Accelerated cell divisions drive the outgrowth of the regenerating spinal cord in axolotls

Axolotls are unique in their ability to regenerate the spinal cord. However, the mechanisms that underlie this phenomenon remain poorly understood. Previously, we showed that regenerating stem cells in the axolotl spinal cord revert to a molecular state resembling embryonic neuroepithelial cells and functionally acquire rapid proliferative divisions (Rodrigo Albors et al., 2015). Here, we refine the analysis of cell proliferation in space and time and identify a high- proliferation zone in the regenerating spinal cord that shifts posteriorly over time. By tracking sparsely-labeled cells, we also quantify cell influx into the regenerate. Taking a mathematical modeling approach, we integrate these quantitative datasets of cell proliferation, neural stem cell activation and cell influx, to predict regenerative tissue outgrowth. Our model shows that while cell influx and neural stem cell activation play a minor role, the acceleration of the cell cycle is the major driver of regenerative spinal cord outgrowth in axolotls.Facultad de Ciencias ExactasInstituto de Física de Líquidos y Sistemas Biológico

Dynamics of competing heterogeneous clones in blood cancers explains multiple observations - a mathematical modeling approach

Heterogeneity of stem cell clones provide a key ingredient in altered hematopoiesis and is of main interest in the study of predisease states as well as in the development of blood cancers such as chronic myeloid leukemia (CML) and the Philadelphia-negative myeloprofilerative neoplasms (MPNs). A mathematical model based on biological mechanisms and basic cell descriptors such as proliferation rates and apoptosis rates is suggested, connecting stem cell dynamics with mature blood cells and immune mediated feedback. The flexible approach allows for arbitrary numbers of mutated stem cell clones with perturbed properties. In particular, the stem cell niche provides a competition between wild type and mutated stem cells. Hence, the stem cell niche can mediate suppression of the wild type clones and up-regulation of one or more malignant clones. The model is parameterized using clinical data to show typical disease progression in several blood cancers and the hematological and molecular response to treatment. Intriguingly, occasional oscillatory cell counts observed during treatment of CML and MPNs can be explained by heterogeneous stem cell clone dynamics. Thus, the vital heterogeneous stem cell dynamics may be inferred from mathematical modeling in synergy with clinical data to elucidate hematopoiesis, blood cancers and the outcome of interventions

Modeling Reveals the Dependence of Hippocampal Neurogenesis Radiosensitivity on Age and Strain of Rats

Cognitive dysfunction following radiation treatment for brain cancers in both children and adults have been correlated to impairment of neurogenesis in the hippocampal dentate gyrus. Various species and strains of rodent models have been used to study radiation-induced changes in neurogenesis and these investigations have utilized only a limited number of doses, dose-fractions, age and time after exposures conditions. In this paper, we have extended our previous mathematical model of radiation-induced hippocampal neurogenesis impairment of C57BL/6 mice to delineate the time, age, and dose dependent alterations in neurogenesis of a diverse strain of rats. To the best of our knowledge, this is the first predictive mathematical model to be published about hippocampal neurogenesis impairment for a variety of rat strains after acute or fractionated exposures to low linear energy transfer (low LET) radiation, such as X-rays and γ-rays, which are conventionally used in cancer radiation therapy. We considered four compartments to model hippocampal neurogenesis and its impairment following radiation exposures. Compartments include: (1) neural stem cells (NSCs), (2) neuronal progenitor cells or neuroblasts (NB), (3) immature neurons (ImN), and (4) glioblasts (GB). Additional consideration of dose and time after irradiation dependence of microglial activation and a possible shift of NSC proliferation from neurogenesis to gliogenesis at higher doses is established. Using a system of non-linear ordinary differential equations (ODEs), characterization of rat strain and age-related dynamics of hippocampal neurogenesis for unirradiated and irradiated conditions is developed. The model is augmented with the description of feedback regulation on early and late neuronal proliferation following radiation exposure. Predictions for dose-fraction regimes compared to acute radiation exposures, along with the dependence of neurogenesis sensitivity to radiation on age and strain of rats are discussed. A major result of this work is predictions of the rat strain and age dependent differences in radiation sensitivity and sub-lethal damage repair that can be used for predictions for arbitrary dose and dose-fractionation schedules

Effect of Dedifferentiation on Time to Mutation Acquisition in Stem Cell-Driven Cancers

