Molavian Hamid R, Kohandel Mohammad, Milosevic Michael, Sivaloganathan Sivabal
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada.
Cancer Res. 2009 Dec 1;69(23):9141-7. doi: 10.1158/0008-5472.CAN-09-2112. Epub 2009 Nov 17.
Understanding cancer cell metabolism and targeting associated pathways is a field of increasing interest. Helmlinger and colleagues measured average pH and pO(2) as functions of distance from a single blood vessel on the micrometer scale. We show that these results provide unique insight into cancer cell metabolism in vivo when combined with an appropriate mathematical model. We calculate pH as a function of distance from a single blood vessel and for a given metabolism while incorporating a single CO(2) buffer with effective diffusion constants. By assuming that cancer cell metabolism is dominated by respiration with a smaller component of glycolysis in the normoxic state, by more balanced respiration and glycolysis in the hypoxic state, and by glycolysis alone in the anoxic state, we are able to semiquantitatively derive the experimental results of Helmlinger and colleagues. We also apply our model to glycolysis-impaired metabolism and show that the low pH and high pO(2) observed in these tumors may be related to the substantial shift from a respiration-dominated metabolism to one in which glutaminolysis dominates. Based on this, we propose an in vivo experimental measurement of pH in a glycolysis-impaired tumor to validate the modeling results.
了解癌细胞代谢并靶向相关通路是一个越来越受关注的领域。赫尔姆林格及其同事在微米尺度上测量了距单一血管距离的函数的平均pH值和pO₂。我们表明，当与适当的数学模型相结合时，这些结果为体内癌细胞代谢提供了独特的见解。我们在纳入具有有效扩散常数的单一CO₂缓冲液的情况下，计算距单一血管距离的函数的pH值以及给定代谢情况下的pH值。通过假设在常氧状态下癌细胞代谢以呼吸作用为主，糖酵解作用占较小部分；在低氧状态下呼吸作用和糖酵解作用更为平衡；在缺氧状态下仅以糖酵解作用为主，我们能够半定量地推导赫尔姆林格及其同事的实验结果。我们还将我们的模型应用于糖酵解受损的代谢情况，并表明在这些肿瘤中观察到的低pH值和高pO₂可能与从以呼吸作用为主的代谢向以谷氨酰胺分解作用为主的代谢的实质性转变有关。基于此，我们提出对糖酵解受损肿瘤中的pH值进行体内实验测量，以验证建模结果。
