Question

1. Constantine’s Conundrum

Constantine is a 51-year-old university professor has never had any significant health issues. He exercises regularly, doesn’t smoke or drink alcohol, and keeps his weight within normal range. Recently, however, he’s been experiencing generalized weakness, frequent muscle cramps (tetanic contractions) and tingling in his fingers. On physical examination, he appeared healthy. However, his blood pressure was significantly elevated at 180/100, both in the supine and in the standing positions. His blood and urine analysis revealed the following:

Table 1: Laboratory Values
Blood analysis
Serum Na+	149 mEq/L
Serum K+	2.0 mEq/L
Serum creatinine	Normal
Serum renin	Low (normal)
Urinalysis
Na+ excretion	Below normal
K+ excretion	Above normal
Urinary catecholamines	Normal
Urinary cortisol	Normal

1. Provide a tentative etiology (i.e. underlying pathology) that is consistent with all of Constantine’s blood and urine values. Refer to specific values above to support your answer (or to rule out other pathologies).

2. Explain the difference between a tetanic contraction and a muscle twitch. Why is Constantine susceptible to tetanic contractions in his current condition? Explain the underlying mechanism.

Answer 1

Diagnosis:hypokalemic muscle twitch

Skeletal muscles respond to a single electric shock of sufficient magnitude by rapid, intense contractions called phasic contractions. If the ends of a frog sartorius muscle (at 0 °C) are fixed to prevent shortening, the tension increases for about 200 milliseconds and then begins to decrease, at first rather rapidly and then more slowly. More happens during this mechanical response to a single stimulation, called a twitch, than the tension record suggests.

The mechanical response to repeated stimulation depends on the rate of the stimulation. Muscle, like other excitable tissues, has a period following its action potential during which the membrane will not respond to stimulation regardless of the strength. This absolute refractory period in the frog sartorius at 0 °C lasts about 10 milliseconds after stimulation. Therefore, a second pulse within that time span will not elicit any response. If, however, the pulses are 300 milliseconds apart, the muscle will be relaxing when the second pulse is given, and the tension will appear in waves in phase with the stimulation, causing an unfused tetanus. It is possible to stimulate the muscle at a frequency between these extremes so that the tension developed by the muscle remains constant. This latter type of contraction is called a fused tetanus, and the rate of stimulation that produces it is called the fusion frequency. The exact rate depends upon the particular muscle and the temperature.

Usually, the maximum tetanus tension is from 1.2 to 1.8 times greater than the maximum tension during a twitch. Within the muscle, many elastic structures, connected in series with the contractile elements, are stretched during contraction. The attachment of the muscle fibres to the tendons at the end of the muscle and the attachment of the thin filaments to the Z line contribute to this elastic component. In single fibres, however, most of the elasticity of the series of elastic elements is contributed by the actin-myosin cross bridges themselves. Full maximum tension is not apparent at the end of the muscle until the contractile elements have shortened enough to stretch the elastic elements—somewhat like taking up the slack in a rope before a pull on one end can be felt at the other end. In a twitch, the activity of the muscle is so brief that the contractile elements cannot extend the elastic elements completely before relaxation begins; as a result, the tension at the ends of the muscle does not reach the maximum possible level. During a tetanus, on the other hand, the activity of the contractile elements is maintained, and they can eventually shorten enough to extend fully the series of elastic elements. When this has been accomplished, the maximum tension is apparent at the ends of the muscle.

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Twitch and tetanus responses

Skeletal muscles respond to a single electric shock of sufficient magnitude by rapid, intense contractions called phasic contractions. If the ends of a frog sartorius muscle (at 0 °C) are fixed to prevent shortening, the tension increases for about 200 milliseconds and then begins to decrease, at first rather rapidly and then more slowly. More happens during this mechanical response to a single stimulation, called a twitch, than the tension record suggests.

The mechanical response to repeated stimulation depends on the rate of the stimulation. Muscle, like other excitable tissues, has a period following its action potential during which the membrane will not respond to stimulation regardless of the strength. This absolute refractory period in the frog sartorius at 0 °C lasts about 10 milliseconds after stimulation. Therefore, a second pulse within that time span will not elicit any response. If, however, the pulses are 300 milliseconds apart, the muscle will be relaxing when the second pulse is given, and the tension will appear in waves in phase with the stimulation, causing an unfused tetanus. It is possible to stimulate the muscle at a frequency between these extremes so that the tension developed by the muscle remains constant. This latter type of contraction is called a fused tetanus, and the rate of stimulation that produces it is called the fusion frequency. The exact rate depends upon the particular muscle and the temperature.

