Structure and conformational dynamics of scaffolded DNA origami nanoparticles.

Synthetic DNA is a highly programmable nanoscale material that can be designed to self-assemble into 3D structures that are fully determined by underlying Watson-Crick base pairing. The double crossover (DX) design motif has demonstrated versatility in synthesizing arbitrary DNA nanoparticles on the 5-100 nm scale for diverse applications in biotechnology. Prior computational investigations of these assemblies include all-atom and coarse-grained modeling, but modeling their conformational dynamics remains challenging due to their long relaxation times and associated computational cost. We apply all-atom molecular dynamics and coarse-grained finite element modeling to DX-based nanoparticles to elucidate their fine-scale and global conformational structure and dynamics. We use our coarse-grained model with a set of secondary structural motifs to predict the equilibrium solution structures of 45 DX-based DNA origami nanoparticles including a tetrahedron, octahedron, icosahedron, cuboctahedron and reinforced cube. Coarse-grained models are compared with 3D cryo-electron microscopy density maps for these five DNA nanoparticles and with all-atom molecular dynamics simulations for the tetrahedron and octahedron. Our results elucidate non-intuitive atomic-level structural details of DX-based DNA nanoparticles, and offer a general framework for efficient computational prediction of global and local structural and mechanical properties of DX-based assemblies that are inaccessible to all-atom based models alone.

Computing Nonequilibrium Conformational Dynamics of Structured Nucleic Acid Assemblies.

Synthetic nucleic acids can be programmed to form precise three-dimensional structures on the nanometer-scale. These thermodynamically stable complexes can serve as structural scaffolds to spatially organize functional molecules including multiple enzymes, chromophores, and force-sensing elements with internal dynamics that include substrate reaction-diffusion, excitonic energy transfer, and force-displacement response that often depend critically on both the local and global conformational dynamics of the nucleic acid assembly. However, high molecular weight assemblies exhibit long time-scale and large length-scale motions that cannot easily be sampled using all-atom computational procedures such as molecular dynamics. As an alternative, here we present a computational framework to compute the overdamped conformational dynamics of structured nucleic acid assemblies and apply it to a DNA-based tweezer, a nine-layer DNA origami ring, and a pointer-shaped DNA origami object, which consist of 204, 3,600, and over 7,000 basepairs, respectively. The framework employs a mechanical finite element model for the DNA nanostructure combined with an implicit solvent model to either simulate the Brownian dynamics of the assembly or alternatively compute its Brownian modes. Computational results are compared with an all-atom molecular dynamics simulation of the DNA-based tweezer. Several hundred microseconds of Brownian dynamics are simulated for the nine-layer ring origami object to reveal its long time-scale conformational dynamics, and the first ten Brownian modes of the pointer-shaped structure are predicted.

Inferring transient particle transport dynamics in live cells.

Live-cell imaging and particle tracking provide rich information on mechanisms of intracellular transport. However, trajectory analysis procedures to infer complex transport dynamics involving stochastic switching between active transport and diffusive motion are lacking. We applied Bayesian model selection to hidden Markov modeling to infer transient transport states from trajectories of mRNA-protein complexes in live mouse hippocampal neurons and metaphase kinetochores in dividing human cells. The software is available at http://hmm-bayes.org/.

Lattice-free prediction of three-dimensional structure of programmed DNA assemblies.

DNA can be programmed to self-assemble into high molecular weight 3D assemblies with precise nanometer-scale structural features. Although numerous sequence design strategies exist to realize these assemblies in solution, there is currently no computational framework to predict their 3D structures on the basis of programmed underlying multi-way junction topologies constrained by DNA duplexes. Here, we introduce such an approach and apply it to assemblies designed using the canonical immobile four-way junction. The procedure is used to predict the 3D structure of high molecular weight planar and spherical ring-like origami objects, a tile-based sheet-like ribbon, and a 3D crystalline tensegrity motif, in quantitative agreement with experiments. Our framework provides a new approach to predict programmed nucleic acid 3D structure on the basis of prescribed secondary structure motifs, with possible application to the design of such assemblies for use in biomolecular and materials science.

Structure-based model for light-harvesting properties of nucleic acid nanostructures.

Programmed self-assembly of DNA enables the rational design of megadalton-scale macromolecular assemblies with sub-nanometer scale precision. These assemblies can be programmed to serve as structural scaffolds for secondary chromophore molecules with light-harvesting properties. Like in natural systems, the local and global spatial organization of these synthetic scaffolded chromophore systems plays a crucial role in their emergent excitonic and optical properties. Previously, we introduced a computational model to predict the large-scale 3D solution structure and flexibility of nucleic acid nanostructures programmed using the principle of scaffolded DNA origami. Here, we use Förster resonance energy transfer theory to simulate the temporal dynamics of dye excitation and energy transfer accounting both for overall DNA nanostructure architecture as well as atomic-level DNA and dye chemical structure and composition. Results are used to calculate emergent optical properties including effective absorption cross-section, absorption and emission spectra and total power transferred to a biomimetic reaction center in an existing seven-helix double stranded DNA-based antenna. This structure-based computational framework enables the efficient in silico evaluation of nucleic acid nanostructures for diverse light-harvesting and photonic applications.

