Coarse Graining to Invesitigate Peptide-Lipid Interactions

Experimental characterization of molecular details is challenging, and although single molecule experiments have gained prominence, oligomer characterization remains largely unexplored. The ability to monitor the time evolution of individual molecules while they self assemble is essential in providing mechanistic insights about biological events. Molecular dynamics (MD) simulations can fill the gap in knowledge between single molecule experiments and ensemble studies like NMR, and are increasingly used to gain a better understanding of microscopic properties. Coarse-grained (CG) models aid in both exploring longer length and time scale molecular phenomena, and narrowing down the key interactions responsible for significant system characteristics. Over the past decade, CG techniques have made a significant impact in understanding physicochemical processes. However, the realm of peptide-lipid interfacial interactions, primarily binding, partitioning and folding of amphipathic peptides, remains largely unexplored compared to peptide folding in solution. The main drawback of existing CG models is the inability to capture environmentally sensitive changes in dipolar interactions, which are indigenous to protein folding, and lipid dynamics. We have used the Drude oscillator approach to incorporate structural polarization and dipolar interactions in CG beads to develop a minimalistic peptide model, WEPPROM (Water Explicit Polarizable PROtein Model), and a lipid model WEPMEM (Water Explicit Polarizable MEmbrane Model). The addition of backbone dipolar interactions in a CG model for peptides enabled us to achieve alpha-beta secondary structure content de novo, without any added bias. As a prelude to studying amphipathic peptide-lipid membrane interactions, the balance between hydrophobicity and backbone dipolar interactions in driving ordered peptide aggregation in water and at a hydrophobic-hydrophilic interface, was explored. We found that backbone dipole interactions play a crucial role in driving ordered peptide aggregation, both in water and at hydrophobic-hydrophilic interfaces; while hydrophobicity is more relevant for aggregation in water. A zwitterionic (POPC: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) and an anionic lipid (POPS: 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine) are used as model lipids for WEPMEM. The addition of head group dipolar interactions in lipids significantly improved structural, dynamic and dielectric properties of the model bilayer. Using WEPMEM and WEPPROM, we studied membrane-induced peptide folding of a cationic antimicrobial peptide with anticancer activity, SVS-1. We found that membrane-induced peptide folding is driven by both (a) cooperativity in peptide self interaction and (b) cooperativity in membrane-peptide interactions. The dipolar interactions between the peptide and the lipid head-groups contribute to stabilizing folded conformations. The role of monovalent ion size and peptide concentration in driving lipid domain formation in anionic/zwitterionic lipid mixtures was also investigated. Our study suggest monovalent ion size to be a crucial determinant of interaction with lipid head groups, and hence domain formation in lipid mixtures. This study reinforces the role of dipole interactions in protein folding, lipid membrane properties, membrane induced peptide folding and lipid domain formation. Therefore, the models developed in this thesis can be used to explore a multitude of biomolecular processes, both at longer time-scales and larger system sizes.

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.