Losing the battle but winning the war: game theoretic analysis of the competition between motoneurons innervating a skeletal muscle

A neural algorithm for computing bipartite matchings

Finding optimal bipartite matchings-e.g., matching medical students to hospitals for residency, items to buyers in an auction, or papers to reviewers for peer review-is a fundamental combinatorial optimization problem. We found a distributed algorithm for computing matchings by studying the development of the neuromuscular circuit. The neuromuscular circuit can be viewed as a bipartite graph formed between motor neurons and muscle fibers. In newborn animals, neurons and fibers are densely connected, but after development, each fiber is typically matched (i.e., connected) to exactly one neuron. We cast this synaptic pruning process as a distributed matching (or assignment) algorithm, where motor neurons "compete" with each other to "win" muscle fibers. We show that this algorithm is simple to implement, theoretically sound, and effective in practice when evaluated on real-world bipartite matching problems. Thus, insights from the development of neural circuits can inform the design of algorithms for fundamental computational problems.

Potassium currents dynamically set the recruitment and firing properties of F-type motoneurons in neonatal mice

In neonatal mice, fast- and slow-type motoneurons display different patterns of discharge. In response to a long liminal current pulse, the discharge is delayed up to several seconds in fast-type motoneurons and their firing frequency accelerates. In contrast, slow-type motoneurons discharge immediately, and their firing frequency decreases at the beginning of the pulse. Here, we identify the ionic currents that underlie the delayed firing of fast-type motoneurons. We find that the firing delay is caused by a combination of an A-like potassium current that transiently suppresses firing on a short time scale and a slowly-inactivating potassium current that inhibits the discharge over a much longer time scale. We then show how these intrinsic currents dynamically shape the discharge threshold and the frequency-input function of fast-type motoneurons. These currents contribute to the orderly recruitment of motoneurons in neonates and might play a role in the postnatal maturation of motor units.