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FIGURE 5.1 Variation in the frequency of discharge of a single motor cortex cell during movement in different

directions. Upper half: Each small tick indicates an action potential; the display shows impulse activity during

five repetitions (trials) of movements made in each of the eight directions indicated in the center diagram. Trials

are oriented to the onset of movement M. Lower half: Direction tuning curve of the same cell; the average

frequency of cell activity during the response time and movement time is plotted for each of the eight directions.

(From Reference 12, Figure 4, with permission.)

Copyright © 2005 CRC Press LLC

where d is the frequency of discharge, b0 is the intercept, bx–bz are partial regression

coefficients, [x, y, z] are the direction cosines of the three-dimensional movement

vector, and e is an error term. Equation 5.1 implies that there is a direction C for

which the discharge of the cell is the highest, which is the preferred direction of the

cell. One can relate the discharge rate of a cell for movement in direction M relative

to the discharge for its preferred direction C using Equation 5.2:

d(M) = b0 + kcos θCM


where b0 and k are regression coefficients, and θCM is the angle formed by the cell’s

preferred direction C and a particular direction of movement M. In other words, if

we know the discharge of a cell for the preferred direction we can predict the

discharge for any other direction of movement.

The experiment was significant in a number of respects. It provided strong

evidence that, during naturalistic behaviors, neurons in the motor cortex were best

related to the direction of movement in space. It described the direction tuning

properties of these neurons, forming a link with much of the other literature on

direction coding and tuning in other systems.14,15 It introduced the idea of population

coding of movement variables, forming the basis of later work on the population

vector. Finally, because the data presented in the paper provided strong support for

the coding of a kinematic movement variable, the paper inadvertently led to a

polarization of opinion in the motor control community into camps advocating

kinematic and kinetic coding of movement; this debate is as vibrant now as when

the paper was published.


The population coding of movement direction was put forward first as a suggestion,12

then as a formal hypothesis,16,17 and finally with detailed neural data for movements

in two17 and three dimensions.18,19 The concept underlying population coding is as

follows: for a population of directionally tuned neurons, each neuron will make a

vectorial contribution to the code in its preferred direction, and at a magnitude that

is proportional to the angle between its preferred direction and the intended direction

of movement. In other words, cells with a preferred direction close to the direction

of movement make a greater contribution; those further away, a smaller one. The

vector sum of the contributions of a population of cells is used to form the population

vector that predicts the direction of the upcoming movement. In formal terms, the

population vector can be expressed as follows:


P( M ) =

∑ w ( M )C




i =1

where P(M) is the neural population vector in movement direction M; Ci is the

preferred direction of the ith cell in the population; and wi (M) is a weighting function

that reflects the magnitude of the contribution of ith cell to the population vector

for movement in direction M.

Copyright © 2005 CRC Press LLC

FIGURE 5.2 (see color figure) An example of the population coding of movement direction.

The blue lines represent the vectorial contribution of individual cells in the population (N =

475). The actual movement direction is in yellow and the direction of the population vector

is in red. (From Reference 19, Figure 1, with permission.)







.3 sec

FIGURE 5.3 Evolution of the population vector in time, before and during an instructed arm

movement. A time series of population (P) and movement (M) vectors is shown. The instructed

movement direction is indicated by a small arrow on the far left. The population vector can

be seen to increase in size and point in the direction of the upcoming movement before the

movement occurs. Stim is onset of target instruction; MOV is onset of movement. (Adapted

from Reference 19, Figure 4, with permission.)

The population vector is an accurate reflection of the direction of movement

(Color Figure 5.2*). It can also be derived during the response time or in delay periods

before movement actually begins. In these contexts, the population vector may reflect

the “intention” of a population of motor cortex cells in relation to movement

* See color insert following page 170.

