Multiscale simulation of microbe structure and dynamics

Using Bibliometric Analysis to Map the Impact of a Simulation Program's Published Scholarly Works

SUMMARY STATEMENT

Bibliometrics quantitatively evaluates the targeted literature sources and can help define research and scholarly publications' impact and demonstrate connections for authors, departments, or universities. This article presents a methodology for simulation programs to evaluate their influence in terms of both impact and scope of their published simulation-based healthcare scholarly output. Using the authors' home university and healthcare system as an example, the article outlines a methodology to map research and scholarly works networks within the systems, identify and map connections outside the system, and quantifiably score the overall impact of the simulation program's scholarly output using a common scoring metric, the h-index. This generates an objective measure of impact, rather than a subjective opinion of an organization's research and scholarly impact. The combination of an institutional h-index with mapping of simulation-based healthcare scholarly output provides a full, objective description of the institution's output and provides a benchmark for other simulation programs for comparison.

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.

Engineering virus-like particles as vaccine platforms

Virus-like particles (VLPs) have been utilized as vaccine platforms to increase the immunogenicity of heterologous antigens. A variety of diverse VLP types can serve as vaccine platforms, and research has focused on engineering VLPs to improve their efficacy as vaccines, enhance their stability, and allow for more versatile display of antigens. Here, we review selected VLP vaccine platforms, highlight efforts to improve these platforms through structure-informed rational design, and point to areas of future research that will assist in these efforts.

Biomolecular engineering of virus-like particles aided by computational chemistry methods

Multi-scale investigation of VLP self-assembly aided by computational methods is facilitating the design, redesign, and modification of functionalized VLPs.

Differential structural dynamics and antigenicity of two similar influenza H5N1 virus HA-specific HLA-A*0201-restricted CLT epitopes

The free RI-10 and KI-10 peptides showed bent rather than extended conformations as binding in the cleft of the HLA-A*0201 molecule, and KI-10–HLA-A*0201 processed a much higher flexibility than RI-10–HLA-A*0201.

Modeling biology spanning different scales: an open challenge

It is coming nowadays more clear that in order to obtain a unified description of the different mechanisms governing the behavior and causality relations among the various parts of a living system, the development of comprehensive computational and mathematical models at different space and time scales is required. This is one of the most formidable challenges of modern biology characterized by the availability of huge amount of high throughput measurements. In this paper we draw attention to the importance of multiscale modeling in the framework of studies of biological systems in general and of the immune system in particular.

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.

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.

Bioengineering virus-like particles as vaccines

Virus-like particle (VLP) technology seeks to harness the optimally tuned immunostimulatory properties of natural viruses while omitting the infectious trait. VLPs that assemble from a single protein have been shown to be safe and highly efficacious in humans, and highly profitable. VLPs emerging from basic research possess varying levels of complexity and comprise single or multiple proteins, with or without a lipid membrane. Complex VLP assembly is traditionally orchestrated within cells using black-box approaches, which are appropriate when knowledge and control over assembly are limited. Recovery challenges including those of adherent and intracellular contaminants must then be addressed. Recent commercial VLPs variously incorporate steps that include VLP in vitro assembly to address these problems robustly, but at the expense of process complexity. Increasing research activity and translation opportunity necessitate bioengineering advances and new bioprocessing modalities for efficient and cost-effective production of VLPs. Emerging approaches are necessarily multi-scale and multi-disciplinary, encompassing diverse fields from computational design of molecules to new macro-scale purification materials. In this review, we highlight historical and emerging VLP vaccine approaches. We overview approaches that seek to specifically engineer a desirable immune response through modular VLP design, and those that seek to improve bioprocess efficiency through inhibition of intracellular assembly to allow optimal use of existing purification technologies prior to cell-free VLP assembly. Greater understanding of VLP assembly and increased interdisciplinary activity will see enormous progress in VLP technology over the coming decade, driven by clear translational opportunity.

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.

Hierarchical Multiscale Modeling of Macromolecules and their Assemblies

Soft materials (e.g., enveloped viruses, liposomes, membranes and supercooled liquids) simultaneously deform or display collective behaviors, while undergoing atomic scale vibrations and collisions. While the multiple space-time character of such systems often makes traditional molecular dynamics simulation impractical, a multiscale approach has been presented that allows for long-time simulation with atomic detail based on the co-evolution of slowly-varying order parameters (OPs) with the quasi-equilibrium probability density of atomic configurations. However, this approach breaks down when the structural change is extreme, or when nearest-neighbor connectivity of atoms is not maintained. In the current study, a self-consistent approach is presented wherein OPs and a reference structure co-evolve slowly to yield long-time simulation for dynamical soft-matter phenomena such as structural transitions and self-assembly. The development begins with the Liouville equation for N classical atoms and an ansatz on the form of the associated N-atom probability density. Multiscale techniques are used to derive Langevin equations for the coupled OP-configurational dynamics. The net result is a set of equations for the coupled stochastic dynamics of the OPs and centers of mass of the subsystems that constitute a soft material body. The theory is based on an all-atom methodology and an interatomic force field, and therefore enables calibration-free simulations of soft matter, such as macromolecular assemblies.

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.

Compartmentalization and metabolic channeling for multienzymatic biosynthesis: practical strategies and modeling approaches

: The construction of efficient enzyme complexes for multienzymatic biosynthesis is of increasing interest in order to achieve maximum yield and to minimize the interference due to shortcomings that are typical for straightforward one-pot multienzyme catalysis. These include product or intermediate feedback inhibition, degeneration, and diffusive losses of reaction intermediates, consumption of co-factors, and others. The main mechanisms in nature to tackle these effects in transient or stable protein associations are the formation of metabolic channeling and microcompartments, processes that are desirable also for multienzymatic biosynthesis in vitro. This chapter provides an overview over two main aspects. First, numerous recent strategies for establishing compartmentalized multienzyme associations and constructed synthetic enzyme complexes are reviewed. Second, the computational methods at hand to investigate and optimize such associations systematically, especially with focus on large multienzyme complexes and metabolic channeling, are discussed. Perspectives on future studies of multienzymatic biosynthesis concerning compartmentalization and metabolic channeling are presented.

