New Methods to Improve Protein Structure Modeling

Proteins are considered the central compound necessary for life, as they play a crucial role in governing several life processes by performing the most essential biological and chemical functions in every living cell. Understanding protein structures and functions will lead to a significant advance in life science and biology. Such knowledge is vital for various fields such as drug development and synthetic biofuels production. Most proteins have definite shapes that they fold into, which are the most stable state they can adopt. Due to the fact that the protein structure information provides important insight into its functions, many research efforts have been conducted to determine the protein 3-dimensional structure from its sequence. The experimental methods for protein 3-dimensional structure determination are often time-consuming, costly, and even not feasible for some proteins. Accordingly, recent research efforts focus more and more on computational approaches to predict protein 3-dimensional structures. Template-based modeling is considered one of the most accurate protein structure prediction methods. The success of template-based modeling relies on correctly identifying one or a few experimentally determined protein structures as structural templates that are likely to resemble the structure of the target sequence as well as accurately producing a sequence alignment that maps the residues in the target sequence to those in the template. In this work, we aim at improving the template-based protein structure modeling by enhancing the correctness of identifying the most appropriate templates and precisely aligning the target and template sequences. Firstly, we investigate employing inter-residue contact score to measure the favorability of a target sequence fitting in the folding topology of a certain template. Secondly, we design a multi-objective alignment algorithm extending the famous Needleman-Wunsch algorithm to obtain a complete set of alignments yielding Pareto optimality. Then, we use protein sequence and structural information as objectives and generate the complete Pareto optimal front of alignments between target sequence and template. The alignments obtained enable one to analyze the trade-offs between the potentially conflicting objectives. These approaches lead to accuracy enhancement in template-based protein structure modeling

Thermodynamic Analysis of Interacting Nucleic Acid Strands

Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality

Improved Constrained Global Optimization for Estimating Molecular Structure From Atomic Distances

Determination of molecular structure is commonly posed as a nonlinear optimization problem. The objective functions rely on a vast amount of structural data. As a result, the objective functions are most often nonconvex, nonsmooth, and possess many local minima. Furthermore, introduction of additional structural data into the objective function creates barriers in finding the global minimum, causes additional computational issues associated with evaluating the function, and makes physical constraint enforcement intractable. To combat the computational problems associated with standard nonlinear optimization formulations, Williams et al. (2001) proposed an atom-based optimization, referred to as GNOMAD, which complements a simple interatomic distance potential with van der Waals (VDW) constraints to provide better quality protein structures. However, the improvement in more detailed structural features such as shape and chirality requires the integration of additional constraint types. This dissertation builds on the GNOMAD algorithm in using structural data to estimate the three-dimensional structure of a protein. We develop several methods to make GNOMAD capable of effectively and efficiently handling non-distance information including torsional angles and molecular surface data. In specific, we propose a method for using distances to effectively satisfy known torsional information and show that use of this method results in a significant improvement in the quality of α-helices and β-strands within the protein. We also show that molecular surface data in combination with our improved secondary structure estimation method and long-range distance data offer increased accuracy in spatial proximity of α-helices and β-strands within the protein, and thus provide better estimates of tertiary protein structure. Lastly, we show that the enhanced GNOMAD molecular structure estimation framework is effective in predicting protein structures in the context of comparative modeling

Inferring Regulatory Networks by Combining Perturbation Screens and Steady State Gene Expression Profiles

Reconstructing transcriptional regulatory networks is an important task in functional genomics. Data obtained from experiments that perturb genes by knockouts or RNA interference contain useful information for addressing this reconstruction problem. However, such data can be limited in size and/or are expensive to acquire. On the other hand, observational data of the organism in steady state (e.g. wild-type) are more readily available, but their informational content is inadequate for the task at hand. We develop a computational approach to appropriately utilize both data sources for estimating a regulatory network. The proposed approach is based on a three-step algorithm to estimate the underlying directed but cyclic network, that uses as input both perturbation screens and steady state gene expression data. In the first step, the algorithm determines causal orderings of the genes that are consistent with the perturbation data, by combining an exhaustive search method with a fast heuristic that in turn couples a Monte Carlo technique with a fast search algorithm. In the second step, for each obtained causal ordering, a regulatory network is estimated using a penalized likelihood based method, while in the third step a consensus network is constructed from the highest scored ones. Extensive computational experiments show that the algorithm performs well in reconstructing the underlying network and clearly outperforms competing approaches that rely only on a single data source. Further, it is established that the algorithm produces a consistent estimate of the regulatory network.Comment: 24 pages, 4 figures, 6 table