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.

Adhesion molecules and chemokines: relation to anthropometric, body composition, biochemical and dietary variables

Introduction: Among the inflammatory mediators involved in the pathogenesis of obesity, the cell adhesion molecules P-selectin, E-selectin, VCAM-1, ICAM-1 and the chemokine MCP-1 stand out. They play a crucial role in adherence of cells to endothelial surfaces, in the integrity of the vascular wall and can be modulated by body composition and dietary pattern. Objectives: To describe and discuss the relation of these cell adhesion molecules and chemokines to anthropometric, body composition, dietary and biochemical markers. Methods: Papers were located using scientific databases by topic searches with no restriction on year of publication. Results: All molecules were associated positively with anthropometric markers, but controversial results were found for ICAM-1 and VCAM-1. Not only obesity, but visceral fat is more strongly correlated with E-selectin and MCP-1 levels. Weight loss influences the reduction in the levels of these molecules, except VCAM-1. The distribution of macronutrients, excessive consumption of saturated and trans fat and a Western dietary pattern are associated with increased levels. The opposite could be observed with supplementation of w-3 fatty acid, healthy dietary pattern, high calcium diet and high dairy intake. Regarding the biochemical parameters, they have inverse relation to HDLC and positive relation to total cholesterol, triglycerides, blood glucose, fasting insulin and insulin resistance. Conclusion: Normal anthropometric indicators, body composition, biochemical parameters and eating pattern positively modulate the subclinical inflammation that results from obesity by reducing the cell adhesion molecules and chemokines.

Assessments of body composition and bone parameters of lactating rats treated with diet containing flaxseed meal (Linum usitatissinum) during post-weaning period

Introduction: There are few studies on body composition and the effects of diet on weight postpartum women. The aim was to evaluate the body composition and bone parameters in lactating rats treated with diet containing flaxseed flour during postweaning period. Methods: After weaning, the lactating rat were divided in control (n = 6) and experimental (F, n = 6) group, treated with 25% flaxseed flour diet. After 30 days, body composition by dual-energy X-ray absorptiometry, serum analysis, organs and intra-abdominal fat mass, femur and lumbar vertebra parameters were determined. Results: The groups showed similar food intake, body mass and bone parameters. While F group showed the following: lower body (-5%), gonadal (-17%), mesenteric (-23%) and intra-abdominal (-6%) fat mass. Increase of HDL-cholesterol (+10%) and lower glucose (-15%), triglycerides (P < 0.05, -37%) and cholesterol (P < 0.05, -21%). Conclusions: The findings highlight the effects of flaxseed for control of adiposity and to maintain a healthy biochemical profile during the postnatal period.

Swimming training repercussion on metabolic and structural bone development: benefits of the incorporation of whole body vibration or pilometric training; the RENACIMIENTO project

Introduction: Enviromental factors such as exercise participation and nutrition have often been linked to bone improvements. However, not all sports have the same effects, being non-osteogenic sports such as swimming defined as negative or neutral sports to practice regarding bone mass by some authors, similarly exercise-diet interaction in especific groups is still not clear. Objective: To present the methodology of the RENACIMENTO project that aims to evaluate body composition and more specifically bone mass by several techniques in adolescent swimmers and to observe the effects and perdurability of whole body vibration (WBV) and jumping intervention (JIN) on body composition and fitness on this population and explore posible diet interactions. Design: Randomized controlled trial. Methods: 78 swimmers (12-17 y) and 26 sex- and age-matched controls will participate in this study. Dual energy X-ray, peripheral Quantitative Computed Tomography, Quantitative Ultrasound, Bioelectrical Impedance Analysis, and anthropometry measurements will be performed in order to evaluate body composition. Physical activity, nutrition, pubertal development and socio-economical status may act as confounders of body composition and therefore will also be registered. Several fitness factors regarding strength, endurance, performance and others will also be registered to evaluate differences with controls and act as confounders. A 7-month WBV therapy will be performed by 26 swimmers consisting of a training of 15 minutes 3 times per week. An 8 month JIM will also be performed by 26 swimmers 3 times per week. The remaining 26 swimmers will continue their normal swimming training. Four evaluations will be performed, the first one in order to describe differences between swimmers and controls. The second one to describe the effects of the interventions and the third and fourth evaluations to describe the perdurability of the effects of the WBV and JIN. Conclusion: The RENACIMIENTO project will allow to answer several questions regarding body composition, fitness, bone mass and interaction with diet of adolescent swimmers, describe swimming as a positive, negative or neutral sport to practice regarding these parameters and elucidate the effects and perdurability of WBV and JIM on body composition.

