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Cardiac muscle: a miracle of creation
International Elsevier
CARD10
Journal
of Cardiology, 24 (1989) 251-265
257
00918
Review
Cardiac muscle: a miracle of creation Stephen Department
of Cardiology,
(Received
Seely S. Cardiac
muscle:
a miracle
Seely
University of Manchester,
1 November
of creation.
1988; Revision
The Royal Infirmary, accepted
Int J Cardiol
15 March
Manchester,
U.K.
1989)
1989;24:257-26.5.
The paper proposes that energy conversion in muscle is a two-step process, chemical energy being first converted into electrical energy which is then converted into mechanical work. The chemo-electrical transducers are, in effect, minute voltaic cells - more precisely calcium-magnesium cells - with the magnesium electrodes on myosin heads and the calcium electrodes on the C subunits of troponin molecules associated with actin filaments. These cells are established when, after the passage of an action potential, calcium ions are admitted to the sarcomere. In an energy-consuming process, calcium ions are bound to troponin molecules, the energy for the process being supplied by hydrolysis of adenosine triphosphate. The electro-mechanical transducer utilises the electrostatic field established between the oppositely charged electrodes of the voltaic cell. As the two are pulled towards each other, doing mechanical work, energy is supplied by the voltaic cells. In the course of this action, calcium ions go back into solution. The action ceases when, after the passage of an action potential, calcium ions are withdrawn into the sarcoplasmic reticulum. Key words:
Cardiac
muscle;
Muscular
contraction
Introduction The human heart, and its prime mover, cardiac muscle, must undoubtedly be among the most notable achievements of nature. In the longest-living individuals, the heart works continuously for a hundred or more years, executing something like 4000 million working strokes. In individuals who die of heart disease, it is not usually the cardiac muscle that fails, but some of the comparatively simple mechanisms serving the heart, like arteries
Correspondence to: S. Seely, Dept. of Cardiology, University of Manchester, The Royal Infirmary, Manchester Ml3 9WL. U.K. 0167-5273/89/$03.50
0 1989 Elsevier Science
Publishers
or the pacemaker. Among other notable features of cardiac muscle is its virtual immunity from cancer and high resistance to inflammatory diseases. As the object of medical science is to give a helping hand to ailing and failing organs, those as near perfection as cardiac muscle are of comparatively little interest to it. Organs remarkable for their reliability can be left alone to do their work without interference. Consequently muscle research lacks the urgency demanded by more vulnerable organs. Apart from that, muscles appear to be of great complexity and the understanding of their mode of functioning is immensely difficult. Muscles are chemo-mechanical energy transducers, and theories of muscular contraction
B.V. (Biomedical
Division)
25R
should tell us how they carry out this conversion. Early theories did not even attempt to do so. The generally accepted cross-bridge theory [1,2], put forward in the 195Os, does not go back as far as the basic mechanism of conversion. It takes up the thread only when some unknown mechanism has already converted chemical energy into mechanical work, namely the sweeping action of myosin heads, and attempts to explain events from then , onward. Let us take a brief look, first of all, at the functions attributed to the unknown energy transducer. It can, apparently, cause myosin heads to make contact with an adjacent actin filament at a given point, move it with a sweeping action, disengage from ;It, return to the original position and repeat the action, making contact with the same actin filament, +t “i different point. Furthermore, the distance between adjacent .actin and myosin filaments i,s variable, because the volume of the sarcomere is constant, so that, when it shortens, its diameter has to increase. The spacing between adjacent actin and myosin filaments changes from 22 to 30 nm between extreme elongation and contraction. The shaft diameter of myosin filaments is 12 nm. The protruding length of the myosin heads is 10 nm. So, the tip of the heads can just about reach the nearest actin filament in the state of extreme elongation, but their protruding length must be nearly doubled to do so at The hypothetical energy extreme contraction. transducer, therefore, can not only convert chemical energy into the sweeping action of myosin heads, but can also cause the heads to jut out further from their shafts under some conditions than under others. I suggest that only imaginary mechanisms can be credited with versatility of this order. Even if the primary energy transducer is taken for granted, the mode of action attributed to it by the cross-bridge theory is an impossibility. because it disregards the physical limitations of the protein filaments involved in the action. A microscopically thin structure can .have mechanical strength only in tension, not in compression, bending or torsion. A comparatively heavy weight can be pulled by a strand of hair (which is then under tension), but not pushed by it (imposing a com-
pressive stress), or moved by it with a sweeping action (imposing a bending stress). Myosin heads cannot be rigid enough to move actin filaments with the sweeping action assumed by the crossbridge theory, the same way as a rowing boat could not be moved with soft rubber oars. A more plausible suggestion is that conversion of chemo-mechanical energy in muscle is a twostep process. Chemical energy is first converted into electrical energy and that into mechanical work. The body can undoubtedly convert chemical into electrical energy, as demonstrated by nerve impulses or the pacemaking mechanism of the heart. It may also be noted that the electric organs of electric fishes, which can generate potentials of the order of 100 volts, are morphologically and phylogenetically related to muscle. It is not so easy to find evidence that the animal body is also capable of executing the second step, the electro-mechanical energy conversion. Electro-mechanical transducers, namely electric motors, are readily available in human technology, but they work on the principle of electromagnetic induction which does not seem practicable under biological conditions. In any case, the understanding of the basic principle of energy conversion can be a far cry from knowing how the actual complex mechanism functions. This is the reason why so many different mechanisms have been suggested in the past, all of which must, for the time being, be regarded as only tentative models. The review of Iwazumi and Noble [3] which follows, apart from presenting their own theory, gives references to the work of the pioneers in this field. Hence, the present review can immediately proceed with the discussion of the technical problems of two-step conversion and put forward my suggestions how nature may have solved some of these problems. Two-Step
Energy
The chemo-electric
Conversion
in Muscle
transducer
