The impact of male-killing bacteria on host evolutionary processes

Male-killing bacteria are maternally inherited endosymbionts that selectively kill male offspring of their arthropod hosts. Using both analytical techniques and computer simulations, we studied the impact of these bacteria on the population genetics of their hosts. In particular, we derived and corroborated formulas for the fixation probability of mutant alleles, mean times to fixation and fixation or extinction, and heterozygosity for varying male-killer prevalence. Our results demonstrate that infections with male-killing bacteria impede the spread of beneficial alleles, facilitate the spread of deleterious alleles, and reduce genetic variation. The reason for this lies in the strongly reduced fitness of infected females combined with no or very limited gene flow from infected females to uninfected individuals. These two properties of male-killer-infected populations reduce the population size relevant for the initial emergence and spread of mutations. In contrast, use of Wright's equation relating sex ratio to effective population size produces misleading predictions. We discuss the relationship to the similar effect of background selection, the impact of other sex-ratio-distorting endosymbionts, and how our results affect the interpretation of empirical data on genetic variation in male-killer-infected populations.     

Lattice and non-lattice models of tumour angiogenesis

In order to progress from the relatively harmless avascular state to the potentially lethal vascular state, solid tumours must induce the growth of new blood vessels from existing ones, a process called angiogenesis. The capillary growth centres around endothelial cells: there are several cell-based models of this process in the literature and these have reproduced some of the key microscopic features of capillary growth. The most common approach is to simulate the movement of leading endothelial cells on a regular lattice. Here, we apply a circular random walk model to the process of angiogenesis, and thus allow the cells to move independently of a lattice; the results display good agreement with empirical observations. We also run simulations of two lattice-based models in order to make a critical comparison of the different modelling approaches. Finally, non-lattice simulations are carried out in the context of a realistic model of tumour angiogenesis, and potential anti-angiogenic strategies are evaluated.     

The impact of autophagic processes on the intracellular fate of Helicobacter pylori

Helicobacter pylori is a Gram-negative pathogen that colonizes the gastric epithelium of 50–60% of the world’s population. Approximately one-fifth of the infected individuals manifest severe diseases such as peptic ulcers or gastric cancer. H. pylori infection has proven difficult to cure despite intensive antibiotic treatment. One possible reason for the relatively high resistance to antimicrobial therapy is the ability of H. pylori to reside inside host cells. Although considered by most as an extracellular pathogen, H. pylori can invade both gastric epithelial cells and immunocytes to some extent. The intracellular survival of H. pylori has been implicated in its ability to persist in the stomach, evade host immune responses and resist eradication by membrane-impermeable antibiotics. Interestingly, recent evidence suggests that macroautophagy, a cellular self-degradation process characterized by the formation of double-membraned autophagosomes, plays an important role in determining the intracellular fate of H. pylori. Detailed understanding of the interaction between H. pylori and host cell autophagic processes is anticipated to provide novel insights into the molecular mechanisms of macroautophagy and H. pylori pathogenesis, opening new avenues for the therapeutic intervention of autophagy-related and H. pylori-related disorders.     

The impact of adhesion on cellular invasion processes in cancer and development

In this paper we consider a simple continuous model to describe cell invasion, incorporating the effects of both cell-cell adhesion and cell-matrix adhesion, along with cell growth and proteolysis by cells of the surrounding extracellular matrix (ECM). We demonstrate that the model is capable of supporting both noninvasive and invasive tumour growth according to the relative strength of cell-cell to cell-matrix adhesion. Specifically, for sufficiently strong cell-matrix adhesion and/or sufficiently weak cell-cell adhesion, degradation of the surrounding ECM accompanied by cell-matrix adhesion pulls the cells into the surrounding ECM. We investigate the criticality of matrix heterogeneity on shaping invasion, demonstrating that a highly heterogeneous ECM can result in a “fingering” of the invasive front, echoing observations in real-life invasion processes ranging from malignant tumour growth to neural crest migration during embryonic development.     

