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.

De novo design and molecular assembly of a transmembrane diporphyrin-binding protein complex.

The de novo design of membrane proteins remains difficult despite recent advances in understanding the factors that drive membrane protein folding and association. We have designed a membrane protein PRIME (PoRphyrins In MEmbrane) that positions two non-natural iron diphenylporphyrins (Fe(III)DPP's) sufficiently close to provide a multicentered pathway for transmembrane electron transfer. Computational methods previously used for the design of multiporphyrin water-soluble helical proteins were extended to this membrane target. Four helices were arranged in a D(2)-symmetrical bundle to bind two Fe(II/III) diphenylporphyrins in a bis-His geometry further stabilized by second-shell hydrogen bonds. UV-vis absorbance, CD spectroscopy, analytical ultracentrifugation, redox potentiometry, and EPR demonstrate that PRIME binds the cofactor with high affinity and specificity in the expected geometry.