Typical delay determines waiting time on periodic-food schedules: Static and dynamic tests.

Pigeons and other animals soon learn to wait (pause) after food delivery on periodic-food schedules before resuming the food-rewarded response. Under most conditions the steady-state duration of the average waiting time, t, is a linear function of the typical interfood interval. We describe three experiments designed to explore the limits of this process. In all experiments, t was associated with one key color and the subsequent food delay, T, with another. In the first experiment, we compared the relation between t (waiting time) and T (food delay) under two conditions: when T was held constant, and when T was an inverse function of t. The pigeons could maximize the rate of food delivery under the first condition by setting t to a consistently short value; optimal behavior under the second condition required a linear relation with unit slope between t and T. Despite this difference in optimal policy, the pigeons in both cases showed the same linear relation, with slope less than one, between t and T. This result was confirmed in a second parametric experiment that added a third condition, in which T + t was held constant. Linear waiting appears to be an obligatory rule for pigeons. In a third experiment we arranged for a multiplicative relation between t and T (positive feedback), and produced either very short or very long waiting times as predicted by a quasi-dynamic model in which waiting time is strongly determined by the just-preceding food delay.

A miR-34a-Numb Feedforward Loop Triggered by Inflammation Regulates Asymmetric Stem Cell Division in Intestine and Colon Cancer.

Emerging evidence suggests that microRNAs can initiate asymmetric division, but whether microRNA and protein cell fate determinants coordinate with each other remains unclear. Here, we show that miR-34a directly suppresses Numb in early-stage colon cancer stem cells (CCSCs), forming an incoherent feedforward loop (IFFL) targeting Notch to separate stem and non-stem cell fates robustly. Perturbation of the IFFL leads to a new intermediate cell population with plastic and ambiguous identity. Lgr5+ mouse intestinal/colon stem cells (ISCs) predominantly undergo symmetric division but turn on asymmetric division to curb the number of ISCs when proinflammatory response causes excessive proliferation. Deletion of miR-34a inhibits asymmetric division and exacerbates Lgr5+ ISC proliferation under such stress. Collectively, our data indicate that microRNA and protein cell fate determinants coordinate to enhance robustness of cell fate decision, and they provide a safeguard mechanism against stem cell proliferation induced by inflammation or oncogenic mutation.