Hierarchy of simulation models in predicting molecular recognition mechanisms from the binding energy landscapes: structural analysis of the peptide complexes with SH2 domains.

Computer simulations using the simplified energy function and simulated tempering dynamics have accurately determined the native structure of the pYVPML, SVLpYTAVQPNE, and SPGEpYVNIEF peptides in the complexes with SH2 domains. Structural and equilibrium aspects of the peptide binding with SH2 domains have been studied by generating temperature-dependent binding free energy landscapes. Once some native peptide-SH2 domain contacts are constrained, the underlying binding free energy profile has the funnel-like shape that leads to a rapid and consistent acquisition of the native structure. The dominant native topology of the peptide-SH2 domain complexes represents an extended peptide conformation with strong specific interactions in the phosphotyrosine pocket and hydrophobic interactions of the peptide residues C-terminal to the pTyr group. The topological features of the peptide-protein interface are primarily determined by the thermodynamically stable phosphotyrosyl group. A diversity of structurally different binding orientations has been observed for the amino-terminal residues to the phosphotyrosine. The dominant native topology for the peptide residues carboxy-terminal to the phosphotyrosine is tolerant to flexibility in this region of the peptide-SH2 domain interface observed in equilibrium simulations. The energy landscape analysis has revealed a broad, entropically favorable topology of the native binding mode for the bound peptides, which is robust to structural perturbations. This could provide an additional positive mechanism underlying tolerance of the SH2 domains to hydrophobic conservative substitutions in the peptide specificity region.

Deciphering common failures in molecular docking of ligand-protein complexes.

Common failures in predicting crystal structures of ligand-protein complexes are investigated for three ligand-protein systems by a combined thermodynamic and kinetic analysis of the binding energy landscapes. Misdocked predictions in ligand-protein docking are classified as 'soft' and 'hard' failures. While a soft failure arises when the search algorithm is unable to find the global energy minimum corresponding to the crystal structure, a hard failure results from a flaw of the energy function to qualify the crystal structure as the predicted lowest energy conformation in docking simulations. We find that neither the determination of a single structure with the lowest energy nor finding the most common binding mode is sufficient to predict crystal structures of the complexes, which belong to the category of hard failures. In a proposed hierarchical approach, structural similarity clustering of the conformations, generated from equilibrium simulations with the simplified energy function, is followed by energy refinement with the AMBER force field. This protocol, that involves a hierarchy of energy functions, resolves some common failures in ligand-protein docking and detects crystallographic binding modes that were not found during docking simulations.

Towards understanding the mechanisms of molecular recognition by computer simulations of ligand-protein interactions.

The thermodynamic and kinetic aspects of molecular recognition for the methotrexate (MTX)-dihydrofolate reductase (DHFR) ligand-protein system are investigated by the binding energy landscape approach. The impact of 'hot' and 'cold' errors in ligand mutations on the thermodynamic stability of the native MTX-DHFR complex is analyzed, and relationships between the molecular recognition mechanism and the degree of ligand optimization are discussed. The nature and relative stability of intermediates and thermodynamic phases on the ligand-protein association pathway are studied, providing new insights into connections between protein folding and molecular recognition mechanisms, and cooperativity of ligand-protein binding. The results of kinetic docking simulations are rationalized based on the thermodynamic properties determined from equilibrium simulations and the shape of the underlying binding energy landscape. We show how evolutionary ligand selection for a receptor active site can produce well-optimized ligand-protein systems such as MTX-DHFR complex with the thermodynamically stable native structure and a direct transition mechanism of binding from unbound conformations to the unique native structure.

Thermodynamics and kinetics of ligand-protein binding studied with the weighted histogram analysis method and simulated annealing.

The thermodynamics of ligand-protein molecular recognition is investigated by the energy landscape approach for two systems: methotrexate(MTX)--dihydrofolate reductase(DHFR) and biotin-streptavidin. The temperature-dependent binding free energy profile is determined using the weighted histogram analysis method. Two different force fields are employed in this study: a simplified model of ligand-protein interactions and the AMBER force field with a soft core smoothing component, used to soften the repulsive part of the potential. The results of multiple docking simulations are rationalized from the shape of the binding free energy profile that characterizes the thermodynamics of the binding process.

Species dependence of enzyme-substrate encounter rates for triose phosphate isomerases.

