Mauro Lapelosa

Theory of binless multi-state free energy estimation with applications to protein-ligand binding

The weighted histogram analysis method (WHAM) is routinely used for computing free energies and expectations from multiple ensembles. Existing derivations of WHAM require observations to be discretized into a finite number of bins. Yet, WHAM formulas seem to hold even if the bin sizes are made arbitrarily small. The purpose of this article is to demonstrate both the validity and value of the multi-state Bennet acceptance ratio (MBAR) method seen as a binless extension of WHAM. We discuss two statistical arguments to derive the MBAR equations, in parallel to the self-consistency and maximum likelihood derivations already known for WHAM. We show that the binless method, like WHAM, can be used not only to estimate free energies and equilibrium expectations, but also to estimate equilibrium distributions. We also provide a number of useful results from the statistical literature, including the determination of MBAR estimators by minimization of a convex function. This leads to an approach to the computation of MBAR free energies by optimization algorithms, which can be more effective than existing algorithms. The advantages of MBAR are illustrated numerically for the calculation of absolute protein-ligand binding free energies by alchemical transformations with and without soft-core potentials. We show that binless statistical analysis can accurately treat sparsely distributed interaction energy samples as obtained from unmodified interaction potentials that cannot be properly analyzed using standard binning methods. This suggests that binless multi-state analysis of binding free energy simulations with unmodified potentials offers a straightforward alternative to the use of soft-core potentials for these alchemical transformations.

In silico vaccine design based on molecular simulations of rhinovirus chimeras presenting HIV-1 gp41 epitopes

A cluster of promising epitopes for the development of human immunodeficiency virus (HIV) vaccines is located in the membrane-proximal external region (MPER) of the gp41 subunit of the HIV envelope spike structure. The crystal structure of the peptide corresponding to the so-called ELDKWA epitope (HIV-1 HxB2 gp41 residues 662-668), in complex with the corresponding broadly neutralizing human monoclonal antibody 2F5, provides a target for structure-based vaccine design strategies aimed at finding macromolecular carriers that are able to present this MPER-derived epitope with optimal antigenic activity. To this end, a series of replica exchange molecular dynamics computer simulations was conducted to characterize the distributions of conformations of ELDKWA-based epitopes inserted into a rhinovirus carrier and to identify those with the highest fraction of conformations that are able to bind 2F5. The length, hydrophobic character, and precise site of insertion were found to be critical for achieving structural similarity to the target crystal structure. A construct with a high degree of complementarity to the corresponding determinant region of 2F5 was obtained. This construct was employed to build a high-resolution structural model of the complex between the 2F5 antibody and the chimeric human rhinovirus type 14:HIV-1 ELDKWA virus particle. Additional simulations, which were conducted to study the conformational propensities of the ELDKWA region in solution, confirm the hypothesis that the ELDKWA region of gp41 is highly flexible and capable of assuming helical conformations (as in the postfusion helical bundle structure) and beta-turn conformations (as in the complex with the 2F5 antibody). These results also suggest that the ELDKWA epitope can be involved in intramolecular--and likely intermolecular--hydrophobic interactions. This tendency offers an explanation for the observation that mutations decreasing the hydrophobic character of the MPER in many cases result in conformational changes that increase the affinity of this region for the 2F5 antibody.

Antigenic Characteristics of Rhinovirus Chimeras Designed in silico for En5hanced Presentation of HIV-1 gp41 Epitopes

The development of an effective AIDS vaccine remains the most promising long-term strategy to combat human immunodeficiency virus (HIV)/AIDS. Here, we report favorable antigenic characteristics of vaccine candidates isolated from a combinatorial library of human rhinoviruses displaying the ELDKWA epitope of the gp41 glycoprotein of HIV-1. The design principles of this library emerged from the application of molecular modeling calculations in conjunction with our knowledge of previously obtained ELDKWA-displaying chimeras, including knowledge of a chimera with one of the best 2F5-binding characteristics obtained to date. The molecular modeling calculations identified the energetic and structural factors affecting the ability of the epitope to assume conformations capable of fitting into the complementarity determining region of the ELDKWA-binding, broadly neutralizing human mAb 2F5. Individual viruses were isolated from the library following competitive immunoselection and were tested using ELISA and fluorescence quenching experiments. Dissociation constants obtained using both techniques revealed that some of the newly isolated chimeras bind 2F5 with greater affinity than previously identified chimeric rhinoviruses. Molecular dynamics simulations of two of these same chimeras confirmed that their HIV inserts were partially preorganized for binding, which is largely responsible for their corresponding gains in binding affinity. The study illustrates the utility of combining structure-based experiments with computational modeling approaches for improving the odds of selecting vaccine component designs with preferred antigenic characteristics. The results obtained also confirm the flexibility of HRV as a presentation vehicle for HIV epitopes and the potential of this platform for the development of vaccine components against AIDS.

