Accurate SAXS Profile Computation and its Assessment by Contrast Variation Experiments

AbstractA major challenge in structural biology is to characterize structures of proteins and their assemblies in solution. At low resolution, such a characterization may be achieved by small angle x-ray scattering (SAXS). Because SAXS analyses often require comparing profiles calculated from many atomic models against those determined by experiment, rapid and accurate profile computation from molecular structures is needed. We developed fast open-source x-ray scattering (FoXS) for profile computation. To match the experimental profile within the experimental noise, FoXS explicitly computes all interatomic distances and implicitly models the first hydration layer of the molecule. For assessing the accuracy of the modeled hydration layer, we performed contrast variation experiments for glucose isomerase and lysozyme, and found that FoXS can accurately represent density changes of this layer. The hydration layer model was also compared with a SAXS profile calculated for the explicit water molecules in the high-resolution structures of glucose isomerase and lysozyme. We tested FoXS on eleven protein, one DNA, and two RNA structures, revealing superior accuracy and speed versus CRYSOL, AquaSAXS, the Zernike polynomials-based method, and Fast-SAXS-pro. In addition, we demonstrated a significant correlation of the SAXS score with the accuracy of a structural model. Moreover, FoXS utility for analyzing heterogeneous samples was demonstrated for intrinsically flexible XLF-XRCC4 filaments and Ligase III-DNA complex. FoXS is extensively used as a standalone web server as a component of integrative structure determination by programs IMP, Chimera, and BILBOMD, as well as in other applications that require rapidly and accurately calculated SAXS profiles

Calculations of protein-protein interactions with the fast multipole method

I present a physical model to calculate protein-protein interactions. General formulations to calculate the electrostatic and the van der Waals free energies are brought by the boundary element method of solving linearized Poission-Boltzmann equation in an electrolyte solution, then further expanded to the application of the Fast Multipole Method(FMM). We built an efficient solver to investigate how the mutations on the active site of the protein-protein interface affect changes in binding affinities of protein complexes. Calculated results in addition to the structural analysis help us to understand the protein-protein interaction energy and provide a model to the important applications such as protein crystallization. The osmotic second virial coefficient B2 is directly related to the solubility of protein molecule in electrolyte solution and determined by molecular interactions involving both solvent and solute molecules. Calculations of interaction energies account for the electrostatic and the van der Waals interactions with the structural anisotropic properties of protein molecules. The orientation dependence of interaction energies between two proteins is determined by the crystal space operations and small number of protein-protein pair configurations according to the anisotropic patch model are required to calculate B2. With the extended FMMs, double-tree and single-tree algorithms, the boundary element formulations of interaction energies can be applied with low computational cost to the proteins. B2 Calculations of Bovine Pancreatic Trypsin Inhibitor are firstly performed to validate our model and the results of lysozyme protein under different salts, concentrations, pH and temperatures are correlated to the experimental B2. The reduced number of pair interaction energies between two proteins are interpolated to predict all pair interaction energies in the patch model as a precursor of the protein phase diagram calculation

Kinetic Solvers with Adaptive Mesh in Phase Space

An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for solving multi-dimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a tree of trees data structure. The mesh in r-space is automatically generated around embedded boundaries and dynamically adapted to local solution properties. The mesh in v-space is created on-the-fly for each cell in r-space. Mappings between neighboring v-space trees implemented for the advection operator in configuration space. We have developed new algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive mesh in velocity space: importance sampling, multi-point projection method, and the variance reduction method. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions in a Lorentz gas. New AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce computational cost and memory usage for solving challenging kinetic problems

Ab initio RNA folding

RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, experimental determination of RNA structures through X-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.Comment: 28 pages, 18 figure

Deriving Protein Structures Efficiently by Integrating Experimental Data into Biomolecular Simulations

