Predicting multibody assembly of proteins

textThis thesis addresses the multi-body assembly (MBA) problem in the context of protein assemblies. [...] In this thesis, we chose the protein assembly domain because accurate and reliable computational modeling, simulation and prediction of such assemblies would clearly accelerate discoveries in understanding of the complexities of metabolic pathways, identifying the molecular basis for normal health and diseases, and in the designing of new drugs and other therapeutics. [...] [We developed] F²Dock (Fast Fourier Docking) which includes a multi-term function which includes both a statistical thermodynamic approximation of molecular free energy as well as several of knowledge-based terms. Parameters of the scoring model were learned based on a large set of positive/negative examples, and when tested on 176 protein complexes of various types, showed excellent accuracy in ranking correct configurations higher (F² Dock ranks the correcti solution as the top ranked one in 22/176 cases, which is better than other unsupervised prediction software on the same benchmark). Most of the protein-protein interaction scoring terms can be expressed as integrals over the occupied volume, boundary, or a set of discrete points (atom locations), of distance dependent decaying kernels. We developed a dynamic adaptive grid (DAG) data structure which computes smooth surface and volumetric representations of a protein complex in O(m log m) time, where m is the number of atoms assuming that the smallest feature size h is [theta](r[subscript max]) where r[subscript max] is the radius of the largest atom; updates in O(log m) time; and uses O(m)memory. We also developed the dynamic packing grids (DPG) data structure which supports quasi-constant time updates (O(log w)) and spherical neighborhood queries (O(log log w)), where w is the word-size in the RAM. DPG and DAG together results in O(k) time approximation of scoring terms where k << m is the size of the contact region between proteins. [...] [W]e consider the symmetric spherical shell assembly case, where multiple copies of identical proteins tile the surface of a sphere. Though this is a restricted subclass of MBA, it is an important one since it would accelerate development of drugs and antibodies to prevent viruses from forming capsids, which have such spherical symmetry in nature. We proved that it is possible to characterize the space of possible symmetric spherical layouts using a small number of representative local arrangements (called tiles), and their global configurations (tiling). We further show that the tilings, and the mapping of proteins to tilings on arbitrary sized shells is parameterized by 3 discrete parameters and 6 continuous degrees of freedom; and the 3 discrete DOF can be restricted to a constant number of cases if the size of the shell is known (in terms of the number of protein n). We also consider the case where a coarse model of the whole complex of proteins are available. We show that even when such coarse models do not show atomic positions, they can be sufficient to identify a general location for each protein and its neighbors, and thereby restricts the configurational space. We developed an iterative refinement search protocol that leverages such multi-resolution structural data to predict accurate high resolution model of protein complexes, and successfully applied the protocol to model gp120, a protein on the spike of HIV and currently the most feasible target for anti-HIV drug design.Computer Science

Structure and assembly of the S-layer determine virulence in C. difficile

Many bacteria and archaea possess a cell surface layer – S-layer – made of a 2D protein array that covers the entire cell. As the outermost component of the cell envelope, S-layers play crucial roles in many aspects of cell physiology. Importantly, many clinically relevant bacterial pathogens possess a distinct S-layer that forms an initial interface with the host, making it a potential target for development of species-specific antimicrobials. Targeted therapeutics are particularly important for antibiotic resistant pathogens such as Clostridioides difficile, the most frequent cause of hospital acquired diarrhea, which relies on disruption of normal microbiota through antibiotic usage. Despite the ubiquity of S-layers, only partial structural information from a very limited number of species is available and their function and organization remains poorly understood. Here we report the first complete atomic level structure and in situ assembly model of an S-layer from a bacterial pathogen and reveal its role in disease severity. SlpA, the main C. difficile S-layer protein, assembles through tiling of triangular prisms abutting the cell wall, interlocked by distinct ridges facing the environment. This forms a tightly packed array, unlike the more porous S-layer models previously described. We report that removing one of the SlpA ridge features dramatically reduces disease severity, despite being dispensable for overall SlpA structure and S-layer assembly. Remarkably, the effect on disease severity is independent of toxin production and bacterial colonization within the mouse model of disease. Our work combines X-ray and electron crystallography to reveal a novel S-layer organization in atomic detail, highlighting the need for multiple technical approaches to obtain structural information on these paracrystalline arrays. These data also establish a direct link between specific structural elements of S-layer and virulence for the first time, in a crucial paradigm shift in our understanding of C. difficile disease, currently largely attributed to the action of potent toxins. This work highlights the crucial role of S-layers in pathogenicity and the importance of detailed structural information for providing new therapeutic avenues, targeting the S-layer. Understanding the interplay between S-layer and other virulence factors will further enhance our ability to tackle pathogens carrying an S-layer. We anticipate that this work provides a solid basis for development of new, C. difficile-specific therapeutics, targeting SlpA structure and S-layer assembly to reduce the healthcare burden of these infections.

