Speed-invariant encoding of looming object distance requires power law spike rate adaptation Stephen E. Clarkea,1, Richard Naudb, André Longtina,b, and Leonard Malera Departments of aCellular and Molecular Medicine and bPhysics, University of Ottawa, Ottawa, ON, Canada K1H 8M5 Edited by Terrence J. Sejnowski, Salk Institute for Biological Studies, La Jolla, CA, and approved June 28, 2013 (received for review April 5, 2013) Neural representations of a moving object’s distance and approach Looming stimuli are obviously important for survival and are speed are essential for determining appropriate orienting responses, processed by CNS networks of both invertebrates (4) and verte- such as those observed in the localization behaviors of the weakly brates (5). During environmental navigation, looming motion electric fish, Apteronotus leptorhynchus. We demonstrate that a forms a basic component of the electrosensory signals experienced power law form of spike rate adaptation transforms an electrorecep- by Apteronotus leptorhynchus, particularly during prey capture (6, tor afferent’s response to “looming” object motion, effectively pars- 7). As an object draws near the body, its presence is sensed by the ing information about distance and approach speed into distinct fish as a perturbation to a self-generated electric field, whose measures of the firing rate. Neurons with dynamics characterized amplitude drives the activity of ∼16,000 cutaneous electrore- by fixed time scales are shown to confound estimates of object ceptors (8). An approaching object, whose electric conductivity distance and speed. Conversely, power law adaptation modifies is greater than that of the surrounding water, causes the electric an electroreceptor afferent’s response according to the time scales potential to rise locally (Fig. 1A) and evokes increases in the present in the stimulus, generating a rate code for looming object discharge rate of the electroreceptor afferents. Previous work has distance that is invariant to speed and acceleration. Consequently, carefully detailed the change in transdermal electric potential as estimates of both object distance and approach speed can be a function of object distance (9). Following this protocol, we uniquely determined from an electroreceptor afferent’s firing implanted a transdermal recording dipole on an immobilized fish rate, a multiplexed neural code operating over the extended and moved a brass sphere at constant speeds along the lateral axis, time scales associated with behaviorally relevant stimuli. toward the dipole center. Fig. 1B shows data obtained from the recording dipole with an overlay of the expected change in electric NEUROSCIENCE spike frequency adaptation | perceptual invariance | potential according to an empirically derived relationship (9). sensory transformations | neural coding Using this model, we generated mimic looming signals corre- sponding to object approach for 6 cm along the lateral axis at etermining how nervous systems maintain perceptual in- speeds ranging from 0.5 to 5 cm/s. These signals were used as input Dvariance in the face of multifeatured sensory input is a general for spike rate adaptation models and as looming stimuli while problem when attempting to connect sensory physiology to high- recording in vivo from electroreceptor afferents. level perception. For instance, spatial parameters, such as an Results object’s size, distance, and orientation, are inextricably confounded Speed-Invariant Coding of Object Distance. We recorded from 24 in sensory images projected onto the retina (1). This becomes an electroreceptor afferents (seven fish) whose range of spontane- even more acute problem for the encoding of dynamic stimuli ous firing rates (100–400 Hz) was similar to that previously (1); when presented with a temporally modulated visual stimulus, reported (3). Although a function of object distance as expected, retinal ganglion cells are sensitive to as many as six different Fig. 2A demonstrates the remarkable fact that the firing rate of features of the input (2). In its most reduced form, a generic an electroreceptor afferent is practically independent of ap- neuron’s conversion of input current into membrane potential is SI Text SI Text proach speed (regardless of object size; ). In the absence characterized by a membrane time constant ( ). A single of stimulation, fluctuations in electroreceptor afferent firing rate response time constant endows a neuron with the ability to en- are normally distributed and thought to represent intrinsic noise fi code variations in stimulus intensity faithfully over one speci c (10, 11). Illustrated in the context of this variability, Fig. 2B time scale. Because naturalistic stimuli can vary over a wide shows the largest difference in firing rate between the looming range of time scales, there will be inevitable mismatches between speed responses of Fig. 2A, plotted as a function of distance. the rate at which the stimulus intensity changes and the temporal These small discrepancies in rate are clearly insignificant because dynamics that