Copyright © 2005 CRC Press LLC

(Figure 5.3). The population vector can be calculated in time (e.g., every 10 msec)

and therefore gives a continuous readout of the activity of cells that predicts motor

behavior in advance. For the population vector analysis to accurately predict the

direction of movement, the following three conditions need to be satisfied:19 (1) the

directional tuning function is one of a broad category of functions that are radially

symmetric around a preferred direction; (2) the preferred directions of the tuned

cells are uniformly distributed; and (3) the values of the tuning parameters k and b

are randomly distributed relative to the preferred directions. The accuracy of the

population vector is relatively resistant to cell loss and is a good predictor of

movement direction with as little as 20 tuned cells.20



Although the directional properties of both single cells and populations of cells are

strongly correlated with the direction of movement, this does not necessarily mean

that the cells code for the direction of movement alone. There are many other

variables, such as muscle activity, that also covary with movement direction and thus

might be reflected in cell activity. It is known that single cells in motor cortex generally

engage several motoneuronal pools21–23 and thus influence the activity of many muscles often distributed across more than one joint.24 It can be reasonably assumed that

cells may engage different muscles at different strengths resulting in a set of muscles

with a preferred direction. The combinatorial possibilities of different muscles,

grouped together in distinct sets with different weights, would result in a very large

number of potential preferred directions to which motor cortex cells might relate.

Because the set of muscles to which a particular cell projects is likely to be active

for movements in many different directions, the direction tuning will be quite broad.

This view of the structure-function relation between motor cortex cells and muscles

is consistent with the results of experiments on preferred direction and population

vector. Therefore, the direction of movement in space is not the only interpretation

of the population vector derived from groups of cells, or the preferred direction in

individual motor cortex cells; nevertheless, it is perhaps the most parsimonious.



The issue of what is represented in the activity of motor cortex neurons is not new.

It dates back at least, and most famously, to the writings of Hughlins Jackson toward

the end of the 19th century. That the topic should still be hotly debated is just as

remarkable as if current geneticists and molecular biologists were battling it out

over some seminal statement of Gregor Mendel. Jackson wrote, “To speak figuratively, the central nervous system [read “motor cortex”] knows nothing of muscles,

it only knows movements.”25,26 Unfortunately, the statement has been interpreted

literally and not “figuratively,” and thus has created two polarized groups within the

motor control community. One group holds that motor cortex “knows nothing of

Copyright © 2005 CRC Press LLC

muscles,” while the other, adopting an equally extreme position, believes that motor

cortex knows nothing of movements.


It is obvious what the brain must do for us to successfully make voluntary movements

to a target. The target is initially represented within the visual system in retinotopic

coordinate space. We assume that the representation of the target is then transformed

into a coordinate frame that is relevant to the upper limb: either allocentric or “world

space,” or an egocentric frame that is anchored to the body. Finally, the brain

commands the arm to move toward the appropriately transformed target. What form

do these commands take? Does the motor cortex specify the exact activation of the

muscles around the shoulder and elbow joints, so that the appropriate torques are

produced to bring the arm to its target (the extreme kinetic position)? There is no

disagreement that these torques have to be specified at some level for movement to

occur; the issue is whether this specification takes place in the motor cortex. Alternatively, does the motor cortex plan the spatial trajectory of the movement alone

(the extreme kinematic position)? Movement kinetics refers to the forces produced

and their derivatives. At the lowest or most fundamental level, these are the forces

produced by individual muscles. However, the level of control could equally well

be that of the torques produced at specific joints or, indeed, the total force generated

by the limb. Kinematics refers to the spatial variables of movement, such as position,

velocity, acceleration, and direction. As is the case with kinetics, the kinematic

variables can be defined for muscles, joints, or the whole limb. The class of variable,

kinetic or kinematic variable, and the coordinate frame for movement control are

hypothetically independent. Nevertheless, kinetic coding is much more likely in

muscle or joint space. Similarly, kinematic coding is more probable in allocentric

(or extrinsic) space.


More than two decades ago, Morasso11 demonstrated what in retrospect seems

obvious: that it is computationally much less demanding to control the kinematics

of the endpoint than the kinematics at the component joints during movements of

the arm (Figure 5.4). There is compelling evidence from the psychophysical literature

that movement is indeed planned in terms of extrinsic coordinates,27–30 although

there are other views.31 However, though knowledge of the intrinsic geometry of the

limb may be a necessary part of the planning process.32,33 Viviani and colleagues

have put forward a “vector coding” hypothesis which holds that during voluntary

movement the target information delivered to the motor system is in vector format

in extrinsic coordinates. Of course, the executive motor system, and particularly the

motor cortex, is under no obligation to operate directly on the information in this

vector format, although, again, it may be the most parsimonious approach.