Usually, the maximum tetanus tension is from 1.2 to 1.8 times greater than the maximum tension during a twitch. Within the muscle, many elastic structures, connected in series with the contractile elements, are stretched during contraction. The attachment of the muscle fibres to the tendons at the end of the muscle and the attachment of the thin filaments to the Z line contribute to this elastic component. In single fibres, however, most of the elasticity of the series of elastic elements is contributed by the actin-myosin cross bridges themselves. Full maximum tension is not apparent at the end of the muscle until the contractile elements have shortened enough to stretch the elastic elements—somewhat like taking up the slack in a rope before a pull on one end can be felt at the other end. In a twitch, the activity of the muscle is so brief that the contractile elements cannot extend the elastic elements completely before relaxation begins; as a result, the tension at the ends of the muscle does not reach the maximum possible level. During a tetanus, on the other hand, the activity of the contractile elements is maintained, and they can eventually shorten enough to extend fully the series of elastic elements. When this has been accomplished, the maximum tension is apparent at the ends of the muscle.

Length-tension relationship

The force developed by a muscle, whether it is contracting or resting, is strongly dependent on the length of the muscle. Resting skeletal muscle does not exert any force at lengths less than the normal length of the resting muscle in the body. When resting skeletal muscle is extended somewhat beyond the normal length of the muscle, however, a passive force begins to assert itself. The exact length at which this passive force occurs depends on the particular muscle. This force is characterized as passive because it is developed in noncontracting or inactive muscles by the elastic elements of the muscle.

Load-velocity relation

When a muscle is to lift a constant load (isotonic conditions) after stimulation starts, the force increases, just as in an isometric contraction, and, when the force is equal to the load, the muscle begins to shorten and lifts the load. When both the activity of the muscle and the force in it begin to decline, the load stretches the muscle back to its initial length. The tension in the muscle is equal to the load during the shortening and the lengthening of the muscle, except during brief periods of acceleration as the muscle begins to move. Only after the muscle has returned to its initial length does the tension begin to diminish. The size of the load also determines the velocity of shortening; this relationship between load and velocity also applies to cardiac and smooth muscles.

Energy transformations

When a chemical reaction occurs, energy is absorbed or released. In a contracting muscle, chemical reactions release energy that appears either as mechanical work or as heat. The first law of thermodynamics, or the law of conservation of energy, states that the heat and work produced must equal the energy released by the chemical reactions. The muscles that shorten and do external work liberate more energy as heat and work than do those that contract under isometric conditions and do not shorten or do external work. In light of the first law of thermodynamics, this finding means that the amount of chemical reaction that takes place during contraction depends on the type of contraction performed by the muscle. In other words, the flow of energy is subject to regulation.

The efficiency of the process of muscle contraction depends on the fate of the free energy released in chemical reactions—i.e., whether it is converted primarily into work or is degraded into heat. The second law of thermodynamics sets limits to the amount of energy that can be transformed into mechanical work. Although the production of heat can detract from the efficiency of working muscle, energy that appears as heat is not always wasted. In warm-blooded animals, for example, the heat released by muscles maintains a constant body temperature regardless of the environmental temperature. When an animal shivers in the cold, a large amount of heat is generated in the muscles. The muscles alternately contract and relax, releasing energy chiefly as heat.

Source of energy for muscle work

Muscles use the free energy released by chemical reactions by coupling the chemical reaction to physical changes in the contractile proteins. The exact molecular details of this fundamental coupling process are not yet completely known. Of the reactions that have been identified, the splitting of ATP is the energy-yielding reaction nearest to the contractile event. Water participates in this reaction in which ATP is broken down to ADP and phosphate (Pi); the reaction that occurs in the muscle, during which chemical free energy is converted into work, can be written as follows:ATP + H2O + contractile elements → ADP + P i + contractile elements + work + heatThis equation emphasizes the obligatory role of the contractile elements and the coupled nature of the reaction that produces work.

Energy stores

In skeletal muscle most ATP is produced in metabolic pathways involving reactions of the sugar glucose or some other carbohydrate derived from glucose. During contraction, for example, glucose is made available for these reactions by the breakdown of glycogen, the storage form of carbohydrate in animal cells. The concentration of Ca2+ is transiently increased on activation of muscle. The ions are also activators of the process of glycogen breakdown. During the recovery period, the glycogen supply is replenished by synthesizing glycogen from glucose supplied to the muscle tissue by the blood. For a more detailed discussion of the metabolic pathways producing ATP, see metabolism.

In a resting vertebrate muscle, the available supply of ATP can sustain maximal muscle work for less than one second. The muscle, therefore, must continuously replenish its ATP store, and this is done in many different ways. One mechanism for the formation of ATP operates so rapidly that for a long time scientists were unable to detect any change in the amount of ATP in the muscle as a result of contraction. This immediate rebuilding of ATP is accomplished by the reactions of compounds called phosphagens. All of these compounds contain phosphorus in a chemical unit called a phosphoryl group, which they transfer to ADP to produce ATP (these compounds are also referred to as high-energy phosphates).

During rapid and intense contraction, phosphagen can be utilized to rebuild ATP rapidly and maintain its level as long as the phosphagen lasts, which in a maximally working human muscle is just a few seconds. After contraction, ATP is utilized to form phosphagen from creatine; ADP is also formed.

The amount of phosphagen is higher in skeletal muscle than it is in cardiac or smooth muscle. This correlates with the type of activity of the muscles. Skeletal muscle operates in bursts of activity, whereas cardiac and smooth muscle contract in a regular pattern. Skeletal muscle needs an immediate supply of a large amount of ATP, which is provided by the phosphagen reaction; cardiac and smooth muscle, which use ATP at a lower rate, rely on slower reactions to fill their energy requirements.

