Vertebrates and arthropods are both capable of load compensation during aimed limb movements, such as reaching and grooming. We measured the kinematics and activity of individual motoneurons in loaded and unloaded leg movements in an insect. To evaluate the role of active and passive musculoskeletal properties in aiming and load compensation, we used a neuromechanical model of the femur-tibia joint that transformed measured extensor and flexor motoneuron spikes into joint kinematics. The model comprises three steps: first, an activation dynamics module that determines the time course of isometric force; second, a pair of antagonistic muscle models that determine the joint torque; and third, a forward dynamics simulation that calculates the movement of the limb. The muscles were modeled in five variants, differing in the presence or absence of force-length-velocity characteristics of the contractile element, a parallel passive elastic element, and passive joint damping. Each variant was optimized to yield the best simulation of measured behavior.Passive muscle force and viscous joint damping were sufficient and necessary to simulate the observed movements. Elastic or damping properties of the active contractile element could not replace passive elements. Passive elastic forces were similar in magnitude to active forces caused by muscle contraction, generating substantial joint stiffness. Antagonistic muscles co-contract, although there was no motoneuronal coactivation, because of slow dynamics of muscle activation. We quantified how co-contraction simplified load compensation by demonstrating that a small variation of the motoneuronal input caused a large change in joint torque.

Limb movements that are aimed toward tactile stimuli of the body provide a powerful paradigm with which to study the transformation of motor activity into context-dependent action. We relate the activity of excitatory motor neurons of the locust femoro-tibial joint to the consequent kinematics of hind leg movements made during aimed scratching. There is posture-dependence of motor neuron activity, which is stronger in large amplitude (putative fast) than in small (putative slow and intermediate) motor neurons. We relate this posture dependency to biomechanical aspects of the musculo-skeletal system and explain the occurrence of passive tibial movements that occur in the absence of agonistic motor activity. There is little recorded co-activation of antagonistic tibial extensor and flexor motor neurons, and there is differential recruitment of proximal and distal flexor motor neurons. Large-amplitude motor neurons are often recruited soon after a switch in joint movement direction. Motor bursts containing large-amplitude spikes exhibit high spike rates of smallamplitude motor neurons. The fast extensor tibiae neuron, when recruited, exhibits a pattern of activity quite different to that seen during kicking, jumping, or righting: there is no co-activation of flexor motor neurons and no full tibial flexion. Changes in femorotibial joint angle and angular velocity are most strongly dependent on variations in the number of motor neuron spikes and the duration of motor bursts rather than on firing frequency. Our data demonstrate how aimed scratching movements result from interactions between biomechanical features of the musculo-skeletal system and patterns of motor neuron recruitment.

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In computational modelling of sensory-motor control, the dynamics of muscle contraction is an important determinant of movement timing and joint stiffness. This is particularly so in animals with many slow muscles, as is the case in insects—many of which are important models for sensory-motor control. A muscle model is generally used to transform motoneuronal input into muscle force. Although standard models exist for vertebrate muscle innervated by many motoneurons, there is no agreement on a parametric model for single motoneuron stimulation of invertebrate muscle. Although several different models have been proposed, they have never been evaluated using a common experimental data set. We evaluate five models for isometric force production of a well-studied model system: the locust hind leg tibial extensor muscle. The response of this muscle to motoneuron spikes is best modelled as a non-linear low-pass system. Linear first-order models can approximate isometric force time courses well at high spike rates, but they cannot account for appropriate force time courses at low spike rates. A linear third-order model performs better, but only non-linear models can account for frequency-dependent change of decay time and force potentiation at intermediate stimulus frequencies. Some of the differences among published models are due to differences among experimental data sets. We developed a comprehensive toolbox for modelling muscle activation dynamics, and optimised model parameters using one data set. The “Hatze-Zakotnik model” that emphasizes an accurate single-twitch time course and uses frequency-dependent modulation of the twitch for force potentiation performs best for the slow motoneuron. Frequency-dependent modulation of a single twitch works less well for the fast motoneuron. The non-linear “Wilson” model that optimises parameters to all data set parts simultaneously performs better here. Our open-access toolbox provides powerful tools for researchers to fit appropriate models to a range of insect muscles.

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