A spiking neural network model for proprioception of limb kinematics in insect locomotion

Abstract

Proprioception plays a key role in all behaviours that involve the control of force, posture or movement. Computationally, many proprioceptive afferents share three common features: First, their strictly local encoding of stimulus magnitudes leads to range fractionation in sensory arrays. As a result, encoding of large joint angle ranges requires integration of convergent afferent information by first-order interneurons. Second, their phasic-tonic response properties lead to fractional encoding of the fundamental sensory magnitude and its derivatives (e.g., joint angle and angular velocity). Third, the distribution of disjunct sensory arrays across the body accounts for distributed encoding of complex movements, e.g., at multiple joints or by multiple limbs. The present study models the distributed encoding of limb kinematics, proposing a multi-layer spiking neural network for distributed computation of whole-body posture and movement. Spiking neuron models are biologically plausible because they link the sub-threshold state of neurons to the timing of spike events. The encoding properties of each network layer are evaluated with experimental data on whole-body kinematics of unrestrained walking and climbing stick insects, comprising concurrent joint angle time courses of 6 x 3 leg joints. The first part of the study models strictly local, phasic-tonic encoding of joint angle by proprioceptive hair field afferents by use of Adaptive Exponential Integrate-and-Fire neurons. Convergent afferent information is then integrated by two types of first-order interneurons, modelled as Leaky Integrate-and-Fire neurons, tuned to encode either joint position or velocity across the entire working range with high accuracy. As in known velocity-encoding antennal mechanosensory interneurons, spike rate increases linearly with angular velocity. Building on distributed position/velocity encoding, the second part of the study introduces second- and third-order interneurons. We demonstrate that simple combinations of two or three position/velocity inputs from disjunct arrays can encode high-order movement information about step cycle phases and converge to encode overall body posture. Author summaryWhen stick insects climb through a bramble bush at night, they successfully navigate through highly complex terrain with little more sensory information than touch and proprioception of their own body posture and movement. To achieve this, their central nervous system needs to monitor the position and motion of all limbs, and infer information about whole-body movement from integration in a multi-layer neural network. Although the encoding properties of some proprioceptive inputs to this network are known, the integration and processing of distributed proprioceptive information is poorly understood. Here, we use a computational model of a spiking neural network to simulate peripheral encoding of 6 x 3 joint angles and angular velocities. The second part of the study explores how higher-order information can be integrated across multiple joints and limbs. For evaluation, we use experimental data from unrestrained walking and climbing stick insects. Spiking neurons model the key response properties known from their real biological counterparts. In particular, we show that the first integration layer of the model is able to encode joint angle and velocity both linearly and accurately from an array of phasic-tonic input elements. The model is simple, accurate and based, where possible, on biological evidence.