations is increased, the helix ``melts'' and
all memory of intrinsic helical structure is lost. Spontaneous twist of the
cross--section leads to resonant dependence of the persistence length on the
twist rate.Comment: 5 figure
Early Stages of Homopolymer Collapse
Interest in the protein folding problem has motivated a wide range of
theoretical and experimental studies of the kinetics of the collapse of
flexible homopolymers. In this Paper a phenomenological model is proposed for
the kinetics of the early stages of homopolymer collapse following a quench
from temperatures above to below the theta temperature. In the first stage,
nascent droplets of the dense phase are formed, with little effect on the
configurations of the bridges that join them. The droplets then grow by
accreting monomers from the bridges, thus causing the bridges to stretch.
During these two stages the overall dimensions of the chain decrease only
weakly. Further growth of the droplets is accomplished by the shortening of the
bridges, which causes the shrinking of the overall dimensions of the chain. The
characteristic times of the three stages respectively scale as the zeroth, 1/5
and 6/5 power of the the degree of polymerization of the chain.Comment: 11 pages, 3 figure
Self- generated disorder and structural glass formation in homopolymer globules
We have investigated the interrelation between the spin glasses and the
structural glasses. Spin glasses in this case are random magnets without
reflection symmetry (e.g. - spin interaction spin glasses and Potts
glasses) which contain quenched disorder, whereas the structural glasses are
here exemplified by the homopolymeric globule, which can be viewed as a liquid
of connected molecules on nano scales. It is argued that the homopolymeric
globule problem can be mapped onto a disorder field theoretical model whose
effective Hamiltonian resembles the corresponding one for the spin glass model.
In this sense the disorder in the globule is self - generated (in contrast to
spin glasses) and can be related with competitive interactions (virial
coefficients of different signs) and the chain connectivity. The work is aimed
at giving a quantitative description of this analogy. We have investigated the
phase diagram of the homopolymeric globule where the transition line from the
liquid to glassy globule is treated in terms of the replica symmetry breaking
paradigm. The configurational entropy temperature dependence is also discussed.Comment: 22 pages, 4 figures, submitted to Phys. Rev.