Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments

Abstract

Abstract. This review aims at presenting a synoptic, if not exhaustive, point of view on some of the problems encountered by biologists and physicians who deal with natural cell proliferation and disruptions of its physiological control in cancer disease. It also aims at suggesting how mathematicians are naturally challenged by these questions and how they might help, not only biologists to deal theoretically with biological complexity, but also physicians to optimise therapeutics, on which last point the focus will be set here. To this purpose, mathematical modelling should represent proliferating cell population dynamics with natural built-in control targets (which implies modelling the cell division cycle), together with the distribution of drugs in the organism and their molecular actions on different targets at the cell level on proliferation, i.e., molecular pharmacokinetics-pharmacodynamics of antiproliferative drugs. This should make possible optimal control of drug delivery with constraints to be determined according to the main pharmacological issues encountered in the clinic: unwanted toxic side-effects, occurrence of drug resistance. Mathematical modelling should also take into account physiological determinants of cell and tissue proliferation, such as intervention of the immune system, circadian control on cell cycle checkpoint proteins, and activity of intracellular drug processing enzymes together with individual variations in the activities of these proteins (genetic polymorphism). Taking these points into account will add to the rich scenery of normal or disrupted cell and tissue regulations, and their corrections by drugs, a natural environmental, whole body physiological, frame. It is necessary indeed to consider such a framework if one wants to eventually be actually helpful to clinicians who routinely treat by combinations of drugs living Humans with their complex whole body regulations, often dependent on genotypic variations, and not isolated cells or tissues.Key words: cell proliferation, population dynamics, physiologically structured partial differential equations, pharmacological control, pharmacokinetics-pharmacodynamics, physiological modelling, cancer treatments, therapeutic optimisation, individualised medicine AMS subject classification: 92-02, 92B05 Biological common knowledge on cancerThis section shortly presents the general scenery of cancer evolution and features that must be included in models designed to describe and control it, bearing in mind a more descriptive (physicist's) than a therapeutic (physician's) point of view, only to reverse this perspective in the following sections, in which will be stressed the interest of modelling from the point of view of control, at least if one wants to design models for therapeutic applications. This biological section will be only a short sketch, if one considers that on this subject many books have already been written, e.g. [24,78,96,97,223]. Cancer: a challenging public health problemCardiovascular diseases and cancer are by fa...

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

“…becomes a problem with two populations, healthy and cancer, that are partly proliferating, partly dying, both evolving under the same drug insult, however with structural dynamic differences between them. This question has been the object of several studies [17,27,30,50,51,52], taking into account for some of them heterogeneity with respect to age phases in the cell division cycle [27,28,29,30], but so far heterogeneity with respect to phenotypes determining drug resistance had only been sketched as prospective work [27,51].…”

Optimisation of Cancer Drug Treatments Using Cell Population Dynamics

“…However, this approach, obviously valuable to provide new weapons in the war against cancer, by its nature cannot take into account the constraints linked to toxicity or drug resistance issues, which must be considered at the cell population level in a whole-body drug delivery optimisation perspective. This molecular biology approach should also be completed by whole-body pharmacokineticpharmacodynamic molecular modelling to represent the fate of drugs in the organism, as sketched above and in [37,38]. In other words, these approaches may be thought of as understanding the target and the weapon, whereas, to stay in this metaphor, optimisation of drug control is training to shoot in all conditions to safely reach the target.…”

“…As sketched elsewhere [37,38], theoretic drug delivery optimisation is the last step of therapeutic optimisation, which must rely firstly on an accurate representation of the behaviour of targets (wanted and unwanted) without treatment and on the changes the means of action of the physician -drugs -exert on them.…”

Multiphase and Multiscale Trends in Cancer Modelling

“…In some structured population models of cancer, which is the main topic of this issue, the evolution along the cell cycle is related to the activation of specific signalling pathways, or to the internal molecular content, e.g., DNA (see also, in this issue, the paper by Friedman [32] and the review by Clarimbault [25], where more references can be found). In particular, in [27] the transitions through the restriction point is related to the presence of specific control proteins, e.g., cyclin/CDK complexes.…”