Proteine sind molekulare Nanomaschinen in biologischen Zellen. Sie sind wesentliche Bausteine aller bekannten Lebensformen, von Einzellern bis hin zu Menschen, und erfüllen vielfältige Funktionen, wie beispielsweise den Sauerstofftransport im Blut oder als Bestandteil von Haaren. Störungen ihrer physiologischen Funktion können jedoch schwere degenerative Krankheiten wie Alzheimer und Parkinson verursachen. Die Entwicklung wirksamer Therapien für solche Proteinfehlfaltungserkrankungen erfordert ein tiefgreifendes Verständnis der molekularen Struktur und Dynamik von Proteinen. Da Proteine aufgrund ihrer lichtmikroskopisch nicht mehr auflösbaren Größe nur indirekt beobachtet werden können, sind experimentelle Strukturdaten meist uneindeutig. Dieses Problem lässt sich in silico mittels physikalischer Modellierung biomolekularer Dynamik lösen. In diesem Feld haben sich datengestützte Molekulardynamiksimulationen als neues Paradigma für das Zusammenfügen der einzelnen Datenbausteine zu einem schlüssigen Gesamtbild der enkodierten Proteinstruktur etabliert. Die Strukturdaten werden dabei als integraler Bestandteil in ein physikbasiertes Modell eingebunden. In dieser Arbeit untersuche ich, wie sogenannte strukturbasierte Modelle verwendet werden können, um mehrdeutige Strukturdaten zu komplementieren und die enthaltenen Informationen zu extrahieren. Diese Modelle liefern eine effiziente Beschreibung der aus der evolutionär optimierten nativen Struktur eines Proteins resultierenden Dynamik. Mithilfe meiner systematischen Simulationsmethode XSBM können biologische Kleinwinkelröntgenstreudaten mit möglichst geringem Rechenaufwand als physikalische Proteinstrukturen interpretiert werden. Die Funktionalität solcher datengestützten Methoden hängt stark von den verwendeten Simulationsparametern ab. Eine große Herausforderung besteht darin, experimentelle Informationen und theoretisches Wissen in geeigneter Weise relativ zueinander zu gewichten. In dieser Arbeit zeige ich, wie die entsprechenden Simulationsparameterräume mit Computational-Intelligence-Verfahren effizient erkundet und funktionale Parameter ausgewählt werden können, um die Leistungsfähigkeit komplexer physikbasierter Simulationstechniken zu optimieren. Ich präsentiere FLAPS, eine datengetriebene metaheuristische Optimierungsmethode zur vollautomatischen, reproduzierbaren Parametersuche für biomolekulare Simulationen. FLAPS ist ein adaptiver partikelschwarmbasierter Algorithmus inspiriert vom Verhalten natürlicher Vogel- und Fischschwärme, der das Problem der relativen Gewichtung verschiedener Kriterien in der multivariaten Optimierung generell lösen kann. Neben massiven Fortschritten in der Verwendung von künstlichen Intelligenzen zur Proteinstrukturvorhersage ermöglichen leistungsoptimierte datengestützte Simulationen detaillierte Einblicke in die komplexe Beziehung von biomolekularer Struktur, Dynamik und Funktion. Solche computergestützten Methoden können Zusammenhänge zwischen den einzelnen Puzzleteilen experimenteller Strukturinformationen herstellen und so unser Verständnis von Proteinen als den Grundbausteinen des Lebens vertiefen

Improving the accuracy and efficiency of docking methods

Computational methods for predicting macromolecular complexes are useful tools for studying biological systems. They are used in areas such as drug design and for studying protein-protein interactions. While considerable progress has been made in this field over the decades, enhancing the speed and accuracy of these computational methods remains an important challenge. This work describes two different enhancements to the accuracy of ClusPro, a method for performing protein-protein docking, as well as an enhancement to the efficiency of global rigid body docking. SAXS is a high throughput technique collected for molecules in solution, and the data provides information about the shape and size of molecules. ClusPro was enhanced with the ability to SAXS data collected for protein complexes to guide docking by selecting conformations by how well they match the experimental data, which improved docking accuracy when such data is available. Various other experimental techniques, such as NMR, FRET, or chemical cross linking can provide information about protein-protein interfaces, and such information can be used to generate distance-based restraints between pairs of residues across the interface. A second enhancement to ClusPro enables the use of such distance restraints to improve docking accuracy. Finally, an enhancement to the efficiency of FFT based global docking programs was developed. This enhancement allows for the efficient search of multiple sidechain conformations, and this improved program was applied to the flexible computational solvent mapping program FTFlex.2018-07-09T00:00:00

Towards a microscopic understanding of phonon heat conduction

Heat conduction by phonons is a ubiquitous process that incorporates a wide range of physics and plays an essential role in applications ranging from space power generation to LED lighting. Heat conduction has been studied for over two hundred years, yet many microscopic aspects of heat conduction have remained unclear in most crystalline solids, including which phonons carry heat and how natural and artificial structures scatter specific phonons. Fortunately, recent advances in both computation and experiment are enabling an unprecedented microscopic view of thermal transport by phonons. In this topical review, we provide an overview of these methods, the insights they are providing, and their impact on the science and engineering of heat conduction

Incorporating Fresnel-Propagation into Electron Holographic Tomography: A possible way towards three-dimensional atomic resolution

