PACKMOL: A Package for Building Initial Configurations for Molecular Dynamics Simulations

Adequate initial configurations for molecular dynamics simulations consist of arrangements of molecules distributed in space in such a way to approximately represent the system`s overall structure. In order that the simulations are not disrupted by large van der Waals repulsive interactions, atoms from different molecules Must keep safe pairwise distances. Obtaining Such a molecular arrangement can be considered it packing problem: Each type molecule must satisfy spatial constraints related to the geometry of the system, and the distance between atoms of different molecules Must be greater than some specified tolerance. We have developed a code able to pack millions of atoms. grouped in arbitrarily complex molecules, inside a variety of three-dimensional regions. The regions may be intersections of spheres, ellipses, cylinders, planes, or boxes. The user must provide only the structure of one molecule of each type and the geometrical constraints that each type of molecule must satisfy. Building complex mixtures, interfaces, solvating biomolecules in water, other solvents, or mixtures of solvents, is straight forward. In addition. different atoms belonging to the same molecule may also be restricted to different spatial regions, in Such a way that more ordered molecular arrangements call be built, as micelles. lipid double-layers, etc. The packing time for state-of-the-art molecular dynamics systems varies front a few seconds to a few Minutes in a personal Computer. The input files are simple and Currently compatible with PDB, Tinker, Molden, or Moldy coordinate files. The package is distributed as free software and call be downloaded front http://www.ime.unicamp.br/similar to martinez/packmol/. (C) 2009 Wiley Periodicals. Inc. J Comput Chem 30: 2157-2164, 2009

SUPPORT OF MAXIMIZING MEASURES FOR TYPICAL C(0) DYNAMICS ON COMPACT MANIFOLDS

Given a compact manifold X, a continuous function g : X -> IR, and a map T : X -> X, we study properties of the T-invariant Borel probability measures that maximize the integral of g. We show that if X is a n-dimensional connected Riemaniann manifold, with n >= 2, then the set of homeomorphisms for which there is a maximizing measure supported on a periodic orbit is meager. We also show that, if X is the circle, then the ""topological size"" of the set of endomorphisms for which there are g maximizing measures with support on a periodic orbit depends on properties of the function g. In particular, if g is C(1), it has interior points.

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

Towards a maximal extension of Pelczynski`s decomposition method in Banach spaces

l Suppose that X, Y. A and B are Banach spaces such that X is isomorphic to Y E) A and Y is isomorphic to X circle plus B. Are X and Y necessarily isomorphic? In this generality. the answer is no, as proved by W.T. Cowers in 1996. In the present paper, we provide a very simple necessary and sufficient condition on the 10-tuples (k, l, m, n. p, q, r, s, u, v) in N with p+q+u >= 3, r+s+v >= 3, uv >= 1, (p,q)$(0,0), (r,s)not equal(0,0) and u=1 or v=1 or (p. q) = (1, 0) or (r, s) = (0, 1), which guarantees that X is isomorphic to Y whenever these Banach spaces satisfy X(u) similar to X(p)circle plus Y(q), Y(u) similar to X(r)circle plus Y(s), and A(k) circle plus B(l) similar to A(m) circle plus B(n). Namely, delta = +/- 1 or lozenge not equal 0, gcd(lozenge, delta (p + q - u)) divides p + q - u and gcd(lozenge, delta(r + s - v)) divides r + s - v, where 3 = k - I - in + n is the characteristic number of the 4-tuple (k, l, m, n) and lozenge = (p - u)(s - v) - rq is the discriminant of the 6-tuple (p, q, r, s, U, v). We conjecture that this result is in some sense a maximal extension of the classical Pelczynski`s decomposition method in Banach spaces: the case (1, 0. 1, 0, 2. 0, 0, 2. 1. 1). (C) 2009 Elsevier Inc. All rights reserved.

Crossed products by twisted partial actions and graded algebras

For a twisted partial action e of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A x(Theta) G is proved to be associative. Given a G-graded k-algebra B = circle plus(g is an element of G) B-g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B-1 x(Theta) G for some twisted partial action of G on B-1. The equality BgBg-1 B-g = B-g (for all g is an element of G) is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G. (c) 2008 Elsevier Inc. All rights reserved.

Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

Generalizations of Pelczynski`s decomposition method for Banach spaces containing a complemented copy of their squares

Suppose that X and Y are Banach spaces isomorphic to complemented subspaces of each other. In 1996, W. T. Gowers solved the Schroeder- Bernstein Problem for Banach spaces by showing that X is not necessarily isomorphic to Y. However, if X-2 is complemented in X with supplement A and Y-2 is complemented in Y with supplement B, that is, { X similar to X-2 circle plus A Y similar to Y-2 circle plus B, then the classical Pelczynski`s decomposition method for Banach spaces shows that X is isomorphic to Y whenever we can assume that A = B = {0}. But unfortunately, this is not always possible. In this paper, we show that it is possible to find all finite relations of isomorphism between A and B which guarantee that X is isomorphic to Y. In order to do this, we say that a quadruple (p, q, r, s) in N is a P-Quadruple for Banach spaces if X is isomorphic to Y whenever the supplements A and B satisfy A(p) circle plus B-q similar to A(r) circle plus B-s . Then we prove that (p, q, r, s) is a P-Quadruple for Banach spaces if and only if p - r = s - q = +/- 1.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

Cantor-Bernstein Sextuples for Banach Spaces

Let X and Y be Banach spaces isomorphic to complemented subspaces of each other with supplements A and B. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain a necessary and sufficient condition on the sextuples (p, q, r, s, u, v) in N with p + q >= 1, r + s >= 1 and u, v is an element of N*, to provide that X is isomorphic to Y, whenever these spaces satisfy the following decomposition scheme A(u) similar to X(P) circle plus Y(q) B(v) similar to X(r) circle plus Y(s). Namely, Phi = (p - u)(s - v) - (q + u)(r + v) is different from zero and Phi divides p + q and r + s. These sextuples are called Cantor-Bernstein sextuples for Banach spaces. The simplest case (1, 0, 0, 1, 1, 1) indicates the well-known Pelczynski`s decomposition method in Banach space. On the other hand, by interchanging some Banach spaces in the above decomposition scheme, refinements of the Schroeder-Bernstein problem become evident.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Boutet de Monvel`s calculus and groupoids I

Can Boutet de Monvel`s algebra on a compact manifold with boundary be obtained as the algebra Psi(0)(G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C*-algebra C*(G). While the answer to the above question remains open, we exhibit in this paper a groupoid G such that C*(G) possesses an ideal I isomorphic to G. In fact, we prove first that G similar or equal to Psi circle times K with the C*-algebra Psi generated by the zero order pseudodifferential operators on the boundary and the algebra K of compact operators. As both Psi circle times K and I are extensions of C(S*Y) circle times K by K (S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic.

Conformational Properties of Angiotensin II and Its Active and Inactive TOAC-Labeled Analogs in the Presence of Micelles. Electron Paramagnetic Resonance, Fluorescence, and Circular Dichroism Studies

The interaction between angiotensin II (AII, DRVYIHPF) and its analogs carrying 2,2,6,6-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid (TOAC) and detergents-negatively charged sodium dodecyl sulfate (SDS) and zwitterionic N-hexadecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate (HPS)-was examined by means of EPR, CD, and fluorescence. EPR spectra of partially active TOAC(1)-AII and inactive TOAC(3)-AII in aqueous solution indicated fast tumbling, the freedom of motion being greater at the N-terminus. Line broadening occurred upon interaction with micelles. Below SDS critical micelle concentration, broader lines indicated complex formation with tighter molecular packing than in micelles. Small changes in hyperfine splittings evinced TOAC location at the micelle-water interface. The interaction with anionic micelles was more effective than with zwitterionic micelles. Peptide-micelle interaction caused fluorescence increase. The TOAC-promoted intramolecular fluorescence quenching was more, pronounced for TOAC(3)-AII because of the proximity between the nitroxide and Tyr(4). CD spectra showed that although both AII and TOAC(1)-AII presented flexible conformations in water, TOAC(3)-AII displayed conformational restriction because of the TOAC-imposed bend (Schreier et al., Biopolymers 2004, 74, 389). In HPS, conformational changes were observed for the labeled peptides at neutral and basic pH. In SDS, all peptides underwent pH-dependent conformational changes. Although the spectra suggested similar folds for All and TOAC(1)-AII, different conformations were acquired by TOAC(3)-AII. The membrane environment has been hypothesized to shift conformational equilibria so as to stabilize the receptor-bound conformation of ligands. The fact that TOAC(3)-AII is unable to acquire conformations similar to those of native AII and partially active TOAC(1)-AII is probably the explanation for its lack of biological activity. (C) 2009 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 92: 525-537, 2009.

