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Molecular Forces in Anesthesia
Molecular Forces in Anesthesia B. P. SCHOENBORN" Medical Research Council Laboratory of Molecular Biology, University Post-Graduate Medical School, Cambridge, England AND
R. M. FEATHERSTONE" Department of Pharmacology, Middlesex Hospital Medical School, London, England
I. Introduction . . . . . . . . . . . 11. Characteristics and Importance of Weak Bonds . . . 111. van der Waals' Forces . . . . . . . . . IV. Comparison of van der Waals' with Hydrogen Bonds . V. Binding Studies by X-Ray Diffraction Analysis . . . A. The Binding of Xenon to Sperm Whale Metmyoglobin B. The Binding of Xenon to Horse Methemoglobin . . C. The Binding of Xenon to Other Proteins and Viruses VI. Conclusion . . . . . . . . . . . References . . . . . . . . . . .
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2 5 9 12 14 14 15 15
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1. introduction
This article is not so much a review as it is a commentary on studies of the binding of certain anesthetic agents to macromolecules as facilitated by X-ray diffraction techniques, and is preceded by a superficial survey of weak molecular binding forces. Several observations and ideas on possible anesthesia mechanism (Featherstone and Muehlbaecher, 1963) have been presented as theories and have created considerable controversies, indicating that these proposed ideas are more in the nature of interesting, thought-provoking hypotheses than they are actual scientific theories. All these hypotheses are based on correlations between anesthetic potency and some physical
* Present address of both authors: Department of Pharmacology, University of California, San Francisco, California.
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B. P. SCHOENBORN AND R. M. FEATHERSTONE
properties of the relevant agents such as solubility, polarizability, refractivity, etc. These properties are all intimately interrelated and are consequences of atomic structure. The merits and pitfalls of the various published hypotheses will not be discussed, nor will another hypothesis be presented. Instead, the basic molecular interactions in which anesthetic agents can be involved in their biological surroundings will be discussed. This study will be gcnerally restricted to the so-called “inert gaseous anesthetic agents” which exert their biological effects without undergoing any change in their own chemical structures. Attention must be focused on the behavior and distribution of these discrete molecules in their biological surrounding. It takes little insight to realize that these anesthetic molecules must intcract with some of the constitucnts of the system they entcr if they are to produce anesthesia. In order to elucidate how such “inert” chemical agents produce such gross physiological changes, it is of great help to understand the forces through which these interactions occur. It is the purpose of this paper to study the ways by which these moleculcs are able to interact and bind to the molecules that make up large physiological structures, and not to study the effect anesthetics have on the function of membranes or whole organs. A comparison of the sizes of anesthetic molecules with proteins (Fig. 1) and lipids which make up most membranes and other macroscopic structures shows immediately that an anesthetic agent does not interact with proteins or membranes as a whole, but can only directly associate with small groups of atoms which constitute these various macromolecules and large aggregates. It is therefore pertinent t o study in some detail the various ways such interactions can take place and, later, it should be possible, in conjunction with the present rapidly accumulating structural knowledge of macromolecules, to elucidate the consequences such changes have on the physiological functions performed by these macromolecules and aggregates. II. Characteristics and Importance of Weak Bonds
Since only “inert anesthetic agents” (xcnon,l cyclopropane, ethylene, etc.), which themselves do not undergo any chemical change, are being considered, covalent bonding cannot occur by definition. Pure ionic and hydrogen bonds can also be excluded with this type of substance. There remain, therc fore, only the secondary bonds which are relatively weak compared with covalent or ionic bonds. These weak bonds must be di‘No indication has bccn found that xenon in biological systems involves the typc of bonding present in thc novel xenon compounds like xenon tetrafluoride, etc.
FIG.1 . Coinparison of niolrrnlar sizes hctwccn cthylene, xcnnn, and t h c sm:tll protrin Iriyoglohin (rnurt,csy of .J. C . Krndrrw). FIG.6. hIodrl of myoglol~iiistructure in the region of the xenon binding site. (a) shows tlic view of the xenon atom in respect to t h e closest pyrrole ring, (b) in respect to the heme-linked histidine, and (c) shoxs particularly well the cavity the xenon occupies.
MOLECULAR FORCES IN ANESTHESIA
3
vided into several categories according to their different origins, even if they are generally referred to collectively as van der Waals’ bonds. Before describing the various van der Waals’ bonds in detail, it is necessary to look a t some general characteristics of bond for,mation. If two atoms or molecules can collide, they will form a bond if the total energy of the bonded unit is lower than the energy sum of the individual units. I n some cases, however, such bonding will not occur spontaneously unless some form of energy is present to trigger the reaction. This trigger or activation energy does not affect the equilibrium between bonded and unbonded states (discussed below) but only the rate a t which equilibrium is reached. The difference in energy between the bonded and unbonded states is equivalent to the “bond energy.” This energy is released when a bond is formed and must be supplied when a bond is broken. In the case of the weak van der Waals’ forces, bonds are mainly broken by collision with other molecules having sufficient kinetic energy (thermal movement). I n an undisturbed system an equilibrium situation will be reached where the bond breaking process is equivalent to the bond formation process. The rate of bond breakage is obviously related to the number of molecules which possess enough kinetic energy to initiate the break. Under normal biological conditions (37’ C) the average thermal energy is about 0.6 kcal per mole, but some molecules will have energies higher than this, and others will possess less thermal energy. A bond exists, therefore, only for a reasonable time if the bond energy is a few times larger than this average value. By introducing a few simple concepts from statistical mechanics, i t will be easy to calculate the equilibrium constant, which is a measure of the proportion of bonded to unbonded units according to the law of mass action Eq. (1) :
where ( A B ) = concentration of bonded molecules; ( A ) = concentration of molecules A ; and ( B ) = concentration of molecules B . This quantity is related to the change in Gibbs free energy, which is a measure of the amount of work a system can perform. The formal relationship is given in Eq. (2): AG
=
-RTInK
(2)
where AG = change in Gibbs free energy; R = universal gas constant; T = absolute temperature in degrees Kelvin; and In K = natural logarithm of the equilibriu’m constant. It is also related to the amount
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B. P. SCHOENBORN AND R. M. FEATHERSTONE
of heat evolved or absorbed by the reaction and to the entropy change, which is related to the degree of order of the atoms, Eq. (3) : AG
=
AH - TAS
(3)
where AH = change in enthalpy2 and A S = change in entropy.: The concept of Gibbs free energy, which applies to constant temperature and constant pressure systems, is particularly favorable for dealing with the various manifestations of weak bonds in biological surroundings and therefore deserves some further comment. The Gibbs free energy always decreases in a spontaneous process until equilibrium is reached. The free energy lost (-AG) is transformed into heat ( A H ) or is used to increase the order of the involved molecules (TAX). An example of increased order is the crystallization (higher order + lower entropy) process from solutions (high disorder 3 high entropy). A more extensive description and mathematical treatment of these quantities is beyond the scope of this article and can be found in many excellent books on thermodynamics and statistical mechanics. From the relationships stated above, one can calculate the minimal free energy which will yield a reasonable proportion of associated molecules a t 37” C. Introducing the various values in Eq. (2) with K = 100, the Gibbs free energy is calculated to be 3 kcal per mole, and with K = 10, the Gibbs free energy is 1.5 kcal per mole. This shows that bond energies greater than a few kilocalories per mole are strong enough to keep a large percentage of the participants associated. The only type of bonds that the “inert anesthetics” form with biological molecules are weak bonds (van der Waals’ bonds), as discussed earlier, which have energies between 1 to 15 kcal per mole. I n any system, especially in a liquid one like thc interior of a cell, all molecules form these secondary bonds to some degree. The duration of such bonding is, in most cases, very short; otherwise a cell would be solid. The rate of bond breakage a t a particular temperature depends, as mentioned previI n thermodynamics, certain mathematical combinations of basic quantities are often given symbols and names, like entropy and enthalpy. Since these terms are combinations of basic quantities (e.g., volume, temperature, pressure) a number of physical pictures would have to be described to explain these terms completely, and such descriptions would involve lengthy arguments. Enthalpy is the sum of internal energy and a pressure volume product; i t is a measure of the heat content of a body. Entropy change is the heat absorbed divided by the absolute temperature of an infinitesimal process. Thermodynamic relationships show that entropy is therefore a measure of the capacity of a system to undergo spontaneous change. I n connection with statistical mechanics, entropy can be shown to be a measure of disorder of a system.
