Prerequisite skill structure graphs represent the relationships between knowledge components. Prerequisite structure graphs also propose the order in which students in a given curriculum need to be taught specific knowledge components in order to assist them build on previous knowledge and improve achievement in those subject domains. The importance of accurate prerequisite skill structure graphs can therefore not be overemphasized. In view of this, many approaches have been employed by domain experts to design and implement these prerequisite structures. A number of data mining techniques have also been proposed to infer these knowledge structures from learner performance data. These methods have achieved varied degrees of success. Moreover, to the best of our knowledge, none of the methods have employed extensive randomized controlled trials to learn about prerequisite skill relationships among skills. In this dissertation, we motivate the need for using randomized controlled trials to refine prerequisite skill structure graphs. Additionally, we present PLACEments, an adaptive testing system that uses a prerequisite skill structure graph to identify gaps in students’ knowledge. Students with identified gaps are assisted with more practice assignments to ensure that the gaps are closed. PLACEments additionally allows for randomized controlled experiments to be performed on the underlying prerequisite skill structure graph for the purpose of refining the structure. We present some of the different experiment categories which are possible in PLACEments and report the results of one of these experiment categories. The ultimate goal is to inform domain experts and curriculum designers as they create policies that govern the sequencing and pacing of contents in learning domains whose content lend themselves to sequencing. By extension students and teachers who apply these policies benefit from the findings of these experiments.

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The flow of genetic information from genes to proteins is mediated through proteins which interact with the nucleic acids at several stages to successfully transmit the information from the nucleus to the cell cytoplasm. Unlike in the case of protein-protein interactions, the principles behind protein-nucleic acid interactions are still not very (Pabo and Nekludova, 2000) and efforts are still underway to arrive at the basic principles behind the specific recognition of nucleic acids by proteins (Prabakaran et al., 2006). This is mainly due to the innate complexity involved in recognition of nucleotides by proteins, where, even within a given family of DNA binding proteins, different modes of binding and recognition strategies are employed to suit their function (Luscomb et al., 2000). Such difficulties have also not made possible, a thorough classification of DNA/RNA binding proteins based on the mode of interaction as well as the specificity of recognition of the nucleotides. The availability of a large number of structures of protein-nucleic acids complexes (albeit lesser than the number of protein structures present in the PDB) in the past few decades has provided the knowledge-base for understanding the details behind their molecular mechanisms (Berman et al., 1992). Previously, studies have been carried out to characterize these interactions by analyzing specific non-covalent interactions such as hydrogen bonds, van der Walls, and hydrophobic interactions between a given amino acid and the nucleic acid (DNA, RNA) in a pair-wise manner, or through the analysis of interface areas of the protein-nucleic acid complexes (Nadassy et al., 1998; Jones et al., 1999). Though the studies have deciphered the common pairing preferences of a particular amino acid with a given nucleotide of DNA or RNA, there is little room for understanding these specificities in the context of spatial interactions at a global level from the protein-nucleic acid complexes. The representation of the amino acids and the nucleotides as components of graphs, and trying to explore the nature of the interactions at a level higher than exploring the individual pair-wise interactions, could provide greater details about the nature of these interactions and their specificity. This thesis reports the study of protein-nucleic interactions using graph and network based approaches. The evaluation of the parameters for characterizing protein-nucleic acid graphs have been carried out for the first time and these parameters have been successfully employed to capture biologically important non-covalent interactions as clusters of interacting amino acids and nucleotides from different protein-DNA and protein-RNA complexes. Graph and network based approaches are well established in the field of protein structure analysis for analyzing protein structure, stability and function (Kannan and Vishveshwara, 1999; Brinda and Vishveshwara, 2005). However, the use of graph and network principles for analyzing structures of protein-nucleic acid complexes is so far not accomplished and is being reported the first time in this thesis. The matter embodied in the thesis is presented as ten chapters. Chapter 1 lays the foundation for the study, surveying relevant literature from the field. Chapter 2 describes in detail the methods used in constructing graphs and networks from protein-nucleic acid complexes. Initially, only protein structure graphs and networks are constructed from proteins known to interact with specific DNA or RNA, and inferences with regard to nucleic acid binding and recognition were indirectly obtained . Subsequently, parameters were evaluated for representing both the interacting amino acids and the nucleotides as components of graphs and a direct evaluation of protein-DNA and Protein-RNA interactions as graphs has been carried out. Chapter 3 and 4 discuss the graph and network approaches applied to proteins from a dataset of DNA binding proteins complexed with DNA. In chapter 3, the protein structure graphs were constructed on the basis of the non-covalent interactions existing between the side chains of amino acids. Clusters of interacting