![Figure 4.5: An Agent-Based Model [48] designed to represent the same biological phenomenon mentioned in Fig. 4.4. (a) The drug resistance phenomenon reported in [231]: evolution from sensitive (PC9) to surviving but non proliferating (DTP) and finally to surviving and proliferating (DTEP) cells. The ABM representation, as the IDE-PDE one shown on Fig. 4.4, is compatible with the observed total reversibility of sensitivity when the drug is washed out. (b) Evolution of the cancer cell population in the (x, y) phenotype phase plane. (c) The computational algorithm, in which non genetic instability is represented by stochastic variation in the phenotype (x, y). (d) Three different simulations of individual cell fates with followup of the survival potential x and of the proliferation potential y. The averages of these trajectories on large numbers of stochastic simulations recover the deterministic trajectories of the IDE-PDE model, as shown in [48].](/figures/figure-4-5-an-agent-based-model-48-designed-to-represent-the-1b4sgohr.webp)
Q2. What kind of model has been proposed to take account of drug resistance in cancer cell populations?
in particular in the last decade, mathematical models coming from ecology, namely models of adaptive dynamics [65, 66], have been developed to take account of drug resistance in cancer cell populations by proposing cell population models structured by traits to describe relevant heterogeneity in those cell populations.
Q3. What is the definition of a deterministic dynamical system?
In control science, a dynamical system represents an evolving phenomenon that mathematicians or engineers want to keep within prescribed limits (control) or lead to a desired endpoint (optimal control) by exerting external means that have known effects on known targets in some of its constituents.
Q4. What is the purpose of the soma of sexually reproducing animals?
According to the fundamental theoretical work of August Weismann (1834–1914), the only mission of the soma of sexually reproducing animals is to serve, preserve and transmit the germ line (or germ plasm, i.e., the genome as contained in germinal cells).
Q5. What are the mathematical models that have been proposed to represent evolution in cancer cell populations?
the authors briefly review some mathematical models that have been proposed to represent evolution in cancer cell populations and the authors discuss their possible use to set theoretical therapeutic optimisation in the framework of optimal control problems, focussing on continuous phenotypically structured models.
Q6. What is the fundamental hypothesis of tissue organisational field theory?
It is also the fundamental hypothesis of tissue organisational field theory (TOFT, see above) that cancer is the result not so much of the progeny of a single renegade cell, but mainly of a diseased surrounding tissue engendering cellular stress [236, 237].
Q7. How can the authors determine the probability distribution of single cell phenotypes across a cell?
Hardly amenable to large networkrepresentations (hubs in large networks absent)it is in their opinion mandatory to perform phenotype analyses at the single-cell level in the same cell population to reconstruct (by large sampling of individual cell data through, for instance, fluorescence-activated cell sorting) the probability distribution of single-cell phenotypes across a cell population.
Q8. What is the reason to set the magnifying glass on cancer physiopathology at the cell?
A second reason to set the magnifying glass on cancer physiopathology at the cell-population scale is that, by taking into account heterogeneity at the cancer cell population level, it may be possible to explain why most anticancer drugs, even recently developed targeted therapies that try to hit intracellular pathways at supposed hubs, have generally and inexplicably led to so many treatment failures [67, 102, 228, 254] despite being seemingly efficient at the single-cell level.
Q9. What is the difference between ABMs and deterministic models?
Unlike deterministic models, ABMs can capture extinction and the occurrence of unusual events; however, they are generally more computationally expensive, which imposes limitations on the size of the population modelled.
Q10. What other variables are used to characterise relevant biological variability?
Other variables may also be used to characterise relevant biological variability at the level of a cell in a proliferating cell population, such as age (a lumped variable assumed to represent the sum of products of protein synthesis), size at division or at cell cycle phase transitions, and in any cell population, the expression of genes of interest, the activity of cellulular detoxification enzymes or membrane proteins such as ABC transporters [107], the determinants of energy metabolism (such as number and quality of mitochondria), to name but a few.