Analyzing and controlling large nanosystems with physics-trained neural networks

In dieser Arbeit wird untersucht, wie Neuronale Netze genutzt werden können, um die Auswertung von Experimenten durch Minimierung des Simulationsaufwandes beschleunigen zu können. Für die Rekonstruktion von Silber-Nanoclustern aus Einzelschuss-Weitwinkel-Streubildern können diese bereits aus kleinen Datenätzen allgemeine Rekonstruktionsregeln ableiten und ermöglichen durch direktes Training auf der Streuphysik unerreichte Detailtiefen. Für Giant-Dipole-Zustände von Rydbergexzitonen in Kupferoxydul wird mittels Deep Reinforcement Learning ein Anregungsschema aus Simulationen hergeleitet.This thesis investigates the possible application of neural networks in accelerating the evaluation of physical experiments while minimizing the required simulation effort. Neural networks are capable of inferring universal reconstruction rules for reconstructing silver nanoclusters from single wide-angle scattering patterns from a small set of simulated data and when trained directly on scattering theory reaching unmatched accuracy. A dynamic excitation for giant dipole states of Rydberg excitons in cuprous oxide is derived through deep reinforcement learning interacting and simulation data

Structure of the APPL1 BAR-PH domain and characterization of its interaction with Rab5

APPL1 is an effector of the small GTPase Rab5. Together, they mediate a signal transduction pathway initiated by ligand binding to cell surface receptors. Interaction with Rab5 is confined to the amino (N)-terminal region of APPL1. We report the crystal structures of human APPL1 N-terminal BAR-PH domain motif. The BAR and PH domains, together with a novel linker helix, form an integrated, crescent-shaped, symmetrical dimer. This BAR–PH interaction is likely conserved in the class of BAR-PH containing proteins. Biochemical analyses indicate two independent Rab-binding sites located at the opposite ends of the dimer, where the PH domain directly interacts with Rab5 and Rab21. Besides structurally supporting the PH domain, the BAR domain also contributes to Rab binding through a small surface region in the vicinity of the PH domain. In stark contrast to the helix-dominated, Rab-binding domains previously reported, APPL1 PH domain employs β-strands to interact with Rab5. On the Rab5 side, both switch regions are involved in the interaction. Thus we identified a new binding mode between PH domains and small GTPases

Self-Assembling Peptide Nanomaterials: Molecular Dynamics Studies, Computational Designs And Crystal Structure Characterizations

Peptides present complicated three-dimensional folds encoded in primary amino acid sequences of no more than 50 residues, providing cost-effective routes to the development of self-assembling nanomaterials.� The complexity and subtlety of the molecular interactions in such systems make it interesting to study and to understand the fundamental principles that determine the self-assembly of nanostructures and morphologies in solution. Such principles can then be applied to design novel self-assembling nanomaterials of precisely defined local structures and to controllably engineer new advanced functions into the materials. We first report the rational engineering of complementary hydrophobic interactions to control β-fibril type peptide self-assemblies that form hydrogel networks. Complementary to the experimental observations of the two distinct branching morphologies present in the two β-fibril systems that share a similar sequence pattern, we investigated on network branching, hydrogel properties by molecular dynamics simulations to provide a molecular picture of the assemblies. Next, we present the theory-guided computational design of novel peptides that adopt predetermined local nanostructures and symmetries upon solution assembly. Using such an approach, we discovered a non-natural, single peptide tetra-helical motif that can be used as a common building block for distinct predefined material nanostructures. The crystal structure of one designed peptide assembly demonstrates the atomistic match of the motif structure to the prediction, as well as provides fundamental feedback to the methods used to design and evaluate the computationally designed peptide candidates. This study could potentially improve the success rate of future designs of peptide-based self-assembling nanomaterials

