THE weighted histogram analysis method for free-energy calculations on biomolecules. I. The method

The Weighted Histogram Analysis Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomolecular Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calculations. This algorithm possesses the following advantages over methods that are currently employed: (1) It provides a built-in estimate of sampling errors thereby yielding objective estimates of the optimal location and length of additional simulations needed to achieve a desired level of precision; (2) it yields the “best” value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addition to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better estimates of the free-energy differences. By recasting the Ferrenberg–Swendsen Multiple Histogram equations in a form suitable for molecular mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine. © 1992 by John Wiley & Sons, Inc.     

Optimization of a linear function over the set of stochastic efficient solutions

In this paper we study the problem of optimization over an integer efficient set of a Multiple Objective Integer Linear Stochastic Programming problem. Once the problem is converted into a deterministic one by adapting the $2$ -levels recourse approach, a new pivoting technique is applied to generate an optimal efficient solution without having to enumerate all of them. This method combines both techniques, the L-shaped method and the combined method developed in Chaabane and Pirlot (J Ind Manag Optim 6:811–823, 2010). A detailed didactic example is given to illustrate different steps of our algorithm.     

Activated bentonite (Maghnite-H+) as green catalyst for ring-opening polymerization of 1,3,5,7-tetravinyltetramethylcyclotetrasiloxane

Research on Chemical Intermediates - A new green technique to synthesize polysiloxane-type polymers is suggested based on use of chemically modified clay (Maghnite-H+) as heterogeneous,...     

Asymptotic modelling of a Signorini problem of generalized Marguerre-von Kármán shallow shells

Chacha and Bensayah [Asymptotic modeling of a Coulomb frictional Signorini problem for the von Kármán plates, C. R. Mécanique 336 (2008), pp. 846–850] have studied the asymptotic modelling of Coulomb frictional unilateral contact problem between an elastic nonlinear von Kármán plate and a rigid obstacle. The main result obtained is that the leading term of the asymptotic expansion is characterized by a two-dimensional Signorini problem but without friction. In this article, we extend this study to the case of a shallow shell under generalized Marguerre-von Kármán conditions.     

Examining ligand-protein interactions with binding-energy landscapes

Binding-energy landscapes are used to investigate the thermodynamics of molecular recognition for the pteridine ring, a recognition anchor in binding with dihydrofolate reductase, and two molecules with the same shape but different heteroatom substitutions. The relative importance of hydrogen bonding and hydrophobic interactions in this system is analyzed by comparing these three different decorations of the pteridine scaffold. Received: 5 May 1998 / Accepted: 3 September 1998 / Published online: 17 December 1998     

Multidimensional free-energy calculations using the weighted histogram analysis method

The recently formulated weighted histogram analysis method (WHAM)¹ is an extension of Ferrenberg and Swendsen's multiple histogram technique for free-energy and potential of mean force calculations. As an illustration of the method, we have calculated the two-dimensional potential of mean force surface of the dihedrals gamma and chi in deoxyadenosine with Monte Carlo simulations using the all-atom and united-atom representation of the AMBER force fields. This also demonstrates one of the major advantages of WHAM over umbrella sampling techniques. The method also provides an analysis of the statistical accuracy of the potential of mean force as well as a guide to the most efficient use of additional simulations to minimize errors. © 1995 John Wiley & Sons, Inc.     

Fractal Dimensions for Some Increments of the Uniform Empirical Process

In this paper, we investigate the limiting behavior of increments of the uniform empirical process. More precisely, we are concerned by sets of exceptional oscillation points related to large and small increments. We prove that these sets are random fractals and evaluate their Hausdorff dimensions. This work is a complement to the previous investigations carried out by Deheuvels and Mason⁽⁶⁾ where Csörg–Révész–Stute-type increments are studied.     

Polymorphism of Anhydrous Cadmium Iodate Structure of ε‐Cd(IO3)2

The investigation of CdCl₂‐HIO₃ system, in aqueous and HNO₃ solutions, revealed that anhydrous cadmium iodate presents a marked polymorphism. No less than four new Cd(IO₃)₂polymorphs have been isolated and characterized, two of which showing second harmonic generation activity. Single crystals of ε‐Cd(IO₃)₂ are obtained by slowly evaporating, at 60 °C, a saturated solution of γ‐Cd(IO₃)₂ in 30 % nitric acid. This compound crystallizes in the orthorhombic space group Pca2₁ [a = 17.581(2), b = 5.495(2), c = 11.163(2) Å]. The basic structural unit can be described as the connection of two cadmium polyhedrons with a short metal – metal distance of 3.88Å. These units are further linked through two other iodate bridges resulting in layers parallel to the (100) plane. The 3D linkage is ensured by short bonds of the fourth iodate group.     

Asymptotic justification of dynamical equations for generalized Marguerre–von Kármán anisotropic shallow shells

In this paper, using technics from asymptotic analysis, we show that the three-dimensional dynamical model for a non-linearly elastic shallow shell made of anisotropic material, with boundary conditions of generalized Marguerre–von Kármán’s type, reduces to two-dimensional dynamical model.     

Crystal Structure of a Cadmium Iodate Monohydrate: Cd(IO3)2·H2O

Single crystals of Cd(IO₃)₂·H₂O are obtained by slow evaporation of aqueous solutions of CdCl₂ and KIO₃. This compound crystallizes in the triclinic space group P1¯ [a = 7.119(2), b = 7.952(2), c = 6.646(2)Å, α = 102.17(2)°, β = 114.13(2)°, γ = 66.78(4)°]. The structure consists in Cd — (μ2‐O)₂ — Cd dimers with a metal — metal distance of 3.74Å. These dimers are connected through two iodate bridges resulting in layers parallel to the (010) plane. The 3D linkage is ensured by I1 — O1 long bonds (2.775Å).