Tomographic electron holography combines tomography, the reconstruction of three-dimensionally resolved data from multiple measurements with different specimen orientations, with electron holography, an interferometrical method for measuring the complex wave function inside a transmission electron microscope (TEM). Due to multiple scattering and free wave propagation conventional, ray projection based, tomography does perform badly when approaching atomic resolution. This is remedied by incorporating propagation effects into the projection while maintaining linearity in the object potential. Using the Rytov approach an approximation is derived, where the logarithm of the complex wave is linear in the potential. The ray projection becomes a convolution with a Fresnel propagation kernel, which is considerably more computationally expensive. A framework for such calculations has been implemented in Python. So has a multislice electron scattering algorithm, optimised for large fields of view and high numbers of atoms for simulations of scattering at nanoparticles. The Rytov approximation gives a remarkable increase in resolution and signal quality over the conventional approach in the tested system of a tungsten disulfide nanotube. The response to noise seems to be similar as in conventional tomography, so rather benign. This comes at the downside of much longer calculation time per iteration.Tomographische Elektronenholographie kombiniert Tomographie, die Rekonstruktion dreidimensional aufgelößter Daten aus einem Satz von mehreren Messungen bei verschiedenen Objektorientierungen, mit Elektronenholographie, eine interferrometrische Messung der komplexen Elektronenwelle im Transmissionselektronenmikroskop (TEM). Wegen Mehrfachstreuung und Propagationseffekten erzeugt konventionelle, auf einer Strahlprojektion basierende, Tomography ernste Probleme bei Hochauflösung hin zu atomarer Auflösung. Diese sollen durch ein Modell, welches Fresnel-Propagation beinhaltet, aber weiterhin linear im Potential des Objektes ist, vermindert werden. Mit dem Rytov-Ansatz wird eine Näherung abgeleitet, wobei der Logarithmus der komplexen Welle linear im Potential ist. Die Strahlen-Projektion ist dann eine Faltung mit dem Fresnel-Propagations-Faltungskernel welche rechentechnisch wesentlich aufwendiger ist. Ein Programm-Paket für solche Rechnungen wurde in Python implementiert. Weiterhin wurde ein Multislice Algorithmus für große Gesichtsfelder und Objekte mit vielen Atomen wie Nanopartikel optimiert. Die Rytov-Näherung verbessert sowohl die Auflösung als auch die Signalqualität immens gegenüber konventioneller Tomographie, zumindest in dem getesteten System eines Wolframdisulfid-Nanoröhrchens. Das Rauschverhalten scheint ähnlich der konventionallen Tomographie zu sein, also eher gutmütig. Im Gegenzug braucht die Tomographie basierend auf der Rytov-Näherung wesentlich mehr Rechenzeit pro Iteration

Efficient Geometry and Illumination Representations for Interactive Protein Visualization

This dissertation explores techniques for interactive simulation and visualization for large protein datasets. My thesis is that using efficient representations for geometric and illumination data can help in developing algorithms that achieve better interactivity for visual and computational proteomics. I show this by developing new algorithms for computation and visualization for proteins. I also show that the same insights that resulted in better algorithms for visual proteomics can also be turned around and used for more efficient graphics rendering. Molecular electrostatics is important for studying the structures and interactions of proteins, and is vital in many computational biology applications, such as protein folding and rational drug design. We have developed a system to efficiently solve the non-linear Poisson-Boltzmann equation governing molecular electrostatics. Our system simultaneously improves the accuracy and the efficiency of the solution by adaptively refining the computational grid near the solute-solvent interface. In addition, we have explored the possibility of mapping the PBE solution onto GPUs. We use pre-computed accumulation of transparency with spherical-harmonics-based compression to accelerate volume rendering of molecular electrostatics. We have also designed a time- and memory-efficient algorithm for interactive visualization of large dynamic molecules. With view-dependent precision control and memory-bandwidth reduction, we have achieved real-time visualization of dynamic molecular datasets with tens of thousands of atoms. Our algorithm is linearly scalable in the size of the molecular datasets. In addition, we present a compact mathematical model to efficiently represent the six-dimensional integrals of bidirectional surface scattering reflectance distribution functions (BSSRDFs) to render scattering effects in translucent materials interactively. Our analysis first reduces the complexity and dimensionality of the problem by decomposing the reflectance field into non-scattered and subsurface-scattered reflectance fields. While the non-scattered reflectance field can be described by 4D bidirectional reflectance distribution functions (BRDFs), we show that the scattered reflectance field can also be represented by a 4D field through pre-processing the neighborhood scattering radiance transfer integrals. We use a novel reference-points scheme to compactly represent the pre-computed integrals using a hierarchical and progressive spherical harmonics representation. Our algorithm scales linearly with the number of mesh vertices