Biaxial Nematic Order in Liver Tissue

Understanding how biological cells organize to form complex functional tissues is a question of key interest at the interface between biology and physics. The liver is a model system for a complex three-dimensional epithelial tissue, which performs many vital functions. Recent advances in imaging methods provide access to experimental data at the subcellular level. Structural details of individual cells in bulk tissues can be resolved, which prompts for new analysis methods. In this thesis, we use concepts from soft matter physics to elucidate and quantify structural properties of mouse liver tissue. Epithelial cells are structurally anisotropic and possess a distinct apico-basal cell polarity that can be characterized, in most cases, by a vector. For the parenchymal cells of the liver (hepatocytes), however, this is not possible. We therefore develop a general method to characterize the distribution of membrane-bound proteins in cells using a multipole decomposition. We first verify that simple epithelial cells of the kidney are of vectorial cell polarity type and then show that hepatocytes are of second order (nematic) cell polarity type. We propose a method to quantify orientational order in curved geometries and reveal lobule-level patterns of aligned cell polarity axes in the liver. These lobule-level patterns follow, on average, streamlines defined by the locations of larger vessels running through the tissue. We show that this characterizes the liver as a nematic liquid crystal with biaxial order. We use the quantification of orientational order to investigate the effect of specific knock-down of the adhesion protein Integrin ß-1. Building upon these observations, we study a model of nematic interactions. We find that interactions among neighboring cells alone cannot account for the observed ordering patterns. Instead, coupling to an external field yields cell polarity fields that closely resemble the experimental data. Furthermore, we analyze the structural properties of the two transport networks present in the liver (sinusoids and bile canaliculi) and identify a nematic alignment between the anisotropy of the sinusoid network and the nematic cell polarity of hepatocytes. We propose a minimal lattice-based model that captures essential characteristics of network organization in the liver by local rules. In conclusion, using data analysis and minimal theoretical models, we found that the liver constitutes an example of a living biaxial liquid crystal.:1. Introduction 1 1.1. From molecules to cells, tissues and organisms: multi-scale hierarchical organization in animals 1 1.2. The liver as a model system of complex three-dimensional tissue 2 1.3. Biology of tissues 5 1.4. Physics of tissues 9 1.4.1. Continuum descriptions 11 1.4.2. Discrete models 11 1.4.3. Two-dimensional case study: planar cell polarity in the fly wing 15 1.4.4. Challenges of three-dimensional models for liver tissue 16 1.5. Liquids, crystals and liquid crystals 16 1.5.1. The uniaxial nematic order parameter 19 1.5.2. The biaxial nematic ordering tensor 21 1.5.3. Continuum theory of nematic order 23 1.5.4. Smectic order 25 1.6. Three-dimensional imaging of liver tissue 26 1.7. Overview of the thesis 28 2. Characterizing cellular anisotropy 31 2.1. Classifying protein distributions on cell surfaces 31 2.1.1. Mode expansion to characterize distributions on the unit sphere 31 2.1.2. Vectorial and nematic classes of surface distributions 33 2.1.3. Cell polarity on non-spherical surfaces 34 2.2. Cell polarity in kidney and liver tissues 36 2.2.1. Kidney cells exhibit vectorial polarity 36 2.2.2. Hepatocytes exhibit nematic polarity 37 2.3. Local network anisotropy 40 2.4. Summary 41 3. Order parameters for tissue organization 43 3.1. Orientational order: quantifying biaxial phases 43 3.1.1. Biaxial nematic order parameters 45 3.1.2. Co-orientational order parameters 51 3.1.3. Invariants of moment tensors 52 3.1.4. Relation between these three schemes 53 3.1.5. Example: nematic coupling to an external field 55 3.2. A tissue-level reference field 59 3.3. Orientational order in inhomogeneous systems 62 3.4. Positional order: identifying signatures of smectic and columnar order 64 3.5. Summary 67 4. The liver lobule exhibits biaxial liquid-crystal order 69 4.1. Coarse-graining reveals nematic cell polarity patterns on the lobulelevel 69 4.2. Coarse-grained patterns match tissue-level reference field 73 4.3. Apical and basal nematic cell polarity are anti-correlated 74 4.4. Co-orientational order: nematic cell polarity is aligned with network anisotropy 76 4.5. RNAi knock-down perturbs orientational order in liver tissue 78 4.6. Signatures of smectic order in liver tissue 81 4.7. Summary 86 5. Effective models for cell and network polarity coordination 89 5.1. Discretization of a uniaxial nematic free energy 89 5.2. Discretization of a biaxial nematic free energy 91 5.3. Application to cell polarity organization in liver tissue 92 5.3.1. Spatial profile of orientational order in liver tissue 93 5.3.2. Orientational order from neighbor-interactions and boundary conditions 94 5.3.3. Orientational order from coupling to an external field 99 5.4. Biaxial interaction model 101 5.5. Summary 105 6. Network self-organization in a liver-inspired lattice model 107 6.1. Cubic lattice geometry motivated by liver tissue 107 6.2. Effective energy for local network segment interactions 110 6.3. Characterizing network structures in the cubic lattice geometry 113 6.4. Local interaction rules generate macroscopic network structures 115 6.5. Effect of mutual repulsion between unlike segment types on network structure 118 6.6. Summary 121 7. Discussion and Outlook 123 A. Appendix 127 A.1. Mean field theory fo the isotropic-uniaxial nematic transition 127 A.2. Distortions of the Mollweide projection 129 A.3. Shape parameters for basal membrane around hepatocytes 130 A.4. Randomized control for network segment anisotropies 130 A.5. The dihedral symmetry group D2h 131 A.6. Relation between orientational order parameters and elements of the super-tensor 134 A.7. Formal separation of molecular asymmetry and orientation 134 A.8. Order parameters under action of axes permutation 137 A.9. Minimal integrity basis for symmetric traceless tensors 139 A.10. Discretization of distortion free energy on cubic lattice 141 A.11. Metropolis Algorithm for uniaxial cell polarity coordination 142 A.12. States in the zero-noise limit of the nearest-neighbor interaction model 143 A.13. Metropolis Algorithm for network self-organization 144 A.14. Structural quantifications for varying values of mutual network segment repulsion 146 A.15. Structural quantifications for varying values of self-attraction of network segments 148 A.16. Structural quantifications for varying values of cell demand 150 Bibliography 152 Acknowledgements 17

