Global dynamics of two-compartment models for cell production systems with regulatory mechanisms

We present a global stability analysis of two-compartment models of a hierarchical cell production system with a nonlinear regulatory feedback loop. The models describe cell differentiation processes with the stem cell division rate or the self-renewal fraction regulated by the number of mature cells. The two-compartment systems constitute a basic version of the multicompartment models proposed recently by Marciniak-Czochra and collaborators [25] to investigate the dynamics of the hematopoietic system. Using global stability analysis, we compare different regulatory mechanisms. For both models, we show that there exists a unique positive equilibrium that is globally asymptotically stable if and only if the respective reproduction numbers exceed one. The proof is based on constructing Lyapunov functions, which are appropriate to handle the specific nonlinearities of the model. Additionally, we propose a new model to test biological hypothesis on the regulation of the fraction of differentiating cells. We show that such regulatory mechanism is incapable of maintaining homeostasis and leads to unbounded cell growth. Potential biological implications are discussed

Stability analysis of multi-compartment models for cell production systems

We study two-and three-compartment models of a hierarchical cell production system with cell division regulated by the level of mature cells. We investigate the structure of equilibria with respect to parameters as well as local stability properties for the equilibria. To interpret the results we adapt the concept of reproduction numbers, which is well known in ecology, to stem cell population dynamics. In the two-compartment model, the positive equilibrium is stable wherever it exists. In the three-compartment model, we find that the intermediate stage of differentiation is responsible for the emergence of an instability region in the parameter plane. Moreover, we prove that this region shrinks as the mortality rate for mature cells increases and discuss this result

A model for stem cell population dynamics with regulated maturation delay

We develop a structured population model for the maturation process of stem cells in the form of a state-dependent delay differential equation. Moreover, results on existence, uniqueness and positivity of solutions as well as conditions of existence for equilibria and representations of these are established. We give biological interpretations for the conditions of existence of equilibria

On the dynamics of a non-local parabolic equation arising from the Gierer-Meinhardt system

This is an author-created, un-copyedited version of an article accepted for publication in Nonlinearity. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://iopscience.iop.org/article/10.1088/1361-6544/aa64b2/metaThe purpose of the current paper is to contribute to the comprehension of the dynamics of the shadow system of an activator-inhibitor system known as a Gierer-Meinhardt model. Shadow systems are intended to work as an intermediate step between single equations and reaction-diffusion systems. In the case where the inhibitor's response to the activator's growth is rather weak, then the shadow system of the Gierer-Meinhardt model is reduced to a single though non-local equation whose dynamics will be investigated. We mainly focus on the derivation of blow-up results for this non-local equation which can be seen as instability patterns of the shadow system. In particular, a {\it diffusion driven instability (DDI)}, or {\it Turing instability}, in the neighbourhood of a constant stationary solution, which it is destabilised via diffusion-driven blow-up, is obtained. The latter actually indicates the formation of some unstable patterns, whilst some stability results of global-in-time solutions towards non-constant steady states guarantee the occurrence of some stable patterns

Influence of very low doses of mediators on fungal laccase activity - nonlinearity beyond imagination

Laccase, an enzyme responsible for aerobic transformations of natural phenolics, in industrial applications requires the presence of low-molecular substances known as mediators, which accelerate oxidation processes. However, the use of mediators is limited by their toxicity and the high costs of exploitation. The activation of extracellular laccase in growing fungal culture with highly diluted mediators, ABTS and HBT is described. Two high laccase-producing fungal strains, Trametes versicolor and Cerrena unicolor, were used in this study as a source of enzyme. Selected dilutions of the mediators significantly increased the activity of extracellular laccase during 14 days of cultivation what was distinctly visible in PAGE technique and in colorimetric tests. The same mediator dilutions increased demethylation properties of laccase, which was demonstrated during incubation of enzyme with veratric acid. It was established that the activation effect was assigned to specific dilutions of mediators. Our dose-response dilution process smoothly passes into the range of action of homeopathic dilutions and is of interest for homeopaths

Serum after Autologous Transplantation Stimulates Proliferation and Expansion of Human Hematopoietic Progenitor Cells

Regeneration after hematopoietic stem cell transplantation (HSCT) depends on enormous activation of the stem cell pool. So far, it is hardly understood how these cells are recruited into proliferation and self-renewal. In this study, we have addressed the question if systemically released factors are involved in activation of hematopoietic stem and progenitor cells (HPC) after autologous HSCT. Serum was taken from patients before chemotherapy, during neutropenia and after hematopoietic recovery. Subsequently, it was used as supplement for in vitro culture of CD34+ cord blood HPC. Serum taken under hematopoietic stress (4 to 11 days after HSCT) significantly enhanced proliferation, maintained primitive immunophenotype (CD34+, CD133+, CD45−) for more cell divisions and increased colony forming units (CFU) as well as the number of cobblestone area-forming cells (CAFC). The stimulatory effect decays to normal levels after hematopoietic recovery (more than 2 weeks after HSCT). Chemokine profiling revealed a decline of several growth-factors during neutropenia, including platelet-derived growth factors PDGF-AA, PDGF-AB and PDGF-BB, whereas expression of monocyte chemotactic protein-1 (MCP-1) increased. These results demonstrate that systemically released factors play an important role for stimulation of hematopoietic regeneration after autologous HSCT. This feedback mechanism opens new perspectives for in vivo stimulation of the stem cell pool

Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two examples arising from cancer invasion