Emergence of Anti-Cancer Drug Resistance: Exploring the Importance of the Microenvironmental Niche via a Spatial Model

Practically, all chemotherapeutic agents lead to drug resistance. Clinically, it is a challenge to determine whether resistance arises prior to, or as a result of, cancer therapy. Further, a number of different intracellular and microenvironmental factors have been correlated with the emergence of drug resistance. With the goal of better understanding drug resistance and its connection with the tumor microenvironment, we have developed a hybrid discrete-continuous mathematical model. In this model, cancer cells described through a particle-spring approach respond to dynamically changing oxygen and DNA damaging drug concentrations described through partial differential equations. We thoroughly explored the behavior of our self-calibrated model under the following common conditions: a fixed layout of the vasculature, an identical initial configuration of cancer cells, the same mechanism of drug action, and one mechanism of cellular response to the drug. We considered one set of simulations in which drug resistance existed prior to the start of treatment, and another set in which drug resistance is acquired in response to treatment. This allows us to compare how both kinds of resistance influence the spatial and temporal dynamics of the developing tumor, and its clonal diversity. We show that both pre-existing and acquired resistance can give rise to three biologically distinct parameter regimes: successful tumor eradication, reduced effectiveness of drug during the course of treatment (resistance), and complete treatment failure

Direct competition results from strong competiton for limited resource

We study a model of competition for resource through a chemostat-type model where species consume the common resource that is constantly supplied. We assume that the species and resources are characterized by a continuous trait. As already proved, this model, although more complicated than the usual Lotka-Volterra direct competition model, describes competitive interactions leading to concentrated distributions of species in continuous trait space. Here we assume a very fast dynamics for the supply of the resource and a fast dynamics for death and uptake rates. In this regime we show that factors that are independent of the resource competition become as important as the competition efficiency and that the direct competition model is a good approximation of the chemostat. Assuming these two timescales allows us to establish a mathematically rigorous proof showing that our resource-competition model with continuous traits converges to a direct competition model. We also show that the two timescales assumption is required to mathematically justify the corresponding classic result on a model consisting of only finite number of species and resources (MacArthur, R. Theor. Popul. Biol. 1970:1, 1-11). This is performed through asymptotic analysis, introducing different scales for the resource renewal rate and the uptake rate. The mathematical difficulty relies in a possible initial layer for the resource dynamics. The chemostat model comes with a global convex Lyapunov functional. We show that the particular form of the competition kernel derived from the uptake kernel, satisfies a positivity property which is known to be necessary for the direct competition model to enjoy the related Lyapunov functional

Activation of the Fas/Fas ligand pathway in hypertensive renal disease in Dahl/Rapp rats

BACKGROUND: Hypertensive nephrosclerosis is the second most common cause of end-stage renal failure in the United States. The mechanism by which hypertension produces renal failure is incompletely understood. Recent evidence demonstrated that an unscheduled and inappropriate increase in apoptosis occurred in the Dahl/Rapp rat, an inbred strain of rat that uniformly develops hypertension and hypertensive nephrosclerosis; early correction of the hypertension prevents the renal injury. The present study examined the role of the Fas/FasL pathway in this process. METHODS: Young male Dahl/Rapp salt-sensitive (S) and Sprague-Dawley rats were fed diets that contained 0.3% or 8.0% NaCl diets. Kidneys were examined at days 7 and 21 of the study. RESULTS: An increase in Fas and FasL expression was observed in glomerular and tubular compartments of kidneys of hypertensive S rats, whereas dietary salt did not change expression of either of these molecules in normotensive Sprague-Dawley rats. Associated with this increase was cleavage of Bid and activation of caspase-8, the initiator caspase in this apoptotic pathway, by day 21 of the study. CONCLUSIONS: Augmented expression of apoptotic signaling by the Fas/FasL pathway occurred during development of end-stage renal failure in this model of hypertensive nephrosclerosis

Computational Approaches and Analysis for a Spatio-Structural-Temporal Invasive Carcinoma Model

Spatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the urokinase plasminogen activator (uPA) wherein uPA binds uPA receptors on the cancer cell surface, allowing plasminogen to be cleaved into plasmin, which degrades the extracellular matrix and this way leads to enhanced cancer cell migration. In this paper, we develop a novel numerical approach and associated analysis for spatio-structuro-temporal modelling of the uPA system for up to two-spatial and two-structural dimensions. This is accompanied by analytical exploration of the numerical techniques used in simulating this system, with special consideration being given to the proof of stability within numerical regimes encapsulating a central differences approach to approximating numerical gradients. The stability analysis performed here reveals instabilities induced by the coupling of the structural binding and proliferative processes. The numerical results expound how the uPA system aids the tumour in invading the local stroma, whilst the inhibitor to this system may impede this behaviour and encourage a more sporadic pattern of invasion.PostprintPeer reviewe

Revisiting and modelling the woodland farming system of the early Neolithic Linear Pottery Culture (LBK), 5600–4900 B.C

International audienceThis article presents the conception and the conceptual results of a modelling representation of the farming systems of the Linearbandkeramik Culture (LBK). Assuming that there were permanent fields (PF) then, we suggest four ways that support the sustainability of such a farming system over time: a generalized pollarding and coppicing of trees to increase the productivity of woodland areas for foddering more livestock, which itself can then provide more manure for the fields, a generalized use of pulses grown together with cereals during the same cropping season, thereby reducing the needs for manure. Along with assumptions limiting bias on village and family organizations, the conceptual model which we propose for human environment in the LBK aims to be sustainable for long periods and can thereby overcome doubts about the PFs hypothesis for the LBK farming system. Thanks to a reconstruction of the climate of western Europe and the consequent vegetation pattern and productivity arising from it, we propose a protocol of experiments and validation procedures for both testing the PFs hypothesis and defining its eco-geographical area

Deterministic mathematical modelling for cancer chronotherapeutics: cell population dynamics and treatment optimisation

Chronotherapeutics has been designed and used for more than twenty years as an effective treatment against cancer by a few teams around the world, among whom one of the first is Francis Lévi's at Paul-Brousse hospital (Villejuif, France), in application of circadian clock physiology to determine best infusion times within the 24-hour span for anticancer drug delivery. Mathematical models have been called in the last ten years to give a rational basis to such optimised treatments, for use in the laboratory and ultimately in the clinic. While actual clinical applications of the theoretical optimisation principles found have remained elusive so far to improve chronotherapeutic treatments in use, mathematical models provide proofs of concepts and tracks to be explored experimentally, to progress from theory to bedside. Starting from a simple ordinary differential equation model that allowed setting and numerically solving a drug delivery optimisation problem with toxicity constraints, this modelling enterprise has been extended to represent the division cycle in proliferating cell populations with different molecular targets, to allow for the representation of anticancer drug combinations that are used in clinical oncology. The main point to be made precise in such a therapeutic optimisation problem is to establish, here in the frame of circadian chronobiology, physiologically based differences between healthy and cancer cell populations in their responses to drugs. To this aim, clear biological evidence at the molecular level is still lacking, so that, starting from indirect observations at the experimental and clinical levels and from theoretical considerations on the model, speculations have been made, that will be exposed in this review of cancer chronotherapeutics models with the corresponding optimisation problems and their numerical solutions, to represent these differences between the two cell populations, with regard to circadian clock control