side chains from the graphs were obtained using the graph spectral method. The clusters from the protein-DNA interface were analyzed in detail for the interaction geometry and biological importance (Sathyapriya and Vishveshwara, 2004). Chapter 4 also uses the same dataset of DNA binding proteins, but a network-based approach is presented. From the analysis of the protein structure networks from these DNA binding proteins, interesting observations relating the presence of highly connected nodes(or hubs) of the network to functionally important amino acids in the structure, emerged. Also, the comparison between the hubs identified from the protein-protein and the protein-DNA interfaces in terms of their amino acid composition and their connectivity are also presented (Sathyapriya and Vishveshwara, 2006) Chapter 5 and 6 deal with the graph and network applications to a specific system of protein-RNA complex (aminoacyl-tRNA synthetases) to gain insights into their interface biology based on amino acid connectivity. Chapter 5 deals with a dataset of aminoacyl-tRNA synthetase (aaRS) complexes obtained with various ligands like ATP, tRNA and L-amino acids. A graph based identification of side chain clusters from these ligand-bound aaRS structures has highlighted important features of ligand-binding at the catalytic sites of the two structurally different classes of aaRS (Class I and Class II). Side chain clusters from other regions of aaRS such as the anticodon binding region and the ligand-activation sites are discussed. A network approach is used in a specific system of aaRS(E.coli Glutaminyl-tRNA synthetase (GlnRS) complexed with its ligands, to specifically understand the effects of different ligand binding., in chapter 6. The structure networks of E.coli GlnRS in the ligand-free and different ligand-bound states are constructed. The ligand-free and the ligand-bound complexes are compared by analyzing their network properties and the presence of hubs to understand the effect of ligand-binding. These properties have elegantly captured the effects of ligand-binding to the GlnRS structure and have also provided an alternate method for comparing three dimensional structures of proteins in different ligand-bound states (Sathyapriya and Vishveshwara, 2007). In contrast to protein structure graphs (PSG), both the interacting amino acids and nucleotides (DNA/RNA) form the components of the protein-nucleic acid graphs (PNG) from protein-nucleic acid complexes. These graphs are constructed based on the non-covalent interactions existing between the side chains of the amino acids and nucleotides. After representing the interacting nucleotides and amino acids as graphs, clusters of the interacting components are identified. These clusters are the strongly interacting amino acids and nucleotides from the protein-nucleic acid complexes. These clusters can be generated at different strengths of interaction between the amino acid side chain and the nucleotide (measured in terms of its atomic connectivity) and can be used for detecting clusters of non-specific as well as specific interactions of amino acids and nucleotides. Though the methodology of graph construction and cluster identification are given in chapter 2, the details of the parameters evaluated for constructing PNG are given in chapter 7. Unlike in the previous chapters, the succeeding chapters deal exclusively with results that are obtained from the analyses of PNG. Two examples of obtaining clusters from a PNG are given, one each for a protein-DNA and a protein-RNA complex. In the first example, a nucleosome core particle is subjected to the graph based analysis and different clusters of amino acids with different regions of the DNA chain such as phosphate, deoxyribose sugar and the base are identified. Another example of aminoacyl-tRNA synthetase complexed with its cognate tRNA is used to illustrate the method with a protein-RNA complex. Further, the method of constructing and analyzing protein-nucleic acid graphs has been applied to the macromolecular machinery of the pre-translocation complex of the T. thermophilus 70S ribosome. Chapter 8 deals exclusively with the results identified from the analysis of this magnificent macromolecular ensemble. The availability of the method that can handle interactions between both amino acids and the nucleotides of the protein-nucleic acid complexes has given us the basis fro evaluating these interactions in a level higher than that of analyzing pair-wise interactions. A study on the evaluation of short hydrogen bonds(SHB) in proteins, which does not fall under the realm of the main objective of the thesis, is discussed in the Chapter 9. The short hydrogen bonds, defined by the geometrical distance and angle parameters, are identified from a non-redundant dataset of proteins. The insights into their occurrence, amino acid composition and secondary structural preferences are discussed. The SHB are present in distinct regions of protein three-dimensional structures, such that they mediate specific geometrical constraints that are necessary for stability of the structure (Sathyapriya and Vishveshwara, 2005). The significant conclusions of various studies carried out are summarized in the last chapter (Chapter 10). In conclusion, this thesis reports the analyses performed with protein-nucleic acid complexes using graph and network based methods. The parameters necessary for representing both amino acids and the nucleotides as components of a graph, are evaluated for the first time and can be used subsequently for other analyses. More importantly, the use of graph-based methods has resulted in considering the interaction between the amino acids and the nucleotides at a global level with respect to their topology of the protein-nucleic acid complexes. Such studies performed on a wide variety of protein-nucleic acid complexes could provide more insights into the details of protein-nucleic acid recognition mechanisms. The results of these studies can be used for rational design of experimental mutations that ascertain the structure-function relationships in proteins and protein-nucleic acid complexes.

