An integrated mathematical model of thrombin-, histamine-and VEGF-mediated signalling in endothelial permeability.

BACKGROUND: Endothelial permeability is involved in injury, inflammation, diabetes and cancer. It is partly regulated by the thrombin-, histamine-, and VEGF-mediated myosin-light-chain (MLC) activation pathways. While these pathways have been investigated, questions such as temporal effects and the dynamics of multi-mediator regulation remain to be fully studied. Mathematical modeling of these pathways facilitates such studies. Based on the published ordinary differential equation models of the pathway components, we developed an integrated model of thrombin-, histamine-, and VEGF-mediated MLC activation pathways. RESULTS: Our model was validated against experimental data for calcium release and thrombin-, histamine-, and VEGF-mediated MLC activation. The simulated effects of PAR-1, Rho GTPase, ROCK, VEGF and VEGFR2 over-expression on MLC activation, and the collective modulation by thrombin and histamine are consistent with experimental findings. Our model was used to predict enhanced MLC activation by CPI-17 over-expression and by synergistic action of thrombin and VEGF at low mediator levels. These may have impact in endothelial permeability and metastasis in cancer patients with blood coagulation. CONCLUSION: Our model was validated against a number of experimental findings and the observed synergistic effects of low concentrations of thrombin and histamine in mediating the activation of MLC. It can be used to predict the effects of altered pathway components, collective actions of multiple mediators and the potential impact to various diseases. Similar to the published models of other pathways, our model can potentially be used to identify important disease genes through sensitivity analysis of signalling components.

CHARMM: the biomolecular simulation program.

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

A "Reverse-Schur" Approach to Optimization With Linear PDE Constraints: Application to Biomolecule Analysis and Design.

We present a partial-differential-equation (PDE)-constrained approach for optimizing a molecule's electrostatic interactions with a target molecule. The approach, which we call reverse-Schur co-optimization, can be more than two orders of magnitude faster than the traditional approach to electrostatic optimization. The efficiency of the co-optimization approach may enhance the value of electrostatic optimization for ligand-design efforts-in such projects, it is often desirable to screen many candidate ligands for their viability, and the optimization of electrostatic interactions can improve ligand binding affinity and specificity. The theoretical basis for electrostatic optimization derives from linear-response theory, most commonly continuum models, and simple assumptions about molecular binding processes. Although the theory has been used successfully to study a wide variety of molecular binding events, its implications have not yet been fully explored, in part due to the computational expense associated with the optimization. The co-optimization algorithm achieves improved performance by solving the optimization and electrostatic simulation problems simultaneously, and is applicable to both unconstrained and constrained optimization problems. Reverse-Schur co-optimization resembles other well-known techniques for solving optimization problems with PDE constraints. Model problems as well as realistic examples validate the reverse-Schur method, and demonstrate that our technique and alternative PDE-constrained methods scale very favorably compared to the standard approach. Regularization, which ordinarily requires an explicit representation of the objective function, can be included using an approximate Hessian calculated using the new BIBEE/P (boundary-integral-based electrostatics estimation by preconditioning) method.

Optimal linearized Poisson-Boltzmann theory applied to the simulation of flexible polyelectrolytes in solution.

Optimal linearized Poisson-Boltzmann (OLPB) theory is applied to the simulation of flexible polyelectrolytes in solution. As previously demonstrated in the contexts of the cell model [H. H. von Grunberg, R. van Roij, and G. Klein, Europhys. Lett. 55, 580 (2001)] and a particle-based model [B. Beresfordsmith, D. Y. C. Chan, and D. J. Mitchell, J. Colloid Interface Sci. 105, 216 (1985)] of charged colloids, OLPB theory is applicable to thermodynamic states at which conventional, Debye-Huckel (DH) linearization of the Poisson-Boltzmann equation is rendered invalid by violation of the condition that the electrostatic coupling energy of a mobile ion be much smaller than its thermal energy throughout space, |nu(alpha)e psi(r)|<

Substantial energetic improvement with minimal structural perturbation in a high affinity mutant antibody.

