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Chapter 1: Motor Units and Muscle Receptors

James Knierim, Ph.D., Department of Neuroscience, The Johns Hopkins University


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1.1 What is Motor Control?

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Figure 1.1
Sensory receptors provide information about the environment, which is then used to produce action to change the environment. Sometimes the pathway from sensation to action is direct, as in a reflex. In most cases, however, cognitive processing occurs to make actions adaptive and appropriate for the particular situation.

Much of the brain and nervous system is devoted to the processing of sensory input, in order to construct detailed representations of the external environment.

Through vision, audition, somatosensation, and the other senses, we perceive the world and our relationship to it. This elaborate processing would be of limited value, however, unless we had a way to act upon the environment that we are sensing, whether that action consist of running away from a predator; seeking shelter against the rain; searching for food when one is hungry; moving one’s lips and vocal cords in order to communicate with others; or performing the countless other varieties of actions that make up our daily lives. In some cases the relationship between the sensory input and the motor output are simple and direct; for example, touching a hot stove elicits an immediate withdrawal of the hand (Figure 1.1). Usually, however, our conscious actions require not only sensory input but a host of other cognitive processes that allow us to choose the most appropriate motor output for the given circumstances. In each case, the final output is a set of commands to certain muscles in the body to exert force against some other object or forces (e.g., gravity). This entire process falls under the subject of motor control.

1.2 Some Necessary Components of Proper Motor Control

  1. Volition. The motor system must generate movements that are adaptive and that accomplish the goals of the organism. These goals are evaluated and set by high-order areas of the brain. The motor system must transform the goals into the appropriate activations of muscles to perform the desired movements.
  2. Coordination of signals to many muscle groups. Few movements are restricted to the activation of a single muscle. For example, the act of moving your hand from inside your pocket to a position in front of you requires the coordinated activity of the shoulder, elbow, and wrist. Making the same movement while removing a 2-lb weight from your pocket may result in the same trajectory of your hand, but will require different sets of forces on the muscles that make the movement. The task of the motor system is to determine the necessary forces and coordination at each joint in order to produce the final, smooth motion of the arm.
  3. Proprioception. In order to make a desired movement (e.g., raising your hand to ask a question), it is essential for the motor system to know the starting position of the hand. Raising one’s hand from a resting position on a desk, compared to a resting position on top of the head, results in the same final position of the arm, but these two movements require different patterns of muscle activation. The motor system has a set of sensory inputs (called proprioceptors) that inform it of the length of muscles and the forces being applied to them; it uses this information to calculate joint position and other variables necessary to make the appropriate movement.
  4. Postural adjustments. The motor system must constantly produce postural adjustments in order to compensate for changes in the body’s center of mass as we move our limbs, head, and torso. Without these automatic adjustments, the simple act of reaching for a cup would cause us to fall, as the body’s center of mass shifts to a location in front of the body axis.
  5. Sensory feedback. In addition to the use of proprioception to sense the position of the body before a movement, the motor system must use other sensory information in order to perform the movement accurately. By comparing desired activity with actual activity, sensory feedback allows for corrections in movements as they take place, and it also allows modifications to motor programs so that future movements are performed more accurately.
  6. Compensation for the physical characteristics of the body and muscles. To exert a defined force on an object, it is not sufficient to know only the characteristics of the object (e.g., its mass, size, etc.). The motor system must account for the physical characteristics of the body and muscles themselves. The bones and muscles have mass that must be considered when moving a joint, and the muscles themselves have a certain degree of resistance to movement.
  7. Unconscious processing. The motor system must perform many procedures in an automatic fashion, without the need for high-order control. Imagine if walking across the room required thinking about planting the foot at each step, paying attention to the movement of each muscle in the leg and making sure that the appropriate forces and contraction speeds are taking place. It would be hard to do anything else but that one task. Instead, many motor tasks are performed in an automatic fashion that does not require conscious processing. For example, many of the postural adjustments that the body makes during movement are performed without our awareness. These unconscious processes allow higher-order brain areas to concern themselves with broad desires and goals, rather than low-level implementations of movements.
  8. Adaptability. The motor system must adapt to changing circumstances. For example, as a child grows and its body changes, different constraints are placed on the motor system in terms of the size and mass of bones and muscles. The motor commands that work to raise the hand of an infant would fail completely to raise the hand of an adult. The system must adapt over time to change its output to accomplish the same goals. Furthermore, if the system were unable to adapt, we would never be able to acquire motor skills, such as playing a piano, hitting a baseball, or performing microsurgery.