I have already proposed that the chemo-electric transducer in muscle was essentially a voltaic cell [4]. In such cells, two electrodes are immersed in a liquid, the electrolyte, the most important electrolyte being water. The electrolyte contains sub-
259
stances which tend to dissociate in solution into positively and negatively charged ions. Metals and hydrogen are electropositive in character and they tend to form positive ions. Elements of the chlorine group and some acid radicals, like sulphate, nitrate and phosphate, form negative ions. If such charged ions are brought into contact with an electron donor (or acceptor), so that they can lose their charge and become electrically neutral, energy-yielding reactions can result. The electrodes, to a limited extent, may be electron donors or acceptors themselves. But, if an electron-conducting connection is made between them, the electrons accepted by one of the electrodes can be transferred to the other acting as an electron donor, resulting in a continuous current flow. This arrangement forms a closed electric circuit, in one part of which current is in form of electron flow in a solid medium. in the other in form of ion migration in a fluid medium. The energy-yielding chemical changes take place at the liquid-solid interfaces, and the energy liberated by the chemical process can be utilised as an energy source, by, for example, inserting a resistance in the electron circuit. It may be pointed out that the energy-yielding reactions are the same which would arise if positively and negatively charged ions could directly exchange electrons in solution. but apparently they cannot, Water does not accept electrons and acts as an insulator to their direct exchange between solutes. Consequently, positively and negatively charged ions migrate in the electrolyte in opposite directions to give up their charges to electrodes in preference to exchanging them directly in the electrolyte. The energy-yielding reaction does not necessarily involve chemical changes. The tendency of
some metals to go into solution with the liberation of energy can also be utilised. Some metals of this nature are lithium, sodium, potassium, calcium magnesium. If such metals are made the electrodes of voltaic cells, they produce high electrode potentials, e.g. lithium -3.045, calcium -2.866, magnesium -2.363 volts. If both the anode an@ cathode of a voltaic cell produces a negative electrode potential, the terminal voltage of the cell is the difference of the two electrode potentials. For example, that of a calcium-magnesium cell would be -0.503 volts, and the cell would function by the metal with the higher electrode potential, calcium, going into solution, and the one with the weaker electrode potential. magnesium, driven out of solution. The action of cells of this nature is reversible. Thus, if an external source provided more than 0.5 volts to oppose the electrode potential of calcium and support that of magnesium, magnesium ions would go into solution and calcium ions would precipitate as metallic calcium. In other words, the cell can be charged from an external source as well as allowed to discharge itself and serve as an energy source. According to my theory [4], the active sarcomere incorporates a calcium-magnesium cell, as well as a device capable of reversing or controlling its action. The magnesium electrode is associated with myosin heads and takes the form of a complex of adenosine triphosphate and magnesium. as shown in Fig. la. In the resting sarcomere, there is no calcium electrode. When muscle is activated by an action potential, calcium ions are admitted to the intracellular fluid in the sarcomere and become bound to troponin molecules of actin filaments. This precipitation of calcium ions is an energy consuming process. As already pointed out, metallic calcium tends to go into solution with the
y2+ o((I)
o-
ADENOSINE-O--_-O-b-O-~-O-
tdg2+ / \ ;_ b__
‘\
o(b)
ADENOSINE-O-b-O-6-0-
Fig. 1. (a) ATP- and (b) ADP-magnesium complexes
260
liberation of energy. When it comes out of solution, the same amount of energy has to be supplied to it. The presumable source of this energy is the breaking up of the complexes of adenosine triphosphate and magnesium shown in Fig. la. The triphosphate can be assumed to be hydrolised into a diphosphate, releasing a phosphate ion and a quantity of energy. It also releases the magnesium bound to it. Hence, a further quantity of energy arising from magnesium going into solution. These two energy sources together force calcium ions out of solution, thus forming the calcium electrode of a calcium-magnesium cell. In the next phase, hydrolysis of adenosine triphosphate ceases and the newly constituted calciummagnesium cell begins to function as such, calcium going back into solution and magnesium coming out of it, with the liberation of energy. In effect, the cell is first charged, then allowed to discharge. The magnesium ions driven out of solution form complexes with adenosine diphosphate, as shown in Fig. lb. One more point needs to be discussed before turning to the electro-mechanical transducer. As pointed out in the review of Iwazumi and Noble which follows, an often heard objection against electrostatic theories of muscular contraction is that no significant potential difference can be established between two points within a muscle cell, because the intracellular fluid is a good conductor, and the potential difference would immediately be dissipated by current flow. This argument is certainly not valid for the electrolyte of a voltaic cell. If the connection between the two electrodes is broken, the potential difference be-
tween them still remains, but the current flow stops. Ions migrate to the electrodes only if those can accept or donate electrons. If there is no electron flow in an external conductor, there is no ion migration in the electrolyte. The electro-mechanical
energy transducer
It is my proposal that the electro-mechanical transducer in the sarcomere is, in effect, a variable capacitor. A capacitor in its simplest form is a block of insulating material sandwiched between two conducting plates bearing an electric charge. This can serve for the storage of electrical energy, because the electrostatic field imposed on the insulator distorts electron orbits in its atoms, causing them to become elliptical instead of circular. The change of electron orbits absorbs energy, which is returned when they can resume their normal path. The energy stored by the capacitor is $CE’. where C is capacitance and E is the potential difference between the conducting plates. Capacitance depends on the apposed surface area of the conductors, the distance between them, and the dielectric constant of the insulator. A variable capacitor is a device the capacitance of which can be changed, for example, by pulling the conducting plates apart or replacing the insulator with one of a higher or lower dielectric constant. For the ease of visualisation, the homology can be made between a capacitor and a container of compressed gas. The energy of compressed gas is 4 VP’, where V is the volume of the container and P is pressure. If the volume is variable ~ if the container is a cylinder, one end of which is a
++++++
21++++++ Fig. 2. Concentric
cylinder
capacitor.
