Omniligase-1-Mediated Phage-Peptide Library Modification and Insulin Engineering.

Chemical and enzymatic modifications of peptide-displayed libraries have been successfully employed to expand the phage display library. However, the requirement of specific epitopes and scaffolds has limited the scope of protein engineering using phage display. In this study, we present a novel approach utilizing omniligase-1-mediated selective and specific ligation on the phage pIII protein, offering a high conversion rate and compatibility with commercially available phage libraries. We applied this method to perform high-throughput engineering of insulin analogues with randomized B chain C-terminal regions. Insulin analogues with different B chain C-terminal segments were selected and exhibited biological activity equivalent to that of human insulin. Molecular dynamics studies of insulin analogues revealed a novel interaction between the insulin B27 residue and insulin receptor L1 domain. In summary, our findings highlight the potential of omniligase-1-mediated phage display in the development and screening of disulfide-rich peptides and proteins. This approach holds promise for the creation of novel insulin analogues with enhanced therapeutic properties and exhibits potential for the development of other therapeutic compounds.

B-cell epitope discovery: The first protein flexibility-based algorithm-Zika virus conserved epitope demonstration.

Antibody-antigen interaction-at antigenic local environments called B-cell epitopes-is a prominent mechanism for neutralization of infection. Effective mimicry, and display, of B-cell epitopes is key to vaccine design. Here, a physical approach is evaluated for the discovery of epitopes which evolve slowly over closely related pathogens (conserved epitopes). The approach is 1) protein flexibility-based and 2) demonstrated with clinically relevant enveloped viruses, simulated via molecular dynamics. The approach is validated against 1) seven structurally characterized enveloped virus epitopes which evolved the least (out of thirty-nine enveloped virus-antibody structures), 2) two structurally characterized non-enveloped virus epitopes which evolved slowly (out of eight non-enveloped virus-antibody structures), and 3) eight preexisting epitope and peptide discovery algorithms. Rationale for a new benchmarking scheme is presented. A data-driven epitope clustering algorithm is introduced. The prediction of five Zika virus epitopes (for future exploration on recombinant vaccine technologies) is demonstrated. For the first time, protein flexibility is shown to outperform solvent accessible surface area as an epitope discovery metric.

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.

Amphiphile self-assembly dynamics at the solution-solid interface reveal asymmetry in head/tail desorption.

Amphiphilic alkoxybenzonitriles (ABNs) of varying chain length are studied at the solution/graphite interface to analyze dynamics of assembly. Competitive self-assembly between ABNs and alkanoic acid solvent is shown by scanning tunneling microscopy (STM) to be controlled by concentration and molecular size. Molecular dynamics (MD) simulations reveal key roles of the sub-nanosecond fundamental steps of desorption, adsorption, and on-surface motion. We discovered asymmetry in desorption-adsorption steps. Desorption starting from alkyl chain detachment from the surface is favored due to dynamic occlusion by neighbouring chains. Even though the nitrile head has a strong solvent affinity, it more frequently re-adsorbs following a detachment event.

Multiscale Molecular Dynamics Approach to Energy Transfer in Nanomaterials.

After local transient fluctuations are dissipated, in an energy transfer process, a system evolves to a state where the energy density field varies slowly in time relative to the dynamics of atomic collisions and vibrations. Furthermore, the energy density field remains strongly coupled to the atomic scale processes (collisions and vibrations), and it can serve as the basis of a multiscale theory of energy transfer. Here, a method is introduced to capture the long scale energy density variations as they coevolve with the atomistic state in a way that yields insights into the basic physics and implies an efficient algorithm for energy transfer simulations. The approach is developed based on the N-atom Liouville equation and an interatomic force field and avoids the need for conjectured phenomenological equations for energy transfer and other processes. The theory is demonstrated for sodium chloride and silicon dioxide nanoparticles immersed in a water bath via molecular dynamics simulations of the energy transfer between a nanoparticle and its aqueous host fluid. The energy density field is computed for different sets of symmetric grid densities, and the multiscale theory holds when slowly varying energy densities at the nodes are obtained. Results strongly depend on grid density and nanoparticle constituent material. A nonuniform temperature distribution, larger thermal fluctuations in the nanoparticle than in the bath, and enhancement of fluctuations at the surface, which are expressed due to the atomic nature of the systems, are captured by this method rather than by phenomenological continuum energy transfer models.

