State-space receptive fields of semicircular canal afferent neurons in the bullfrog

Models of vestibular semicircular canal afferent neuron firing activity

Semicircular canal afferent neurons transmit information about head rotation to the brain. Mathematical models of how they do this have coevolved with concepts of how brains perceive the world. A 19th-century "camera" metaphor, in which sensory neurons project an image of the world captured by sense organs into the brain, gave way to a 20th-century view of sensory nerves as communication channels providing inputs to dynamical control systems. Now, in the 21st century, brains are being modeled as Bayesian observers who infer what is happening in the world given noisy, incomplete, and distorted sense data. The semicircular canals of the vestibular apparatus provide an experimentally accessible, low-dimensional system for developing and testing dynamical Bayesian generative models of sense data. In this review, we summarize advances in mathematical modeling of information transmission by semicircular canal afferent sensory neurons since the first such model was proposed nearly a century ago. Models of information transmission by vestibular afferent neurons may provide a foundation for developing realistic models of how brains perceive the world by inferring the causes of sense data.

Predation and the origin of neurones

The core design of spiking neurones is remarkably similar throughout the animal kingdom. Their basic function as fast-signalling thresholding cells might have been established very early in their evolutionary history. Identifying the selection pressures that drove animals to evolve spiking neurones could help us interpret their design and function today. We review fossil, ecological and molecular evidence to investigate when and why animals evolved spiking neurones. Fossils suggest that animals evolved nervous systems soon after the advent of animal-on-animal predation, 550 million years ago (MYa). Between 550 and 525 MYa, we see the first fossil appearances of many animal innovations, including eyes. Animal behavioural complexity increased during this period as well, as evidenced by their traces, suggesting that nervous systems were an innovation of that time. Fossils further suggest that, before 550 MYa, animals were either filter feeders or microbial mat grazers. Extant sponges and Trichoplax perform these tasks using energetically cheaper alternatives than spiking neurones. Genetic evidence testifies that nervous systems evolved before the protostome-deuterostome split. It is less clear whether nervous systems evolved before the cnidarian-bilaterian split, so cnidarians and bilaterians might have evolved their nervous systems independently. The fossil record indicates that the advent of predation could fit into the window of time between those two splits, though molecular clock studies dispute this claim. Collectively, these lines of evidence indicate that animals evolved spiking neurones soon after they started eating each other. The first sensory neurones could have been threshold detectors that spiked in response to other animals in their proximity, alerting them to perform precisely timed actions, such as striking or fleeing.

Detection thresholds of macaque otolith afferents

The vestibular system is our sixth sense and is important for spatial perception functions, yet the sensory detection and discrimination properties of vestibular neurons remain relatively unexplored. Here we have used signal detection theory to measure detection thresholds of otolith afferents using 1 Hz linear accelerations delivered along three cardinal axes. Direction detection thresholds were measured by comparing mean firing rates centered on response peak and trough (full-cycle thresholds) or by comparing peak/trough firing rates with spontaneous activity (half-cycle thresholds). Thresholds were similar for utricular and saccular afferents, as well as for lateral, fore/aft, and vertical motion directions. When computed along the preferred direction, full-cycle direction detection thresholds were 7.54 and 3.01 cm/s(2) for regular and irregular firing otolith afferents, respectively. Half-cycle thresholds were approximately double, with excitatory thresholds being half as large as inhibitory thresholds. The variability in threshold among afferents was directly related to neuronal gain and did not depend on spike count variance. The exact threshold values depended on both the time window used for spike count analysis and the filtering method used to calculate mean firing rate, although differences between regular and irregular afferent thresholds were independent of analysis parameters. The fact that minimum thresholds measured in macaque otolith afferents are of the same order of magnitude as human behavioral thresholds suggests that the vestibular periphery might determine the limit on our ability to detect or discriminate small differences in head movement, with little noise added during downstream processing.

Using hardware models to quantify sensory data acquisition across the rat vibrissal array

Our laboratory investigates how animals acquire sensory data to understand the neural computations that permit complex sensorimotor behaviors. We use the rat whisker system as a model to study active tactile sensing; our aim is to quantitatively describe the spatiotemporal structure of incoming sensory information to place constraints on subsequent neural encoding and processing. In the first part of this paper we describe the steps in the development of a hardware model (a 'sensobot') of the rat whisker array that can perform object feature extraction. We show how this model provides insights into the neurophysiology and behavior of the real animal. In the second part of this paper, we suggest that sensory data acquisition across the whisker array can be quantified using the complete derivative. We use the example of wall-following behavior to illustrate that computing the appropriate spatial gradients across a sensor array would enable an animal or mobile robot to predict the sensory data that will be acquired at the next time step.