define a neuron’s response. Therefore, during they are masked by the inherent fluctuations in spiking activity. sensation, neurons may be highly sensitive to both stimulus in- Furthermore, speed-induced variations to a distance rate code tensity and the time course over which it evolves. This introduces are negligible compared with the high firing rates over which the ambiguity into the estimation of stimulus features from a neuron’s electrosensory afferents operate (3). At each point along the firing rate and presents a further challenge for understanding lateral axis, Fig. 2C shows the maximum differences from Fig. 2B how neural systems maintain perceptual invariance. plotted as a percent error of the averaged firing rate for that given An object moving toward an animal provides a concrete ex- distance. This measure of rate code corruption was determined for ample of such a problem because two variables of interest, the object’s distance and approach speed, are both expected to influence the firing rate of a primary sensory neuron. These Author contributions: S.E.C. and L.M. designed research; S.E.C. performed all experiments “looming” stimuli arise commonly in many sensory systems, and model simulations. S.E.C., R.N., and A.L. worked on the analysis of speed and accel- eration dependency for the models of exponential and power law adaptation; S.E.C. including the electrosense, and appear to pose the same rate- analyzed data; S.E.C., R.N., A.L., and L.M. provided input on the design of the figures, coding dilemma for the electroreceptor afferents, whose firing which were made by S.E.C.; and S.E.C., A.L., and L.M. wrote the paper. rate has previously been described as sensitive to both stimulus The authors declare no conflict of interest. intensity and its temporal derivative (3). By studying responses of This article is a PNAS Direct Submission. the electroreceptor afferents to this natural problem of distance 1To whom correspondence should be addressed. E-mail: [email protected]. perception, we identify a mechanism for the temporal disam- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. biguation of stimulus intensity from a neuron’s firing rate. 1073/pnas.1306428110/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1306428110 PNAS Early Edition | 1of6 Downloaded by guest on September 28, 2021 A B form of adaptation (10). Previous experiments and modeling studies have shown that the time constant of exponential adap- tation is very short (≈10 ms) and can successfully account for spontaneous interspike-interval correlations, as well as responses to constant intensity stimuli and high-frequency communication signals (10, 14, 26). However, when processing looming signals, such rapid adaptation is not well suited for accurate distance estimation (SI Text). In fact, regardless of the choice of time constant, the exponential adaptation model’s firing rate is a function of both object distance and approach speed, confound- ing estimates of these values (SI Text). In this case, a decoder of firing rate must extract information about both the spatial and temporal features of a moving object from a scalar value, a A Fig. 1. Object distance and the electrosense. (A) Model plot of the electric potential (measured in millivolts) produced by the self-generated electric field of A. leptorhynchus. The presence of conducting objects, such as this brass sphere (r = 0.635 cm), causes a local increase in the electric potential, as measured with a transdermal recording dipole (white dots). Natural exam- ples of relative conductors include aquatic plants, predators, and prey. (B) Recorded stimulus-induced change in transdermal potential (blue) is plotted as a function of the brass sphere’s lateral distance. The overlying red curve is the change in potential predicted by a previously existing model (9). Signals of this form are considered in the following figures. all 24 cells in response to the looming stimuli, and an average error was computed. This global error measure showed no sig- nificant trend as a function of distance (SI Text); therefore, we calculated a total average of 0.98%. At a distance of 6.25 cm from the fish’s skin, the brass sphere from Fig. 1 causes a change in transdermal potential of 0.15 μV, a signal weaker than the limit of B behavioral detection (12). The percent error measured at this point is not significantly different from when the sphere is 0.25 cm away, causing a change in transdermal potential of 350 μV. This confirms that minute discrepancies in firing rate, introduced by approach speed, are no more deleterious for a distance rate code than endogenous noise acting in the absence of stimulation. Speed Invariance Arises from Power Law Adaptation. The electro- receptor afferents are not passive rate coders and show strong C spike rate adaptation in response to sustained stimulation (13, 14). Spike rate, or spike frequency adaptation (SFA), is a ubiquitous and conserved feature of neural processing, which has been well documented in systems ranging from invertebrate sensory neu- rons to mammalian cortex (15, 16).