Biochemistry 1989, 28, 3687-3691 Engelhard, M., Gerwert, K., Hess, B., Kreutz, W., & Siebert, F. (1985) Biochemistry 24, 400-407. Fodor, S . P. A,, Pollard, W. T., Gebhard, R., van den Berg, E. M. M., Lugtenburg, J., & Mathies, R. A. (1988a) Proc. Natl. Acad. Sci. U.S.A.85, 2156-2160. Fodor, S . P. A., Ames, J. B., Gebhard, R., van den Berg, E. M. M., Stoeckenius, W., Lugtenburg, J., & Mathies, R. A. (1988b) Biochemistry 27, 7097-7101. Hanamoto, J. H., Dupuis, P., & El-Sayed, M. A. (1984) Proc. Natl. Acad. Sci. U.S.A.81, 7083-7087. Harbison, G. S., Smith, S. O., Pardoen, J. A., Winkel, C., Lugtenburg, J., Herzfeld, J., Mathies, R., & Griffin, R. G. (1984) Proc. Natl. Acad. Sci. U.S.A. 81, 1706-1709. Harbison, G. S., Smith, S. O., Pardoen, J. A., Courtin, J. M. L., Lugtenburg, J., Herzfeld, J., Mathies, R. A,, & Griffin, R. G. (1985) Biochemistry 24, 6955-6962. Hess, B., & Kuschmitz, D. (1977) FEES Lett. 74, 20-24. Kouyama, T., Kouyama, A. N., Ikegami, A., Mathew, M. K., & Stoeckenius, W. (1988) Biochemistry 27, 5855-5863. Li, Q. Q., Govindjee, R., & Ebrey, T. G. (1984) Proc. Natl. Acad. Sci. U.S.A. 81, 7079-7082. Mathies, R., Oseroff, A. R., & Stryer, L. (1976) Proc. Natl. Acad. U.S.A. 73, 1-5. Mathies, R. A., Brito Cruz, C. H., Pollard, W. T., & Shank, C. V. (1988) Science 240, 777-779. McMaster, E., & Lewis, A. (1988) Biochem. Biophys. Res. Commun. 156, 86-91. Ohno, K., Takeuchi, Y., & Yoshida, M. (1981) Photochem. Photobiol. 33, 573-578. Ort, D. R., & Parson, W. W. (1978) J . Biol. Chem. 253, 61 58-6164. Pardoen, J. A., Winkel, C., Mulder, P. P. J., & Lugtenburg, J. (1984) R e d . Trav. Chim. Pays-Bas 103, 135-141.
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Scherrer, P., Mathew, M. K., Sperling, W., & Stoeckenius, W. (1989) Biochemistry 28, 829-834. Schulten, K., & Tavan, P. (1978) Nature (London) 272, 85-86. Smith, S . O., Pardoen, J. A., Mulder, P. P. J., Curry, B., Lugtenburg, J., & Mathies, R. (1983) Biochemistry 22, 61 41-61 48. Smith, S. O., Myers, A. B., Pardoen, J., Winkel, C., Mulder, P. P. J., Lugtenburg, J., & Mathies, R. (1984) Proc. Natl. Acad. Sci. U.S.A. 81, 2055-2059. Smith, S. O., Lugtenburg, J., & Mathies, R. A. (1985a) J. Membr. Biol. 85, 95-109. Smith, S. O., Myers, A. B., Mathies, R. A., Pardoen, J. A., Winkel, C., van den Berg, E. M. M., & Lugtenburg, J. (1985b) Biophys. J . 47, 653-664. Smith, S . O., Hornung, I., van der Steen, R., Pardoen, J., Braiman, M. S., Lugtenburg, J., & Mathies, R. A. (1986) Proc. Natl. Acad. Sci. U.S.A.83, 967-971. Smith, S . O., Braiman, M. S., Myers, A. B., Pardoen, J. A., Courtin, J. M. L., Winkel, C., Lugtenburg, J., & Mathies, R. A. (1987a) J . A m . Chem. SOC.109, 3108-3125. Smith, S. O., Pardoen, J. A., Lugtenburg, J., & Mathies, R. A. (198713) J. Phys. Chem. 91, 804-819. Smith, S. O., Courtin, J., van den Berg, E., Winkel, C., Lugtenburg, J., Herzfeld, J., & Griffin, R. G. (1989) Biochemistry 28, 237-243. Stoeckenius, W., & Bogomolni, R. A. (1982) Annu. Rev. Biochem. 51, 587-616. Warshel, A., & Karplus, M. (1974) J . Am. Chem. SOC.96, 5677-5689. Wilson, E. B., Decius, J. C., & Cross, P. C. (1955) Molecular Vibrations, McGraw-Hill, New York.
