29,875 research outputs found
Thermodynamic Prediction of Protein Neutrality
We present a simple theory that uses thermodynamic parameters to predict the
probability that a protein retains the wildtype structure after one or more
random amino acid substitutions. Our theory predicts that for large numbers of
substitutions the probability that a protein retains its structure will decline
exponentially with the number of substitutions, with the severity of this
decline determined by properties of the structure. Our theory also predicts
that a protein can gain extra robustness to the first few substitutions by
increasing its thermodynamic stability. We validate our theory with simulations
on lattice protein models and by showing that it quantitatively predicts
previously published experimental measurements on subtilisin and our own
measurements on variants of TEM1 beta-lactamase. Our work unifies observations
about the clustering of functional proteins in sequence space, and provides a
basis for interpreting the response of proteins to substitutions in protein
engineering applications
MLD Relations of Pisot Substitution Tilings
We consider 1-dimensional, unimodular Pisot substitution tilings with three
intervals, and discuss conditions under which pairs of such tilings are locally
isomorhphic (LI), or mutually locally derivable (MDL). For this purpose, we
regard the substitutions as homomorphisms of the underlying free group with
three generators. Then, if two substitutions are conjugated by an inner
automorphism of the free group, the two tilings are LI, and a conjugating outer
automorphism between two substitutions can often be used to prove that the two
tilings are MLD. We present several examples illustrating the different
phenomena that can occur in this context. In particular, we show how two
substitution tilings can be MLD even if their substitution matrices are not
equal, but only conjugate in . We also illustrate how the (in
our case fractal) windows of MLD tilings can be reconstructed from each other,
and discuss how the conjugating group automorphism affects the substitution
generating the window boundaries.Comment: Presented at Aperiodic'09 (Liverpool
Incoherent non-Fermi liquid scattering in a Kondo lattice
One of the most notorious non-Fermi liquid properties of both archetypal
heavy-fermion systems [1-4] and the high-Tc copper oxide superconductors [5] is
an electrical resistivity that evolves linearly with temperature, T. In the
heavy-fermion superconductor CeCoIn5 [5], this linear behaviour was one of the
first indications of the presence of a zero-temperature instability, or quantum
critical point. Here, we report the observation of a unique control parameter
of T-linear scattering in CeCoIn5, found through systematic chemical
substitutions of both magnetic and non-magnetic rare-earth, R, ions into the Ce
sub-lattice. We find that the evolution of inelastic scattering in Ce1-xRxCoIn5
is strongly dependent on the f-electron configuration of the R ion, whereas two
other key properties -- Cooper-pair breaking and Kondo-lattice coherence -- are
not. Thus, T-linear resistivity in CeCoIn5 is intimately related to the nature
of incoherent scattering centers in the Kondo lattice, which provides insight
into the anomalous scattering rate synonymous with quantum criticality [7].Comment: 4 pages, 3 figures (published version
Predicting the Volumes of Crystals
New crystal structures are frequently derived by performing ionic
substitutions on known crystal structures. These derived structures are then
used in further experimental analysis, or as the initial guess for structural
optimization in electronic structure calculations, both of which usually
require a reasonable guess of the lattice parameters. In this work, we propose
two lattice prediction schemes to improve the initial guess of a candidate
crystal structure. The first scheme relies on a one-to-one mapping of species
in the candidate crystal structure to a known crystal structure, while the
second scheme relies on data-mined minimum atom pair distances to predict the
crystal volume of the candidate crystal structure and does not require a
reference structure. We demonstrate that the two schemes can effectively
predict the volumes within mean absolute errors (MAE) as low as 3.8% and 8.2%.
We also discuss the various factors that may impact the performance of the
schemes. Implementations for both schemes are available in the open-source
pymatgen software.Comment: 8 figures, 2 table
Controlled Fuzzy Parallel Rewriting
We study a Lindenmayer-like parallel rewriting system to model the growth of filaments (arrays of cells) in which developmental errors may occur. In essence this model is the fuzzy analogue of the derivation-controlled iteration grammar. Under minor assumptions on the family of control languages and on the family of fuzzy languages in the underlying iteration grammar, we show (i) regular control does not provide additional generating power to the model, (ii) the number of fuzzy substitutions in the underlying iteration grammar can be reduced to two, and (iii) the resulting family of fuzzy languages possesses strong closure properties, viz. it is a full hyper-AFFL, i.e., a hyper-algebraically closed full Abstract Family of Fuzzy Languages
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