Multiscale time-dependent density functional theory: Demonstration for plasmons.

Plasmon properties are of significant interest in pure and applied nanoscience. While time-dependent density functional theory (TDDFT) can be used to study plasmons, it becomes impractical for elucidating the effect of size, geometric arrangement, and dimensionality in complex nanosystems. In this study, a new multiscale formalism that addresses this challenge is proposed. This formalism is based on Trotter factorization and the explicit introduction of a coarse-grained (CG) structure function constructed as the Weierstrass transform of the electron wavefunction. This CG structure function is shown to vary on a time scale much longer than that of the latter. A multiscale propagator that coevolves both the CG structure function and the electron wavefunction is shown to bring substantial efficiency over classical propagators used in TDDFT. This efficiency follows from the enhanced numerical stability of the multiscale method and the consequence of larger time steps that can be used in a discrete time evolution. The multiscale algorithm is demonstrated for plasmons in a group of interacting sodium nanoparticles (15-240 atoms), and it achieves improved efficiency over TDDFT without significant loss of accuracy or space-time resolution.

Reverse Coarse-Graining for Equation-Free Modeling: Application to Multiscale Molecular Dynamics.

Constructing atom-resolved states from low-resolution data is of practical importance in many areas of science and engineering. This problem is addressed in this article in the context of multiscale factorization methods for molecular dynamics. These methods capture the crosstalk between atomic and coarse-grained scales arising in macromolecular systems. This crosstalk is accounted for by Trotter factorization, which is used to separate the all-atom from the coarse-grained phases of the computation. In this approach, short molecular dynamics runs are used to advance in time the coarse-grained variables, which in turn guide the all-atom state. To achieve this coevolution, an all-atom microstate consistent with the updated coarse-grained variables must be recovered. This recovery is cast here as a nonlinear optimization problem that is solved with a quasi-Newton method. The approach yields a Boltzmann-relevant microstate whose coarse-grained representation and some of its fine-scale features are preserved. Embedding this algorithm in multiscale factorization is shown to be accurate and scalable for simulating proteins and their assemblies.

Implicit Time Integration for Multiscale Molecular Dynamics Using Transcendental Padé Approximants.

Molecular dynamics systems evolve through the interplay of collective and localized disturbances. As a practical consequence, there is a restriction on the time step imposed by the broad spectrum of time scales involved. To resolve this restriction, multiscale factorization was introduced for molecular dynamics as a method that exploits the separation of time scales by coevolving the coarse-grained and atom-resolved states via Trotter factorization. Developing a stable time-marching scheme for this coevolution, however, is challenging because the coarse-grained dynamical equations depend on the microstate; therefore, these equations cannot be expressed in closed form. The objective of this paper is to develop an implicit time integration scheme for multiscale simulation of large systems over long periods of time and with high accuracy. The scheme uses Padé approximants to account for both the stochastic and deterministic features of the coarse-grained dynamics. The method is demonstrated for a protein either undergoing a conformational change or migrating under the influence of an external force. The method shows promise in accelerating multiscale molecular dynamics without a loss of atomic precision or the need to conjecture the form of coarse-grained governing equations.

Multiscale Modeling in the Clinic: Drug Design and Development.