The complementary use of theoretical structure prediction and X-ray powder diffraction data in crystal structure determination

The successful prediction of the crystal structure and symmetry of a material can give valuable insight into many of its properties, as well as the feasibility of thermodynamically stable poly-morphs to exist. It is not uncommon, however, for numerous theoretical structures to be found within a narrow energy range, making absolute characterisation of the crystal structure impossi-ble. The aim of this project was to investigate a number of structures from this scenario, high-lighting the key differences between three potential methods for the automated comparison of predicted and experimental crystal structures. This work was carried out by comparing the simulated powder diffraction patterns of theoretical predicted crystal structures of small organic materials with their experimental powder diffraction patterns, so that the experimentally identified structure could be automatically singled out from the many calculated. The use of traditional agreement factors (eg. Rwp) was compared with more sophisticated approaches namely PolySNAP, which uses principal-component analysis, and Compare.x, an algorithm based on weighted cross-correlation. Five structures were analysed, two of which had not been previously characterised. As the structure prediction calculations are carried out at 0K, and experimental data were collected over a range of temperatures (10K-293K), the effect of the resulting variations in lattice parameters on the automated processes is discussed. In all cases, Rwp has proven to be a poor and unreliable discriminator in the comparison of pre-dicted and experimental structures. The more contemporary methods based on PolySNAP and Compare.x both gave encouraging results when used to study the three known structures imida-zole, chlorothalonil and 5-azauracil, and they have consequently been used in the successful so-lution of the two previously unknown structures adenine and guanine. A difference in sensitivity in the matching of data collected at different temperatures between the latter approaches was noted. It was found that although there is considerable overlap between the two methods, they are not absolutely interchangeable, and this distinction may be exploited in future work where more case-specific comparisons are carried out. Automated comparison techniques cannot yet replace visual comparison completely, but they reduce it drastically. Ultimately, comparisons made computationally serve as a complement to human judgement, but they may not yet elimi-nate it

Frustration in Biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with a finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of "frustration" in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and how structure connects to function. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding, how a large part of the biological functions of proteins are related to subtle local frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. We hope to illustrate how Frustration is a fundamental concept in relating function to structural biology.Comment: 97 pages, 30 figure