A caracterização das flutuações dos resíduos da proteína em torno do seu estado nativo é essencial para estudar mudanças conformacionais, interação proteína-proteína e interação proteína-ligante. Tal caracterização pode ser capturada pelo modelo de rede gaussiana (GNM). Este modelo tem sido modificado e novas propostas têm surgido nos últimos anos. Nesta Tese, apresentamos um estudo sobre como melhorar o GNM e exploramos o seu desempenho em predizer os fatores-B experimentais. Modelos de redes elásticas são construídos a partir das coordenadas experimentais dos levando em consideração pares de átomos de C? distantes entre si até um dado raio de corte Rc . Estes modelos descrevem as interações entre os atómos por molas com a mesma constante de força. Desenvolvemos um método baseado em simulações numéricas com um campo de forças simplificado para atribuir pesos a estas constantes de mola. Este método considera o tempo em que dois átomos de C? permanecem conectados na rede durante o desenovelamento parcial, estabelecendo assim uma forma de medir a intensidade de cada ligação. Examinamos dois diferentes campos de forças simplificados e exploramos o cálculo desses pesos a partir do desenovelamento das estruturas nativas. Nós comparamos o seu desempenho na predição dos fatores-B com outros modelos de rede elástica. Avaliamos tal desempenho utilizando o coeficiente de correlação entre os fatores-B preditos e experimentais. Mostramos como o nosso modelo pode descrever melhor os fatores-B / The characterization of the fluctuations in protein residues around its native state is essential to study conformational changes, protein binding interaction and protein-protein interaction. Such characterization can be captured by simple elastic network models as the Gaussian Network Model (GNM). This model has been modified and new proposals have emerged in recent years. In this Thesis we propose an extended version of GNM, namely wGNM. Elastic network models are built on the experimental C? coordinates,and they only take the pairs of C? atoms within a given cutoff distance Rc into account. These models describe the interactions by elastic springs with the same force constant to predicted the experimental B-factors, providing insights into the structure-function properties of proteins. We have developed a method based on numerical simulations with a simple coarse-grained force field, to attribute weights to these spring constants. This method considers the time that two C? atoms remain connected in the network during partial unfolding, establishing a means of measuring the strength of each link. We examined two different coarse-grained force fields and explored the computation of these weights by unfolding native structures. We compare the B-factors predicted by different elastic network models with the experimental ones employing the correlation coefficient between these two quantities. We show that wGNM performs better and consequently provides better evaluation of the B-factors

Conformational selection is the idea that proteins traverse positions on the conformational space represented by their potential energy landscape, and in particular positions considered as local energy minima. Conformational selection a useful concept in ligand binding studies and in exploring the behavior of protein structures within that energy landscape. Often, research that explores protein function requires the generation of conformational ensembles, or collections of protein conformations from a single structure. We describe a method of conformational ensemble generation that uses joint-constrained rigid-body dynamics (an approach that allows for explicit consideration of rigidity) and the elastic network model (providing structurally derived directional guides for the rigid-body model). We test our model on a selection of unbound proteins and examine the structural validity of the resulting ensembles, as well as the ability of such an approach to generate conformations with structural overlaps close to the ligand-bound versions of the proteins.

