Modeling of the three-dimensional structure of polypeptides in solution using potential-scaled/hot-solute molecular dynamics.

We present here an efficient and accurate procedure for modeling of the three-dimensional structures of polypeptides in the explicit solvent water based on molecular dynamics calculations. Using the toxic domain analog of heat-stable enterotoxin as a model peptide, we examined the utilities of two molecular dynamics techniques with the system containing the explicit solvent. One is the potential-scaled molecular dynamics that had been designed for effective conformational analyses of biomolecules with the explicit solvent water by partially scaling down the potential energies involved in the solute molecules. The other is the variation of Berendsen's weak coupling method (referred to as "hot-solute" method), in which only the solute of the system is heated to a high temperature while the solvent is kept at a normal temperature. Each method successfully increased the rate of folding of the peptides, and the most effective was a combination of the two methods. Moreover, the final structure obtained via cooling process successfully reproduced the experimentally known structure from the extended amino acid sequence using only the distance restraints representing three disulfide bonds in the peptide. Additional distance restraints derived from some of the NOE cross peaks accelerated the folding of the peptide, but gave almost the same structure as in the case without these additional restraints. Because a similar calculation without the explicit solvent could not reproduce the known structure, it is suggested that the explicit solvent water could play an important role in the modeling. The methods presented here have the potential for accurate modeling even when less experimental information was available.     

Improved prediction of RNA tertiary structure with insights into native state dynamics

The importance of RNA tertiary structure is evident from the growing number of published high resolution NMR and X-ray crystallographic structures of RNA molecules. These structures provide insights into function and create a knowledge base that is leveraged by programs such as Assemble, ModeRNA, RNABuilder, NAST, FARNA, Mc-Sym, RNA2D3D, and iFoldRNA for tertiary structure prediction and design. While these methods sample native-like RNA structures during simulations, all struggle to capture the native RNA conformation after scoring. We propose RSIM, an improved RNA fragment assembly method that preserves RNA global secondary structure while sampling conformations. This approach enhances the quality of predicted RNA tertiary structure, provides insights into the native state dynamics, and generates a powerful visualization of the RNA conformational space. RSIM is available for download from http://www.github.com/jpbida/rsim.     

Close correspondence between the motions from principal component analysis of multiple HIV-1 protease structures and elastic network modes

The large number of available HIV-1 protease structures provides a remarkable sampling of conformations of the different conformational states, which can be viewed as direct structural information about the dynamics of the HIV-1 protease. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide similar sampling of conformations.     

Describing RNA structure by libraries of clustered nucleotide doublets

The rapidly increasing wealth of structural information on RNA and knowledge of its varying roles in biology have facilitated the study of RNA structure using computational methods. Here, we present a new method to describe RNA structure based on nucleotide doublets, where a doublet is any two nucleotides in a structure. We restrict our search to doublets that are close together in space, but not necessarily in sequence, and obtain doublet libraries of various sizes by clustering a large set of doublets taken from a data set of high-resolution RNA structures. We demonstrate that these libraries are able to both capture structural features present in RNA and fit local RNA structure with a high level of accuracy. Libraries ranging in size from ten to 100 doublets are examined, and a detailed analysis shows that a library with as few as 30 doublets is sufficient to capture the most common structural features, while larger libraries would be more appropriate for accurate modeling. We anticipate many uses for these libraries, from annotation to structure refinement and prediction.     

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.     

Global Quantitative Modeling of Chromatin Factor Interactions

Chromatin is the driver of gene regulation, yet understanding the molecular interactions underlying chromatin factor combinatorial patterns (or the “chromatin codes”) remains a fundamental challenge in chromatin biology. Here we developed a global modeling framework that leverages chromatin profiling data to produce a systems-level view of the macromolecular complex of chromatin. Our model ultilizes maximum entropy modeling with regularization-based structure learning to statistically dissect dependencies between chromatin factors and produce an accurate probability distribution of chromatin code. Our unsupervised quantitative model, trained on genome-wide chromatin profiles of 73 histone marks and chromatin proteins from modENCODE, enabled making various data-driven inferences about chromatin profiles and interactions. We provided a highly accurate predictor of chromatin factor pairwise interactions validated by known experimental evidence, and for the first time enabled higher-order interaction prediction. Our predictions can thus help guide future experimental studies. The model can also serve as an inference engine for predicting unknown chromatin profiles — we demonstrated that with this approach we can leverage data from well-characterized cell types to help understand less-studied cell type or conditions.     

