Accurate thermophysical property data are crucial for designing efficient chemical processes. For this reason, the Design Institute for Physical Properties (DIPPR 801) provides evaluated experimental data and prediction of various thermophysical properties. The critical temperature (Tc), critical density (ρc), critical pressure (Pc), critical compressibility factor (Zc), and normal boiling point (Tb) are important constants to check for thermodynamic consistency and to estimate other properties. The n-alkane family is of primary interest because it is generally assumed that other families of compounds behave similarly to the n-alkane family with increasing chain-length. Unfortunately, due to thermal decomposition, experimental measurements of Tc, ρc, and Pc for large n-alkanes are scarce and potentially unreliable. For this reason, molecular simulation is an attractive alternative for estimating the critical constants. However, molecular simulation has often been viewed as a tool that is limited to providing qualitative insight. One key reason for this perceived weakness is the difficulty in quantifying the uncertainty of the simulation results. This research focuses on a systematic top-down approach to quantifying the uncertainty in Gibbs Ensemble Monte Carlo (GEMC) simulations for large n-alkanes. We implemented four different methods in order to obtain quantitatively reliable molecular simulation results. First, we followed a rigorous statistical analysis to assign the uncertainty of the critical constants when obtained from GEMC. Second, we developed an improved method for predicting Pc with the standard force field models in the literature. Third, we implemented an experimental design to reduce the uncertainty associated with Tc, ρc, Pc, and Zc. Finally, we quantified the uncertainty associated with the Lennard-Jones 12-6 potential parameters. This research demonstrates how uncertainty quantification renders molecular simulation a quantitative tool for thermophysical property evaluation. Specifically, by quantifying and reducing the uncertainty associated with molecular simulation results, we were able to discern between different experimental data sets and prediction models for the critical constants. In this regard, our results enabled the development of improved prediction models for Tc, ρc, Pc, and Zc for large n-alkanes. In addition, we developed a new Tb prediction model in order to ensure thermodynamic consistency between Tc, Pc, and Tb.

Molecular dynamics simulations are an increasingly valuable tool to biochemical researchers: advances in computational power have expanded the range of biomolecules that can be simulated, and parameters describing these interactions are increasingly accurate. Despite substantial progress in force field parameterization, recent simulations of protein molecules using state-of-the-art, fixed-charge force fields revealed that the interactions among and within protein molecules can be too favorable, resulting in unrealistic aggregation or structural collapse of the proteins being simulated. To understand why these protein-protein interactions are so over-stabilized, I first assessed the ability of simulation force fields to represent accurately the interactions of individual amino acids, employing an osmotic pressure simulation apparatus that enabled direct comparison with experiment. Surprisingly, simulations of most of the amino acids resulted in behavior that was in strong agreement with experiment. A number of amino acids, however—notably those that contain hydroxyl groups and those that carry a formal charge—interacted in ways that were clearly inaccurate. Additionally, some commonly-used force fields failed to accurately represent the interactions of amino acids in a consistent manner. By further investigating the interactions of the functional groups of these amino acids, I was able not only to determine some of the root causes of individual amino acid inaccuracies, but also to implement simple modifications that brought the interactions of these small molecules and amino acids in stronger accord with experiment. These studies have highlighted some of the shortcomings in popular simulation force fields, and have proposed useful modifications to address them. Still, there is additional work that must be—and is being—conducted in order to correctly model the interaction behavior of proteins in simulation.