Multiscale macromolecular simulation: role of evolving ensembles

Multiscale analysis provides an algorithm for the efficient simulation of macromolecular assemblies. This algorithm involves the coevolution of a quasiequilibrium probability density of atomic configurations and the Langevin dynamics of spatial coarse-grained variables denoted order parameters (OPs) characterizing nanoscale system features. In practice, implementation of the probability density involves the generation of constant OP ensembles of atomic configurations. Such ensembles are used to construct thermal forces and diffusion factors that mediate the stochastic OP dynamics. Generation of all-atom ensembles at every Langevin time step is computationally expensive. Here, multiscale computation for macromolecular systems is made more efficient by a method that self-consistently folds in ensembles of all-atom configurations constructed in an earlier step, history, of the Langevin evolution. This procedure accounts for the temporal evolution of these ensembles, accurately providing thermal forces and diffusions. It is shown that efficiency and accuracy of the OP-based simulations is increased via the integration of this historical information. Accuracy improves with the square root of the number of historical timesteps included in the calculation. As a result, CPU usage can be decreased by a factor of 3-8 without loss of accuracy. The algorithm is implemented into our existing force-field based multiscale simulation platform and demonstrated via the structural dynamics of viral capsomers.

Gauging the flexibility of the active site in soybean lipoxygenase-1 (SLO-1) through an atom-centered density matrix propagation (ADMP) treatment that facilitates the sampling of rare events

We present a computational methodology to sample rare events in large biological enzymes that may involve electronically polarizing, reactive processes. The approach includes simultaneous dynamical treatment of electronic and nuclear degrees of freedom, where contributions from the electronic portion are computed using hybrid density functional theory and the computational costs are reduced through a hybrid quantum mechanics/molecular mechanics (QM/MM) treatment. Thus, the paper involves a QM/MM dynamical treatment of rare events. The method is applied to probe the effect of the active site elements on the critical hydrogen transfer step in the soybean lipoxygenase-1 (SLO-1) catalyzed oxidation of linoleic acid. It is found that the dynamical fluctuations and associated flexibility of the active site are critical toward maintaining the electrostatics in the regime where the reactive process can occur smoothly. Physical constraints enforced to limit the active site flexibility are akin to mutations and, in the cases studied, have a detrimental effect on the electrostatic fluctuations, thus adversely affecting the hydrogen transfer process.

Discovering free energy basins for macromolecular systems via guided multiscale simulation

An approach for the automated discovery of low free energy states of macromolecular systems is presented. The method does not involve delineating the entire free energy landscape but proceeds in a sequential free energy minimizing state discovery; i.e., it first discovers one low free energy state and then automatically seeks a distinct neighboring one. These states and the associated ensembles of atomistic configurations are characterized by coarse-grained variables capturing the large-scale structure of the system. A key facet of our approach is the identification of such coarse-grained variables. Evolution of these variables is governed by Langevin dynamics driven by thermal-average forces and mediated by diffusivities, both of which are constructed by an ensemble of short molecular dynamics runs. In the present approach, the thermal-average forces are modified to account for the entropy changes following from our knowledge of the free energy basins already discovered. Such forces guide the system away from the known free energy minima, over free energy barriers, and to a new one. The theory is demonstrated for lactoferrin, known to have multiple energy-minimizing structures. The approach is validated using experimental structures and traditional molecular dynamics. The method can be generalized to enable the interpretation of nanocharacterization data (e.g., ion mobility-mass spectrometry, atomic force microscopy, chemical labeling, and nanopore measurements).

Space warping order parameters and symmetry: application to multiscale simulation of macromolecular assemblies

Coarse-grained features of macromolecular assemblies are understood via a set of order parameters (OPs) constructed in terms of their all-atom configuration. OPs are shown to be slowly changing in time and capture the large-scale spatial features of macromolecular assemblies. The relationship of these variables to the classic notion of OPs based on symmetry breaking phase transitions is discussed. OPs based on space warping transformations are analyzed in detail as they naturally provide a connection between overall structure of an assembly and all-atom configuration. These OPs serve as the basis of a multiscale analysis that yields Langevin equations for OP dynamics. In this context, the characteristics of OPs and PCA modes are compared. The OPs enable efficient all-atom multiscale simulations of the dynamics of macromolecular assemblies in response to changes in microenvironmental conditions, as demonstrated on the structural transitions of cowpea chlorotic mottle virus capsid (CCMV) and RNA of the satellite tobacco mosaic virus (STMV).

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.

Multi-scale modeling in biology: how to bridge the gaps between scales?

Human physiological functions are regulated across many orders of magnitude in space and time. Integrating the information and dynamics from one scale to another is critical for the understanding of human physiology and the treatment of diseases. Multi-scale modeling, as a computational approach, has been widely adopted by researchers in computational and systems biology. A key unsolved issue is how to represent appropriately the dynamical behaviors of a high-dimensional model of a lower scale by a low-dimensional model of a higher scale, so that it can be used to investigate complex dynamical behaviors at even higher scales of integration. In the article, we first review the widely-used different modeling methodologies and their applications at different scales. We then discuss the gaps between different modeling methodologies and between scales, and discuss potential methods for bridging the gaps between scales.