Abstract:

Game theory is usually applied to biology through evolutionary games. However, many competitive processes in biology may be better understood by analyzing them on a shorter time-scale than the time-course considered in evolutionary dynamics. Instead of the change in the "fitness" of a player, which is the traditional payoff in evolutionary games, we define the payoff function, tailored to the specific questions addressed. In this work we analyze the developmental competition that arises between motoneurons innervating the same muscle. The "size principle" - a fundamental principle in the organization of the motor system, stating that motoneurons with successively higher activation-threshold innervate successively larger portions of the muscle - emerges as a result of this competition. We define a game, in which motoneurons compete to innervate a maximal number of muscle-fibers. The strategies of the motoneurons are their activation-thresholds. By using a game theoretical approach we succeed to explain the emergence of the size principle and to reconcile seemingly contradictory experimental data on this issue. The evolutionary advantage of properties as the size principle, emerging as a consequence of competition rather than being genetically hardwired, is that it endows the system with adaptation capabilities, such that the outcome may be fine-tuned to fit the environment. In accordance with this idea the present study provides several experimentally-testable predictions regarding the magnitude of the size principle in different muscles.

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