Aminoacyl-tRNA synthetases (aaRSs) are at the center of the question of the origin of life and are essential proteins found in all living organisms. AARSs arose early in evolution to interpret genetic code and are believed to be a group of ancient proteins. They constitute a family of enzymes integrating the two levels of cellular organization: nucleic acids and proteins. These enzymes ensure the fidelity of transfer of genetic information from the DNA to the protein. They are responsible for attaching amino acid residues to their cognate tRNA molecules by virtue of matching the nucleotide triplet, which is the first step in the protein synthesis. The translation of genetic code into protein sequence is mediated by tRNA, which accurately picks up the cognate amino acids. The attachment of the cognate amino acid to tRNA is catalyzed by aaRSs, which have binding sites for the anticodon region of tRNA and for the amino acid to be attached. The two binding sites are separated by ≈ 76 Å and experiments have shown that the communication does not go through tRNA (Gale et al., 1996). The problem addressed here is how the information of binding of tRNA anticodon near the anticodon binding site is communicated to the active site through the protein structure. These enzymes are modular with distinct domains on which extensive kinetic and mutational experiments and supported by structural data are available, highlighting the role of inter-domain communication (Alexander and Schimmel, 2001). Hence these proteins present themselves as excellent systems for in-silico studies. Various methods involved for the construction of protein structure networks are well established and analyzed in a variety of ways to gain insights into different aspects of protein structure, stability and function (Kannan and Vishveshwara, 1999; Brinda and Vishveshwara, 2005). In the present study, we have incorporated network parameters for the analysis of molecular dynamics (MD) simulation data, representing the global dynamic behavior of protein in a more elegant way. MD simulations have been performed on the available (and modeled) structures of aaRSs bound to a variety of ligands, and the protein structure networks (PSN) of non-covalent interactions have been characterized in dynamical equilibrium. The changes in the structure networks are used to understand the mode of communication, and the paths between the two sites of interest identified by the analysis of the shortest path. The allosteric concept has played a key role in understanding the biological functions of aaRSs. The rigidity/plasticity and the conformational population are the two important ideas invoked in explaining the allosteric effect. We have explored the conformational changes in the complexes of aaRSs through novel parameters such as cliques and communities (Palla et al., 2005), which identify the rigid regions in the protein structure networks (PSNs) constructed from the non-covalent interactions of amino acid side chains. The thesis consists of 7 chapters. The first chapter constitutes the survey of the literature and also provides suitable background for this study. The aims of the thesis are presented in this chapter. Chapter 2 describes various techniques employed and the new techniques developed for the analysis of PSNs. It includes a brief description of well -known methods of molecular dynamics simulations, essential dynamics, and cross correlation maps. The method used for the construction of graphs and networks is also described in detail. The incorporation of network parameters for the analysis of MD simulation data are done for the first time and has been applied on a well studied protein lysozyme, as described in chapter 3. Chapter 3 focuses on the dynamical behavior of protein structure networks, examined by considering the example of T4-lysozyme. The equilibrium dynamics and the process of unfolding are followed by simulating the protein with explicit water molecules at 300K and at higher temperatures (400K, 500K) respectively. Three simulations of 10ns duration have been performed at 500K to ensure the validity of the results. The snapshots of the protein structure from the simulations are represented as Protein Structure Networks (PSN) of non-covalent interactions. The strength of the non-covalent interaction is evaluated and used as an important criterion in the construction of edges. The profiles of the network parameters such as the degree distribution and the size of the largest cluster (giant component) have been examined as a function of interaction strength (Ghosh et al., 2007). We observe a critical strength of interaction (Icritical) at which there is a transition in the size of the largest cluster. Although the transition profiles at all temperatures show behavior similar to those found in the crystal structures, the 500K simulations show that the non-native structures have lower Icritical values. Based on the interactions evaluated at Icritical