Emerick Brooks, Schleiniger Gilberto, Boman Bruce M
Department of Mathematics, Trinity College, Hartford, CT, 06106, USA.
Department of Mathematical Sciences, University of Delaware, Newark, DE, 19711, USA.
J Math Biol. 2017 Nov;75(5):1171-1202. doi: 10.1007/s00285-017-1112-y. Epub 2017 Mar 7.
The Wnt/[Formula: see text]-catenin pathway plays a crucial role in stem cell renewal and differentiation in the normal human colonic crypt. The balance between [Formula: see text]-catenin and APC along the crypt axis determines its normal functionality. The mechanism that deregulates this balance may give insight into the initiation of colorectal cancer. This is significant because the spatial dysregulation of [Formula: see text]-catenin by the mutated tumor suppressor gene/protein APC in human colonic crypts is responsible for the initiation and growth of colorectal cancer. We consider a regulatory function that promotes APC synthesis within the cell and its effect on the accumulation of the Wnt target protein, [Formula: see text]-catenin. It is evident that an APC gradient exists along the crypt axis; however, the mechanism by which APC expression is regulated within the cell is not well known. We investigate the dynamics of an APC regulatory mechanism with an increased level of Axin at the subcellular level. Model output shows an increase of APC for a diminished Wnt signal, which explains the APC gradient along the crypt. We find that the dynamic interplay between [Formula: see text]-catenin, APC, and Axin produces oscillatory behavior, which is controlled by the Wnt stimulus. In the presence of reduced functional APC, the oscillations are amplified, which suggests that the cell remains in a more proliferative state for longer periods of time. Increased Axin levels (typical of mammalian cells) reduce oscillatory behavior and minimize the levels of [Formula: see text]-catenin within the cell while raising the levels of APC.
Wnt/β-连环蛋白信号通路在正常人类结肠隐窝的干细胞更新和分化中起着关键作用。沿隐窝轴的β-连环蛋白和腺瘤性息肉病基因（APC）之间的平衡决定了其正常功能。破坏这种平衡的机制可能有助于深入了解结直肠癌的起始过程。这一点很重要，因为人类结肠隐窝中由突变的肿瘤抑制基因/蛋白APC导致的β-连环蛋白空间失调是结直肠癌起始和生长的原因。我们考虑一种促进细胞内APC合成的调节功能及其对Wnt靶蛋白β-连环蛋白积累的影响。显然，沿隐窝轴存在APC梯度；然而，细胞内APC表达的调控机制尚不清楚。我们在亚细胞水平研究Axin水平升高时APC调节机制的动力学。模型输出显示，Wnt信号减弱时APC增加，这解释了沿隐窝的APC梯度。我们发现β-连环蛋白、APC和Axin之间的动态相互作用产生振荡行为，该行为受Wnt刺激控制。在功能性APC减少的情况下，振荡会放大，这表明细胞在更长时间内保持在更增殖的状态。Axin水平升高（哺乳动物细胞的典型特征）会减少振荡行为，并使细胞内β-连环蛋白水平降至最低，同时提高APC水平。
