A method for mapping response fields and determining intrinsic reference frames of single-unit activity: Applied to 3D head-unrestrained gaze shifts

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Abstract

Natural movements towards a target show metric variations between trials. When movements combine contributions from multiple body-parts, such as head-unrestrained gaze shifts involving both eye and head rotation, the individual body-part movements may vary even more than the overall movement. The goal of this investigation was to develop a general method for both mapping sensory or motor response fields of neurons and determining their intrinsic reference frames, where these movement variations are actually utilized rather than avoided. We used head-unrestrained gaze shifts, three-dimensional (3D) geometry, and naturalistic distributions of eye and head orientation to explore the theoretical relationship between the intrinsic reference frame of a sensorimotor neuron's response field and the coherence of the activity when this response field is fitted non-parametrically using different kernel bandwidths in different reference frames. We measure how well the regression surface predicts unfitted data using the PREdictive Sum-of-Squares (PRESS) statistic. The reference frame with the smallest PRESS statistic was categorized as the intrinsic reference frame if the PRESS statistic was significantly larger in other reference frames. We show that the method works best when targets are at regularly spaced positions within the response field's active region, and that the method identifies the best kernel bandwidth for response field estimation. We describe how gain-field effects may be dealt with, and how to test neurons within a population that fall on a continuum between specific reference frames. This method may be applied to any spatially coherent single-unit activity related to sensation and/or movement during naturally varying behaviors.

Introduction

In any goal-directed action the location of the goal in sensory coordinates must be transformed into a motor command in an effector-specific frame (Andersen, 1995, Crawford et al., 2004). The reference frame of the sensory input is that of the part of the body to which the sensor is embedded (i.e., the eye for vision). The movement reference frame is generally the more stable insertion point of a muscle—i.e., the end that moves less when the muscle contracts. So, for example, to use the eyes and head to look toward a visual stimulus, an eye-centered visual signal must be transformed into the appropriate commands for the eye muscles fixed in the head, and the neck muscles fixed to the torso (Klier et al., 2003, Martinez-Trujillo et al., 2004).

These problems are well-defined at the level of ‘black box’ input–output, but it is much less clear which, if any, reference frames are used by individual neurons involved in the intermediate transformations. Some have questioned the validity of the notion that individual neurons encode information in a particular reference frame (Pouget et al., 2002, Scott, 2008). However, the characterization of neural reference frames remains one of our best methods for understanding how the brain encodes space and produces spatial transformations at the level of individual neurons (Stricanne et al., 1996, Klier et al., 2001, Avillac et al., 2005, Mullette-Gillman et al., 2005, Pesaran et al., 2006, Porter et al., 2006, Blohm et al., 2008).

The current paper develops a novel method for determining the intrinsic reference frame of single-unit sensory or motor response fields. In principle this method can be applied to any neural activity that is involved in encoding spatial information, but we have developed the method specifically for the example of the rotation of eyes and head associated with gaze shifts. Most previous studies of intrinsic neural reference frames have used either 1D or 2D approaches to characterizing the response field and varying initial eye position, generally in head-fixed preparations (e.g., Stricanne et al., 1996, Avillac et al., 2005, Porter et al., 2006). These approaches have limitations that motivated our development of the current analytic technique. In particular they (1) cannot distinguish between head- and body- or space-fixed reference frames; (2) do not allow for the coordinated eye and head movements that comprise normal gaze shifts made in head-unrestrained conditions; (3) usually limit eye position between a few discrete positions; (4) do not account for torsional variations in eye and head position that become significant in head-unrestrained conditions; and (5) neither account for, nor allow, the exploration of models related to the non-linear elements of rotation that predominate in the larger range of head-unrestrained gaze shifts.

Another approach to the question of intrinsic reference frames is to electrically stimulate a group of neurons in a given brain area, identifying the reference frame in which the consequent movement response is most coherent across a variety of initial positions. For microstimulation, experimental and analytic techniques have been developed which address some of the above problems—i.e., head-unrestrained 3D recordings have been combined with non-linear 3D analysis and comparison with model simulations (Klier et al., 2001, Martinez-Trujillo et al., 2004, Constantin et al., 2007). These studies have demonstrated the importance of the non-linear 3D components in head-unrestrained conditions. However, stimulation and unit recording provide different, complementary sets of information about the system, especially when 3D geometry requires that the neurons involved in reference frame transformations should show different frames when tested using these two different techniques—i.e., unit recording showing the input frame to the neuron, and stimulation showing the output frame (Smith and Crawford, 2005, Blohm et al., 2008). Thus there remains the problem of developing a complementary technique for single-unit recordings.

Determining the intrinsic reference frame for a neuron is closely linked to the concept of its response field (i.e., its sensory receptive field or movement field). A neuron's receptive field is the region of space in which the presence of a stimulus will change the firing rate activity of the neuron (Hubel and Wiesel, 1959). Similarly, a neuron's movement field is the region of space that contains the movements associated with the neuron's non-background activity (Wurtz, 1969). These concepts are only meaningful when they are defined in some specific reference frame, which compels us to ask what that intrinsic reference frame for a given neuron's response field is. Moreover, in structures like the superior colliculus, where some neurons show sensory properties, some show motor properties, and many show both (Munoz and Wurtz, 1995a, Munoz and Wurtz, 1995b), the mapping of the neuron's receptive and movement fields and the determination of their intrinsic reference frames provide separate pieces of information that are clues to the function of both individual neurons and the overall neural population (Schlag et al., 1980, Pouget et al., 2002, Smith and Crawford, 2005, Blohm et al., 2008). Therefore, we developed a method that is applicable to determining the intrinsic reference frames of both sensory receptive fields and movement fields.

