Cover-Encodings of Fitness Landscapes

The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a feature of the typically rugged landscapes encountered arrest the progress of the search process. Another way of tackling optimization problems is by the use of heuristic approximations to estimate a global cost minimum. Here, we present a combination of these two approaches by using cover-encoding maps which map processes from a larger search space to subsets of the original search space. The key idea is to construct cover-encoding maps with the help of suitable heuristics that single out near-optimal solutions and result in landscapes on the larger search space that no longer exhibit trapping local minima. We present cover-encoding maps for the problems of the traveling salesman, number partitioning, maximum matching and maximum clique; the practical feasibility of our method is demonstrated by simulations of adaptive walks on the corresponding encoded landscapes which find the global minima for these problems.     

Predicting the Evolution of Sex on Complex Fitness Landscapes

Most population genetic theories on the evolution of sex or recombination are based on fairly restrictive assumptions about the nature of the underlying fitness landscapes. Here we use computer simulations to study the evolution of sex on fitness landscapes with different degrees of complexity and epistasis. We evaluate predictors of the evolution of sex, which are derived from the conditions established in the population genetic literature for the evolution of sex on simpler fitness landscapes. These predictors are based on quantities such as the variance of Hamming distance, mean fitness, additive genetic variance, and epistasis. We show that for complex fitness landscapes all the predictors generally perform poorly. Interestingly, while the simplest predictor, ΔVar_HD, also suffers from a lack of accuracy, it turns out to be the most robust across different types of fitness landscapes. ΔVar_HD is based on the change in Hamming distance variance induced by recombination and thus does not require individual fitness measurements. The presence of loci that are not under selection can, however, severely diminish predictor accuracy. Our study thus highlights the difficulty of establishing reliable criteria for the evolution of sex on complex fitness landscapes and illustrates the challenge for both theoretical and experimental research on the origin and maintenance of sexual reproduction.     

Fitness Landscapes for Effects of Shape on Chemotaxis and Other Behaviors of Bacteria

Data on the shapes of 218 genera of free-floating or free-swimming bacteria reveal groupings around spherical shapes and around rod-like shapes of axial ratio about 3. Motile genera are less likely to be spherical and have larger axial ratios than nonmotile genera. The effects of shape on seven possible components of biological fitness were determined, and actual fitness landscapes in phenotype space are presented. Ellipsoidal shapes were used as models, since their hydrodynamic drag coefficients can be rigorously calculated in the world of low Reynolds number, where bacteria live. Comparing various shapes of the same volume, and assuming that departures from spherical have a cost that varies with the minimum radius of curvature, led to the following conclusions. Spherical shapes have the largest random dispersal by Brownian motion. Increased surface area occurs in oblate ellipsoids (disk-like), which rarely occur. Elongation into prolate ellipsoids (rod-like) reduces sinking speed, and this may explain why some nonmotile genera are rod-like. Elongation also favors swimming efficiency (to a limited extent) and the ability to detect stimulus gradients by any of three mechanisms. By far the largest effect (several hundred-fold) is on temporal detection of stimulus gradients, and this explains why rod-like shapes and this mechanism of chemotaxis are common.     

The Effect of Bacterial Recombination on Adaptation on Fitness Landscapes with Limited Peak Accessibility

There is ample empirical evidence revealing that fitness landscapes are often complex: the fitness effect of a newly arisen mutation can depend strongly on the allelic state at other loci. However, little is known about the effects of recombination on adaptation on such fitness landscapes. Here, we investigate how recombination influences the rate of adaptation on a special type of complex fitness landscapes. On these landscapes, the mutational trajectories from the least to the most fit genotype are interrupted by genotypes with low relative fitness. We study the dynamics of adapting populations on landscapes with different compositions and numbers of low fitness genotypes, with and without recombination. Our results of the deterministic model (assuming an infinite population size) show that recombination generally decelerates adaptation on these landscapes. However, in finite populations, this deceleration is outweighed by the accelerating Fisher-Muller effect under certain conditions. We conclude that recombination has complex effects on adaptation that are highly dependent on the particular fitness landscape, population size and recombination rate.     

Gene Fitness Landscapes of Vibrio cholerae at Important Stages of Its Life Cycle

Vibrio cholerae has evolved to adeptly transition between the human small intestine and aquatic environments, leading to water-borne spread and transmission of the lethal diarrheal disease cholera. Using a host model that mimics the pathology of human cholera, we applied high density transposon mutagenesis combined with massively parallel sequencing (Tn-seq) to determine the fitness contribution of >90% of all non-essential genes of V. cholerae both during host infection and dissemination. Targeted mutagenesis and validation of 35 genes confirmed our results for the selective conditions with a total false positive rate of 4%. We identified 165 genes never before implicated for roles in dissemination that reside within pathways controlling many metabolic, catabolic and protective processes, from which a central role for glycogen metabolism was revealed. We additionally identified 76 new pathogenicity factors and 414 putatively essential genes for V. cholerae growth. Our results provide a comprehensive framework for understanding the biology of V. cholerae as it colonizes the small intestine, elicits profuse secretory diarrhea, and disseminates into the aquatic environment.     