The scope of this work focuses on computationally modeling compounds with protein structures. While the impetus of drug discovery is the innovation of new therapeutic molecules, it also involves distinguishing molecules that would not be an effective drug. This can be achieved by inventing new tools or by refining old tools. Virtual screening (VS, also called docking), the computational modeling of a molecule in a receptor structure, is a staple in predicting a molecule's affinity for an intended target. In our Virtual Target Screening system (also called inverse-docking), VS is used to find high-affinity targets, which can potentially explain absorption, distribution, metabolism, and excretion (ADME) of a molecule of interest in the human body. The next project, low-mode docking (LD), attempts to improve VS by incorporating protein flexibility into traditional docking where a static receptor structure has potential to produce poor results due to incorrectly predicted ligand poses. Finally, VS, performed mostly on small molecules, is scaled up to cyclic peptides by employing Monte Carlo simulations and molecular dynamics to mimic the steps of small molecule VS. The first project discussed is Virtual Target Screening (also called inverse-docking) where a small molecule is virtually screened against a library of protein structures. Predicting receptors to which a synthesized compound may bind would give insights to drug repurposing, metabolism, toxicity, and lead optimization. Our protocol calibrates each protein entry with a diverse set of small molecule structures, the NCI Diversity Set I. Our test set, 20 kinase inhibitors, was predicted to have a high percentage of kinase "hits" among approximately 1500 protein structures. Further, approved drugs within the test set generally had better rates of kinase hits. Next, normal mode analysis (NMA), which can computationally describe the fundamental motions of a receptor structure, is utilized to approach the rigid body bias problem in traditional docking techniques. Traditional docking involves the selection of a static receptor structure for VS; however, protein structures are dynamic. Simulation of the induced fit effect in protein-ligand binding events is modeled by full articulation of the approximated large-scale low-frequency normal modes of vibration, or "low-modes," coupled with the docking of a ligand structure. Low-mode dockings of 40 cyclin dependent 2 (CDK2) inhibitors into 54 low-modes of CDK2 yielded minimum root-mean-square deviation (RMSD) values of 1.82 – 1.20 Å when compared to known coordinate data. The choice of pose is currently limited to docking score, however, with ligand pose RMSD values of 3.87 – 2.07 Å. When compared to corresponding traditional dockings with RMSD values of 5.89 – 2.33 Å, low-mode docking was more accurate. The last discussion involves the rational docking of a cyclic peptide to the murine double minute 2 (MDM2) oncoprotein. The affinity for a cyclic peptide (synthesized by Priyesh Jain, McLaughin Lab, University of South Florida), PJ-8-73, in MDM2 was found to be within an order of magnitude of a cyclic peptide from the Robinson Lab at the University of Zurich in Switzerland. Both are Β-hairpin cyclic peptides with IC50 values of 650 nm and 140 nm, respectively. Using the co-crystalized structure of the Robinson peptide (PDB 2AXI), we modeled the McLaughlin peptide based on an important interaction of the 6-chloro-tryptophan residue of the Robinson peptide occupying the same pocket in MDM2 as the tryptophan residue by the native p53 transactivation helical domain. By preserving this interaction in initial cyclic peptide poses, the resulting pose of PJ-8-73 structure in MDM2 possessed comparable active site residue contacts and surface area. These protocols will aid medical research by using computer technology to reduce cost and time. VTS utilizes a unique structural and statistical calibration to virtually assay thousands of protein structures to predict high affinity binding. Determining unintended protein targets aids in creating more effective drugs. In low-mode docking, the accuracy of virtual screening was increased by including the fundamental motions of proteins. This newfound accuracy can decrease false negative results common in virtual screening. Lastly, docking techniques, usually for small molecules, were applied to larger peptide molecules. These modifications allow for the prediction of peptide therapeutics in protein-protein interaction modulation, a growing interest in medicine. Impactful in their own ways, these procedures contribute to the discovery of drugs, whether they are small molecules or cyclic peptides.

Conformational selection is the idea that proteins traverse positions on the conformational space represented by their potential energy landscape, and in particular positions considered as local energy minima. Conformational selection a useful concept in ligand binding studies and in exploring the behavior of protein structures within that energy landscape. Often, research that explores protein function requires the generation of conformational ensembles, or collections of protein conformations from a single structure. We describe a method of conformational ensemble generation that uses joint-constrained rigid-body dynamics (an approach that allows for explicit consideration of rigidity) and the elastic network model (providing structurally derived directional guides for the rigid-body model). We test our model on a selection of unbound proteins and examine the structural validity of the resulting ensembles, as well as the ability of such an approach to generate conformations with structural overlaps close to the ligand-bound versions of the proteins.

