154 research outputs found
Two-dimensional protein crystallization via metal-ion coordination by naturally occurring surface histidines
A powerful and potentially general approach to the targeting and crystallization of proteins on lipid interfaces through coordination of surface histidine residues to lipid-chelated divalent metal ions is presented. This approach, which should be applicable to the crystallization of a wide range of naturally occurring or engineered proteins, is illustrated here by the crystallization of streptavidin on a monolayer of an iminodiacetate-Cu(II) lipid spread at the air-water interface. This method allows control of the protein orientation at interfaces, which is significant for the facile production of highly ordered protein arrays and for electron density mapping in structural analysis of two-dimensional crystals. Binding of native streptavidin to the iminodiacetate-Cu lipids occurs via His-87, located on the protein surface near the biotin binding pocket. The two-dimensional streptavidin crystals show a previously undescribed microscopic shape that differs from that of crystals formed beneath biotinylated lipids
On the linearization of the generalized Ermakov systems
A linearization procedure is proposed for Ermakov systems with frequency
depending on dynamic variables. The procedure applies to a wide class of
generalized Ermakov systems which are linearizable in a manner similar to that
applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into
this category but others, more generic, systems are also included
Tzitz\'eica transformation is a dressing action
We classify the simplest rational elements in a twisted loop group, and prove
that dressing actions of them on proper indefinite affine spheres give the
classical Tzitz\'eica transformation and its dual. We also give the group point
of view of the Permutability Theorem, construct complex Tzitz\'eica
transformations, and discuss the group structure for these transformations
Generalizing the autonomous Kepler Ermakov system in a Riemannian space
We generalize the two dimensional autonomous Hamiltonian Kepler Ermakov
dynamical system to three dimensions using the sl(2,R) invariance of Noether
symmetries and determine all three dimensional autonomous Hamiltonian Kepler
Ermakov dynamical systems which are Liouville integrable via Noether
symmetries. Subsequently we generalize the autonomous Kepler Ermakov system in
a Riemannian space which admits a gradient homothetic vector by the
requirements (a) that it admits a first integral (the Riemannian Ermakov
invariant) and (b) it has sl(2,R) invariance. We consider both the
non-Hamiltonian and the Hamiltonian systems. In each case we compute the
Riemannian Ermakov invariant and the equations defining the dynamical system.
We apply the results in General Relativity and determine the autonomous
Hamiltonian Riemannian Kepler Ermakov system in the spatially flat Friedman
Robertson Walker spacetime. We consider a locally rotational symmetric (LRS)
spacetime of class A and discuss two cosmological models. The first
cosmological model consists of a scalar field with exponential potential and a
perfect fluid with a stiff equation of state. The second cosmological model is
the f(R) modified gravity model of {\Lambda}_{bc}CDM. It is shown that in both
applications the gravitational field equations reduce to those of the
generalized autonomous Riemannian Kepler Ermakov dynamical system which is
Liouville integrable via Noether integrals.Comment: Reference [25] update, 21 page
Generalized Hamiltonian structures for Ermakov systems
We construct Poisson structures for Ermakov systems, using the Ermakov
invariant as the Hamiltonian. Two classes of Poisson structures are obtained,
one of them degenerate, in which case we derive the Casimir functions. In some
situations, the existence of Casimir functions can give rise to superintegrable
Ermakov systems. Finally, we characterize the cases where linearization of the
equations of motion is possible
Computational analysis of anti-HIV-1 antibody neutralization panel data to identify potential functional epitope residues
Advances in single-cell antibody cloning methods have led to the identification of a variety of broadly neutralizing anti–HIV-1 antibodies. We developed a computational tool (Antibody Database) to help identify critical residues on the HIV-1 envelope protein whose natural variation affects antibody activity. Our simplifying assumption was that, for a given antibody, a significant portion of the dispersion of neutralization activity across a panel of HIV-1 strains is due to the amino acid identity or glycosylation state at a small number of specific sites, each acting independently. A model of an antibody’s neutralization IC_(50) was developed in which each site contributes a term to the logarithm of the modeled IC_(50). The analysis program attempts to determine the set of rules that minimizes the sum of the residuals between observed and modeled IC_(50) values. The predictive quality of the identified rules may be assessed in part by whether there is support for rules within individual viral clades. As a test case, we analyzed antibody 8ANC195, an anti-glycoprotein gp120 antibody of unknown specificity. The model for this antibody indicated that several glycosylation sites were critical for neutralization. We evaluated this prediction by measuring neutralization potencies of 8ANC195 against HIV-1 in vitro and in an antibody therapy experiment in humanized mice. These experiments confirmed that 8ANC195 represents a distinct class of glycan-dependent anti–HIV-1 antibody and validated the utility of computational analysis of neutralization panel data
On a direct approach to quasideterminant solutions of a noncommutative KP equation
A noncommutative version of the KP equation and two families of its solutions
expressed as quasideterminants are discussed. The origin of these solutions is
explained by means of Darboux and binary Darboux transformations. Additionally,
it is shown that these solutions may also be verified directly. This approach
is reminiscent of the wronskian technique used for the Hirota bilinear form of
the regular, commutative KP equation but, in the noncommutative case, no
bilinearising transformation is available.Comment: 11 page
Darboux transformations for a 6-point scheme
We introduce (binary) Darboux transformation for general differential
equation of the second order in two independent variables. We present a
discrete version of the transformation for a 6-point difference scheme. The
scheme is appropriate to solving a hyperbolic type initial-boundary value
problem. We discuss several reductions and specifications of the
transformations as well as construction of other Darboux covariant schemes by
means of existing ones. In particular we introduce a 10-point scheme which can
be regarded as the discretization of self-adjoint hyperbolic equation
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