ARTICLE / ARTICLE
Encoding mechanisms for sensory neurons
studied with a multielectrode array in the cat
dorsal root ganglion
1
R.B. Stein, Y. Aoyagi, D.J. Weber, S. Shoham, and R.A. Normann
Abstract: Recent advances in microelectrode array technology now permit a direct examination of the way populations
of sensory neurons encode information about a limb’s position in space. To address this issue, we recorded nerve im-
pulses from about 100 single units simultaneously in the L6 and L7 dorsal root ganglia (DRG) of the anesthetized cat.
Movement sensors, placed near the hip, knee, ankle, and foot, recorded passive movements of the cat’s limb while it
was moved pseudo-randomly. The firing rate of the neurons was correlated with the position of the limb in various co-
ordinate systems. The firing rates were less correlated to the position of the foot in Cartesian coordinates (x, y) than in
joint angular coordinates (hip, knee, ankle), or in polar coordinates. A model was developed in which position and its
derivatives are encoded linearly, followed by a nonlinear spike-generating process. Adding the nonlinear portion signifi-
cantly increased the correlations in all coordinate systems, and the full models were able to accurately predict the fir-
ing rates of various types of sensory neurons. The observed residual variability is captured by a simple stochastic
model. Our results suggest that compact encoding models for primary afferents recorded at the DRG are well repre-
sented in polar coordinates, as has previously been suggested for the cortical and spinal representation of movement.
This study illustrates how sensory receptors encode a sense of limb position, and it provides a general framework for
modeling sensory encoding by populations of neurons.
Key words: sensory, encoding, multielectrode, dorsal root ganglion, cutaneous, muscle. 768
Résumé : Grâce aux progrès récents de la technologie des réseaux de microélectrodes, nous pouvons maintenant obser-
ver directement comment les populations de neurones sensoriels encodent l’information relative à la position d’un
membre dans l’espace. Pour étudier cette question, nous avons enregistré les impulsions nerveuses d’une centaine
d’unités discriminables, simultanément dans les ganglions de la racine dorsale (GRD) L6 et L7 d’un chat sous anes-
thésie. Des détecteurs du mouvement, placés près de la hanche, du genou, de la cheville et du pied, ont enregistré les
mouvements passifs du membre du chat pendant que celui-ci était déplacé de façon pseudo-aléatoire. La cadence des
neurones a été mise en corrélation avec la position du membre dans divers systèmes de coordonnées. La corrélation
entre la cadence et la position du pied était moins grande dans les coordonnées cartésiennes (x, y) que dans les coor-
données articulaires (hanche, genou, cheville) ou dans les coordonnées angulaires. Un modèle a été conçu, dans lequel
la position et ses dérivés sont encodés de façon linéaire, suivi par un processus non linéaire générateur de pointes.
L’ajout de la portion non linéaire augmente de façon significative les corrélations dans tous les systèmes de coordon-
nées et les modèles complets ont pu prédire avec précision la cadence des divers types de neurones sensoriels. La va-
riabilité résiduelle observée est bien saisie par un simple modèle stochastique. En conclusion, nos résultats semblent
indiquer que les modèles d’encodage compact pour les afférents primaires enregistrés au GRD sont bien représentés
dans les coordonnées angulaires, comme cela a déjà été indiqué pour la représentation corticale et spinale du mouve-
ment. Cette étude illustre comment les récepteurs sensoriels encodent la position d’un membre et fournissent un cadre
général pour la modélisation de l’encodage sensoriel par des populations de neurones.
Can. J. Physiol. Pharmacol. 82: 757–768 (2004) doi: 10.1139/Y04-075 ? 2004 NRC Canada
757
Received 6 July 2004. Accepted 6 July 2004. Published on the NRC Research Press Web site at http://cjpp.nrc.ca on 1 October
2004.
R.B. Stein,
2
Y. Aoyagi, and D.J. Weber. Centre for Neuroscience, University of Alberta, 513 Heritage Medical Research Institute,
Edmonton, AB T6G 2S2, Canada.
S. Shoham and R.A. Normann. Department of Bioengineering, University of Utah, Salt Lake City, UT, USA.
1
This paper is one of a selection of papers published in this Special Issue, entitled Nerve, muscle, and beyond: the R.B. Stein
Symposium.
2
Corresponding author: (email: richard.stein@ualberta.ca).

Mots clés : sensoriel, codage, multi-électrodes, ganglion de la racine dorsale, cutané, muscle.
[Traduit par la Rédaction] Stein et al.
Introduction
The senior author of this article (R.B.S.) has had a life-long
interest in the mechanisms involved in encoding information
in sensory neurons (Matthews and Stein 1969; Stein 1967).