These are some of the many components of the motor system that allow us to perform complex movements in a seemingly effortless way. The brain has evolved exceedingly complex and sophisticated mechanisms to perform these tasks, and researchers have only scratched the surface in understanding the principles that underlie the brain’s control of movement.

1.3 Motor Control Requires Sensory Input

One of the major principles of the motor system is that motor control requires sensory input to accurately plan and execute movements. This principle applies to low levels of the hierarchy, such as spinal reflexes, and to higher levels. As we shall see throughout this material on the motor system, our abilities to make movements that are accurate, properly timed, and with proper force depend critically on the sensory input that is ubiquitous at all levels of the motor system hierarchy.

1.4 Functional Segregation and Hierarchical Organization

The ease with which we make most of our movements belies the enormous sophistication and complexity of the motor system. Engineers have spent decades trying to make machines perform simple tasks that we take for granted, yet the most advanced robotic systems do not come close to emulating the precision and smoothness of movement, under all types of conditions, that we achieve effortlessly and automatically. How does the brain do it? Although many of the details are not understood, two broad principles appear to be key concepts toward understanding motor control:

The motor system hierarchy consists of 4 levels (Figure 1.2): the spinal cord, the brain stem, the motor cortex, and the association cortex. It also contains two side loops: the basal ganglia and the cerebellum, which interact with the hierarchy through connections with the thalamus.

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Figure 1.2
Schematic representation of the different levels and interconnections of the motor system hierarchy. The brain figure on the left is a schematic version of an idealized brain section that contains the major structures of the motor system hierarchy for illustrative purposes; no actual brain section would contain all of these structures. Move the cursor over each box on the right to highlight the inputs (blue) and outputs (red) of each region.

 

1.5 The Spinal Cord: The First Hierarchical Level

The spinal cord is the first level of the motor hierarchy. It is the site where motor neurons are located. It is also the site of many interneurons and complex neural circuits that perform the “nuts and bolts” processing of motor control. These circuits execute the low-level commands that generate the proper forces on individual muscles and muscle groups to enable adaptive movements. The spinal cord also contains complex circuitry for such rhythmic behaviors as walking. Because this low level of the hierarchy takes care of these basic functions, higher levels (such as the motor cortex) can process information related to the planning of movements, the construction of adaptive sequences of movements, and the coordination of whole-body movements, without having to encode the precise details of each muscle contraction.

1.6 Motor Neurons

Alpha motor neurons (also called lower motor neurons) innervate skeletal muscle and cause the muscle contractions that generate movement. Motor neurons release the neurotransmitter acetylcholine at a synapse called the neuromuscular junction. When the acetylcholine binds to acetylcholine receptors on the muscle fiber, an action potential is propagated along the muscle fiber in both directions (see Chapter 4 of Section I for review). The action potential triggers the contraction of the muscle. If the ends of the muscle are fixed, keeping the muscle at the same length, then the contraction results on an increased force on the supports (isometric contraction). If the muscle shortens against no resistance, the contraction results in constant force (isotonic contraction). The motor neurons that control limb and body movements are located in the anterior horn of the spinal cord, and the motor neurons that control head and facial movements are located in the motor nuclei of the brainstem. Even though the motor system is composed of many different types of neurons scattered throughout the CNS, the motor neuron is the only way in which the motor system can communicate with the muscles. Thus, all movements ultimately depend on the activity of lower motor neurons. The famous physiologist Sir Charles Sherrington referred to these motor neurons as the “final common pathway” in motor processing.

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Figure 1.3
Spinal cord with motor neuron in anterior horn.

Motor neurons are not merely the conduits of motor commands generated from higher levels of the hierarchy. They are themselves components of complex circuits that perform sophisticated information processing. As shown in Figure 1.3, motor neurons have highly branched, elaborate dendritic trees, enabling them to integrate the inputs from large numbers of other neurons and to calculate proper outputs.

Two terms are used to describe the anatomical relationship between motor neurons and muscles: the motor neuron pool and the motor unit.