Biomechanical models for radial distance determination by the rat vibrissal system

Rats use active, rhythmic movements of their whiskers to acquire tactile information about three-dimensional object features. There are no receptors along the length of the whisker; therefore all tactile information must be mechanically transduced back to receptors at the whisker base. This raises the question: how might the rat determine the radial contact position of an object along the whisker? We developed two complementary biomechanical models that show that the rat could determine radial object distance by monitoring the rate of change of moment (or equivalently, the rate of change of curvature) at the whisker base. The first model is used to explore the effects of taper and inherent whisker curvature on whisker deformation and used to predict the shapes of real rat whiskers during deflections at different radial distances. Predicted shapes closely matched experimental measurements. The second model describes the relationship between radial object distance and the rate of change of moment at the base of a tapered, inherently curved whisker. Together, these models can account for recent recordings showing that some trigeminal ganglion (Vg) neurons encode closer radial distances with increased firing rates. The models also suggest that four and only four physical variables at the whisker base -- angular position, angular velocity, moment, and rate of change of moment -- are needed to describe the dynamic state of a whisker. We interpret these results in the context of our evolving hypothesis that neural responses in Vg can be represented using a state-encoding scheme that includes combinations of these four variables.

Evolution of the cerebellum as a neuronal machine for Bayesian state estimation

The cerebellum evolved in association with the electric sense and vestibular sense of the earliest vertebrates. Accurate information provided by these sensory systems would have been essential for precise control of orienting behavior in predation. A simple model shows that individual spikes in electrosensory primary afferent neurons can be interpreted as measurements of prey location. Using this result, I construct a computational neural model in which the spatial distribution of spikes in a secondary electrosensory map forms a Monte Carlo approximation to the Bayesian posterior distribution of prey locations given the sense data. The neural circuit that emerges naturally to perform this task resembles the cerebellar-like hindbrain electrosensory filtering circuitry of sharks and other electrosensory vertebrates. The optimal filtering mechanism can be extended to handle dynamical targets observed from a dynamical platform; that is, to construct an optimal dynamical state estimator using spiking neurons. This may provide a generic model of cerebellar computation. Vertebrate motion-sensing neurons have specific fractional-order dynamical characteristics that allow Bayesian state estimators to be implemented elegantly and efficiently, using simple operations with asynchronous pulses, i.e. spikes. The computational neural models described in this paper represent a novel kind of particle filter, using spikes as particles. The models are specific and make testable predictions about computational mechanisms in cerebellar circuitry, while providing a plausible explanation of cerebellar contributions to aspects of motor control, perception and cognition.

Dynamics and the single spike

Responses of vestibular primary afferent neurons to head rotation exhibit fractional-order dynamics. As a consequence, the head tends to be in a localized region of its state-space at spike times of a particular neuron during arbitrary head movements, and single spikes can be interpreted as state measurements. We are developing a model of neural computations underlying trajectory prediction and control tasks, based on this experimental observation. This is a step toward a formal neural calculus in which single spikes are modeled realistically as the operands of neural computation.

Second-Order Vestibular Neurons Form Separate Populations With Different Membrane and Discharge Properties

Membrane and discharge properties were determined in second-order vestibular neurons (2°VN) in the isolated brain of grass frogs. 2°VN were identified by monosynaptic excitatory postsynaptic potentials after separate electrical stimulation of the utricular nerve, the lagenar nerve, or individual semicircular canal nerves. 2°VN were classified as vestibulo-ocular or -spinal neurons by the presence of antidromic spikes evoked by electrical stimulation of the spinal cord or the oculomotor nuclei. Differences in passive membrane properties, spike shape, and discharge pattern in response to current steps and ramp-like currents allowed a differentiation of frog 2°VN into two separate, nonoverlapping types of vestibular neurons. A larger subgroup of 2°VN (78%) was characterized by brief, high-frequency bursts of up to five spikes and the absence of a subsequent continuous discharge in response to positive current steps. In contrast, the smaller subgroup of 2°VN (22%) exhibited a continuous discharge with moderate adaptation in response to positive current steps. The differences in the evoked spike discharge pattern were paralleled by differences in passive membrane properties and spike shapes. Despite these differences in membrane properties, both types, i.e., phasic and tonic 2°VN, occupied similar anatomical locations and displayed similar afferent and efferent connectivities. Differences in response dynamics of the two types of 2°VN match those of their pre- and postsynaptic neurons. The existence of distinct populations of 2°VN that differ in response dynamics but not in the spatial organization of their afferent inputs and efferent connectivity to motor targets suggests that frog 2°VN form one part of parallel vestibulomotor pathways.