value, the folding/unfolding transition region has been identified from the 500K simulation trajectories. Furthermore, the residues in the largest cluster obtained at interaction strength higher than Icritical have been identified to be important for folding. Thus, the compositions of the top largest clusters in the 500K simulations have been monitored to understand the dynamical processes such as folding/unfolding and domain formation/disruption. The results correlate well with experimental findings. In addition, the highly connected residues in the network have been identified from the 300K and 400K simulations and have been correlated with the protein stability as determined from mutation experiments. Based on these analyses, certain residues, on which experimental data is not available, have been predicted to be important for the folding and the stability of the protein. The method can also be employed as a valuable tool in the analysis of MD simulation data, since it captures the details at a global level, which may elude conventional pair-wise interaction analysis. After standardizing the concept of dynamical network analysis using Lysozyme, it was applied to our system of interest, the aaRSs. The investigations carried out on Methionyl-tRNA synthetases (MetRS) are presented in chapter 4. This chapter is divided into three parts: Chapter 4A deals with the introduction to aminoacyl tRNA synthetases (aaRS). Classification and functional insights of aaRSs obtained through various studies are presented. Chapter 4B is again divided into parts: BI and BII. Chapter 4BI elucidates a new technique developed for finding communication pathways essential for proper functioning of aaRS. The enzymes of the family of tRNA synthetases perform their functions with high precision, by synchronously recognizing the anticodon region and the amino acylation region, which is separated by about 70Å in space. This precision in function is brought about by establishing good communication paths between the two regions. We have modelled the structure of E.coli Methionyl tRNA synthetase, which is complexed with tRNA and activated methionine. Molecular dynamics simulations have been performed on the modeled structure to obtain the equilibrated structure of the complex and the cross correlations between the residues in MetRS. Furthermore, the network analysis on these structures has been carried out to elucidate the paths of communication between the aminoacyl activation site and the anticodon recognition site (Ghosh and Vishveshwara, 2007). This study has provided the detailed paths of communication, which are consistent with experimental results. A similar study on the (MetRS + activated methionine) and (MetRS+tRNA) complexes along with ligand free-native enzyme has also been carried out. A comparison of the paths derived from the four simulations has clearly shown that the communication path is strongly correlated and unique to the enzyme complex, which is bound to both the tRNA and the activated methionine. The method developed here could also be utilized to investigate any protein system where the function takes place through long distance communication. The details of the method of our investigation and the biological implications of the results are presented in this chapter. In chapter 4BII, we have explored the conformational changes in the complexes of E.coli Methionyl tRNA synthetase (MetRS) through novel parameters such as cliques and communities, which identify the rigid regions in the protein structure networks (PSNs). The rigidity/plasticity and the conformational population are the two important ideas invoked in explaining the allosteric effect. MetRS belongs to the aminoacyl tRNA Synthetases (aaRSs) family that play a crucial role in initiating the protein synthesis process. The network parameters evaluated here on the conformational ensembles of MetRS complexes, generated from molecular dynamics simulations, have enabled us to understand the inter-domain communication in detail. Additionally, the characterization of conformational changes in terms of cliques/communities has also become possible, which had eluded conventional analyses. Furthermore, we find that most of the residues participating in clique/communities are strikingly different from those that take part in long-range communication. The cliques/communities evaluated here for the first time on PSNs have beautifully captured the local geometries in their detail within the framework of global topology. Here the allosteric effect is revealed at the residue level by identifying the important residues specific for structural rigidity and functional flexibility in MetRS. Chapter 4C focuses on MD simulations of Methionyl tRNA synthetase (AmetRS) from a thermophilic bacterium, Aquifex aeolicus. As describe in Chapter 4B, we have explored the communication pathways between the anticodon binding region and the aminoacylation site, and the conformational