1,014 research outputs found
Origin of Scaling Behavior of Protein Packing Density: A Sequential Monte Carlo Study of Compact Long Chain Polymers
Single domain proteins are thought to be tightly packed. The introduction of
voids by mutations is often regarded as destabilizing. In this study we show
that packing density for single domain proteins decreases with chain length. We
find that the radius of gyration provides poor description of protein packing
but the alpha contact number we introduce here characterize proteins well. We
further demonstrate that protein-like scaling relationship between packing
density and chain length is observed in off-lattice self-avoiding walks. A key
problem in studying compact chain polymer is the attrition problem: It is
difficult to generate independent samples of compact long self-avoiding walks.
We develop an algorithm based on the framework of sequential Monte Carlo and
succeed in generating populations of compact long chain off-lattice polymers up
to length . Results based on analysis of these chain polymers suggest
that maintaining high packing density is only characteristic of short chain
proteins. We found that the scaling behavior of packing density with chain
length of proteins is a generic feature of random polymers satisfying loose
constraint in compactness. We conclude that proteins are not optimized by
evolution to eliminate packing voids.Comment: 9 pages, 10 figures. Accepted by J. Chem. Phy
Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
We examine how to construct a spatial manifold and its geometry from the
entanglement structure of an abstract quantum state in Hilbert space. Given a
decomposition of Hilbert space into a tensor product of factors,
we consider a class of "redundancy-constrained states" in that
generalize the area-law behavior for entanglement entropy usually found in
condensed-matter systems with gapped local Hamiltonians. Using mutual
information to define a distance measure on the graph, we employ classical
multidimensional scaling to extract the best-fit spatial dimensionality of the
emergent geometry. We then show that entanglement perturbations on such
emergent geometries naturally give rise to local modifications of spatial
curvature which obey a (spatial) analog of Einstein's equation. The Hilbert
space corresponding to a region of flat space is finite-dimensional and scales
as the volume, though the entropy (and the maximum change thereof) scales like
the area of the boundary. A version of the ER=EPR conjecture is recovered, in
that perturbations that entangle distant parts of the emergent geometry
generate a configuration that may be considered as a highly quantum wormhole.Comment: 37 pages, 5 figures. Updated notation, references, and
acknowledgemen
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