Accumulating evidence suggests that many tumors have a hierarchical organization, with the bulk of the tumor composed of relatively differentiated short-lived progenitor cells that are maintained by a small population of undifferentiated long-lived cancer stem cells. It is unclear, however, whether cancer stem cells originate from normal stem cells or from dedifferentiated progenitor cells. To address this, we mathematically modeled the effect of dedifferentiation on carcinogenesis. We considered a hybrid stochastic-deterministic model of mutation accumulation in both stem cells and progenitors, including dedifferentiation of progenitor cells to a stem cell-like state. We performed exact computer simulations of the emergence of tumor subpopulations with two mutations, and we derived semi-analytical estimates for the waiting time distribution to fixation. Our results suggest that dedifferentiation may play an important role in carcinogenesis, depending on how stem cell homeostasis is maintained. If the stem cell population size is held strictly constant (due to all divisions being asymmetric), we found that dedifferentiation acts like a positive selective force in the stem cell population and thus speeds carcinogenesis. If the stem cell population size is allowed to vary stochastically with density-dependent reproduction rates (allowing both symmetric and asymmetric divisions), we found that dedifferentiation beyond a critical threshold leads to exponential growth of the stem cell population. Thus, dedifferentiation may play a crucial role, the common modeling assumption of constant stem cell population size may not be adequate, and further progress in understanding carcinogenesis demands a more detailed mechanistic understanding of stem cell homeostasis

Examples of mathematical modeling tales from the crypt

Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al. (2007) Proc. Natl. Acad. Sci. USA 104, 4008-4013, to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters

Mechanisms of blood homeostasis: lineage tracking and a neutral model of cell populations in rhesus macaques.

BACKGROUND:How a potentially diverse population of hematopoietic stem cells (HSCs) differentiates and proliferates to supply more than 10(11) mature blood cells every day in humans remains a key biological question. We investigated this process by quantitatively analyzing the clonal structure of peripheral blood that is generated by a population of transplanted lentivirus-marked HSCs in myeloablated rhesus macaques. Each transplanted HSC generates a clonal lineage of cells in the peripheral blood that is then detected and quantified through deep sequencing of the viral vector integration sites (VIS) common within each lineage. This approach allowed us to observe, over a period of 4-12 years, hundreds of distinct clonal lineages. RESULTS:While the distinct clone sizes varied by three orders of magnitude, we found that collectively, they form a steady-state clone size-distribution with a distinctive shape. Steady-state solutions of our model show that the predicted clone size-distribution is sensitive to only two combinations of parameters. By fitting the measured clone size-distributions to our mechanistic model, we estimate both the effective HSC differentiation rate and the number of active HSCs. CONCLUSIONS:Our concise mathematical model shows how slow HSC differentiation followed by fast progenitor growth can be responsible for the observed broad clone size-distribution. Although all cells are assumed to be statistically identical, analogous to a neutral theory for the different clone lineages, our mathematical approach captures the intrinsic variability in the times to HSC differentiation after transplantation

Modelling spatially regulated B-catenin dynamics & invasion in intestinal crypts

Experimental data (e.g., genetic lineage and cell population studies) on intestinal crypts reveal that regulatory features of crypt behavior, such as control via morphogen gradients, are remarkably well conserved among numerous organisms (e.g., from mouse and rat to human) and throughout the different regions of the small and large intestines. In this article, we construct a partial differential equation model of a single colonic crypt that describes the spatial distribution of Wnt pathway proteins along the crypt axis. The novelty of our continuum model is that it is based upon assumptions that can be directly related to processes at the cellular and subcellular scales. We use the model to predict how the distributions of Wnt pathway proteins are affected by mutations. The model is then extended to investigate how mutant cell populations can invade neighboring crypts. The model simulations suggest that cell crowding caused by increased proliferation and decreased cell loss may be sufficient for a mutant cell population to colonize a neighboring healthy crypt

Colorectal Cancer Through Simulation and Experiment

Colorectal cancer has continued to generate a huge amount of research interest over several decades, forming a canonical example of tumourigenesis since its use in Fearon and Vogelstein’s linear model of genetic mutation. Over time, the field has witnessed a transition from solely experimental work to the inclusion of mathematical biology and computer-based modelling. The fusion of these disciplines has the potential to provide valuable insights into oncologic processes, but also presents the challenge of uniting many diverse perspectives. Furthermore, the cancer cell phenotype defined by the ‘Hallmarks of Cancer’ has been extended in recent times and provides an excellent basis for future research. We present a timely summary of the literature relating to colorectal cancer, addressing the traditional experimental findings, summarising the key mathematical and computational approaches, and emphasising the role of the Hallmarks in current and future developments. We conclude with a discussion of interdisciplinary work, outlining areas of experimental interest which would benefit from the insight that mathematical and computational modelling can provide