Genetic sequences are being collected at an ever increasing rate due to rapid cost reductions; however, experimental approaches to determine the structure and function of the protein(s) each gene codes are not keeping pace. Therefore, computational methods to augment experimental structures with comparative (i.e. homology) models using physics-based methods for building residues, loops and domains are needed to thread new sequences onto homologous structures. In addition, even experimental structure determination relies on analogous first principles structure refinement and prediction algorithms to place structural elements that are not defined by the data alone. Computational methods developed to find the global free energy minimum of an amino acid sequence (i.e. the protein folding problem) are increasingly successful, but limitations in accuracy and efficiency remain. Optimization efforts have focused on subsets of systems and environments by utilizing potential energy functions ranging from fixed charged force fields (Fiser, Do, & Sali, 2000; Jacobson et al., 2004), statistical or knowledge based potentials (Das & Baker, 2008) and/or potentials incorporating experimental data (Brunger, 2007; Trabuco, Villa, Mitra, Frank, & Schulten, 2008). Although these methods are widely used, limitations include 1) a target function global minimum that does not correspond to the actual free energy minimum and/or 2) search protocols that are inefficient or not deterministic due to rough energy landscapes characterized by large energy barriers between multiple minima. Our Global Optimization Using Metadynamics and a Polarizable Force Field (GONDOLA) approach tackles the first limitation by incorporating experimental data (i.e. from X-ray crystallography, CryoEM or NMR experiments) into a hybrid target function that also includes information from a polarizable molecular mechanics force field (Lopes, Roux, & MacKerell, 2009; Ponder & Case, 2003). The second limitation is overcome by driving the sampling of conformational space by adding a time-dependent bias to the objective function, which pushes the search toward unexplored regions (Alessandro Barducci, Bonomi, & Parrinello, 2011; Zheng, Chen, & Yang, 2008). The GONDOLA approach incorporates additional efficiency constructs for search space exploration that include Monte Carlo moves and fine grained minimization. Furthermore, the dimensionality of the search is reduced by fixing atomic coordinates of known structural regions while atoms of interest explore new coordinate positions. The overall approach can be used for optimization of side-chains (i.e. set side-chain atoms active while constraining backbone atoms), residues (i.e. side-chain atoms and backbone atoms active), ligand binding pose (i.e. set atoms along binding interface active), protein loops (i.e. set atoms connecting two terminating residues active) or even entire protein domains or complexes. Here we focus on using the GONDOLA general free energy driven optimization strategy to elucidate the structural details of missing protein loops, which are often missing from experimental structures due to conformational heterogeneity and/or limitations in the resolution of the data. We first show that the correlation between experimental data and AMOEBA (i.e. a polarizable force field) structural minima is stronger than that for OPLS-AA (i.e. a fixed charge force field). This suggests that the higher order multipoles and polarization of the AMOEBA force field more accurately represented the true crystalline environment than the simpler OPLS-AA model. Thus, scoring and optimization of loops with AMOEBA is more accurate than with OPLS-AA, albeit at a slightly increased computational cost. Next, missing PDZ domain protein loops and protein loops from a loop decoy data set were optimized for 5 ns using the GONDOLA approach (i.e. under the AMOEBA polarizable force field) as well as a commonly used global optimization procedure (i.e. simulated annealing under the OPLS-AA fixed charge force field). The GONDOLA procedure was shown to provide more accurate structures in terms of both experimental metrics (i.e. lower Rfree values) and structural metrics (i.e. using the MolProbity structure validation tool). In terms of Rfree, only one out of seven simulated annealing results was better than the Gondola global optimization. Similarly, one simulated anneal loop had a better MolProbity score, but none of the simulated annealing loops were better in both categories. On average, GONDOLA achieved an Rfree value 19.48 and simulated annealing saw an average Rfree value of 19.63, and the average MolProbity scores were 1.56 for GONDOLA and 1.75 for simulated annealing. In addition to providing more accurate predictions, GONDOLA was shown to converge much faster than the simulated annealing protocol. Ten separate 5 ns optimizations of the 4 residue loop missing from one of the PDZ domains were conducted. Five were done using GONDOLA and five with the simulated annealing protocol. The fastest four converging results belonged to the GONDOLA approach. Thus, this work demonstrates that GONDOLA is well-suited to refine or predict the coordinates of missing residues and loops because it is both more accurate and converges more rapidly.

<p>The absorption properties of the Pt1 chromophore at room temperature have been studied. Stretch, bend and torsion parameters for Pt(II), P, C (type 1, 2 and 4) and H have been parameterized for use in the MM3 force field. Parameters were fitted to energies computed at the B3LYP level of theory. The parameterized model was used to perform molecular dynamics simulations at room temperature. This was done for several environments and for time periods of up to 200 ps. Absorption properties were computed for snapshots from the dynamics, from which average absorption spectra were created. A conformational broadening of around 40 nm was found in the theoretical spectra, which is in good agreement with experiments. Due to a lack of solvent-solute interactions and the use of a less extensive basis set, a systematic blue shift of 40 nm is evident in the computed spectra.</p>

Thesis (M.A. (Industrial Psychology))--North-West University, Potchefstroom Campus, 2007.

