Final answer:
The absence of the APC gene in mice leads to inappropriate proliferation of gut stem cells due to the unchecked Wnt signaling pathway, potentially leading to tumor development.
Step-by-step explanation:
In mice lacking the APC gene, which is a critical tumor suppressor gene in the Wnt signaling pathway, one would predict that there will be inappropriate proliferation of gut stem cells. This is because the APC gene's function in normal cells acts as a 'brake pedal,' inhibiting cell division and proliferation by degrading the beta-catenin protein, which would otherwise go on to activate TCF and promote expression of Wnt-responsive genes that lead to cell proliferation. In the absence of APC, the Wnt signaling is left unchecked, resulting in constant activation of TCF and persistent cell division, even in the absence of Wnt signals, potentially leading to tumor development in the gut lining.