97 research outputs found
Geometry of compact tubes and protein structures
Proteins form a very important class of polymers. In spite of major advances
in the understanding of polymer science, the protein problem has remained
largely unsolved. Here, we show that a polymer chain viewed as a tube not only
captures the well-known characteristics of polymers and their phases but also
provides a natural explanation for many of the key features of protein
behavior. There are two natural length scales associated with a tube subject to
compaction -- the thickness of the tube and the range of the attractive
interactions. For short tubes, when these length scales become comparable, one
obtains marginally compact structures, which are relatively few in number
compared to those in the generic compact phase of polymers. The motifs
associated with the structures in this new phase include helices, hairpins and
sheets. We suggest that Nature has selected this phase for the structures of
proteins because of its many advantages including the few candidate strucures,
the ability to squeeze the water out from the hydrophobic core and the
flexibility and versatility associated with being marginally compact. Our
results provide a framework for understanding the common features of all
proteins.Comment: 15 pages, 3 eps figure
Structural motifs of biomolecules
Biomolecular structures are assemblies of emergent anisotropic building
modules such as uniaxial helices or biaxial strands. We provide an approach to
understanding a marginally compact phase of matter that is occupied by proteins
and DNA. This phase, which is in some respects analogous to the liquid crystal
phase for chain molecules, stabilizes a range of shapes that can be obtained by
sequence-independent interactions occurring intra- and intermolecularly between
polymeric molecules. We present a singularityfree self-interaction for a tube
in the continuum limit and show that this results in the tube being positioned
in the marginally compact phase. Our work provides a unified framework for
understanding the building blocks of biomolecules.Comment: 13 pages, 5 figure
Geometry and symmetry presculpt the free-energy landscape of proteins
We present a simple physical model which demonstrates that the native state
folds of proteins can emerge on the basis of considerations of geometry and
symmetry. We show that the inherent anisotropy of a chain molecule, the
geometrical and energetic constraints placed by the hydrogen bonds and sterics,
and hydrophobicity are sufficient to yield a free energy landscape with broad
minima even for a homopolymer. These minima correspond to marginally compact
structures comprising the menu of folds that proteins choose from to house
their native-states in. Our results provide a general framework for
understanding the common characteristics of globular proteins.Comment: 23 pages, 5 figure
Network Structures from Selection Principles
We present an analysis of the topologies of a class of networks which are
optimal in terms of the requirements of having as short a route as possible
between any two nodes while yet keeping the congestion in the network as low as
possible. Strikingly, we find a variety of distinct topologies and novel phase
transitions between them on varying the number of links per node. Our results
suggest that the emergence of the topologies observed in nature may arise both
from growth mechanisms and the interplay of dynamical mechanisms with a
selection process.Comment: 4 pages, 5 figure
Protein sequence and structure: Is one more fundamental than the other?
We argue that protein native state structures reside in a novel "phase" of
matter which confers on proteins their many amazing characteristics. This phase
arises from the common features of all globular proteins and is characterized
by a sequence-independent free energy landscape with relatively few low energy
minima with funnel-like character. The choice of a sequence that fits well into
one of these predetermined structures facilitates rapid and cooperative
folding. Our model calculations show that this novel phase facilitates the
formation of an efficient route for sequence design starting from random
peptides.Comment: 7 pages, 4 figures, to appear in J. Stat. Phy
Scaling of the Random-Field Ising Model at Zero Temperature
The exact determination of ground states of small systems is used in a
scaling study of the random-field Ising model. While three variants of the
model are found to be in the same universality class in 3 dimensions, the
Gaussian and bimodal models behave distinctly in 4 dimensions with the latter
apparently having a discontinuous jump in the magnetization. A finite-size
scaling analysis is presented for this transition.Comment: 14 pages Latex, 4 figure
Disorder-induced critical behavior in driven diffusive systems
Using dynamic renormalization group we study the transport in driven
diffusive systems in the presence of quenched random drift velocity with
long-range correlations along the transport direction. In dimensions
we find fixed points representing novel universality classes of
disorder-dominated self-organized criticality, and a continuous phase
transition at a critical variance of disorder. Numerical values of the scaling
exponents characterizing the distributions of relaxation clusters are in good
agreement with the exponents measured in natural river networks
Optimal shapes of compact strings
Optimal geometrical arrangements, such as the stacking of atoms, are of
relevance in diverse disciplines. A classic problem is the determination of the
optimal arrangement of spheres in three dimensions in order to achieve the
highest packing fraction; only recently has it been proved that the answer for
infinite systems is a face-centred-cubic lattice. This simply stated problem
has had a profound impact in many areas, ranging from the crystallization and
melting of atomic systems, to optimal packing of objects and subdivision of
space. Here we study an analogous problem--that of determining the optimal
shapes of closely packed compact strings. This problem is a mathematical
idealization of situations commonly encountered in biology, chemistry and
physics, involving the optimal structure of folded polymeric chains. We find
that, in cases where boundary effects are not dominant, helices with a
particular pitch-radius ratio are selected. Interestingly, the same geometry is
observed in helices in naturally-occurring proteins.Comment: 8 pages, 3 composite ps figure
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