Global Minimum Energy Conformation Research Articles

Restricted dead‐end elimination: Protein redesign with a bounded number of residue mutations

Dead-end elimination (DEE) has emerged as a powerful structure-based, conformational search technique enabling computational protein redesign. Given a protein with n mutable residues, the DEE criteria guide the search toward identifying the sequence of amino acids with the global minimum energy conformation (GMEC). This approach does not restrict the number of permitted mutations and allows the identified GMEC to differ from the original sequence in up to n residues. In practice, redesigns containing a large number of mutations are often problematic when taken into the wet-lab for creation via site-directed mutagenesis. The large number of point mutations required for the redesigns makes the process difficult, and increases the risk of major unpredicted and undesirable conformational changes. Preselecting a limited subset of mutable residues is not a satisfactory solution because it is unclear how to select this set before the search has been performed. Therefore, the ideal approach is what we define as the kappa-restricted redesign problem in which any kappa of the n residues are allowed to mutate. We introduce restricted dead-end elimination (rDEE) as a solution of choice to efficiently identify the GMEC of the restricted redesign (the kappaGMEC). Whereas existing approaches require n-choose-kappa individual runs to identify the kappaGMEC, the rDEE criteria can perform the redesign in a single search. We derive a number of extensions to rDEE and present a restricted form of the A* conformation search. We also demonstrate a 10-fold speed-up of rDEE over traditional DEE approaches on three different experimental systems.

3D-QSAR analysis of cycloguanil derivatives as inhibitors of A16V + S108T mutant Plasmodium falciparum dihydrofolate reductase enzyme

A three-dimensional quantitative structure–activity relationship (3D-QSAR) study was carried out on cycloguanil derivatives which are reported as growth inhibitors of Plasmodium falciparum clone (T9/94 RC17) which harbors A16V + S108T mutant dihydrofolate reductase (DHFR) enzyme. Comparative of Molecular Field Analysis (CoMFA) and Comparative of Molecular Similarity Indices Analysis (CoMSIA) were carried out to investigate the structural requirements for the activities of these compounds and to derive predictive models that may be used for designing novel PfDHFR enzyme inhibitors. The global minimum energy (within the search space) conformation of the most active compound ( 38) was obtained by using simulated annealing, and was subsequently used as a template to build the structures of the rest molecules used in the study. The CoMFA model gave statistically significant results with r cv 2 and r ncv 2 values of 0.654 and 0.951, respectively. The combination of steric, electrostatic and hydrophobic fields resulted in the best CoMSIA model with r cv 2 and r ncv 2 values of 0.669 and 0.907, respectively. The predictive abilities of the CoMFA and CoMSIA models were also evaluated using test compounds which gave r pred 2 values of 0.735 and 0.557, respectively. The results of bootstrapping analyses also confirmed that the generated models are robust and reliable. The models were graphically interpreted using CoMFA and CoMSIA contour plots. The structural regions responsible for the differences in anti-plasmodial activities were analyzed with respect to their electrostatic, steric and hydrophobic nature. The results obtained from this study could be used for rational design of potent inhibitors against A16V + S108T mutant PfDHFR enzyme.

Rotamer optimization for protein design through MAP estimation and problem‐size reduction

The search for the global minimum energy conformation (GMEC) of protein side chains is an important computational challenge in protein structure prediction and design. Using rotamer models, the problem is formulated as a NP-hard optimization problem. Dead-end elimination (DEE) methods combined with systematic A* search (DEE/A*) has proven useful, but may not be strong enough as we attempt to solve protein design problems where a large number of similar rotamers is eligible and the network of interactions between residues is dense. In this work, we present an exact solution method, named BroMAP (branch-and-bound rotamer optimization using MAP estimation), for such protein design problems. The design goal of BroMAP is to be able to expand smaller search trees than conventional branch-and-bound methods while performing only a moderate amount of computation in each node, thereby reducing the total running time. To achieve that, BroMAP attempts reduction of the problem size within each node through DEE and elimination by lower bounds from approximate maximum-a-posteriori (MAP) estimation. The lower bounds are also exploited in branching and subproblem selection for fast discovery of strong upper bounds. Our computational results show that BroMAP tends to be faster than DEE/A* for large protein design cases. BroMAP also solved cases that were not solved by DEE/A* within the maximum allowed time, and did not incur significant disadvantage for cases where DEE/A* performed well. Therefore, BroMAP is particularly applicable to large protein design problems where DEE/A* struggles and can also substitute for DEE/A* in general GMEC search.

