1,425 research outputs found
An algorithm for series expansions based on hierarchical rate equations
We propose a computational method to obtain series expansions in powers of
time for general dynamical systems described by a set of hierarchical rate
equations. The method is generally applicable to problems in both equilibrium
and nonequilibrium statistical mechanics such as random sequential adsorption,
diffusion-reaction dynamics, and Ising dynamics. New result of random
sequential adsorption of dimers on a square lattice is presented.Comment: LaTeX, 9 pages including 1 figur
Unfolding and unzipping of single-stranded DNA by stretching
We present a theoretical study of single-stranded DNA under stretching.
Within the proposed framework, the effects of basepairing on the mechanical
response of the molecule can be studied in combination with an arbitrary
underlying model of chain elasticity. In a generic case, we show that the
stretching curve of ssDNA exhibits two distinct features: the second-order
"unfolding" phase transition, and a sharp crossover, reminiscent of the
first-order "unzipping" transition in dsDNA. We apply the theory to the
particular cases of Worm-like Chain (WLC) and Freely-Joint Chain (FJC) models,
and discuss the universal and model--dependent features of the mechanical
response of ssDNA. In particular, we show that variation of the width of the
unzipping crossover with interaction strength is very sensitive to the
energetics of hairpin loops. This opens a new way of testing the elastic
properties of ssDNA.Comment: 7 pages, 4 figures, substantially revised versio
Ephemeral active regions and coronal bright points: A solar maximum Mission 2 guest investigator study
A dominate association of coronal bright points (as seen in He wavelength 10830) was confirmed with the approach and subsequent disappearance of opposite polarity magnetic network. While coronal bright points do occur with ephemeral regions, this association is a factor of 2 to 4 less than with sites of disappearing magnetic flux. The intensity variations seen in He I wavelength 10830 are intermittent and often rapid, varying over the 3 minute time resolution of the data; their bright point counterparts in the C IV wavelength 1548 and 20 cm wavelength show similar, though not always coincident time variations. Ejecta are associated with about 1/3 of the dark points and are evident in the C IV and H alpha data. These results support the idea that the anti-correlation of X-ray bright points with the solar cycle can be explained by the correlation of these coronal emission structures with sites of cancelling flux, indicating that, in some cases, the process of magnetic flux removal results in the release of energy. That the intensity variations are rapid and variable suggests that this process works intermittently
Effects of mechanical strain on thermal denaturation of DNA
As sections of a strand duplexed DNA denature when exposed to high
temperature, the excess linking number is taken up by the undenatured portions
of the molecule. The mechanical energy that arises because of the overwinding
of the undenatured sections can, in principle, alter the nature of the thermal
denaturation process. Assuming that the strains associated with this
overwinding are not relieved, we find that a simple model of strain-altered
melting leads to a suppression of the melting transition when the unaltered
transition is continuous. When the melting transition is first order in the
absence of strain associated with overwinding, the modification is to a third
order phase transition.Comment: 4 pages, 5 figures, RevTe
Microscopic formulation of the Zimm-Bragg model for the helix-coil transition
A microscopic spin model is proposed for the phenomenological Zimm-Bragg
model for the helix-coil transition in biopolymers. This model is shown to
provide the same thermophysical properties of the original Zimm-Bragg model and
it allows a very convenient framework to compute statistical quantities.
Physical origins of this spin model are made transparent by an exact mapping
into a one-dimensional Ising model with an external field. However, the
dependence on temperature of the reduced external field turns out to differ
from the standard one-dimensional Ising model and hence it gives rise to
different thermophysical properties, despite the exact mapping connecting them.