When this method is applied to head-unrestrained conditions, while advantages (such as separation of the head frame from the body/space frame, and more natural behavior) arise, complications do as well. The method common to all approaches for determining the intrinsic reference frame of a neuron's activity has been to measure this activity over widely separated positions in the receptive or movement field while dissociating the possible reference frames. For example, a neuron's activity in response to visual targets at regularly spaced positions can be measured using different initial eye positions, so that the target positions for different trials form a discrete set in both eye and head coordinates (e.g., Stricanne et al., 1996). The underlying assumption (which we support here) is that the response field will be more coherent – i.e., show less variability across trials within spatial positions averaged across all positions – if plotted in the correct (intrinsic) reference frame. Most previous studies have approached this problem by measuring activity repetitively from a small number of initial and final positions, and then using an analytic method that treats position as a discrete quantity. However, this approach is not possible in behaviors such as naturally coordinated head-unrestrained gaze shifts, because any gaze direction in space is naturally produced in successive trials by combining different head and eye-in-head positions (Glenn and Vilis, 1992). Thus, a different analytic method must be used in such conditions—one that treats position as a continuous quantity.

The use of head-unrestrained conditions also results in increased analytic opportunities and problems related to 3D rotation. The most obvious of these relates to torsional rotation of the eye and head around the line of sight. In head-fixed conditions, head torsion does not change and eye torsion is strictly limited by Listing's law (Ferman et al., 1987, Tweed et al., 1990, Tweed and Vilis, 1990). In head-unrestrained conditions, however, head and eye torsion are much more variable, resulting in eye-in-space torsion values as large as 20° (Tweed et al., 1998). As a result, the direction of any space-fixed target will vary in eye coordinates (and nearly as much in head coordinates) for successive trials using a single gaze direction. Moreover, if one does not account for the non-linear aspects of rotation in 3D when performing coordinate transformations on gaze, eye, and head orientations in the head-unrestrained range (for example, if the computation of target in eye coordinates is approximated as a vector subtraction of gaze position from target position in space) then mathematical errors in target direction as large as 90° are possible. Failure to account for these various factors would result in large systematic and variable errors, which would obscure the signal and mislead the experimenter. Fortunately, the necessary experimental techniques and analysis required to account for these rotational aspects in head-unrestrained monkeys are essentially already available (Crawford et al., 1999, Martinez-Trujillo et al., 2004), and allow testing between models that are indistinguishable in linear approximations (Klier et al., 2001).

The goal of the current study was to develop an analytic method by which the response fields of neurons could be mapped and their associated intrinsic reference frames identified, using single-unit recording methods in head-unrestrained monkeys. The method treated gaze, head, and eye positions as continuous variables, and used the correct geometry of 3D rotations in its transformations. Our method was based on the same assumption as that used in previous 1D and 2D head-fixed studies (e.g., Stricanne et al., 1996, Avillac et al., 2005, Porter et al., 2006), namely that a neuron's intrinsic reference frame is the reference frame in which the activity was most coherent at each position when averaged across all positions.

We developed this method for the purpose of analyzing superior colliculus unit activity during head-free gaze shifts (DeSouza et al., 2008), but soon found that we were dealing with a very complex and general set of issues. Hence, the current paper. And although we are already applying this method for use with real data, we develop the method here strictly with the use of simulated data so that we can fully control the test set and compare results with known underlying properties of the model (which cannot be done for experimental situations). We have, however, taken great care to incorporate our years of experience using this experimental paradigm and data into the simulations in order to maintain maximum realism.

We begin by developing a method for determining the spatial coherence of response field activity in different reference frames using non-parametric regression on the neural activity data, and measuring how well the regression surface predicted the unfitted data using the PREdictive Sum-of-Squares (PRESS) statistic. The reference frame with the smallest PRESS statistic was identified as the intrinsic reference frame if the PRESS statistic was significantly larger (determined using the Brown–Forsythe test) in other candidate reference frames. We applied this method to the head-unrestrained gaze-shift paradigm, using the correct geometry of rotations in 3D on all spatial quantities, and considered the question of gain fields, intermediate reference frames, and the combining of data from neuron populations. Allowing for differences in experimental measurements and geometry, the same analytic method could be applied to any neural receptive or movement field data related to the motion of two or more egocentric reference frames during natural behaviors.

Section snippets

The basic approach using non-parametric regression

To develop and test the basic properties of a general method for estimating a neuron's response field and identifying its intrinsic reference frame, we used 1D simulated data before applying the method to realistic simulations using 3D geometry. Fig. 1A shows a simulated neuron's 1D visual response field (black dashed curve) defined in space (i.e., lab) frame. Fifty trials were generated. In each trial, while the subject fixated a visual home-target located at the zero (straight-ahead)

Overview

Previous studies determining the intrinsic reference frame of neuron activity did so by rigidly controlling the spatial positions at which this activity was measured. Head position was generally fixed, and the remaining spatial position variables, such as eye or target position, limited to a small set of widely spaced values. A statistical comparison of the coherence of the neuron's activity at these discrete positions defined in different reference frames allowed the intrinsic reference frame

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