Evolution of a structured cell population endowed with plasticity of traits under constraints on and between the traits

Homeostasis represents the idea that a feature may remain invariant despite changes in some external parameters. We establish a connection between homeostasis and injectivity for reaction network models. In particular, we show that a reaction network cannot exhibit homeostasis if a modified version of the network (which we call homeostasis-associated network) is injective. We provide examples of reaction networks which can or cannot exhibit homeostasis by analyzing the injectivity of their homeostasis-associated networks.

     

Relationships between neuronal cell adhesion molecule and LHRH neurons in the urodele brain: a developmental immunohistochemical study.

Polysialic acid (PSA), a homopolymer attached to neural cell adhesion molecule (NCAM) is considered a major hallmark of vertebrate cell migration. We studied the distribution of PSA-NCAM by immunohistochemistry, during brain development, in two urodele amphibians, Pleurodeles waltl and the neotenic newt Ambystoma mexicanum. In both species a gradual increase of immunolabelling was observed throughout the brain from developmental stage 30 to stage 52. At the onset of metamorphosis, some differences became evident: in Pleurodeles immunostaining was gradually restricted to the olfactory system while in Ambystoma, PSA-NCAM maintained a more extended distribution (for example throughout the telencephalic walls) suggesting, for the brain of this latter species, a rather preserved neuronal plasticity. The aim of the present work was to correlate the above described PSA-NCAM-immunoreactivity (IR) with the distribution of luteinizing hormone-releasing hormone (LH-RH) containing neurons, which represent a well known example of neural elements migrating from the olfactory placode. LHRH-IR, undetectable till stage 30, was later found together with PSA-NCAM-IR in both the olfactory system and septo-hypothalamic areas. Such observations further support a role of PSA in providing a migration route toward the establishment of a part, at least, of the urodele LHRH system. The possible functional meaning of the LHRH-containing neurons localized between dorsal and ventral thalamus of Ambystoma, never reported before in this area, almost devoid of PSA-NCAM-IR, is discussed.     

Commitment of Mathematicians in Medicine: A Personal Experience, and Generalisations

I will present here a personal point of view on the commitment of mathematicians in medicine. Starting from my personal experience, I will suggest generalisations including favourable signs and caveats to show how mathematicians can be welcome and helpful in medicine, both in a theoretical and in a practical way.     

A combined experimental and mathematical approach for molecular-based optimization of irinotecan circadian delivery

Circadian timing largely modifies efficacy and toxicity of many anticancer drugs. Recent findings suggest that optimal circadian delivery patterns depend on the patient genetic background. We present here a combined experimental and mathematical approach for the design of chronomodulated administration schedules tailored to the patient molecular profile. As a proof of concept we optimized exposure of Caco-2 colon cancer cells to irinotecan (CPT11), a cytotoxic drug approved for the treatment of colorectal cancer. CPT11 was bioactivated into SN38 and its efflux was mediated by ATP-Binding-Cassette (ABC) transporters in Caco-2 cells. After cell synchronization with a serum shock defining Circadian Time (CT) 0, circadian rhythms with a period of 26 h 50 (SD 63 min) were observed in the mRNA expression of clock genes REV-ERBα, PER2, BMAL1, the drug target topoisomerase 1 (TOP1), the activation enzyme carboxylesterase 2 (CES2), the deactivation enzyme UDP-glucuronosyltransferase 1, polypeptide A1 (UGT1A1), and efflux transporters ABCB1, ABCC1, ABCC2 and ABCG2. DNA-bound TOP1 protein amount in presence of CPT11, a marker of the drug PD, also displayed circadian variations. A mathematical model of CPT11 molecular pharmacokinetics-pharmacodynamics (PK-PD) was designed and fitted to experimental data. It predicted that CPT11 bioactivation was the main determinant of CPT11 PD circadian rhythm. We then adopted the therapeutics strategy of maximizing efficacy in non-synchronized cells, considered as cancer cells, under a constraint of maximum toxicity in synchronized cells, representing healthy ones. We considered exposure schemes in the form of an initial concentration of CPT11 given at a particular CT, over a duration ranging from 1 to 27 h. For any dose of CPT11, optimal exposure durations varied from 3h40 to 7h10. Optimal schemes started between CT2h10 and CT2h30, a time interval corresponding to 1h30 to 1h50 before the nadir of CPT11 bioactivation rhythm in healthy cells.     

An age-and-cyclin-structured cell population model for healthy and tumoral tissues

We present a nonlinear model of the dynamics of a cell population divided into proliferative and quiescent compartments. The proliferative phase represents the complete cell cycle (G ₁−S−G ₂−M) of a population committed to divide at its end. The model is structured by the time spent by a cell in the proliferative phase, and by the amount of Cyclin D/(CDK4 or 6) complexes. Cells can transit from one compartment to the other, following transition rules which differ according to the tissue state: healthy or tumoral. The asymptotic behaviour of solutions of the nonlinear model is analysed in two cases, exhibiting tissue homeostasis or tumour exponential growth. The model is simulated and its analytic predictions are confirmed numerically.     

Period shift induction by intermittent stimulation in a Drosophila model of PER protein oscillations

PER protein circadian oscillations in Drosophila have been described by Goldbeter according to a five-dimensional model that includes the possibility of genetic mutation described by changing one parameter, the maximum degradation rate of the PER protein. Assuming that, in a mutant Drosophila this parameter is unreachable, we modify another parameter, the translation rate between the mRNA and the nonphosphorylated form of PER protein, by periodic intermittent activation or inhibition. We show how such a modification, simulated in the model by a periodic, on/off, piecewise constant stimulation (which increases or decreases this parameter) allows the entrainment of oscillations exactly at, or close to, a desired period. In a different context, this suggests that some diseases may be corrected using pharmacological agents according to specific periodic delivery schedules. (Chronobiology International,17(1), 1-14, 2000)