Understanding original antigenic sin in influenza with a dynamical system.

Original antigenic sin is the phenomenon in which prior exposure to an antigen leads to a subsequent suboptimal immune response to a related antigen. Immune memory normally allows for an improved and rapid response to antigens previously seen and is the mechanism by which vaccination works. I here develop a dynamical system model of the mechanism of original antigenic sin in influenza, clarifying and explaining the detailed spin-glass treatment of original antigenic sin. The dynamical system describes the viral load, the quantities of healthy and infected epithelial cells, the concentrations of naïve and memory antibodies, and the affinities of naïve and memory antibodies. I give explicit correspondences between the microscopic variables of the spin-glass model and those of the present dynamical system model. The dynamical system model reproduces the phenomenon of original antigenic sin and describes how a competition between different types of B cells compromises the overall effect of immune response. I illustrate the competition between the naïve and the memory antibodies as a function of the antigenic distance between the initial and subsequent antigens. The suboptimal immune response caused by original antigenic sin is observed when the host is exposed to an antigen which has intermediate antigenic distance to a second antigen previously recognized by the host's immune system.

A multi-scale model for correlation in B cell VDJ usage of zebrafish.

The zebrafish (Danio rerio) is one of the model animals used for the study of immunology because the dynamics in the adaptive immune system of zebrafish are similar to that in higher animals. In this work, we built a multi-scale model to simulate the dynamics of B cells in the primary and secondary immune responses of zebrafish. We use this model to explain the reported correlation between VDJ usage of B cell repertoires in individual zebrafish. We use a delay ordinary differential equation (ODE) system to model the immune responses in the 6-month lifespan of a zebrafish. This mean field theory gives the number of high-affinity B cells as a function of time during an infection. The sequences of those B cells are then taken from a distribution calculated by a 'microscopic' random energy model. This generalized NK model shows that mature B cells specific to one antigen largely possess a single VDJ recombination. The model allows first-principle calculation of the probability, p, that two zebrafish responding to the same antigen will select the same VDJ recombination. This probability p increases with the B cell population size and the B cell selection intensity. The probability p decreases with the B cell hypermutation rate. The multi-scale model predicts correlations in the immune system of the zebrafish that are highly similar to that from experiment.

Evolution of H3N2 influenza virus in a guinea pig model.

Studies of influenza virus evolution under controlled experimental conditions can provide a better understanding of the consequences of evolutionary processes with and without immunological pressure. Characterization of evolved strains assists in the development of predictive algorithms for both the selection of subtypes represented in the seasonal influenza vaccine and the design of novel immune refocused vaccines. To obtain data on the evolution of influenza in a controlled setting, naïve and immunized Guinea pigs were infected with influenza A/Wyoming/2003 (H3N2). Virus progeny from nasal wash samples were assessed for variation in the dominant and other epitopes by sequencing the hemagglutinin (HA) gene to quantify evolutionary changes. Viral RNA from the nasal washes from infection of naïve and immune animals contained 6% and 24.5% HA variant sequences, respectively. Analysis of mutations relative to antigenic epitopes indicated that adaptive immunity played a key role in virus evolution. HA mutations in immunized animals were associated with loss of glycosylation and changes in charge and hydrophobicity in and near residues within known epitopes. Four regions of HA-1 (75-85, 125-135, 165-170, 225-230) contained residues of highest variability. These sites are adjacent to or within known epitopes and appear to play an important role in antigenic variation. Recognition of the role of these sites during evolution will lead to a better understanding of the nature of evolution which help in the prediction of future strains for selection of seasonal vaccines and the design of novel vaccines intended to stimulated broadened cross-reactive protection to conserved sites outside of dominant epitopes.

Predicting Fixation Tendencies of the H3N2 Influenza Virus by Free Energy Calculation.

Influenza virus evolves to escape from immune system antibodies that bind to it. We used free energy calculations with Einstein crystals as reference states to calculate the difference of antibody binding free energy (ΔΔG) induced by amino acid substitution at each position in epitope B of the H3N2 influenza hemagglutinin, the key target for antibody. A substitution with positive ΔΔG value decreases the antibody binding constant. On average an uncharged to charged amino acid substitution generates the highest ΔΔG values. Also on average, substitutions between small amino acids generate ΔΔG values near to zero. The 21 sites in epitope B have varying expected free energy differences for a random substitution. Historical amino acid substitutions in epitope B for the A/Aichi/2/1968 strain of influenza A show that most fixed and temporarily circulating substitutions generate positive ΔΔG values. We propose that the observed pattern of H3N2 virus evolution is affected by the free energy landscape, the mapping from the free energy landscape to virus fitness landscape, and random genetic drift of the virus. Monte Carlo simulations of virus evolution are presented to support this view.