Application of body mass index adjusted for fat mass (BMIfat) obtained by bioelectrical impedance in adults

Introduction: Body mass index (BMI) has been one of the methods most frequently used for diagnose obesity, but it isn't consider body composition. Objective: This study intends to apply one new adiposity index, the BMI adjusted for fat mass (BMIfat) developed by Mialich, et al. (2011), in a adult Brazilian sample. Methods: A cross-sectional study with 501 individuals of both genders (366 women, 135 men) aged 17 to 38 years and mean age was 20.4 ± 2.8 years, mean weight 63.0 ± 13.5 kg, mean height 166.9 ± 9.0 cm, and BMI 22.4 ± 3.4 kg/m². Results and discussion: High and satisfactory R2 values were obtained, i.e., 91.1%, 91.9% and 88.8% for the sample as a whole and for men and women, respectively. Considering this BMIfat were developed new ranges, as follows: 1.35 to 1.65 (nutritional risk for malnutrition), > 1.65 and ≤ 2.0 (normal weight) and > 2.0 (obesity). The BMIfat had a more accurate capacity of detecting obese individuals (0.980. 0.993, 0.974) considering the sample as a whole and women and men, respectively, compared to the traditional BMI (0.932, 0.956, 0.95). Were also defined new cut-off points for the traditional BMI for the classification of obesity, i.e.: 25.24 kg/m² and 28.38 kg/m² for men and women, respectively. Conclusion: The BMIfat was applied for the present population and can be adopted in clinical practice. Further studies are needed to determine its application to different ethnic groups and to compare this index to others previously described in the scientific literature.

Wind turbine rotor blade monitoring using digital image correlation: a comparison to aeroelastic simulations of a multi-megawatt wind turbine

Optical full-field measurement methods such as Digital Image Correlation (DIC) provide a new opportunity for measuring deformations and vibrations with high spatial and temporal resolution. However, application to full-scale wind turbines is not trivial. Elaborate preparation of the experiment is vital and sophisticated post processing of the DIC results essential. In the present study, a rotor blade of a 3.2 MW wind turbine is equipped with a random black-and-white dot pattern at four different radial positions. Two cameras are located in front of the wind turbine and the response of the rotor blade is monitored using DIC for different turbine operations. In addition, a Light Detection and Ranging (LiDAR) system is used in order to measure the wind conditions. Wind fields are created based on the LiDAR measurements and used to perform aeroelastic simulations of the wind turbine by means of advanced multibody codes. The results from the optical DIC system appear plausible when checked against common and expected results. In addition, the comparison of relative out-of-plane blade deflections shows good agreement between DIC results and aeroelastic simulations.

