Brownian dynamics simulations of molecular recognition in an antibody-antigen system.

The crystal structure for an antibody-antigen system, that of the anti-hen egg lysozyme monoclonal antibody HyHEL-5 complexed to lysozyme, is used as the starting point for computer simulations of diffusional encounters between the two proteins. The investigation consists of two parts: first, the linearized Poisson-Boltzmann equation is solved to determine the long-range electrostatic forces between antibody and antigen, and then, the relative motion as influenced by these forces is modeled within Brownian motion theory. The effects of various point mutations on the calculated reaction rate are considered. It is found that charged residues close to the binding site exert the greatest influence in steering the proteins into a configuration favorable for their binding, while more distant mutations are qualitatively described by the Smoluchowski model for the mutual diffusion of two uniformly charged spheres. The antibody residues involved in forming salt links with the lysozyme, Glu-H35 and Glu-H50, appear to be particularly important in electrostatic steering, as neutralization of both of them yields reaction rates that are two to three orders of magnitude below those of wild-type rates. The relative rates obtained from the simulations can be tested through kinetic measurements on mutant protein complexes. Kinetically efficient partners can also be designed and constructed through directed mutagenesis.

Role of electrostatics in antibody-antigen association: anti-hen egg lysozyme/lysozyme complex (HyHEL-5/HEL).

A recently developed multigrid-based Newton method for solving the nonlinear Poisson-Boltzmann equation is applied in an investigation of molecular recognition in the system consisting of the monoclonal antibody HyHEL-5 and hen egg lysozyme. The electrostatic free energy of binding is calculated for the wild-type complex and various mutants in which electrostatic interactions between the two proteins are altered. Mutations which neutralize or reverse the charge of any of the residues involved in salt-links in the native system always yield decreased binding affinities. The stability of the complex can be enhanced through the formation of a new salt-bridge obtained by mutating an asparagine residue of the lysozyme to the negatively-charged aspartate. Ionic strength effects are also examined and found to be significant in some cases.

Protein electrostatics: rapid multigrid-based Newton algorithm for solution of the full nonlinear Poisson-Boltzmann equation.

A new method for solving the full nonlinear Poisson-Boltzmann equation is outlined. This method is robust and efficient, and uses a combination of the multigrid and inexact Newton algorithms. The novelty of this approach lies in the appropriate combination of the two methods, neither of which by themselves are capable of solving the nonlinear problem accurately. Features of the Poisson-Boltzmann equation are fully exploited by each component of the hybrid algorithm to provide robustness and speed. The advantages inherent in this method increase with the size of the problem. The efficacy of the method is illustrated by calculations of the electrostatic potential around the enzyme Superoxide Dismutase. The CPU time required to solve the full nonlinear equation is less than half that needed for a conjugate gradient solution of the corresponding linearized Poisson-Boltzmann equation. The solutions reveal that the field around the active sites is significantly reduced as compared to that obtained by solving the corresponding linearized Poisson-Boltzmann equation. This new method for the nonlinear Poisson-Boltzmann equation will enable fast and accurate solutions of large protein electrostatics problems.

Toward an understanding of the role of DNA adduct conformation in defining mutagenic mechanism based on studies of the major adduct (formed at N(2)-dG) of the potent environmental carcinogen, benzo[a]pyrene.

The process of carcinogenesis is initiated by mutagenesis, which often involves replication past damaged DNA. One question - what exactly is a DNA polymerase seeing when it incorrectly copies a damaged DNA base (e.g., inserting dATP opposite a dG adduct)? - has not been answered in any case. Herein, we reflect on this question, principally by considering the mutagenicity of one activated form of benzo[a]pyrene, (+)-anti-B[a]PDE, and its major adduct [+ta]-B[a]P-N(2)-dG. In previous work, [+ta]-B[a]P-N(2)-dG was shown to be capable of inducing>95% G-->T mutations in one sequence context (5'-TGC), and approximately 95% G-->A mutations in another (5'-AGA). This raises the question - how can a single chemical entity induce different mutations depending upon DNA sequence context? Our current working hypothesis is that adduct conformational complexity causes adduct mutational complexity, where DNA sequence context can affect the former, thereby influencing the latter. Evidence supporting this hypothesis was discussed recently (Seo et al., Mutation Res. [in press]). Assuming this hypothesis is correct (at least in some cases), one goal is to consider what these mutagenic conformations might be. Based on molecular modeling studies, 16 possible conformations for [+ta]-B[a]P-N(2)-dG are proposed. A correlation between molecular modeling and mutagenesis work suggests a hypothesis (Hypothesis 3): a base displaced conformation with the dG moiety of the adduct in the major vs. minor groove gives G-->T vs. G-->A mutations, respectively. (Hypothesis 4, which is a generalized version of Hypothesis 3, is also proposed, and can potentially rationalize aspects of both [+ta]-B[a]P-N(2)-dG and AP-site mutagenesis, as well as the so-called "A-rule".) Finally, there is a discussion of how conformational complexity might explain some unusual mutagenesis results that suggest [+ta]-B[a]P-N(2)-dG can become trapped in different conformations, and why we think it makes sense to interpret adduct mutagenesis results by modeling ds-DNA (at least in some cases), even though the mutagenic event must occur at a ss/ds-DNA junction in the presence of a DNA polymerase.

