Reaction diffusion equation with non-local term arises as a mean field limit of the master equation
Kazuhisa Ichikawa Mahemauti Rouzimaimaiti Takashi Suzuki
We formulate a reaction diffusion equation with non-local term as a mean field equation of the master equation where the particle density is defined continuously in space and time. In the case of the constant mean waiting time, this limit equation is associated with the diffusion coefficient of A. Einstein, the reaction rate in phenomenology, and the Debye term under the presence of potential.
keywords: Reaction probability. Stochastic reaction Reaction radius
Synergistic effect of blocking cancer cell invasion revealed by computer simulations
Kazuhisa Ichikawa
Invasion and metastasis are the main cause of death in cancer patients. The initial step of invasion is the degradation of extracellular matrix (ECM) by primary cancer cells in a tissue. Membranous metalloproteinase MT1-MMP and soluble metalloproteinase MMP-2 are thought to play an important role in the degradation of ECM. In the previous report, we found that the repetitive insertion of MT1-MMP to invadopodia was crucial for the effective degradation of ECM (Hoshino, D., et al., PLoS Comp. Biol., 2012, e1002479). However, the role of MMP-2 and the effect of inhibitors for these ECM-degrading proteases were still obscure. Here we investigated these two problems by using the same model as in the previous report. First we tested the effect of MMP-2 and found that while MT1-MMP played a major role in the degradation of ECM, MMP-2 played only a marginal effect on the degradation of ECM. Based on these findings, we next tested the effect of a putative inhibitor for MT1-MMP and found that such inhibitor was ineffective in blocking ECM degradation. Then we tested combined strategy including inhibitor for MT1-MMP, reduction of its turnover and its content in vesicles. A synergistic effect of combined strategy was observed in the decrease in the efficacy of ECM degradation. Our simulation study suggests the importance of combined strategy in blocking cancer invasion and metastasis.
keywords: invasion MT1-MMP therapeutic targets. MMP-2 Cancer

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