Interaction of cationic bilayer fragments with a model oligonucleotide

The interaction between cationic bilayer fragments and a model oligonucleotide was investigated by differential scanning calorimetry, turbidimetry, determination of excimer to monomer ratio of 2-(10-(1-pyrene)-decanoyl)-phosphatidyl-choline in bilayer fragment dispersions and dynamic light scattering for sizing and zeta-potential analysis. Salt (Na(2)HPO(4)), mononucleotide (2`-deoxyadenosine-5`-monophosphate) or poly (dA) oligonucleotide (3`-AAA AAA AAA A-5`) affected structure and stability of dioctadecyldimethylammonium bromide bilayer fragments. Oligonucleotide and salt increased bilayer packing due to bilayer fragment fusion. Mononucleotide did not reduce colloid stability or did not cause bilayer fragment fusion. Charge neutralization of bilayer fragments by poly (dA) at 1:10 poly (dA):dioctadecyldimethylammonium bromide molar ratio caused extensive aggregation, maximal size and zero of zeta-potential for the assemblies. Above charge neutralization, assemblies recovered colloid stability due to charge overcompensation. For bilayer fragments/poly (dA), the nonmonotonic behavior of colloid stability as a function of poly (dA) concentration was unique for the oligonucleotide and was not observed for Na(2)HPO(4) or 2`-deoxyadenosine-5`-monophosphate. For the first time, such interactions between cationic bilayer fragments and mono- or oligonucleotide were described in the literature. Bilayer fragments/oligonucleotide assemblies may find interesting applications in drug delivery. (c) 2010 Elsevier B.V. All rights reserved.

Multiple stages of detergent-erythrocyte membrane interaction-A spin label study

The various stages of the interaction between the detergent Triton X-100 (TTX-100) and membranes of whole red blood cells (RBC) were investigated in a broad range of detergent concentrations. The interaction was monitored by RBC hemolysis-assessed by release of intracellular hemoglobin (Hb) and inorganic phosphate- and by analysis of EPR spectra of a fatty acid spin probe intercalated in whole RBC suspensions, as well as pellets and supernatants obtained upon centrifugation of detergent-treated cells. Hemolysis finished at ca. 0.9 mM TTX-100. Spectral analysis and calculation of order parameters (S) indicated that a complex sequence of events takes place, and allowed the characterization of various structures formed in the different stages of detergent-membrane interaction. Upon reaching the end of cell lysis, essentially no pellet was detected, the remaining EPR signal being found almost entirely in the supernatants. Calculated order parameters revealed that whole RBC suspensions, pellets, and supernatants possessed a similar degree of molecular packing, which decreased to a small extent up to 2.5 mM detergent. Between 3.2 and 10 mM TTX-100, a steep decrease in S was observed for both whole RBC suspensions and supernatants. Above 10 mM detergent, S decreased in a less pronounced manner and the EPR spectra approached that of pure TTX-100 micelles. The data were interpreted in terms of the following events: at the lower detergent concentrations, an increase in membrane permeability occurs: the end of hemolysis coincides with the lack of pellet upon centrifugation. Up to 2.5 mM TTX-100 the supernatants consist of a (very likely) heterogeneous population of membrane fragments with molecular packing similar to that of whole cells. As the detergent concentration increases, mixed micelles are formed containing lipid and/or protein, approaching the packing found in pure TTX-100 micelles. This analysis is in agreement with the models proposed by Lasch (Biochim. Biophys Acta 1241 (1995) 269-292) and by Le Maire and coworkers (Biochim. Biophys. Acta 1508 (2000) 86-111). (C) 2010 Elsevier B.V. All rights reserved.