Modeling the clonal heterogeneity of stem cells

Recent experimental studies suggest that tissue stem cell pools are composed of functionally diverse clones. Metapopulation models in ecology concentrate on collections of populations and their role in stabilizing coexistence and maintaining selected genetic or epigenetic variation. Such models are characterized by expansion and extinction of spatially distributed populations. We develop a mathematical framework derived from the multispecies metapopulation model of Tilman et al (1994) to study the dynamics of heterogeneous stem cell metapopulations. In addition to normal stem cells, the model can be applied to cancer cell populations and their response to treatment. In our model disturbances may lead to expansion or contraction of cells with distinct properties, reflecting proliferation, apoptosis, and clonal competition. We first present closed-form expressions for the basic model which defines clonal dynamics in the presence of exogenous global disturbances. We then extend the model to include disturbances which are periodic and which may affect clones differently. Within the model framework, we propose a method to devise an optimal strategy of treatments to regulate expansion, contraction, or mutual maintenance of cells with specific properties

Interactions between growth-dependent changes in cell size, nutrient supply and cellular elemental stoichiometry of marine Synechococcus

The factors that control elemental ratios within phytoplankton, like carbon:nitrogen:phosphorus (C:N:P), are key to biogeochemical cycles. Previous studies have identified relationships between nutrient-limited growth and elemental ratios in large eukaryotes, but little is known about these interactions in small marine phytoplankton like the globally important Cyanobacteria. To improve our understanding of these interactions in picophytoplankton, we asked how cellular elemental stoichiometry varies as a function of steady-state, N- and P-limited growth in laboratory chemostat cultures of Synechococcus WH8102. By combining empirical data and theoretical modeling, we identified a previously unrecognized factor (growth-dependent variability in cell size) that controls the relationship between nutrient-limited growth and cellular elemental stoichiometry. To predict the cellular elemental stoichiometry of phytoplankton, previous theoretical models rely on the traditional Droop model, which purports that the acquisition of a single limiting nutrient suffices to explain the relationship between a cellular nutrient quota and growth rate. Our study, however, indicates that growth-dependent changes in cell size have an important role in regulating cell nutrient quotas. This key ingredient, along with nutrient-uptake protein regulation, enables our model to predict the cellular elemental stoichiometry of Synechococcus across a range of nutrient-limited conditions. Our analysis also adds to the growth rate hypothesis, suggesting that P-rich biomolecules other than nucleic acids are important drivers of stoichiometric variability in Synechococcus. Lastly, by comparing our data with field observations, our study has important ecological relevance as it provides a framework for understanding and predicting elemental ratios in ocean regions where small phytoplankton like Synechococcus dominates

Vectorial dissipative solitons in vertical-cavity surface-emitting Lasers with delays

We show that the nonlinear polarization dynamics of a vertical-cavity surface-emitting laser placed into an external cavity leads to the formation of temporal vectorial dissipative solitons. These solitons arise as cycles in the polarization orientation, leaving the total intensity constant. When the cavity round-trip is much longer than their duration, several independent solitons as well as bound states (molecules) may be hosted in the cavity. All these solutions coexist together and with the background solution, i.e. the solution with zero soliton. The theoretical proof of localization is given by the analysis of the Floquet exponents. Finally, we reduce the dynamics to a single delayed equation for the polarization orientation allowing interpreting the vectorial solitons as polarization kinks.Comment: quasi final resubmission version, 12 pages, 9 figure

Extinction Debt in Source-Sink Metacommunities

In an increasingly modified world, understanding and predicting the consequences of landscape alteration on biodiversity is a challenge for ecologists. To this end, metacommunity theory has developed to better understand the complexity of local and regional interactions that occur across larger landscapes. While metacommunity ecology has now provided several alternative models of species coexistence at different spatial scales, predictions regarding the consequences of landscape alteration have been done exclusively for the competition-colonization trade off model (CC). In this paper we investigate the effects of landscape perturbation on source-sink metacommunities. We show that habitat destruction perturbs the equilibria among species competitive effects within the metacommunity, driving both direct extinctions and an indirect extinction debt. As in CC models, we found a time lag for extinction following habitat destruction that varied in length depending upon the relative importance of direct and indirect effects. However, in contrast to CC models, we found that the less competitive species are more affected by habitat destruction. The best competitors can sometimes even be positively affected by habitat destruction, which corresponds well with the results of field studies. Our results are complementary to those results found in CC models of metacommunity dynamics. From a conservation perspective, our results illustrate that landscape alteration jeopardizes species coexistence in patchy landscapes through complex indirect effects and delayed extinctions patterns

Multifractal Spatial Patterns and Diversity in an Ecological Succession

We analyzed the relationship between biodiversity and spatial biomass heterogeneity along an ecological succession developed in the laboratory. Periphyton (attached microalgae) biomass spatial patterns at several successional stages were obtained using digital image analysis and at the same time we estimated the species composition and abundance. We show that the spatial pattern was self-similar and as the community developed in an homogeneous environment the pattern is self-organized. To characterize it we estimated the multifractal spectrum of generalized dimensions Dq. Using Dq we analyze the existence of cycles of heterogeneity during succession and the use of the information dimension D1 as an index of successional stage. We did not find cycles but the values of D1 showed an increasing trend as the succession developed and the biomass was higher. D1 was also negatively correlated with Shannon's diversity. Several studies have found this relationship in different ecosystems but here we prove that the community self-organizes and generates its own spatial heterogeneity influencing diversity. If this is confirmed with more experimental and theoretical evidence D1 could be used as an index, easily calculated from remote sensing data, to detect high or low diversity areas

Processes and patterns of oceanic nutrient limitation

Microbial activity is a fundamental component of oceanic nutrient cycles. Photosynthetic microbes, collectively termed phytoplankton, are responsible for the vast majority of primary production in marine waters. The availability of nutrients in the upper ocean frequently limits the activity and abundance of these organisms. Experimental data have revealed two broad regimes of phytoplankton nutrient limitation in the modern upper ocean. Nitrogen availability tends to limit productivity throughout much of the surface low-latitude ocean, where the supply of nutrients from the subsurface is relatively slow. In contrast, iron often limits productivity where subsurface nutrient supply is enhanced, including within the main oceanic upwelling regions of the Southern Ocean and the eastern equatorial Pacific. Phosphorus, vitamins and micronutrients other than iron may also (co-)limit marine phytoplankton. The spatial patterns and importance of co-limitation, however, remain unclear. Variability in the stoichiometries of nutrient supply and biological demand are key determinants of oceanic nutrient limitation. Deciphering the mechanisms that underpin this variability, and the consequences for marine microbes, will be a challenge. But such knowledge will be crucial for accurately predicting the consequences of ongoing anthropogenic perturbations to oceanic nutrient biogeochemistry. © 2013 Macmillan Publishers Limited. All rights reserved