Here, we compare an antibody with the highest known engineered affinity (K(d)=270 fM) to its high affinity wild-type (K(d)=700 pM) through thermodynamic, kinetic, structural, and theoretical analyses. The 4M5.3 anti-fluorescein single chain antibody fragment (scFv) contains 14 mutations from the wild-type 4-4-20 scFv and has a 1800-fold increase in fluorescein-binding affinity. The dissociation rate is approximately 16,000 times slower in the mutant; however, this substantial improvement is offset somewhat by the association rate, which is ninefold slower in the mutant. Enthalpic contributions to binding were found by calorimetry to predominate in the differential binding free energy. The crystal structure of the 4M5.3 mutant complexed with antigen was solved to 1.5A resolution and compared with a previously solved structure of an antigen-bound 4-4-20 Fab fragment. Strikingly, the structural comparison shows little difference between the two scFv molecules (backbone RMSD of 0.6A), despite the large difference in affinity. Shape complementarity exhibits a small improvement between the variable light chain and variable heavy chain domains within the antibody, but no significant improvement in shape complementarity of the antibody with the antigen is observed in the mutant over the wild-type. Theoretical modeling calculations show electrostatic contributions to binding account for -1.2 kcal/mol to -3.5 kcal/mol of the binding free energy change, of which -1.1 kcal/mol is directly associated with the mutated residue side-chains. The electrostatic analysis reveals several mechanistic explanations for a portion of the improvement. Collectively, these data provide an example where very high binding affinity is achieved through the cumulative effect of many small structural alterations.

Side-chain repacking calculations for predicting structures and stabilities of heterodimeric coiled coils.

An important goal in biology is to predict from sequence data the high-resolution structures of proteins and the interactions that occur between them. In this paper, we describe a computational approach that can make these types of predictions for a series of coiled-coil dimers. Our method comprises a dual strategy that augments extensive conformational sampling with molecular mechanics minimization. To test the performance of the method, we designed six heterodimeric coiled coils with a range of stabilities and solved x-ray crystal structures for three of them. The stabilities and structures predicted by the calculations agree very well with experimental data: the average error in unfolding free energies is <1 kcal/mol, and nonhydrogen atoms in the predicted structures superimpose onto the experimental structures with rms deviations <0.7 A. We have also tested the method on a series of homodimers derived from vitellogenin-binding protein. The predicted relative stabilities of the homodimers show excellent agreement with previously published experimental measurements. A critical step in our procedure is to use energy minimization to relax side-chain geometries initially selected from a rotamer library. Our results show that computational methods can predict interaction specificities that are in good agreement with experimental data.

Optimization of binding electrostatics: charge complementarity in the barnase-barstar protein complex.

Theoretical and experimental studies have shown that the large desolvation penalty required for polar and charged groups frequently precludes their involvement in electrostatic interactions that contribute strongly to net stability in the folding or binding of proteins in aqueous solution near room temperature. We have previously developed a theoretical framework for computing optimized electrostatic interactions and illustrated use of the algorithm with simplified geometries. Given a receptor and model assumptions, the method computes the ligand-charge distribution that provides the most favorable balance of desolvation and interaction effects on binding. In this paper the method has been extended to treat complexes using actual molecular shapes. The barnase-barstar protein complex was investigated with barnase treated as a target receptor. The atomic point charges of barstar were varied to optimize the electrostatic binding free energy. Barnase and natural barstar form a tight complex (K(d) approximately 10(-14) M) with many charged and polar groups near the interface that make this a particularly relevant system for investigating the role of electrostatic effects on binding. The results show that sets of barstar charges (resulting from optimization with different constraints) can be found that give rise to relatively large predicted improvements in electrostatic binding free energy. Principles for enhancing the effect of electrostatic interactions in molecular binding in aqueous environments are discussed in light of the optima. Our findings suggest that, in general, the enhancements in electrostatic binding free energy resulting from modification of polar and charged groups can be substantial. Moreover, a recently proposed definition of electrostatic complementarity is shown to be a useful tool for examining binding interfaces. Finally, calculational results suggest that wild-type barstar is closer to being affinity optimized than is barnase for their mutual binding, consistent with the known roles of these proteins.

Altering dimerization specificity by changes in surface electrostatics.

Arc repressor forms a homodimer in which the subunits intertwine to create a single globular domain. To obtain Arc sequences that fold preferentially as heterodimers, variants with surface patches of excess positive or negative charge were designed. Several but not all oppositely charged sequence pairs showed preferential heterodimer formation. In the most successful design pair, alpha helix B of one subunit contained glutamic acids at positions 43, 46, 47, 48, and 50, whereas the other subunit contained lysines or arginines at these positions. A continuum electrostatic model captures many features of the experimental results and suggests that the most successful designs include elements of both positive and negative design.

Barstar is electrostatically optimized for tight binding to barnase.

We used a novel charge optimization technique to study the small ribonuclease barnase and to analyze its interaction with a natural tight binding inhibitor, the protein barstar. The approach uses a continuum model to explicitly determine the charge distributions that lead to the most favorable electrostatic contribution to binding when competing desolvation and interaction effects are included. Given its backbone fold, barstar is electrostatically optimized for tight binding to barnase when compared with mutants where residues have been substituted with one of the 20 common amino acids. Natural proteins thus appear to use optimization of electrostatic interactions as one strategy for achieving tight binding.

Rational modification of protein stability by the mutation of charged surface residues.

