Can we negotiate with a tumor?

Recent progress in deciphering the molecular portraits of tumors promises an era of more personalized drug choices. However, current protocols still follow standard fixed-time schedules, which is not entirely coherent with the common observation that most tumors do not grow continuously. This unpredictability of the increases in tumor mass is not necessarily an obstacle to therapeutic efficiency, particularly if tumor dynamics could be exploited. We propose a model of tumor mass evolution as the integrated result of the dynamics of two linked complex systems, tumor cell population and tumor microenvironment, and show the practical relevance of this nonlinear approach.

Interaction between Gambogic acid and dihydrofolate reductase and synergistic lethal effects with methotrexate on hepatoma cells.

Gambogic acid (GA), a natural xanthone, has a wide spectrum of pharmacological activities, including repression of telomerase expression and induction of apoptosis of cancer cells. GA has also been reported to reduce the steady-state level of thymidylate synthetase mRNA in a gastric carcinoma cell line. Therefore, it has recently emerged as a candidate for use in cancer treatment. Using hepatoma cells with a dihydrofolate reductase (DHFR) gene amplification and cells transfected with an inducible DHFR transgene, we observed a negative relationship between DHFR expression and resistance to GA. Furthermore, DHFR assays in vitro indicated that in the presence of GA, DHFR activity was slightly inhibited and the affinity of the enzyme for dihydrofolate was markedly decreased. Treatment of rat hepatoma and other human and murine cancer cell lines with methotrexate and GA revealed that the two drugs displayed a marked synergistic lethal effect.

Unmasking chaotic attributes in time series of living cell populations.

BACKGROUND: Long-range oscillations of the mammalian cell proliferation rate are commonly observed both in vivo and in vitro. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes related to proliferation rate, including metabolic activity, telomere homeostasis, gene expression, and tumor growth. METHODOLOGY/PRINCIPAL FINDINGS: Using a simple, original, nonlinear method based on return maps, we previously found a geometrical deterministic structure coordinating such fluctuations in populations of various cell types. However, nonlinearity and determinism are only necessary conditions for chaos; they do not by themselves constitute a proof of chaotic dynamics. Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators. All four systems also display this geometrical structure, coordinating the oscillations of one or two variables of the oscillator. No such structure could be observed in periodic or stochastic fluctuations. CONCLUSION/SIGNIFICANCE: Theoretical models predict various cell population dynamics, from stable through periodically oscillating to a chaotic regime. Periodic and stochastic fluctuations were first described long ago in various mammalian cells, but by contrast, chaotic regulation had not previously been evidenced. The findings with our nonlinear geometrical approach are entirely consistent with the notion that fluctuations of cell populations can be chaotically controlled.

Sinusoidal swinging dynamics of the telomere repair and cell growth activation functions of telomerase in rat liver cancer cells.

Telomerase is a multimolecular complex of reverse transcriptase, RNA template, and regulatory proteins. It has two known functions: catalysis of the addition of [TTAGGG] repeats to telomeric DNA and the activation of various genes controlling cell proliferation. The possible coordination of these two functions is a key issue in understanding the growth of cancer cells. We report long-term changes to this complex system, as shown by specific data analysis methods. We show that the dynamics of the two functions of telomerase are tightly linked, with a change in predominant function every 13-14 weeks. The conservative behavior of this dynamic system probably accounts for the persistent proliferation of cancer cells.

Reversal of hepatoma cells resistance to anticancer drugs is correlated to cell proliferation kinetics, telomere length and telomerase activity.

BACKGROUND: Clinical and experimental observations indicate that resistance to anticancer drugs may be spontaneously reversible over time. MATERIALS AND METHODS: This work is a mathematical and statistical analysis of the relationship, during a 9-month experiment, between the resistance of repeatedly re-seeded hepatoma cells to methotrexate (MTX) or to cisplatin (cisP) and untreated cell proliferation, telomere length and telomerase activity. RESULTS: All variables showed complex oscillations, as previously published. In this work, cell proliferation was modelized by the logistic model, and the proliferation rates (a-values) together with their variations (va-values) were calculated. CONCLUSION: Significant correlations were discovered between cell resistance to treatments and a-values, va-values, telomere length and telomerase activities. These results open new insights into the handling of chemotherapy in the treatment of cancers.

Deterministic dynamics control oscillations of bone marrow cell proliferation.

OBJECTIVE: The production of blood cells in vivo, both normal and tumoral, displays oscillatory dynamics. Many cells in long-term cultures also show large amplitude oscillations of proliferative rate. Therefore we examined the proliferation dynamics of mouse bone marrow cells (MBM) and their clonogenic progenitor production (BMP), in order to characterize these dynamics. METHODS: Five Dexter-type cultures of MBM cells and their clonogenic BMP production were examined for up to seven-months periods of time. The recorded time series exhibited a complex pattern of oscillations with variable amplitudes. We previously reported a method that allowed analysis of such nonlinear dynamics of hepatoma cell proliferation. We applied this method, based on the two-dimensional recurrent representation of data, to analyze the fluctuations of bone marrow cells proliferation. RESULTS: The proliferation rate of mouse bone marrow cells shows large amplitude oscillations every 2 to 3 weeks. Mathematical analysis revealed a deterministic mechanism that controls all proliferation local maxima of MBM cells. Dynamics for progenitor production resembled that of parental cells. This reflects a predominant negative feedback on bone marrow cell proliferation. CONCLUSION: These dynamics were opposite of that previously described for hepatoma cells where the dominant control is applied to the local minima (troughs of proliferation). Therefore, the complex system of cell proliferation is controlled by a bipolar mechanism, with a predominant dampening command depending on the cell type. We propose that the dominant dampening control of local maxima in bone marrow cells protects the stock of stem cells.