MOLECULAR FORCES IN ANESTHESIA
5
ously, upon the bond energy which, in turn, depends solely upon the molecular properties of the particular molecules. This means that a molecule will move around in a cell until (if ever) it encounters a molecule with just the right properties with which to form a stronger bond (it will remain longer with it). This type of selective van der Waals'bonding is extremely important in cellular reactions and accounts for many enzymesubstrate affinities as well as for interaction of anesthetics with certain biological molecules. The reason for the existence of particularly favorable bonding situations will emerge in the discussion of the molecular properties which cause weak bonds. I l l . van der Waals' Forces
The observation that real gases did not fit the theoretically derived gas law for ideal gases Eq. (4)
pV = nkT (4) (where p = pressure; V = volume; n = number of atoms; k = Boltzmann constant3; and T = "Kelvin) was explained by postulating a weak bonding force (attractive or repulsive, depending upon distance) which acts between real gas atoms (molecules). At first it was considered that only one such weak force exists, but as the electronic structure of atoms beca,me better understood, it was soon recognized that various different weak forces exist, each arising from a different structural feature. There are basically three attractive forces which are generally referred to as van der Waals' forces. These are named the Keesom, Debye, and London forces. I n addition, the repulsive Born force must be mentioned. The Born force (Born and Mayer, 1932) arises from the electrostatic repulsions of the electron clouds and the nuclei of the assembled atoms, is extremely short ranged, and plays a role only when the electron clouds of the bonded atoms overlap. If such a close approach distance is reached, however, even a very small reduction in this bond distance would produce tremendously large repulsive forces (Fig. 2). The Born repulsion energy is given by Eq. ( 5 )
where E , = Born repulsion energy; B = constant for given pair of atoms; r = radial distance; and n is a constant between 7 and 12, depending on the given pair of atoms, e.g., He, n = 7 ; Xe, n = 12. 'The Boltamann constant k is the gas constant per atom.
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B. P. SCHOENBORN AND R. M. FEATHERSTONE
The Keesom force (Keesom, 1921) (related to the Stockmayer potential) arises from interactions between two dipolar molecules. Dipoles exist in molecules that are electrically neutral but which have asymmetrically distributed charges resulting from differences in electronegativity of covalently bonded atoms. When such a dipolar molecule is exposed to an electric field it will preferentially orient itself to minimize its own energy. A dipole produces its own electric field which will interact with the dipole of the other molecule. The energy of interaction will be a function of the orientation of the dipoles as depicted in Fig. 3. If the thermal motion (temperature) were very high, the orientation would be completely random and no net stabilization would occur. If, however, the temperature is lowered, the energy of favorable orientations will counter-
Fro. 2. van der Waals' interaction energy ( E ) as a function of atomic approach ( 7 ) ; (I=van der Waals' radii; E =maximum binding energy.
distance
act the thermal motion and net stabilization results. The stabilization energy given in Eq. (6) is therefore a function of the temperature and naturally also a function of the dipole strength and the separation between the molecules
where E , = Keesom energy; U = dipole moment; r = distance between atoms; Ic = Boltzmann constant; and T = "Kelvin. Equation (6) is obtained by averaging the interaction energies over all possible orientations. The binding energy of dipolar molecules is further enhanced by the Debye force (Debye, 1920), or dipole-induced dipole force. This case is, however, better illustrated by a nonpolar molecule next to a dipolar one, but is equally valid for dipolar molecules alone. Figure 4 shows the de-
MOLECULAR FORCES IN ANESTHESIA
7
localization of the electron cloud of a nonpolar atom due to the electric field of the dipole. Such a shift in the electron cloud creates a new dipole in a way that attracts the two molecules; this so-called induced dipole is proportional to the strength of the permanent dipole and the
L
I
+
I
IC)
(e1
FIG.3. Various orientations of dipolar molecules: configuration (a) depicting the most stable state (largest binding energy) with progressively less stable configurations shown in (b), (c), and (d), with (e) depicting the most unfavorable arrangement.
polariaability of the nonpolar atom. The polariaability a! depends mainly on the atomic volume of the nonpolar atom. The Debye energy is given by Eq. (7) :
where E D = Debye energy; a = polariaability; U = permanent dipole moment; and r = distance between molecules. Equation (7) is again obtained by averaging over all possible orientations, but unlike Eq. (6) for the Keesom energy, it does not depend on temperature. This is due to the fact that all orientations produce favorable interaction, in contrast to the Keesom interactions.
8
T).
P. SCHOENBORN AND R. M. FEATHERSTONE
The most interesting, and, in the case of “inert” anesthetics, the most important, of these van der Waals’ forces is the London force (London, 1937) or Lennard-Jones potential, which was postulated to explain the observed attractive force between the inert gases which have no permanent dipole moments. Only with the advent of wave mechanics was it possible to realize that any atom will possess fluctuating dipoles according to the particular instantaneous distribution of the electrons. These
FIG.4. (a) shows a spherical atom while (b) shows the same atom next to a dipolar molecule with the resulting delocalization of its electron cloud giving risc t o a dipole (induced dipole).
instantaneous dipoles constantly change in direction and magnitude, each existing only for a fleeting moment, but still producing an instantaneous electric field. The fluidity of the electron clouds, however, will allow neighbors to produce corrcsponding induced dipoles similar t o the Debyeinduced dipole, with the only difference being that such a particular induced dipole lasts only for a minute fraction of time compared to the Debye-induced moment. The London energy between identical atoms is given in Eq. ( 8 ) :
E L = - -3a2P 4r
where EL = London energy; = atomic polarizability; I = atomic ionization energy4; and r = distance between atoms. This formula again is (Y
‘The ionization energy is the amount of energy that is required to remove an electron from a neutral atom.
MOLECULAR FORCES I N ANESTHESIA
9
independent of temperature, as in the case of the Debye energy. This energy is obviously dependent upon the polarizability and, a t first sight rather strangely, on the ionization energy, This is best understood if it is realized that the ionization energy is also a measure of the deformability of the electron cloud which will affect the rate of formation of the instantaneous dipoles. IV. Comparison of van der Waals’ with Hydrogen Bonds
Before giving examples of the% various van der Waals’ forces, a few general implications of the stated equations should be reiterated in context with other weak bonds like hydrogen and ionic bonds (Pauling, 1960). I n all three types of van der Waals’ bonds mentioned, the attractive forces (Fig. 2 ) are of short range and only the interactions between nearest neighbors have to be considered, unlike ionic bonds, where even fourth and ,more distant neighbors are involved. Perhaps the most important property of the van der Waals’ forces is their independence of the number of bonds formed. A molecule can form a great number of such bonds, with the total bonding energy being the sum of all bonds. Small saturation effects will take place if a very large number of bonds are formed, but they are only of interest when very accurate bond energy calculations are made. Such an additive bonding system can be a very effective binding mechanism-one which is stable enough to withstand the disruptive influence of random thermal action if a molecular arrangement is possible which allows numerous van der Waals’ bonds to be formed. At this point it would be interesting to compare how these theoretically derived terms for weak interaction agree with some experimental observations. The best way to study this is naturally with processes where only weak forces play a role. The experimental determination of the heats of sublimation are ideal for this and agree generally within 10% with the calculated values (Bird et al., 1958). In cases where the London forces play the major role (nondipolar molecules) these discrepancies become larger until a more complicated treatment of the London force is introduced using magnetic coupling effects. Of these three attractive van der Waals’ forces, the London energy is generally the largest except in the case of molecules with very strong dipoles (e.g., H,O) ‘It should be noted here that all London interactions are of the same sign and therefore purely additive, while in the case of the Keesom and Debye forces a particular interaction term can either by negative or positive, so that in summing up all the Keesom or Debye terms some of the terms will cancel each other, therefore yielding a relatively small total energy even when individual terms are rather large.