Lipid Chains and Cholesterol in Model Membranes: A Monte Carlo Study? H. L. Scott* and S . Kalaskart Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078 Received July 29, 1988; Revised Manuscript Received January 30, 1989 ABSTRACT: The Monte Carlo method has been employed to study the equilibrium properties of a planar array of hydrocarbon chains interacting with a cholesterol molecule. The chains are arranged to model one monolayer of a lipid bilayer and within this monolayer are allowed to move laterally and change conformations by gauche rotations. In the simulation cell there are 90 lipid chains and a single cholesterol molecule. Periodic boundary conditions are imposed upon the cell. The primary results of the calculations are order parameter profiles for the C-C bonds. These are calculated for (i) all chains, (ii) the 6 chains which are nearest neighbors to the cholesterol, and (iii) the 12 chains which are next-nearest neighbors to the cholesterol. Calculations are carried out for C-14, C-16, and C-18 chains. T h e results show that cholesterol strongly affects the upper portions of the chains, leaving them less able to change conformations. For C-16 and C-18 chains, the chain termini of the cholesterol neighbors are more disordered than the bulk chain termini. T h e magnitude of the effect depends strongly on the chain length. The results suggest that the changes in the lipid phase transition caused by cholesterol are a consequence of each cholesterol hindering the rotameric freedom of five to seven lipid chains.
%e role of cholesterol in animal cell membranes (and other sterols in plant cell membranes) has been debated for many Supported in part by National Science Foundation Grant DMB 8703644. *Present address: Department of Chemistry, Utah State University, Logan, UT 84321.
0006-2960/89/0428-3687$01 .50/0
years [for a recent review, see Presti (1985)l. On the one hand, calorimetric studies show that cholesterol acts as a “disordering” agent in lipid bilayers in the sense that the otherwise sharp main lipid chain melting phase transition becomes broad and diffuse with increasing cholesterol concentration (Hinz & Sturtevant, 1972; Mabrey et al., 1978; Estep et al., 1978). On the other hand, cholesterol acts as an
0 1989 American Chemical Society
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Biochemistry, Vol. 28, No. 9, 1989
“ordering” agent in lipid bilayers in the sense that lipid chain mobility and the average area per lipid molecule are reduced with increasing cholesterol concentration (above the main lipid phase transition) (Demel et al., 1972; Jacobs & Oldfield, 1979). At temperatures below the main lipid phase transition lipid chain mobility is increased (Delmelle et al., 1980), and the ripple separation in the P, phase increases (Copeland & MConnell, 1980). While early suggestions that the cholesterol hydroxyl group hydrogen bonds to lipid carbonyl oxygens have been ruled out by spectroscopic data, it is possible that the hydroxyl may hydrogen bond to a glycerol oxygen [see Presti (1985)]. The experimental data present a picture of extremely complex interactions between cholesterol or other non-lipid perturbants and phospholipid molecules. By contrast, theoretical efforts have been largely limited to two-dimensional or mean field models (Marcelja, 1976; Scott & Coe, 1984; Pink & Chapman, 1979) which are unable to directly incorporate the detailed molecular structures and conformations in the theories. The theories proposed so far either do not adequately describe all the diverse data or do so only with a high degree of phenomenology. It is therefore natural to turn to numerical simulation as a tool which can carry out theoretical analysis of models containing more detailed structural information than is possible to incorporate in purely analytical theories. There have been a number of fully three-dimensional Monte Carlo and molecular dynamics calculations of the properties of lipid bilayers (van der Ploeg & Berendsen, 1983; Kox et al., 1980; Scott, 1977, 1986; Scott & Cherng, 1978), as well as several simulations of two-dimensional lattice models [for a review, see Mouritsen (1984)l. In general the results of both the molecular dynamics (MD) and the Monte Carlo (MC) simulations of systems with extended chains consist of chain order parameter profiles and “snapshots” of instantaneous configurations of the systems (the MD calculations also give some dynamical information over very small time scales). The general agreement between thee MC and MD calculations and experimental data indicates that the computer calculations have included most of the relevant interactions for the study of chain packing issues. It is then natural to attempt to study more complex packing problems with the numerical tools, and lipid-cholesterol packing simulations are a straightforward extension of the pure lipid calculations. The only other attempt to study lipid-cholesterol interactions in a model which explicitly included flexible chains is that of Scott and Cherng (1978). This work was a Monte Carlo simulation of a small number of hard-sphere chains surrounding a rigid cylinder which represented a cholesterol molecule. The present work takes advantage of the great improvement in computer technology since 1978 to simulate a much larger system with more realistic interactions. As in earlier work (Scott & Cherng, 1978) the objective of this effort is to ascertain the manner by which a single cholesterol molecule perturbs neighboring lipid chains. Since the chain length is likely to be an important factor, calculations are performed for chains of 14, 16, and 18 carbon atoms, all with saturated bonds. MATERIALS A N D METHODS The Monte Carlo method used for these calculations is nearly identical with that used in earlier work (Scott, 1977, 1986). Namely, a planar array of lipid chains is constructed, and one chain is replaced by a cholesterol molecule. The Monte Carlo algorithm then vists each molecule, including the cholesterol, in sequence and changes the state of the molecule by a small random translation in the layer plane and one or
