A mathematical model for antibiotic control of bacteria in peritoneal dialysis associated peritonitis.

A study of the process of pharmacokinetics-pharmacodynamics (PKPD) of antibiotics and their interaction with bacteria during peritoneal dialysis associated peritonitis (PDAP) is presented. We propose a mathematical model describing the evolution of bacteria population in the presence of antibiotics for different peritoneal dialysis regimens. Using the model along with experimental data, clinical parameters, and physiological values, we compute variations in PD fluid distributions, drug concentrations, and number of bacteria in peritoneal and extra-peritoneal cavities. Scheduling algorithms for the PD exchanges that minimize bacteria count are investigated.

Surface tension and modeling of cellular intercalation during zebrafish gastrulation.

In this paper we discuss a model of zebrafish embryo notochord development based on the effect of surface tension of cells at the boundaries. We study the process of interaction of mesodermal cells at the boundaries due to adhesion and cortical tension, resulting in cellular intercalation. From in vivo experiments, we obtain cell outlines of time-lapse images of cell movements during zebrafish embryo development. Using Cellular Potts Model, we calculate the total surface energy of the system of cells at different time intervals at cell contacts. We analyze the variations of total energy depending on nature of cell contacts. We demonstrate that our model can be viable by calculating the total surface energy value for experimentally observed configurations of cells and showing that in our model these configurations correspond to a decrease in total energy values in both two and three dimensions.

Initiation of convergence and extension movements of lateral mesoderm during zebrafish gastrulation.

Embryonic morphogenesis is accomplished by cellular movements, rearrangements, and cell fate inductions. Vertebrate gastrulation entails morphogenetic processes that generate three germ layers, endoderm, mesoderm, and ectoderm, shaped into head, trunk, and tail. To understand how cell migration mechanistically contributes to tissue shaping during gastrulation, we examined migration of lateral mesoderm in the zebrafish. Our results illustrate that cell behaviors, different from mediolaterally oriented cell intercalation, also promote convergence and extension (C&E). During early gastrulation, upon internalization, individually migrating mesendodermal cells contribute to the elongation of the mesoderm by moving animally, without dorsal movement. Convergence toward dorsal starts later, by 70% epiboly (7.7 hpf). Depending on location along the Animal-Vegetal axis, an animal or vegetal bias is added to the dorsalward movement, so that paths fan out and the lateral mesoderm both converges and extends. Onset of convergence is independent of noncanonical Wnt signaling but is delayed when Stat3 signaling is compromised. To understand which aspects of motility are controlled by guidance cues, we measured turning behavior of lateral mesodermal cells. We show that cells exhibit directional preference, directionally-regulated speed, and turn toward dorsal when off-course. We estimate that ectoderm could supply from a fraction to all the dorsalward displacement seen in mesoderm cells. Using mathematical modeling, we demonstrate that directional preference is sufficient to account for mesoderm convergence and extension, and that, at minimum, two sources of guidance cues could orient cell paths realistically if located in the dorsal midline.