10
B. P. SCHOENBORN AND R. M. FEATHERSTONE
where the Keesom energy can be considerably larger. The Debye energy is often neglected since it seldom contributes more than 10% of the total van der Waals’ energy. The importance of these weak bonds in biological structures is great. The shapes of macromolecules are determined by van der Waals’ and hydrogen bonds, as demonstrated in the three-dimensional structures of lysozyme and myoglobin which have been determined by X-ray diffraction. One fact emphasizing the importance of these weak bonds is that nonpolar groups are buried in the interior of the molecule, while the polar ones are on the surface. To demonstiate this point a little better, the relationships among hydrogen, van der Waals’, and the (misnamed) hydrophobic bonds, must be considered. A hydrogen bond (Pauling, 1960) arises if a hydrogen atom is shared between two atoms. This occurs if a hydrogen which is covalently bound to oxygen or nitrogen is located next to a negatively charged nitrogen or oxygen. Such bonds are, however, highly directional and are only reasonably strong (3-10 kcal per mole) if the covalent hydrogen bond points directly to the electronegative receptor atom. Hydrogen bonds are, therefore, much more specific and generally stronger than van der Waals’ bonds. From the above description it becomes clear that hydrogen bonds are often a special case of ionic bonds. An ionic bond is one in which two groups with opposite charges interact with each other according to the Coulomb attraction, Eq. (9) :
Ec =
--
qT
(9)
where Ec = Coulomb energy; q = charge of group; and T = distance between groups. Such ionic bonds occur frequently with amino acids which possess a positively charged amino group (NH,’) and a negatively charged carboxyl group (COO-) . Certain partial ionic bonds could also be considered a special form of the Debye force. This occurs if a dipole with very large separation of the charges or an ion is situated next to a nonpolar atom. I n such a case only the charge (ion) next to the nonpolar atom needs to be considered as effective in inducing a dipole. The energy of such a charge-induced dipole is given by Eq. (10) :
where E , = energy (charge induced dipole) ; a = polarizability; q = charge of ion; and T = distance between atoms. Last but not least, a particular type of interaction between van der
MOLECULAR FORCES IN ANESTHESIA
11
Waals and hydrogen bonds called the “hydrophobic” bond needs to be considered. If water, which forms strong hydrogen bonds, is mixed with ether, which cannot form hydrogen bonds, and is left standing, it will soon separate again. This observation is the basis of hydrophobic bonds and demonstrates that hydrogen bonding molecules preferentially associate with each other to form the maximum number of such bonds, while the nonhydrogen bonding molecules associate with each other to form the strongest van der Waals’ bonds. Hydrogen bonds are generally stronger than van der Waals’bonds, as demonstrated by the much higher boiling points of hydrogen bonded liquids (particularly water) compared with van der Waals’ bonded solutions (ether). If nonhydrogen bonding molecules are dispersed in aqueous media, they prevent their neighboring water molecules from forming the highest possible number of hydrogen bonds (a water molecule can form up to four hydrogen bonds) with the result that the particular water molecules are not in their lowest energy (equilibrium) state. For this reason nonpolar molecules will aggregate by forming their best possible London interactions between themselves with a minimal interaction with the water molecules. This tendency of water to exclude nonpolar groups was misnamed “hydrophobic” binding. This phenomenon is not due to particular bonds, but is due to the general absence of bonds between polar and nonpolar groups. This preferential association of polar and nonpolar groups with their own kind is responsible for the arrangement of protein chains so that polar residues are generally outside (in contact with water) and nonpolar residues inside (hydrophobic area) macromolecules. An analysis of these various bonding concepts should surely enable one to determine a t what site and with what types of bonds a molecule will bind to particular proteins or lipids. Unfortunately, this is not yet possible, since little is known about the thermodynamic properties of macromolecules. A lot of information can, however, be gained by considering similar but more simple systems. The adsorption of gases on zeolyte structures, also known as molecular sieves (crystalline aluminosilicates), is perhaps the best system for this, since these structures possess centers of polar, nonpolar, and ionic groups, similar to proteins. For these zeolite structures it has been found that nonpolar gases are bound mainly by London forces. Debye- and ion-induced dipole forces seem to play a generally minor role, although they can become significant when strong ions are present on particularly exposed sites (Barrer e t al., 1966; Benson and King, 1965). Such ion-induced dipole moments are, however, very unlikely to play a major role in the binding of anesthetics to biological molecules since such sites are generally neutralized by copi-
12
B. P. SCHOENBORN AND R. M. FEATHERSTONE
ously occurring inorganic ions of opposite charge or by hydrogen bonding to water, which results in most cases in more stable complexes than ioninduced dipole bonding would provide. V. Binding Studies by X-Ray Diffraction Analysis
It has now become feasible t o determine the binding sites of molecules on proteins by X-ray diffraction techniques and to deduce the types of bonding involved. This is, however, only possible if the complete threedimensional structure of the protein to atamic resolution has been elucidated by X-ray analysis-a task of tremendous magnitude. The first detailed determination of the tertiary structure of a protein has been achieved only recently by Kendrew e t al. in the case of myoglobin wherc nearly all 1260 nonhydrogen atoms have been located (Kendrew and Watson, 1967). When a protcin crystal is exposed to a thin beam of Xrays (Perutz, 1963; Kendrew, 1961), a regular pattern of diffracted rays is produced which can be recorded on a film (where it produces spots) or measured by a radiation counter. The geometrical arrangement of these spots contains the information of the molecular arrangement in the crystal. Information on the atomic arrangement within the molecule is contained in the amplitudes and phases of the numerous diffraction beams. Very unfortunately, however, it is only possible to measure the intensities of these waves, which are related t o the amplitude-but these do not contain the phase information. At this stage X-ray crystallography of proteins would have met with a sad end had not a very clever ruse been found by which it became possible to determine the phases. This ruse is called the “heavy atom” method. If an atom with a much higher atomic number (heavy), than the normal constituent atoms of a protein is attached to the protcin without changing the basic crystal structure (isomorphous structure), the intensities of the various spots will be changed slightly. If these intcnsity differences for a t least two different such “heavy atom” protein complexes can be measured, i t is often possiblc to determine the relative location of the two heavy atoms and from these the phases can be calculated. This, however, involves a considerable amount of work, with the measuring and processing of several thousands to a million reflections (spots), depending upon the size of the protein. If, however, the phases, and therefore the structure, of a protein are known, it is relatively simple to determine the binding site of an additional atom or molecule, provided that this does not alter the crystallographic structure, i.e., the new derivative has to be isomorphous with the native structure. This is done by a so-called difference Fourier analysis, in which the intensities of the new protein derivative (protein to which the particular atom or molecule is bound) are first collected and
MOLECULAR FORCES I N ANESTHESIA
13
then the already known intensities of the native crystal are subtracted from them. These differences are then used, together with the known phases, to calculate a difference electron density map which shows where the second structure differs from the first one. This is normally done by calculating the electron density a t closely spaced intervals (20,000100,000 points) throughout the space occupied by a molecule. If, however, the atomic group in question is reasonably “heavy,” a short cut can be used which reduces the necessary data collecting and calculations con-
p(
- . x
FIQ.5. Difference electron density maps (myoglobin-xenon) for two projection planes which enable the determination of the three coordinates z’,y’, z’ which locate the exact site of this atom (xenon) within the protein (myoglobin). It should be noted that the peak height in the X Z plane is nearly twice as large as that in the X Y projection. This is due to different crystallographic properties of the two projection planes.
siderably. This is done by calculating only projections of the difference electron density maps (Fig. 5 ) . Such a projection, for example into the xz plane, is obtained by adding all electron densities along the whole of y for each point in the xz plane. If this is done for two or three projection planes, all three coordinates of the differences can be determined. Such projections are easier to calculate since only a fraction of the total amount of diffraction data (spots) is needed to give all necessary information so long as the molecule is relatively simple and only a small number of binding sites exist.
