The cellular basis of cell sorting kinetics.

Cell sorting is a dynamical cooperative phenomenon that is fundamental for tissue morphogenesis and tissue homeostasis. According to Steinberg's differential adhesion hypothesis, the structure of sorted cell aggregates is determined by physical characteristics of the respective tissues, the tissue surface tensions. Steinberg postulated that tissue surface tensions result from quantitative differences in intercellular adhesion. Several experiments in cell cultures as well as in developing organisms support this hypothesis. The question of how tissue surface tension might result from differential adhesion was addressed in some theoretical models. These models describe the cellular interdependence structure once the temporal evolution has stabilized. In general, these models are capable of reproducing sorted patterns. However, the model dynamics at the cellular scale are defined implicitly and are not well-justified. The precise mechanism describing how differential adhesion generates the observed sorting kinetics at the tissue level is still unclear. It is necessary to formulate the concepts of cell level kinetics explicitly. Only then it is possible to understand the temporal development at the cellular and tissue scales. Here we argue that individual cell mobility is reduced the more the cells stick to their neighbors. We translate this assumption into a precise mathematical model which belongs to the class of stochastic interacting particle systems. Analyzing this model, we are able to predict the emergent sorting behavior at the population level. We describe qualitatively the geometry of cell segregation depending on the intercellular adhesion parameters. Furthermore, we derive a functional relationship between intercellular adhesion and surface tension and highlight the role of cell mobility in the process of sorting. We show that the interaction between the cells and the boundary of a confining vessel has a major impact on the sorting geometry.

The epidemiological consequences of leprosy-tuberculosis co-infection.

While in antiquity both leprosy and tuberculosis were prevalent in Europe, leprosy declined thereafter and, simultaneously, tuberculosis prevalence increased. Since both diseases are caused by mycobacterial infections, it has been suggested that there might be a causal relationship between both epidemics. Chaussinand observed the inverse prevalence of leprosy and tuberculosis and suggested that individuals with a latent tuberculosis infection are protected from acquiring leprosy. His cross-immunity hypothesis has been countered more recently by a co-infection hypothesis. The latter suggestion, proposed by Donoghue, states that people being infected with multi-bacillary leprosy are more susceptible to tuberculosis, which leads to increased mortality from the disease. This study utilizes mathematical modeling to explore the epidemiological consequences of the co-infection hypothesis for realistically confined parameter values. While the co-infection hypothesis appears plausible at first glance, a second thought reveals that it comprises also substantial consequences for tuberculosis epidemics: if co-infection raises the mortality rate above that of purely tuberculosis infected persons, then tuberculosis might as well be eradicated by leprosy. It is the specific interplay of both increased susceptibility towards tuberculosis and increased death rate when co-infected that determines the epidemiological fate. As a result of this analysis, it is shown that there is a large parameter region where the eventual disappearance of leprosy could indeed be explained by co-infection. This parameter region is considerably larger than that predicted by the cross-immunity hypothesis. This shows that the co-infection hypothesis should be considered a significant alternative to the cross-immunity hypothesis. The time scales at which the effects of co-infection are observed depend critically on the spatial distribution of the individuals but reach epidemiologically realistic values for rather immobile individuals with local interaction.