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.

The recently formulated weighted histogram analysis method (WHAM)' is an extension of Ferrenberg and Swendsen's multiple histogram technique for freeenergy 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. 0

The base pairs in double helical nucleic acids have been compared to see how they can be recognized by proteins. We conclude that a single hydrogen bond is inade~qate for uniquely identifying any particular base pair, as this leads to numerous degeneracies. However, using two hydrogen bonds, fidelity of base pair recognition may be achieved. We propose specific amino-acid side chain interactions involving two hydrogen bonds as a component of the recognition system for base pairs. In the major groove we suggest that asparagine or glutamine binds to adenine of the base pair, or arginine binds to guanine. In the minor groove, we suggest an interaction between asparagine or glutamine with guanine of the base pair. We also discuss the role that ions and other amino-aci side chains may play in recognition interactions.

Membrane co-transport proteins that utilize a 5-helix inverted repeat motif have recently emerged as one of the largest structural class of secondary active transporters1,2. However, despite many structural advances there is no clear evidence as to how ion and substrate transport are coupled. Here, we report a comprehensive study of the Sodium-Galactose Transporter from Vibrio parahaemolyticus (vSGLT) consisting of molecular dynamics simulations, biochemical characterization, and a new crystal structure of the inward-open conformation at 2.7 Å resolution. Our data show that sodium exit causes a reorientation of transmembrane helix 1 (TM1) opening an inner gate required for substrate exit, while also triggering minor rigid body movements in two sets of transmembrane helical bundles. This cascade of events, initiated by sodium release, ensures proper timing of ion and substrate release. Once set in motion, these molecular changes weaken substrate binding to the transporter and allow galactose to readily enter the intracellular space. Additionally, we identify an allosteric pathway between the sodium binding sites, the unwound portion of TM1, and the substrate binding site that is essential in the coupling of co-transport.

The crystal structure of the complex between Eco RI endonuclease and the cognate oligonucleotide TCGCGAATTCGCG provides a detailed example of the structural basis of sequence-specific DNA-protein interactions. The structure was determined, to 3 A resolution, by the ISIR (iterative single isomorphous replacement) method with a platinum isomorphous derivative. The complex has twofold symmetry. Each subunit of the endonuclease is organized into an alpha/beta domain consisting a five-stranded beta sheet, alpha helices, and an extension, called the "arm," which wraps around the DNA. The large beta sheet consists of antiparallel and parallel motifs that form the foundations for the loops and alpha helices responsible for DNA strand scission and sequence-specific recognition, respectively. The DNA cleavage site is located in a cleft that binds the DNA backbone in the vicinity of the scissile bond. Sequence specificity is mediated by 12 hydrogen bonds originating from alpha helical recognition modules. Arg200 forms two hydrogen bonds with guanine while Glu144 and Arg145 form four hydrogen bonds to adjacent adenine residues. These interactions discriminate the Eco RI hexanucleotide GAATTC from all other hexanucleotides because any base substitution would require rupture of at least one of these hydrogen bonds.

The original model of Eco RI endonuclease (1) proved refractory to crystallographic refinement, whereby model coordinates were adjusted to optimize the fit to the observed diffraction data (the best R factor for the original model is 0.25). We The new data yielded a multiple isomorphous replacement (MIR) electron density map that suggests a different connectivity between elements of secondary structure in the protein (3). A model based on that connectivity has refined robustly by the X-PLOR and Konnert-Hendrickson methods (4) to an R factor of 0.20 (no ordered solvent has been included in this model, nor have coordinates for the first 16 amino acid residues, which appear disordered) (5). The root-mean-square deviations in bond distance, angle distance, and 1-4 dihedral distance are 0.016 A, 0.031 A, and 0.031 A,

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The 3 A electron density map of a co-crystalline recognition complex between EcoRI endonuclease and the oligonucleotide TCGCGAATTCGCG reveals that a tight, complementary interface between the enzyme and the major groove of the DNA is the major determinant of sequence specificity. The DNA contains a torsional kink and other departures from the B conformation which unwind the DNA and thereby widen the major groove in the recognition site.