Spatial geometric arrangements of disulfide-crosslinked loops in nonplanar proteins

The method presented earlier [T. Kikuchi, G. Némethy, and H.A. Scheraga, (1986) J. Comput. Chem. 7 , 67] for the classification of patterns of the three-dimensional folding of a covalently crosslinked polypeptide chain has been extended to nonplanar proteins. The procedure described earlier was applicable only to proteins termed planar, i.e., with a connexity of the crosslinks (e.g., disulfide bonds) that can be represented in a planar diagram. The procedure described in the present work is applicable to any (planar or nonplanar) pattern of crosslinking. The classification is based on a systematic and objective method of enumeration of spatial geometric arrangements of loops (SGAL) using no information other than the location of the disulfide bonds in the amino acid sequence. Various SGAL classes correspond to the presence of different ways of mutual penetration of loops, called thrustings and entanglements. Information on SGAL classes can be of use in structural predictions of folding patterns of proteins.     

Asymptotics for the Fredholm determinant of the sine kernel on a union of intervals

In the bulk scaling limit of the Gaussian Unitary Ensemble of hermitian matrices the probability that an interval of lengths contains no eigenvalues is the Fredholm determinant of the sine kernel over this interval. A formal asymptotic expansion for the determinant ass tends to infinity was obtained by Dyson. In this paper we replace a single interval of lengths bysJ, whereJ is a union ofm intervals and present a proof of the asymptotics up to second order. The logarithmic derivative with respect tos of the determinant equals a constant (expressible in terms of hyperelliptic integrals) timess, plus a bounded oscillatory function ofs (zero ifm=1, periodic ifm=2, and in general expressible in terms of the solution of a Jacobi inversion problem), pluso(1). Also determined are the asymptotics of the trace of the resolvent operator, which is the ratio in the same model of the probability that the set contains exactly one eigenvalue to the probability that it contains none. The proofs use ideas from orthogonal polynomial theory.Research supported by National Science Foundation grant DMS-9216203.     

On nonnegative solvability of linear operator equations

LetE be a Banach lattice having order continuous norm. Suppose, moreover,T is a nonnegative reducible operator having a compact iterate and which mapsE into itself. The purpose of this work is to extend the previous results of the authors, concerning nonnegative solvability of (kernel) operator equations on generalL ^p-spaces. In particular, we provide necessary and sufficient conditions for the operator equation x=T x+y to possess a nonnegative solutionxE wherey is a given nonnegative and nontrivial element ofE and is any given positive parameter.     

Level-spacing distributions and the Airy kernel

Scaling level-spacing distribution functions in the bulk of the spectrum in random matrix models ofN×N hermitian matrices and then going to the limitN leads to the Fredholm determinant of thesine kernel sin(x–y)/(x–y). Similarly a scaling limit at the edge of the spectrum leads to theAiry kernel [Ai(x)Ai(y)–Ai(x)Ai(y)]/(x–y). In this paper we derive analogues for this Airy kernel of the following properties of the sine kernel: the completely integrable system of P.D.E.'s found by Jimbo, Miwa, Môri, and Sato; the expression, in the case of a single interval, of the Fredholm determinant in terms of a Painlevé transcendent; the existence of a commuting differential operator; and the fact that this operator can be used in the derivation of asymptotics, for generaln, of the probability that an interval contains preciselyn eigenvalues.     

On orthogonal and symplectic matrix ensembles

The focus of this paper is on the probability,E (O;J), that a setJ consisting of a finite union of intervals contains no eigenvalues for the finiteN Gaussian Orthogonal (=1) and Gaussian Symplectic (=4) Ensembles and their respective scaling limits both in the bulk and at the edge of the spectrum. We show how these probabilities can be expressed in terms of quantities arising in the corresponding unitary (=2) ensembles. Our most explicit new results concern the distribution of the largest eigenvalue in each of these ensembles. In the edge scaling limit we show that these largest eigenvalue distributions are given in terms of a particular Painlevé II function.     

Quantum-chaotic scattering effects in semiconductor microstructures

We show that classical chaotic scattering has experimentally measurable consequences for the quantum conductance of semiconductor microstructures. These include the existence of conductance fluctuations-a sensitivity of the conductance to either Fermi energy or magnetic field-and weak-localization-a change in the average conductance upon applying a magnetic field. We develop a semiclassical theory and present numerical results for these two effects in which we model the microstructures by billiards attached to leads. We find that the difference between chaotic and regular classical scattering produces a qualitative difference in the fluctuation spectrum and weak-localization lineshape of chaotic and nonchaotic structures. While the semiclassical theory within the diagonal approximation accounts well for the weak-localization lineshape and for the spectrum of the fluctuations, we uncover a surprising failure of the semiclassical diagonal-approximation theory in describing the magnitude of these quantum transport effects.     

