Circadian rhythm and tumour growth
Circadian rhythm and tumour growth
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DOI：
10.1016/j.crma.2005.10.029
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发表时间：
2006-01-01
影响因子：
0.8
通讯作者：
Perthame, B
中科院分区：
文献类型：
--
作者：
Clairambault, J;Michel, P;Perthame, B
我们解决以下问题：一个人能维持，数学模型的基础上，癌细胞，昼夜节律的控制的损失有利于更快的增长？这个问题来自于观察到小鼠肿瘤的生长通过实验性的昼夜节律的破坏而增强，可以通过细胞周期的数学模型来解决。为此，我们考虑一个年龄结构的人口模型与控制的死亡（凋亡）率和相变，和两个特征值：一个周期性的控制系数（通过一个变量的Floquet理论在无限维）和一个常系数（作为时间平均的周期性的情况下）。我们表明，一个直接的证据，令人惊讶的是，考虑到上述观察，周期性特征值总是大于稳态特征值时，唯一的凋亡率的关注。我们还表明，当细胞周期的阶段之间的过渡率的数值模拟关注，没有进一步的假设，两个特征值之间不存在自然的层次结构。这至少表明，如果这些模型要考虑到上述观察结果，则阶段内的死亡率控制是不够的，阶段之间的转换率是增殖控制的关键目标。
We address the following question: can one sustain, on the basis of mathematical models, that for cancer cells, the loss of control by circadian rhythm favours a faster growth? This question, which comes from the observation that tumour growth in mice is enhanced by experimental disruption of the circadian rhythm, may be tackled by mathematical modelling of the cell cycle. For this purpose we consider an age-structured population model with control of death (apoptosis) rates and phase transitions, and two eigenvalues: one for periodic control coefficients (via a variant of Floquet theory in infinite dimension) and one for constant coefficients (taken as the time average of the periodic case). We show by a direct proof that, surprisingly enough considering the above-mentioned observation, the periodic eigenvalue is always greater than the steady state eigenvalue when the sole apoptosis rate is concerned. We also show by numerical simulations when transition rates between the phases of the cell cycle are concerned, that, without further hypotheses, no natural hierarchy between the two eigenvalues exists. This at least shows that, if such models are to take account of the above-mentioned observation, control of death rates inside phases is not sufficient, and that transition rates between phases are a key target in proliferation control.