Multi-body simulation of a canine hind limb: model development, experimental validation and calculation of ground reaction forces

Background: Among other causes the long-term result of hip prostheses in dogs is determined by aseptic loosening. A prevention of prosthesis complications can be achieved by an optimization of the tribological system which finally results in improved implant duration. In this context a computerized model for the calculation of hip joint loadings during different motions would be of benefit. In a first step in the development of such an inverse dynamic multi-body simulation (MBS-) model we here present the setup of a canine hind limb model applicable for the calculation of ground reaction forces. Methods: The anatomical geometries of the MBS-model have been established using computer tomography- (CT-) and magnetic resonance imaging- (MRI-) data. The CT-data were collected from the pelvis, femora, tibiae and pads of a mixed-breed adult dog. Geometric information about 22 muscles of the pelvic extremity of 4 mixed-breed adult dogs was determined using MRI. Kinematic and kinetic data obtained by motion analysis of a clinically healthy dog during a gait cycle (1 m/s) on an instrumented treadmill were used to drive the model in the multi-body simulation. Results and Discussion: As a result the vertical ground reaction forces (z-direction) calculated by the MBS-system show a maximum deviation of 1.75%BW for the left and 4.65%BW for the right hind limb from the treadmill measurements. The calculated peak ground reaction forces in z- and y-direction were found to be comparable to the treadmill measurements, whereas the curve characteristics of the forces in y-direction were not in complete alignment. Conclusion: In conclusion, it could be demonstrated that the developed MBS-model is suitable for simulating ground reaction forces of dogs during walking. In forthcoming investigations the model will be developed further for the calculation of forces and moments acting on the hip joint during different movements, which can be of help in context with the in silico development and testing of hip prostheses.

A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method

A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.

Sexual self-awareness and body Image

broadly describes the internal representations of the body structure and the physical appearance of the individual in regards him/herself and others. Sexual self-awareness (ACS) can be understood as the evaluation that each of us makes of his/her feelings and actions related to his/her sexuality and sexual behaviour, describing what each of us thinks about sex and what we feel about behaviours. Objective: Identify dimensions of sexual self-awareness and body image in sexual satisfaction of the young. Methods Correlational descriptive study, a convenience sample of 84 students of a health school (29.8 % male, 20.2 % female), with ages between 19 and 34 years. As data collection instrument a poll through questionnaire, incorporating a Body Image Satisfaction and a Multidimensional Sexual Self-awareness scale, was used. Results The majority of the sample subjects indicate having a partner (59.5 %), perceive themselves as having the ideal weight (75.0 %), the ideal height (65.5 %) and a normal appearance (76.2 %). Globally a high and statistically significant ACS was observed (t-Student = 12.520; GL = 83; p-value < 0.001) and significant statistical differences exist between having/not having a partner and the ACS (Student t = 2,965; GL = 82; p-value = 0.004) showing that those who mention having a partner have a higher average ACS (average = 3.812; SD = 0.412) compared to those without (average = 3.496; SD = 0.563). No statistically significant correlations were observed between ACS and Body Image.

Estimation of whole body muscle, adipose/fat mass, validation in health and during weight loss. Development of prediction equations using MRI as reference method

