Calculations of the electrostatic free energy contributions to the binding free energy of sulfonamides to carbonic anhydrase

The interactions between biologically important enzymes and drugs are of great interest. In order to address some aspects of these interactions we have initiated a program to investigate enzymedrug interactions. Specifically, the interactions between one of the isozymes of carbonic anhydrase and a family of drugs known as sulfonamides have been studied using computational methods. In particular the electrostatic free energy of binding of carbonic anhydrase II with acetazolamide, methazolamide,p-chlorobenzenesulfonamide,p-aminobenzenesulfonamide and three new compounds (MK1, MK2, and MK3) has been computed using finite-difference Poisson-Boltzmann (FDPB) [1] method and the semimacroscopic version [2, 3] of the protein dipole Langevin dipole (PDLD) method [4]. Both methods, FDPB and PDLD, give similar results for the electrostatic free energy of binding even though different charges and different treatments were used for the protein. The calculated electrostatic binding free energies are in reasonable agreement with the experimental data. The potential and the limitation of electrostatic models for studies of binding energies are discussed.     

Dynamic Formation of Hybrid Peptidic Capsules by Chiral Self‐Sorting and Self‐Assembly

Owing to their versatility and biocompatibility, peptide‐based self‐assembled structures constitute valuable targets for complex functional designs. It is now shown that artificial capsules based on β‐barrel binding motifs can be obtained by means of dynamic covalent chemistry (DCC) and self‐assembly. Short peptides (up to tetrapeptides) are reversibly attached to resorcinarene scaffolds. Peptidic capsules are thus selectively formed in either a heterochiral or a homochiral way by simultaneous and spontaneous processes, involving chiral sorting, tautomerization, diastereoselective induction of inherent chirality, and chiral self‐assembly. Self‐assembly is shown to direct the regioselectivity of reversible chemical reactions. It is also responsible for shifting the tautomeric equilibrium for one of the homochiral capsules. Two different tautomers (keto‐enamine hemisphere and enol‐imine hemisphere) are observed in this capsule, allowing the structure to adapt for self‐assembly.     

Statistical Inference in a Linear Model for Spatially Located Sensors and Random Input

In the paper we consider a random linear model for observations provided by spatially located sensors measuring signals coming from one source. For this model a set of sufficient and complete statistics are found, and it is shown that the maximum likelihood estimators of unknown parameters (characteristics of the source) are functions of those statistics. The problem of nonnegative estimators of variance components of the model is shortly discussed. Comparisons of the mean squared errors of several estimators are given. Numerical example concerning hunting for defects in solar cells is considered in details.     

Boundary and initial fluctuation effect on dynamic behaviour of a laminated solid

Two problems will be studied in this contribution. First, we analyse some phenomena which take place in a laminated solid and are caused by a fluctuation of time-dependent boundary tractions. Second, we investigate the transient effect of initial displacement fluctuations on the behaviour of a laminate. To solve the above problems we propose a new macroscopic 3D model for investigations of initial-boundary value problems in elastodynamics of a laminated medium.     

On the modelling of dynamic problems for plates with a periodic structure

Summary The subject of analysis is the bending of elastic plates exhibiting a nonhomogeneous periodic structure and/or a periodically variable thickness in a certain direction parallel to the plate's midplane. The fundamental modelling problem is how to obtain an effective 2D-model of a plate under consideration, i.e., a 2D-model represented by PDEs with constant coefficients. This problem for periodic plates has been solved independently in [5] and [10], using asymptotic homogenization. However, homogenization neglects dynamic phenomena related to the plate's rotational inertia and cannot be applied to the analysis of higher-order vibration frequences. The main aim of this contribution is to formulate a new non-asymptotic effective 2D-model of a periodic plate which is free from the mentioned drawbacks and describes the dynamic behaviour of plates having the thickness of the order of the period length. The proposed model is applied to the analysis of some vibration problems.     

Polarisation control of light by light in a nonlinear polymer

Received: 11 December 1997/Revised version: 11 May 1998     

The large-amplitude motions in quasi-symmetric top molecules with internal C3v rotors: Interpretation of the low frequency Raman spectrum of disiloxane

The vibration-torsion-rotation Hamiltonian developed previously has been used to study the skeletal bending-torsion-rotation energy levels of disiloxane. The zeroth-order skeletal bending-torsion-rotation Hamiltonian for a molecule of this type is presented. The symmetry classification of the molecular wavefunctions and energy levels as well as infrared and Raman selection rules are considered. The energies of the skeletal bending-torsional-rotational states have been calculated and these results are used to interpret the low frequency Raman spectra of gaseous disiloxane-d₀ and disiloxane-d₆. It is shown that the treatment presented enables one to properly interpret these spectra. The results are compared to those obtained with other more approximate Hamiltonians.     

The Matrix Algebras of Continuous Groups with Antilinear Operations

The corepresentation theory of continuous groups is presented without the assumption that the subgroup G of the group with antilinear operations is unitary. Continuous groups of the form: G+a ₀ G are defined, where G denotes a linear Lie group and a ₀ denotes an antilinear operation which fulfils the condition a²₀=±1a^{2}_{0}=\pm1. The matrix algebras connected with the groups G+a ₀ G are defined. The structural constants of these algebras fulfill the conditions following from the Jacobi identities. Applications are presented to the groups G=SU(d), d=1,2,… , for a ₀=K, the complex conjugation operation, and to the group SL(2,C) for a ₀=K or Θ, the time-reversal operation.