Chimeric Rhinoviruses Displaying MPER Epitopes Elicit Anti-HIV Neutralizing Responses

Background The development of an effective AIDS vaccine has been a formidable task, but remains a critical necessity. The well conserved membrane-proximal external region (MPER) of the HIV-1 gp41 glycoprotein is one of the crucial targets for AIDS vaccine development, as it has the necessary attribute of being able to elicit antibodies capable of neutralizing diverse isolates of HIV. Methodology/Principle Findings Guided by X-ray crystallography, molecular modeling, combinatorial chemistry, and powerful selection techniques, we designed and produced six combinatorial libraries of chimeric human rhinoviruses (HRV) displaying the MPER epitopes corresponding to mAbs 2F5, 4E10, and/or Z13e1, connected to an immunogenic surface loop of HRV via linkers of varying lengths and sequences. Not all libraries led to viable chimeric viruses with the desired sequences, but the combinatorial approach allowed us to examine large numbers of MPER-displaying chimeras. Among the chimeras were five that elicited antibodies capable of significantly neutralizing HIV-1 pseudoviruses from at least three subtypes, in one case leading to neutralization of 10 pseudoviruses from all six subtypes tested. Conclusions Optimization of these chimeras or closely related chimeras could conceivably lead to useful components of an effective AIDS vaccine. While the MPER of HIV may not be immunodominant in natural infection by HIV-1, its presence in a vaccine cocktail could provide critical breadth of protection.

Molecular Simulations of the Pairwise Interaction of Monoclonal Antibodies

Molecular simulations are employed to compute the free energy of pairwise monoclonal antibodies (mAbs) association using a conformational sampling algorithm with a scoring function. The work reported here is aimed at investigating the mAb-mAb association driven by weak interactions with a computational method capable of predicting experimental observations of low binding affinity. The simulations are able to explore the free energy landscape. A steric interaction component, electrostatic interactions, and a nonpolar component of the free energy form the energy scoring function. Electrostatic interactions are calculated by solving the Poisson-Boltzmann equation. The nonpolar component is derived from the van der Waals interactions upon close contact of the protein surfaces. Two mAbs with similar IgG1 framework but with small sequence differences, mAb1 and mAb2, are considered for their different viscosity and propensity to form a weak interacting dimer. mAb1 presents favorable free energy of association at pH 6 with 15 mM of ion concentration reproducing experimental trends of high viscosity and dimer formation at high concentration. Free energy landscape and minimum free energy configurations of the dimer, as well as the second virial coefficient (B22) values are calculated. The energy distributions for mAb1 are obtained, and the most probable configurations are seen to be consistent with experimental measurements. In contrast, mAb2 shows an unfavorable average free energy at the same buffer conditions due to poor electrostatic complementarity, and reversible dimer configurations with favorable free energy are found to be unlikely. Finally, the simulations of the mAb association dynamics provide insights on the self-association responsible for bulk solution behavior and aggregation, which are important to the processing and the quality of biopharmaceuticals.

Molecular simulations of micellar aggregation of polysorbate 20 ester fractions and their interaction with N-phenyl-1-naphthylamine dye

Micellar aggregation behavior of polysorbate 20 (PS20) has generated significant interest because of the wide use of PS20 as a surfactant to minimize protein surface adsorption and mitigate protein aggregation. Thus, there is a need for better molecular understanding of what drives the biophysical behavior of PS20 in solution. We observe that a complex amphipathic PS20 molecule, which contains both hydrophobic tail and relatively large hydrophilic head, self-associates strongly within the course of a molecular dynamics simulation performed with a fully atomistic representation of the molecule and an explicit water solvent model. The in silico behavior is consistent with micellar models of PS20 in solution. The dynamics of this self-association is rather complex involving both internal reorganization of the molecule and diffusion to form stable micelle-like aggregates. The micellar aggregates of PS20 are long-lived and are formed by the balance between the large hydrophobic interactions associated with the aliphatic tail of PS20, and the steric repulsion of the hydrophilic sorbitan head structure. In the present work, molecular models of PS20 that represent naturally occurring PS20 fractions were produced and characterized in silico. The study investigated the monoester and diester fractions: PS20M, and PS20D. These fractions present differences in the strength of their hydrophobic effect, which influences the aggregation behavior. Adaptive biasing force (ABF) simulations were carried out with the PS20M and PS20D molecular constructs to calculate the free energy of their pairwise interaction. The free energy barrier for the dissociation is higher for PS20D compared with PS20M. The results show that hydrogen bonds can form when head groups are in close proximity, such as in the PS20 aggregate assembly, and the free energy of interaction can be used to predict the morphology of the micellar aggregate for the different PS20 fractions. We were also able to simulate PS20 in the presence of N-phenyl-1-naphthylamine (NPN) to study the solution behavior of the hydrophobic molecule and of the mechanism in which it is sequestered in the hydrophobic core of the PS20 micellar aggregate.

