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The antimicrobial resistance crisis has persisted despite broad attempts at intervention. It has been proposed that an important driver of resistance is selection imposed on bacterial populations that are not the intended target of antimicrobial therapy. But to date, there has been limited quantitative measure of the mean and variance of resistance following antibiotic exposure. Here we focus on the important nosocomial pathogen Enterococcus faecium in a hospital system where resistance to daptomycin is evolving despite standard interventions. We hypothesized that the intravenous use of daptomycin generates off-target selection for resistance in transmissible gastrointestinal (carriage) populations of E . faecium . We performed a cohort study in which the daptomycin resistance of E . faecium isolated from rectal swabs from daptomycin-exposed patients was compared to a control group of patients exposed to linezolid, a drug with similar indications. In the daptomycin-exposed group, daptomycin resistance of E . faecium from the off-target population was on average 50% higher than resistance in the control group ( n = 428 clones from 22 patients). There was also greater phenotypic diversity in daptomycin resistance within daptomycin-exposed patients. In patients where multiple samples over time were available, a wide variability in temporal dynamics were observed, from long-term maintenance of resistance to rapid return to sensitivity after daptomycin treatment stopped. Sequencing of isolates from a subset of patients supports the argument that selection occurs within patients. Our results demonstrate that off-target gastrointestinal populations rapidly respond to intravenous antibiotic exposure. Focusing on the off-target evolutionary dynamics may offer novel avenues to slow the spread of antibiotic resistance.

Antibiotics are used for the treatment of bacterial infections. However, the increased use of antibiotics has coincided with a rapid increase in the prevalence of antibiotic-resistant bacteria, threatening the overall efficacy of antibiotics and posing significant public health challenges. In this thesis, I explore how two processes, resistance evolution and resistance transmission, shaped the prevalence of antibiotic-resistant bacteria within the hospital. Using isolates obtained and sequenced from a hospital surveillance program, I also aim to understand the factors that underlie these population dynamics. We focus our efforts on studying these processes in the nosocomial, opportunistic pathogen Enterococcus faecium, which is a leading cause of hospital acquired infections.In Chapter 1, we analyze the role of resistance evolution and transmission in the overall incidence of resistance infections in a hospital associated pathogen. Leveraging our unique dataset of sequenced surveillance isolates collected over 5 years, we describe and quantify using phylogenetic comparative analysis, the probability that resistance arose de novo or transmission in each daptomycin resistant blood stream infection in the hospital. We find strong molecular, phenotypic, and clinical evidence supporting the role of both resistance transmission and resistance evolution in new resistant infections.Chapters 2 and 3 detail the evolution of resistant isolates in vitro and in vivo. Despite the differences in these environments, analyzing bacterial evolution in these conditions can provide insight into the population dynamics of resistant bacteria in important settings: antibiotic free environments and the gut microbiome. In both settings, we observe the maintenance of resistance among certain classes of bacterial strains. Using laboratory evolution in antibiotic-free media, we find that transmitted daptomycin resistant strains of E. faecium generally maintained resistance throughout laboratory evolution. Diversity was minimal, with the founding strain comprising most of the evolved population. Similarly, in surveillance swabs obtained from serially sampled patients, deep sequencing revealed domination by single strains with minimal levels of diversity. Additional trends and features of the population dynamics in vitro are explored using the mathematical modelling of fitness and in vivo through population genetic models. Together, these projects highlight the dynamic nature of E. faecium. E. faecium has shown a remarkable ability to migrate between hosts and evolve resistance to antibiotics, consequently making it a problem endemic to hospitals worldwide. Our results here show possible reasons for this species’ success with possible implications for reducing its future health burden.

Multiple sclerosis (MS) is an autoimmune inflammatory demyelinating disease of the central nervous system. Dysregulation of STAT3, a transcription factor pivotal to various cellular processes including Th17 cell differentiation, has been implicated in MS. Here, we report that STAT3 is activated in infiltrating monocytic cells near active MS lesions and that activation of STAT3 in myeloid cells is essential for leukocyte infiltration, neuroinflammation, and demyelination in experimental autoimmune encephalomyelitis (EAE). Genetic disruption of Stat3 in peripheral myeloid lineage cells abrogated EAE, which was associated with decreased antigen-specific T helper cell responses. Myeloid cells from immunized Stat3 mutant mice exhibited impaired antigen-presenting functions and were ineffective in driving encephalitogenic T cell differentiation. Single-cell transcriptome analyses of myeloid lineage cells from preclinical wild-type and mutant mice revealed that loss of myeloid STAT3 signaling disrupted antigen-dependent cross-activation of myeloid cells and T helper cells. This study identifies a previously unrecognized requisite for myeloid cell STAT3 in the activation of myelinreactive T cells and suggests myeloid STAT3 as a potential therapeutic target for autoimmune demyelinating disease.