261
movable piston - the arrangement tends to enlarge its volume, thereby reducing pressure. If the piston moves against a load, it is capable of converting the potential energy of the compressed gas into mechanical work. A simple form of variable capacitor is shown in Fig. 2. This consists of two coaxial cylinders containing an electrostatic charge, separated by a dielectric. On the same principle, by which a cylinder filled with compressed gas tends to increase its volume, the charged capacitor tends to increase its capacitance. In the given case, this can be done by the inner cylinder sliding further into the outer cylinder, increasing the apposed surface area. With increasing capacitance, the potential difference between the two conducting surfaces decreases, and with it the stored energy of the construction. This loss of energy can be converted into mechanical work, if, for example. the sliding movement of the cylinder in Fig. 2 were made to pull a weight. This is exactly analogous with the piston of a compressed air cylinder moving against a load, except that the piston would push the load, the sliding cylinder in Fig. 2 pull it. Naturally, this is an essential difference, because, as already pointed out, thin filaments have mechanical strength only in tension; they can only pull, not push. The construction in Fig. 2 bears some resemblance to that of the sarcomere. The inner cylinder can be regarded the equivalent of a myosin filament, the outer cylinder representing 6 actin filaments surrounding it. If a potential difference E is assumed to exist between the two cylinders, the force appearing between them in an axial direction, so as to shorten the sarcomere, would be
F=
E27TC*Cr
log, ( R/r )
where R and r are the radii of outer and inner cylinders, E,, is a physical constant (absolute permittivity), er is relative permittivity, (the dielectric constant of the medium separating the cylinders). Numerical data relating to the sarcomere are: F = 20 newtons maximum per cm2 of muscle. no. of myosin filaments per cm’ of muscle = 6 X lo”, R (depending on elongation of the sarcomere)
about 20-28 nm. r (over myosin heads) 16 nm, er (for water) = 80, co = 8.85 X lOPi’. Substituting these values in the above equation it can be calculated that the potential difference between actin and myosin filaments should be about 200 mV to enable muscle to develop a maximum force of 20 newtons per cm2. This figure is only a rough approximation, because the 6 actin filaments surrounding a myosin filament were assumed to constitute a complete cylinder. The result, therefore, errs on the low side, but appears to be at least of the right order in comparison with the theoretical 500 mV output of the voltaic cell described in the previous section. The operational characteristics of the simple device shown in Fig. 2, however, are not in agreement with those of muscle. In a simple variable capacitor, as shown in Fig. 2, attractive force in the axial direction acts on the edge of the cylinders, so that the axial pull remains unchanged as the inner cylinder is drawn into the outer one. It becomes zero when the two completely overlap. In contrast, muscle exerts increasing force with the increasing interdigitation of actin and myosin filaments, and is capable of further contraction (supercontraction) when interdigitation is complete. Fig. 3a shows a variable capacitor in which axial pull increases with the progressive overlap of the two cylinders. These two cylinders are essentially as in Fig. 2, but they are divided into a number of insulated segments. To begin with, only the first segment of each cylinder is charged. When the inner cylinder has moved so far that its first segment overlaps that of the outer cylinder, the second segment of the latter is energized. And so on. A charged segment on the outer cylinder always appears a step ahead of the first segment of the inner cylinder. In this manner, the inner cylinder can be pulled completely into the outer cylinder. The energy expended in charging the outer cylinder segment by segment is the same as if the whole cylinder had been energized in the first place. And so is the work done. The difference is that, after a time interval, the first segment of the outer cylinder can be re-energized and engage with another segment of the inner cylinder. On the assumption that the period of recovery is twice as long as the active period, Fig. 2b shows conditions
262
109
8
7
6
5
4
3
21
(b) 1098 P
”
76
“1
I
54
-
32
1
'
-
I
w
I
I
,
,
I
12345678910
3
Fig. 3. Concentric
cylinder
capacitors
divided
into insulated
when two charged segments interact with each other on both cylinders. Another two steps later, three segments on each cylinder could be activated, so that the axial force increases with interdigitation. The sarcomere is divided not into segments, but minute areas. It is assumed that, on myosin filaments, only the heads carry complexes of magnesium and adenosine triphosphate, on actin filaments, only a subunit of troponin molecules, troponin C, can act as a binding site of calcium. The troponin molecules are located at regular intervals on tropomyosin filaments which. in turn, are wound helically on actin filaments. The mode of action is assumed to be as follows. The sarcomere is activated by the admission of calcium ions to the intracellular fluid in which the sarcomere is immersed. These calcium ions have no effect on any part of the sacromere where, at a given moment, there are only myosin or only actin filaments. Action begins only when they reach a region containing both filaments. Even then there are directional limitations. It can be assumed that the energy-producing complexes are present only in locations which could be described as the throat
segments.
Black segments
are charged.
light segments
uncharged.
of myosin heads. Troponin molecules have a directional feature, in that the globe-shaped molecule consists of three subunits. One of these is the base of the globule, fixed to the tropomyosin filament, the calcium-binding part, troponin C, is facing forward and troponin I is facing backward. Calcium ions have to diffuse into the space between the throat of a myosin head and the C part of a troponin molecule facing it, in which case the action described in the previous section begins. Myosin heads release magnesium ions. troponin C binds calcium, thus establishing a calcium-magnesium cell. When this cell produces a potential difference, its electrodes become parts of a variable capacitor with the intracellular fluid as the dielectric. When the electrostatic attraction between the two sides of the capacitor results in movement against a load, the energy for the mechanical work involved in the movement is provided by the calcium-magnesium cell, calcium bound by troponin C going into solution and magnesium ions re-complexing with adenosine tri- or diphosphate. By the time the interacting myosin head and troponin C unit are pulled in line with each other, the force of attraction between them disap-
263
