Modelling the firing pattern of bullfrog vestibular neurons responding to naturalistic stimuli

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.

Semicircular canal biomechanics in health and disease

The semicircular canals are responsible for sensing angular head motion in three-dimensional space and for providing neural inputs to the central nervous system (CNS) essential for agile mobility, stable vision, and autonomic control of the cardiovascular and other gravity-sensitive systems. Sensation relies on fluid mechanics within the labyrinth to selectively convert angular head acceleration into sensory hair bundle displacements in each of three inner ear sensory organs. Canal afferent neurons encode the direction and time course of head movements over a broad range of movement frequencies and amplitudes. Disorders altering canal mechanics result in pathological inputs to the CNS, often leading to debilitating symptoms. Vestibular disorders and conditions with mechanical substrates include benign paroxysmal positional nystagmus, direction-changing positional nystagmus, alcohol positional nystagmus, caloric nystagmus, Tullio phenomena, and others. Here, the mechanics of angular motion transduction and how it contributes to neural encoding by the semicircular canals is reviewed in both health and disease.

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.

Direction discrimination thresholds of vestibular and cerebellar nuclei neurons

To understand the roles of the vestibular system in perceptual detection and discrimination of self-motion, it is critical to account for response variability in computing the sensitivity of vestibular neurons. Here we study responses of neurons with no eye movement sensitivity in the vestibular (VN) and rostral fastigial nuclei (FN) using high-frequency (2 Hz) oscillatory translational motion stimuli. The axis of translation (i.e., heading) varied slowly (1 degrees /s) in the horizontal plane as the animal was translated back and forth. Signal detection theory was used to compute the threshold sensitivity of VN/FN neurons for discriminating small variations in heading around all possible directions of translation. Across the population, minimum heading discrimination thresholds averaged 16.6 degrees +/- 1 degrees SE for FN neurons and 15.3 degrees +/- 2.2 degrees SE for VN neurons, severalfold larger than perceptual thresholds for heading discrimination. In line with previous studies and theoretical predictions, maximum discriminability was observed for directions where firing rate changed steeply as a function of heading, which occurs at headings approximately perpendicular to the maximum response direction. Forward/backward heading thresholds tended to be lower than lateral motion thresholds, and the ratio of lateral over forward heading thresholds averaged 2.2 +/- 6.1 (geometric mean +/- SD) for FN neurons and 1.1 +/- 4.4 for VN neurons. Our findings suggest that substantial pooling and/or selective decoding of vestibular signals from the vestibular and deep cerebellar nuclei may be important components of further processing. Such a characterization of neural sensitivity is critical for understanding how early stages of vestibular processing limit behavioral performance.

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.

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.

Optimal firing rate estimation

We define a measure for evaluating the quality of a predictive model of the behavior of a spiking neuron. This measure, information gain per spike (Is), indicates how much more information is provided by the model than if the prediction were made by specifying the neuron's average firing rate over the same time period. We apply a maximum Is criterion to optimize the performance of Gaussian smoothing filters for estimating neural firing rates. With data from bullfrog vestibular semicircular canal neurons and data from simulated integrate-and-fire neurons, the optimal bandwidth for firing rate estimation is typically similar to the average firing rate. Precise timing and average rate models are limiting cases that perform poorly. We estimate that bullfrog semicircular canal sensory neurons transmit in the order of 1 bit of stimulus-related information per spike.

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

Receptive fields are commonly used to describe spatial characteristics of sensory neuron responses. They can be extended to characterize temporal or dynamical aspects by mapping neural responses in dynamical state spaces. The state-space receptive field of a neuron is the probability distribution of the dynamical state of the stimulus-generating system conditioned upon the occurrence of a spike. We have computed state-space receptive fields for semicircular canal afferent neurons in the bullfrog (Rana catesbeiana). We recorded spike times during broad-band Gaussian noise rotational velocity stimuli, computed the frequency distribution of head states at spike times, and normalized these to obtain conditional pdfs for the state. These state-space receptive fields quantify what the brain can deduce about the dynamical state of the head when a single spike arrives from the periphery.