Free Energy of Binding and Mechanism of Interaction for the MEEVD-TPR2A Peptide–Protein Complex

The association between the MEEVD C-terminal peptide from the heat shock protein 90 (Hsp90) and tetratricopeptide repeat A (TPR2A) domain of the heat shock organizing protein (Hop) is a useful prototype to study the fundamental molecular details about the Hop-Hsp90 interaction. We study here the mechanism of binding/unbinding and compute the standard binding free energy and potential of mean force for the association of the MEEVD peptide to the TPR2A domain using the Adaptive Biasing Force (ABF) methodology. We observe conformational changes of the peptide and the protein receptor induced by binding. We measure the binding free energy of -8.4 kcal/mol, which is consistent with experimental estimates. The simulations achieve multiple unbinding and rebinding events along a consistent pathway connecting the binding site to solvent. The MEEVD peptide slowly dissociates disrupting the hydrogen bonds first, then tilting on the side while preserving the interaction with the side chain of residue Asp 5 of the peptide. After this initial displacement, the peptide completely dissociates and moves into the solvent. Rebinding of the MEEVD peptide from the solvent to the receptor binding site occurs slowly through the portal of entry. Unbinding and rebinding go through intermediate states characterized by the peptide interacting with a lateral helix, helix A1, of the receptor with mainly Asp 5, Val 4, and Glu 3 of the peptide. This newly discovered intermediate structure is characterized by numerous contacts with the receptor which lead to complete formation of the bound complex. The structure of the bound complex obtained after rebinding is structurally very similar to the crystal structure of the complex (0.48 Å root-mean square deviation). The residues Asp 5, Val 4, and Glu 3 adopt conformations and intermolecular contacts with excellent structural similarity with the native ones. Finally, the dissociation and reassociation of MEEVD induce hydration/dehydration transitions, which provide insights on the role of desolvation and solvation processes in protein-peptide binding.

Modeling of protein-anion exchange resin interaction for the human growth hormone charge variants.

Modeling ion exchange chromatography (IEC) behavior has generated significant interest because of the wide use of IEC as an analytical technique as well as a preparative protein purification process; indeed there is a need for better understanding of what drives the unique behavior of protein charge variants. We hypothesize that a complex protein molecule, which contains both hydrophobic and charged moieties, would interact strongly with an in silico designed resin through charged electrostatic patches on the surface of the protein. In the present work, variants of recombinant human growth hormone that mimic naturally-occurring deamidation products were produced and characterized in silico. The study included these four variants: rhGH, N149D, N152D, and N149D/N152D. Poisson-Boltzmann calculations were used to determine surface electrostatic potential. Metropolis Monte Carlo simulations were carried out with the resulting variants to simulate IEC systems, examining the free energy of the interaction of the protein with an in silico anion exchange column represented by polylysine polypeptide. The results show that the charge variants have different average binding energies and the free energy of interaction can be used to predict the retention time for the different variants.

Conformational dynamics and free energy of BHRF1 binding to Bim BH3

The interaction between the Bim BH3 peptide and the viral protein BHRF1 is pivotal to understanding the fundamental molecular details of the mechanism used by the Epstein-Barr virus to trick the mammalian immune system. Here, we study the mechanism of binding/unbinding and compute the free energy for the association of the Bim peptide to the BHRF1 protein. Key elements of the binding mechanism are the conformational rearrangement together with a main free energy barrier of 11.5kcal/mol. The simulations show complete unbinding and rebinding of the Bim peptide to BHRF1. The peptide slowly dissociates, disrupting the hydrophobic contacts, then tilting to one side. The peptide then completely disrupts all the remaining interactions and moves into the bulk solvent. The rebinding of the peptide from the solvent to the receptor binding site occurs slowly. This is because the helix partially unfolds in the unbound state. Rebinding involves an intermediate state, in which the peptide interacts with the hydrophobic binding pocket, which mainly involves Leu 62, Arg 63, Ile 65, and Phe 69. This novel intermediate structure forms 65 contacts with the receptor before the peptide again reaches the bound state. The standard binding free energy value is close to the experimental Kd in the nanomolar range. Finally, we observe how the breathing motions of α3-α4 are coupled with the binding/unbinding of the Bim BH3 peptide. The structure of the intermediate can be used for designing novel peptide inhibitors of the BHRF1 protein.

Correction: Chimeric Rhinoviruses Displaying MPER Epitopes Elicit Anti-HIV Neutralizing Responses

[This corrects the article on p. e72205 in vol. 8.].