pears, partly because the troponin C unit has lost the calcium bound to it, and partly because the directional requirements are no longer satisfied. The troponin globule faces the side of the myosin head, not its throat, and the myosin head faces the I subunit of the troponin globule, so that the active parts are shielded from each other. When the previously active myosin head and troponin molecule are pulled in line with each other, the throat of the myosin head faces the next troponin molecule on the line, and the C unit of the previously active troponin molecule faces the myosin head immediately behind the one with which it was previously engaged. In both cases, conditions are the same as at the commencement of the previous phase of activity. Calcium ions are in solution, the troponin C units are ready to take them up, and magnesium complexed with adenosine tri- or diphosphate is available in myosin heads. The result is continuous action, until calcium ions are actively withdrawn after the passage of action potentials. Complexes of magnesium with adenosine diphosphate are re-converted into those complexes with triphosphates with the absorption of energy in the resting muscle. But, if muscle works until the exhaustion of its energy resources, a complex with diphosphate can also be a source of energy, the diphosphate being capable of conversion to adenosine monophosphate. The calculation of the potential difference required to produce a given force is obviously more difficult than in the simple cases represented by Figs. 2 or 3. If a myosin head interacts not with the troponin molecule immediately adjacent to it, but with the next one on the line, the distance between areas bearing electrostatic charges of opposite sign is far greater than assumed in the previous calculation, of the order of 40 nm instead of 4-12 nm. Against that, the pull is almost entirely in the axial direction, and many units in tandem work at a given time. A half sarcomere contains about 150 myosin heads in 9 rows, so that in full interdigitation 16 myosin heads could be active in a row. Also, in the given case a closer approximation could be made if sarcomeres were not regarded coaxial cylinders, but active myosin heads and troponin C units were taken as individ-
ual point sources. and the total pull tending to shorten the sarcomere obtained from the summation of these forces. An unknown factor is the relative duration of the charge and discharge periods of the assumed voltaic cells. No attempt is made in this paper to perform a more accurate calculation. Perhaps it will suffice to say that some of the differences between Fig. 2 and actual conditions tend to increase, other to decrease the 200 mV figure obtained before, which can still be assumed to give a reasonable approximation to the correct value. The discussion above gave a general outline of a theory of muscular contraction, leaving many questions to be answered. A few of these are discussed below. When muscle is excited under isometric conditions, it can develop a force, but is prevented from doing work. Conditions are essentially similar to those represented in Fig. 2, if the two cylinders are immovable. It may be noted that a charged capacitor does not hold its charge indefinitely; gradually it loses it by leakage, the same way as a compressed gas may slowly escape from its container. The rate of leakage depends on the imperfection of the sealing. In the microscopic world of the sarcomere the rate of leakage is high, and also in a long chain of sarcomeres there is some movement under isometric conditions, a proportion of the sarcomeres contract while others are stretched, so that the muscle consumes energy. When a muscle is excited and tends to contract, but in fact it is elongated by a superior force, conditions are as if in Fig. 2 the two cylinders were pulled apart, or if a compressed gas were further compressed by the inward motion of the piston. In other words, a variable capacitor is an energy transducer in both directions, it can convert electrical energy into mechanical work, or mechanical work into electrical energy. Hence, the force required to elongate contracting muscle is partly that needed to counteract the force developed by the muscle and partly that which the muscle under given conditions converts into electrical energy. A considerable part of my previous paper on muscular contraction [4] was devoted to the problem of lateral stability. When the sarcomere devel-
264
Fig. 4. The arrangement of actin and transverse section.
myosin
filaments
in
ops force in an axial direction, so as to shorten itself, it also develops forces in the lateral direction, drawing actin and myosin filaments closer to each other. As, however, the filaments constitute symmetrical patterns, each myosin filament being surrounded by 6 actin filaments and each actin filament by 3 myosin filaments (Fig. 4), lateral forces balance each other at least in the bulk of the muscle, though unbalanced lateral forces may appear at their boundaries. The more probable solution of this problem. as explained in this paper, is that the power sources are shielded from each other laterally, and only minor lateral forces have to be balanced by symmetry. In the half sarcomere, the length of myosin filaments is about 820 nm, of which about 100 nm at the M line contains only myosin tails. The length containing myosin heads is about 720 nm. The length of the actin filaments is about 1000 nm, so that when the two filaments are fully interdigitated, the end of the actin filaments touching the M line, nearly 20% of the full length of the actin filaments is still disengaged. In supercontraction, this additional length interdigitates with myosin filaments, developing maximal force of contraction. At the M lines, a double overlap is assumed to take place, as the tips of actin filaments from one half sarcomere enter the other ha!f. I do not quite agree with this assumption. When tips of actin filaments reach the last 100 nm of myosin filaments, no myosin heads are available for interaction, hence they assume a passive state. Normal interactions can still take place in the rest of the half sarcomere, including
interactions between heads on the leading end of myosin filaments and troponin molecules on the still disengaged edge of actin filaments. Further interdigitation, therefore, proceeds normally. The movement of the actin filaments, and the probable resistance M lines present to further movement, puts a compressive stress on the tips of the actin filaments, which, therefore, coil up at the M lines, a length of 280 nm being compressed into a 100 nm long space. This takes place at a time when the diameter of the sarcomere is at its maximum. so that there is no difficulty in accommodating a small coil of actin filaments. As pointed out in the review of Iwazumi and Noble [3], the troponin complexes are located on actin filaments at 38 nm intervals, while myosin heads in corresponding positions on myosin heads are located at 43 nm intervals. One possible explanation is that both filaments are stretchable, but the thin filaments stretch more under tensile stress than the thick filaments. In fact, the different spacing of myosin heads and troponin molecules is only a part of a greater problem, to understand the extremely complicated arrangement of myosin heads and troponin molecules. In a given cross-section of muscle, there are twice as many actin as myosin filaments, so that each myosin filament must interact with two actin filaments. Myosin heads are arranged on their filament along a 3-start helical path, so that successive heads are 40” apart. while the actin filaments surrounding each myosin filament are 60” apart. The whole arrangement presents a picture of such complexity that its exact understanding will have to await further research. Lastly, I mentioned earlier that the electric organs of electric fishes are muscle-like structures. A moderate voltage generated by a muscle-like organ could be greatly increased by sudden stretching, the mechanical energy effecting the stretching being converted into electrical energy. Electric organs are in the side of fishes and could be suddenly stretched by the jerking of an antagonistic muscle on the other side of the fish,
Acknowledgements My thanks are due to the Editor of the Journal, Professor Robert H. Anderson, for support and
265
encouragement, and to the referee of the paper, Professor Mark Noble, for constructive and thought-provoking criticism. References 1 Huxley HE, Hansen J. Changes in the cross-striations of muscle during contraction and stretch, and their structural interpretation. Nature 1954;173:973-976.