Peptide Secondary Structures in the Gas Phase: Consensus Motif of N-Linked Glycoproteins

The possibility of secondary structure acting as a primary determinant in nature's choice of the consensus sequon, NXS/T in all N-linked glycoproteins, has been addressed by determining the intrinsic secondary structures of the capped oligopeptide, Ac-NGS-NHBn, and two "mutants", Ac-QGS-NHBn and Ac-NPS-NHBn, by use of infrared laser ion dip spectroscopy in the gas phase coupled with ab initio and density functional theory calculation. Their global minimum energy conformations, exclusively or preferentially populated in all three peptides, display marked differences. NGS adopts an open, S-shaped backbone conformation rather than the C(10) "Asx" turn structure that all previous measurements have identified in solution; the difference can be related to the high dipole moment of the "Asx" conformation and structural selection in a polar environment. QGS adopts a similar but more rigid backbone structure, supported by markedly stronger hydrogen bonds. NPS adopts an Asx turn coupled with a C(10) beta-turn backbone conformation, a structure also adopted in a crystal environment. These and other more subtle structural differences, particularly those involving interactions with the carboxamide side chain, provide strong evidence for the operation of structural constraints, and a potential insight into the unique reactivity of the asparagine side chain toward enzymatic glycosylation.

The minimized dead‐end elimination criterion and its application to protein redesign in a hybrid scoring and search algorithm for computing partition functions over molecular ensembles

One of the main challenges for protein redesign is the efficient evaluation of a combinatorial number of candidate structures. The modeling of protein flexibility, typically by using a rotamer library of commonly-observed low-energy side-chain conformations, further increases the complexity of the redesign problem. A dominant algorithm for protein redesign is dead-end elimination (DEE), which prunes the majority of candidate conformations by eliminating rigid rotamers that provably are not part of the global minimum energy conformation (GMEC). The identified GMEC consists of rigid rotamers (i.e., rotamers that have not been energy-minimized) and is thus referred to as the rigid-GMEC. As a postprocessing step, the conformations that survive DEE may be energy-minimized. When energy minimization is performed after pruning with DEE, the combined protein design process becomes heuristic, and is no longer provably accurate: a conformation that is pruned using rigid-rotamer energies may subsequently minimize to a lower energy than the rigid-GMEC. That is, the rigid-GMEC and the conformation with the lowest energy among all energy-minimized conformations (the minimized-GMEC) are likely to be different. While the traditional DEE algorithm succeeds in not pruning rotamers that are part of the rigid-GMEC, it makes no guarantees regarding the identification of the minimized-GMEC. In this paper we derive a novel, provable, and efficient DEE-like algorithm, called minimized-DEE (MinDEE), that guarantees that rotamers belonging to the minimized-GMEC will not be pruned, while still pruning a combinatorial number of conformations. We show that MinDEE is useful not only in identifying the minimized-GMEC, but also as a filter in an ensemble-based scoring and search algorithm for protein redesign that exploits energy-minimized conformations. We compare our results both to our previous computational predictions of protein designs and to biological activity assays of predicted protein mutants. Our provable and efficient minimized-DEE algorithm is applicable in protein redesign, protein-ligand binding prediction, and computer-aided drug design.

Global Optimization of a Three-Dimensional HP Protein

The conformational space annealing (CSA) method is an efficient global optimization algorithm for sampling low-lying local-minimum-energy conformations of a physical system. In this work, the CSA method is applied to the three-dimensional HP lattice model of a protein, where a conformation is defined as a self-avoiding chain on the three-dimensional cubic lattice. The 27-residue chain with a particular sequence H2PHP2HPHPHPH2P3HP2H3P2HP is considered, for which compact conformations filling a 3 × 3 × 3 cube have been exhaustively enumerated in an earlier work, and only one compact conformation with the lowest energy has been shown to exist. The CSA algorithm finds non-compact conformations with energies lower than any compact conformation, for several independent runs, proving that the global minimum energy conformation is not a compact structure.

The HP model of protein folding: A challenging testing ground for Wang–Landau sampling

The hydrophobic-polar (HP) lattice protein model has gained much attention as a standard in assessing the efficiency of computational methods for protein structure prediction as well as for exploring the statistical physics of protein folding. In this work we show that Wang–Landau sampling, in connection with a suitable move set (pull moves), provides a powerful route for both the search of global energy minimum conformations and the precise determination of the density of states for HP sequences with up to 100 monomers in two and three dimensions. The main advantage of our approach lies in its general applicability to a broad range of lattice protein models that go beyond the scope of the HP model.