Background: Body composition is affected by diseases, and affects responses to medical treatments, dosage of medicines, etc., while an abnormal body composition contributes to the causation of many chronic diseases. While we have reliable biochemical tests for certain nutritional parameters of body composition, such as iron or iodine status, and we have harnessed nuclear physics to estimate the body’s content of trace elements, the very basic quantification of body fat content and muscle mass remains highly problematic. Both body fat and muscle mass are vitally important, as they have opposing influences on chronic disease, but they have seldom been estimated as part of population health surveillance. Instead, most national surveys have merely reported BMI and waist, or sometimes the waist/hip ratio; these indices are convenient but do not have any specific biological meaning. Anthropometry offers a practical and inexpensive method for muscle and fat estimation in clinical and epidemiological settings; however, its use is imperfect due to many limitations, such as a shortage of reference data, misuse of terminology, unclear assumptions, and the absence of properly validated anthropometric equations. To date, anthropometric methods are not sensitive enough to detect muscle and fat loss. Aims: The aim of this thesis is to estimate Adipose/fat and muscle mass in health disease and during weight loss through; 1. evaluating and critiquing the literature, to identify the best-published prediction equations for adipose/fat and muscle mass estimation; 2. to derive and validate adipose tissue and muscle mass prediction equations; and 3.to evaluate the prediction equations along with anthropometric indices and the best equations retrieved from the literature in health, metabolic illness and during weight loss. Methods: a Systematic review using Cochrane Review method was used for reviewing muscle mass estimation papers that used MRI as the reference method. Fat mass estimation papers were critically reviewed. Mixed ethnic, age and body mass data that underwent whole body magnetic resonance imaging to quantify adipose tissue and muscle mass (dependent variable) and anthropometry (independent variable) were used in the derivation/validation analysis. Multiple regression and Bland-Altman plot were applied to evaluate the prediction equations. To determine how well the equations identify metabolic illness, English and Scottish health surveys were studied. Statistical analysis using multiple regression and binary logistic regression were applied to assess model fit and associations. Also, populations were divided into quintiles and relative risk was analysed. Finally, the prediction equations were evaluated by applying them to a pilot study of 10 subjects who underwent whole-body MRI, anthropometric measurements and muscle strength before and after weight loss to determine how well the equations identify adipose/fat mass and muscle mass change. Results: The estimation of fat mass has serious problems. Despite advances in technology and science, prediction equations for the estimation of fat mass depend on limited historical reference data and remain dependent upon assumptions that have not yet been properly validated for different population groups. Muscle mass does not have the same conceptual problems; however, its measurement is still problematic and reference data are scarce. The derivation and validation analysis in this thesis was satisfactory, compared to prediction equations in the literature they were similar or even better. Applying the prediction equations in metabolic illness and during weight loss presented an understanding on how well the equations identify metabolic illness showing significant associations with diabetes, hypertension, HbA1c and blood pressure. And moderate to high correlations with MRI-measured adipose tissue and muscle mass before and after weight loss. Conclusion: Adipose tissue mass and to an extent muscle mass can now be estimated for many purposes as population or groups means. However, these equations must not be used for assessing fatness and categorising individuals. Further exploration in different populations and health surveys would be valuable.

Relationship between internal derangement of temporomandibular joint and changes in body posture

Background: The presence of body posture changes among patients with temporomandibular disorders (TMD) has been a controversial issue in the literature, in which it supporters point out the muscular origin as the main etiological factors, mainly associated with postural changes in head. Due to this controversy, it is pertinent to check whether this relationship exists on the most common etiology of TMD, the disk displacement, which translates a biomechanical internal disorder of the temporomandibular joint (TMJ). Objectives: Assess body posture changes in subjects with internal derangement of the TMJ when compared to subjects without this biomechanical dysfunction, characterize the patterns of the jaw movements and assess to the muscle activation during jaw movements. Methods: 21 subjects with TMJ disc displacement (DD) (test group) and 21 subjects without any TMD (control group) was assessed for body posture changes through evaluation of several body segments by posturography and also was evaluated the postural balance reactions through the center of mass during jaw movements using a balance platform. For the characterization of the jaw movement patterns it was done a kinematic analysis during jaw movements (active ROM and path of the jaw). For the muscle activation during jaw movements it was evaluated the masseter, sternocleidomastoid and spinae erector muscles by surface electromyography (EMG). Results Discussion: Both groups show forward head posture and extension of the cervical spine, not noticing any other significant body posture changes in subjects with DD, and if we had to see in detail, in general, subjects without TMD shows more body posture changes than subjects with DD. The pattern of jaw movements is similar in both groups, but in subjects with DD the closing movements are more instable than the opening movements, related to a less effective movement control to counteract the force of gravity and the disk displacement. The bilateral muscle activation during jaw movements is higher in subjects with DD, likely related to a less stable pattern of movement which leads in a higher muscle activation to guide the movement and ensure the best as possible articular stability. Conclusion: The disk displacement with reduction should be viewed as part of a set of signs and symptoms that require an accurate musculoskeletal and psychosocial assessment towards an earlier diagnosis for reduction and control of the functional limiting factors. In this direction, it seems that the relevant set of limiting signs and symptoms deserve a particular attention by health care practitioners involved in the assessment and treatment of TMD, in order to define effective therapeutic options.

