TY - JOUR T1 - Analytical solution of a bilateral Brown-type central pattern generator for symmetric and asymmetric locomotion JF - bioRxiv DO - 10.1101/146993 SP - 146993 AU - Anton Sobinov AU - Sergiy Yakovenko Y1 - 2017/01/01 UR - http://biorxiv.org/content/early/2017/06/07/146993.abstract N2 - The coordinated activity of muscles is produced in part by spinal rhythmogenic neural circuits termed the central pattern generators (CPGs). A classical CPG model proposed conceptually by T.G. Brown in 1911 is a system of coupled oscillators transforming locomotor drive into coordinated and gait-specific patterns of muscle recruitment. A system of ordinary differential equations with physiologically inspired coupling locus of interactions captures the timing relationship for the bilateral coordination of limbs in locomotion and is typically solved numerically. Consequently, it is intriguing to have a full analytical description of this plausible CPG architecture to illuminate the functionality within this structure. Here, we provided a closed form analytical solution contrasted against the previous numerical method. The computational load of the analytical solution was decreased by an order of magnitude compared to the comparable numerical approach (with relative errors <0.01%). The analytical solution tested and supported the previous finding that the input to the model can be expressed in the units of the desired limb locomotor speed. Furthermore, we performed the parametric sensitivity analysis in the context of controlling asymmetric locomotion and documented two possible mechanisms associated either with an external drive or the intrinsic CPG parameters. The results support the idea that many different combinations of network states even within the same anatomical structure of CPG may generate the same behavioral outcomes.Author Summary Using a simple process of leaky integration, we have developed an analytical solution to a robust model of the spinal pattern generation. We have analyzed the ability of this neural element to exert locomotor control with the signal associated with limb speeds, which represent high-level modality within the motor system. Furthermore, we tested the ability of this simple structure to embed the steering control using the velocity signal in model’s inputs or within the internal connectivity of its elements. Both mechanisms can produce the same behavioral outcome, which points to the methodological challenges of modeling CPGs and demonstrates the possibility of spinal circuit adaptations to asymmetric short- or long-term conditions in health and disease. ER -