Den kopparbindande egenskapen hos prionproteiner är sannolikt kopplad till proteinets funtion. Det mänskliga prionproteinet innehåller ett kopparbindande oktapeptidområde, där PHGGGWGQ-sekvensen upprepas fyra gånger i följd. Syftet med detta arbete är att undersöka strukturen och dynamiken i oktapeptidområdet genom att använda teoretiska metoder. Med kvantkemisk strukturoptimering genomfördes en detaljerad jämförelse av växelverkan mellan flera katjoner och det kopparbindande området. Enligt dessa beräkningar är rodium(III) en möjlig ersättare för koppar(II) i NMR-specktroskopiska koordinationsstudier. Alternativa solvatiseringsmodeller i molekyldynamiksimuleringar har också jämförts. Periodiska randvillkor är mest lämpade för användning i de system som undersöks i detta arbete. Molekyldynamiksimuleringar användes för att jämföra oktapeptidområdets struktur och dynamik med och utan kopparjoner. Växelverkan mellan aminosyrornas ringar påverkar starkt strukturen i detta område i frånvaro av kopparjoner. Fyra olika icke-bindande och bindande modeller har studerats, vilka skiljer i sin beskrivning av växelverkan mellan koppar och proteinet. Teoretiska EXAFS spektra beräknades från dem simulerade strukturerna. Spektra som genererats för den bindande modellen är nästan identiska med experimentiella resultat, vilket stöder användandet av den bindande modellen. Detta arbete visar att kopparjoner interagerar med histidin imidazolringens Nδ, deprotonerade amidkväven hos de därpå följande glycinerna samt karbonylsyret hos den andra glycinen. Simuleringarna kunde visa att kopparjonen inte stabilt binder några axiella vattenmolekyler i lösning, till skillnad från en kristallstruktur av koordinationsstrukturen. Indolringen hos tryptofan interagerar direkt med kopparjonen genom stabiliserande katjon-π växelverkan utan direkt medverkan av någon vattenmolekyl. Växelverkan mellan indolringen och kopparjonen var väldefinierad och observerades kunna ske på båda sidor av koordinationsplanet. Molekyldynamiksimuleringarna med kopparjoner och oktapeptidområdet visade hur närvaron av kopparjoner ledde till ett mer strukturerat oktapeptidområde. / The copper-binding ability of the prion protein is thought to be closely related to its function. The human prion protein contains a copper-binding octapeptide region, where the octapeptide PHGGGWGQ is repeated four times consecutively. This work focuses on investigation of the structure and the dynamics of the octapeptide region by means of theoretical methods. Quantum chemical structural optimization allowed a detailed comparison of the interaction of several cations at the copper coordination site. These calculations identified rhodium(III) as a potent substitute for copper(II) that could be used to study the coordination site with NMR-spectroscopic methods. Solvation models that could be used in molecular dynamics simulations as an alternative to periodic boundary conditions were evaluated. Periodic boundary conditions are the best method for modeling the aqueous bulk in the kind of systems that are studied in this work. Molecular dynamics simulations were used to compare the behavior of the octapeptide region in the absence and presence of copper ions. Interaction between nonpolar rings strongly influences the structure of the region in the absence of copper ions. Four different non-bonded and bonded models for describing the interaction between copper and the protein were evaluated. Theoretical EXAFS spectra were calculated from the simulated structures. The results obtained for the bonded model are nearly identical with experimental data, which validates the use of the bonded model. This work thus shows strong evidence for copper(II) ions interacting with the octapeptide region through the histidine imidazole Nδ, the deprotonated nitrogen atoms of the following two glycine residues and the carbonyl oxygen atom of the second glycine residue. Notably, the simulations show that the axial sites of the copper ion do not stably coordinate water molecules in solution, as opposed to the crystal structure reported for the coordination site. Instead, the tryptophan indole ring interacted directly with the copper ion through stabilizing cation-π interaction without water mediation. The interaction of the indole ring with the copper ion was well-defined and was observed to occur on both sides of the coordination plane. The investigations of the interaction between copper ions and the octapeptide region with molecular dynamics simulations show how the presence of copper ions results in a more structured octapeptide region. / QC 20100816

The absorption properties of the Pt1 chromophore at room temperature have been studied. Stretch, bend and torsion parameters for Pt(II), P, C (type 1, 2 and 4) and H have been parameterized for use in the MM3 force field. Parameters were fitted to energies computed at the B3LYP level of theory. The parameterized model was used to perform molecular dynamics simulations at room temperature. This was done for several environments and for time periods of up to 200 ps. Absorption properties were computed for snapshots from the dynamics, from which average absorption spectra were created. A conformational broadening of around 40 nm was found in the theoretical spectra, which is in good agreement with experiments. Due to a lack of solvent-solute interactions and the use of a less extensive basis set, a systematic blue shift of 40 nm is evident in the computed spectra.