The Demobilized Body: Transgressions of Personal Space and Political Participation

Grounded in the intersection between gender politics and electoral studies, this dissertation examines the demobilizing effects of violations of personal space (in the form of domestic violence, control over mobility, emotional abuse, and sexual harassment) on the propensity to vote. Using quantitative methods across four survey datasets concerning Lebanon, the United States, Morocco, and Yemen, this research concludes that cross-regionally, familial control over mobility reduces the propensity to vote among women. Conversely, mechanisms of empowerment such as education and employment increase the propensity to vote.

Mesh Adaption for Tracking Vortex Structures in OVERTURNS Simulation of the S-76 Rotor in Hover

The constant need to improve helicopter performance requires the optimization of existing and future rotor designs. A crucial indicator of rotor capability is hover performance, which depends on the near-body flow as well as the structure and strength of the tip vortices formed at the trailing edge of the blades. Computational Fluid Dynamics (CFD) solvers must balance computational expenses with preservation of the flow, and to limit computational expenses the mesh is often coarsened in the outer regions of the computational domain. This can lead to degradation of the vortex structures which compose the rotor wake. The current work conducts three-dimensional simulations using OVERTURNS, a three-dimensional structured grid solver that models the flow field using the Reynolds-Averaged Navier-Stokes equations. The S-76 rotor in hover was chosen as the test case for evaluating the OVERTURNS solver, focusing on methods to better preserve the rotor wake. Using the hover condition, various computational domains, spatial schemes, and boundary conditions were tested. Furthermore, a mesh adaption routine was implemented, allowing for the increased refinement of the mesh in areas of turbulent flow without the need to add points to the mesh. The adapted mesh was employed to conduct a sweep of collective pitch angles, comparing the resolved wake and integrated forces to existing computational and experimental results. The integrated thrust values saw very close agreement across all tested pitch angles, while the power was slightly over predicted, resulting in under prediction of the Figure of Merit. Meanwhile, the tip vortices have been preserved for multiple blade passages, indicating an improvement in vortex preservation when compared with previous work. Finally, further results from a single collective pitch case were presented to provide a more complete picture of the solver results.

I. Quantal effects in biochemical cooperativity and a proposed mechanism for the differentiation of calcium signaling in synaptic plasticity. II. Evolutionary algorithms for the optimization of methods in computational chemistry

In Part 1 of this thesis, we propose that biochemical cooperativity is a fundamentally non-ideal process. We show quantal effects underlying biochemical cooperativity and highlight apparent ergodic breaking at small volumes. The apparent ergodic breaking manifests itself in a divergence of deterministic and stochastic models. We further predict that this divergence of deterministic and stochastic results is a failure of the deterministic methods rather than an issue of stochastic simulations.

Ergodic breaking at small volumes may allow these molecular complexes to function as switches to a greater degree than has previously been shown. We propose that this ergodic breaking is a phenomenon that the synapse might exploit to differentiate Ca$^{2+}$ signaling that would lead to either the strengthening or weakening of a synapse. Techniques such as lattice-based statistics and rule-based modeling are tools that allow us to directly confront this non-ideality. A natural next step to understanding the chemical physics that underlies these processes is to consider \textit{in silico} specifically atomistic simulation methods that might augment our modeling efforts.

In the second part of this thesis, we use evolutionary algorithms to optimize \textit{in silico} methods that might be used to describe biochemical processes at the subcellular and molecular levels. While we have applied evolutionary algorithms to several methods, this thesis will focus on the optimization of charge equilibration methods. Accurate charges are essential to understanding the electrostatic interactions that are involved in ligand binding, as frequently discussed in the first part of this thesis.

Engineering a Quantum Many-body Hamiltonian with Trapped Ions

While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.