We discuss how this point has been frequently overlooked in the recent
literature.Comment: 11 pages, 2 figure
Globular Structures of a Helix-Coil Copolymer: Self-Consistent Treatment
A self-consistent field theory was developed in the grand-canonical ensemble
formulation to study transitions in a helix-coil multiblock globule. Helical
and coil parts are treated as stiff rods and self-avoiding walks of variable
lengths correspondingly. The resulting field-theory takes, in addition to the
conventional Zimm-Bragg (B.H. Zimm, I.K. Bragg, J. Chem. Phys. 31, 526 (1959))
parameters, also three-dimensional interaction terms into account. The
appropriate differential equations which determine the self-consistent fields
were solved numerically with finite element method. Three different phase
states are found: open chain, amorphous globule and nematic liquid-crystalline
(LC) globule. The LC-globule formation is driven by the interplay between the
hydrophobic helical segments attraction and the anisotropic globule surface
energy of an entropic nature. The full phase diagram of the helix-coil
copolymer was calculated and thoroughly discussed. The suggested theory shows a
clear interplay between secondary and tertiary structures in globular
homopolypeptides.Comment: 26 pages, 30 figures, corrected some typo
Theoretical investigation of finite size effects at DNA melting
We investigated how the finiteness of the length of the sequence affects the
phase transition that takes place at DNA melting temperature. For this purpose,
we modified the Transfer Integral method to adapt it to the calculation of both
extensive (partition function, entropy, specific heat, etc) and non-extensive
(order parameter and correlation length) thermodynamic quantities of finite
sequences with open boundary conditions, and applied the modified procedure to
two different dynamical models. We showed that rounding of the transition
clearly takes place when the length of the sequence is decreased. We also
performed a finite-size scaling analysis of the two models and showed that the
singular part of the free energy can indeed be expressed in terms of an
homogeneous function. However, both the correlation length and the average
separation between paired bases diverge at the melting transition, so that it
is no longer clear to which of these two quantities the length of the system
should be compared. Moreover, Josephson's identity is satisfied for none of the
investigated models, so that the derivation of the characteristic exponents
which appear, for example, in the expression of the specific heat, requires
some care
Osmotic pressure induced coupling between cooperativity and stability of a helix-coil transition
Most helix-coil transition theories can be characterized by a set of three
parameters: energetic, describing the (free) energy cost of forming a helical
state in one repeating unit; entropic, accounting for the decrease of entropy
due to the helical state formation; and geometric, indicating how many
repeating units are affected by the formation of one helical state. Depending
on their effect on the helix-coil transition, solvents or co-solutes can be
classified with respect to their action on these parameters. Solvent
interactions that alter the entropic cost of helix formation by their osmotic
action can affect both the stability (transition temperature) and the
cooperativity (transition interval) of the helix-coil transition. A consistent
inclusion of osmotic pressure effects in a description of helix-coil transition
for poly(L-glutamic acid) in solution with polyethylene glycol can offer an
explanation of the experimentally observed linear dependence of transition
temperature on osmotic pressure as well as the concurrent changes in the
cooperativity of the transition.Comment: 5 pages, 3 figures. To be submitted to Phys.Rev.Let
Competition for hydrogen bond formation in the helix-coil transition and protein folding
The problem of the helix-coil transition of biopolymers in explicit solvents,
like water, with the ability for hydrogen bonding with solvent is addressed
analytically using a suitably modified version of the Generalized Model of
Polypeptide Chains. Besides the regular helix-coil transition, an additional
coil-helix or reentrant transition is also found at lower temperatures. The
reentrant transition arises due to competition between polymer-polymer and
polymer-water hydrogen bonds. The balance between the two types of hydrogen
bonding can be shifted to either direction through changes not only in
temperature, but also by pressure, mechanical force, osmotic stress or other
external influences. Both polypeptides and polynucleotides are considered
within a unified formalism. Our approach provides an explanation of the
experimental difficulty of observing the reentrant transition with pressure;
and underscores the advantage of pulling experiments for studies of DNA.
Results are discussed and compared with those reported in a number of recent
publications with which a significant level of agreement is obtained.Comment: 21 pages, 3 figures, submitted to Phys Rev
Ab initio theory of helix-coil phase transition
In this paper we suggest a theoretical method based on the statistical
mechanics for treating the alpha-helix-random coil transition in alanine
polypeptides. We consider this process as a first-order phase transition and
develop a theory which is free of model parameters and is based solely on
fundamental physical principles. It describes essential thermodynamical
properties of the system such as heat capacity, the phase transition
temperature and others from the analysis of the polypeptide potential energy
surface calculated as a function of two dihedral angles, responsible for the
polypeptide twisting. The suggested theory is general and with some
modification can be applied for the description of phase transitions in other
complex molecular systems (e.g. proteins, DNA, nanotubes, atomic clusters,
fullerenes).Comment: 24 pages, 3 figure
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