3D QSAR Studies of DAMNI Analogs as Possible Non‐nucleoside Reverse Transcriptase Inhibitors

The non‐nucleoside inhibitors of HIV‐1‐reverse transcriptase (NNRTIs) are an important class of drugs employed in antiviral therapy. Recently, a novel family of NNRTIs commonly referred to as 1‐[2‐diarylmethoxy] ethyl) 2‐methyl‐5‐nitroimidazoles (DAMNI) derivatives have been discovered. The 3D‐QSAR studies on DAMNI derivatives as NNRTIs was performed by comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) methods to determine the factors required for the activity of these compounds. The global minimum energy conformer of the template molecule 15, the most active molecule of the series, was obtained by simulated annealing method and used to build the structures of the molecules in the dataset. The combination of steric and electrostatic fields in CoMSIA gave the best results with cross‐validated and conventional correlation coefficients of 0.654 and 0.928 respectively. The predictive ability of CoMFA and CoMSIA were determined using a test set of ten DAMNI derivatives giving predictive correlation coefficients of 0.92 and 0.98 respectively indicating good predictive power. Further, the robustness of the models was verified by bootstrapping analysis. The information obtained from CoMFA and CoMSIA 3D contour maps may be of utility in the design of more potent DAMNI analogs as NNRTIs in future.

Structural diversity in imidazolidinone organocatalysts: a synchrotron and computational study

(S)-1-(Methylaminocarbonyl)-3-phenylpropanaminium chloride (S2 x HCl), C10H15N2O+ x Cl-, crystallizes in the orthorhombic space group P2(1)2(1)2(1) with a single formula unit per asymmetric unit. (5R/S)-5-benzyl-2,2,3-trimethyl-4-oxoimidazolidin-1-ium chloride (R3 and S3), C13H19N2O+ x Cl-, crystallize in the same space group as S2 x HCl but contain three symmetry-independent formula units. (R/S)-5-benzyl-2,2,3-trimethyl-4-oxoimidazolidin-1-ium chloride monohydrate (R4 and S4), C13H19N2O+ x Cl- x H2O, crystallize in the space group P2(1) with a single formula unit per asymmetric unit. Calculations at the B3LYP/6-31G(d,p) and B3LYP/6-311G(d,p) levels of the conformational energies of the cation in R3, S3, R4 and S4 indicate that the ideal gas-phase global energy minimum conformation is not observed in the solid state. Rather, the effects of hydrogen-bonding and van der Waals interactions in the crystal structure cause the molecules to adopt higher-energy conformations, which correspond to local minima in the molecular potential energy surface.

Dead-End Elimination with Backbone Flexibility

Dead-End Elimination (DEE) is a powerful algorithm capable of reducing the search space for structure-based protein design by a combinatorial factor. By using a fixed backbone template, a rotamer library, and a potential energy function, DEE identifies and prunes rotamer choices that are provably not part of the Global Minimum Energy Conformation (GMEC), effectively eliminating the majority of the conformations that must be subsequently enumerated to obtain the GMEC. Since a fixed-backbone model biases the algorithm predictions against protein sequences for which even small backbone movements may result in a significantly enhanced stability, the incorporation of backbone flexibility can improve the accuracy of the design predictions. If explicit backbone flexibility is incorporated into the model, however, the traditional DEE criteria can no longer guarantee that the flexible-backbone GMEC, the lowest-energy conformation when the backbone is allowed to flex, will not be pruned. We derive a novel DEE pruning criterion, flexible-backbone DEE (BD), that is provably accurate with backbone flexibility, guaranteeing that no rotamers belonging to the flexible-backbone GMEC are pruned; we also present further enhancements to BD for improved pruning efficiency. The results from applying our novel algorithms to redesign the beta1 domain of protein G and to switch the substrate specificity of the NRPS enzyme GrsA-PheA are then compared against the results from previous fixed-backbone DEE algorithms. We confirm experimentally that traditional-DEE is indeed not provably-accurate with backbone flexibility and that BD is capable of generating conformations with significantly lower energies, thus confirming the feasibility of our novel algorithms. Contact authors for source code.

