367 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
Determination of Interaction Potentials of Amino Acids from Native Protein Structures: Test on Simple Lattice Models
We propose a novel method for the determination of the effective interaction
potential between the amino acids of a protein. The strategy is based on the
combination of a new optimization procedure and a geometrical argument, which
also uncovers the shortcomings of any optimization procedure. The strategy can
be applied on any data set of native structures such as those available from
the Protein Data Bank (PDB). In this work, however, we explain and test our
approach on simple lattice models, where the true interactions are known a
priori. Excellent agreement is obtained between the extracted and the true
potentials even for modest numbers of protein structures in the PDB.
Comparisons with other methods are also discussed.Comment: 24 pages, 4 figure
Subgraphs and network motifs in geometric networks
Many real-world networks describe systems in which interactions decay with
the distance between nodes. Examples include systems constrained in real space
such as transportation and communication networks, as well as systems
constrained in abstract spaces such as multivariate biological or economic
datasets and models of social networks. These networks often display network
motifs: subgraphs that recur in the network much more often than in randomized
networks. To understand the origin of the network motifs in these networks, it
is important to study the subgraphs and network motifs that arise solely from
geometric constraints. To address this, we analyze geometric network models, in
which nodes are arranged on a lattice and edges are formed with a probability
that decays with the distance between nodes. We present analytical solutions
for the numbers of all 3 and 4-node subgraphs, in both directed and
non-directed geometric networks. We also analyze geometric networks with
arbitrary degree sequences, and models with a field that biases for directed
edges in one direction. Scaling rules for scaling of subgraph numbers with
system size, lattice dimension and interaction range are given. Several
invariant measures are found, such as the ratio of feedback and feed-forward
loops, which do not depend on system size, dimension or connectivity function.
We find that network motifs in many real-world networks, including social
networks and neuronal networks, are not captured solely by these geometric
models. This is in line with recent evidence that biological network motifs
were selected as basic circuit elements with defined information-processing
functions.Comment: 9 pages, 6 figure
Proteins and polymers
Proteins, chain molecules of amino acids, behave in ways which are similar to
each other yet quite distinct from standard compact polymers. We demonstrate
that the Flory theorem, derived for polymer melts, holds for compact protein
native state structures and is not incompatible with the existence of
structured building blocks such as -helices and -strands. We
present a discussion on how the notion of the thickness of a polymer chain,
besides being useful in describing a chain molecule in the continuum limit,
plays a vital role in interpolating between conventional polymer physics and
the phase of matter associated with protein structures.Comment: 7 pages, 6 figure
Origin of Nonuniversality in Micellar Solutions: Comment
Rhynchospora caucasica Palla (Cyperaceae) Doğu Karadeniz'de, Rize'den tespit edilmiş ve Türkiye florası için yeni bir tür kaydı olarak verilmiştir. Taksonun betimi ve coğrafik dağılımı belirtilmiş, yakın akrabaları olan R. rugosa (Vahl) Gale subsp. rugosa ve R. rugosa (Vahl) Gale subsp. brownii (Roemer & Schultes) T.Koyama taksonları ile karşılaştırılmıştırR. caucasica Palla (Cyperaceae) is reported as a new record for Turkish flora in Rize province, NE Anatolia, Turkey. The description and distribution of the species are given. Also, it is compared with related taxa R. rugosa (Vahl) Gale subsp. rugosa and R. rugosa subsp. brownii (Roemer & Schultes) T. Koyam
Some asymptotic properties of duplication graphs
Duplication graphs are graphs that grow by duplication of existing vertices,
and are important models of biological networks, including protein-protein
interaction networks and gene regulatory networks. Three models of graph growth
are studied: pure duplication growth, and two two-parameter models in which
duplication forms one element of the growth dynamics. A power-law degree
distribution is found to emerge in all three models. However, the parameter
space of the latter two models is characterized by a range of parameter values
for which duplication is the predominant mechanism of graph growth. For
parameter values that lie in this ``duplication-dominated'' regime, it is shown
that the degree distribution either approaches zero asymptotically, or
approaches a non-zero power-law degree distribution very slowly. In either
case, the approach to the true asymptotic degree distribution is characterized
by a dependence of the scaling exponent on properties of the initial degree
distribution. It is therefore conjectured that duplication-dominated,
scale-free networks may contain identifiable remnants of their early structure.
This feature is inherited from the idealized model of pure duplication growth,
for which the exact finite-size degree distribution is found and its asymptotic
properties studied.Comment: 19 pages, including 3 figure
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