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.

Design and fabrication of electro-thermal microcantilevers for ultrafast molecular sorting and delivery

Improvements to the current state of the art in microfabricated cantilevers are investigated in order to realize enhanced functionality and increased versatility for use in ultrafast electrophoretic molecular sorting and delivery. Design rationale and fabrication process flow are described for six types of electro-thermal microcantilevers. Devices have been tailored for the process of separating mixtures of heterogeneous molecules into discrete detectable bands based on electrophoretic mobility, and delivering them to a conductive substrate using electric fields. Four device types include integrated heating elements capable of warming samples to catalyze reactions or cleaning the device for reuse. Similar devices have been shown to be capable of targeting temperatures between ambient conditions and the melting point of silicon, to within 0.1˚C precision or better. All microcantilevers types are equipped with a highly doped conductive silicon tip capable of interacting with a conductive substrate to deliver molecules under the presence of an electric field. Devices are equipped with additional electrodes to aid in sorting molecules on the surface of the probe end. Two designs contain two legs and one additional sorting electrode while four designs contain three legs and have two sorting electrodes. Devices having two sorting electrodes are designed to be capable of sorting three or more molecular species, a distinctive advancement in the state of the art. A detailed process flow of the fabrication process for all six electro-thermal cantilever designs are explained in detail.

Molecular mechanisms involved in cell response to mechanical forces

New devices were designed to generate a localized mechanical vibration of flexible gels where human umbilical vein endothelial cells (HUVECs) were cultured. The stimulation setups were able to apply relatively large strains (30%~50%) at high temporal frequencies (140~207 Hz) in a localized subcellular region. One of the advantages of this technique was to be less invasive to the innate cellular functions because there was no direct contact between the stimulating probe and the cell body. A mechanical vibration induced by the device in the substrate gel where cells were seeded could mainly cause global calcium responses of the cells. This global response was initiated by the influx of calcium across the stretch-activated channels in the plasma membrane. The subsequent production of inositol triphosphate (IP3) via phospholipase C (PLC) activation triggered the calcium release from the endoplasmic reticulum (ER) to cause a global intracellular calcium fluctuation over the whole cell body. This global calcium response was also shown to depend on actomyosin contractility and F-actin integrity, probably controlling the membrane stretch-activated channels. The localized nature of the stimulation is one of the most important features of these new designs as it allowed the observation of the calcium signaling propagation by ER calcium release. The next step was to focus on the calcium influx, more specifically the TRPM7 channels. As TRPM7 expression may modulate cell adhesion, an adhesion assay was developed and tested on HUVECs seeded on gel substrates with different treatments: normal treatment on gels showed highest attachment rate, followed by the partially treated gels (only 5% of usual fibronectin amount) and untreated gels, with the lowest attachment rate. The trend of the attachment rates correlated to the magnitude of the calcium signaling observed after mechanical stimulation. TRPM7 expression inhibition by siRNA caused an increased attachment rate when compared to both control and non-targeting siRNA-treated cells, but resulted in an actual weaker response in terms of calcium signaling. It suggests that TRPM7 channels are indeed important for the calcium signaling in response to mechanical stimulation. A complementary study was also conducted consisting in the mechanical stimulation of a dissected Drosophila embryo. Although ionomycin treatment showed calcium influx in the tissue, the mechanical stimulation delivered as a vertical vibration did not elicited calcium signaling in response. One possible reason is the dissection procedure causing desensitization of the tissue due to the scrapings and manipulations to open the embryo.