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B. P. SCHOENBORN AND R. M. FEATHERSTONE
A. THEBINDINGOF XENONTO SPERMWHALE METMYOGLOBIN The intensities were collected for three projection planes of metmyoglobin crystals (Schoenborn e t al., 1965) which were equilibrated with 2 atm xenon (to assure high xenon occupancy). From these data, the previously described difference Fourier projections were calculated. Each of the difference electron density maps calculated shows only one nearly circular peak corresponding to one spherical atom. The remaining areas of the maps are featureless, indicating that the binding of the xenon atom did not disturb the myoglobin molecule a t all and that xenon atoms are not present a t subsidiary sites to any appreciable degree. The xenon atom is located nearly equidistant from the heme-linked histidine and from a pyrrole ring of the heme group as wcll as scveral other groups (see Fig. 6 facing p. 2 ) . This xenon site in the interior of the myoglobin molecule shows the Debyc and London type of van der Waals’ bonds as well as a small contribution from an ion-induced dipole bond. Since Xe is not a natural dipole, Kcesom interactions are not possible. The major component of the bonding energy is the London type and this accounts for approximately 90% of the total energy. London interactions are particularly favorable in this case since xenon rests in a nearly closed cavity (just big enough t o accommodate one xenon atom) with 32 neighboring atoms less than 5.5 A away. The Debye- and ioninduced dipole interactions are relatively weak and contribute only about 10% of thc stabilization energy. Unfortunately, the sizes of the various dipoles and the charge distribution on the heme group are not yet known accurately enough to make possible precise calculations of the Debye- and the charge-induccd dipole energies. The actual London energy can bc cnlculatcd, since the various approach distances are known to within 1 0 . 3 A, and a figure of approximatcly 10 kcal per mole is obtained. All approach distances were larger than the combined van der Waals radii, indicating that the Born repulsive force can probably be ncglcctcd. Since, however, all these approach distances are only accurate to &0.3 A, it might just be possible that one or another of three shorter approach distances results in a repulsion rather than attraction, somewhat diminishing the total binding energy. It should also be pointed out that this is not a hydrophobic stabilization, since there is no indication in the three-dimensional Fourier synthesis of the native proteins, that a water molecule occupies the xenon site under normal conditions.
B. THEBINDINGOF XENONTO HORSEMETHEMOGLOBIN A study of the xenon binding to hemoglobin (Schoenborn, 1965) was possible, even if the structure of hemoglobin is not yet known to the
MOLECULAR FORCES I N ANESTHESIA
15
atomic details of myoglobin. The pioneering work of Perutz e t al. has, however, progressed far enough for one to be certain of the general structural features of the molecule (Perutz, 1965). The intensities for three projection planes were again measured for the xenon hemoglobin crystal and processed in a similar manner to that described for myoglobin. This time, however, phases for two of the three projection planes were available only for a smaller amount of reflections than in the case of myoglobin, and there was a consequent loss of contrast in the electron density maps. One projection (the high contrast map) showed two elongated peaks, while another projection showed four circular peaks a t corresponding coordinate positions, indicating that the elongated peaks in the latter are each made up of two superimposed peaks. B y comparing the sites of these peaks with the present provisional model of hemoglobin (Perutz, 1965), it can be seen that one xenon atom belongs to each of the two a and p chains of the hemoglobin molecule. The location of the sites, lying inside the subunits but close to their external surfaces, is quite different from that in myoglobin. The exact analysis of the xenon sites will have to await the determination of the hemoglobin structure a t higher resolution. On the basis of Perutz’s tentative atomic model of hemoglobin, the nearest neighbors of all xenon sites are valine, leucine, and phenylalanine. This complex is, therefore, presumably stabilized mainly by London interactions, as in myoglobin.
C. THEBINDINGOF XENONTO OTHERPROTEINS AND VIRUSES The use of xenon as a “heavy atom” is of some interest in protein crystallography and has recently been tried on several macromolecules. Xenon is a little “lighter” than desirable for a heavy atom, but this is counteracted by the fact that xenon protein complexes show a very high degree of isomorphism with the native crystals-a fact often not true with most of the com8monlyused “heavy atoms” which are generally ionic groups capable of inducing some disorder into the native structure. Such trials have shown that xenon does not bind to hen egg lysozyme, chymotrypsin, or horse heart cytochrome (Dickerson, 1966) , but it does bind to rennin and to the protein subunits of intact tobacco mosaic virus (TMV) (Schoenborn and Holmes, 1967). I n both latter cases the structural analysis is not yet advanced enough to say anything about the binding sites. VI. Conclusion
The various binding forces through which the so-called “inert gaseous anesthetic agents” associate with macromolecules have been discussed in order tQ demonstrate what conditions are prerequisite for binding. If,
16
B. P. SCHOENBORN AND R. M. FEATHERSTONE
then, thc molecular natures of particular binding sites are determined, it will be feasible to elucidate how such an interaction affects the function of the systems. Recent advances in protein crystallography have made it now possible to study drug-protein interaction on a truly molecular level. Detailed knowledge of protein structures is a t present limited to myoglobin (Kendrew and Watson, 1967) and lysozyme (Blake et al., 1965), but within the next two or three years the three-dimensional structures of many other enzymes will be known. This will open up a completely new approach to the study of drug receptor action which, complernentcd by the large amount of clinical and biochemical results, will allow hitherto unknown possibilities in the field of drug design. It might be argued here that since X-ray diffraction studies are performed on crystallinc enzymes, the surrounding is quite different from that of the enzyme’s natural biological one. Attention has been given to this problem by a number of workers (Banaszak et al., 1963; Perutz et al., 1964) and it has been shown that several rcactions are possible in crystalline material-consistent with identical protein structure in solution and in crystal form. Observed differences in reaction rates with crystallized enzymes (Chance et al., 1966) are probably due to small increases in activation energies. This could be caused by restrictions in some of their rotationaI or translational degrees of freedom due to the packing of the molecules in the crystal lattice (intermolecular van der Waals bonding). ADDENDUM It has recently been shown that xenon binds to deoxymyoglobin at the same spcrific site as in metmyoglobin (Schoenborn and Nobbs, 1966). An x-ray diffraction analysis of the binding of cyclopropane to metmyoglobin showed that cyclopropane binds to myoglobin a t thc same site that xcnon does, but that the slightly larger cyclopropanc necessitates a reorientation of a neighboring phcnylalanine as well as some minor adjustments in other neighboring groups (Schoenborn, 1967). It has also recently been shown that the binding of xenon to myoglobin affects the affinity of rnrbon monoxide to myoglobin (Lumry, 1966; Schoenborn et al., 1967).
ACKNOWLEDOMENTS This publication was supported in part by the United States Public Health Service Grant NB03625. We wish to thank 0. Jardetzky for his advice. REFERENCES
Banasxak, L. J., Eylor, E. H., and Gurd, F. R. N. (193). J . B i d . Chem. 238, 1989. Barrer, R. M.,Peterson, D. L., and Schoenborn, B. P. (1966). Science 153, 555. Benson, S. W.,and King, J. W. (1965). Science 150, 1710. Bird, R. B.,Hirschfelder, J. O.,and Curtiss, C. F. (1W).In “Handbook of Physics” (E. U. Condon and H. Odishaw, eds.). McGraw-Hill, New York.