  1. Motor neurons are clustered in columnar, spinal nuclei called motor neuron pools (or motor nuclei). All of the motor neurons in a motor neuron pool innervate a single muscle (Figure 1.4), and all motor neurons that innervate a particular muscle are contained in the same motor neuron pool. Thus, there is a one-to-one relationship between a muscle and a motor neuron pool.
  2. Each individual muscle fiber in a muscle is innervated by one, and only one, motor neuron (make sure you understand the difference between a muscle and a muscle fiber). A single motor neuron, however, can innervate many muscle fibers. The combination of an individual motor neuron and all of the muscle fibers that it innervates is called a motor unit. The number of fibers innervated by a motor unit is called its innervation ratio.

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Figure 1.4
Motor unit and motor neuron pool.

If a muscle is required for fine control or for delicate movements (e.g., movement of the fingers or hands), its motor units will tend to have small innervation ratios. That is, each motor neuron will innervate a small number of muscle fibers (10-100), enabling many nuances of movement of the entire muscle. If a muscle is required only for coarse movements (e.g., a thigh muscle), its motor units will tend to have a high innervation ratio (i.e., each motor neuron innervating 1000 or more muscle fibers), as there is no necessity for individual muscle fibers to undergo highly coordinated, differential contractions to produce a fine movement.

1.7 Control of Muscle Force

A motor neuron controls the amount of force that is exerted by muscle fibers. There are two principles that govern the relationship between motor neuron activity and muscle force: the rate code and the size principle.

  1. Rate Code. Motor neurons use a rate code to signal the amount of force to be exerted by a muscle. An increase in the rate of action potentials fired by the motor neuron causes an increase in the amount of force that the motor unit generates. This code is illustrated in Figure 1.5. When the motor neuron fires a single action potential (Play 1), the muscle twitches slightly, and then relaxes back to its resting state. If the motor neuron fires after the muscle has returned to baseline, then the magnitude of the next muscle twitch will be the same as the first twitch. However, if the rate of firing of the motor neuron increases, such that a second action potential occurs before the muscle has relaxed back to baseline, then the second action potential produces a greater amount of force than the first (i.e., the strength of the muscle contraction summates) (Play 2). With increasing firing rates, the summation grows stronger, up to a limit. When the successive action potentials no longer produce a summation of muscle contraction (because the muscle is at its maximum state of contraction), the muscle is in a state called tetanus (Play 3).

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    Figure 1.5
    Rate code for muscle force. The upper trace on the oscilloscope shows the action potentials generated by the alpha motor neuron. The lower trace shows the force generated by the isometrically contracting muscle. PLAY 1: Single spikes by the motor neuron produce small twitches of the muscle. PLAY 2: Multiple spikes in succession summate to produce larger contractions. PLAY 3: Very high rates of spikes produce maximal contraction called tetanus.

  2. Size Principle. When a signal is sent to the motor neurons to execute a movement, motor neurons are not all recruited at the same time or at random. The motor neuron size principle states that, with increasing strength of input onto motor neurons, smaller motor neurons are recruited and fire action potentials before larger motor neurons are recruited. Why does this orderly recruitment occur? Recall the relationship between voltage, current, and resistance (Ohm’s Law): V = IR. Because smaller motor neurons have a smaller membrane surface area, they have fewer ion channels, and therefore a larger input resistance. Larger motor neurons have more membrane surface and correspondingly more ion channels; therefore, they have a smaller input resistance. Because of Ohm’s Law, a small amount of synaptic current will be sufficient to cause the membrane potential of a small motor neuron to reach firing threshold, while the large motor neuron stays below threshold. As the amount of current increases, the membrane potential of the larger motor neuron also increases, until it also reaches firing threshold.