abstract: The goal of this theoretical study of infrared spectra was to ascertain to what degree molecules may be identified from their IR spectra and which spectral regions are best suited for this purpose. The frequencies considered range from the lowest frequency molecular vibrations in the far-IR, terahertz region (below ~3 THz or 100 cm-1) up to the highest frequency vibrations (~120 THz or 4000 cm-1). An emphasis was placed on the IR spectra of chemical and biological threat molecules in the interest of detection and prevention. To calculate IR spectra, the technique of normal mode analysis was applied to organic molecules ranging in size from 8 to 11,352 atoms. The IR intensities of the vibrational modes were calculated in terms of the derivative of the molecular dipole moment with respect to each normal coordinate. Three sets of molecules were studied: the organophosphorus G- and V-type nerve agents and chemically related simulants (15 molecules ranging in size from 11 to 40 atoms); 21 other small molecules ranging in size from 8 to 24 atoms; and 13 proteins ranging in size from 304 to 11,352 atoms. Spectra for the first two sets of molecules were calculated using quantum chemistry software, the last two sets using force fields. The "middle" set used both methods, allowing for comparison between them and with experimental spectra from the NIST/EPA Gas-Phase Infrared Library. The calculated spectra of proteins, for which only force field calculations are practical, reproduced the experimentally observed amide I and II bands, but they were shifted by approximately +40 cm-1 relative to experiment. Considering the entire spectrum of protein vibrations, the most promising frequency range for differentiating between proteins was approximately 600-1300 cm-1 where water has low absorption and the proteins show some differences. / Dissertation/Thesis / Ph.D. Physics 2012

A caracterização das flutuações dos resíduos da proteína em torno do seu estado nativo é essencial para estudar mudanças conformacionais, interação proteína-proteína e interação proteína-ligante. Tal caracterização pode ser capturada pelo modelo de rede gaussiana (GNM). Este modelo tem sido modificado e novas propostas têm surgido nos últimos anos. Nesta Tese, apresentamos um estudo sobre como melhorar o GNM e exploramos o seu desempenho em predizer os fatores-B experimentais. Modelos de redes elásticas são construídos a partir das coordenadas experimentais dos levando em consideração pares de átomos de C? distantes entre si até um dado raio de corte Rc . Estes modelos descrevem as interações entre os atómos por molas com a mesma constante de força. Desenvolvemos um método baseado em simulações numéricas com um campo de forças simplificado para atribuir pesos a estas constantes de mola. Este método considera o tempo em que dois átomos de C? permanecem conectados na rede durante o desenovelamento parcial, estabelecendo assim uma forma de medir a intensidade de cada ligação. Examinamos dois diferentes campos de forças simplificados e exploramos o cálculo desses pesos a partir do desenovelamento das estruturas nativas. Nós comparamos o seu desempenho na predição dos fatores-B com outros modelos de rede elástica. Avaliamos tal desempenho utilizando o coeficiente de correlação entre os fatores-B preditos e experimentais. Mostramos como o nosso modelo pode descrever melhor os fatores-B / The characterization of the fluctuations in protein residues around its native state is essential to study conformational changes, protein binding interaction and protein-protein interaction. Such characterization can be captured by simple elastic network models as the Gaussian Network Model (GNM). This model has been modified and new proposals have emerged in recent years. In this Thesis we propose an extended version of GNM, namely wGNM. Elastic network models are built on the experimental C? coordinates,and they only take the pairs of C? atoms within a given cutoff distance Rc into account. These models describe the interactions by elastic springs with the same force constant to predicted the experimental B-factors, providing insights into the structure-function properties of proteins. We have developed a method based on numerical simulations with a simple coarse-grained force field, to attribute weights to these spring constants. This method considers the time that two C? atoms remain connected in the network during partial unfolding, establishing a means of measuring the strength of each link. We examined two different coarse-grained force fields and explored the computation of these weights by unfolding native structures. We compare the B-factors predicted by different elastic network models with the experimental ones employing the correlation coefficient between these two quantities. We show that wGNM performs better and consequently provides better evaluation of the B-factors

