A novel strategy for molecular interfaces optimization: the case of ferritin-transferrin receptor interaction

Protein-protein interactions regulate almost all cellular functions and rely on a fine tune of surface amino acids properties involved on both molecular partners. The disruption of a molecular association can be caused even by a single residue mutation, often leading to a pathological modification of a biochemical pathway. Therefore the evaluation of the effects of amino acid substitutions on binding, and the ad hoc design of protein-protein interfaces, is one of the biggest challenges in computational biology. Here, we present a novel strategy for computational mutation and optimization of protein-protein interfaces. Modeling the interaction surface properties using the Zernike polynomials, we describe the shape and electrostatics of binding sites with an ordered set of descriptors, making possible the evaluation of complementarity between interacting surfaces. With a Monte Carlo approach, we obtain protein mutants with controlled molecular complementarities. Applying this strategy to the relevant case of the interaction between Ferritin and Transferrin Receptor, we obtain a set of Ferritin mutants with increased or decreased complementarity. The extensive molecular dynamics validation of the method results confirms its efficacy, showing that this strategy represents a very promising approach in designing correct molecular interfaces

Spatio–temporal analysis of changes of shape for constituent bodies within biomolecular aggregates

Changes of shape are important in many situations of interest in biology at different typical length scales. Approaches for modelling the behaviour of droplets in suspension and thermallydriven motion of the molecular chains in enzymes are presented. Both models use orthogonal basis functions to describe the spatial dependences in a spherical geometry. Both models also describe the effect of time-dependent boundary data on the shape of the bodies involved, a stochastic response for the enzyme model (dimensions of the order 10−9 m) and smooth response for the colloidal model (dimensions of the order 10−6 m). The first model presented considers the behaviour of a droplet of fluid surrounded by a thin film of host fluid, both fluids being Newtonian and immiscible, with a well-defined continuous and smooth interface between these regions. The flows for the droplet and host fluid are assumed axisymmetric with small Reynold numbers. An extension of traditional lubrication theory is used to model the flow for the host fluid and a multi-modal Stokes flow is used to derive the flow within the droplet, subject to continuity conditions at the interface between the droplet and host fluid. The interface is free to move in response to the flows, under the effects of interfacial tension. Asymptotic expansions for the flow variables and interface are used to find the simplest behaviour of the system beyond the leading order. The second unique modelling approach used is the method of Zernike moments. Zernike moments are an extension of spherical harmonics to include more general radial dependence and the ability to model holes, folded layers etc. within and on the unit sphere. The method has traditionally been used to describe the shape of enzymes in a static time-independent manner. This approach is extended to give results based on the thermally-driven motion of atoms in molecules about their equilibrium positions. The displacements are assumed to be fitted by Normal probability distributions. The precision and accuracy of this model are considered and compared to similar models. Results are plotted and discussed for both regimes and further extensions, improvements and basis for further work are discussed for both approaches

Using diffusion distances for flexible molecular shape comparison

<p>Abstract</p> <p>Background</p> <p>Many molecules are flexible and undergo significant shape deformation as part of their function, and yet most existing molecular shape comparison (MSC) methods treat them as rigid bodies, which may lead to incorrect shape recognition.</p> <p>Results</p> <p>In this paper, we present a new shape descriptor, named Diffusion Distance Shape Descriptor (DDSD), for comparing 3D shapes of flexible molecules. The diffusion distance in our work is considered as an average length of paths connecting two landmark points on the molecular shape in a sense of inner distances. The diffusion distance is robust to flexible shape deformation, in particular to topological changes, and it reflects well the molecular structure and deformation without explicit decomposition. Our DDSD is stored as a histogram which is a probability distribution of diffusion distances between all sample point pairs on the molecular surface. Finally, the problem of flexible MSC is reduced to comparison of DDSD histograms.</p> <p>Conclusions</p> <p>We illustrate that DDSD is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. The presented algorithm is robust and does not require any prior knowledge of the flexible regions.</p

Fingerprint-based structure retrieval using electron density

We present a computational approach that can quickly search a large protein structural database to identify structures that fit a given electron density, such as determined by cryo-electron microscopy. We use geometric invariants (fingerprints) constructed using 3D Zernike moments to describe the electron density, and reduce the problem of fitting of the structure to the electron density to simple fingerprint comparison. Using this approach, we are able to screen the entire Protein Data Bank and identify structures that fit two experimental electron densities determined by cryo-electron microscopy

Liquid-Solid Transitions with Applications to Self-Assembly.

