9,787 research outputs found
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
Alpha helix-coil phase transition: analysis of ab initio theory predictions
In the present paper we present results of calculations obtained with the use
of the theoretical method described in our preceding paper [1] and perform
detail analysis of alpha helix-random coil transition in alanine polypeptides
of different length. We have calculated the potential energy surfaces of
polypeptides with respect to their twisting degrees of freedom and construct a
parameter-free partition function of the polypeptide using the suggested method
[1]. From the build up partition function we derive various thermodynamical
characteristics for alanine polypeptides of different length as a function of
temperature. Thus, we analyze the temperature dependence of the heat capacity,
latent heat and helicity for alanine polypeptides consisting of 21, 30, 40, 50
and 100 amino acids. Alternatively, we have obtained same thermodynamical
characteristics from the use of molecular dynamics simulations and compared
them with the results of the new statistical mechanics approach. The comparison
proves the validity of the statistical mechanic approach and establishes its
accuracy.Comment: 34 pages, 12 figure
Statistical Mechanical Treatments of Protein Amyloid Formation
Protein aggregation is an important field of investigation because it is
closely related to the problem of neurodegenerative diseases, to the
development of biomaterials, and to the growth of cellular structures such as
cyto-skeleton. Self-aggregation of protein amyloids, for example, is a
complicated process involving many species and levels of structures. This
complexity, however, can be dealt with using statistical mechanical tools, such
as free energies, partition functions, and transfer matrices. In this article,
we review general strategies for studying protein aggregation using statistical
mechanical approaches and show that canonical and grand canonical ensembles can
be used in such approaches. The grand canonical approach is particularly
convenient since competing pathways of assembly and dis-assembly can be
considered simultaneously. Another advantage of using statistical mechanics is
that numerically exact solutions can be obtained for all of the thermodynamic
properties of fibrils, such as the amount of fibrils formed, as a function of
initial protein concentration. Furthermore, statistical mechanics models can be
used to fit experimental data when they are available for comparison.Comment: Accepted to IJM
A Criterion That Determines Fast Folding of Proteins: A Model Study
We consider the statistical mechanics of a full set of two-dimensional
protein-like heteropolymers, whose thermodynamics is characterized by the
coil-to-globular () and the folding () transition temperatures.
For our model, the typical time scale for reaching the unique native
conformation is shown to scale as , where
, is the number of residues, and scales
algebraically with . We argue that scales linearly with the inverse of
entropy of low energy non-native states, whereas is almost
independent of it. As , non-productive intermediates
decrease, and the initial rapid collapse of the protein leads to structures
resembling the native state. Based solely on {\it accessible} information,
can be used to predict sequences that fold rapidly.Comment: 10 pages, latex, figures upon reques
Equations for Stochastic Macromolecular Mechanics of Single Proteins: Equilibrium Fluctuations, Transient Kinetics and Nonequilibrium Steady-State
A modeling framework for the internal conformational dynamics and external
mechanical movement of single biological macromolecules in aqueous solution at
constant temperature is developed. Both the internal dynamics and external
movement are stochastic; the former is represented by a master equation for a
set of discrete states, and the latter is described by a continuous
Smoluchowski equation. Combining these two equations into one, a comprehensive
theory for the Brownian dynamics and statistical thermodynamics of single
macromolecules arises. This approach is shown to have wide applications. It is
applied to protein-ligand dissociation under external force, unfolding of
polyglobular proteins under extension, movement along linear tracks of motor
proteins against load, and enzyme catalysis by single fluctuating proteins. As
a generalization of the classic polymer theory, the dynamic equation is capable
of characterizing a single macromolecule in aqueous solution, in probabilistic
terms, (1) its thermodynamic equilibrium with fluctuations, (2) transient
relaxation kinetics, and most importantly and novel (3) nonequilibrium
steady-state with heat dissipation. A reversibility condition which guarantees
an equilibrium solution and its thermodynamic stability is established, an
H-theorem like inequality for irreversibility is obtained, and a rule for
thermodynamic consistency in chemically pumped nonequilibrium steady-state is
given.Comment: 23 pages, 4 figure
Statistical Mechanics of Membrane Protein Conformation: A Homopolymer Model
The conformation and the phase diagram of a membrane protein are investigated
via grand canonical ensemble approach using a homopolymer model. We discuss the
nature and pathway of -helix integration into the membrane that results
depending upon membrane permeability and polymer adsorptivity. For a membrane
with the permeability larger than a critical value, the integration becomes the
second order transition that occurs at the same temperature as that of the
adsorption transition. For a nonadsorbing membrane, the integration is of the
first order due to the aggregation of -helices.Comment: RevTeX with 5 postscript figure
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