3D-QSAR studies of substituted 1-(3, 3-diphenylpropyl)-piperidinyl amides and ureas as CCR5 receptor antagonists

3D-QSAR studies on the derivatives of 1-(3,3-diphenylpropyl)-piperidinyl amide and urea as CCR5 receptor antagonists were performed by comparative molecular field analysis (CoMFA) and comparative molecular similarity indices (CoMSIA) methods to rationalize the structural requirements responsible for the inhibitory activity of these compounds. The global minimum energy conformer of the template molecule, the most active and pharmacokinetically stable molecule of the series, was obtained by systematic search and used to build structures of the molecules in the dataset. The best predictions for the CCR5-receptor were obtained with the CoMFA standard model (q (2) = 0.787, r (2) = 0.962) and CoMSIA model combined steric, electrostatic and hydrophobic fields (q (2) = 0.809, r (2) = 0.951). The predictive ability of CoMFA and CoMSIA were determined using a test set of 12 compounds giving predictive correlation coefficients of 0.855 and 0.83, respectively, indicating good predictive power. Further, the robustness of the model was verified by bootstrapping analysis. The contour maps produced by the CoMFA and CoMSIA models were used to identify the structural features relevant to the biological activity in this series. Based on the CoMFA and CoMSIA analysis, we have identified some key features in the series that are responsible for CCR5 antagonistic activity which may be used to design more potent 1-(3,3-diphenylpropyl)-piperidinyl derivatives and predict their activity prior to synthesis.

Mixed-Integer Linear Programming Algorithm for a Computational Protein Design Problem

The computational protein design problem or the side-chain positioning problem is a central part in computational methods for predicting protein structure and designing protein sequences. However, the computational protein design problem is NP-complete, and it is also NP-complete to find a reasonable approximate solution to this problem. Here, we present a critical finding that the network flow structure embedded in the integer linear programming formulation of the computational protein design problem makes it equivalent to a mixed-integer linear programming formulation with fewer binary variables. This novel formulation effectively reduces the combinatorial difficulty of the computational protein design problem, thereby allowing the sequence selection of the global minimum energy conformation for large proteins to become tractable by using the standard optimization algorithms. Our preliminary calculation results for 20 core redesigned proteins show that the mixed-integer linear programming algorithm with a validated physical model is faster than its integer linear programming counterpart by up to 3 times. More importantly, the specific mathematical structure underlying the mixed-integer linear programming formulation paves the way for developing even faster combinatorial searching strategies by using stronger cutting planes for mixed-integer programming.

Molecular dynamics simulation of the aqueous solvation shell of cellulose and xanthate ester derivatives

AbstractMD simulations of a pentasaccharide having D‐glucopyranoside residues connected by (1→4)‐β glycosidic linkages, as a model of cellulose solvated in water, were carried out comparing the solvation of the hydroxyl group at C2 of the central ring of the pentamer and that of a single glucopyranose ring. MD simulations of 10 nsec were carried under NPT and periodic boundary conditions at 298 K and 1 atm. Explicit solvent (TIP3) and the force field CHARMM27 (modified for xanthate ester derivatives) were used in the molecular dynamics simulations. RDF calculations with respect to O2 of the central ring of the pentamer showed a well structured first solvation shell followed by secondary shells. When comparing the simulations of the pentamer to a single glucopyranose ring, it was observed that the solvation of O2 was lower for one repetitive unit, indicating that the pentamer had a stronger H‐bond structure of water around O2 due to the cooperative effect of the neighboring residues. When the O2 of the central ring of the pentamer was substituted by a p‐nitrobenzylxanthate moiety (pentXNB) there was a strong decrease in the hydration of the substituted O2 but the carbon and the sulfur of the thiocarbonyl group were clearly hydrated compared to the sulfur bridge. The global minimum energy conformation showed the p‐nitrobenzyl group folded over the neighboring glucose ring. However, the simulations showed that the XNB group oscillates over the pentamer in periods of ca. 3000 psec. Copyright © 2006 John Wiley & Sons, Ltd.

Understanding the antitumor activity of novel tricyclicpiperazinyl derivatives as farnesyltransferase inhibitors using CoMFA and CoMSIA

