Thomas A. Darden

Gene assessment and sample classification for gene expression data using a genetic algorithm/k-nearest neighbor method.

Recent tools that analyze microarray expression data have exploited correlation-based approaches such as clustering analysis. We describe a new method for assessing the importance of genes for sample classification based on expression data. Our approach combines a genetic algorithm (GA) and the k-nearest neighbor (KNN) method to identify genes that jointly can discriminate between two types of samples (e.g. normal vs. tumor). First, many such subsets of differentially expressed genes are obtained independently using the GA. Then, the overall frequency with which genes were selected is used to deduce the relative importance of genes for sample classification. Sample heterogeneity is accommodated; that is, the method should be robust against the existence of distinct subtypes. We applied GA / KNN to expression data from normal versus tumor tissue from human colon. Two distinct clusters were observed when the 50 most frequently selected genes were used to classify all of the samples in the data sets stu died and the majority of samples were classified correctly. Identification of a set of differentially expressed genes could aid in tumor diagnosis and could also serve to identify disease subtypes that may benefit from distinct clinical approaches to treatment.

Heparan/chondroitin sulfate biosynthesis. Structure and mechanism of human glucuronyltransferase I.

Human β1,3-glucuronyltransferase I (GlcAT-I) is a central enzyme in the initial steps of proteoglycan synthesis. GlcAT-I transfers a glucuronic acid moiety from the uridine diphosphate-glucuronic acid (UDP-GlcUA) to the common linkage region trisaccharide Galβ1–3Galβ1–4Xyl covalently bound to a Ser residue at the glycosaminylglycan attachment site of proteoglycans. We have now determined the crystal structure of GlcAT-1 at 2.3 Å in the presence of the donor substrate product UDP, the catalytic Mn2+ ion, and the acceptor substrate analog Galβ1–3Galβ1–4Xyl. The enzyme is a α/β protein with two subdomains that constitute the donor and acceptor substrate binding site. The active site residues lie in a cleft extending across both subdomains in which the trisaccharide molecule is oriented perpendicular to the UDP. Residues Glu227, Asp252, and Glu281 dictate the binding orientation of the terminal Gal-2 moiety. Residue Glu281 is in position to function as a catalytic base by deprotonating the incoming 3-hydroxyl group of the acceptor. The conserved DXD motif (Asp194, Asp195, Asp196) has direct interaction with the ribose of the UDP molecule as well as with the Mn2+ ion. The key residues involved in substrate binding and catalysis are conserved in the glucuronyltransferase family as well as other glycosyltransferases.

Differential Transactivation by the p53 Transcription Factor Is Highly Dependent on p53 Level and Promoter Target Sequence

ABSTRACT Little is known about the mechanisms that regulate differential transactivation by p53. We developed a system in the yeast Saccharomyces cerevisiae that addresses p53 transactivation capacity from 26 different p53 response elements (REs) under conditions where all other factors, such as chromatin, are kept constant. The system relies on a tightly regulated promoter (rheostatable) that can provide for a broad range of p53 expression. The p53 transactivation capacity toward each 20- to 22-bp-long RE could be ranked by using a simple phenotypic assay. Surprisingly, there was as much as a 1,000-fold difference in transactivation. There was no correlation between the functional rank and statistical predictions of binding energy of the REs. Instead we found that the central sequence element in an RE greatly affects p53 transactivation capacity, possibly because of DNA structural properties. Our results suggest that intrinsic DNA binding affinity and p53 protein levels are important contributors to p53-induced differential transactivation. These results are also relevant to understanding the regulation by other families of transcription factors that recognize several sequence-related response elements and/or have tightly regulated expression. We found that p53 had weak activity towards half the apoptotic REs. In addition, p53 alleles associated with familial breast cancer, previously classified as wild type, showed subtle differences in transactivation capacity towards several REs.