Molecular modeling of the conformational complexity of (+)-anti-B[a]PDE-adducted DNA using simulated annealing.

Benzo[a]pyrene (B[a]P), a potent mutagen/carcinogen, reacts with DNA following metabolism to its corresponding (+)-anti-7,8-diol-9,10-epoxide [(+)-anti-B[a]PDE], giving a major adduct (+)-trans-anti-B[a]P-N2-dG. Evidence suggests that this adduct is responsible for most of the different kinds of mutations (e.g. G-->T, G-->A, etc.) induced by (+)-anti-B[a]PDE, raising the question of how can a single adduct cause many different kinds of mutations? One hypothesis is that different mutations are induced depending upon the conformation of this adduct when bypassed during DNA replication. If true, then it becomes imperative to explore different reasonable conformations for this adduct. Herein a simulated annealing protocol is employed to study the conformation of (+)-trans-anti-B[a]P-N2-dG with the B[a]P moiety in the minor groove and pointing toward the base on its 5'-side in a 5'-CGC-3' sequence context in duplex DNA. This conformation and sequence were chosen because there is a structure derived from NMR constraints for comparison. A four step procedure is followed: the adduct is docked in canonical B-DNA, after which the structure is subjected to an initial conjugate gradient minimization, followed by simulated annealing and a final conjugate gradient minimization. The quality and final energy of structures is assessed as a function of changes in six parameters, including the length of the DNA helix, the initial annealing temperature (T0), the annealing time (t), the molecular dynamics time step (tau) and two other parameters. While there is no single set of optimum parameters, reasonable low energy structures were obtained using the values t approximately 40 ps (or longer), T0 approximately 750 K and tau approximately 1.0 fs with a helix length of 7 bp. The structures that emerge all retain the basic features of the input structure, being B-DNA-like with the B[a]P moiety in the minor groove pointing toward the base on the 5'-side. However, within this broad category there are at least six subclasses of structures, of which four have lowest energy members that differ by < approximately 5 kcal/mol. The fact that a variety of distinct but related structures emerge from a single starting structure as this parameter set is varied suggests that the use of a large but manageable number of simulated annealing runs should be considered in the search for a cohort of related structures. This is especially important given that this breadth of potentially relevant structures of approximately the same energy may indeed be relevant to the hypothesis that different mutations arise from a single adduct in different conformations.

Molecular modeling of the major adduct of (+)-anti-B[a]PDE (N2-dG) in the eight conformations and the five DNA sequences most relevant to base substitution mutagenesis.

The potent mutagen/carcinogen 7R,8S-dihydroxy-9S, 10R-epoxy-7,8,9,10-tetrahydrobenzo[a]pyrene [(+)-anti-B[a]PDE], which is the activated form of benzo[a]pyrene (B[a]P), is able to induce different kinds of mutations (G-->T, G-->A, etc.). One hypothesis for this is that different mutations are induced depending upon the conformation of its major adduct ([+ta]-B[a]P-N2-dG) when bypassed during DNA replication. Based on molecular modeling, there appear to be at least 16 potential conformations that the major adduct [+ta]-B[a]P-N2-dG can adopt in dsDNA. Regarding base substitution mutagenesis, eight conformations are most likely to be relevant. In two conformations the dG moiety of the adduct is base paired with its complementary dC and the B[a]P moiety is in the minor groove. In two others the dG moiety of the adduct is in the Hoogsteen orientation and the B[a]P moiety is in the major groove. There are four base displaced structures in which the B[a]P moiety of the adduct is stacked with the surrounding base pairs, two with dG in the major groove and two with dG in the minor groove. Using a simulated annealing protocol, these eight conformations were evaluated in five different DNA sequence contexts (5'-TGC-3', 5'-CGT-3', 5'-AGA-3', 5'-CGG-3' and 5'-GGG-3'); the latter were chosen because they may be particularly revealing about mutagenic mechanism based on studies with [+ta]-B[a]P-N2-dG and (+)-anti-B[a]PDE. For each conformation and each sequence context, 25 simulated annealing runs were conducted by systematically varying several parameters (such as the initial annealing temperature) based on a protocol established recently. The goal of this work was to exclude conformations that are clearly inferior. Three conformations are virtually always high in energy, including the two Hoogsteen oriented species and one of the base displaced species with dG in the major groove. Remarkably, the remaining five conformations are often quite close in energy and are deemed most likely to be relevant to mutagenesis (see accompanying paper).