MOLECULAR FORCES IN ANESTHESIA
17
Blake, C. C. F., Koenig, D. F., Mair, G. A., North, A. C. T., Phillips, D. C., and Sarma, V. R. (1965).Nature aOa, 757. Born, M., and Mayer, J. E. (1952).2. Physik 75, 1. Chance, B., Ravilly, A., and Rumen, N. (1966). J . M o l . Biol. 21, 195. Debye, P. (1920).Physik. Z . 21, 178. Dickerson, R. E. (1966). Private communication. Featherstone, R. M., and Muehlbaecher, C. A. (1963). Pharmacol. R e v . 15, 97. Keesom, W. H. (19’21). Physik. 2. 22, 129, 643. Kendrew, J. C. (1961). Sci. A m . 205, Dez. Kendrew, J. C., and Watson, H. C. (1967). J . Mol. Biol. To be published. London, F. (1937). Trans. Faraday Soc. 28, 333. Lumry, R. (1966). Private communication. Pauling, L. (1960). “Nature of Chemical Bond.” Cornell Univ. Press, Ithaca, New York. Perutz, M. F. (1963). Science 140, 863. Perutz, M. F. (1965). J. Mol. Biol. 13, 646. Perutz, M. F., Bolton, W., Diamond, R., Muirhead, H., and Watson, H. C. (1964). Nature 203, 687. Schoenborn, B. P. (1965). Nature 208, 760. Schoenborn, B. P. (1967). Nature 215. Schoenborn, B. P., and Holmes, K. C. (1967). J . Mol. Biol. To be published. Schoenborn, B. P., and Nobbs, C. L. (1966). Mol. Pharmacol. 2, 491. Schoenborn, B. P., Watson, H. C., and Kendrew, J. C. (1965). Nature 207, 28. Schoenborn, B. P., Settle, W., and Featherstone, R. M. (1967). To be published.
R. M. FEATHERSTONE" Department of Pharmacology, Middlesex Hospital Medical School, London, England
I. Introduction . . . . . . . . . . . 11. Characteristics and Importance of Weak Bonds . . . 111. van der Waals' Forces . . . . . . . . . IV. Comparison of van der Waals' with Hydrogen Bonds . V. Binding Studies by X-Ray Diffraction Analysis . . . A. The Binding of Xenon to Sperm Whale Metmyoglobin B. The Binding of Xenon to Horse Methemoglobin . . C. The Binding of Xenon to Other Proteins and Viruses VI. Conclusion . . . . . . . . . . . References . . . . . . . . . . .
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1
2 5 9 12 14 14 15 15
16
1. introduction
This article is not so much a review as it is a commentary on studies of the binding of certain anesthetic agents to macromolecules as facilitated by X-ray diffraction techniques, and is preceded by a superficial survey of weak molecular binding forces. Several observations and ideas on possible anesthesia mechanism (Featherstone and Muehlbaecher, 1963) have been presented as theories and have created considerable controversies, indicating that these proposed ideas are more in the nature of interesting, thought-provoking hypotheses than they are actual scientific theories. All these hypotheses are based on correlations between anesthetic potency and some physical
* Present address of both authors: Department of Pharmacology, University of California, San Francisco, California.
2
B. P. SCHOENBORN AND R. M. FEATHERSTONE
properties of the relevant agents such as solubility, polarizability, refractivity, etc. These properties are all intimately interrelated and are consequences of atomic structure. The merits and pitfalls of the various published hypotheses will not be discussed, nor will another hypothesis be presented. Instead, the basic molecular interactions in which anesthetic agents can be involved in their biological surroundings will be discussed. This study will be gcnerally restricted to the so-called “inert gaseous anesthetic agents” which exert their biological effects without undergoing any change in their own chemical structures. Attention must be focused on the behavior and distribution of these discrete molecules in their biological surrounding. It takes little insight to realize that these anesthetic molecules must intcract with some of the constitucnts of the system they entcr if they are to produce anesthesia. In order to elucidate how such “inert” chemical agents produce such gross physiological changes, it is of great help to understand the forces through which these interactions occur. It is the purpose of this paper to study the ways by which these moleculcs are able to interact and bind to the molecules that make up large physiological structures, and not to study the effect anesthetics have on the function of membranes or whole organs. A comparison of the sizes of anesthetic molecules with proteins (Fig. 1) and lipids which make up most membranes and other macroscopic structures shows immediately that an anesthetic agent does not interact with proteins or membranes as a whole, but can only directly associate with small groups of atoms which constitute these various macromolecules and large aggregates. It is therefore pertinent t o study in some detail the various ways such interactions can take place and, later, it should be possible, in conjunction with the present rapidly accumulating structural knowledge of macromolecules, to elucidate the consequences such changes have on the physiological functions performed by these macromolecules and aggregates. II. Characteristics and Importance of Weak Bonds
Since only “inert anesthetic agents” (xcnon,l cyclopropane, ethylene, etc.), which themselves do not undergo any chemical change, are being considered, covalent bonding cannot occur by definition. Pure ionic and hydrogen bonds can also be excluded with this type of substance. There remain, therc fore, only the secondary bonds which are relatively weak compared with covalent or ionic bonds. These weak bonds must be di‘No indication has bccn found that xenon in biological systems involves the typc of bonding present in thc novel xenon compounds like xenon tetrafluoride, etc.
FIG.1 . Coinparison of niolrrnlar sizes hctwccn cthylene, xcnnn, and t h c sm:tll protrin Iriyoglohin (rnurt,csy of .J. C . Krndrrw). FIG.6. hIodrl of myoglol~iiistructure in the region of the xenon binding site. (a) shows tlic view of the xenon atom in respect to t h e closest pyrrole ring, (b) in respect to the heme-linked histidine, and (c) shoxs particularly well the cavity the xenon occupies.
MOLECULAR FORCES IN ANESTHESIA
3
vided into several categories according to their different origins, even if they are generally referred to collectively as van der Waals’ bonds. Before describing the various van der Waals’ bonds in detail, it is necessary to look a t some general characteristics of bond for,mation. If two atoms or molecules can collide, they will form a bond if the total energy of the bonded unit is lower than the energy sum of the individual units. I n some cases, however, such bonding will not occur spontaneously unless some form of energy is present to trigger the reaction. This trigger or activation energy does not affect the equilibrium between bonded and unbonded states (discussed below) but only the rate a t which equilibrium is reached. The difference in energy between the bonded and unbonded states is equivalent to the “bond energy.” This energy is released when a bond is formed and must be supplied when a bond is broken. In the case of the weak van der Waals’ forces, bonds are mainly broken by collision with other molecules having sufficient kinetic energy (thermal movement). I n an undisturbed system an equilibrium situation will be reached where the bond breaking process is equivalent to the bond formation process. The rate of bond breakage is obviously related to the number of molecules which possess enough kinetic energy to initiate the break. Under normal biological conditions (37’ C) the average thermal energy is about 0.6 kcal per mole, but some molecules will have energies higher than this, and others will possess less thermal energy. A bond exists, therefore, only for a reasonable time if the bond energy is a few times larger than this average value. By introducing a few simple concepts from statistical mechanics, i t will be easy to calculate the equilibrium constant, which is a measure of the proportion of bonded to unbonded units according to the law of mass action Eq. (1) :
where ( A B ) = concentration of bonded molecules; ( A ) = concentration of molecules A ; and ( B ) = concentration of molecules B . This quantity is related to the change in Gibbs free energy, which is a measure of the amount of work a system can perform. The formal relationship is given in Eq. (2): AG
=
-RTInK
(2)
where AG = change in Gibbs free energy; R = universal gas constant; T = absolute temperature in degrees Kelvin; and In K = natural logarithm of the equilibriu’m constant. It is also related to the amount
4
B. P. SCHOENBORN AND R. M. FEATHERSTONE
of heat evolved or absorbed by the reaction and to the entropy change, which is related to the degree of order of the atoms, Eq. (3) : AG
=
AH - TAS
(3)
where AH = change in enthalpy2 and A S = change in entropy.: The concept of Gibbs free energy, which applies to constant temperature and constant pressure systems, is particularly favorable for dealing with the various manifestations of weak bonds in biological surroundings and therefore deserves some further comment. The Gibbs free energy always decreases in a spontaneous process until equilibrium is reached. The free energy lost (-AG) is transformed into heat ( A H ) or is used to increase the order of the involved molecules (TAX). An example of increased order is the crystallization (higher order + lower entropy) process from solutions (high disorder 3 high entropy). A more extensive description and mathematical treatment of these quantities is beyond the scope of this article and can be found in many excellent books on thermodynamics and statistical mechanics. From the relationships stated above, one can calculate the minimal free energy which will yield a reasonable proportion of associated molecules a t 37” C. Introducing the various values in Eq. (2) with K = 100, the Gibbs free energy is calculated to be 3 kcal per mole, and with K = 10, the Gibbs free energy is 1.5 kcal per mole. This shows that bond energies greater than a few kilocalories per mole are strong enough to keep a large percentage of the participants associated. The only type of bonds that the “inert anesthetics” form with biological molecules are weak bonds (van der Waals’ bonds), as discussed earlier, which have energies between 1 to 15 kcal per mole. I n any system, especially in a liquid one like thc interior of a cell, all molecules form these secondary bonds to some degree. The duration of such bonding is, in most cases, very short; otherwise a cell would be solid. The rate of bond breakage a t a particular temperature depends, as mentioned previI n thermodynamics, certain mathematical combinations of basic quantities are often given symbols and names, like entropy and enthalpy. Since these terms are combinations of basic quantities (e.g., volume, temperature, pressure) a number of physical pictures would have to be described to explain these terms completely, and such descriptions would involve lengthy arguments. Enthalpy is the sum of internal energy and a pressure volume product; i t is a measure of the heat content of a body. Entropy change is the heat absorbed divided by the absolute temperature of an infinitesimal process. Thermodynamic relationships show that entropy is therefore a measure of the capacity of a system to undergo spontaneous change. I n connection with statistical mechanics, entropy can be shown to be a measure of disorder of a system.