We study the thermodynamic and kinetic pathways by which liquids transform into solids, and their relation to the metastable states that commonly arise in self-assembly applications. As a case study in the formation of ordered metastable solids, we investigate the atomistic mechanism by which quasicrystals form. We show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal "nucleus" to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In a related study, we propose a two-part mechanism for forming 3d dodecagonal quasicrystals by self-assembly. Our mechanism involves (1) attaching small mobile particles to the surface of spherical particles to encourage icosahedral packing and (2) allowing a subset of particles to deviate from the ideal spherical shape, to discourage close-packing. In addition to studying metastable ordered solids, we investigate the phenomenology and mechanism of the glass transition. We report measurements of spatially heterogeneous dynamics in a system of air-driven granular beads approaching a jamming transition, and show that the dynamics in our granular system are quantitatively indistinguishable from those for a supercooled liquid approaching a glass transition. In a second study of the glass transition, we use transition path sampling to study the structure, statistics and dynamics of localized excitations for several model glass formers. We show that the excitations are sparse and localized, and their size is temperature-independent. We show that their equilibrium concentration is proportional to exp[-Ja(1/T-1/To)], where "Ja" is the energy scale for irreversible particle displacements of length "a," and "To" is an onset temperature. We show that excitation dynamics is facilitated by the presence of other excitations, causing dynamics to slow in a hierarchical way as temperature is lowered. To supplement our studies of liquid-solid transitions, we introduce a shape matching framework for characterizing structural transitions in systems with complex particle shapes or morphologies. We provide an overview of shape matching methods, explore a particular class of metrics known as "harmonic descriptors," and show that shape matching methods can be applied to a wide range of nanoscale and microscale assembly applications.Ph.D.Chemical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/78931/1/askeys_1.pd

Comprehensive analysis of lectin-glycan interactions reveals determinants of lectin specificity

Lectin-glycan interactions facilitate inter- and intracellular communication in many processes including protein trafficking, host-pathogen recognition, and tumorigenesis promotion. Specific recognition of glycans by lectins is also the basis for a wide range of applications in areas including glycobiology research, cancer screening, and antiviral therapeutics. To provide a better understanding of the determinants of lectin-glycan interaction specificity and support such applications, this study comprehensively investigates specificity-conferring features of all available lectin-glycan complex structures. Systematic characterization, comparison, and predictive modeling of a set of 221 complementary physicochemical and geometric features representing these interactions highlighted specificity-conferring features with potential mechanistic insight. Univariable comparative analyses with weighted Wilcoxon-Mann-Whitney tests revealed strong statistical associations between binding site features and specificity that are conserved across unrelated lectin binding sites. Multivariable modeling with random forests demonstrated the utility of these features for predicting the identity of bound glycans based on generalized patterns learned from non-homologous lectins. These analyses revealed global determinants of lectin specificity, such as sialic acid glycan recognition in deep, concave binding sites enriched for positively charged residues, in contrast to high mannose glycan recognition in fairly shallow but well-defined pockets enriched for non-polar residues. Focused fine specificity analysis of hemagglutinin interactions with human-like and avian-like glycans uncovered features representing both known and novel mutations related to shifts in influenza tropism from avian to human tissues. As the approach presented here relies on co-crystallized lectin-glycan pairs for studying specificity, it is limited in its inferences by the quantity, quality, and diversity of the structural data available. Regardless, the systematic characterization of lectin binding sites presented here provides a novel approach to studying lectin specificity and is a step towards confidently predicting new lectin-glycan interactions

Validação de heterogeneidade estrutural em dados de Crio-ME por comitês de agrupadores

