Evaluation of linear and non-linear activation dynamics models for insect muscle.

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.

Motor inhibition affects the speed but not accuracy of aimed limb movements in an insect.

When reaching toward a target, human subjects use slower movements to achieve higher accuracy, and this can be accompanied by increased limb impedance (stiffness, viscosity) that stabilizes movements against motor noise and external perturbation. In arthropods, the activity of common inhibitory motor neurons influences limb impedance, so we hypothesized that this might provide a mechanism for speed and accuracy control of aimed movements in insects. We recorded simultaneously from excitatory leg motor neurons and from an identified common inhibitory motor neuron (CI1) in locusts that performed natural aimed scratching movements. We related limb movement kinematics to recorded motor activity and demonstrate that imposed alterations in the activity of CI1 influenced these kinematics. We manipulated the activity of CI1 by injecting depolarizing or hyperpolarizing current or killing the cell using laser photoablation. Naturally higher levels of inhibitory activity accompanied faster movements. Experimentally biasing the firing rate downward, or stopping firing completely, led to slower movements mediated by changes at several joints of the limb. Despite this, we found no effect on overall movement accuracy. We conclude that inhibitory modulation of joint stiffness has effects across most of the working range of the insect limb, with a pronounced effect on the overall velocity of natural movements independent of their accuracy. Passive joint forces that are greatest at extreme joint angles may enhance accuracy and are not affected by motor inhibition.