Calculation of protein–ligand binding free energy by using a polarizable potential

The binding of charged ligands benzamidine and diazamidine to trypsin was investigated by using a polarizable potential energy function and explicit-water molecular dynamics simulations. The binding free energies were computed from the difference between the free energies of decoupling the ligand from water and protein environments. Both the absolute and the relative free energies from the perturbation simulations agree with experimental measurements to within 0.5 kcal·mol−1. Comparison of free-energy components sampled from different thermodynamic paths indicates that electrostatics is the main driving force behind benzamidine recognition of trypsin. The contribution of electronic polarization to binding appears to be crucial. By computing the free-energy contribution caused by the polarization between the ligand and its surroundings, we found that polarization has the opposite effect in dissimilar environments. Although polarization favors ligand solvation in water, it weakens the protein–ligand attraction by screening the electrostatic interaction between trypsin and benzamidine. We also examined the relative binding free energies of a benzamidine analog diazamidine to trypsin. The changes in free energy on benzamidine-diazamidine substitution were tens of kilocalories in both water and trypsin environments; however, the change in the total binding free energy is <2 kcal·mol−1 because of cancellation, consistent with the experimental results. Overall, our results suggest that the use of a polarizable force field, given adequate sampling, is capable of achieving chemical accuracy in molecular simulations of protein–ligand recognition.

Towards accurate solvation dynamics of divalent cations in water using the polarizable amoeba force field: From energetics to structure

Molecular dynamics simulations were performed using a modified amoeba force field to determine hydration and dynamical properties of the divalent cations Ca2+ and Mg2+. The extension of amoeba to divalent cations required the introduction of a cation specific parametrization. To accomplish this, the Thole polarization damping model parametrization was modified based on the ab initio polarization energy computed by a constrained space orbital variation energy decomposition scheme. Excellent agreement has been found with condensed phase experimental results using parameters derived from gas phase ab initio calculations. Additionally, we have observed that the coordination of the calcium cation is influenced by the size of the periodic water box, a recurrent issue in first principles molecular dynamics studies.

Towards a force field based on density fitting

Total intermolecular interaction energies are determined with a first version of the Gaussian electrostatic model (GEM-0), a force field based on a density fitting approach using s-type Gaussian functions. The total interaction energy is computed in the spirit of the sum of interacting fragment ab initio (SIBFA) force field by separately evaluating each one of its components: electrostatic (Coulomb), exchange repulsion, polarization, and charge transfer intermolecular interaction energies, in order to reproduce reference constrained space orbital variation (CSOV) energy decomposition calculations at the B3LYP/aug-cc-pVTZ level. The use of an auxiliary basis set restricted to spherical Gaussian functions facilitates the rotation of the fitted densities of rigid fragments and enables a fast and accurate density fitting evaluation of Coulomb and exchange-repulsion energy, the latter using the overlap model introduced by Wheatley and Price [Mol. Phys. 69, 50718 (1990)]. The SIBFA energy scheme for polarization and charge transfer has been implemented using the electric fields and electrostatic potentials generated by the fitted densities. GEM-0 has been tested on ten stationary points of the water dimer potential energy surface and on three water clusters (n = 16,20,64). The results show very good agreement with density functional theory calculations, reproducing the individual CSOV energy contributions for a given interaction as well as the B3LYP total interaction energies with errors below kBT at room temperature. Preliminary results for Coulomb and exchange-repulsion energies of metal cation complexes and coupled cluster singles doubles electron densities are discussed.

Multigrid methods for classical molecular dynamics simulations of biomolecules

We present an O(N) multigrid-based method for the efficient calculation of the long-range electrostatic forces needed for biomolecular simulations, that is suitable for implementation on massively parallel architectures. Along general lines, the method consists of: (i) a charge assignment scheme, which both interpolates and smoothly assigns the charges onto a grid; (ii) the solution of Poisson’s equation on the grid via multigrid methods; and (iii) the back interpolation of the forces and energy from the grid to the particle space. Careful approaches for the charge assignment and the force interpolation, and a Hermitian approximation of Poisson’s equation on the grid allow for the generation of the high-accuracy solutions required for high-quality molecular dynamics simulations. Parallel versions of the method scale linearly with the number of particles for a fixed number of processors, and with the number of processors, for a fixed number of particles.