Specific recognition of ligands including metal ions by proteins is the key of many crucial biological functions and systems. Accurate prediction of the binding strength not only sheds light on the mechanism of the molecular recognition but also provides the most important prerequisite of drug discovery. Computational modeling of molecular binding has gained a great deal of attentions in the last few decades since the advancement of computer power and availability of high-resolution crystal structures. However there still exist two major challenges in the field of molecular modeling, i.e. sampling issue and accuracy of the models. In this work, I have dedicated to tackling these two problems with a noval polarizable force field which is believed to produce more accurate description of molecular interactions than classic non-polarizable force fields. We first developed the model for divalent cations Mg²⁺ and Ca²⁺, deriving the parameters from quantum mechanics. To understand the hydration thermodynamics of these ions we have performed molecular dynamics simulations using our AMOEBA force field. Both the water structures around ions and the solvation free energies were in great accordance with experiment data. We have also simulated and calculated the binding free energies of a series of benzamidine-like inhibitors to trypsin using explicit solvent approach by free energy perturbation. The calculated binding free energies are well within the accuracy of experimental measurement and the direction of change is predicted correctly in all cases. Finally, we computed the hydration free energies of a few organic molecules and automated the calculation procedure. / text

Optical tweezers have been widely used by biophysicists to measure forces in single molecular processes, such as the force of a motor molecule walking and the force of a DNA molecule winding and unwinding. In these and similar force measurements, the usual assumption is that the force applied to a particle inside the tweezers is proportional to the displacement of the particle away from the trap center like Hookean springs, which would imply that the force field is conservative. However, the Gaussian beam model has indicated that the force field generated by optical tweezers is actually nonconservative, yet no experiments have measured or accounted for this effect. We introduce an experimental method -- the local drift method -- that can measure the force field in optical tweezers with high precision without any assumptions about the functional form of the force field. The force field is determined by analyzing the Brownian motion of a trapped particle. We successfully applied this method to different sizes of particles and measured the three dimensional force field with 10 nm spatial resolution and femtonewton precision in force. We find that the force field is indeed nonconservative. The nonconservative contribution increases radially away from the optical axis for both small and large particles. The curl vector field -- a measurement of the nonconservative force field -- reverses direction from counter-clockwise for small particles in the Rayleigh regime to clockwise for large particles in the ray optics regime, consistent with the different scattering force profiles in the two distinct scattering regimes. Together with the thermal fluctuations of the trapped particle, the nonconservative force can cause a complex flux of energy into the system. Optically-confined Brownian motion is further used to probe nanostructures such as a biopolymer network. This technique -- thermal noise imaging -- uses a Brownian particle as a "natural scanner" to explore a biopolymer network by moving the Brownian particle through the network with optical tweezers. The position fluctuations of the probe particle reflect the location of individual filaments as excluded volumes. The resolution of thermal noise imaging is directly coupled to the size of the probe particle. A smaller probe is capable of exploring smaller pore sizes formed by dense network. Previously, a 200 nm polystyrene particle had been used to probe an agar network. In this work, 100 nm gold probe particles are used to enhance the resolution. A 100 nm particle explore a network with mesh 2³ times smaller and therefore enhance the network resolution by 2³ times. A 100 nm particle also improves the imaging speed by a factor of 2 because of its faster diffusion. Three-dimensional thermal noise images of agarose filaments are obtained and a resolution of 10 nm for the position of the filaments is achieved. In addition, a gold particle is trapped with significantly less power than a polystyrene particle of the same size, indicating the possibility for using even smaller gold particles to further improve the resolution. / text

Movement is essential to human life because it provides us with the freedom of mobility and the power to affect our surroundings. Moreover, movements are vital to communication: from hand and finger movements when writing, mouth and throat movements when speaking, to painting, dancing, and other forms of artistic self expression. As people grow and experience new environments, adaptively maintaining the accuracy of movements is a critical function of the motor system. In this dissertation, I explore the key mechanisms that underlie the adaptability of simple visually guided reaching movements. I specifically focus on two key facets of this adaptability: how motor learning rate can be predicted by motor variability and how motor learning affects the mechanisms which underlie movement planning. Inspired by reinforcement learning, I hypothesized that greater amounts of motor variability aligned with a task will produce more effective exploration, leading to faster learning rates. I discovered that this relationship predicts person-to-person and task-to-task differences in learning rate for both reward-based and error-based learning tasks. Moreover, I found that the motor system actively and enduringly reshapes motor output variability, aligning it with a task to improve learning. These results indicate that the structure of motor variability is an activelyregulated, critical feature of the motor system which plays a fundamental role in determining motor learning ability. Combining prominent theories in motor control, I created a model which describes the planning of visually guided reaching movements. This model computes a weighted average of two independent feature-based motor plans: one based on the goal location of a movement, and the other based on an intended movement vector. Employing this model to characterize the generalization of adaptation to movements and movement sequences, I find that both features, movement vector and goal location, contribute significantly to movement planning, and that each feature is remapped by motor adaptation. My results show that multiple features contribute to the planning of both point-to-point and sequential reaching movements. Moreover, a computational model which is based on the remapping of multiple features accurately predicts how visuomotor adaptation affects the planning of movement sequences. / Engineering and Applied Sciences