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.

Three-dimensional, in-silico breast phantom for multimodality image simulations

We report on the construction of anatomically realistic three-dimensional in-silico breast phantoms with adjustable sizes, shapes and morphologic features. The concept of multiscale spatial resolution is implemented for generating breast tissue images from multiple modalities. Breast epidermal boundary and subcutaneous fat layer is generated by fitting an ellipsoid and 2nd degree polynomials to reconstructive surgical data and ultrasound imaging data. Intraglandular fat is simulated by randomly distributing and orienting adipose ellipsoids within a fibrous region immediately within the dermal layer. Cooper’s ligaments are simulated as fibrous ellipsoidal shells distributed within the subcutaneous fat layer. Individual ductal lobes are simulated following a random binary tree model which is generated based upon probabilistic branching conditions described by ramification matrices, as originally proposed by Bakic et al [3, 4]. The complete ductal structure of the breast is simulated from multiple lobes that extend from the base of the nipple and branch towards the chest wall. As lobe branching progresses, branches are reduced in height and radius and terminal branches are capped with spherical lobular clusters. Biophysical parameters are mapped onto the complete anatomical model and synthetic multimodal images (Mammography, Ultrasound, CT) are generated for phantoms of different adipose percentages (40%, 50%, 60%, and 70%) and are analytically compared with clinical examples. Results demonstrate that the in-silico breast phantom has applications in imaging performance evaluation and, specifically, great utility for solving image registration issues in multimodality imaging.

Idealized modeling of the role of stability and shear on mesoscale gravity wave evolution

Mesoscale Gravity Waves (MGWs) are large pressure perturbations that form in the presence of a stable layer at the surface either behind Mesoscale Convective Systems (MCSs) in summer or over warm frontal surfaces behind elevated convection in winter. MGWs are associated with damaging winds, moderate to heavy precipitation, and occasional heat bursts at the surface. The forcing mechanism for MGWs in this study is hypothesized to be evaporative cooling occurring behind a convective line. This evaporatively-cooled air generates a downdraft that then depresses the surface-based stable layer and causes pressure decreases, strong wind speeds and MGW genesis. Using the Weather Research and Forecast Model (WRF) version 3.0, evaporative cooling is simulated using an imposed cold thermal. Sensitivity studies examine the response of MGW structure to different thermal and shear profiles where the strength and depth of the inversion are varied, as well as the amount of wind shear. MGWs are characterized in terms of response variables, such as wind speed perturbations (U'), temperature perturbations (T'), pressure perturbations (P'), potential temperature perturbations (Θ'), and the correlation coefficient (R) between U' and P'. Regime Diagrams portray the response of MGW to the above variables in order to better understand the formation, causes, and intensity of MGWs. The results of this study indicate that shallow, weak surface layers coupled with deep, neutral layers above favor the formation of waves of elevation. Conversely, deep strong surface layers coupled with deep, neutral layers above favor the formation of waves of depression. This is also the type of atmospheric setup that tends to produce substantial surface heating at the surface.

Toward assessing the effects of aerosols on deep convection: a numerical study using the WRF-Chemistry model

As the formative agents of cloud droplets, aerosols play an undeniably important role in the development of clouds and precipitation. Few meteorological models have been developed or adapted to simulate aerosols and their contribution to cloud and precipitation processes. The Weather Research and Forecasting model (WRF) has recently been coupled with an atmospheric chemistry suite and is jointly referred to as WRF-Chem, allowing atmospheric chemistry and meteorology to influence each other’s evolution within a mesoscale modeling framework. Provided that the model physics are robust, this framework allows the feedbacks between aerosol chemistry, cloud physics, and dynamics to be investigated. This study focuses on the effects of aerosols on meteorology, specifically, the interaction of aerosol chemical species with microphysical processes represented within the framework of the WRF-Chem. Aerosols are represented by eight size bins using the Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) sectional parameterization, which is linked to the Purdue Lin bulk microphysics scheme. The aim of this study is to examine the sensitivity of deep convective precipitation modeled by the 2D WRF-Chem to varying aerosol number concentration and aerosol type. A systematic study has been performed regarding the effects of aerosols on parameters such as total precipitation, updraft/downdraft speed, distribution of hydrometeor species, and organizational features, within idealized maritime and continental thermodynamic environments. Initial results were obtained using WRFv3.0.1, and a second series of tests were run using WRFv3.2 after several changes to the activation, autoconversion, and Lin et al. microphysics schemes added by the WRF community, as well as the implementation of prescribed vertical levels by the author. The results of WRFv3.2 runs contrasted starkly with WRFv3.0.1 runs. The WRFv3.0.1 runs produced a propagating system resembling a developing squall line, whereas the WRFv3.2 runs did not. The response of total precipitation, updraft/downdraft speeds, and system organization to increasing aerosol concentrations were opposite between runs with different versions of WRF. Results of the WRFv3.2 runs, however, were in better agreement in timing and magnitude of vertical velocity and hydrometeor content with a WRFv3.0.1 run using single-moment Lin et al. microphysics, than WRFv3.0.1 runs with chemistry. One result consistent throughout all simulations was an inhibition in warm-rain processes due to enhanced aerosol concentrations, which resulted in a delay of precipitation onset that ranged from 2-3 minutes in WRFv3.2 runs, and up to 15 minutes in WRFv.3.0.1 runs. This result was not observed in a previous study by Ntelekos et al. (2009) using the WRF-Chem, perhaps due to their use of coarser horizontal and vertical resolution within their experiment. The changes to microphysical processes such as activation and autoconversion from WRFv3.0.1 to WRFv3.2, along with changes in the packing of vertical levels, had more impact than the varying aerosol concentrations even though the range of aerosol tested was greater than that observed in field studies. In order to take full advantage of the input of aerosols now offered by the chemistry module in WRF, the author recommends that a fully double-moment microphysics scheme be linked, rather than the limited double-moment Lin et al. scheme that currently exists. With this modification, the WRF-Chem will be a powerful tool for studying aerosol-cloud interactions and allow comparison of results with other studies using more modern and complex microphysical parameterizations.