2 Huxley AF, Niedergerke R. Structural changes during contraction. Nature 1954;173:971-973. 3 Iwazumi T. Noble M. An electrostatic mechanism lar contraction. Int J Cardiol 1989;24:267-275. 4 Seely S. An electrodynamic (moving field) theory lar contraction. J Theor Biol 1986:121:233-242.
in muscle of muscuof muscu-
CARD10
Journal
of Cardiology, 24 (1989) 251-265
257
00918
Review
Cardiac muscle: a miracle of creation Stephen Department
of Cardiology,
(Received
Seely S. Cardiac
muscle:
a miracle
Seely
University of Manchester,
1 November
of creation.
1988; Revision
The Royal Infirmary, accepted
Int J Cardiol
15 March
Manchester,
U.K.
1989)
1989;24:257-26.5.
The paper proposes that energy conversion in muscle is a two-step process, chemical energy being first converted into electrical energy which is then converted into mechanical work. The chemo-electrical transducers are, in effect, minute voltaic cells - more precisely calcium-magnesium cells - with the magnesium electrodes on myosin heads and the calcium electrodes on the C subunits of troponin molecules associated with actin filaments. These cells are established when, after the passage of an action potential, calcium ions are admitted to the sarcomere. In an energy-consuming process, calcium ions are bound to troponin molecules, the energy for the process being supplied by hydrolysis of adenosine triphosphate. The electro-mechanical transducer utilises the electrostatic field established between the oppositely charged electrodes of the voltaic cell. As the two are pulled towards each other, doing mechanical work, energy is supplied by the voltaic cells. In the course of this action, calcium ions go back into solution. The action ceases when, after the passage of an action potential, calcium ions are withdrawn into the sarcoplasmic reticulum. Key words:
Cardiac
muscle;
Muscular
contraction
Introduction The human heart, and its prime mover, cardiac muscle, must undoubtedly be among the most notable achievements of nature. In the longest-living individuals, the heart works continuously for a hundred or more years, executing something like 4000 million working strokes. In individuals who die of heart disease, it is not usually the cardiac muscle that fails, but some of the comparatively simple mechanisms serving the heart, like arteries
Correspondence to: S. Seely, Dept. of Cardiology, University of Manchester, The Royal Infirmary, Manchester Ml3 9WL. U.K. 0167-5273/89/$03.50
0 1989 Elsevier Science
Publishers
or the pacemaker. Among other notable features of cardiac muscle is its virtual immunity from cancer and high resistance to inflammatory diseases. As the object of medical science is to give a helping hand to ailing and failing organs, those as near perfection as cardiac muscle are of comparatively little interest to it. Organs remarkable for their reliability can be left alone to do their work without interference. Consequently muscle research lacks the urgency demanded by more vulnerable organs. Apart from that, muscles appear to be of great complexity and the understanding of their mode of functioning is immensely difficult. Muscles are chemo-mechanical energy transducers, and theories of muscular contraction
B.V. (Biomedical
Division)
25R
should tell us how they carry out this conversion. Early theories did not even attempt to do so. The generally accepted cross-bridge theory [1,2], put forward in the 195Os, does not go back as far as the basic mechanism of conversion. It takes up the thread only when some unknown mechanism has already converted chemical energy into mechanical work, namely the sweeping action of myosin heads, and attempts to explain events from then , onward. Let us take a brief look, first of all, at the functions attributed to the unknown energy transducer. It can, apparently, cause myosin heads to make contact with an adjacent actin filament at a given point, move it with a sweeping action, disengage from ;It, return to the original position and repeat the action, making contact with the same actin filament, +t “i different point. Furthermore, the distance between adjacent .actin and myosin filaments i,s variable, because the volume of the sarcomere is constant, so that, when it shortens, its diameter has to increase. The spacing between adjacent actin and myosin filaments changes from 22 to 30 nm between extreme elongation and contraction. The shaft diameter of myosin filaments is 12 nm. The protruding length of the myosin heads is 10 nm. So, the tip of the heads can just about reach the nearest actin filament in the state of extreme elongation, but their protruding length must be nearly doubled to do so at The hypothetical energy extreme contraction. transducer, therefore, can not only convert chemical energy into the sweeping action of myosin heads, but can also cause the heads to jut out further from their shafts under some conditions than under others. I suggest that only imaginary mechanisms can be credited with versatility of this order. Even if the primary energy transducer is taken for granted, the mode of action attributed to it by the cross-bridge theory is an impossibility. because it disregards the physical limitations of the protein filaments involved in the action. A microscopically thin structure can .have mechanical strength only in tension, not in compression, bending or torsion. A comparatively heavy weight can be pulled by a strand of hair (which is then under tension), but not pushed by it (imposing a com-
pressive stress), or moved by it with a sweeping action (imposing a bending stress). Myosin heads cannot be rigid enough to move actin filaments with the sweeping action assumed by the crossbridge theory, the same way as a rowing boat could not be moved with soft rubber oars. A more plausible suggestion is that conversion of chemo-mechanical energy in muscle is a twostep process. Chemical energy is first converted into electrical energy and that into mechanical work. The body can undoubtedly convert chemical into electrical energy, as demonstrated by nerve impulses or the pacemaking mechanism of the heart. It may also be noted that the electric organs of electric fishes, which can generate potentials of the order of 100 volts, are morphologically and phylogenetically related to muscle. It is not so easy to find evidence that the animal body is also capable of executing the second step, the electro-mechanical energy conversion. Electro-mechanical transducers, namely electric motors, are readily available in human technology, but they work on the principle of electromagnetic induction which does not seem practicable under biological conditions. In any case, the understanding of the basic principle of energy conversion can be a far cry from knowing how the actual complex mechanism functions. This is the reason why so many different mechanisms have been suggested in the past, all of which must, for the time being, be regarded as only tentative models. The review of Iwazumi and Noble [3] which follows, apart from presenting their own theory, gives references to the work of the pioneers in this field. Hence, the present review can immediately proceed with the discussion of the technical problems of two-step conversion and put forward my suggestions how nature may have solved some of these problems. Two-Step
Energy
The chemo-electric
