Analysis of Molecular Dynamics Simulations of Protein Folding

Microsecond long Molecular Dynamics (MD) trajectories of biomolecular processes are now possible due to advances in computer technology. Soon, trajectories long enough to probe dynamics over many milliseconds will become available. Since these timescales match the physiological timescales over which many small proteins fold, all atom MD simulations of protein folding are now becoming popular. To distill features of such large folding trajectories, we must develop methods that can both compress trajectory data to enable visualization, and that can yield themselves to further analysis, such as the finding of collective coordinates and reduction of the dynamics. Conventionally, clustering has been the most popular MD trajectory analysis technique, followed by principal component analysis (PCA). Simple clustering used in MD trajectory analysis suffers from various serious drawbacks, namely, (i) it is not data driven, (ii) it is unstable to noise and change in cutoff parameters, and (iii) since it does not take into account interrelationships amongst data points, the separation of data into clusters can often be artificial. Usually, partitions generated by clustering techniques are validated visually, but such validation is not possible for MD trajectories of protein folding, as the underlying structural transitions are not well understood. Rigorous cluster validation techniques may be adapted, but it is more crucial to reduce the dimensions in which MD trajectories reside, while still preserving their salient features. PCA has often been used for dimension reduction and while it is computationally inexpensive, being a linear method, it does not achieve good data compression. In this thesis, I propose a different method, a nonmetric multidimensional scaling (nMDS) technique, which achieves superior data compression by virtue of being nonlinear, and also provides a clear insight into the structural processes underlying MD trajectories. I illustrate the capabilities of nMDS by analyzing three complete villin headpiece folding and six norleucine mutant (NLE) folding trajectories simulated by Freddolino and Schulten [1]. Using these trajectories, I make comparisons between nMDS, PCA and clustering to demonstrate the superiority of nMDS. The three villin headpiece trajectories showed great structural heterogeneity. Apart from a few trivial features like early formation of secondary structure, no commonalities between trajectories were found. There were no units of residues or atoms found moving in concert across the trajectories. A flipping transition, corresponding to the flipping of helix 1 relative to the plane formed by helices 2 and 3 was observed towards the end of the folding process in all trajectories, when nearly all native contacts had been formed. However, the transition occurred through a different series of steps in all trajectories, indicating that it may not be a common transition in villin folding. The trajectories showed competition between local structure formation/hydrophobic collapse and global structure formation in all trajectories. Our analysis on the NLE trajectories confirms the notion that a tight hydrophobic core inhibits correct 3-D rearrangement. Only one of the six NLE trajectories folded, and it showed no flipping transition. All the other trajectories get trapped in hydrophobically collapsed states. The NLE residues were found to be buried deeply into the core, compared to the corresponding lysines in the villin headpiece, thereby making the core tighter and harder to undo for 3-D rearrangement. Our results suggest that the NLE may not be a fast folder as experiments suggest. The tightness of the hydrophobic core may be a very important factor in the folding of larger proteins. It is likely that chaperones like GroEL act to undo the tight hydrophobic core of proteins, after most secondary structure elements have been formed, so that global rearrangement is easier. I conclude by presenting facts about chaperone-protein complexes and propose further directions for the study of protein folding.

Functional surface chemistry of carbon-based nanostructures

The recently discovered abilities to synthesize single-walled carbon nanotubes and prepare single layer graphene have spurred interest in these sp2-bonded carbon nanostructures. In particular, studies of their potential use in electronic devices are many as silicon integrated circuits are encountering processing limitations, quantum effects, and thermal management issues due to rapid device scaling. Nanotube and graphene implementation in devices does come with significant hurdles itself. Among these issues are the ability to dope these materials and understanding what influences defects have on expected properties. Because these nanostructures are entirely all-surface, with every atom exposed to ambient, introduction of defects and doping by chemical means is expected to be an effective route for addressing these issues. Raman spectroscopy has been a proven characterization method for understanding vibrational and even electronic structure of graphene, nanotubes, and graphite, especially when combined with electrical measurements, due to a wealth of information contained in each spectrum. In Chapter 1, a discussion of the electronic structure of graphene is presented. This outlines the foundation for all sp2-bonded carbon electronic properties and is easily extended to carbon nanotubes. Motivation for why these materials are of interest is readily gained. Chapter 2 presents various synthesis/preparation methods for both nanotubes and graphene, discusses fabrication techniques for making devices, and describes characterization methods such as electrical measurements as well as static and time-resolved Raman spectroscopy. Chapter 3 outlines changes in the Raman spectra of individual metallic single-walled carbon nantoubes (SWNTs) upon sidewall covalent bond formation. It is observed that the initial degree of disorder has a strong influence on covalent sidewall functionalization which has implications on developing electronically selective covalent chemistries and assessing their selectivity in separating metallic and semiconducting SWNTs. Chapter 4 describes how optical phonon population extinction lifetime is affected by covalent functionalization and doping and includes discussions on static Raman linewidths. Increasing defect concentration is shown to decrease G-band phonon population lifetime and increase G-band linewidth. Doping only increases G-band linewidth, leaving non-equilibrium population decay rate unaffected. Phonon mediated electron scattering is especially strong in nanotubes making optical phonon decay of interest for device applications. Optical phonon decay also has implications on device thermal management. Chapter 5 treats doping of graphene showing ambient air can lead to inadvertent Fermi level shifts which exemplifies the sensitivity that sp2-bonded carbon nanostructures have to chemical doping through sidewall adsorption. Removal of this doping allows for an investigation of electron-phonon coupling dependence on temperature, also of interest for devices operating above room temperature. Finally, in Chapter 6, utilizing the information obtained in previous chapters, single carbon nanotube diodes are fabricated and characterized. Electrical performance shows these diodes are nearly ideal and photovoltaic response yields 1.4 nA and 205 mV of short circuit current and open circuit voltage from a single nanotube device. A summary and discussion of future directions in Chapter 7 concludes my work.