Continuum methods were used to calculate the electrostatic contributions of charged and polar side chains to the overall stability of a small 41-residue helical protein, the peripheral subunit-binding domain. The results of these calculations suggest several residues that are destabilizing, relative to hydrophobic isosteres. One position was chosen to test the results of these calculations. Arg8 is located on the surface of the protein in a region of positive electrostatic potential. The calculations suggest that Arg8 makes a significant, unfavorable electrostatic contribution to the overall stability. The experiments described in this paper represent the first direct experimental test of the theoretical methods, taking advantage of solid-phase peptide synthesis to incorporate approximately isosteric amino acid substitutions. Arg8 was replaced with norleucine (Nle), an amino acid that is hydrophobic and approximately isosteric, or with alpha-amino adipic acid (Aad), which is also approximately isosteric but oppositely charged. In this manner, it is possible to isolate electrostatic interactions from the effects of hydrophobic and van der Waals interactions. Both Arg8Nle and Arg8Aad are more thermostable than the wild-type sequence, testifying to the validity of the calculations. These replacements led to stability increases at 52.6 degrees C, the T(m) of the wild-type, of 0.86 and 1.08 kcal mol(-)(1), respectively. The stability of Arg8Nle is particularly interesting as a rare case in which replacement of a surface charge with a hydrophobic residue leads to an increase in the stability of the protein.

Electrostatic interactions in the GCN4 leucine zipper: substantial contributions arise from intramolecular interactions enhanced on binding.

The GCN4 leucine zipper is a peptide homodimer that has been the subject of a number of experimental and theoretical investigations into the determinants of affinity and specificity. Here, we utilize this model system to investigate electrostatic effects in protein binding using continuum calculations. A particularly novel feature of the computations made here is that they provide an interaction-by-interaction breakdown of the electrostatic contributions to the free energy of docking that includes changes in the interaction of each functional group with solvent and changes in interactions between all pairs of functional groups on binding. The results show that (1) electrostatic effects disfavor binding by roughly 15 kcal/mol due to desolvation effects that are incompletely compensated in the bound state, (2) while no groups strongly stabilize binding, the groups that are most destabilizing are charged and polar side chains at the interface that have been implicated in determining binding specificity, and (3) attractive intramolecular interactions (e.g., backbone hydrogen bonds) that are enhanced on binding due to reduced solvent screening in the bound state contribute significantly to affinity and are likely to be a general effect in other complexes. A comparison is made between the results obtained in an electrostatic analysis carried out calculationally and simulated results corresponding to idealized data from a scanning mutagenesis experiment. It is shown that scanning experiments provide incomplete information on interactions and, if overinterpreted, tend to overestimate the energetic effect of individual side chains that make attractive interactions. Finally, a comparison is made between the results available from a continuum electrostatic model and from a simpler surface-area dependent solvation model. In this case, although the simpler model neglects certain interactions, on average it performs rather well.

Charge optimization leads to favorable electrostatic binding free energy.

Variational optimization of molecular electrostatic charge distributions is a tool for the study of association reactions of molecules in solution. In principle, this method can be used in drug design and protein folding to analyze and improve molecular interactions and to provide electrostatic templates for molecular design. This optimization problem reduces to an inverse source problem in classical electrostatics, where the sources are determined by a combination of external and self-polarization potentials. In this paper, we show that the electrostatic portion of the free energy of association for electrostatically optimized molecules has an upper bound of zero in many situations of physical interest. That is, variational optimization provides a ligand-charge distribution that contributes favorably to the energetics of binding, even in a strongly polar medium. This stabilizing effect on association reactions is contrary to the usual role of electrostatics in aqueous complexes, in which desolvation effects generally dominate. We also show the existence and nonuniqueness of the variational solution and make a connection to the electrostatic image charge problem.

High-resolution protein design with backbone freedom.

Recent advances in computational techniques have allowed the design of precise side-chain packing in proteins with predetermined, naturally occurring backbone structures. Because these methods do not model protein main-chain flexibility, they lack the breadth to explore novel backbone conformations. Here the de novo design of a family of alpha-helical bundle proteins with a right-handed superhelical twist is described. In the design, the overall protein fold was specified by hydrophobic-polar residue patterning, whereas the bundle oligomerization state, detailed main-chain conformation, and interior side-chain rotamers were engineered by computational enumerations of packing in alternate backbone structures. Main-chain flexibility was incorporated through an algebraic parameterization of the backbone. The designed peptides form alpha-helical dimers, trimers, and tetramers in accord with the design goals. The crystal structure of the tetramer matches the designed structure in atomic detail.

Effects of salt bridges on protein structure and design.