Bacterial pathogens that are successful in hospital environments must survive times of intense antibiotic exposure and times of no antibiotic exposure. When these organisms are closely associated with human hosts, they must also transmit from one patient to another for the resistance to spread. The resulting evolutionary dynamics have, in some settings, led to rising levels of resistance in hospitals. Here, we focus on an important but understudied aspect of this dynamic: the loss of resistance when the resistant organisms evolve in environments where the antibiotic pressure is removed. Based on prior data, we hypothesize that resistance arising in the context of strong selection may carry a high cost and revert to sensitivity quickly once the selective pressure is removed. Conversely, resistant isolates that persist through times of no antibiotic pressure should carry a lower cost and revert less quickly. To test this hypothesis, we utilize a genetically diverse set of patient-derived, daptomycin-resistant isolates that include cases of both emergence of resistance within patients and putatively transmitted resistance. Both of these sets of strains have survived periods of antibiotic exposure, but only putatively transmitted resistant strains have survived extended periods without antibiotic exposure. These strains were then allowed to evolve in antibiotic free laboratory conditions. We find that putatively transmitted resistant strains tended to have lower level resistance but that evolution in antibiotic-free conditions resulted in minimal loss of resistance. In contrast, resistance that arose within patients was higher level but exhibited greater declines in resistance . Sequencing of the experimentally evolved isolates revealed that reversal of high level resistance resulted from evolutionary pathways that were frequently genetically associated with the unique resistance mutations of that strain. Thus, the rapid reversal of high-level resistance was associated with accessible evolutionary pathways where an increase in fitness is associated with decreased resistance. We describe how this rapid loss of resistance may limit the spread of resistance within the hospital and shape the diversity of resistance phenotypes across patients.

The Kalman filter operates by storing a Gaussian description of the state estimate in the form of a mean and covariance. Instead of storing and manipulating the covariance matrix directly, a square-root Kalman filter only forms and updates a triangular matrix square root of the covariance matrix. The resulting algorithm is more numerically stable than a traditional Kalman filter, benefiting from double the working precision. This paper presents a formulation of the square root Kalman filter that leverages the QR decomposition to dramatically simplify the resulting algorithm.

Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be computed using the implicit function theorem, enabling efficient differentiation of these optimizers for a fraction of the cost of the total solution time. In the presence of active inequality constraints, this technique is only capable of providing discontinuous subgradients that present a challenge to algorithms that rely on the smoothness of these derivatives. This paper presents a technique for relaxing primal-dual solutions with a logarithmic barrier to provide smooth derivatives near active inequality constraints, with the ability to specify a uniform and consistent amount of smoothing. We pair this with an efficient primal-dual interior-point algorithm for solving an always-feasible \\(\\ell_1\\)-penalized variant of a convex quadratic program, eliminating the issues surrounding learning potentially infeasible problems. This parallelizable and smoothly differentiable solver is demonstrated on a range of robotics tasks where smoothing is important. An open source implementation in JAX is available at github.com/kevin-tracy/qpax.

Accurate and stable spacecraft pointing is a requirement of many astronomical observations. Pointing particularly challenges nanosatellites because of an unfavorable surface area to mass ratio and proportionally large volume required for even the smallest attitude control systems. This work explores the limitations on astrophysical attitude knowledge and control in a regime unrestricted by actuator precision or actuator-induced disturbances such as jitter. The external disturbances on an archetypal 6U CubeSat are modeled and the limiting sensing knowledge is calculated from the available stellar flux and grasp of a telescope within the available volume. These inputs are integrated using a model-predictive control scheme. For a simple test case at 1 Hz, with an 85 mm telescope and a single 11th magnitude star, the achievable body pointing is predicted to be 0.39 arcseconds. For a more general limit, integrating available star light, the achievable attitude sensing is approximately 1 milliarcsecond, which leads to a predicted body pointing accuracy of 20 milliarcseconds after application of the control model. These results show significant room for attitude sensing and control systems to improve before astrophysical and environmental limits are reached.

Collision detection between objects is critical for simulation, control, and learning for robotic systems. However, existing collision detection routines are inherently non-differentiable, limiting their applications in gradient-based optimization tools. In this work, we propose DCOL: a fast and fully differentiable collision-detection framework that reasons about collisions between a set of composable and highly expressive convex primitive shapes. This is achieved by formulating the collision detection problem as a convex optimization problem that solves for the minimum uniform scaling applied to each primitive before they intersect. The optimization problem is fully differentiable with respect to the configurations of each primitive and is able to return a collision detection metric and contact points on each object, agnostic of interpenetration. We demonstrate the capabilities of DCOL on a range of robotics problems from trajectory optimization and contact physics, and have made an open-source implementation available.

Collision detection plays an important role in simulation, control, and learning for robotic systems. However, no existing method is differentiable with respect to the configurations of the objects, greatly limiting the sort of algorithms that can be built on top of collision detection. In this work, we propose a set of differentiable collision detection algorithms between capsules and padded polygons by formulating these problems as differentiable convex quadratic programs. The resulting algorithms are able to return a proximity value indicating if a collision has taken place, as well as the closest points between objects, all of which are differentiable. As a result, they can be used reliably within other gradient-based optimization methods, including trajectory optimization, state estimation, and reinforcement learning methods.

We present a unified framework for solving trajectory optimization problems in a derivative-free manner through the use of sequential convex programming. Traditionally, nonconvex optimization problems are solved by forming and solving a sequence of convex optimization problems, where the cost and constraint functions are approximated locally through Taylor series expansions. This presents a challenge for functions where differentiation is expensive or unavailable. In this work, we present a derivative-free approach to form these convex approximations by computing samples of the dynamics, cost, and constraint functions and letting the solver interpolate between them. Our framework includes sample-based trajectory optimization techniques like model-predictive path integral (MPPI) control as a special case and generalizes them to enable features like multiple shooting and general equality and inequality constraints that are traditionally associated with derivative-based sequential convex programming methods. The resulting framework is simple, flexible, and capable of solving a wide variety of practical motion planning and control problems.