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.     

Turning limited experimental information into 3D models of RNA

Our understanding of RNA functions in the cell is evolving rapidly. As for proteins, the detailed three-dimensional (3D) structure of RNA is often key to understanding its function. Although crystallography and nuclear magnetic resonance (NMR) can determine the atomic coordinates of some RNA structures, many 3D structures present technical challenges that make these methods difficult to apply. The great flexibility of RNA, its charged backbone, dearth of specific surface features, and propensity for kinetic traps all conspire with its long folding time, to challenge in silico methods for physics-based folding. On the other hand, base-pairing interactions (either in runs to form helices or isolated tertiary contacts) and motifs are often available from relatively low-cost experiments or informatics analyses. We present RNABuilder, a novel code that uses internal coordinate mechanics to satisfy user-specified base pairing and steric forces under chemical constraints. The code recapitulates the topology and characteristic L-shape of tRNA and obtains an accurate noncrystallographic structure of the Tetrahymena ribozyme P4/P6 domain. The algorithm scales nearly linearly with molecule size, opening the door to the modeling of significantly larger structures.     

Quantifying the interplay between environmental and social effects on aggregated-fish dynamics

Demonstrating and quantifying the respective roles of social interactions and external stimuli governing fish dynamics is key to understanding fish spatial distribution. If seminal studies have contributed to our understanding of fish spatial organization in schools, little experimental information is available on fish in their natural environment, where aggregations often occur in the presence of spatial heterogeneities. Here, we applied novel modeling approaches coupled to accurate acoustic tracking for studying the dynamics of a group of gregarious fish in a heterogeneous environment. To this purpose, we acoustically tracked with submeter resolution the positions of twelve small pelagic fish (Selar crumenophthalmus) in the presence of an anchored floating object, constituting a point of attraction for several fish species. We constructed a field-based model for aggregated-fish dynamics, deriving effective interactions for both social and external stimuli from experiments. We tuned the model parameters that best fit the experimental data and quantified the importance of social interactions in the aggregation, providing an explanation for the spatial structure of fish aggregations found around floating objects. Our results can be generalized to other gregarious species and contexts as long as it is possible to observe the fine-scale movements of a subset of individuals.     

Molecular simulation of self-assembly of hydrophilic functionalized aromatics in aqueous solutions

This study identifies mechanisms of self-assembly of hydrophilic functionalized aromatic molecules—a distinct class of lyotropic materials. Results from molecular dynamics studies used to understand the moieties of the lyotropic molecule that affect the structure are consistent with experimental observations of these self-assembled structures. Coulombic forces, dominated by π–π interactions drives the self-assembly of this class of materials. Intra-molecular configurations of the aromatic rings—the extent of torsion or bending between the rings—as well as the structure of functional groups connected to the rings affect the self-assembled structures. In addition, the chemistry of the functional groups also affects how the molecules are oriented as they self assemble. Molecular modeling provides insight into design of these molecules.     

Resolving distance variations by single-molecule FRET and EPR spectroscopy using rotamer libraries

Förster resonance energy transfer (FRET) and electron paramagnetic resonance (EPR) spectroscopy are complementary techniques for quantifying distances in the nanometer range. Both approaches are commonly employed for probing the conformations and conformational changes of biological macromolecules based on site-directed fluorescent or paramagnetic labeling. FRET can be applied in solution at ambient temperature and thus provides direct access to dynamics, especially if used at the single-molecule level, whereas EPR requires immobilization or work at cryogenic temperatures but provides data that can be more reliably used to extract distance distributions. However, a combined analysis of the complementary data from the two techniques has been complicated by the lack of a common modeling framework. Here, we demonstrate a systematic analysis approach based on rotamer libraries for both FRET and EPR labels to predict distance distributions between two labels from a structural model. Dynamics of the fluorophores within these distance distributions are taken into account by diffusional averaging, which improves the agreement with experiment. Benchmarking this methodology with a series of surface-exposed pairs of sites in a structured protein domain reveals that the lowest resolved distance differences can be as small as ∼0.25 nm for both techniques, with quantitative agreement between experimental and simulated transfer efficiencies within a range of ±0.045. Rotamer library analysis thus establishes a coherent way of treating experimental data from EPR and FRET and provides a basis for integrative structural modeling, including studies of conformational distributions and dynamics of biological macromolecules using both techniques.     

