The effect of correlations on the population dynamics of lymphocytes

Recent studies of the population dynamics of a system of lymphocytes in an in vitro immune response have reported strong correlations in cell division times, both between parents and their progeny, and between those of sibling cells. The data also show a high level of correlation in the ultimate number of divisions achieved by cells within the same clone. Such correlations are often ignored in mathematical models of cell dynamics as they violate a standard assumption in the theory of branching processes, that of the statistical independence of cells. In this article we present a model in which these correlations can be incorporated, and have used this model to study the effect of these correlations on the population dynamics of a system of cells. We found that correlation in the division times between parents and their progeny can alter the mean population size of clones within the system, while all of the correlations can affect the variance in the sizes of different clones. The model was then applied to experimental data obtained from time-lapse video microscopy of a system of CpG stimulated B lymphocytes and it was found that inclusion of the correct correlation structure is necessary to accurately reproduce the observed population dynamics. We conclude that correlations in the dynamics of cells within an ensemble will affect the population dynamics of the system, and the effects will become more pronounced as the number of divisions increases.     

The evolution of tumor metastases during clonal expansion

Cancer is a leading cause of morbidity and mortality in many countries. Solid tumors generally initiate at one particular site called the primary tumor, but eventually disseminate and form new colonies in other organs. The development of such metastases greatly diminishes the potential for a cure of patients and is thought to represent the final stage of the multi-stage progression of human cancer. The concept of early metastatic dissemination, however, postulates that cancer cell spread might arise early during the development of a tumor. It is important to know whether metastases are present at diagnosis since this determines treatment strategies and outcome. In this paper, we design a stochastic mathematical model of the evolution of tumor metastases in an expanding cancer cell population. We calculate the probability of metastasis at a given time during tumor evolution, the expected number of metastatic sites, and the total number of cancer cells as well as metastasized cells. Furthermore, we investigate the effect of drug administration and tumor resection on these quantities and predict the survival time of cancer patients. The model presented in this paper allows us to determine the probability and number of metastases at diagnosis and to identify the optimum treatment strategy to maximally prolong survival of cancer patients.     

Growth promotion of Suillus luteus by adenosine in vitro

In this work, adenosine has been shown to stimulate Suillus luteus mycelial growth, branching, and aggregates on solid substrate. Adenosine promoted S. luteus mycelial growth and branching, and the fungus responded significantly at a concentration as low as 0.01 mg/ml. The highest mycelial biomass and density of three strains were observed at 0.16 mg/ml in SNP-20, 0.08 mg/ml in SAF-501, and 0.16 mg/ml in PT-501. Adenosine enhanced mycelial aggregate at concentration of 0.02 mg/ml in SNP-20. The study suggests that adenosine promotes S. luteus mycelial growth, branching, and aggregation. Thus, it may be a good candidate as a biological elicitor of mycelial growth for S. luteus.     

Markov invariants, plethysms, and phylogenetics

We explore model-based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we establish a commonality in some special cases. We show that the simplest Markov invariant forms the foundation of the Log–Det distance measure. We take as our primary tool group representation theory, and show that it provides a general framework for analyzing Markov processes on trees. From this algebraic perspective, the inherent symmetries of these processes become apparent, and focusing on plethysms, we are able to define Markov invariants and give existence proofs. We give an explicit technique for constructing the invariants, valid for any number of character states and taxa. For phylogenetic trees with three and four leaves, we demonstrate that the corresponding Markov invariants can be fruitfully exploited in applied phylogenetic studies.     

The effect of superspreading on epidemic outbreak size distributions

Recently, evidence has been presented to suggest that there are significant heterogeneities in the transmission of communicable diseases. Here, a stochastic simulation model of an epidemic process that allows for these heterogeneities is used to demonstrate the potentially considerable effect that heterogeneity of transmission will have on epidemic outbreak size distributions. Our simulation results agree well with approximations gained from the theory of branching processes. Outbreak size distributions have previously been used to infer basic epidemiological parameters. We show that if superspreading does occur then such distributions must be interpreted with care. The simulation results are discussed in relation to measles epidemics in isolated populations and in predominantly urban scenarios. The effect of three different disease control policies on outbreak size distributions are shown for varying levels of heterogeneity and disease control effort.     

Estimating the variation in S phase duration from flow cytometric histograms

A stochastic model for interpreting BrdUrd DNA FCM-derived data is proposed. The model is based on branching processes and describes the progression of the DNA distribution of BrdUrd-labelled cells through the cell cycle. With the main focus on estimating the S phase duration and its variation, the DNA replication rate is modelled by a piecewise linear function, while assuming a gamma distribution for the S phase duration. Estimation of model parameters was carried out using maximum likelihood for data from two different cell lines. The results provided quite a good fit to the data, suggesting that stochastic models may be a valuable tool for analysing this kind of data.     

Heparin binding VEGF isoforms attenuate hyperoxic embryonic lung growth retardation via a FLK1-neuropilin-1-PKC dependent pathway

Background

Previous work in our laboratory demonstrated that hyperoxia suppressed the expression of vascular endothelial growth factor (VEGF) by the embryonic lung, leading to increased epithelial cell apoptosis and failure of explant airway growth and branching that was rescued by the addition of Vegf165. The aims of this study were to determine protective pathways by which VEGF isoforms attenuate hyperoxic lung growth retardation and to identify the target cell for VEGF action.

Methods

Timed pregnant CD-1 or fetal liver kinase (FLK1)-eGFP lung explants cultured in 3% or 50% oxygen were treated ± Vegf121, VEGF164/Vegf165 or VEGF188 in the presence or absence of anti-rat neuropilin-1 (NRP1) antibody or GO6983 (protein kinase C (PKC) pan-inhibitor) and lung growth and branching quantified. Immunofluorescence studies were performed to determine apoptosis index and location of FLK1 phosphorylation and western blot studies of lung explants were performed to define the signaling pathways that mediate the protective effects of VEGF.

Results

Heparin-binding VEGF isoforms (VEGF164/Vegf165 and VEGF188) but not Vegf121 selectively reduced epithelial apoptosis and partially rescued lung bud branching and growth. These protective effects required NRP1-dependent FLK1 activation in endothelial cells. Analysis of downstream signaling pathways demonstrated that the VEGF-mediated anti-apoptotic effects were dependent on PKC activation.

Conclusions

Vegf165 activates FLK1-NRP1 signaling in endothelial cells, leading to a PKC-dependent paracrine signal that in turn inhibits epithelial cell apoptosis.     

Polyp oriented modelling of coral growth

The morphogenesis of colonial stony corals is the result of the collective behaviour of many coral polyps depositing coral skeleton on top of the old skeleton on which they live. Yet, models of coral growth often consider the polyps as a single continuous surface. In the present work, the polyps are modelled individually. Each polyp takes up resources, deposits skeleton, buds off new polyps and dies. In this polyp oriented model, spontaneous branching occurs. We argue that branching is caused by a so called “polyp fanning effect” by which polyps on a convex surface have a competitive advantage relative to polyps on a flat or concave surface. The fanning effect generates a more potent branching mechanism than the Laplacian growth mechanism that we have studied previously (J. Theor. Biol. 224 (2003) 153). We discuss the application of the polyp oriented model to the study of environmentally driven morphological plasticity in stony corals. In a few examples we show how the properties of the individual polyps influence the whole colony morphology. In our model, the spacing of polyps influences the thickness of coral branches and the overall compactness of the colony. Density variations in the coral skeleton may also be important for the whole colony morphology, which we address by studying two variants of the model. Finally, we discuss the importance of small scale resource translocation in the coral colony and its effects on the morphology of the colony.