A dynamical system-Markov model for active postsynaptic responses of muscle spindle afferent nerve

Abstract

Motoneuron is the control unit of skeletal muscles, and the dynamic frequency-regulating feedback from the afferent nerve of receptors like muscle spindles forms the physical basis of its closed-loop regulation. Focused on the synapses of muscle spindle afferents, this paper established a dynamical system-Markov model starting from presynaptic stimulations to postsynaptic responses, and further verified the model via comparisons between theoretical results and relevant experimental data. With the purpose of describing the active features of dendritic membrane, we employed the methods of dynamical systems rather than the traditional passive cable theory, and identified the physical meaning of parameters involved. For the dynamic behavior of postsynaptic currents, we adopted simplified Markov models so that the analytical solutions for the open dynamics of postsynaptic receptors can be obtained. The model in this paper is capable of simulating the actual non-uniformity of channel density, and is suitable for complex finite element analysis of neurons; thus it facilitates the exploration of the frequency-regulating feedback and control mechanisms of motoneurons. The operation of skeletal muscle is a typically bioelectrochemical closed-loop control process, which is regulated by the action potential (AP) fired by motoneurons. The contraction length/speed and tension of the muscle are fed back by the afferent nerves of muscle spindles and tendon organs within it, and these signals are simultaneously transmitted to the central nervous system (CNS) and the motoneuron itself [1-3]. As an important receptor, the muscle spindle is equivalent to the displacement/speed transducer of skeletal muscle, as the real-time firing rate of its afferent nerves (I a afferents) varies with the length and contraction speed of the muscle. We have proposed the bioelectrochemical frequency-regulating control mechanism for skeletal muscle based on the characteristics of the APs on muscle fibers [4], i.e. the working process of muscle is regulated by the frequency of AP in real time. The afferent signals influence the firing behavior of motoneurons, and thus the feedback of a muscle spindle to the motoneuron forms a local closed loop, which is pivotal to the stability of muscle operation. The researches on the working mechanism of skeletal muscle have lasted for many decades, while the regulation and control mechanisms of muscle are seldom touched; therefore our understanding of the control principium is far from satisfactory. On the other hand, in order to explore the closedloop control properties, the key point is to take extensive researches on the feedback effects of the afferents, and this involves the synaptic transmission between I a afferents and motoneurons.Motoneurons are myelinated neurons with their dendrites and somas located in the spinal cord [5]. The signals of muscle spindles are excitatory afferents, whose terminals extend into the spinal cord and are connected with the dendritic shafts or spines of motoneurons, and the den...

A Highly Efficient Semiphenomenological Model of a Half-Sarcomere for Real-Time Prediction of Mechanical Behavior

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