Conversion
in Muscle
transducer
I have already proposed that the chemo-electric transducer in muscle was essentially a voltaic cell [4]. In such cells, two electrodes are immersed in a liquid, the electrolyte, the most important electrolyte being water. The electrolyte contains sub-
259
stances which tend to dissociate in solution into positively and negatively charged ions. Metals and hydrogen are electropositive in character and they tend to form positive ions. Elements of the chlorine group and some acid radicals, like sulphate, nitrate and phosphate, form negative ions. If such charged ions are brought into contact with an electron donor (or acceptor), so that they can lose their charge and become electrically neutral, energy-yielding reactions can result. The electrodes, to a limited extent, may be electron donors or acceptors themselves. But, if an electron-conducting connection is made between them, the electrons accepted by one of the electrodes can be transferred to the other acting as an electron donor, resulting in a continuous current flow. This arrangement forms a closed electric circuit, in one part of which current is in form of electron flow in a solid medium. in the other in form of ion migration in a fluid medium. The energy-yielding chemical changes take place at the liquid-solid interfaces, and the energy liberated by the chemical process can be utilised as an energy source, by, for example, inserting a resistance in the electron circuit. It may be pointed out that the energy-yielding reactions are the same which would arise if positively and negatively charged ions could directly exchange electrons in solution. but apparently they cannot, Water does not accept electrons and acts as an insulator to their direct exchange between solutes. Consequently, positively and negatively charged ions migrate in the electrolyte in opposite directions to give up their charges to electrodes in preference to exchanging them directly in the electrolyte. The energy-yielding reaction does not necessarily involve chemical changes. The tendency of
some metals to go into solution with the liberation of energy can also be utilised. Some metals of this nature are lithium, sodium, potassium, calcium magnesium. If such metals are made the electrodes of voltaic cells, they produce high electrode potentials, e.g. lithium -3.045, calcium -2.866, magnesium -2.363 volts. If both the anode an@ cathode of a voltaic cell produces a negative electrode potential, the terminal voltage of the cell is the difference of the two electrode potentials. For example, that of a calcium-magnesium cell would be -0.503 volts, and the cell would function by the metal with the higher electrode potential, calcium, going into solution, and the one with the weaker electrode potential. magnesium, driven out of solution. The action of cells of this nature is reversible. Thus, if an external source provided more than 0.5 volts to oppose the electrode potential of calcium and support that of magnesium, magnesium ions would go into solution and calcium ions would precipitate as metallic calcium. In other words, the cell can be charged from an external source as well as allowed to discharge itself and serve as an energy source. According to my theory [4], the active sarcomere incorporates a calcium-magnesium cell, as well as a device capable of reversing or controlling its action. The magnesium electrode is associated with myosin heads and takes the form of a complex of adenosine triphosphate and magnesium. as shown in Fig. la. In the resting sarcomere, there is no calcium electrode. When muscle is activated by an action potential, calcium ions are admitted to the intracellular fluid in the sarcomere and become bound to troponin molecules of actin filaments. This precipitation of calcium ions is an energy consuming process. As already pointed out, metallic calcium tends to go into solution with the
y2+ o((I)
o-
ADENOSINE-O--_-O-b-O-~-O-
tdg2+ / \ ;_ b__
‘\
o(b)
ADENOSINE-O-b-O-6-0-
Fig. 1. (a) ATP- and (b) ADP-magnesium complexes
260
liberation of energy. When it comes out of solution, the same amount of energy has to be supplied to it. The presumable source of this energy is the breaking up of the complexes of adenosine triphosphate and magnesium shown in Fig. la. The triphosphate can be assumed to be hydrolised into a diphosphate, releasing a phosphate ion and a quantity of energy. It also releases the magnesium bound to it. Hence, a further quantity of energy arising from magnesium going into solution. These two energy sources together force calcium ions out of solution, thus forming the calcium electrode of a calcium-magnesium cell. In the next phase, hydrolysis of adenosine triphosphate ceases and the newly constituted calciummagnesium cell begins to function as such, calcium going back into solution and magnesium coming out of it, with the liberation of energy. In effect, the cell is first charged, then allowed to discharge. The magnesium ions driven out of solution form complexes with adenosine diphosphate, as shown in Fig. lb. One more point needs to be discussed before turning to the electro-mechanical transducer. As pointed out in the review of Iwazumi and Noble which follows, an often heard objection against electrostatic theories of muscular contraction is that no significant potential difference can be established between two points within a muscle cell, because the intracellular fluid is a good conductor, and the potential difference would immediately be dissipated by current flow. This argument is certainly not valid for the electrolyte of a voltaic cell. If the connection between the two electrodes is broken, the potential difference be-
tween them still remains, but the current flow stops. Ions migrate to the electrodes only if those can accept or donate electrons. If there is no electron flow in an external conductor, there is no ion migration in the electrolyte. The electro-mechanical
energy transducer
It is my proposal that the electro-mechanical transducer in the sarcomere is, in effect, a variable capacitor. A capacitor in its simplest form is a block of insulating material sandwiched between two conducting plates bearing an electric charge. This can serve for the storage of electrical energy, because the electrostatic field imposed on the insulator distorts electron orbits in its atoms, causing them to become elliptical instead of circular. The change of electron orbits absorbs energy, which is returned when they can resume their normal path. The energy stored by the capacitor is $CE’. where C is capacitance and E is the potential difference between the conducting plates. Capacitance depends on the apposed surface area of the conductors, the distance between them, and the dielectric constant of the insulator. A variable capacitor is a device the capacitance of which can be changed, for example, by pulling the conducting plates apart or replacing the insulator with one of a higher or lower dielectric constant. For the ease of visualisation, the homology can be made between a capacitor and a container of compressed gas. The energy of compressed gas is 4 VP’, where V is the volume of the container and P is pressure. If the volume is variable ~ if the container is a cylinder, one end of which is a
++++++
21++++++ Fig. 2. Concentric
cylinder
capacitor.