Molecular mechanisms of contraction

The nerve impulse that ultimately results in muscle contraction appears as an action potential at the sarcolemma, the membrane that surrounds the muscle fibre. This electrical signal is communicated to the myofilaments inside the fibre in the following way. When the action potential reaches the opening of the transverse tubules (channels that open through the sarcolemma to the space outside the fibre; see above The myofibril) in the surface of the fibre, it travels down into the fibre along the tubular membranes, which are continuous with the surface membrane, to within a fraction of a micrometre of each functional contractile unit (Figure 7). In frog muscle the transverse tubules surround the myofibril at the level of each Z line, and in mammalian muscles they are located at the edge of the A bands and I bands. At the triads (the three-element complex consisting of one transverse tubule and two cisternae, which are enlarged saclike membranes), the transverse tubule walls are close to the membranes of the terminal cisternae of the sarcoplasmic reticulum.

By some as-yet-unknown mechanism, the change in the electrical properties of the transverse tubules during an action potential causes the rapid release by the terminal cisternae of relatively large amounts of calcium ions into the sarcoplasm. As the concentration of calcium ions increases in the sarcoplasm, they become bound to the troponin in the thin filaments. This releases (or removes) the troponin-tropomyosin-mediated inhibition of the myosin-actin interaction. As the stimulation of the muscle continues, the terminal cisternae continue to release calcium ions. At the same time, however, some of the calcium ions are being removed from the sarcoplasm by another portion of the sarcoplasmic reticulum, the longitudinal tubules. Once the calcium ions are inside the lumen (cavity) of the longitudinal tubules, many of them slowly diffuse back to the terminal cisternae, where they are bound to a protein, calsequestrin, as a storage site. The removal of calcium ions from the sarcoplasm by the sarcoplasmic reticulum is energy-requiring. The breakdown of ATP is the chemical reaction that supplies the energy, and two calcium ions are apparently removed from the sarcoplasm for each ATP molecule that is split.

Robert E. DaviesNancy A. CurtinJohn Gergely

Cardiac muscle

The heart is the pump that keeps blood circulating throughout the body and thereby transports nutrients, breakdown products, antibodies, hormones, and gases to and from the tissues. The heart consists mostly of muscle; the myocardial cells (collectively termed the myocardium) are arranged in ways that set it apart from other types of muscle. The outstanding characteristics of the action of the heart are its contractility, which is the basis for its pumping action, and the rhythmicity of the contraction.

Heart muscle differs from its counterpart, skeletal muscle, in that it exhibits rhythmic contractions. The amount of blood pumped by the heart per minute (the cardiac output) varies to meet the metabolic needs of the peripheral tissues (muscle, kidney, brain, skin, liver, heart, and gastrointestinal tract). The cardiac output is determined by the contractile force developed by the muscle cells of the heart (myocytes), as well as by the frequency at which they are activated (rhythmicity). The factors affecting the frequency and force of heart muscle contraction are critical in determining the normal pumping performance of the heart and its response to changes in demand.

Structure and organization

The heart is a network of highly branched cardiac cells 110 μm in length and 15 μm in width, which are connected end to end by intercalated disks. The cells are organized into layers of myocardial tissue that are wrapped around the chambers of the heart. The contraction of the individual heart cells produces force and shortening in these bands of muscle, with a resultant decrease in the heart chamber size and the consequent ejection of the blood into the pulmonary and systemic vessels. Important components of each heart cell involved in excitation and metabolic recovery processes are the plasma membrane and transverse tubules in registration with the Z lines, the longitudinal sarcoplasmic reticulum and terminal cisternae, and the mitochondria. The thick (myosin) and thin (actin, troponin, and tropomyosin) protein filaments are arranged into contractile units (that is, the sarcomere extending from Z line to Z line) that have a characteristic cross-striated pattern similar to that seen in skeletal muscle.

The frequency of contraction

The rate at which the heart contracts and the synchronization of atrial and ventricular contraction required for the efficient pumping of blood depend on the electrical properties of the myocardial cells and on the conduction of electrical information from one region of the heart to another. The action potential (activation of the muscle) is divided into five phases (0–4) and is graphed in Figure 9. Each of the phases of the action potential is caused by time-dependent changes in the permeability of the plasma membrane to potassium ions (K+), sodium ions (Na+), and calcium ions (Ca2+). The resting potential of the myocytes of the ventricle (phase 4) begins with the outside of the cell being positive—i.e., having a greater concentration of positive ions. Atrial and ventricular myocytes are normally quiescent (nonrhythmic); however, when the resting membrane potential is depolarized to a critical potential (Ecrit), a self-generating action potential follows, leading to muscle contraction. Phase 0, the upstroke, is associated with a sudden increase in membrane permeability to Na+. Phases 1, 2, and 3 result from changes in membrane permeability and conductance to Na+, K+, and Ca2+.