MOLECULAR FORCES IN ANESTHESIA
5
ously, upon the bond energy which, in turn, depends solely upon the molecular properties of the particular molecules. This means that a molecule will move around in a cell until (if ever) it encounters a molecule with just the right properties with which to form a stronger bond (it will remain longer with it). This type of selective van der Waals'bonding is extremely important in cellular reactions and accounts for many enzymesubstrate affinities as well as for interaction of anesthetics with certain biological molecules. The reason for the existence of particularly favorable bonding situations will emerge in the discussion of the molecular properties which cause weak bonds. I l l . van der Waals' Forces
The observation that real gases did not fit the theoretically derived gas law for ideal gases Eq. (4)
pV = nkT (4) (where p = pressure; V = volume; n = number of atoms; k = Boltzmann constant3; and T = "Kelvin) was explained by postulating a weak bonding force (attractive or repulsive, depending upon distance) which acts between real gas atoms (molecules). At first it was considered that only one such weak force exists, but as the electronic structure of atoms beca,me better understood, it was soon recognized that various different weak forces exist, each arising from a different structural feature. There are basically three attractive forces which are generally referred to as van der Waals' forces. These are named the Keesom, Debye, and London forces. I n addition, the repulsive Born force must be mentioned. The Born force (Born and Mayer, 1932) arises from the electrostatic repulsions of the electron clouds and the nuclei of the assembled atoms, is extremely short ranged, and plays a role only when the electron clouds of the bonded atoms overlap. If such a close approach distance is reached, however, even a very small reduction in this bond distance would produce tremendously large repulsive forces (Fig. 2). The Born repulsion energy is given by Eq. ( 5 )
where E , = Born repulsion energy; B = constant for given pair of atoms; r = radial distance; and n is a constant between 7 and 12, depending on the given pair of atoms, e.g., He, n = 7 ; Xe, n = 12. 'The Boltamann constant k is the gas constant per atom.
6
B. P. SCHOENBORN AND R. M. FEATHERSTONE
The Keesom force (Keesom, 1921) (related to the Stockmayer potential) arises from interactions between two dipolar molecules. Dipoles exist in molecules that are electrically neutral but which have asymmetrically distributed charges resulting from differences in electronegativity of covalently bonded atoms. When such a dipolar molecule is exposed to an electric field it will preferentially orient itself to minimize its own energy. A dipole produces its own electric field which will interact with the dipole of the other molecule. The energy of interaction will be a function of the orientation of the dipoles as depicted in Fig. 3. If the thermal motion (temperature) were very high, the orientation would be completely random and no net stabilization would occur. If, however, the temperature is lowered, the energy of favorable orientations will counter-
Fro. 2. van der Waals' interaction energy ( E ) as a function of atomic approach ( 7 ) ; (I=van der Waals' radii; E =maximum binding energy.
distance
act the thermal motion and net stabilization results. The stabilization energy given in Eq. (6) is therefore a function of the temperature and naturally also a function of the dipole strength and the separation between the molecules
where E , = Keesom energy; U = dipole moment; r = distance between atoms; Ic = Boltzmann constant; and T = "Kelvin. Equation (6) is obtained by averaging the interaction energies over all possible orientations. The binding energy of dipolar molecules is further enhanced by the Debye force (Debye, 1920), or dipole-induced dipole force. This case is, however, better illustrated by a nonpolar molecule next to a dipolar one, but is equally valid for dipolar molecules alone. Figure 4 shows the de-
MOLECULAR FORCES IN ANESTHESIA
7
localization of the electron cloud of a nonpolar atom due to the electric field of the dipole. Such a shift in the electron cloud creates a new dipole in a way that attracts the two molecules; this so-called induced dipole is proportional to the strength of the permanent dipole and the
L
I
+
I
IC)
(e1
FIG.3. Various orientations of dipolar molecules: configuration (a) depicting the most stable state (largest binding energy) with progressively less stable configurations shown in (b), (c), and (d), with (e) depicting the most unfavorable arrangement.
polariaability of the nonpolar atom. The polariaability a! depends mainly on the atomic volume of the nonpolar atom. The Debye energy is given by Eq. (7) :
where E D = Debye energy; a = polariaability; U = permanent dipole moment; and r = distance between molecules. Equation (7) is again obtained by averaging over all possible orientations, but unlike Eq. (6) for the Keesom energy, it does not depend on temperature. This is due to the fact that all orientations produce favorable interaction, in contrast to the Keesom interactions.
8
T).
P. SCHOENBORN AND R. M. FEATHERSTONE
The most interesting, and, in the case of “inert” anesthetics, the most important, of these van der Waals’ forces is the London force (London, 1937) or Lennard-Jones potential, which was postulated to explain the observed attractive force between the inert gases which have no permanent dipole moments. Only with the advent of wave mechanics was it possible to realize that any atom will possess fluctuating dipoles according to the particular instantaneous distribution of the electrons. These
FIG.4. (a) shows a spherical atom while (b) shows the same atom next to a dipolar molecule with the resulting delocalization of its electron cloud giving risc t o a dipole (induced dipole).
instantaneous dipoles constantly change in direction and magnitude, each existing only for a fleeting moment, but still producing an instantaneous electric field. The fluidity of the electron clouds, however, will allow neighbors to produce corrcsponding induced dipoles similar t o the Debyeinduced dipole, with the only difference being that such a particular induced dipole lasts only for a minute fraction of time compared to the Debye-induced moment. The London energy between identical atoms is given in Eq. ( 8 ) :
E L = - -3a2P 4r
where EL = London energy; = atomic polarizability; I = atomic ionization energy4; and r = distance between atoms. This formula again is (Y
‘The ionization energy is the amount of energy that is required to remove an electron from a neutral atom.
