455 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
Linearity and Scaling of a Statistical Model for the Species Abundance Distribution
We derive a linear recursion relation for the species abundance distribution
in a statistical model of ecology and demonstrate the existence of a scaling
solution
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
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
Correlations in Systems of Complex Directed Macromolecules
An ensemble of directed macromolecules on a lattice is considered, where the
constituting molecules are chosen as a random sequence of N different types.
The same type of molecules experiences a hard-core (exclusion) interaction. We
study the robustness of the macromolecules with respect to breaking and
substituting individual molecules, using a 1/N expansion. The properties depend
strongly on the density of macromolecules. In particular, the macromolecules
are robust against breaking and substituting at high densities.Comment: 9 pages, 4 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
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