A wide range of length and time scales are relevant to pharmacology, especially in drug development, drug design and drug delivery. Therefore, multiscale computational modeling and simulation methods and paradigms that advance the linkage of phenomena occurring at these multiple scales have become increasingly important. Multiscale approaches present in silico opportunities to advance laboratory research to bedside clinical applications in pharmaceuticals research. This is achievable through the capability of modeling to reveal phenomena occurring across multiple spatial and temporal scales, which are not otherwise readily accessible to experimentation. The resultant models, when validated, are capable of making testable predictions to guide drug design and delivery. In this review we describe the goals, methods, and opportunities of multiscale modeling in drug design and development. We demonstrate the impact of multiple scales of modeling in this field. We indicate the common mathematical and computational techniques employed for multiscale modeling approaches used in pharmacometric and systems pharmacology models in drug development and present several examples illustrating the current state-of-the-art models for (1) excitable systems and applications in cardiac disease; (2) stem cell driven complex biosystems; (3) nanoparticle delivery, with applications to angiogenesis and cancer therapy; (4) host-pathogen interactions and their use in metabolic disorders, inflammation and sepsis; and (5) computer-aided design of nanomedical systems. We conclude with a focus on barriers to successful clinical translation of drug development, drug design and drug delivery multiscale models.

Broad spectrum assessment of the epitope fluctuation--Immunogenicity hypothesis.

Prediction of immunogenicity is a substantial barrier in vaccine design. Here, a molecular dynamics approach to assessing the immunogenicity of nanoparticles based on structure is presented. Molecular properties of epitopes on nonenveloped viral particles are quantified via a set of metrics. One such metric, epitope fluctuation (and implied flexibility), is shown to be inversely correlated with immunogenicity for each of a broad spectrum of nonenveloped viruses. The molecular metrics and experimentally determined immunogenicities for these viruses are archived in the open-source vaccine computer-aided design database. Results indicate the promise of computer-aided vaccine design to bring greater efficiency to traditional lab-based vaccine discovery approaches.

Prospective on multiscale simulation of virus-like particles: Application to computer-aided vaccine design.

Simulations of virus-like particles needed for computer-aided vaccine design highlight the need for new algorithms that accelerate molecular dynamics. Such simulations via conventional molecular dynamics present a practical challenge due to the millions of atoms involved and the long timescales of the phenomena of interest. These phenomena include structural transitions, self-assembly, and interaction with a cell surface. A promising approach for addressing this challenge is multiscale factorization. The approach is distinct from coarse-graining techniques in that it (1) avoids the need for conjecturing phenomenological governing equations for coarse-grained variables, (2) provides simulations with atomic resolution, (3) captures the cross-talk between disturbances at the atomic and the whole virus-like particle scale, and (4) achieves significant speedup over molecular dynamics. A brief review of multiscale factorization method is provided, as is a prospective on its development.

Early stage P22 viral capsid self-assembly mediated by scaffolding protein: atom-resolved model and molecular dynamics simulation.

Molecular dynamics simulation of an atom-resolved bacteriophage P22 capsid model is used to delineate the underlying mechanism of early stage P22 self-assembly. A dimer formed by the C-terminal fragment of scaffolding protein with a new conformation is demonstrated to catalyze capsomer (hexamer and pentamer) aggregation efficiently. Effects of scaffolding protein/coat protein binding patterns and scaffolding protein concentration on efficiency, fidelity, and capsid curvature of P22 self-assembly are identified.

Multiscale Factorization Method for Simulating Mesoscopic Systems with Atomic Precision.

Mesoscopic N-atom systems derive their structural and dynamical properties from processes coupled across multiple scales in space and time. A multiscale method for simulating these systems in the friction dominated regime from the underlying N-atom formulation is presented. The method integrates notions of multiscale analysis, Trotter factorization, and a hypothesis that the momenta conjugate to coarse-grained variables constitute a stationary process on the time scale of coarse-grained dynamics. The method is demonstrated for lactoferrin, nudaurelia capensis omega virus, and human papillomavirus to assess its accuracy.

A multiscale variational approach to the kinetics of viscous classical liquids: the coarse-grained mean field approximation.