Figure 1.6 demonstrates how the size principle governs the amount of force generated by a muscle. Because motor units are recruited in an orderly fashion, weak inputs onto motor neurons will cause only a few motor units to be active, resulting in a small force exerted by the muscle (Play 1). With stronger inputs, more motor neurons will be recruited, resulting in more force applied to the muscle (Play 2 and Play 3). Moreover, different types of muscle fibers are innervated by small and larger motor neurons. Small motor neurons innervate slow-twitch fibers; intermediate-sized motor neurons innervate fast-twitch, fatigue-resistant fibers; and large motor neurons innervate fast-twitch, fatigable muscle fibers. The slow-twitch fibers generate less force than the fast-twitch fibers, but they are able to maintain these levels of force for long periods. These fibers are used for maintaining posture and making other low-force movements. Fast-twitch, fatigue-resistant fibers are recruited when the input onto motor neurons is large enough to recruit intermediate-sized motor neurons. These fibers generate more force than slow-twitch fibers, but they are not able to maintain the force as long as the slow-twitch fibers. Finally, fast-twitch, fatigable fibers are recruited when the largest motor neurons are activated. These fibers produce large amounts of force, but they fatigue very quickly. They are used when the organism must generate a burst of large amounts of force, such as in an escape mechanism. Most muscles contain both fast- and slow-twitch fibers, but in different proportions. Thus, the white meat of a chicken, used to control the wings, is composed primarily of fast-twitch fibers, whereas the dark meat, used to maintain balance and posture, is composed primarily of slow-twitch fibers.

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Figure 1.6
Size principle of muscle force. Upper trace of oscilloscope represents the action potentials of a descending pathway axon. With low rates of activity of the descending pathway, only small alpha motor neurons are activated, producing small amounts of muscle force (lower trace of oscilloscope). With increasing rates of descending pathway activity, intermediate-size alpha motor neurons are activated in addition to the small neurons. Because more motor units are activated, the muscle produces more force. Finally, with the highest rates of descending activity, the largest alpha motor neurons are recruited, producing maximal muscle force.

1.8 Muscle Receptors and Proprioception

The motor system requires sensory input in order to function properly. In addition to sensory information about the external environment, the motor system also requires sensory information about the current state of the muscles and limbs themselves. Proprioception is the sense of the body’s position in space based on specialized receptors that reside in the muscles and tendons. The muscle spindle signals the length of a muscle and changes in the length of a muscle. The Golgi tendon organ signals the amount of force being applied to a muscle.

Muscle Spindles

Muscle spindles are collections of 6-8 specialized muscle fibers that are located within the muscle mass itself (Figure 1.7). These fibers do not contribute significantly to the force generated by the muscle. Rather, they are specialized receptors that signal (a) the length and (b) the rate of change of length (velocity) of the muscle. Because of the fusiform shape of the muscle spindle, these fibers are referred to as intrafusal fibers. The large majority of muscle fibers that allow the muscle to do work are termed extrafusal fibers. Each muscle contains many muscle spindles; muscles that are necessary for fine movements contain more spindles than muscles that are used for posture or coarse movements.

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Figure 1.7
Muscle spindle and Golgi tendon organ.

1.9 Types of Muscle Spindle Fibers

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Figure 1.8
Muscle spindle.

There are 3 types of muscle spindle fibers, characterized by their shape and the type of information they convey (Figure 1.8).

  1. Nuclear Chain fibers. These fibers are so-named because their nuclei are aligned in a single row (chain) in the center of the fiber. They signal information about the static length of the muscle.
  2. Static Nuclear Bag fibers. These fibers are so-named because their nuclei are collected in a bundle in the middle of the fiber. Like the nuclear chain fiber, these fibers signal information about the static length of a muscle.
  3. Dynamic Nuclear Bag fibers. These fibers are anatomically similar to the static nuclear bag fibers, but they signal primarily information about the rate of change (velocity) of muscle length.
    A typical muscle spindle is composed of 1 dynamic nuclear bag fiber, 1 static nuclear bag fiber, and ~5 nuclear chain fibers.

1.10 Sensory Innervation of Muscle Spindles

Because the muscle spindle is located in parallel with the extrafusal fibers, it will stretch along with the muscle. The muscle spindle signals muscle length and velocity to the CNS through two types of specialized sensory fibers that innervate the intrafusal fibers. These sensory fibers have stretch receptors that open and close as a function of the length of the intrafusal fiber.

  1. Group Ia afferents (also called primary afferents) wrap around the central portion of all 3 types of intrafusal fibers; these specialized endings are called annulospiral endings. Because they innervate all 3 types of intrafusal fibers, Group Ia afferents provide information about both length and velocity.
  2. Group II afferents (also called secondary afferents) innervate the ends of the nuclear chain fibers and the static nuclear bag fibers at specialized junctions termed flower spray endings. Because they do not innervate the dynamic nuclear bag fibers, Group II afferents signal information about muscle length only.