3D-QSAR studies of some tricyclicpiperazinyl derivatives as farnesyltransferase inhibitors were performed by comparative molecular field analysis (CoMFA) and comparative molecular similarity indices (CoMSIA) methods to rationalize the structural requirements responsible for the inhibitory activity of these compounds. The global minimum energy conformer of the template molecule 35, the most active and pharmacokinetically stable molecule of the series, was obtained by simulated annealing method and used to build structures of the molecules in the dataset. The CoMFA model obtained after the removal of outliers produced statistically significant results with cross-validated and conventional correlation coefficients of 0.550 and 0.969, respectively. The combination of steric, electrostatic, hydrogen bond acceptor and hydrophobic fields in CoMSIA gave the best results with cross-validated and conventional correlation coefficients of 0.611 and 0.986, respectively. The predictive ability of CoMFA and CoMSIA were determined using a test set of 24 tricyclicpiperazinyl derivatives giving predictive correlation coefficients of 0.543 and 0.663, respectively, indicating good predictive power. Further the robustness of the model was verified by bootstrapping analysis. Based on the CoMFA and CoMSIA analysis we have identified some key features in the tricyclicpiperazinyl series that are responsible for farnesyltransferase inhibitory activity that may be used to design more potent tricyclicpiperazinyl derivatives and predict their activity prior to synthesis.

Improved Pruning algorithms and Divide-and-Conquer strategies for Dead-End Elimination, with application to protein design

Structure-based protein redesign can help engineer proteins with desired novel function. Improving computational efficiency while still maintaining the accuracy of the design predictions has been a major goal for protein design algorithms. The combinatorial nature of protein design results both from allowing residue mutations and from the incorporation of protein side-chain flexibility. Under the assumption that a single conformation can model protein folding and binding, the goal of many algorithms is the identification of the Global Minimum Energy Conformation (GMEC). A dominant theorem for the identification of the GMEC is Dead-End Elimination (DEE). DEE-based algorithms have proven capable of eliminating the majority of candidate conformations, while guaranteeing that only rotamers not belonging to the GMEC are pruned. However, when the protein design process incorporates rotameric energy minimization, DEE is no longer provably-accurate. Hence, with energy minimization, the minimized-DEE (MinDEE) criterion must be used instead. In this paper, we present provably-accurate improvements to both the DEE and MinDEE criteria. We show that our novel enhancements result in a speedup of up to a factor of more than 1000 when applied in redesign for three different proteins: Gramicidin Synthetase A, plastocyanin, and protein G. Contact authors for source code.

Polymeric grape-seed procyanidins, but not monomeric catechins and oligomeric procyanidins, impair degranulation and membrane ruffling in RBL-2H3 cells

Grape-seed proanthocyanidins (GSPs) are catechin polymers that are predicted to form helices in their global minimum-energy conformation and to have a mean degree of polymerization of seven (mDP = 7). The highly polymerized GSP-H fraction (mDP = 10) was found to impair degranulation in RBL-2H3 cells after stimulation with an antigen (Ag) and treatment with the Ca-ATPase inhibitor thapsigargin (Tg). In addition, GSP-H affected actin cytoskeleton and inhibited membrane ruffling in these cells, resulting in the suppression of exocytosis. By contrast, monomeric epicatechin, the dimeric procyanidins PA-1, PA-2, and PB-2, and the oligomerized GSP-L (mDP = 3) had no effect on membrane ruffling and degranulation. These findings indicate that the molecular size and length of GSP-H are needed for the inhibition of membrane ruffling and degranulation in RBL-2H3 mast-cell lines.

A Novel Ensemble-Based Scoring and Search Algorithm for Protein Redesign and Its Application to Modify the Substrate Specificity of the Gramicidin Synthetase A Phenylalanine Adenylation Enzyme

Realization of novel molecular function requires the ability to alter molecular complex formation. Enzymatic function can be altered by changing enzyme-substrate interactions via modification of an enzyme's active site. A redesigned enzyme may either perform a novel reaction on its native substrates or its native reaction on novel substrates. A number of computational approaches have been developed to address the combinatorial nature of the protein redesign problem. These approaches typically search for the global minimum energy conformation among an exponential number of protein conformations. We present a novel algorithm for protein redesign, which combines a statistical mechanics-derived ensemble-based approach to computing the binding constant with the speed and completeness of a branch-and-bound pruning algorithm. In addition, we developed an efficient deterministic approximation algorithm, capable of approximating our scoring function to arbitrary precision. In practice, the approximation algorithm decreases the execution time of the mutation search by a factor of ten. To test our method, we examined the Phe-specific adenylation domain of the nonribosomal peptide synthetase gramicidin synthetase A (GrsA-PheA). Ensemble scoring, using a rotameric approximation to the partition functions of the bound and unbound states for GrsA-PheA, is first used to predict binding of the wildtype protein and a previously described mutant (selective for leucine), and second, to switch the enzyme specificity toward leucine, using two novel active site sequences computationally predicted by searching through the space of possible active site mutations. The top scoring in silico mutants were created in the wetlab and dissociation/binding constants were determined by fluorescence quenching. These tested mutations exhibit the desired change in specificity from Phe to Leu. Our ensemble-based algorithm, which flexibly models both protein and ligand using rotamer-based partition functions, has application in enzyme redesign, the prediction of protein-ligand binding, and computer-aided drug design.