Comparative evaluation of spin-label modeling methods for protein structural studies

Site-directed spin-labeling electron paramagnetic resonance spectroscopy is a powerful technique for the investigation of protein structure and dynamics. Accurate spin-label modeling methods are essential to make full quantitative use of site-directed spin-labeling electron paramagnetic resonance data for protein modeling and model validation. Using a set of double electron-electron resonance data from seven different site pairs on maltodextrin/maltose-binding protein under two different conditions using five different spin labels, we compare the ability of two widely used spin-label modeling methods, based on accessible volume sampling and rotamer libraries, to predict experimental distance distributions. We present a spin-label modeling approach inspired by canonical side-chain modeling methods and compare modeling accuracy with the established methods.     

Modeling microbial community structure and functional diversity across time and space

Microbial communities exhibit exquisitely complex structure. Many aspects of this complexity, from the number of species to the total number of interactions, are currently very difficult to examine directly. However, extraordinary efforts are being made to make these systems accessible to scientific investigation. While recent advances in high-throughput sequencing technologies have improved accessibility to the taxonomic and functional diversity of complex communities, monitoring the dynamics of these systems over time and space - using appropriate experimental design - is still expensive. Fortunately, modeling can be used as a lens to focus low-resolution observations of community dynamics to enable mathematical abstractions of functional and taxonomic dynamics across space and time. Here, we review the approaches for modeling bacterial diversity at both the very large and the very small scales at which microbial systems interact with their environments. We show that modeling can help to connect biogeochemical processes to specific microbial metabolic pathways.     

PROFcon: novel prediction of long-range contacts

MOTIVATION: Despite the continuing advance in the experimental determination of protein structures, the gap between the number of known protein sequences and structures continues to increase. Prediction methods can bridge this sequence-structure gap only partially. Better predictions of non-local contacts between residues could improve comparative modeling, fold recognition and could assist in the experimental structure determination. RESULTS: Here, we introduced PROFcon, a novel contact prediction method that combines information from alignments, from predictions of secondary structure and solvent accessibility, from the region between two residues and from the average properties of the entire protein. In contrast to some other methods, PROFcon predicted short and long proteins at similar levels of accuracy. As expected, PROFcon was clearly less accurate when tested on sparse evolutionary profiles, that is, on families with few homologs. Prediction accuracy was highest for proteins belonging to the SCOP alpha/beta class. PROFcon compared favorably with state-of-the-art prediction methods at the CASP6 meeting. While the performance may still be perceived as low, our method clearly pushed the mark higher. Furthermore, predictions are already accurate enough to seed predictions of global features of protein structure.     

Bayesian inference for improved single molecule fluorescence tracking

Single molecule tracking is widely used to monitor the change in position of lipids and proteins in living cells. In many experiments in which molecules are tagged with a single or small number of fluorophores, the signal/noise ratio may be limiting, the number of molecules is not known, and fluorophore blinking and photobleaching can occur. All these factors make accurate tracking over long trajectories difficult and hence there is still a pressing need to develop better algorithms to extract the maximum information from a sequence of fluorescence images. We describe here a Bayesian-based inference approach, based on a trans-dimensional sequential Monte Carlo method that utilizes both the spatial and temporal information present in the image sequences. We show, using model data, where the real trajectory of the molecule is known, that our method allows accurate tracking of molecules over long trajectories even with low signal/noise ratio and in the presence of fluorescence blinking and photobleaching. The method is then applied to real experimental data.     