A closed kinetic equation for the single-particle density of a viscous simple liquid is derived using a variational method for the Liouville equation and a coarse-grained mean-field (CGMF) ansatz. The CGMF ansatz is based on the notion that during the characteristic time of deformation a given particle interacts with many others so that it experiences an average interaction. A trial function for the N-particle probability density is constructed using a multiscale perturbation method and the CGMF ansatz is applied to it. The multiscale perturbation scheme is based on the ratio of the average nearest-neighbor atom distance to the total size of the assembly. A constraint on the initial condition is discovered which guarantees that the kinetic equation is mass-conserving and closed in the single-particle density. The kinetic equation has much of the character of the Vlasov equation except that true viscous, and not Landau, damping is accounted for. The theory captures condensation kinetics and takes much of the character of the Gross-Pitaevskii equation in the weak-gradient short-range force limit.

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 fluctuations in the human papillomavirus are under dynamic allosteric control: a computational evaluation of a new vaccine design strategy.

The dynamic properties of the capsid of the human papillomavirus (HPV) type 16 were examined using classical molecular dynamics simulations. By systematically comparing the structural fluctuations of the capsid protein, a strong dynamic allosteric connection between the epitope containing loops and the h4 helix located more than 50 Å away is identified, which was not recognized thus far. Computer simulations show that restricting the structural fluctuations of the h4 helix is key to rigidifying the epitopes, which is thought to be required for eliciting a proper immune response. The allostery identified in the components of the HPV is nonclassical because the mean structure of the epitope carrying loops remains unchanged, but as a result of allosteric effect the structural fluctuations are altered significantly, which in turn changes the biochemical reactivity profile of the epitopes. Exploiting this novel insight, a new vaccine design strategy is proposed wherein a relatively small virus capsid fragment is deposited on a silica nanoparticle in such a way that the fluctuations of the h4 helix are suppressed. The structural and dynamic properties of the epitope carrying loops on this hybrid nanoparticle match the characteristics of epitopes found on the full virus-like particle precisely, suggesting that these nanoparticles may serve as potent, cost-effective, and safe alternatives to traditionally developed vaccines. The structural and dynamic properties of the hybrid nanoparticle are examined in detail to establish the general concepts of the proposed new design.

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.

Variational methods for time-dependent classical many-particle systems.

A variational method for the classical Liouville equation is introduced that facilitates the development of theories for non-equilibrium classical systems. The method is based on the introduction of a complex-valued auxiliary quantity Ψ that is related to the classical position-momentum probability density ρ via ρ = Ψ*Ψ. A functional of Ψ is developed whose extrema imply that ρ satisfies the Liouville equation. Multiscale methods are used to develop trial functions to be optimized by the variational principle. The present variational principle with multiscale trial functions can capture both the microscopic and the coarse-grained descriptions, thereby yielding theories that account for the two way exchange of information across multiple scales in space and time. Equations of the Smoluchowski form for the coarse-grained state probability density are obtained. Constraints on the initial state of the N-particle probability density for which the aforementioned equation is closed and conserves probability are presented. The methodology has applicability to a wide range of systems including macromolecular assemblies, ionic liquids, and nanoparticles.

Hierarchical Order Parameters for Macromolecular Assembly Simulations I: Construction and Dynamical Properties of Order Parameters.

Macromolecular assemblies often display a hierarchical organization of macromolecules or their sub-assemblies. To model this, we have formulated a space warping method that enables capturing overall macromolecular structure and dynamics via a set of coarse-grained order parameters (OPs). This article is the first of two describing the construction and computational implementation of an additional class of OPs that has built into them the hierarchical architecture of macromolecular assemblies. To accomplish this, first, the system is divided into subsystems, each of which is described via a representative set of OPs. Then, a global set of variables is constructed from these subsystem-centered OPs to capture overall system organization. Dynamical properties of the resulting OPs are compared to those of our previous nonhierarchical ones, and implied conceptual and computational advantages are discussed for a 100ns, 2 million atom solvated Human Papillomavirus-like particle simulation. In the second article, the hierarchical OPs are shown to enable a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Langevin equations of stochastic OP dynamics. The latter is demonstrated via a force-field based simulation algorithm that probes key structural transition pathways, simultaneously accounting for all-atom details and overall structure.