New Advancements of Scalable Statistical Methods for Learning Latent Structures in Big Data

Constant technology advances have caused data explosion in recent years. Accord- ingly modern statistical and machine learning methods must be adapted to deal with complex and heterogeneous data types. This phenomenon is particularly true for an- alyzing biological data. For example DNA sequence data can be viewed as categorical variables with each nucleotide taking four different categories. The gene expression data, depending on the quantitative technology, could be continuous numbers or counts. With the advancement of high-throughput technology, the abundance of such data becomes unprecedentedly rich. Therefore efficient statistical approaches are crucial in this big data era.

Previous statistical methods for big data often aim to find low dimensional struc- tures in the observed data. For example in a factor analysis model a latent Gaussian distributed multivariate vector is assumed. With this assumption a factor model produces a low rank estimation of the covariance of the observed variables. Another example is the latent Dirichlet allocation model for documents. The mixture pro- portions of topics, represented by a Dirichlet distributed variable, is assumed. This dissertation proposes several novel extensions to the previous statistical methods that are developed to address challenges in big data. Those novel methods are applied in multiple real world applications including construction of condition specific gene co-expression networks, estimating shared topics among newsgroups, analysis of pro- moter sequences, analysis of political-economics risk data and estimating population structure from genotype data.

Electrostatic Contributions to the Thermodynamics of Ribonuclease P Protein Folding

Electrostatic interactions are of fundamental importance in determining the structure and stability of macromolecules. For example, charge-charge interactions modulate the folding and binding of proteins and influence protein solubility. Electrostatic interactions are highly variable and can be both favorable and unfavorable. The ability to quantify these interactions is challenging but vital to understanding the detailed balance and major roles that they have in different proteins and biological processes. Measuring pKa values of ionizable groups provides a sensitive method for experimentally probing the electrostatic properties of a protein.

pKa values report the free energy of site-specific proton binding and provide a direct means of studying protein folding and pH-dependent stability. Using a combination of NMR, circular dichroism, and fluorescence spectroscopy along with singular value decomposition, we investigated the contributions of electrostatic interactions to the thermodynamic stability and folding of the protein subunit of Bacillus subtilis ribonuclease P, P protein. Taken together, the results suggest that unfavorable electrostatics alone do not account for the fact that P protein is intrinsically unfolded in the absence of ligand because the pKa differences observed between the folded and unfolded state are small. Presumably, multiple factors encoded in the P protein sequence account for its IUP property, which may play an important role in its function.

Electrostatic Energetics of Bacillus subtilis Ribonuclease P Protein Determined by Nuclear Magnetic Resonance-Based Histidine pKa Measurements.

The pKa values of ionizable groups in proteins report the free energy of site-specific proton binding and provide a direct means of studying pH-dependent stability. We measured histidine pKa values (H3, H22, and H105) in the unfolded (U), intermediate (I), and sulfate-bound folded (F) states of RNase P protein, using an efficient and accurate nuclear magnetic resonance-monitored titration approach that utilizes internal reference compounds and a parametric fitting method. The three histidines in the sulfate-bound folded protein have pKa values depressed by 0.21 ± 0.01, 0.49 ± 0.01, and 1.00 ± 0.01 units, respectively, relative to that of the model compound N-acetyl-l-histidine methylamide. In the unliganded and unfolded protein, the pKa values are depressed relative to that of the model compound by 0.73 ± 0.02, 0.45 ± 0.02, and 0.68 ± 0.02 units, respectively. Above pH 5.5, H22 displays a separate resonance, which we have assigned to I, whose apparent pKa value is depressed by 1.03 ± 0.25 units, which is ∼0.5 units more than in either U or F. The depressed pKa values we observe are consistent with repulsive interactions between protonated histidine side chains and the net positive charge of the protein. However, the pKa differences between F and U are small for all three histidines, and they have little ionic strength dependence in F. Taken together, these observations suggest that unfavorable electrostatics alone do not account for the fact that RNase P protein is intrinsically unfolded in the absence of ligand. Multiple factors encoded in the P protein sequence account for its IUP property, which may play an important role in its function.