The most compelling evidence in favor of the kinematic control of movement

comes not from the psychophysical literature, but from direct neural recording in

Copyright © 2005 CRC Press LLC

FIGURE 5.4 Records from one subject during a point-to-point movement on a two-dimensional plane. (A) Change in position at the shoulder and elbow joints. (B) Velocity at the

shoulder and elbow joints. (C) Acceleration at the two joints. (D) Velocity at the hand. It is

obvious that the hand velocity would be the simplest variable to control. (Adapted from

Reference 11, Figure 3, with permission.)

the motor cortex during a variety of motor behaviors. As mentioned above, there is

a large body of work demonstrating that cells in the motor cortex relate strongly to

the direction of arm movement in space.12,18,34–39 Because direction of movement

varies along with several other movement variables, which are also potential control

variables, it was necessary to dissociate these variables systematically during neural

recording studies. Two sets of comprehensive dissociation experiments have been

performed. Alexander and Crutcher40,41 dissociated the direction of arm movement

from the muscles used in a visually controlled task by applying loads to a onedimensional manipulandum. Approximately one third of cells in the monkey motor

cortex were related to muscle activation during the execution of movement41 and an

even smaller proportion during a preparatory period before movement began.40 Kakei

and colleagues42 dissociated muscle activity, posture, and direction of movement in

space during a two-dimensional wrist movement task. They found that about 25%

Copyright © 2005 CRC Press LLC



Up: E


Rt: U


Dn: F


Lf: R




















Up: E


Rt: U






Dn: F


Lf: R







Up: E


Rt: U


Dn: F


Lf: R




500 −500

500 −500


FIGURE 5.5 The records of three single neurons (A, B, C) in the motor cortex for movements

in six different directions (Up, Up and Rt, etc.) in each of three different wrist postures (Pro,

Mid, Sup). All the rasters are aligned to the onset of movement. The tuning of cell B does not

change across the different postures; therefore, it can be categorized as “extrinsic.” The activity

of cell A changes consiberably for the different postures, its preferred direction changing by

79° from Pro to Sup, and can be regarded as “muscle-like.” Cell C is an extrinsic-like neuron

that is also influenced by wrist posture. (From Reference 42, Figure 2, with permission.)

of motor cortex cells had “muscle” properties, while approximately 50% related to

direction of movement in space, and reasonably concluded that both “muscles” and

“movements” were represented in the motor cortex (Figure 5.5).

The motor cortex not only seems to encode relatively static kinematic parameters

such as direction during point-to-point movements, but can also reflect parameters that

change continuously during straight movements such as position, velocity, and

acceleration.43 The coding principles developed for simple, straight movements to

a target also hold true when applied to more complex ones. For example, direction

Copyright © 2005 CRC Press LLC

FIGURE 5.6 Representation of speed in a motor cortex cell. The radial histograms show the

averaged neural activity during center-out reaching movements in the respective directions.

The tick marks under each histogram represent 440 msec (the average response time plus

movement time) and indicate the portion used, through averaging across the 8 directions, to

generate the center-left waveform (nondirectional neural profile). There is remarkable concordance between the nondirectional profile (left, center) and the average speed of the movements (right, center). (From Reference 45, Figure 3, with permission.)

and speed, which vary continuously during drawing or spiral tracing movements,

are strongly reflected in the motor cortex38,44–46 and the population vectors derived

from these parameters can be used to predict a complex hand trajectory accurately

(Figure 5.6).45 In fact, Schwartz and colleagues have shown that models that take

both the direction and speed of movement into account provide more accurate

descriptions of motor cortex activity than those using direction alone. Fitting neural

activity to other time-varying movement parameters like EMG or joint-angle velocity

resulted in a much less accurate model of the data than that obtained for the trajectory

of the hand.45 The obvious conclusion from these studies is that during drawing and

other continuous movements, it is the kinematics of movement in extrinsic space

that is primarily reflected in motor cortex activity.