MOLECULAR FORCES I N ANESTHESIA
9
independent of temperature, as in the case of the Debye energy. This energy is obviously dependent upon the polarizability and, a t first sight rather strangely, on the ionization energy, This is best understood if it is realized that the ionization energy is also a measure of the deformability of the electron cloud which will affect the rate of formation of the instantaneous dipoles. IV. Comparison of van der Waals’ with Hydrogen Bonds
Before giving examples of the% various van der Waals’ forces, a few general implications of the stated equations should be reiterated in context with other weak bonds like hydrogen and ionic bonds (Pauling, 1960). I n all three types of van der Waals’ bonds mentioned, the attractive forces (Fig. 2 ) are of short range and only the interactions between nearest neighbors have to be considered, unlike ionic bonds, where even fourth and ,more distant neighbors are involved. Perhaps the most important property of the van der Waals’ forces is their independence of the number of bonds formed. A molecule can form a great number of such bonds, with the total bonding energy being the sum of all bonds. Small saturation effects will take place if a very large number of bonds are formed, but they are only of interest when very accurate bond energy calculations are made. Such an additive bonding system can be a very effective binding mechanism-one which is stable enough to withstand the disruptive influence of random thermal action if a molecular arrangement is possible which allows numerous van der Waals’ bonds to be formed. At this point it would be interesting to compare how these theoretically derived terms for weak interaction agree with some experimental observations. The best way to study this is naturally with processes where only weak forces play a role. The experimental determination of the heats of sublimation are ideal for this and agree generally within 10% with the calculated values (Bird et al., 1958). In cases where the London forces play the major role (nondipolar molecules) these discrepancies become larger until a more complicated treatment of the London force is introduced using magnetic coupling effects. Of these three attractive van der Waals’ forces, the London energy is generally the largest except in the case of molecules with very strong dipoles (e.g., H,O) ‘It should be noted here that all London interactions are of the same sign and therefore purely additive, while in the case of the Keesom and Debye forces a particular interaction term can either by negative or positive, so that in summing up all the Keesom or Debye terms some of the terms will cancel each other, therefore yielding a relatively small total energy even when individual terms are rather large.
10
B. P. SCHOENBORN AND R. M. FEATHERSTONE
where the Keesom energy can be considerably larger. The Debye energy is often neglected since it seldom contributes more than 10% of the total van der Waals’ energy. The importance of these weak bonds in biological structures is great. The shapes of macromolecules are determined by van der Waals’ and hydrogen bonds, as demonstrated in the three-dimensional structures of lysozyme and myoglobin which have been determined by X-ray diffraction. One fact emphasizing the importance of these weak bonds is that nonpolar groups are buried in the interior of the molecule, while the polar ones are on the surface. To demonstiate this point a little better, the relationships among hydrogen, van der Waals’, and the (misnamed) hydrophobic bonds, must be considered. A hydrogen bond (Pauling, 1960) arises if a hydrogen atom is shared between two atoms. This occurs if a hydrogen which is covalently bound to oxygen or nitrogen is located next to a negatively charged nitrogen or oxygen. Such bonds are, however, highly directional and are only reasonably strong (3-10 kcal per mole) if the covalent hydrogen bond points directly to the electronegative receptor atom. Hydrogen bonds are, therefore, much more specific and generally stronger than van der Waals’ bonds. From the above description it becomes clear that hydrogen bonds are often a special case of ionic bonds. An ionic bond is one in which two groups with opposite charges interact with each other according to the Coulomb attraction, Eq. (9) :
Ec =
--
qT
(9)
where Ec = Coulomb energy; q = charge of group; and T = distance between groups. Such ionic bonds occur frequently with amino acids which possess a positively charged amino group (NH,’) and a negatively charged carboxyl group (COO-) . Certain partial ionic bonds could also be considered a special form of the Debye force. This occurs if a dipole with very large separation of the charges or an ion is situated next to a nonpolar atom. I n such a case only the charge (ion) next to the nonpolar atom needs to be considered as effective in inducing a dipole. The energy of such a charge-induced dipole is given by Eq. (10) :
where E , = energy (charge induced dipole) ; a = polarizability; q = charge of ion; and T = distance between atoms. Last but not least, a particular type of interaction between van der
MOLECULAR FORCES IN ANESTHESIA
11
Waals and hydrogen bonds called the “hydrophobic” bond needs to be considered. If water, which forms strong hydrogen bonds, is mixed with ether, which cannot form hydrogen bonds, and is left standing, it will soon separate again. This observation is the basis of hydrophobic bonds and demonstrates that hydrogen bonding molecules preferentially associate with each other to form the maximum number of such bonds, while the nonhydrogen bonding molecules associate with each other to form the strongest van der Waals’ bonds. Hydrogen bonds are generally stronger than van der Waals’bonds, as demonstrated by the much higher boiling points of hydrogen bonded liquids (particularly water) compared with van der Waals’ bonded solutions (ether). If nonhydrogen bonding molecules are dispersed in aqueous media, they prevent their neighboring water molecules from forming the highest possible number of hydrogen bonds (a water molecule can form up to four hydrogen bonds) with the result that the particular water molecules are not in their lowest energy (equilibrium) state. For this reason nonpolar molecules will aggregate by forming their best possible London interactions between themselves with a minimal interaction with the water molecules. This tendency of water to exclude nonpolar groups was misnamed “hydrophobic” binding. This phenomenon is not due to particular bonds, but is due to the general absence of bonds between polar and nonpolar groups. This preferential association of polar and nonpolar groups with their own kind is responsible for the arrangement of protein chains so that polar residues are generally outside (in contact with water) and nonpolar residues inside (hydrophobic area) macromolecules. An analysis of these various bonding concepts should surely enable one to determine a t what site and with what types of bonds a molecule will bind to particular proteins or lipids. Unfortunately, this is not yet possible, since little is known about the thermodynamic properties of macromolecules. A lot of information can, however, be gained by considering similar but more simple systems. The adsorption of gases on zeolyte structures, also known as molecular sieves (crystalline aluminosilicates), is perhaps the best system for this, since these structures possess centers of polar, nonpolar, and ionic groups, similar to proteins. For these zeolite structures it has been found that nonpolar gases are bound mainly by London forces. Debye- and ion-induced dipole forces seem to play a generally minor role, although they can become significant when strong ions are present on particularly exposed sites (Barrer e t al., 1966; Benson and King, 1965). Such ion-induced dipole moments are, however, very unlikely to play a major role in the binding of anesthetics to biological molecules since such sites are generally neutralized by copi-
12
B. P. SCHOENBORN AND R. M. FEATHERSTONE
ously occurring inorganic ions of opposite charge or by hydrogen bonding to water, which results in most cases in more stable complexes than ioninduced dipole bonding would provide. V. Binding Studies by X-Ray Diffraction Analysis
It has now become feasible t o determine the binding sites of molecules on proteins by X-ray diffraction techniques and to deduce the types of bonding involved. This is, however, only possible if the complete threedimensional structure of the protein to atamic resolution has been elucidated by X-ray analysis-a task of tremendous magnitude. The first detailed determination of the tertiary structure of a protein has been achieved only recently by Kendrew e t al. in the case of myoglobin wherc nearly all 1260 nonhydrogen atoms have been located (Kendrew and Watson, 1967). When a protcin crystal is exposed to a thin beam of Xrays (Perutz, 1963; Kendrew, 1961), a regular pattern of diffracted rays is produced which can be recorded on a film (where it produces spots) or measured by a radiation counter. The geometrical arrangement of these spots contains the information of the molecular arrangement in the crystal. Information on the atomic arrangement within the molecule is contained in the amplitudes and phases of the numerous diffraction beams. Very unfortunately, however, it is only possible to measure the intensities of these waves, which are related t o the amplitude-but these do not contain the phase information. At this stage X-ray crystallography of proteins would have met with a sad end had not a very clever ruse been found by which it became possible to determine the phases. This ruse is called the “heavy atom” method. If an atom with a much higher atomic number (heavy), than the normal constituent atoms of a protein is attached to the protcin without changing the basic crystal structure (isomorphous structure), the intensities of the various spots will be changed slightly. If these intcnsity differences for a t least two different such “heavy atom” protein complexes can be measured, i t is often possiblc to determine the relative location of the two heavy atoms and from these the phases can be calculated. This, however, involves a considerable amount of work, with the measuring and processing of several thousands to a million reflections (spots), depending upon the size of the protein. If, however, the phases, and therefore the structure, of a protein are known, it is relatively simple to determine the binding site of an additional atom or molecule, provided that this does not alter the crystallographic structure, i.e., the new derivative has to be isomorphous with the native structure. This is done by a so-called difference Fourier analysis, in which the intensities of the new protein derivative (protein to which the particular atom or molecule is bound) are first collected and
MOLECULAR FORCES I N ANESTHESIA
13
then the already known intensities of the native crystal are subtracted from them. These differences are then used, together with the known phases, to calculate a difference electron density map which shows where the second structure differs from the first one. This is normally done by calculating the electron density a t closely spaced intervals (20,000100,000 points) throughout the space occupied by a molecule. If, however, the atomic group in question is reasonably “heavy,” a short cut can be used which reduces the necessary data collecting and calculations con-
p(
- . x
FIQ.5. Difference electron density maps (myoglobin-xenon) for two projection planes which enable the determination of the three coordinates z’,y’, z’ which locate the exact site of this atom (xenon) within the protein (myoglobin). It should be noted that the peak height in the X Z plane is nearly twice as large as that in the X Y projection. This is due to different crystallographic properties of the two projection planes.