261
movable piston - the arrangement tends to enlarge its volume, thereby reducing pressure. If the piston moves against a load, it is capable of converting the potential energy of the compressed gas into mechanical work. A simple form of variable capacitor is shown in Fig. 2. This consists of two coaxial cylinders containing an electrostatic charge, separated by a dielectric. On the same principle, by which a cylinder filled with compressed gas tends to increase its volume, the charged capacitor tends to increase its capacitance. In the given case, this can be done by the inner cylinder sliding further into the outer cylinder, increasing the apposed surface area. With increasing capacitance, the potential difference between the two conducting surfaces decreases, and with it the stored energy of the construction. This loss of energy can be converted into mechanical work, if, for example. the sliding movement of the cylinder in Fig. 2 were made to pull a weight. This is exactly analogous with the piston of a compressed air cylinder moving against a load, except that the piston would push the load, the sliding cylinder in Fig. 2 pull it. Naturally, this is an essential difference, because, as already pointed out, thin filaments have mechanical strength only in tension; they can only pull, not push. The construction in Fig. 2 bears some resemblance to that of the sarcomere. The inner cylinder can be regarded the equivalent of a myosin filament, the outer cylinder representing 6 actin filaments surrounding it. If a potential difference E is assumed to exist between the two cylinders, the force appearing between them in an axial direction, so as to shorten the sarcomere, would be
F=
E27TC*Cr
log, ( R/r )
where R and r are the radii of outer and inner cylinders, E,, is a physical constant (absolute permittivity), er is relative permittivity, (the dielectric constant of the medium separating the cylinders). Numerical data relating to the sarcomere are: F = 20 newtons maximum per cm2 of muscle. no. of myosin filaments per cm’ of muscle = 6 X lo”, R (depending on elongation of the sarcomere)
about 20-28 nm. r (over myosin heads) 16 nm, er (for water) = 80, co = 8.85 X lOPi’. Substituting these values in the above equation it can be calculated that the potential difference between actin and myosin filaments should be about 200 mV to enable muscle to develop a maximum force of 20 newtons per cm2. This figure is only a rough approximation, because the 6 actin filaments surrounding a myosin filament were assumed to constitute a complete cylinder. The result, therefore, errs on the low side, but appears to be at least of the right order in comparison with the theoretical 500 mV output of the voltaic cell described in the previous section. The operational characteristics of the simple device shown in Fig. 2, however, are not in agreement with those of muscle. In a simple variable capacitor, as shown in Fig. 2, attractive force in the axial direction acts on the edge of the cylinders, so that the axial pull remains unchanged as the inner cylinder is drawn into the outer one. It becomes zero when the two completely overlap. In contrast, muscle exerts increasing force with the increasing interdigitation of actin and myosin filaments, and is capable of further contraction (supercontraction) when interdigitation is complete. Fig. 3a shows a variable capacitor in which axial pull increases with the progressive overlap of the two cylinders. These two cylinders are essentially as in Fig. 2, but they are divided into a number of insulated segments. To begin with, only the first segment of each cylinder is charged. When the inner cylinder has moved so far that its first segment overlaps that of the outer cylinder, the second segment of the latter is energized. And so on. A charged segment on the outer cylinder always appears a step ahead of the first segment of the inner cylinder. In this manner, the inner cylinder can be pulled completely into the outer cylinder. The energy expended in charging the outer cylinder segment by segment is the same as if the whole cylinder had been energized in the first place. And so is the work done. The difference is that, after a time interval, the first segment of the outer cylinder can be re-energized and engage with another segment of the inner cylinder. On the assumption that the period of recovery is twice as long as the active period, Fig. 2b shows conditions
262
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Fig. 3. Concentric
cylinder
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when two charged segments interact with each other on both cylinders. Another two steps later, three segments on each cylinder could be activated, so that the axial force increases with interdigitation. The sarcomere is divided not into segments, but minute areas. It is assumed that, on myosin filaments, only the heads carry complexes of magnesium and adenosine triphosphate, on actin filaments, only a subunit of troponin molecules, troponin C, can act as a binding site of calcium. The troponin molecules are located at regular intervals on tropomyosin filaments which. in turn, are wound helically on actin filaments. The mode of action is assumed to be as follows. The sarcomere is activated by the admission of calcium ions to the intracellular fluid in which the sarcomere is immersed. These calcium ions have no effect on any part of the sacromere where, at a given moment, there are only myosin or only actin filaments. Action begins only when they reach a region containing both filaments. Even then there are directional limitations. It can be assumed that the energy-producing complexes are present only in locations which could be described as the throat
segments.
Black segments
are charged.
light segments
uncharged.
of myosin heads. Troponin molecules have a directional feature, in that the globe-shaped molecule consists of three subunits. One of these is the base of the globule, fixed to the tropomyosin filament, the calcium-binding part, troponin C, is facing forward and troponin I is facing backward. Calcium ions have to diffuse into the space between the throat of a myosin head and the C part of a troponin molecule facing it, in which case the action described in the previous section begins. Myosin heads release magnesium ions. troponin C binds calcium, thus establishing a calcium-magnesium cell. When this cell produces a potential difference, its electrodes become parts of a variable capacitor with the intracellular fluid as the dielectric. When the electrostatic attraction between the two sides of the capacitor results in movement against a load, the energy for the mechanical work involved in the movement is provided by the calcium-magnesium cell, calcium bound by troponin C going into solution and magnesium ions re-complexing with adenosine tri- or diphosphate. By the time the interacting myosin head and troponin C unit are pulled in line with each other, the force of attraction between them disap-
263