NMDA Receptor Activation by HIV-Tat Protein Is Clade Dependent

In countries infected with HIV clade B, some patients develop a rapidly progressive dementia that if untreated results in death. In regions of the world infected with HIV clade C, only milder forms of cognitive impairment have been recognized. HIV-infected macrophages are the principal mediators of dementia. HIV clade C, however, efficiently infects macrophages and HIV-infected macrophages are found in the brains of clade C-infected patients. HIV-infected macrophages release Tat protein, which may act directly on neurons to cause toxicity. We found that Tat released from Tat-expressing cells was at least 1000-fold more toxic than recombinant Tat protein. We determined whether Tat could interact with NMDA receptors and whether these interactions are clade dependent. It is demonstrated that Tat binds directly to the NMDA receptor leading to excitotoxicity. The Cys 30-Cys 31 motif in Tat is critical for exciting the NMDA receptor and the Cys31Ser mutation found in clade C Tat has a significantly attenuated neurotoxic response. Through molecular modeling and site-directed mutagenesis, we predict that Cys 31 disrupts the disulfide bond between Cys 744 and Cys 798 on the NR1 subunit of the NMDA receptor by directly interacting with Cys 744 leading to a free thiol group on Cys 798 and subsequent persistent activation of the NMDA receptor.

An Atomic Model for the Pleated β-Sheet Structure of Aβ Amyloid Protofilaments

Abstract Synchrotron x-ray studies on amyloid fibrils have suggested that the stacked pleated β -sheets are twisted so that a repeating unit of 24 β -strands forms a helical turn around the fibril axis (Sunde et al., 1997. J. Mol. Biol . 273:729–739). Based on this morphological study, we have constructed an atomic model for the twisted pleated β -sheet of human A β amyloid protofilament. In the model, 48 monomers of A β 12–42 stack (four per layer) to form a helical turn of β -sheet. Each monomer is in an antiparallel β -sheet conformation with a turn located at residues 25–28. Residues 17–21 and 31–36 form a hydrophobic core along the fibril axis. The hydrophobic core should play a critical role in initializing A β aggregation and in stabilizing the aggregates. The model was tested using molecular dynamics simulations in explicit aqueous solution, with the particle mesh Ewald (PME) method employed to accommodate long-range electrostatic forces. Based on the molecular dynamics simulations, we hypothesize that an isolated protofilament, if it exists, may not be twisted, as it appears to be when in the fibril environment. The twisted nature of the protofilaments in amyloid fibrils is likely the result of stabilizing packing interactions of the protofilaments. The model also provides a binding mode for Congo red on A β amyloid fibrils. The model may be useful for the design of A β aggregation inhibitors.

Generalization of the Gaussian electrostatic model: extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods.

The simulation of biological systems by means of current empirical force fields presents shortcomings due to their lack of accuracy, especially in the description of the nonbonded terms. We have previously introduced a force field based on density fitting termed the Gaussian electrostatic model-0 (GEM-0) J.-P. Piquemal et al. [J. Chem. Phys. 124, 104101 (2006)] that improves the description of the nonbonded interactions. GEM-0 relies on density fitting methodology to reproduce each contribution of the constrained space orbital variation (CSOV) energy decomposition scheme, by expanding the electronic density of the molecule in s-type Gaussian functions centered at specific sites. In the present contribution we extend the Coulomb and exchange components of the force field to auxiliary basis sets of arbitrary angular momentum. Since the basis functions with higher angular momentum have directionality, a reference molecular frame (local frame) formalism is employed for the rotation of the fitted expansion coefficients. In all cases the intermolecular interaction energies are calculated by means of Hermite Gaussian functions using the McMurchie-Davidson [J. Comput. Phys. 26, 218 (1978)] recursion to calculate all the required integrals. Furthermore, the use of Hermite Gaussian functions allows a point multipole decomposition determination at each expansion site. Additionally, the issue of computational speed is investigated by reciprocal space based formalisms which include the particle mesh Ewald (PME) and fast Fourier-Poisson (FFP) methods. Frozen-core (Coulomb and exchange-repulsion) intermolecular interaction results for ten stationary points on the water dimer potential-energy surface, as well as a one-dimensional surface scan for the canonical water dimer, formamide, stacked benzene, and benzene water dimers, are presented. All results show reasonable agreement with the corresponding CSOV calculated reference contributions, around 0.1 and 0.15 kcal/mol error for Coulomb and exchange, respectively. Timing results for single Coulomb energy-force calculations for (H(2)O)(n), n=64, 128, 256, 512, and 1024, in periodic boundary conditions with PME and FFP at two different rms force tolerances are also presented. For the small and intermediate auxiliaries, PME shows faster times than FFP at both accuracies and the advantage of PME widens at higher accuracy, while for the largest auxiliary, the opposite occurs.