Orientadores: Fernando José Von Zuben, Rodrigo Villares PortugalDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Análise de Partículas Isoladas é uma técnica que permite o estudo da estrutura tridimensional de proteínas e outros complexos macromoleculares de interesse biológico. Seus dados primários consistem em imagens de microscopia eletrônica de transmissão de múltiplas cópias da molécula em orientações aleatórias. Tais imagens são bastante ruidosas devido à baixa dose de elétrons utilizada. Reconstruções 3D podem ser obtidas combinando-se muitas imagens de partículas em orientações similares e estimando seus ângulos relativos. Entretanto, estados conformacionais heterogêneos frequentemente coexistem na amostra, porque os complexos moleculares podem ser flexíveis e também interagir com outras partículas. Heterogeneidade representa um desafio na reconstrução de modelos 3D confiáveis e degrada a resolução dos mesmos. Entre os algoritmos mais populares usados para classificação estrutural estão o agrupamento por k-médias, agrupamento hierárquico, mapas autoorganizáveis e estimadores de máxima verossimilhança. Tais abordagens estão geralmente entrelaçadas à reconstrução dos modelos 3D. No entanto, trabalhos recentes indicam ser possível inferir informações a respeito da estrutura das moléculas diretamente do conjunto de projeções 2D. Dentre estas descobertas, está a relação entre a variabilidade estrutural e manifolds em um espaço de atributos multidimensional. Esta dissertação investiga se um comitê de algoritmos de não-supervisionados é capaz de separar tais "manifolds conformacionais". Métodos de "consenso" tendem a fornecer classificação mais precisa e podem alcançar performance satisfatória em uma ampla gama de conjuntos de dados, se comparados a algoritmos individuais. Nós investigamos o comportamento de seis algoritmos de agrupamento, tanto individualmente quanto combinados em comitês, para a tarefa de classificação de heterogeneidade conformacional. A abordagem proposta foi testada em conjuntos sintéticos e reais contendo misturas de imagens de projeção da proteína Mm-cpn nos estados "aberto" e "fechado". Demonstra-se que comitês de agrupadores podem fornecer informações úteis na validação de particionamentos estruturais independetemente de algoritmos de reconstrução 3DAbstract: Single Particle Analysis is a technique that allows the study of the three-dimensional structure of proteins and other macromolecular assemblies of biological interest. Its primary data consists of transmission electron microscopy images from multiple copies of the molecule in random orientations. Such images are very noisy due to the low electron dose employed. Reconstruction of the macromolecule can be obtained by averaging many images of particles in similar orientations and estimating their relative angles. However, heterogeneous conformational states often co-exist in the sample, because the molecular complexes can be flexible and may also interact with other particles. Heterogeneity poses a challenge to the reconstruction of reliable 3D models and degrades their resolution. Among the most popular algorithms used for structural classification are k-means clustering, hierarchical clustering, self-organizing maps and maximum-likelihood estimators. Such approaches are usually interlaced with the reconstructions of the 3D models. Nevertheless, recent works indicate that it is possible to infer information about the structure of the molecules directly from the dataset of 2D projections. Among these findings is the relationship between structural variability and manifolds in a multidimensional feature space. This dissertation investigates whether an ensemble of unsupervised classification algorithms is able to separate these "conformational manifolds". Ensemble or "consensus" methods tend to provide more accurate classification and may achieve satisfactory performance across a wide range of datasets, when compared with individual algorithms. We investigate the behavior of six clustering algorithms both individually and combined in ensembles for the task of structural heterogeneity classification. The approach was tested on synthetic and real datasets containing a mixture of images from the Mm-cpn chaperonin in the "open" and "closed" states. It is shown that cluster ensembles can provide useful information in validating the structural partitionings independently of 3D reconstruction methodsMestradoEngenharia de ComputaçãoMestre em Engenharia Elétric

Protein contour modelling and computation for complementarity detection and docking