Simulations of droplet dispersion in the wakes of cylinders and icing tunnel spray bars

Simulations of droplet dispersion behind cylinder wakes and downstream of icing tunnel spray bars were conducted. In both cases, a range of droplet sizes were investigated numerically with a Lagrangian particle trajectory approach while the turbulent air flow was investigated with a hybrid Reynolds-Averaged Navier-Stokes/Large-Eddy Simulations approach scheme. In the first study, droplets were injected downstream of a cylinder at sub-critical conditions (i.e. with laminar boundary layer separation). A stochastic continuous random walk (CRW) turbulence model was used to capture the effects of sub-grid turbulence. Small inertia droplets (characterized by small Stokes numbers) were affected by both the large-scale and small-scale vortex structures and closely followed the air flow, while exhibiting a dispersion consistent with that of a scalar flow field. Droplets with intermediate Stokes numbers were centrifuged by the vortices to the outer edges of the wake, yielding an increased dispersion. Large Stokes number droplets were found to be less responsive to the vortex structures and exhibited the least dispersion. Particle concentration was also correlated with vorticity distribution which yielded preferential bias effects as a function of different particle sizes. This trend was qualitatively similar to results seen in homogenous isotropic turbulence, though the influence of particle inertia was less pronounced for the cylinder wake case. A similar study was completed for droplet dispersion within the Icing Research Tunnel (IRT) at the NASA Glenn Research Center, where it is important to obtain a nearly uniform liquid water content (LWC) distribution in the test section (to recreate atmospheric icing conditions).. For this goal, droplets are diffused by the mean and turbulent flow generated from the nozzle air jets, from the upstream spray bars, and from the vertical strut wakes. To understand the influence of these three components, a set of simulations was conducted with a sequential inclusion of these components. Firstly, a jet in an otherwise quiescent airflow was simulated to capture the impact of the air jet on flow turbulence and droplet distribution, and the predictions compared well with experimental results. The effects of the spray bar wake and vertical strut wake were then included with two more simulation conditions, for which it was found that the air jets were the primary driving force for droplet dispersion, i.e. that the spray bar and vertical strut wake effects were secondary.

Three-dimensional kinetic simulations of active suspensions: effect of chemotaxis and steric interaction

In this work, the effects of chemotaxis and steric interactions in active suspensions are analyzed by extending the kinetic model proposed by Saintillan and Shelley [1, 2]. In this model, a conservation equation for the active particle configuration is coupled to the Stokes equation for the flow arising from the force dipole exerted by the particles on the fluid. The fluid flow equations are solved spectrally and the conservation equation is solved by second-order finite differencing in space and second-order Adams-Bashforth time marching. First, the dynamics in suspensions of oxytactic run-and-tumble bacteria confined in thin liquid films surrounded by air is investigated. These bacteria modify their tumbling behavior by making temporal comparisons of the oxygen concentration, and, on average, swim towards high concentrations of oxygen. The kinetic model proposed by Saintillan and Shelley [1, 2] is modified to include run-and-tumble effects and oxygentaxis. The spatio-temporal dynamics of the oxygen and bacterial concentration are analyzed. For small film thicknesses, there is a weak migration of bacteria to the boundaries, and the oxygen concentration is high inside the film as a result of diffusion; both bacterial and oxygen concentrations quickly reach steady states. Above a critical film thickness (approximately 200 micron), a transition to chaotic dynamics is observed and is characterized by turbulent-like 3D motion, the formation of bacterial plumes, enhanced oxygen mixing and transport into the film, and hydrodynamic velocities of magnitudes up to 7 times the single bacterial swimming speed. The simulations demonstrate that the combined effects of hydrodynamic interactions and oxygentaxis create collective three-dimensional instabilities which enhances oxygen availability for the bacteria. Our simulation results are consistent with the experimental findings of Sokolov et al. [3], who also observed a similar transition with increasing film thickness. Next, the dynamics in concentrated suspensions of active self-propelled particles in a 3D periodic domain are analyzed. We modify the kinetic model of Saintillan and Shelley [1, 2] by including an additional nematic alignment torque proportional to the local concentration in the equation for the rotational velocity of the particles, causing them to align locally with their neighbors (Doi and Edwards [4]). Large-scale three- dimensional simulations show that, in the presence of such a torque both pusher and puller suspensions are unstable to random fluctuations and are characterized by highly nematic structures. Detailed measures are defined to quantify the degree and direction of alignment, and the effects of steric interactions on pattern formation will be presented. Our analysis shows that steric interactions have a destabilizing effect in active suspensions.