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.

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.

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.

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.

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.

Alternative splicing regulatory network reconstruction from exon array data.

Pre-mRNA alternative splicing (AS) allows individual genes to produce multiple types of mRNA and associated protein isoforms. While AS regulation enables the production of the hundreds of thousands of types of proteins needed for the normal functioning of the human cell, it also presents many opportunities for the onset of cancer and other diseases. The AS process is known to be regulated by a group of serine/arginine rich (SR) proteins, heterogeneous nuclear ribonucleoproteins (hnRNPs), and small nuclear ribonucleoprotein (snRNP) particles through a complex assembly. Each gene-exon is regulated by one or multiple splicing regulators, from which one may hypothesize the existence of an alternative splicing regulatory network (SRN). The SRN contains a list of gene-exons, for each of which the factors that up/down regulate them are provided. Since defects in the SRN play key roles in human disease, a reconstruction of human SRN could be used to facilitate the design of diagnostic and therapeutic strategies. In this paper, we present a methodology to automate genome-wide SRN reconstruction. We construct SRN based on an extensive correlation analysis of human exon expression microarray data, conventional gene expression microarray profiles, and an experimentally verified AS and transcriptional regulatory interaction training set. This SRN reconstruction methodology is demonstrated and software (AutoNet) that automates the reconstruction of SRN is developed. A genome-wide SRN was constructed for normal human cells and an assessment of the reliability of each predicted interaction is provided. Human SRN we constructed are free available from our web portal: https://ruby.chem.indiana.edu/scorenfl/srn_results/lookup0.php.

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.

Molecular dynamics/order parameter extrapolation for bionanosystem simulations.

A multiscale approach, molecular dynamics/order parameter extrapolation (MD/OPX), to the all-atom simulation of large bionanosystems is presented. The approach starts with the introduction of a set of order parameters (OPs) automatically generated with orthogonal polynomials to characterize the nanoscale features of bionanosystems. The OPs are shown to evolve slowly via Newton's equations, and the all-atom multiscale analysis (AMA) developed earlier (Miao and Ortoleva, J Chem Phys 2006, 125, 44901) demonstrates the existence of their stochastic dynamics, which serve as the justification for our MD/OPX approach. In MD/OPX, a short MD run estimates the rate of change of the OPs, which is then used to extrapolate the state of the system over time that is much longer than the 10(-14) second timescale of fast atomic vibrations and collisions. The approach is implemented in NAMD and demonstrated on cowpea chlorotic mottle virus (CCMV) capsid structural transitions (STs). It greatly accelerates the MD code and its underlying all-atom description of the nanosystems enables the use of a universal interatomic force field, avoiding recalibration with each new application as needed for coarse-grained models. The source code of MD/OPX is distributed free of charge at https://simtk.org/home/mdopx and a web portal will be available via http://sysbio.indiana.edu/virusx.

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.

Transcriptional regulatory network refinement and quantification through kinetic modeling, gene expression microarray data and information theory.

BACKGROUND: Gene expression microarray and other multiplex data hold promise for addressing the challenges of cellular complexity, refined diagnoses and the discovery of well-targeted treatments. A new approach to the construction and quantification of transcriptional regulatory networks (TRNs) is presented that integrates gene expression microarray data and cell modeling through information theory. Given a partial TRN and time series data, a probability density is constructed that is a functional of the time course of transcription factor (TF) thermodynamic activities at the site of gene control, and is a function of mRNA degradation and transcription rate coefficients, and equilibrium constants for TF/gene binding. RESULTS: Our approach yields more physicochemical information that compliments the results of network structure delineation methods, and thereby can serve as an element of a comprehensive TRN discovery/quantification system. The most probable TF time courses and values of the aforementioned parameters are obtained by maximizing the probability obtained through entropy maximization. Observed time delays between mRNA expression and activity are accounted for implicitly since the time course of the activity of a TF is coupled by probability functional maximization, and is not assumed to be proportional to expression level of the mRNA type that translates into the TF. This allows one to investigate post-translational and TF activation mechanisms of gene regulation. Accuracy and robustness of the method are evaluated. A kinetic formulation is used to facilitate the analysis of phenomena with a strongly dynamical character while a physically-motivated regularization of the TF time course is found to overcome difficulties due to omnipresent noise and data sparsity that plague other methods of gene expression data analysis. An application to Escherichia coli is presented. CONCLUSION: Multiplex time series data can be used for the construction of the network of cellular processes and the calibration of the associated physicochemical parameters. We have demonstrated these concepts in the context of gene regulation understood through the analysis of gene expression microarray time series data. Casting the approach in a probabilistic framework has allowed us to address the uncertainties in gene expression microarray data. Our approach was found to be robust to error in the gene expression microarray data and mistakes in a proposed TRN.