Relativistic effective potential SCF calculations of AgH and AuH

Relativistic effective potentials (REP) are now widely used in molecular electronic structure calculations. Tests of these REP are needed to assess their accuracy. This can now be done for AgH and AuH since Lee and McLean have published Dirac-Fock calculations for these molecules. Comparative SCF calculations have been performed for two types of effective potential. Satisfactory agreement between the effective potential results and Dirac-Fock values is found for spectroscopic constants and dipole moments, which supports the use of these potentials for heavy atom containing molecules.     

Adduct formation in electrospray ionization mass spectrometry II. Benzoic acid derivatives

This work serves as a follow-up to Part I of experiments designed to determine the underlying principles in the formation of pseudomolecular, or adduct, ions during electrospray ionization. Aromatic acids were studied by flow injection analysis in the negative ionization mode of electrospray ionization mass spectrometry. Part I dealt with common acidic anti-inflammatory pharmaceuticals. such as ibuprofen and related analogues. Part II deals with functionally less complex molecules, namely benzoic acid (BA) and substituted benzoic acids. Halide-substituted molecules are investigated to deduce the effect of electron-withdrawing substituents (bromo-, chloro-, and fluoro-) and ring position (ortho-, meta- and para-) on the response of a traditional deprotonated molecular ion ([M-H]-) and a sodium-bridged dimer ion ([2M-2 H+Na]-). Amino-substituted benzoic acids are also analyzed in order to study the effect of an additional ionizable group on the molecule, and para-tert.-butyl-BA is analyzed to study the effect of increased hydrophobicity, as they relate to the formation of pseudomolecular ions. This study shows that solution character [octanol-water partition coefficient (or log P) and pKa] of the model compounds controls the relative efficiency of formation of [M-H]- and [2M-2H+Na]- ions. However the relative gas phase character (gas phase basicity and proton affinity) also has a significant effect on the formation of the sodium-bridged dimer ion. For the halide-substituted species, placement of the electron-withdrawing atom at the meta-position gives the greatest enhancement in sensitivity. Observations also show that as the structural complexity of the model compound increases, predictions relating analyte acidity to sodium-bridged dimer ion formation give way to a stronger dependence between log P values and ionization efficiency. Supporting this hypothesis is the nearly ten-fold enhancement in signal for tert.-butyl BA relative to BA. due to the greater hydrophobicity, and consequently, increased surface activity in an electrosprayed droplet of the analyte molecule.     

Nonpeptide inhibitors of cathepsin G: optimization of a novel beta-ketophosphonic acid lead by structure-based drug design

The serine protease cathepsin G (EC 3.4.21.20; Cat G), which is stored in the azurophilic granules of neutrophils (polymorphonuclear leukocytes) and released on degranulation, has been implicated in various pathological conditions associated with inflammation. By employing high-throughput screening, we identified beta-ketophosphonic acid 1 as a moderate inhibitor of Cat G (IC(50) = 4.1 microM). We were fortunate to obtain a cocrystal of 1 with Cat G and solve its structure by X-ray crystallography (3.5 A). Structural details from the X-ray analysis of 1.Cat G served as a platform for optimization of this lead compound by structure-based drug design. With the aid of molecular modeling, substituents were attached to the 3-position of the 2-naphthyl ring of 1, which occupies the S1 pocket of Cat G, to provide an extension into the hydrophobic S3 region. Thus, we arrived at analogue 7 with an 80-fold potency improvement over 1 (IC(50) = 53 nM). From these results, it is evident that the beta-ketophosphonic acid unit can form the basis for a novel class of serine protease inhibitors.     

Computation of the physio-chemical properties and data mining of large molecular collections

Very large data sets of molecules screened against a broad range of targets have become available due to the advent of combinatorial chemistry. This information has led to the realization that ADME (absorption, distribution, metabolism, and excretion) and toxicity issues are important to consider prior to library synthesis. Furthermore, these large data sets provide a unique and important source of information regarding what types of molecular shapes may interact with specific receptor or target classes. Thus, the requirement for rapid and accurate data mining tools became paramount. To address these issues Pharmacopeia, Inc. formed a computational research group, The Center for Informatics and Drug Discovery (CIDD).* In this review we cover the work done by this group to address both in silico ADME modeling and data mining issues faced by Pharmacopeia because of the availability of a large and diverse collection (over 6 million discrete compounds) of drug-like molecules. In particular, in the data mining arena we discuss rapid docking tools and how we employ them, and we describe a novel data mining tool based on a ID representation of a molecule followed by a molecular sequence alignment step. For the ADME area we discuss the development and application of absorption, blood-brain barrier (BBB) and solubility models. Finally, we summarize the impact the tools and approaches might have on the drug discovery process.