Triose phosphate isomerase (TIM) is a diffusion-controlled enzyme whose rate is limited by the diffusional encounter of the negatively charged substrate glyceraldehyde 3-phosphate (GAP) with the homodimeric enzyme's active sites. Translational and orientational steering of GAP toward the active sites by the electrostatic field of chicken muscle TIM has been observed in previous Brownian dynamics (BD) simulations. Here we report simulations of the association of GAP with TIMs from four species with net charges at pH 7 varying from -12e to +12e. Computed second-order rate constants are in good agreement with experimental data. The BD simulations and computation of average Boltzmann factors of substrate-protein interaction energies show that the protein electrostatic potential enhances the rates for all the enzymes. There is much less variation in the computed rates than might be expected on the basis of the net charges. Comparison of the electrostatic potentials by means of similarity indices shows that this is due to conservation of the local electrostatic potentials around the active sites which are the primary determinants of electrostatic steering of the substrate.

Combined conformational search and finite-difference Poisson-Boltzmann approach for flexible docking. Application to an operator mutation in the lambda repressor-operator complex.

The N-terminal domain of the phage lambda repressor binds as a dimer to its palindromic DNA operator sequence. In addition to a helix-turn-helix DNA recognition motif, the first six amino acids of the phage lambda repressor form a flexible peptide segment which wraps around DNA. Site-directed mutagenesis studies have shown that amino acid replacements or partial removal of the arm structure, or changes in the DNA sequence contacting the N-terminal arm, can lower the repressor-operator binding affinity by several orders of magnitude. The finite-difference Poisson-Boltzmann approach in combination with a conformational search procedure was used to study energetic contributions of the lambda arm to repressor-operator recognition based on the high resolution X-ray structure. It allows for the local relaxation of the structure upon changing the DNA sequence in the lambda arm binding region. A simplified potential energy function including torsional, truncated Lennard-Jones and approximate electrostatic terms is used in the initial step to screen out energetically unfavorable structures. The electrostatic energy of selected conformations is subsequently calculated more accurately using the finite-difference Poisson-Boltzmann approach. The method was applied to study the effect of a C-->T mutation at position 6 of the consensus half-site of the operator. This base-pair contacts Lys4 which is part of the arm segment. Keeping only the Lys4 side-chain mobile and with the wild-type DNA operator sequence, several conformations close to the X-ray structure were identified as those with lowest energy. In the case of the DNA mutation, lowest energy conformations differed significantly from those selected for the wild-type sequence. These initial calculations indicate that the approach might be a useful tool to estimate conformational and energetic effects upon mutagenesis of protein-DNA complexes.

Simulation of enzyme-substrate encounter with gated active sites.

We describe a brownian dynamics simulation method that allows investigation of the effects of receptor flexibility on ligand binding rates. The method is applied to the encounter of substrate, glyceraldehyde 3-phosphate, with triose phosphate isomerase, a diffusion-controlled enzyme with flexible peptide loops at its active sites. The simulations show that while the electrostatic field surrounding the enzyme steers the substrate into its active sites, the flexible loops appear to have little influence on the substrate binding rate. The dynamics of the loops may therefore have been optimized during evolution to minimize their interference with the substrate's access to the active sites. The calculated and experimental rate constants are in good agreement.

Gating of the active site of triose phosphate isomerase: Brownian dynamics simulations of flexible peptide loops in the enzyme.

The enzyme triose phosphate isomerase has flexible peptide loops at its active sites. The loops close over these sites upon substrate binding, suggesting that the dynamics of the loops could be of mechanistic and kinetic importance. To investigate these issues, the loop motions in the dimeric enzyme were simulated by Brownian dynamics. The two loops, one on each monomer, were represented by linear chains of appropriately parameterized spheres, each sphere corresponding to an amino acid residue. The loops moved in the electrostatic field of the rest of the enzyme, which was held rigid in its crystallographically observed conformation. In the absence of substrate, the loops exhibited gating of the active site with a period of about 1 ns and occupied "closed" conformations for about half of the time. As the period of gating is much shorter than the enzyme-substrate relaxation time, the motion of the loops does not reduce the rate constant for the approach of substrate from its simple diffusion-controlled value. This suggests that the flexible loops may have evolved to create the appropriate environment for catalysis while, at the same time, minimizing the kinetic penalty for gating the active site.

Poisson-Boltzmann analysis of the lambda repressor-operator interaction.

A theoretical study of the ion atmosphere contribution to the binding free energy of the lambda repressor-operator complex is presented. The finite-difference form of the Poisson-Boltzmann equation was solved to calculate the electrostatic interaction energy of the amino-terminal domain of the lambda repressor with a 9 or 45 base pair oligonucleotide. Calculations were performed at various distances between repressor and operator as well as at different salt concentrations to determine ion atmosphere contributions to the total electrostatic interaction. Details in the distribution of charges on DNA and protein atoms had a strong influence on the calculated total interaction energies. In contrast, the calculated salt contributions are relatively insensitive to changes in the details of the charge distribution. The results indicate that the ion atmosphere contribution favors association at all protein-DNA distances studied. The theoretical number of ions released upon repressor-operator binding appears to be in reasonable agreement with experimental data.