Cells in the motor cortex have prominent projections to the spinal cord, and some

have monosynaptic projections to motoneurons that in turn directly control muscle

activation. Muscles and their output, force, are the obvious control variable for cells

in motor cortex. Evarts4,5 was the first to show a relation between motor cortex

activity and the force generated by the muscles. Since then, a large number of studies

have shown relations between motor cortex and the magnitude, direction, and rate

Copyright © 2005 CRC Press LLC

of change in force. (See References 47 and 48 for reviews.) However, with a relatively

simple behavior it is possible to find a relation between almost any motor variable

and motor cortex activity. Also, more than one variable may be encoded in the

activity of cells.43 The case in favor of kinetic control has rested strongly on showing

that the coding of kinematic variables alone is not a complete explanation of the

variations in cell activity one sees in certain motor behaviors.49,50 These last studies

showed that using different arm configurations to make movements to a set of spatial

targets resulted in changes in the activity of single cells in the motor cortex, which

suggested that the trajectory of the hand in space was not the only aspect of the

behavior being coded, as this did not change significantly for different arm configurations. In addition, other work has demonstrated that the location of the hand, and

hence the configuration of the arm, may have a systematic effect on the direction

tuning of cell activity during an isometric ramp and hold task,53 in which no actual

movements were produced.

Despite the influence of arm posture on the activity of single cells in the motor

cortex, the direction of the population vector, based on the activity of these cells,

has been relatively resistent to changes in arm posture.49 Nevertheless, in some

circumstances, such as when three-dimensional movements are made to targets from

different starting points, even the population vector appears to be modulated by limb

biomechanics.34 Further evidence for the effect of biomechanics on the population

vector comes from experiments in which the biomechanics at the shoulder and elbow

joints were accurately measured, showing that the nonuniformity in the distribution

of population vectors was a function both of velocity and torque at the joints.51

Taking these experiments as a whole, one cannot but conclude that the kinetic output

has a distinct influence on the activity of motor cortex cells, although the effect of

biomechanics on the population vector has been modest. It is obvious that arm

kinematics alone cannot account for the changes in neural activity that have been

observed. However, such a conclusion is quite different from stating that the motor

cortex codes primarily for the kinetics of motor output.


Much has been made, particularly in the psychophysical literature, of the concept

of successive coordinate transformations to explain how visual targets, initially

defined in retinal coordinates, can be reached by the arm, for which the coordinate

frame is defined by the joints and muscles. As discussed above, there is clear evidence

that movement is first specified in terms of kinematics, but the actual movement is

ultimately produced by a weighted activation of groups of muscles (kinetics). The

hypothesis underlying successive coordinate transformations is that different motor

areas, including several sub-areas of parietal cortex, participate in the various stages

of this transformation from kinematics to kinetics. The common wisdom is that the

motor cortex would either be involved in the final stage of the kinematic to kinetic

transformation or would implement the kinetics on instructions from a “higher”

motor area such as the lateral premotor cortex or the supplementary motor area.52

As mentioned above, the idea that the motor cortex implements kinetics alone is not

tenable on the basis of current evidence. There is more evidence in favor of the

Copyright © 2005 CRC Press LLC

motor cortex being instrumental in some kind of kinematic to kinetic transformation,

though the form of such a transformation is not at all clear.34,49,51,53


To paraphrase, or contort, the view of Hughlins Jackson: although the motor cortex

knows of both muscles and movements, it appears to be concerned primarily with

space. In other words, the motor cortex primarily codes for the most relevant spatial

aspects of motor output, both in the case of movement and during behaviors that

are purely isometric.35,47,53–55 One simple experiment illustrates this point. Let us

imagine that one is required to make force pulses in different target directions in

the presence of opposing forces. The muscle forces exerted will not be in the direction

of the targets, because one has to neutralize the opposing forces. Will the activity

of motor cortex cells reflect the actual forces produced by the muscle or the resultant

force (a combination of the muscle force and the opposing force), which is inevitably

in the direction of the target? Using this behavioral paradigm in the monkey, it was

shown that both the single cell and population activity in the motor cortex related

to the resultant force, which was the most relevant spatial variable, and not to the

forces produced by the muscles.55 For more than two decades, motor control has

been dominated by studies examining the relation between motor cortex cells and

the spatial aspects of motor output. If motor cortex codes for the spatial aspects of

behavior, in what coordinate framework does this coding occur? It is likely that the

coding occurs in the coordinate frame that is most relevant for the behavior. For

example, the majority of studies has used reaching movements and it is no surprise

that cell activity in those cases reflects an extrinsic reference frame anchored to the

hand. If instead, one were to perform the behavior using the elbow as a pointer, this

would likely be the reference point. Similarly, manipulation of objects by the hands

would be coded in a reference frame that might well be muscle or joint-based relative

to the hands.

