Department of Industrial Engineering and Management, Jerusalem College of Technology Jerusalem, Israel.
Front Comput Neurosci. 2012 Mar 30;6:16. doi: 10.3389/fncom.2012.00016. eCollection 2012.
The fibers in a skeletal muscle are divided into groups called "muscle units" whereby each muscle unit is innervated by a single neuron. It was found that neurons with low activation thresholds have smaller muscle units than neurons with higher activation thresholds. This results in a fixed recruitment order of muscle units, from smallest to largest, called the "size principle." It is thought that the size principle results from a competitive process-taking place after birth-between the neurons innervating the muscle. The underlying mechanism of the competition was not understood. Moreover, the results in the majority of experiments that manipulated the activity during the competition period seemed to contradict the size principle. Experiments at the isolated muscle fibers showed that the competition is governed by a Hebbian-like rule, whereby neurons with low activation thresholds have a competitive advantage at any single muscle fiber. Thus neurons with low activation thresholds are expected to have larger muscle units in contradiction to what is seen empirically. This state of affairs was termed "paradoxical." In the present study we developed a new game theoretic framework to analyze such competitive biological processes. In this game, neurons are the players competing to innervate a maximal number of muscle fibers. We showed that in order to innervate more muscle fibers, it is advantageous to win (as the neurons with higher activation thresholds do) later competitions. This both explains the size principle and resolves the seemingly paradoxical experimental data. Our model establishes that the competition at each muscle fiber may indeed be Hebbian and that the size principle still emerges from these competitions as an overall property of the system. Thus, the less active neurons "lose the battle but win the war." Our model provides experimentally testable predictions. The new game-theoretic approach may be applied to competitions in other biological systems.
骨骼肌中的纤维分为称为“肌单位”的群组,其中每个肌单位由单个神经元支配。研究发现,激活阈值较低的神经元比激活阈值较高的神经元具有更小的肌单位。这导致肌单位以从小到大的固定募集顺序,即“大小原则”。据认为,大小原则是由于支配肌肉的神经元之间在出生后发生的竞争过程所致。竞争的潜在机制尚不清楚。此外,在大多数操纵竞争期间活动的实验中得出的结果似乎与大小原则相矛盾。在分离的肌肉纤维实验中,竞争受赫布氏学习规则支配,其中激活阈值较低的神经元在任何单个肌肉纤维中都具有竞争优势。因此,预计激活阈值较低的神经元在肌单位中会更大,这与经验观察到的情况相反。这种情况被称为“矛盾”。在本研究中,我们开发了一种新的博弈论框架来分析这种竞争的生物过程。在这种博弈中,神经元是竞争支配最大数量肌纤维的参与者。我们表明,为了支配更多的肌纤维,获胜(就像具有较高激活阈值的神经元那样)是有利的。这样既解释了大小原则,又解决了看似矛盾的实验数据。我们的模型表明,每个肌纤维上的竞争确实可能是赫布氏的,并且大小原则仍然是作为系统的整体属性从这些竞争中产生的。因此,不活跃的神经元“输掉了战斗但赢得了战争”。我们的模型提供了可进行实验测试的预测。新的博弈论方法可应用于其他生物系统中的竞争。