pears, partly because the troponin C unit has lost the calcium bound to it, and partly because the directional requirements are no longer satisfied. The troponin globule faces the side of the myosin head, not its throat, and the myosin head faces the I subunit of the troponin globule, so that the active parts are shielded from each other. When the previously active myosin head and troponin molecule are pulled in line with each other, the throat of the myosin head faces the next troponin molecule on the line, and the C unit of the previously active troponin molecule faces the myosin head immediately behind the one with which it was previously engaged. In both cases, conditions are the same as at the commencement of the previous phase of activity. Calcium ions are in solution, the troponin C units are ready to take them up, and magnesium complexed with adenosine tri- or diphosphate is available in myosin heads. The result is continuous action, until calcium ions are actively withdrawn after the passage of action potentials. Complexes of magnesium with adenosine diphosphate are re-converted into those complexes with triphosphates with the absorption of energy in the resting muscle. But, if muscle works until the exhaustion of its energy resources, a complex with diphosphate can also be a source of energy, the diphosphate being capable of conversion to adenosine monophosphate. The calculation of the potential difference required to produce a given force is obviously more difficult than in the simple cases represented by Figs. 2 or 3. If a myosin head interacts not with the troponin molecule immediately adjacent to it, but with the next one on the line, the distance between areas bearing electrostatic charges of opposite sign is far greater than assumed in the previous calculation, of the order of 40 nm instead of 4-12 nm. Against that, the pull is almost entirely in the axial direction, and many units in tandem work at a given time. A half sarcomere contains about 150 myosin heads in 9 rows, so that in full interdigitation 16 myosin heads could be active in a row. Also, in the given case a closer approximation could be made if sarcomeres were not regarded coaxial cylinders, but active myosin heads and troponin C units were taken as individ-
ual point sources. and the total pull tending to shorten the sarcomere obtained from the summation of these forces. An unknown factor is the relative duration of the charge and discharge periods of the assumed voltaic cells. No attempt is made in this paper to perform a more accurate calculation. Perhaps it will suffice to say that some of the differences between Fig. 2 and actual conditions tend to increase, other to decrease the 200 mV figure obtained before, which can still be assumed to give a reasonable approximation to the correct value. The discussion above gave a general outline of a theory of muscular contraction, leaving many questions to be answered. A few of these are discussed below. When muscle is excited under isometric conditions, it can develop a force, but is prevented from doing work. Conditions are essentially similar to those represented in Fig. 2, if the two cylinders are immovable. It may be noted that a charged capacitor does not hold its charge indefinitely; gradually it loses it by leakage, the same way as a compressed gas may slowly escape from its container. The rate of leakage depends on the imperfection of the sealing. In the microscopic world of the sarcomere the rate of leakage is high, and also in a long chain of sarcomeres there is some movement under isometric conditions, a proportion of the sarcomeres contract while others are stretched, so that the muscle consumes energy. When a muscle is excited and tends to contract, but in fact it is elongated by a superior force, conditions are as if in Fig. 2 the two cylinders were pulled apart, or if a compressed gas were further compressed by the inward motion of the piston. In other words, a variable capacitor is an energy transducer in both directions, it can convert electrical energy into mechanical work, or mechanical work into electrical energy. Hence, the force required to elongate contracting muscle is partly that needed to counteract the force developed by the muscle and partly that which the muscle under given conditions converts into electrical energy. A considerable part of my previous paper on muscular contraction [4] was devoted to the problem of lateral stability. When the sarcomere devel-
264
Fig. 4. The arrangement of actin and transverse section.
myosin
filaments
in
ops force in an axial direction, so as to shorten itself, it also develops forces in the lateral direction, drawing actin and myosin filaments closer to each other. As, however, the filaments constitute symmetrical patterns, each myosin filament being surrounded by 6 actin filaments and each actin filament by 3 myosin filaments (Fig. 4), lateral forces balance each other at least in the bulk of the muscle, though unbalanced lateral forces may appear at their boundaries. The more probable solution of this problem. as explained in this paper, is that the power sources are shielded from each other laterally, and only minor lateral forces have to be balanced by symmetry. In the half sarcomere, the length of myosin filaments is about 820 nm, of which about 100 nm at the M line contains only myosin tails. The length containing myosin heads is about 720 nm. The length of the actin filaments is about 1000 nm, so that when the two filaments are fully interdigitated, the end of the actin filaments touching the M line, nearly 20% of the full length of the actin filaments is still disengaged. In supercontraction, this additional length interdigitates with myosin filaments, developing maximal force of contraction. At the M lines, a double overlap is assumed to take place, as the tips of actin filaments from one half sarcomere enter the other ha!f. I do not quite agree with this assumption. When tips of actin filaments reach the last 100 nm of myosin filaments, no myosin heads are available for interaction, hence they assume a passive state. Normal interactions can still take place in the rest of the half sarcomere, including
interactions between heads on the leading end of myosin filaments and troponin molecules on the still disengaged edge of actin filaments. Further interdigitation, therefore, proceeds normally. The movement of the actin filaments, and the probable resistance M lines present to further movement, puts a compressive stress on the tips of the actin filaments, which, therefore, coil up at the M lines, a length of 280 nm being compressed into a 100 nm long space. This takes place at a time when the diameter of the sarcomere is at its maximum. so that there is no difficulty in accommodating a small coil of actin filaments. As pointed out in the review of Iwazumi and Noble [3], the troponin complexes are located on actin filaments at 38 nm intervals, while myosin heads in corresponding positions on myosin heads are located at 43 nm intervals. One possible explanation is that both filaments are stretchable, but the thin filaments stretch more under tensile stress than the thick filaments. In fact, the different spacing of myosin heads and troponin molecules is only a part of a greater problem, to understand the extremely complicated arrangement of myosin heads and troponin molecules. In a given cross-section of muscle, there are twice as many actin as myosin filaments, so that each myosin filament must interact with two actin filaments. Myosin heads are arranged on their filament along a 3-start helical path, so that successive heads are 40” apart. while the actin filaments surrounding each myosin filament are 60” apart. The whole arrangement presents a picture of such complexity that its exact understanding will have to await further research. Lastly, I mentioned earlier that the electric organs of electric fishes are muscle-like structures. A moderate voltage generated by a muscle-like organ could be greatly increased by sudden stretching, the mechanical energy effecting the stretching being converted into electrical energy. Electric organs are in the side of fishes and could be suddenly stretched by the jerking of an antagonistic muscle on the other side of the fish,
Acknowledgements My thanks are due to the Editor of the Journal, Professor Robert H. Anderson, for support and
265
encouragement, and to the referee of the paper, Professor Mark Noble, for constructive and thought-provoking criticism. References 1 Huxley HE, Hansen J. Changes in the cross-striations of muscle during contraction and stretch, and their structural interpretation. Nature 1954;173:973-976.
2 Huxley AF, Niedergerke R. Structural changes during contraction. Nature 1954;173:971-973. 3 Iwazumi T. Noble M. An electrostatic mechanism lar contraction. Int J Cardiol 1989;24:267-275. 4 Seely S. An electrodynamic (moving field) theory lar contraction. J Theor Biol 1986:121:233-242.
in muscle of muscuof muscu-