Quantifying selection and diversity in viruses by entropy methods, with application to the haemagglutinin of H3N2 influenza.

Many viruses evolve rapidly. For example, haemagglutinin (HA) of the H3N2 influenza A virus evolves to escape antibody binding. This evolution of the H3N2 virus means that people who have previously been exposed to an influenza strain may be infected by a newly emerged virus. In this paper, we use Shannon entropy and relative entropy to measure the diversity and selection pressure by an antibody in each amino acid site of H3 HA between the 1992-1993 season and the 2009-2010 season. Shannon entropy and relative entropy are two independent state variables that we use to characterize H3N2 evolution. The entropy method estimates future H3N2 evolution and migration using currently available H3 HA sequences. First, we show that the rate of evolution increases with the virus diversity in the current season. The Shannon entropy of the sequence in the current season predicts relative entropy between sequences in the current season and those in the next season. Second, a global migration pattern of H3N2 is assembled by comparing the relative entropy flows of sequences sampled in China, Japan, the USA and Europe. We verify this entropy method by describing two aspects of historical H3N2 evolution. First, we identify 54 amino acid sites in HA that have evolved in the past to evade the immune system. Second, the entropy method shows that epitopes A and B on the top of HA evolve most vigorously to escape antibody binding. Our work provides a novel entropy-based method to predict and quantify future H3N2 evolution and to describe the evolutionary history of H3N2.

Selective pressure to increase charge in immunodominant epitopes of the H3 hemagglutinin influenza protein.

The evolutionary speed and the consequent immune escape of H3N2 influenza A virus make it an interesting evolutionary system. Charged amino acid residues are often significant contributors to the free energy of binding for protein-protein interactions, including antibody-antigen binding and ligand-receptor binding. We used Markov chain theory and maximum likelihood estimation to model the evolution of the number of charged amino acids on the dominant epitope in the hemagglutinin protein of circulating H3N2 virus strains. The number of charged amino acids increased in the dominant epitope B of the H3N2 virus since introduction in humans in 1968. When epitope A became dominant in 1989, the number of charged amino acids increased in epitope A and decreased in epitope B. Interestingly, the number of charged residues in the dominant epitope of the dominant circulating strain is never fewer than that in the vaccine strain. We propose these results indicate selective pressure for charged amino acids that increase the affinity of the virus epitope for water and decrease the affinity for host antibodies. The standard PAM model of generic protein evolution is unable to capture these trends. The reduced alphabet Markov model (RAMM) model we introduce captures the increased selective pressure for charged amino acids in the dominant epitope of hemagglutinin of H3N2 influenza (R (2) > 0.98 between 1968 and 1988). The RAMM model calibrated to historical H3N2 influenza virus evolution in humans fit well to the H3N2/Wyoming virus evolution data from Guinea pig animal model studies.

A novel sequence-based antigenic distance measure for H1N1, with application to vaccine effectiveness and the selection of vaccine strains.

H1N1 influenza causes substantial seasonal illness and was the subtype of the 2009 influenza pandemic. Precise measures of antigenic distance between the vaccine and circulating virus strains help researchers design influenza vaccines with high vaccine effectiveness. We here introduce a sequence-based method to predict vaccine effectiveness in humans. Historical epidemiological data show that this sequence-based method is as predictive of vaccine effectiveness as hemagglutination inhibition assay data from ferret animal model studies. Interestingly, the expected vaccine effectiveness is greater against H1N1 than H3N2, suggesting a stronger immune response against H1N1 than H3N2. The evolution rate of hemagglutinin in H1N1 is also shown to be greater than that in H3N2, presumably due to greater immune selection pressure.

The epitope regions of H1-subtype influenza A, with application to vaccine efficacy.

The recent emergence of H1N1 (swine flu) illustrates the ability of the influenza virus to create antigens new to the human immune system, even within a given hemagglutinin and neuraminidase subtype. This new H1N1 strain is sufficiently distinct, for example, from the A/Brisbane/59/2007 (H1N1)-like virus strain of influenza in the 2008/09 Northern hemisphere vaccine that protection is not expected to be substantial. The human immune system responds primarily to the five epitope regions of the hemagglutinin protein. By determining the fraction of amino acids that differ between a vaccine strain and a viral challenge strain in the dominant epitope regions, a measure of antigenic distance that correlates with epidemiological studies of H3 influenza A vaccine efficacy in humans with R(2) = 0.81 is derived. This measure of antigenic distance is called p(epitope). The relation between vaccine efficacy and p(epitope) is given by E = 0.47 - 2.47 x p(epitope). We here identify the epitope regions of H1 hemagglutinin, so that vaccine efficacy may be reliably estimated for H1N1 influenza A.