The aim of this thesis is the development and application of a model that effectively and efficiently integrates the evaluation of geometric and electrostatic complementarity for the protein-protein docking problem. Proteins perform their biological roles by interacting with other biomolecules and forming macromolecular complexes. The structural characterization of protein complexes is important to understand the underlying biological processes. Unfortunately, there are several limitations to the available experimental techniques, leaving the vast majority of these complexes to be determined by means of computational methods such as protein-protein docking. The ultimate goal of the protein-protein docking problem is the in silico prediction of the three-dimensional structure of complexes of two or more interacting proteins, as occurring in living organisms, which can later be verified in vitro or in vivo. These interactions are highly specific and take place due to the simultaneous formation of multiple weak bonds: the geometric complementarity of the contours of the interacting molecules is a fundamental requirement in order to enable and maintain these interactions. However, shape complementarity alone cannot guarantee highly accurate docking predictions, as there are several physicochemical factors, such as Coulomb potentials, van der Waals forces and hydrophobicity, affecting the formation of protein complexes. In order to set up correct and efficient methods for the protein-protein docking, it is necessary to provide a unique representation which integrates geometric and physicochemical criteria in the complementarity evaluation. To this end, a novel local surface descriptor, capable of capturing both the shape and electrostatic distribution properties of macromolecular surfaces, has been designed and implemented. The proposed methodology effectively integrates the evaluation of geometrical and electrostatic distribution complementarity of molecular surfaces, while maintaining efficiency in the descriptor comparison phase. The descriptor is based on the 3D Zernike invariants which possess several attractive features, such as a compact representation, rotational and translational invariance and have been shown to adequately capture global and local protein surface shape similarity and naturally represent physicochemical properties on the molecular surface. Locally, the geometric similarity between two portions of protein surface implies a certain degree of complementarity, but the same cannot be stated about electrostatic distributions. Complementarity in electrostatic distributions is more complex to handle, as charges must be matched with opposite ones even if they do not have the same magnitude. The proposed method overcomes this limitation as follows. From a unique electrostatic distribution function, two separate distribution functions are obtained, one for the positive and one for the negative charges, and both functions are normalised in [0, 1]. Descriptors are computed separately for the positive and negative charge distributions, and complementarity evaluation is then done by cross-comparing descriptors of distributions of charges of opposite signs. The proposed descriptor uses a discrete voxel-based representation of the Connolly surface on which the corresponding electrostatic potentials have been mapped. Voxelised surface representations have received a lot of interest in several bioinformatics and computational biology applications as a simple and effective way of jointly representing geometric and physicochemical properties of proteins and other biomolecules by mapping auxiliary information in each voxel. Moreover, the voxel grid can be defined at different resolutions, thus giving the means to effectively control the degree of detail in the discrete representation along with the possibility of producing multiple representations of the same molecule at different resolutions. A specific algorithm has been designed for the efficient computation of voxelised macromolecular surfaces at arbitrary resolutions, starting from experimentally-derived structural data (X-ray crystallography, NMR spectroscopy or cryo-electron microscopy). Fast surface generation is achieved by adapting an approximate Euclidean Distance Transform algorithm in the Connolly surface computation step and by exploiting the geometrical relationship between the latter and the Solvent Accessible surface. This algorithm is at the base of VoxSurf (Voxelised Surface calculation program), a tool which can produce discrete representations of macromolecules at very high resolutions starting from the three-dimensional information of their corresponding PDB files. By employing compact data structures and implementing a spatial slicing protocol, the proposed tool can calculate the three main molecular surfaces at high resolutions with limited memory demands. To reduce the surface computation time without affecting the accuracy of the representation, two parallel algorithms for the computation of voxelised macromolecular surfaces, based on a spatial slicing procedure, have been introduced. The molecule is sliced in a user-defined number of parts and the portions of the overall surface can be calculated for each slice in parallel. The molecule is sliced with planes perpendicular to the abscissa axis of the Cartesian coordinate system defined in the molecule's PDB entry. The first algorithms uses an overlapping margin of one probe-sphere radius length among slices in order to guarantee the correctness of the Euclidean Distance Transform. Because of this margin, the Connolly surface can be computed nearly independently for each slice. Communications among processes are necessary only during the pocket identification procedure which ensures that pockets spanning through more than one slice are correctly identified and discriminated from solvent-excluded cavities inside the molecule. In the second parallel algorithm the size of the overlapping margin between slices has been reduced to a one-voxel length by adapting a multi-step region-growing Euclidean Distance Transform algorithm. At each step, distance values are first calculated independently for every slice, then, a small portion of the borders' information is exchanged between adjacent slices. The proposed methodologies will serve as a basis for a full-fledged protein-protein docking protocol based on local feature matching. Rigorous benchmark tests have shown that the combined geometric and electrostatic descriptor can effectively identify shape and electrostatic distribution complementarity in the binding sites of protein-protein complexes, by efficiently comparing circular surface patches and significantly decreasing the number of false positives obtained when using a purely-geometric descriptor. In the validation experiments, the contours of the two interacting proteins are divided in circular patches: all possible patch pairs from the two proteins are then evaluated in terms of complementarity and a general ranking is produced. Results show that native patch pairs obtain higher ranks when using the newly proposed descriptor, with respect to the ranks obtained when using the purely-geometric one

Protein Shape Description and its Application to Shape Comparison

ProSHADE Repository: http://fg.oisin.rc-harwell.ac.uk/projects/proshade/There are currently over 138, 000 known macromolecular structures deposited in the wwPDB (Worldwide Protein Data Bank) database. While all the macromolecular structure files contain information about a particular structure, the collection of these files also allows combining the macromolecular structures to obtain statistical information about macromolecules in general. This fact has been the basis for many structural biology methods including the molecular replacement method used in X-ray crystallography or homologous structure restraints in the refinement methods. With the success of methods based on prior information, it is feasible that novel methods could be developed and current methods improved using further prior information; more specifically, by using the structure density-map shape similarity instead of sequence or model similarity. Therefore, this project introduces a mathematical framework for computing three different measures of macromolecular three-dimensional shape similarity and demonstrates how these descriptors can be applied in symmetry detection and protein-domain clustering. The ability to detect cyclic (C), dihedral (D), tetrahedral (T), octahedral (O) and icosahedral (I) symmetry groups as well as computing all associated symmetry elements has direct applications in map averaging and reducing the storage requirements by storing only the asymmetric information. Moreover, by having the capacity to find structures with similar shape, it was possible to reduce the size of the BALBES protein domain database by more than 18.7% and thus achieve proportional speed-up in the searching parts of its applications. Finally, the development of the method described in this project has many possible applications throughout structural biology. The method could, for example, facilitate matching and fitting of protein domains into the density maps produced by the electron-microscopy techniques, or it could allow for molecular-replacement candidate search using shape instead of sequence similarity. To allow for the development of any further applications, software for applying the methods described here is also presented and released for the community.Medical Research Council ( MC_US_A025_1012