Mathematical modelling of angiogenesis using continuous cell-based models

In this work, we develop a mathematical formalism based on a 3D in vitro model that is used to simulate the early stages of angiogenesis. The model treats cells as individual entities that are migrating as a result of chemotaxis and durotaxis. The phenotypes used here are endothelial cells that can be distinguished into stalk and tip (leading) cells. The model takes into account the dynamic interaction and interchange between both phenotypes. Next to the cells, the model takes into account several proteins such as vascular endothelial growth factor, delta-like ligand 4, urokinase plasminogen activator and matrix metalloproteinase, which are computed through the solution of a system of reaction–diffusion equations. The method used in the present study is classified into the hybrid approaches. The present study, implemented in three spatial dimensions, demonstrates the feasibility of the approach that is qualitatively confirmed by experimental results.     

Continuous and discrete mathematical models of tumor-induced angiogenesis

Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial-cell migration, and organize themselves into a dendritic structure. Subsequent cell proliferation near the sprout tip permits further extension of the capillary and ultimately completes the process. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumors. In this paper we present both continuous and discrete mathematical models which describe the formation of the capillary sprout network in response to chemical stimuli (tumor angiogenic factors, TAF) supplied by a solid tumor. The models also take into account essential endothelial cell-extracellular matrix interactions via the inclusion of the matrix macromolecule fibronectin. The continuous model consists of a system of nonlinear partial differential equations describing the initial migratory response of endothelial cells to the TAF and the fibronectin. Numerical simulations of the system, using parameter values based on experimental data, are presented and compared qualitatively with in vivo experiments. We then use a discretized form of the partial differential equations to develop a biased random-walk model which enables us to track individual endothelial cells at the sprout tips and incorporate anastomosis, mitosis and branching explicitly into the model. The theoretical capillary networks generated by computer simulations of the discrete model are compared with the morphology of capillary networks observed in in vivo experiments.     

Hydrodynamical impact on biogeochemical processes in aquatic sediments

Boundary layer flow characteristics and sediment permeability control pathways and magnitude of material exchange in the surface layer of aquatic sediments. In fine-grained cohesive beds, bottom currents and sediment microtopography shape the diffusive boundary layer and locally produce areas where the interfacial solute fluxes are increased or reduced. Where sediment permeabilities exceed 10^–12 m², advective pore water flows driven by boundary flow–topography interaction dominate the sediment–water exchange of matter, with transport rates that exceed those of molecular diffusion by two orders of magnitude and more. The curved paths of the advective pore flows through the surface layers of such sandy beds generate complex three-dimensional biogeochemical patterns with extreme spatial and temporal variability ranging from millimeters to decimeters and seconds to seasons. High filtration rates, a bacterial community firmly attached to the mineral grains, rapidly changing biogeochemical zonations and winnowing of the sediment surface layers by frequent resuspension convert these beds into effective biocatalytical filter systems.     

Animal models and conserved processes

Background

The concept of conserved processes presents unique opportunities for using nonhuman animal models in biomedical research. However, the concept must be examined in the context that humans and nonhuman animals are evolved, complex, adaptive systems. Given that nonhuman animals are examples of living systems that are differently complex from humans, what does the existence of a conserved gene or process imply for inter-species extrapolation?

Methods

We surveyed the literature including philosophy of science, biological complexity, conserved processes, evolutionary biology, comparative medicine, anti-neoplastic agents, inhalational anesthetics, and drug development journals in order to determine the value of nonhuman animal models when studying conserved processes.

Results

Evolution through natural selection has employed components and processes both to produce the same outcomes among species but also to generate different functions and traits. Many genes and processes are conserved, but new combinations of these processes or different regulation of the genes involved in these processes have resulted in unique organisms. Further, there is a hierarchy of organization in complex living systems. At some levels, the components are simple systems that can be analyzed by mathematics or the physical sciences, while at other levels the system cannot be fully analyzed by reducing it to a physical system. The study of complex living systems must alternate between focusing on the parts and examining the intact whole organism while taking into account the connections between the two. Systems biology aims for this holism. We examined the actions of inhalational anesthetic agents and anti-neoplastic agents in order to address what the characteristics of complex living systems imply for inter-species extrapolation of traits and responses related to conserved processes.

Conclusion

We conclude that even the presence of conserved processes is insufficient for inter-species extrapolation when the trait or response being studied is located at higher levels of organization, is in a different module, or is influenced by other modules. However, when the examination of the conserved process occurs at the same level of organization or in the same module, and hence is subject to study solely by reductionism, then extrapolation is possible.     