Theoretical calculations (Hendsch ZS & Tidor B, 1994, Protein Sci 3:211-226) and experiments (Waldburger CD et al., 1995, Nat Struct Biol 2:122-128; Wimley WC et al., 1996, Proc Natl Acad Sci USA 93:2985-2990) suggest that hydrophobic interactions are more stabilizing than salt bridges in protein folding. The lack of apparent stability benefit for many salt bridges requires an alternative explanation for their occurrence within proteins. To examine the effect of salt bridges on protein structure and stability in more detail, we have developed an energy function for simple cubic lattice polymers based on continuum electrostatic calculations of a representative selection of salt bridges found in known protein crystal structures. There are only three types of residues in the model, with charges of -1, 0, or + 1. We have exhaustively enumerated conformational space and significant regions of sequence space for three-dimensional cubic lattice polymers of length 16. The results demonstrate that, while the more highly charged sequences are less stable, the loss of stability is accompanied by a substantial reduction in the degeneracy of the lowest-energy state. Moreover, the reduction in degeneracy is greater due to charges that pair than for lone charges that remain relatively exposed to solvent. We have also explored and illustrated the use of ion-pairing strategies for rational structural design using model lattice studies.

AmbiPack: a systematic algorithm for packing of macromolecular structures with ambiguous distance constraints.

The determination of structures of multimers presents interesting new challenges. The structure(s) of the individual monomers must be found and the transformations to produce the packing interfaces must be described. A substantial difficulty results from ambiguities in assigning intermolecular distance measurements (from nuclear magnetic resonance, for example) to particular intermolecular interfaces in the structure. Here we present a rapid and efficient method to solve the packing and the assignment problems simultaneously given rigid monomer structures and (potentially ambiguous) intermolecular distance measurements. A promising application of this algorithm is to couple it with a monomer searching protocol such that each monomer structure consistent with intramolecular constraints can be subsequently input to the current algorithm to check whether it is consistent with (potentially ambiguous) intermolecular constraints. The algorithm AmbiPack uses a hierarchical division of the search space and the branch-and-bound algorithm to eliminate infeasible regions of the space. Local search methods are then focused on the remaining space. The algorithm generally runs faster as more constraints are included because more regions of the search space can be eliminated. This is not the case for other methods, for which additional constraints increase the complexity of the search space. The algorithm presented is guaranteed to find all solutions to a predetermined resolution. This resolution can be chosen arbitrarily to produce outputs at various level of detail. Illustrative applications are presented for the P22 tailspike protein (a trimer) and portions of beta-amyloid (an ordered aggregate).

Computation of electrostatic complements to proteins: a case of charge stabilized binding.

Recent evidence suggests that the net effect of electrostatics is generally to destabilize protein binding due to large desolvation penalties. A novel method for computing ligand-charge distributions that optimize the tradeoff between ligand desolvation penalty and favorable interactions with a binding site has been applied to a model for barnase. The result is a ligand-charge distribution with a favorable electrostatic contribution to binding due, in part, to ligand point charges whose direct interaction with the binding site is unfavorable, but which make strong intra-molecular interactions that are uncloaked on binding and thus act to lessen the ligand desolvation penalty.

Molecular-modeling calculations of enzymatic enantioselectivity taking hydration into account.

A new molecular-modeling methodology has been applied to explain enzymatic enantioselectivity in water. This methodology, which combines vacuum molecular mechanics and the continuum solvation method, should provide a more realistic view of the solvent-enzyme and solvent-substrate interactions than the heretofore used approaches involving the vacuum molecular mechanics only. The methodology described herein has been validated using the experimental data on alpha-chymotrypsin's enantioselectivity in the hydrolysis of four chiral substrates. The reasons why the vacuum molecular mechanics, although not taking hydration into account, still in most cases provide a satisfactory approximation of reality are discussed.

Protein stabilization by removal of unsatisfied polar groups: computational approaches and experimental tests.

The role of polar and charged side chains in partially buried protein environments has been probed in a variant of Arc repressor (MYL) in which hydrophobic interactions between Met31, Tyr36, and Leu40 replace the wild-type salt-bridge interactions between Arg31, Glu36, and Arg40. In the absence of this salt-bridge triad, three additional side chains were identified by continuum electrostatic calculations as incurring larger desolvation penalties during folding than were recovered in favorable electrostatic interactions in the folded state. These side chains (Asn29, Ser44, and Glu48) were mutated singly and collectively to alanine in the MYL background, and the thermodynamic stabilities of the resulting mutant proteins were found to be increased by 0.1 to 1.3 kcal/mol of dimer. All of the mutants displayed cooperative thermal melts and appeared to have well-packed hydrophobic cores by near-UV circular dichroism spectroscopy, indicating that conformational specificity is maintained. The Arc variant (MYL-NA29/SA44/EA48) in which the entire six-residue polar network is replaced by nonpolar groups is 5.1 kcal/mol of dimer more stable than wild type, indicating that the strategy of replacing buried or partially buried charged and polar side chains with hydrophobic residues can lead to substantial stabilization.