Mathematics of neural stem cells: Linking data and processes.

Adult stem cells are described as a discrete population of cells that stand at the top of a hierarchy of progressively differentiating cells. Through their unique ability to self-renew and differentiate, they regulate the number of end-differentiated cells that contribute to tissue physiology. The question of how discrete, continuous, or reversible the transitions through these hierarchies are and the precise parameters that determine the ultimate performance of stem cells in adulthood are the subject of intense research. In this review, we explain how mathematical modelling has improved the mechanistic understanding of stem cell dynamics in the adult brain. We also discuss how single-cell sequencing has influenced the understanding of cell states or cell types. Finally, we discuss how the combination of single-cell sequencing technologies and mathematical modelling provides a unique opportunity to answer some burning questions in the field of stem cell biology.

Identifying stem cell numbers and functional heterogeneities during postembryonic organ growth.

Uncovering the number of stem cells necessary for organ growth has been challenging in vertebrate systems. Here, we developed a mathematical model characterizing stem cells in the fish gill, an organ displaying non-exhaustive growth. We employ a Markov model, stochastically simulated via an adapted Gillespie algorithm, and further improved through probability theory. The stochastic algorithm produces a simulated dataset for comparison with experimental clonal data by inspecting quantifiable properties. The analytical approach skips the step of artificial data generation and goes directly to the quantification, being more abstract and efficient. We report that a reduced number of stem cells actively contribute to growing and maintaining the gills. The model also highlights a functional heterogeneity among the stem cells involved, where activation and quiescence phases determine their relative growth contribution. Overall, our work presents a method for inferring the number and properties of stem cells required in a lifelong growing system.

Stem cell topography splits growth and homeostatic functions in the fish gill.

While lower vertebrates contain adult stem cells (aSCs) that maintain homeostasis and drive un-exhaustive organismal growth, mammalian aSCs display mainly the homeostatic function. Here, we use lineage analysis in the medaka fish gill to address aSCs and report separate stem cell populations for homeostasis and growth. These aSCs are fate-restricted during the entire post-embryonic life and even during re-generation paradigms. We use chimeric animals to demonstrate that p53 mediates growth coordination among fate-restricted aSCs, suggesting a hierarchical organisation among lineages in composite organs like the fish gill. Homeostatic and growth aSCs are clonal but differ in their topology; modifications in tissue architecture can convert the homeostatic zone into a growth zone, indicating a leading role for the physical niche defining stem cell output. We hypothesise that physical niches are main players to restrict aSCs to a homeostatic function in animals with fixed adult size.

MEIGO: an open-source software suite based on metaheuristics for global optimization in systems biology and bioinformatics.

BACKGROUND: Optimization is the key to solving many problems in computational biology. Global optimization methods, which provide a robust methodology, and metaheuristics in particular have proven to be the most efficient methods for many applications. Despite their utility, there is a limited availability of metaheuristic tools. RESULTS: We present MEIGO, an R and Matlab optimization toolbox (also available in Python via a wrapper of the R version), that implements metaheuristics capable of solving diverse problems arising in systems biology and bioinformatics. The toolbox includes the enhanced scatter search method (eSS) for continuous nonlinear programming (cNLP) and mixed-integer programming (MINLP) problems, and variable neighborhood search (VNS) for Integer Programming (IP) problems. Additionally, the R version includes BayesFit for parameter estimation by Bayesian inference. The eSS and VNS methods can be run on a single-thread or in parallel using a cooperative strategy. The code is supplied under GPLv3 and is available at http://www.iim.csic.es/~gingproc/meigo.html. Documentation and examples are included. The R package has been submitted to BioConductor. We evaluate MEIGO against optimization benchmarks, and illustrate its applicability to a series of case studies in bioinformatics and systems biology where it outperforms other state-of-the-art methods. CONCLUSIONS: MEIGO provides a free, open-source platform for optimization that can be applied to multiple domains of systems biology and bioinformatics. It includes efficient state of the art metaheuristics, and its open and modular structure allows the addition of further methods.