Stochastic models for aggregation processes

Three models are presented, which describe the aggregation of objects into groups and the distributions of groups sizes and group numbers within habitats. The processes regarded are pure accumulation processes which involve only formation and invasion of groups. Invasion represents the special case of fusion when only single objects - and not groups - join a group of certain size. The basic model is derived by a single parameter, the formation probability q, which represents the probability of an object to form a new group. A novel, discrete and finite distribution that results for the group sizes is deduced from this aggregation process and it is shown that it converges to a geometric distribution if the number of objects tends to infinity. Two extensions of this model, which both converge to the Waring distribution, are added: the model can be extended either with a beta distributed formation probability or with the assumption that the invasion probability depends on the group size. Relationships between the limiting distributions involved are discussed.     

Solvable models of neighbor-dependent substitution processes

We prove that a wide class of Markov models of neighbor-dependent substitution processes on the integer line is solvable. This class contains some models of nucleotidic substitutions recently introduced and studied empirically by molecular biologists. We show that the polynucleotidic frequencies at equilibrium solve some finite-size linear systems. This provides, for the first time up to our knowledge, explicit and algebraic formulas for the stationary frequencies of non-degenerate neighbor-dependent models of DNA substitutions. Furthermore, we show that the dynamics of these stochastic processes and their distribution at equilibrium exhibit some stringent, rather unexpected, independence properties. For example, nucleotidic sites at distance at least three evolve independently, and all the sites, when encoded as purines and pyrimidines, evolve independently.     

LFT models of continuous biotechnological processes

The aim of the paper is to obtain suitable state-space models of continuous biotechnological processes (CBTP) in the framework of Linear Fractional Transformation (LFT). The LFT models are starting point in most of the advanced robust control design and analysis methods. Therefore, a linearized process model in the state-space is used whose elements are supposed to vary within certain bounds to represent the nonlinear behaviour of the real plant. The performance specifications are defined in the frequency domain through weighting functions. Two LFT models of CBTP are obtained ready for controller design aimed to optimize robust stability margins and robust performance, respectively.     

Lateral inhibition models of developmental processes

Most mathematical models for embryological pattern formation depend on the phenomenon of local autocatalysis with lateral inhibition (LALI). While the underlying physical and chemical mechanisms hypothesized by the models may be quite different, they all predict very similar kinds of spatial patterns. Therefore, since the underlying mechanism cannot in general be deduced from the pattern itself, other criteria must be applied in evaluating the usefulness of pattern formation models. The author points out how LALI is implemented in neural, chemical, and mechanical models of development, and suggests some general properties of LALI models that may impose limitations on organ shapes in ontogeny and phylogeny.     

The impact of internodal segmentation in biophysical nerve fiber models

Implementation of double cable models to simulate the behavior of myelinated peripheral nerve fibers requires defining a segmentation of the internode between successive nodes of Ranvier. The number of internodal segments is a model parameter that is not well agreed on, with values in the literature ranging from 1 to more than 500. Moreover, a lot of studies also lack a sensitivity study or a rationale behind the implementation used. In a model of a myelinated nerve fiber developed in our group, the segmentation scheme (i.e., the number of segments and their individual morphology) strongly influenced model outcomes such as action potential shape and velocity, stimulation threshold and absolute refractory period. In the present study these influences were investigated systematically in homogeneous neurons with different diameters. Uniformly segmented internodes were found to require several hundreds of segments (and associated computational power) to reach model outcomes differing by less than 1 % from the asymptotic value. In fact, in the majority of segmentation schemes the main determinant is not the number of segments, but the length λ of the internodal segments directly adjacent to the nodes of Ranvier. If λ is larger than approximately 10 μm, model outcomes for the tested fibers are almost independent of the total number of segments. Furthermore, λ can be optimized to enable models using just three segments per internode, to reach physiologically relevant model outcomes with limited computational resources. However, to study anatomical or physiological details of the internode itself, an appropriately detailed segmentation scheme is crucial.     

Competitive exclusion and persistence in models of resource and sexual competition

 We study a combined mathematical model of resource and sexual competition. The population dynamics in this model is analyzed through a coupled system of reaction-diffusion equations. It is shown that strong sexual competition and low birth rate lead to competitive exclusion of the biological species. If sexual competition is weak, then the persistence of the species is possible, depending on the initial density functions and the growth rates of the species. When sexual competition affects both species, persistence and competitive exclusion results are also obtained in terms of the ecological data in the model. Received 1 November 1995; received in revised form 13 January 1996