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.

Nanoparticle dynamics: a multiscale analysis of the Liouville equation.

A theory of nanoparticle dynamics based on scaling arguments and the Liouville equation is presented. We start with a delineation of the scales characterizing the behavior of the nanoparticle/host fluid system. Asymptotic expansions, multiple time and space scale techniques, the resulting coarse-grained dynamics of the probability densities of the Fokker-Planck-Chandrasekhar (FPC) type for the nanoparticle(s), and the hydrodynamic models of the host medium are obtained. Collections of nanoparticles are considered so that problems such as viral self-assembly and the transition from a particle suspension to a solid porous matrix can be addressed via a deductive approach that starts with the Liouville equation and a calibrated atomic force field, and yields a generalized FPC equation. Extensions allowing for the investigation of the rotation and deformation of the nanoparticles are considered in the context of the space-warping formalism. Thermodynamic forces and dissipative effects are accounted for. The notion of configuration-dependent drag coefficients and their implications for coagulation and consolidation are shown to be natural consequences of the analysis. All results are obtained via formal asymptotic expansions in mass, size, and other physical and kinetic parameter ratios.

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.

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.

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.

Simulating cellular dynamics through a coupled transcription, translation, metabolic model.

In order to predict cell behavior in response to changes in its surroundings or to modifications of its genetic code, the dynamics of a cell are modeled using equations of metabolism, transport, transcription and translation implemented in the Karyote software. Our methodology accounts for the organelles of eukaryotes and the specialized zones in prokaryotes by dividing the volume of the cell into discrete compartments. Each compartment exchanges mass with others either through membrane transport or with a time delay effect associated with molecular migration. Metabolic and macromolecular reactions take place in user-specified compartments. Coupling among processes are accounted for and multiple scale techniques allow for the computation of processes that occur on a wide range of time scales. Our model is implemented to simulate the evolution of concentrations for a user-specifiable set of molecules and reactions that participate in cellular activity. The underlying equations integrate metabolic, transcription and translation reaction networks and provide a framework for simulating whole cells given a user-specified set of reactions. A rate equation formulation is used to simulate transcription from an input DNA sequence while the resulting mRNA is used via ribosome-mediated polymerization kinetics to accomplish translation. Feedback associated with the creation of species necessary for metabolism by the mRNA and protein synthesis modifies the rates of production of factors (e.g. nucleotides and amino acids) that affect the dynamics of transcription and translation. The concentrations of predicted proteins are compared with time series or steady state experiments. The expression and sequence of the predicted proteins are compared with experimental data via the construction of synthetic tryptic digests and associated mass spectra. We present the mathematical model showing the coupling of transcription, translation and metabolism in Karyote and illustrate some of its unique characteristics.

Toward Automated Cell Model Development through Information Theory†.

The objective of this paper is to present a methodology for developing and calibrating models of complex reaction/transport systems. In particular, the complex network of biochemical reaction/transport processes and their spatial organization make the development of a predictive model of a living cell a grand challenge for the 21st century. However, advances in reaction/transport modeling and the exponentially growing databases of genomic, proteomic, metabolic, and bioelectric data make cell modeling feasible, if these two elements can be automatically integrated in an unbiased fashion. In this paper, we present a procedure to integrate data with a new cell model, Karyote, that accounts for many of the physical processes needed to attain the goal of predictive modeling. Our integration methodology is based on the use of information theory. The model is integrated with a variety of types and qualities of experimental data using an objective error assessment approach. Data that can be used in this approach include NMR, spectroscopy, microscopy, and electric potentiometry. The approach is demonstrated on the well-studied Trypanosoma brucei system. A major obstacle for the development of a predictive cell model is that the complexity of these systems makes it unlikely that any model presently available will soon be complete in terms of the set of processes accounted for. Thus, one is faced with the challenge of calibrating and running an incomplete model. We present a probability functional method that allows the integration of experimental data and soft information such as choice of error measure, a priori information, and physically motivated regularization to address the incompleteness challenge.

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.