A novel method of analysis of macromolecules has been worked upon through this research. In an effort to understand the dynamics of macromolecules and to further our knowledge, pertaining specifically to the low frequency domain and also to elucidate certain important biological functions associated with it, a theoretical technique of chemical information based Normal Mode Analysis has been developed. These simulations render users with the ability to generate animations of modeshapes as well as key insight on the associated vibration frequencies. Harmonic analysis using atomistic details is performed taking into account appropriate values of masses of constituent atoms of a given macromolecule. In order to substantiate the applicability of such a technique, simple linear molecules were first worked upon. Subsequently, this technique has been applied to relatively more complex structures like amino acids, namely Cysteine. Consequently, this approach was extended to large macromolecules like Lactoferrin. Animations of modeshapes from simulations suggest a one to one correspondence with other computational techniques reported by other researchers. Computed β-factors are also in close agreement with the experimentally observed values of the same. Hence, as opposed to a simple Cα coarse grained model, our method with right masses and reasonable force fields yields not only the correct modeshapes but also provides us with useful information on wavenumbers that can be used to extract useful information about the frequency domain. Moreover, as opposed to conventional Molecular Dynamics’ simulations and Laser spectroscopy, the proposed methodology is significantly faster, cheaper and efficient.

<p dir="ltr">Proteins and their interactions with each other, with nucleic acids, and with other molecules are foundational to all known forms of life. The three-dimensional structures of these interactions are an essential component of a comprehensive understanding of how they function. Molecular-biological hypothesis formulation and rational drug design are both often predicated on a particular structure model of the molecule or complex of interest. While experimental methods capable of determining atomic-detail structures of molecules and complexes exist, such as the popular X-ray crystallography and cryo-electron microscopy, these methods require both laborious sample preparation and expensive instruments with limited throughput. Computational methods of predicting complex structures are therefore desirable if they can enable cheap, high-throughput virtual screening of the space of biological hypotheses. Many common biomolecular contexts have largely been blind spots for predictive modeling of complex structures. In this direction, docking methods are proposed to address extreme conformational change, nonuniform environments, and distance-geometric priors. Flex-LZerD deforms a flexible protein using a novel fitting procedure based on iterated normal mode decomposition and was shown to construct accurate complex models even when an initial input subunit structure exhibits extreme conformational differences from its bound state. Mem-LZerD efficiently constrains the docking search space by augmenting the geometric hashing data structure at the core of the LZerD algorithm and enabled membrane protein complexes to be efficiently and accurately modeled. Finally, atomic distance-based approaches developed during modeling competitions and collaborations with wet lab biologists were shown to effectively integrate domain knowledge into complex modeling pipelines.</p>

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In general, this dissertation is concerned with modeling of mechanical behavior of protein molecules. In particular, we focus on coarse-grained models, which bridge the gap in time and length scale between the atomistic simulation and biological processes. The dissertation presents three independent studies involving such models. The first study is concerned with a rigorous coarse-graining method for dynamics of linear systems. In this method, as usual, the conformational space of the original atomistic system is divided into master and slave degrees of freedom. Under the assumption that the characteristic timescales of the masters are slower than those of the slaves, the method results in Langevin-type equations of motion governed by an effective potential of mean force. In addition, coarse-graining introduces hydrodynamic-like coupling among the masters as well as non-trivial inertial effects. Application of our method to the long-timescale part of the relaxation spectra of proteins shows that such dynamic coupling is essential for reproducing their relaxation rates and modes. The second study is concerned with calibration of elastic network models based on the so-called B-factors, obtained from x-ray crystallographic measurements. We show that a proper calibration procedure must account for rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used elastic network models, leading to potentially erroneous network parameters. We develop an elastic network model that properly takes rigid-body motion and crystalline constraints into account. This model reveals that B-factors are dominated by rigid-body motion rather than deformation, and therefore B-factors are poorly suited for identifying elastic properties of protein molecules. Furthermore, it turns out that B-factors for a benchmark set of three hundred and thirty protein molecules can be well approximated by assuming that the protein molecules are rigid. The third study is concerned with the polymer mediated interaction between two planar surfaces. In particular, we consider the case where a thin polymer layer bridges two parallel plates. We consider two models of monodisperse and polydisperse for the polymer layer and obtain an analytical expression for the force-distance relationship of the two plates. / text