Tuberculosis: A Challenge to the General Practitioner

Of 157 patients dying of tuberculosis in Ontario (1960) 132 (87.4%) suffered from the pulmonary form of the disease (incidence 2.6 per 100,000). In the same year, 1632 of 1847, or 88.3%, active new cases reported had the pulmonary type and 183 additional cases were reported without details as to type of disease. Thus, in 1960, a total of 2030 new cases of tuberculosis were reported in Ontario.Of 1367 patients with pulmonary tuberculosis (reinfection type), 357 (26.1%) had “far advanced” disease and 613 (44.8%) had “moderately advanced” disease.This high percentage of patients with “moderately advanced” to “far advanced” disease at the time of diagnosis constitutes the real challenge to physicians in private practice, who made the diagnosis in 45% of cases.Emergence of resistant strains of bacteria increases the urgency of prompt diagnosis and treatment. The most vulnerable population segment is the 15-30 year age-group, many of whom are negative intracutaneous reactors. A high index of suspicion is necessary, particularly in certain segments of the population with a high incidence of infection, combined with a careful history, meticulous physical examination, intracutaneous tests, chest and other radiographs, and appropriate bacteriological studies.     

Memory and Fitness Optimization of Bacteria under Fluctuating Environments

Bacteria prudently regulate their metabolic phenotypes by sensing the availability of specific nutrients, expressing the required genes for their metabolism, and repressing them after specific metabolites are depleted. It is unclear, however, how genetic networks maintain and transmit phenotypic states between generations under rapidly fluctuating environments. By subjecting bacteria to fluctuating carbon sources (glucose and lactose) using microfluidics, we discover two types of non-genetic memory in Escherichia coli and analyze their benefits. First, phenotypic memory conferred by transmission of stable intracellular lac proteins dramatically reduces lag phases under cyclical fluctuations with intermediate timescales (1–10 generations). Second, response memory, a hysteretic behavior in which gene expression persists after removal of its external inducer, enhances adaptation when environments fluctuate over short timescales (<1 generation). Using a mathematical model we analyze the benefits of memory across environmental fluctuation timescales. We show that memory mechanisms provide an important class of survival strategies in biology that improve long-term fitness under fluctuating environments. These results can be used to understand how organisms adapt to fluctuating levels of nutrients, antibiotics, and other environmental stresses.     

A Mathematical Model of the Inflammatory Response to Pathogen Challenge

The human body’s immune response to bacterial challenge, even when successful in controlling the infection, can result in negative consequences for the host, including reduced functionality of associated tissues. We present and analyze a low-dimensional mathematical model of this immune response to pathogen invasion, incorporating the coordinated actions of active immune cells, and both pro- and anti-inflammatory cytokines. The model simulates both the positive (pathogen reduction) and negative (local tissue dysfunction) effects of the immune response and includes the important role of immunologic memory in the process of a return to stasis. This differential equation-based model is sufficiently general to be applicable to a wide range of human tissues and organs.     

A Dynamic Optimization Solution for Vertical Jumping in Three Dimensions

A three-dimensional model of the human body is used to simulate a maximal vertical jump. The body is modeled as a 10-segment, 23 degree-of-freedom (dof), mechanical linkage, actuated by 54 muscles. Six generalized coordinates describe the position and orientation of the pelvis relative to the ground; the remaining nine segments branch in an open chain from the pelvis. The head, arms, and torso (HAT) are modeled as a single rigid body. The HAT articulates with the pelvis via a 3 dof ball-and-socket joint. Each hip is modeled as a 3 dof ball-and-socket joint, and each knee is modeled as a 1 dof hinge joint. Each foot is represented by a hindfoot and toes segment. The hindfoot articulates with the shank via a 2 dof universal joint, and the toes articulate with the hindfoot via a 1 dof hinge joint. Interaction of the feet with the ground is modeled using a series of spring-damper units placed under the sole of each foot. The path of each muscle is represented by either a series of straight lines or a combination of straight lines and space curves. Each actuator is modeled as a three-element, Hill-type muscle in series with tendon. A first-order process is assumed to model muscle excitation-contraction dynamics. Dynamic optimization theory is used to calculate the pattern of muscle excitations that produces a maximal vertical jump. Quantitative comparisons between model and experiment indicate that the model reproduces the kinematic, kinetic, and muscle-coordination patterns evident when humans jump to their maximum achievable heights.     

A Comparison of Methods to Measure Fitness in Escherichia coli

In order to characterize the dynamics of adaptation, it is important to be able to quantify how a population’s mean fitness changes over time. Such measurements are especially important in experimental studies of evolution using microbes. The Long-Term Evolution Experiment (LTEE) with Escherichia coli provides one such system in which mean fitness has been measured by competing derived and ancestral populations. The traditional method used to measure fitness in the LTEE and many similar experiments, though, is subject to a potential limitation. As the relative fitness of the two competitors diverges, the measurement error increases because the less-fit population becomes increasingly small and cannot be enumerated as precisely. Here, we present and employ two alternatives to the traditional method. One is based on reducing the fitness differential between the competitors by using a common reference competitor from an intermediate generation that has intermediate fitness; the other alternative increases the initial population size of the less-fit, ancestral competitor. We performed a total of 480 competitions to compare the statistical properties of estimates obtained using these alternative methods with those obtained using the traditional method for samples taken over 50,000 generations from one of the LTEE populations. On balance, neither alternative method yielded measurements that were more precise than the traditional method.