Conformational restrictions in ligand binding to the human intestinal di-/tripeptide transporter: implications for design of hPEPT1 targeted prodrugs

The aim of the present study was to develop a computational method aiding the design of dipeptidomimetic pro-moieties targeting the human intestinal di-/tripeptide transporter hPEPT1. First, the conformation in which substrates bind to hPEPT1 (the bioactive conformation) was identified by conformational analysis and 2D dihedral driving analysis of 15 hPEPT1 substrates, which suggested that ψ 1 ∼ 165°, ω 1 ∼ 180°, and ϕ 2 ∼ 280° were descriptive of the bioactive conformation. Subsequently, the conformational energy required to change the peptide backbone conformation (Δ E bbone) from the global energy minimum conformation to the identified bioactive conformation was calculated for 20 hPEPT1 targeted model prodrugs with known K i values. Quantitatively, an inverse linear relationship ( r 2 = 0.81, q 2 = 0.80) was obtained between Δ E bbone and log 1/ K i, showing that Δ E bbone contributes significantly to the experimentally observed affinity for hPEPT1 ligands. Qualitatively, the results revealed that compounds classified as high affinity ligands ( K i < 0.5 mM) all have a calculated Δ E bbone < 1 kcal/mol, whereas medium and low-affinity compounds (0.5 mM < K i < 15 mM) have Δ E bbone values in the range 1–3 kcal/mol. The findings also shed new light on the basis for the experimentally observed stereoselectivity of hPEPT1.

Conformational analysis: crystallographic, molecular mechanics and quantum chemical studies of C--H...O hydrogen bonding in the flexible bis(nosylate) derivative of catechol.

The single-crystal X-ray diffraction analysis of 2-[[(4-nitrophenoxy)sulfonyl]oxy]phenyl 4-nitrophenyl sulfate (4) reveals that an interesting intermolecular or extended structure (a one-dimensional hydrogen-bonded polymer) is formed because of pairs of intermolecular (aryl)C--H...O(nitro) hydrogen bonds between the C(2) symmetry monomer units. The axis of the hydrogen-bonded polymer runs co-linear with the [101] face diagonal of the monoclinic unit cell. Molecular mechanics calculations using a modified version of the MM+ force field and a random conformational search algorithm have been used to locate the important low-energy in vacuo conformations of (4). The MM-calculated conformation of (4) that most closely matches the X-ray structure lies some 26.5 kJ mol(-1) higher in energy than the global minimum-energy conformation, consistent with the notion that the crystallographically observed molecular architecture of (4) is a local energy minimum in the absence of its crystal lattice environment. Since the X-ray conformation of (4) was correctly calculated only when all of the neighbouring molecules in the crystal lattice were included in the simulation, hydrogen bonding and other non-bonded interactions in the crystal lattice clearly dictate the experimentally observed conformation of (4). Quantum chemical calculations (AM1 method) confirm the critical role played by the intermolecular (aryl)C--H...O(nitro) hydrogen bonds in controlling the crystallographically observed conformation of (4) and show that self-recognition in this system by hydrogen bonding is favoured on electrostatic grounds. Collectively, the molecular simulations suggest that because the lowest-energy molecular conformation of (4) does not permit the formation of an extended hydrogen-bonded 'supramolecular' structure, it is not the preferred conformation in the crystalline solid state.

Preprocessing of rotamers for protein design calculations.

We have developed a process that significantly reduces the number of rotamers in computational protein design calculations. This process, which we call Vegas, results in dramatic computational performance increases when used with algorithms based on the dead-end elimination (DEE) theorem. Vegas estimates the energy of each rotamer at each position by fixing each rotamer in turn and utilizing various search algorithms to optimize the remaining positions. Algorithms used for this context specific optimization can include Monte Carlo, self-consistent mean field, and the evaluation of an expression that generates a lower bound energy for the fixed rotamer. Rotamers with energies above a user-defined cutoff value are eliminated. We found that using Vegas to preprocess rotamers significantly reduced the calculation time of subsequent DEE-based algorithms while retaining the global minimum energy conformation. For a full boundary design of a 51 amino acid fragment of engrailed homeodomain, the total calculation time was reduced by 12-fold.