However, a coherent theory of coding in the motor cortex must also account for

the clear effect of biomechanical factors on cell activity.34,49–51,53 Just as gain fields

have been used to explain the interaction of several different frames of reference on

the activity of single neurons in the posterior parietal cortex,56 we can perhaps use

a similar framework to explain findings in motor cortex neural recordings. The

composition of such a gain field is as yet uncertain. The available data suggests that

if such a gain field exists, it is comprised of unequal partners, the neural activity

relating to the spatial output predominating, but modulated in a systematic way

dependent on the biomechanics of the limb. For motor behaviors that are performed

in two dimensions — for example, the reaching movements in monkeys — one

might conceptualize such a field as a plane with a relatively shallow slope. Of course,

we currently lack the type of complete quantitative data that would be necessary in

order to construct such putative gain fields accurately, but systematic studies of this

issue are currently being conducted. We predict that the slope of such gain fields is

likely to be small and that the representation of space by the motor cortex, as in the

parietal cortex,56 is likely to be distributed.

Copyright © 2005 CRC Press LLC


If such gain fields do in fact exist, then a major challenge for those concerned with

the cortical control of motor behavior will be to understand how a cortical representation of space, modulated by limb biomechanics, is translated into the muscle

or joint coordinate frame that will ultimately be required for implementation of the

behavior. There are some intriguing possibilities. Bizzi and colleagues57–60 have

shown, in experiments in the frog and rat, that a set of “motor primitives,” which

could form the basis of activating specific sets of muscles during multiple joint

movement, can be elicited through microsimulation of the spinal gray matter. These

primitives may form the building blocks for voluntary movement by translating

spatial signals from the motor cortex into appropriate muscle output. Recent data

from experiments using long trains of intracortical microstimulation suggest that the

motor cortex may be able to access such primitives directly.61 In addition, other

spinal interneuronal systems such as the propriospinal system in the cat62 have been

shown to be important in the patterned activation of the different muscles required

for reaching. These propriospinal interneurons may participate in the integration of

reaching movements at a spinal level, and may effectively translate signals from

cells in the motor cortex that relate to the direction of force output of the whole

limb55 into appropriate patterns of muscle activation. Another question is how motor

cortex learns to access such motor primitives. It is likely that the association between

motor cortex cell activity and motor primitive “modules” at another level in the

motor system is established through learning and adaptation.

Though conceptually attractive, the idea of successive coordinate transformations in frontal motor areas culminating in a muscle or joint based coding of motor

output in motor cortex63 does not have strong experimental support and should be

abandoned, at least as applied to skilled movements. The search for a direct reflection

of the motor periphery in the motor cortex is likely to be as futile as the quest for

the representation of the single muscle.


1. Fritsch, G. and Hitzig, E., Über die elektrische Erregbarkeit des Grosshirns, Arch.

Anat. Physiol. Wis. Med., 37, 300, 1870.

2. Ferrier, D., Experiments in the brain of monkeys, Proc. R. Soc. Lond. (Biol.), 23,

409, 1875.

3. Leyton, A.S.F. and Sherrington, C.S., Observations on the excitable cortex of the

chimpanzee, orangutan and gorilla, Qu. J. Exp. Physiol., 11, 135, 1917.

4. Evarts, E.V., Relation of pyramidal tract to force exerted during voluntary movement,

J. Neurophysiol., 31, 14, 1968.

5. Evarts, E.V., Activity of pyramidal tract neurons during postural fixation, J. Neurophysiol., 32, 375, 1969.

6. Cheney, P.D. and Fetz, E.E., Functional classes of primate corticomotoneuronal cells

and their relation to active force, J. Neurophysiol., 44, 773, 1980.

7. Smith, A.M., Hepp-Reymond, M.C., and Wyss, U.R., Relation of activity in precentral

cortical neurons to force and rate of force change during isometric contractions of

finger muscles, Exp. Brain Res., 23, 315, 1975.

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