Because of their patterns of innervation onto the three types of intrafusal fibers, Group Ia and Group II afferents respond differently to different types of muscle movements. Figure 1.9 shows the responses of each type of afferent to a linear stretch of the muscle. Initially, both Group Ia and Group II fibers fire at a certain rate, encoding the current length of the muscle. During the stretch, the two types differ in their responses. The Group Ia afferent fires at a very high rate during the stretch, encoding the velocity of the muscle length; at the end of the stretch, its firing decreases, as the muscle is no longer changing length. Note, however, that its firing rate is still higher than it was before the stretch, as it is now encoding the new length of the muscle. Compare the response of the Group Ia afferent to the Group II afferent. The Group II afferent increases its firing rate steadily as the muscle is stretched. Its firing rate does not depend on the rate of change of the muscle; rather, its firing rate depends only on the immediate length of the muscle.

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Figure 1.9
Responses of muscle spindles. The Group Ia afferent responds at a highest rate when the muscle is actively stretching, but also signals the static length of the muscle because of its innervation of the static nuclear bag fiber and the nuclear chain fiber. The Group II afferent signals only the static length of the muscle, increasing its firing rate linearly as a function of muscle length.

1.11 Gamma Motor Neurons

Although intrafusal fibers do not contribute significantly to muscle contraction, they do have contractile elements at their ends that are innervated by motor neurons.

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Figure 1.10
Alpha-gamma coactivation. The muscle starts at a certain length, encoded by the firing of a Ia afferent. When the muscle is stretched, the muscle spindle stretches and the Ia afferent fires more strongly. When the muscle is released from the stretch and contracts, the muscle spindle becomes slack, causing the Ia afferent to fall silent. The muscle spindle is rendered insensitive to further stretches of muscle. To restore sensitivity, gamma motor neurons fire and cause the spindle to contract, thereby becoming taut and able to signal the muscle length again.

Motor neurons are divided into two groups. Alpha motor neurons innervate extrafusal fibers, the highly contracting fibers that supply the muscle with its power. Gamma motor neurons innervate intrafusal fibers, which contract only slightly. The function of intrafusal fiber contraction is not to provide force to the muscle; rather, gamma activation of the intrafusal fiber is necessary to keep the muscle spindle taut, and therefore sensitive to stretch, over a wide range of muscle lengths. This concept is illustrated in Figure 1.10. If a resting muscle is stretched, the muscle spindle becomes stretched in parallel, sending signals through the primary and secondary afferents. A subsequent contraction of the muscle, however, removes the pull on the spindle, and it becomes slack, causing the spindle afferents to cease firing. If the muscle were to be stretched again, the muscle spindle would not be able to signal this stretch. Thus, the spindle is rendered temporarily insensitive to stretch after the muscle has contracted. Activation of gamma motor neurons prevents this temporary insensitivity by causing a weak contraction of the intrafusal fibers, in parallel with the contraction of the muscle. This contraction keeps the spindle taut at all times and maintains its sensitivity to changes in the length of the muscle. Thus, when the CNS instructs a muscle to contract, it not only sends the appropriate signals to the alpha motor neurons, it also instructs gamma motor neurons to contract the intrafusal fibers appropriately; this coordinated process is referred to as alpha-gamma coactivation.

1.12 Golgi Tendon Organ

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Figure 1.11
Golgi tendon organ.

The Golgi tendon organ is a specialized receptor that is located between the muscle and the tendon (Figure 1.7). Unlike the muscle spindle, which is located in parallel with extrafusal fibers, the Golgi tendon organ is located in series with the muscle and signals information about the load or force being applied to the muscle. A Golgi tendon organ is made up of a capsule containing numerous collagen fibers (Figure 1.11). The organ is innervated by primary afferents called Group Ib fibers, which have specialized endings that weave in between the collagen fibers. When force is applied to a muscle, the Golgi tendon organ is stretched, causing the collagen fibers to squeeze and distort the membranes of the primary afferent sensory endings. As a result, the afferent is depolarized, and it fires action potentials to signal the amount of force.

