Modeling adaptive dynamics in microbial populations with applications to the evolution of cellular resource allocation trade-offs

Adaptive evolution is the process by which natural selection, acting on variation within a population, promotes the survival of individuals that are more successful at reproducing and contributing to future generations. Evolutionary processes in microbes occur at the intersection of population genetics, natural selection, and underlying mechanistic constraints, to give rise to the repertoire of adaptation observed in nature. Understanding microbial adaptive evolution is of critical importance for human health for example, through the emergence of pathogenicity and antibiotic resistance. Moreover, the stability and function of natural and artificial ecosystems is contingent on the evolving interactions between microbes, and between microbes and the environment. We present a modelling framework, based on the theory of adaptive dynamics, to investigate how cellular resource allocation trade-offs affect the adaptation process. We used resource-consumer theory, which explicitly models the interactions between cells and their environment, together with matrix models of structured populations, to implement phenotype-determined cellular strategies of resource allocation between mutually exclusive processes. We then analyse the outcome of competitions between different phenotypes across environmental and competitive conditions. We applied our methods to the evolution of strategies (phenotypes) for resource allocation between two competing cellular process in microbial populations growing in chemostat-like environments. We calculated the adaptively stable strategies for several models and showed how state-structured population models can be mapped to simpler chemostat models on invariant manifolds. We then extended our analysis to the case where a limiting nutrient may be utilized using two alternative metabolic pathways. We described how the total population fitness of a metabolic strategy can be constructed from the individual decisions of its constituent members. We developed numerical methods to simulate and analyse general models of adaptive dynamics using principles from graph theory and discrete Markov processes. The methods were used to explore the evolution of nutrient use strategies for microbial populations growing on two and three substitutable nutrients. We highlight the importance of the ancestral phenotype in channelling the adaptation process, which, together with the choice of the mutational kernel, influences the adaptively stable strategies and modes of co-existence. In a related finding, we show how some phenotypes are adaptively stable only in the presence of a competitor lineage that modifies the environment in a manner that permits another phenotype to invade. Our methods also reveal instances where historical contingency and chance have an important effect on determining the stable nutrient use strategies. Finally, we demonstrate the existence of adaptively stable periodic solutions whereby, under some conditions, phenotype successions are cyclical. Our work builds on the foundation of adaptive dynamics theory to provide a general framework for analysing models of microbial adaptation. We focused on understanding the implications of underlying constraints and cellular resource allocation trade-offs in the context of adaptive evolution

Random Matrices in 2D, Laplacian Growth and Operator Theory

Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of theoretical physics, from condensed matter to high energy. The fundamental results obtained so far rely mostly on the theory of random matrices in one dimension (the dimensionality of the spectrum, or equilibrium probability density). In the last few years, this theory has been extended to the case where the spectrum is two-dimensional, or even fractal, with dimensions between 1 and 2. In this article, we review these recent developments and indicate some physical problems where the theory can be applied.Comment: 88 pages, 8 figure

The Bracing Requirements of Steel Beams of Intermediate Slenderness

Steel beams, whether rolled or built-up, contain unavoidable initial imperfections and residual stresses and are subject to unintentional eccentricity of applied loading. Such beams which also possess inadequate lateral restraint are prone to failure as a result of lateral-torsional instability, which occurs under elastic or inelastic conditions depending on the slenderness of the member. A review of the literature pertaining to the bracing requirements of steel beams revealed little published work concerned with the restraint of beams of intermediate and low slenderness which fail inelastically. The provision of adequate midspan restraint for the prevention of inelastic instability in centrally loaded, single span I-beams formed the basis of this study. The non-linear analysis capabilities of the finite element programmes MSC/NASTRAN and FINAS were employed to provide theoretical verification of the results of a series of tests on small-scale, fabricated, steel I-beams. Measured initial geometrical imperfections of the test beams were modelled in the finite element idealisation by suitable adjustment of nodal coordinates and both geometrical and material non-linearites were accounted for in the analysis. Numerical instability and convergence difficulties were encountered in both analyses, although their occurrence was less frequent in FINAS. In FINAS analyses where these difficulties did not arise, collapse loads were determined and post-buckling behaviour followed with relative ease. A bracing fork device for the provision of a predetermined stiffness of midspan restraint was developed and subsequently employed in all tests. Strain gauges attached to the prongs of this device permitted bracing forces to be measured at any stage in the tests. In general, satisfactory correlation was achieved between finite element and experimental results, allowing bracing criteria for single span, centrally loaded and restrained beams to be proposed. As anticipated, the bracing requirements of inelastic beams proved more onerous than those demanded by the classical bifurcation analysis employed in problems of elastic beam buckling. A subsequent series of comparative designs in accordance with the three current (1985) British steelwork codes (BS 449, BS 5950 and BS 5400) revealed that bracing members designed as struts in compliance with the minimum strength and maximum slenderness criteria of these documents provided adequate stiffness and strength of restraint

Liquid-Solid Transitions with Applications to Self-Assembly.

We study the thermodynamic and kinetic pathways by which liquids transform into solids, and their relation to the metastable states that commonly arise in self-assembly applications. As a case study in the formation of ordered metastable solids, we investigate the atomistic mechanism by which quasicrystals form. We show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal "nucleus" to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In a related study, we propose a two-part mechanism for forming 3d dodecagonal quasicrystals by self-assembly. Our mechanism involves (1) attaching small mobile particles to the surface of spherical particles to encourage icosahedral packing and (2) allowing a subset of particles to deviate from the ideal spherical shape, to discourage close-packing. In addition to studying metastable ordered solids, we investigate the phenomenology and mechanism of the glass transition. We report measurements of spatially heterogeneous dynamics in a system of air-driven granular beads approaching a jamming transition, and show that the dynamics in our granular system are quantitatively indistinguishable from those for a supercooled liquid approaching a glass transition. In a second study of the glass transition, we use transition path sampling to study the structure, statistics and dynamics of localized excitations for several model glass formers. We show that the excitations are sparse and localized, and their size is temperature-independent. We show that their equilibrium concentration is proportional to exp[-Ja(1/T-1/To)], where "Ja" is the energy scale for irreversible particle displacements of length "a," and "To" is an onset temperature. We show that excitation dynamics is facilitated by the presence of other excitations, causing dynamics to slow in a hierarchical way as temperature is lowered. To supplement our studies of liquid-solid transitions, we introduce a shape matching framework for characterizing structural transitions in systems with complex particle shapes or morphologies. We provide an overview of shape matching methods, explore a particular class of metrics known as "harmonic descriptors," and show that shape matching methods can be applied to a wide range of nanoscale and microscale assembly applications.Ph.D.Chemical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/78931/1/askeys_1.pd