Assessment of flexible backbone protein design methods for sequence library prediction in the therapeutic antibody Herceptin-HER2 interface

Computational protein design methods can complement experimental screening and selection techniques by predicting libraries of low-energy sequences compatible with a desired structure and function. Incorporating backbone flexibility in computational design allows conformational adjustments that should broaden the range of predicted low-energy sequences. Here, we evaluate computational predictions of sequence libraries from different protocols for modeling backbone flexibility using the complex between the therapeutic antibody Herceptin and its target human epidermal growth factor receptor 2 (HER2) as a model system. Within the program RosettaDesign, three methods are compared: The first two use ensembles of structures generated by Monte Carlo protocols for near-native conformational sampling: kinematic closure (KIC) and backrub, and the third method uses snapshots from molecular dynamics (MD) simulations. KIC or backrub methods were better able to identify the amino acid residues experimentally observed by phage display in the Herceptin-HER2 interface than MD snapshots, which generated much larger conformational and sequence diversity. KIC and backrub, as well as fixed backbone simulations, captured the key mutation Asp98Trp in Herceptin, which leads to a further threefold affinity improvement of the already subnanomolar parental Herceptin-HER2 interface. Modeling subtle backbone conformational changes may assist in the design of sequence libraries for improving the affinity of antibody-antigen interfaces and could be suitable for other protein complexes for which structural information is available.     

Key structural features of the actin filament Arp2/3 complex branch junction revealed by molecular simulation

We investigated the structure, properties and dynamics of the actin filament branch junction formed by actin-related protein (Arp) 2/3 complex using all-atom molecular dynamics (MD) simulations based on a model fit to a reconstruction from electron tomograms. Simulations of the entire structure consisting of 31 protein subunits together with solvent molecules containing ～3 million atoms were performed for an aggregate time of 175 ns. One 75-ns simulation of the original reconstruction was compared to two 50-ns simulations of alternate structures, showing that the hypothesized branch junction structure is very stable. Our simulations revealed that the interface between Arp2/3 complex and the mother actin filament features a large number of salt bridges and hydrophobic contacts, many of which are dynamic and formed/broken on the timescale of the simulation. The simulations suggest that the DNase binding loops in Arp3, and possibly Arp2, form stabilizing contacts with the mother filament. Unbiased comparison of models sampled from the MD simulation trajectory with the primary experimental electron tomography data identified regions were snapshots from the simulation provide atomic details of the model structures and also pinpoints regions where the initial modeling based on the electron tomogram reconstruction may be suboptimal.     

Conserved water molecules in a large family of microbial ribonucleases.

We systematically analyzed the crystallographically determined water molecules of all known structures of RNase T1 and compared them to the ordered solvent in a large number of related microbial nucleases. To assess the crystallographers' impact on the interpretation of the solvent structure, we independently refined five validation structures from diffraction data derived from five isomorphous crystals of RNase T1. We also compared the positions of water molecules found in 11 published isomorphous RNase T1 inhibitor complexes. These data suggest that the positions of most of the waters located on the surface of a protein and that are well-determined in the experimental electron density maps are determined primarily by crystal packing forces. Water molecules with less well-defined electron density are in general unique to one or a small number of crystal structures. Only a small number of the well-defined waters are found to be independent of the crystal environment. These waters have a low accessible surface area and B-factor, and tend to be conserved in the crystal structures of a number of evolutionary related ribonucleases as well. A single water molecule is found conserved in all known microbial ribonucleases.     

Incorporation of evolutionary information into Rosetta comparative modeling

Prediction of protein structures from sequences is a fundamental problem in computational biology. Algorithms that attempt to predict a structure from sequence primarily use two sources of information. The first source is physical in nature: proteins fold into their lowest energy state. Given an energy function that describes the interactions governing folding, a method for constructing models of protein structures, and the amino acid sequence of a protein of interest, the structure prediction problem becomes a search for the lowest energy structure. Evolution provides an orthogonal source of information: proteins of similar sequences have similar structure, and therefore proteins of known structure can guide modeling. The relatively successful Rosetta approach takes advantage of the first, but not the second source of information during model optimization. Following the classic work by Andrej Sali and colleagues, we develop a probabilistic approach to derive spatial restraints from proteins of known structure using advances in alignment technology and the growth in the number of structures in the Protein Data Bank. These restraints define a region of conformational space that is high-probability, given the template information, and we incorporate them into Rosetta's comparative modeling protocol. The combined approach performs considerably better on a benchmark based on previous CASP experiments. Incorporating evolutionary information into Rosetta is analogous to incorporating sparse experimental data: in both cases, the additional information eliminates large regions of conformational space and increases the probability that energy-based refinement will hone in on the deep energy minimum at the native state.