Figure 1.12 illustrates the difference in information conveyed by muscle spindles and Golgi tendon organs. At the resting position, the Ia afferents of spindles in the triceps muscle fire at a steady rate to encode the present length of the muscle, and the Ib afferents of the Golgi tendon organs of the biceps muscle fire at a low rate. When a light object (a balloon) is placed in the hand, there is little change in the firing rate of either afferent. When the hand starts to rise, however, the triceps muscle is stretched, and the Ia afferent fibers increase their firing rate as a function of muscle length. The Ib fibers do not change appreciably, because the balloon does not add much load to the muscle. What if a heavy object (a bowling ball) were placed in the hand instead? Because a heavy load is now placed on the biceps, the Ib afferents fire vigorously. Note that the Ia afferent is not affected, as the muscle length has not changed. When the arm begins to rise, however, the Ia afferents fire, just as with the balloon.

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Figure 1.12
Difference between muscle spindle and Golgi tendon organ.

In summary,

  1. Muscle spindles signal information about the length and velocity of a muscle
  2. Golgi tendon organs signal information about the load or force applied to a muscle

Test Your Knowledge

  • Question 1
  • A
  • B
  • C
  • D
  • E

Types of fibers contained within muscle spindles include...

A. Dynamic nuclear bag fibers

B. Dynamic nuclear chain fibers

C. Group Ib afferent fibers

D. Extrafusal fibers

E. Group IV afferent fibers

Types of fibers contained within muscle spindles include...

A. Dynamic nuclear bag fibers This answer is CORRECT!

B. Dynamic nuclear chain fibers

C. Group Ib afferent fibers

D. Extrafusal fibers

E. Group IV afferent fibers

Types of fibers contained within muscle spindles include...

A. Dynamic nuclear bag fibers

B. Dynamic nuclear chain fibers This answer is INCORRECT.

Nuclear chain fibers signal only static muscle length.

C. Group Ib afferent fibers

D. Extrafusal fibers

E. Group IV afferent fibers

Types of fibers contained within muscle spindles include...

A. Dynamic nuclear bag fibers

B. Dynamic nuclear chain fibers

C. Group Ib afferent fibers This answer is INCORRECT.

Group Ib afferents are associated with Golgi tendon organs.

D. Extrafusal fibers

E. Group IV afferent fibers

Types of fibers contained within muscle spindles include...

A. Dynamic nuclear bag fibers

B. Dynamic nuclear chain fibers

C. Group Ib afferent fibers

D. Extrafusal fibers This answer is INCORRECT.

Extrafusal fibers are outside the muscle spindle.

E. Group IV afferent fibers

Types of fibers contained within muscle spindles include...

A. Dynamic nuclear bag fibers

B. Dynamic nuclear chain fibers

C. Group Ib afferent fibers

D. Extrafusal fibers

E. Group IV afferent fibers This answer is INCORRECT.

Group IV afferent fibers are not part of the muscle spindle.

 

 

 

 

 

 

 

 

  • Question 2
  • A
  • B
  • C
  • D
  • E

Muscle force is controlled in part by...

A. Alpha-gamma coactivation

B. Intrafusal fibers

C. Rate code

D. Golgi tendon organs

E. Gamma motor neurons

Muscle force is controlled in part by...

A. Alpha-gamma coactivation This answer is INCORRECT.

Alpha-gamma coactivation ensures that muscle spindles maintain sensitivity to stretch over a wide range of muscle lengths.

B. Intrafusal fibers

C. Rate code

D. Golgi tendon organs

E. Gamma motor neurons

Muscle force is controlled in part by...

A. Alpha-gamma coactivation

B. Intrafusal fibers This answer is INCORRECT.

Intrafusal fibers do not contribute significantly to muscle force.

C. Rate code

D. Golgi tendon organs

E. Gamma motor neurons

Muscle force is controlled in part by...

A. Alpha-gamma coactivation

B. Intrafusal fibers

C. Rate code This answer is CORRECT!

D. Golgi tendon organs

E. Gamma motor neurons

Muscle force is controlled in part by...

A. Alpha-gamma coactivation

B. Intrafusal fibers

C. Rate code

D. Golgi tendon organs This answer is INCORRECT.

Golgi tendon organs signal information about muscle force, but do not control that force directly.

E. Gamma motor neurons

Muscle force is controlled in part by...

A. Alpha-gamma coactivation

B. Intrafusal fibers

C. Rate code

D. Golgi tendon organs

E. Gamma motor neurons This answer is INCORRECT.

Gamma motor neurons innervate intrafusal fibers, which do not contribute significantly to muscle force.

 

 

 

 

 

 

 

 

 

 

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