changes in the complexes through cliques and communities. The two MetRSs from E.coli and Aquifex aeolicus are structurally and sequentially very close to each other. But the communication pathways between anticodon binding region and the aminoacylation site from A. aeolicus have differed significantly with the communication paths obtained from E.coli. The residue composition and cliques/communities structure participating in communication are not similar in the MetRSs of both these organisms. Furthermore the formation of cliques/communities and hubs in the communication paths are more in A. aeolicus compared to E.coli. The participation of structurally homologous linker peptide, essential for orienting the two domains for efficient communication is same in both the organisms although, the residues composition near domain interface regions including the linker peptide is different. Thus, the diversity in the functioning of two different MetRS has been brought out, by comparing the E.coli and Aquifex aeolicus systems. Protein Structure network analysis of MD simulated trajectories of various ligand bound complexes of Escherichia coli Cysteinyl-tRNA synthetase (CysRS) have been discussed in Chapter 5. The modeling of the complex is done by docking the ligand CysAMP into the tRNA bound structure of E.coli Cysteinyl tRNA synthetase. Molecular dynamics simulations have been performed on the modeled structure and the paths of communications were evaluated using a similar method as used in finding communication paths for MetRS enzymes. Compared to MetRS the evaluation of communication paths in CysRS is complicated due to presence of both direct and indirect readouts. The direct and indirect readouts (DR/IR) involve interaction of protein residues with base-specific functional group and sugar-phosphate backbone of nucleic acids respectively. Two paths of communication between the anticodon region and the activation site has been identified by combining the cross correlation information with the protein structure network constructed on the basis of non-covalent interaction. The complete paths include DR/IR interactions with tRNA. Cliques/communities of non-covalently interacting residues imparting structural rigidity are present along the paths. The reduction of cooperative fluctuation due to the presence of community is compensated by IR/DR interaction and thus plays a crucial role in communication of CysRS. Chapter 6 focuses on free energy calculations of aminoacyl tRNA synthetases with various ligands. The free energy contributions to the binding of the substrates are calculated using a method called MM-PBSA (Massova and Kollman, 2000). The binding free energies were calculated as the difference between the free energy of the enzyme-ligand complex, and the free ligand and protein. The ligand unbinding energy values obtained from the umbrella sampling MD correlates well with the ligand binding energies obtained from MM-PBSA method. Furthermore the essential dynamics was captured from MD simulations trajectories performed on E.coli MetRS, A. aeolius MetRS and E.coli CysRS in terms of the eigenvalues. The top two modes account for more than 50% of the motion in essential space for systems E.coli MetRS, A. aeolius MetRS and E.coli CysRS. Population distribution of protein conformation states are looked at the essential plane defined by the two principal components with highest eigenvalues. This shows how aaRSs existed as a population of conformational states and the variation with the addition of ligands. The population of conformational states is converted into Free energy contour surface. From free energy surfaces, it is evident that the E.coli tRNAMet bound MetRS conformational fluctuations are more, which attributes to less rigidity in the complex. Whereas E.coli tRNACys bound CysRS conformational fluctuations are less and this is reflected in the increase in rigidity of the complex as confirmed by its entropic contribution. Future directions have been discussed in the final chapter (Chapter 7). Specifically, it deals with the ab-initio QM/MM study of the enzymatic reaction involved in the active site of E.coli Methionyl tRNA synthetase. To achieve this, two softwares are integrated: the Quantum Mechanics (QM) part includes small ligands and the Molecular Mechanics (MM) part as protein MetRS are handled using CPMD and Gromacs respectively. The inputs for two reactions pathways are prepared. First reaction involves cyclization reaction of homocysteine in the active site of MetRS and the second reaction deals with charging of methionine in the presence of ATP and magnesium ion. These simulations require very high power computing systems and also time of computation is also very large. With the available computational power we could simulate up to 10ps and it is insufficient for analysis. The future direction will involve the simulations of these systems for longer time, followed by the analysis for reaction pathways.