A Simple Mathematical Model Based on the Cancer Stem Cell Hypothesis Suggests Kinetic Commonalities in Solid Tumor Growth

Background: The Cancer Stem Cell (CSC) hypothesis has gained credibility within the cancer research community. According to this hypothesis, a small subpopulation of cells within cancerous tissues exhibits stem-cell-like characteristics and is responsible for the maintenance and proliferation of cancer. Methodologies/Principal Findings: We present a simple compartmental pseudo-chemical mathematical model for tumor growth, based on the CSC hypothesis, and derived using a ‘‘chemical reaction’ ’ approach. We defined three cell subpopulations: CSCs, transit progenitor cells, and differentiated cells. Each event related to cell division, differentiation, or death is then modeled as a chemical reaction. The resulting set of ordinary differential equations was numerically integrated to describe the time evolution of each cell subpopulation and the overall tumor growth. The parameter space was explored to identify combinations of parameter values that produce biologically feasible and consistent scenarios. Conclusions/Significance: Certain kinetic relationships apparently must be satisfied to sustain solid tumor growth and to maintain an approximate constant fraction of CSCs in the tumor lower than 0.01 (as experimentally observed): (a) the rate of symmetrical and asymmetrical CSC renewal must be in the same order of magnitude; (b) the intrinsic rate of renewal and differentiation of progenitor cells must be half an order of magnitude higher than the corresponding intrinsic rates for cancer stem cells; (c) the rates of apoptosis of the CSC, transit amplifying progenitor (P) cells, and terminally differentiate

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

Male mealworm beetles increase resting metabolic rate under terminal investment.

Harmful parasite infestation can cause energetically costly behavioural and immunological responses, with the potential to reduce host fitness and survival. It has been hypothesized that the energetic costs of infection cause resting metabolic rate (RMR) to increase. Furthermore, under terminal investment theory, individuals exposed to pathogens should allocate resources to current reproduction when life expectancy is reduced, instead of concentrating resources on an immune defence. In this study, we activated the immune system of Tenebrio molitor males via insertion of nylon monofilament, conducted female preference tests to estimate attractiveness of male odours and assessed RMR and mortality. We found that attractiveness of males coincided with significant down-regulation of their encapsulation response against a parasite-like intruder. Activation of the immune system increased RMR only in males with heightened odour attractiveness and that later suffered higher mortality rates. The results suggest a link between high RMR and mortality and support terminal investment theory in T. molitor

A mathematical model of cell cycle progression applied to the MCF-7 breast cancer cell line

In this paper, we present a model of cell cycle progression and apply it to cells of the MCF-7 breast cancer cell line. We consider cells existing in the three typical cell cycle phases determined using flow cytometry: the G1, S, and G2/M phases. We further break each phase up into model phases in order to capture certain features such as cells remaining in phases for a minimum amount of time. The model is also able to capture the environmentally responsive part of the G1 phase, allowing for quantification of the number of environmentally responsive cells at each point in time. The model parameters are carefully chosen using data from various sources in the biological literature. The model is then validated against a variety of experiments, and the excellent fit with experimental results allows for insight into the mechanisms that influence observed biological phenomena. In particular, the model is used to question the common assumption that a 'slow cycling population' is necessary to explain some results. Finally, an extension is proposed, where cell death is included in order to accurately model the effects of tamoxifen, a common first line anticancer drug in breast cancer patients. We conclude that the model has strong potential to be used as an aid in future experiments to gain further insight into cell cycle progression and cell death.Kate Simms, Nigel Bean, Adrian Koerbe

Dynamics of glucose and insulin concentration connected to the <it>β</it>‐cell cycle: model development and analysis

<p>Abstract</p> <p>Background</p> <p>Diabetes mellitus is a group of metabolic diseases with increased blood glucose concentration as the main symptom. This can be caused by a relative or a total lack of insulin which is produced by the <it>β</it>‐cells in the pancreatic islets of Langerhans. Recent experimental results indicate the relevance of the <it>β</it>‐cell cycle for the development of diabetes mellitus.</p> <p>Methods</p> <p>This paper introduces a mathematical model that connects the dynamics of glucose and insulin concentration with the <it>β</it>‐cell cycle. The interplay of glucose, insulin, and <it>β</it>‐cell cycle is described with a system of ordinary differential equations. The model and its development will be presented as well as its mathematical analysis. The latter investigates the steady states of the model and their stability.</p> <p>Results</p> <p>Our model shows the connection of glucose and insulin concentrations to the <it>β</it>‐cell cycle. In this way the important role of glucose as regulator of the cell cycle and the capability of the <it>β</it>‐cell mass to adapt to metabolic demands can be presented. Simulations of the model correspond to the qualitative behavior of the glucose‐insulin regulatory system showed in biological experiments.</p> <p>Conclusions</p> <p>This work focusses on modeling the physiological situation of the glucose‐insulin regulatory system with a detailed consideration of the <it>β</it>‐cell cycle. Furthermore, the presented model allows the simulation of pathological scenarios. Modification of different parameters results in simulation of either type 1 or type 2 diabetes.</p