Mathematical Biology seminar Bob Guy University of California, Davis "Optimality of Metachronal Paddling" Tuesday, April 7, 2026 1-2pm in LCB 215 Abstract: Numerous aquatic organisms, from single cells that are one-hundredth of a millimeter long to large crustaceans such as shrimp and krill, use a common swimming technique known as metachronal paddling. Multiple paddle-like appendages are sequentially rowed in a coordinated, wave-like (i.e., metachronal) rhythm, starting from the rear and progressing to the front of the organism. This limb coordination strategy is utilized by swimmers across a wide range of Reynolds numbers, which suggests that this metachronal rhythm was selected for its optimality of swimming performance. Using a computational fluid dynamics model based on the immersed boundary method with prescribed motion, we find that metachronal propulsion with an approximate quarter-period phase difference between neighboring paddles in a back-to-front wave is the most efficient coordination pattern among all possible phase differences. We also show that this frequency-invariant stroke pattern is the most effective and mechanically efficient paddling rhythm for a wide range of Reynolds numbers. While the optimal paddling rhythm is conserved across Reynolds number, organisms that swim at different Reynolds numbers show differences in the number of paddles, shape of the paddles, and paddle kinematics.  We develop a 3D computational model of a free swimmer and vary the paddle width and Reynolds number. Our results show that narrow paddles are more efficient at low Re, while at higher Re, we observed wider paddles were more efficient. Finally, our previous models considered sinusoidal paddling strokes with a constant phase difference between paddles.  To explore other possible paddling rhythms we apply reinforcement learning to a swimmer at zero Reynolds number. At tight spacing, a back-to-front metachronal wave-like stroke emerges which resembles the commonly observed biological rhythm, but at wide spacing, different limb coordinations are selected. Across all resulting strokes, the fastest stroke is dependent on the number of paddles; however, the most efficient stroke is a back-to-front wave-like stroke regardless of the number of paddles.