Treatment of electrostatic effects in proteins: multigrid-based Newton iterative method for solution of the full nonlinear Poisson-Boltzmann equation.

The nonlinear Poisson-Boltzmann equation (NPBE) provides a continuum description of the electrostatic field in an ionic medium around a macromolecule. Here, a novel approach to the solution of the full NPBE is developed. This robust and efficient algorithm combines multilevel techniques with a damped inexact Newton's method. The CPU time required for solution of the full NPBE, which is less than that for standard single-grid approaches in solving the corresponding linearized equation, is proportional to the number of unknowns enabling applications to very large macromolecular systems. Convergence of the method is demonstrated for a variety of protein systems. Comparison of the solutions to the linearized Poisson-Boltzmann equation shows that the damping of the electrostatic field around the charge is increased and that the potential scales logarithmically with charge. The inclusion of the full nonlinearity thus reduces the impact of highly charged residues on protein surfaces and provides a more realistic representation of electrostatic effects. This is demonstrated through calculation of potential around the active site regions of the 1,266-residue tryptophan synthase dimer and in the computation of rate constants from Brownian dynamics calculations in the superoxide dismutase-superoxide and antibody-antigen systems.

Computer modeling of electrostatic steering and orientational effects in antibody-antigen association.

Brownian dynamics simulations are performed to investigate the role of long-range electrostatic forces in the association of the monoclonal antibody HyHEL-5 with hen egg lysozyme. The electrostatic field of the antibody is obtained from a solution of the nonlinear Poisson-Boltzmann using the x-ray crystal coordinates of this protein. The lysozyme is represented as an asymmetric dumbell consisting of two spheres of unequal size, an arrangement that allows for the modeling of the orientational requirements for docking. Calculations are done with the wild-type antibody and several point mutants at different ionic strengths. Changes in the charge distribution of the lysozyme are also considered. Results are compared with experiment and a simpler model in which the lysozyme is approximately by a single charged sphere.

A hypothesis for what conformation of the major adduct of (+)-anti-B[a]PDE (N2-dG) causes G-->T versus G-->A mutations based upon a correlation between mutagenesis and molecular modeling results.

Molecular modeling (simulated annealing) was used to study the conformations in dsDNA of [+ta]-B[a]P-N2-dG (R.E. Kozack and E.L.Loechler, accompanying paper), which is the major benzo[a]pyrene (B[a]P) adduct. Sixteen classes of conformations were identified, and are analyzed herein vis-a-vis the two most prominent B[a]P mutations, G-->T and G-->A base substitutions. Eight conformations seem more relevant to frameshift mutagenesis, so they are excluded, leaving eight conformations as follows. Two conformations (BPmi5 and BPmi3) retain Watson-Crick G:C base pairing having the B[a]P moiety of the adduct in the minor groove. Two conformations (BPma5 and BPma3) have the Hoogsteen orientation with B[a]P in the major groove. Four conformations are base displaced and have B[a]P stacked in the helix with the dG moiety of the adduct displaced into either the major groove (Gma5 and Gma3) or the minor groove (Gmi5 and Gmi3). Three of these eight conformations (BPma5, BPma3 and Gma3) are universally high in energy. The two conformations that retain G:C base pairing potential (BPmi5 and BPmi3) are likely to be non-mutagenic. Of the three remaining conformations, Gmi5 can be relatively low in energy, but is distorted. A correlation exists between the calculated energies for the remaining two base displaced conformations and mutagenesis for [+ta]-B[a]P-N2-dG, leading to the hypothesis that Gma5 is responsible for G-->T mutations and Gmi3 is responsible for G-->A mutations. Gma5 and Gmi3 resemble each other, except that dG is in the major and minor grooves, respectively. An incipient rationale for this hypothesis is discussed: DNA polymerase might be triggered to follow a different mutagenic pathway depending upon whether a non-informational lesion has bulk protruding into the major or minor groove. A pathway for interconversion between these eight conformations is also proposed and its implications are discussed; e.g. four steps are required to interconvert between Gma5 and Gmi3.