siderably. This is done by calculating only projections of the difference electron density maps (Fig. 5 ) . Such a projection, for example into the xz plane, is obtained by adding all electron densities along the whole of y for each point in the xz plane. If this is done for two or three projection planes, all three coordinates of the differences can be determined. Such projections are easier to calculate since only a fraction of the total amount of diffraction data (spots) is needed to give all necessary information so long as the molecule is relatively simple and only a small number of binding sites exist.
14
B. P. SCHOENBORN AND R. M. FEATHERSTONE
A. THEBINDINGOF XENONTO SPERMWHALE METMYOGLOBIN The intensities were collected for three projection planes of metmyoglobin crystals (Schoenborn e t al., 1965) which were equilibrated with 2 atm xenon (to assure high xenon occupancy). From these data, the previously described difference Fourier projections were calculated. Each of the difference electron density maps calculated shows only one nearly circular peak corresponding to one spherical atom. The remaining areas of the maps are featureless, indicating that the binding of the xenon atom did not disturb the myoglobin molecule a t all and that xenon atoms are not present a t subsidiary sites to any appreciable degree. The xenon atom is located nearly equidistant from the heme-linked histidine and from a pyrrole ring of the heme group as wcll as scveral other groups (see Fig. 6 facing p. 2 ) . This xenon site in the interior of the myoglobin molecule shows the Debyc and London type of van der Waals’ bonds as well as a small contribution from an ion-induced dipole bond. Since Xe is not a natural dipole, Kcesom interactions are not possible. The major component of the bonding energy is the London type and this accounts for approximately 90% of the total energy. London interactions are particularly favorable in this case since xenon rests in a nearly closed cavity (just big enough t o accommodate one xenon atom) with 32 neighboring atoms less than 5.5 A away. The Debye- and ioninduced dipole interactions are relatively weak and contribute only about 10% of thc stabilization energy. Unfortunately, the sizes of the various dipoles and the charge distribution on the heme group are not yet known accurately enough to make possible precise calculations of the Debye- and the charge-induccd dipole energies. The actual London energy can bc cnlculatcd, since the various approach distances are known to within 1 0 . 3 A, and a figure of approximatcly 10 kcal per mole is obtained. All approach distances were larger than the combined van der Waals radii, indicating that the Born repulsive force can probably be ncglcctcd. Since, however, all these approach distances are only accurate to &0.3 A, it might just be possible that one or another of three shorter approach distances results in a repulsion rather than attraction, somewhat diminishing the total binding energy. It should also be pointed out that this is not a hydrophobic stabilization, since there is no indication in the three-dimensional Fourier synthesis of the native proteins, that a water molecule occupies the xenon site under normal conditions.
B. THEBINDINGOF XENONTO HORSEMETHEMOGLOBIN A study of the xenon binding to hemoglobin (Schoenborn, 1965) was possible, even if the structure of hemoglobin is not yet known to the
MOLECULAR FORCES I N ANESTHESIA
15
atomic details of myoglobin. The pioneering work of Perutz e t al. has, however, progressed far enough for one to be certain of the general structural features of the molecule (Perutz, 1965). The intensities for three projection planes were again measured for the xenon hemoglobin crystal and processed in a similar manner to that described for myoglobin. This time, however, phases for two of the three projection planes were available only for a smaller amount of reflections than in the case of myoglobin, and there was a consequent loss of contrast in the electron density maps. One projection (the high contrast map) showed two elongated peaks, while another projection showed four circular peaks a t corresponding coordinate positions, indicating that the elongated peaks in the latter are each made up of two superimposed peaks. B y comparing the sites of these peaks with the present provisional model of hemoglobin (Perutz, 1965), it can be seen that one xenon atom belongs to each of the two a and p chains of the hemoglobin molecule. The location of the sites, lying inside the subunits but close to their external surfaces, is quite different from that in myoglobin. The exact analysis of the xenon sites will have to await the determination of the hemoglobin structure a t higher resolution. On the basis of Perutz’s tentative atomic model of hemoglobin, the nearest neighbors of all xenon sites are valine, leucine, and phenylalanine. This complex is, therefore, presumably stabilized mainly by London interactions, as in myoglobin.
C. THEBINDINGOF XENONTO OTHERPROTEINS AND VIRUSES The use of xenon as a “heavy atom” is of some interest in protein crystallography and has recently been tried on several macromolecules. Xenon is a little “lighter” than desirable for a heavy atom, but this is counteracted by the fact that xenon protein complexes show a very high degree of isomorphism with the native crystals-a fact often not true with most of the com8monlyused “heavy atoms” which are generally ionic groups capable of inducing some disorder into the native structure. Such trials have shown that xenon does not bind to hen egg lysozyme, chymotrypsin, or horse heart cytochrome (Dickerson, 1966) , but it does bind to rennin and to the protein subunits of intact tobacco mosaic virus (TMV) (Schoenborn and Holmes, 1967). I n both latter cases the structural analysis is not yet advanced enough to say anything about the binding sites. VI. Conclusion
The various binding forces through which the so-called “inert gaseous anesthetic agents” associate with macromolecules have been discussed in order tQ demonstrate what conditions are prerequisite for binding. If,
16
B. P. SCHOENBORN AND R. M. FEATHERSTONE
then, thc molecular natures of particular binding sites are determined, it will be feasible to elucidate how such an interaction affects the function of the systems. Recent advances in protein crystallography have made it now possible to study drug-protein interaction on a truly molecular level. Detailed knowledge of protein structures is a t present limited to myoglobin (Kendrew and Watson, 1967) and lysozyme (Blake et al., 1965), but within the next two or three years the three-dimensional structures of many other enzymes will be known. This will open up a completely new approach to the study of drug receptor action which, complernentcd by the large amount of clinical and biochemical results, will allow hitherto unknown possibilities in the field of drug design. It might be argued here that since X-ray diffraction studies are performed on crystallinc enzymes, the surrounding is quite different from that of the enzyme’s natural biological one. Attention has been given to this problem by a number of workers (Banaszak et al., 1963; Perutz et al., 1964) and it has been shown that several rcactions are possible in crystalline material-consistent with identical protein structure in solution and in crystal form. Observed differences in reaction rates with crystallized enzymes (Chance et al., 1966) are probably due to small increases in activation energies. This could be caused by restrictions in some of their rotationaI or translational degrees of freedom due to the packing of the molecules in the crystal lattice (intermolecular van der Waals bonding). ADDENDUM It has recently been shown that xenon binds to deoxymyoglobin at the same spcrific site as in metmyoglobin (Schoenborn and Nobbs, 1966). An x-ray diffraction analysis of the binding of cyclopropane to metmyoglobin showed that cyclopropane binds to myoglobin a t thc same site that xcnon does, but that the slightly larger cyclopropanc necessitates a reorientation of a neighboring phcnylalanine as well as some minor adjustments in other neighboring groups (Schoenborn, 1967). It has also recently been shown that the binding of xenon to myoglobin affects the affinity of rnrbon monoxide to myoglobin (Lumry, 1966; Schoenborn et al., 1967).
ACKNOWLEDOMENTS This publication was supported in part by the United States Public Health Service Grant NB03625. We wish to thank 0. Jardetzky for his advice. REFERENCES
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