Hierarchical Multiscale Modeling of Macromolecules and their Assemblies

Temporally Coarse-Grained All-Atom Molecular Dynamics Achieved via Stochastic Padé Approximants

A Padé approximant scheme for realizing the discrete-time evolution of the state of a many-atom system is introduced. This temporal coarse-graining scheme accounts for the underlying Newtonian physics and avoids the need for construction of spatially coarse-grained variables. Newtonian physics is incorporated through short molecular dynamics simulations at the beginning of each of the large coarse-grained timesteps. The balance between stochastic and coherent dynamics expressed by many-atom systems is captured via incorporation of the Ito formula into a Padé approximant for the time dependence of individual atom positions over large timesteps. Since the time for a many-atom system to express a characteristic ensemble of atomic velocity fluctuations is typically short relative to the characteristic time of large-scale atomic displacements, a computationally efficient and accurate temporal coarse-graining of the atom-resolved Newtonian dynamics is formulated, denoted all-atom Padé-Ito molecular dynamics (APIMD). Evolution of the system over a time step much longer than that required for standard molecular dynamics (MD) is achieved via incorporation of information from the short MD simulations into a Padé approximant extrapolation in time. The extrapolated atomic configuration is subjected to energy minimization and, when needed, thermal equilibration so as to avoid occasional unphysical close encounters deriving from the Padé approximant extrapolation and to represent configurations appropriate for the temperature of interest. APIMD is implemented and tested via comparison with traditional MD simulations of five phenomena: (1) pertussis toxin subunit deformation, (2) structural transition in a T = 1 capsid-like structure of HPV16 L1 protein, (3) coalescence of argon nanodroplets, and structural transitions in dialanine in (4) vacuum, and (5) water. Accuracy of APIMD is demonstrated using semimicroscopic descriptors (rmsd, radius of gyration, residue-residue contact maps, and densities) and the free energy. Significant computational acceleration relative to traditional molecular dynamics is illustrated.

β sheets not required: combined experimental and computational studies of self-assembly and gelation of the ester-containing analogue of an Fmoc-dipeptide hydrogelator

In our work toward developing ester-containing self-assembling peptides as soft biomaterials, we have found that a fluorenylmethoxycarbonyl (Fmoc)-conjugated alanine-lactic acid (Ala-Lac) sequence self-assembles into nanostructures that gel in water. This process occurs despite Fmoc-Ala-Lac's inability to interact with other Fmoc-Ala-Lac molecules via β-sheet-like amide-amide hydrogen bonding, a condition previously thought to be crucial to the self-assembly of Fmoc-conjugated peptides. Experimental comparisons of Fmoc-Ala-Lac to its self-assembling peptide sequence analogue Fmoc-Ala-Ala using a variety of microscopic, spectroscopic, and bulk characterization techniques demonstrate distinct features of the two systems and show that while angstrom-scale self-assembled structures are similar, their nanometer-scale size and morphological properties diverge and give rise to different bulk mechanical properties. Molecular dynamics simulations were performed to gain more insight into the differences between the two systems. An analysis of the hydrogen-bonding and solvent-surface interface properties of the simulated fibrils revealed that Fmoc-Ala-Lac fibrils are stronger and less hydrophilic than Fmoc-Ala-Ala fibrils. We propose that this difference in fibril amphiphilicity gives rise to differences in the higher-order assembly of fibrils into nanostructures seen in TEM. Importantly, we confirm experimentally that β-sheet-type hydrogen bonding is not crucial to the self-assembly of short, conjugated peptides, and we demonstrate computationally that the amide bond in such systems may act mainly to mediate the solvation of the self-assembled single fibrils and therefore regulate a more extensive higher-order aggregation of fibrils. This work provides a basic understanding for future research in designing highly degradable self-assembling materials with peptide-like bioactivity for biomedical applications.

Energy transfer between a nanosystem and its host fluid: a multiscale factorization approach

Energy transfer between a macromolecule or supramolecular assembly and a host medium is considered from the perspective of Newton's equations and Lie-Trotter factorization. The development starts by demonstrating that the energy of the molecule evolves slowly relative to the time scale of atomic collisions-vibrations. The energy is envisioned to be a coarse-grained variable that coevolves with the rapidly fluctuating atomistic degrees of freedom. Lie-Trotter factorization is shown to be a natural framework for expressing this coevolution. A mathematical formalism and workflow for efficient multiscale simulation of energy transfer is presented. Lactoferrin and human papilloma virus capsid-like structure are used for validation.

Epitope engineering and molecular metrics of immunogenicity: a computational approach to VLP-based vaccine design

Developing antiviral vaccines is increasingly challenging due to associated time and cost of production as well as emerging drug-resistant strains. A computer-aided vaccine design strategy is presented that could greatly accelerate the discovery process and yield vaccines with high immunogenicity and thermal stability. Our strategy is based on foreign viral epitopes engineered onto well-established virus-like particles (VLPs) and demonstrates that such constructs present similar affinity for antibodies as does a native virus. This binding affinity serves as one molecular metric of immunogenicity. As a demonstration, we engineered a preS1 epitope of hepatitis B virus (HBV) onto the EF loop of human papillomavirus VLP (HPV-VLP). HBV-associated HzKR127 antibody displayed binding affinity for this structure at distances and strengths similar to those for the complex of the antibody with the full HBV (PDBID: 2EH8). This antibody binding affinity assessment, along with other molecular immunogenicity metrics, could be a key component of a computer-aided vaccine design strategy.