Encoding models describe the transformation that takes place
from a sensory stimulus to a neural response, as well as the
variability of this response (Stein 1965). Early work was
based on a simple linear summation of length and velocity in-
puts to muscle receptors, and the variability of the discharge
was shown to limit the amount of information that could be
transmitted about these variables. Much more complex non-
linear models have since been developed for muscle spindles
and other sensory receptors (Hasan and Houk 1975; Otten et
al. 1995; Prochazka and Gorassini 1998b). Similarly, it has
been suggested that the variability in sensory discharge con-
veys information, rather than simply being neural “noise”
(Perkel and Bullock 1968; Rieke et al. 1997; Stein 1970).
The nervous system is a massively parallel computing sys-
tem that deals with a vast amount of activity in real time.
Can we begin to understand the general processing of activity
in sensory systems, over and above our detailed understand-
ing of single receptors? With the development of multi-
electrode recording techniques (Loeb et al. 1977; Prochazka
et al. 1976; Serruya et al. 2002; Taylor et al. 2002; Wessberg
et al. 2000), we can now record from many neurons and
study properties of the ensemble of signals passing through
a structure, such as the dorsal root ganglion. Previously, sin-
gle neurons were recorded sequentially over many hours or
many preparations to build up a population, with the hope
that conditions remained constant over time and between an-
imals. Now, by recording from a population of neurons si-
multaneously, that assumption is no longer required; the nature
of the processing can be addressed in single experiments.
To deal with a large number of simultaneous signals, we
have developed a variety of automated methods. This ongo-
ing development will be described in this paper. We also
found that the activity of the sensory neurons can be de-
scribed in a general framework. The responses still contain
length and velocity components, but they can be described in
terms of extrinsic variables, such as Cartesian (x, y) or polar
coordinates, and intrinsic variables, such as joint angles. In
addition to linear correlations, we found systematic non-
linearities that are well described by a Wiener cascade. A
Wiener cascade has a linear filter followed by a static non-
linearity (Kearney and Hunter 1990; Korenberg and Hunter
1999). This has an intuitive appeal, because the ionic cur-
rents generated by sensory inputs or synaptic potentials in a
neuron may sum more or less linearly, but there are inherent
nonlinearities in spike generation (see Chander and
Chichilnisky 2001; Shoham 2001). For example, the firing
rate saturates at a maximum determined by the neuron’s re-
fractory period and at a minimum of zero (no firing). Even
with the best linear/nonlinear models, residual variability
still remains between the actual firing and predicted patterns.
This variability can be treated as a stochastic process, the
properties of which are well described by our model. The
major goal of this paper is to describe the methods and
structure that we have developed to understand the encoding
mechanisms in sensory neurons.
Methods
A series of cats were studied, during which methods grad-
ually improved. Three acute experiments were done at the
University of Utah (Salt Lake City, Utah). A manipulandum
with 2 degrees of freedom was attached to the cat’s paw, and
the foot was moved manually in the sagittal plane. From the
2-joint angles of the manipulandum, the position of the cat’s
paw was calculated and compared with the neural signals re-
corded. Three acute experiments were also done at the Uni-
versity of Alberta (Edmonton, Alta.). The local animal
welfare committees at the respective universities approved
all procedures, which were conducted in accordance with the
Helsinki Convention. The results from all experiments were
essentially identical, and we have selected examples to illus-
trate the common findings.
Movement tracking
In the first 2 experiments at the University of Alberta,
movements of the limb were produced manually (Fig. 1),
and were recorded by electromagnetic motion-tracking sen-
sors (6D-Research, Skill Technologies Inc., Phoenix Ariz.).
Four sensors were used: sensor 1 was placed on the skin
near the hip joint, sensor 2 was placed on the lateral
epicondyle of the femur near the knee, sensor 3 was placed
on the lateral malleolus of the tibia near the ankle, and sen-
sor 4 was placed on the surface of a foot holder near the lat-
eral metatarsal joint of the foot. To avoid skin slippage or
displacement during movement, sensors 2 and 3 were rigidly
fixed to the femur and tibia with surgical sutures through
holes drilled in the respective bones. No instruments near
the sensors, including sections of the spinal frame, contained
metal, so that there was no electromagnetic interference with
the signals recorded from the motion sensors. The distance
of each sensor from neighboring joints was measured.
In the most recent experiment, a robotic manipulandum
with 2 DC servo motors (Parker BE233DJ) was programmed
to deliver repeatable movements. To generate random move-
ments, the manipulandum moved sequentially from one po-
sition to the next. The positions were selected at random
from a rectangular grid of points, and the velocity of each
movement was selected at random over a range of speeds up
to 0.6 m/s. The movements continued until all points on the
grid had been reached, so there was a uniform coverage of
the workspace.
Movements were tracked in this experiment with a digital
video camera (JVC DVL9800) at 120 frames/s, using 5-mm
reflective markers placed over the hip, knee, ankle, foot, and
toes. No invasive procedures were used to track motion, so
that the results could be compared with results from awake
behaving animals (Prochazka et al. 2003; Weber et al. 2002).
Because the skin over the knee moved to some extent, the
knee position was calculated using the hip and ankle mark-
? 2004 NRC Canada
758 Can. J. Physiol. Pharmacol. Vol. 82, 2004