Scott and Kalaskar two gauche rotations about randomly chosen bonds (for the cholesterol the translations are suppressed, and rotations occur in the tail of the molecule). In the calculation of the intermolecular interactions, the optimized 6-1 2 potentials of Jorgensen (1977) are used for all methyl and methylene subunits on lipid and cholesterol chains. As an approximation, the carbons on the rigid ring region of the cholesterol molecule are assigned the same 6-12 parameters as the methylenes. Gauche rotations are restricted to values of f 120°, and these rotations are assigned an energy of 500 cal/m if the neighboring segments are in the trans state. Two successive gauche rotations are assigned an energy of 2500 cal/m. The calculations are relatively insensitive to small changes in the interaction constants for the rigid portion of the cholesterol molecule. Moves are accepted or rejected according to standard Metropolis sampling criteria (Metropolis et al., 1953), and running averages of quantities of interest are calculated. In the present case the quantities of interest are the order parameter profiles: ( S , ) = (1/2)(3
COS*
0, - 1 )
where n is the bond number and 0” is the deviation of the nth C-C bond from the angle it makes with the bilayer normal in the trans configuration. Averages are kept for all chains, chains nearest the cholesterol, and the next-nearest neighbor chains to the cholesterol, The simulation cell contains 99 chains which are initialized in all-trans conformations in a hexagonal array with interchain spacing of 6 8, and a single cholesterol molecule. The size of the array is such that the area per chain (the total area divided by 100) is 31.18 A’, which is approximately equal to the area per chain for phospholipid bilayers in the fluid state. The chain coordinates are reproduced from the topmost carbon (which is constrained to lie in the interface but which may move laterally in this plane as the chain translates) by successive rotation and translation operations as in earlier work (Scott, 1986). The cholesterol coordinates are initially hand entered. During the simulation the coordinates of the carbon atoms in the chain portion of the cholesterol are recalculated after moves in the same way as the other chains. For the chains, a move consists of a translation of the entire chain in the layer plane by a small amount in a random direction and a rotation at one or two randomly chosen nonconsecutive bonds. For the cholesterol a move consists of a rotation of the tail chain about a randomly chosen bond but no translation. The cholesterol molecule is placed so that the top carbon of the top ring of the cholesterol lies in the same plane as the top carbon of the chains. None of the molecules in these simulations are allowed to move perpendicular to the bilayer plane. Relaxation of this constraint to allow small perpendicular displacements has practically no effect on the calculations (Chowdhury and Scott, unpublished results). Another limitation is that the cholesterol hydroxyl and the lipid head groups are not included in the simulation. At first glance this seems to be a serious omission, but the likely effect of the polar or hydrogen-bonding interactions between the polar groups should be, in a first approximation, to keep the lipid chains and the cholesterol at precisely the same level. If this is the case, then these interactions are mainly background terms. Since only energy differences are counted in Monte Carlo moves, constant background terms do not contribute, and computer time is saved by not including them. Yet another simplification is the lack of a glycerol backbone connecting pairs of chains. In earlier work (Scott, 1977) it was found that chain ordering is affected mainly by the accessible free volume in the system, and this is the same whether chains are con-
Biochemistry, Vol. 28, No. 9, 1989 3689
Lipid Chains and Cholesterol in Membranes
Table I: Standard Deviations for DPPC Data bond bulk bulk cholesterol bond chains no. chains no. chains 2 3 4 5 6 7 8
t
o.2 0’ 0
1 2
4
6
E
10
12
14
16
Bond Number
Order parameter vs bond number for calculated averages from C-16 simulations: (*) averages for all chains; (+) averages for chains which are nearest neighbors of the cholesterol molecule; (A) experimental data divided by 0.5 as discussed in the text. FIGURE 1:
nected in pairs or not. Differences in sn-1 and sn-2 chain positions are not considered. This is so that we may obtain accurate results for a homogeneous a system as possible. To apply our results to real systems, it is necessary to use the shorter chain calculations for the sn-2 chains and the longer chain calculations for the sn-1 chains. The major improvement in the present work over previous work is the greatly increased system size. As will be seen, the profiles are substantially smoother so that some finite size effects of previous work are diminished. Finally, all calculations were carried out with only one cholesterol molecule in the sample cell. The resulting 1:99 chain:cholesterol ratio is far below that at which lipid perturbation of chain packing is visible experimentally. However, in order to understand lipid-cholesterol interactions at higher cholesterol concentrations, it is essential that the interactions be understood at the single molecule level. Future calculations will build upon the results presented here to simulate lipidcholesterol interactions at higher cholesterol concentrations. To study the 100 molecule systems, earlier code was revised and vectorized, and all simulations were run on the Cray X-MP/48 at the National Center for Supercomputing Applications. For each of the three systems studied the procedure was as follows: (i) initialize a hexagonal array of 100 chains, replacing chain number 55 with hand-entered coordinates for all the cholesterol carbons; (ii) run the M C algorithm for 30 000 passes through the system for equilibration (a total of 3 million configurations); (iii) run another 30000 passes for averaging; (iv) print out intermediate resulsts every 2500 passes to check convergence and to calculate errors. The DMPC and DPPC runs were carrier out at 300 K, and the DSPC runs were carried out at 325 K. In reality all these temperatures are sufficient to allow significant chain disordering. A system as small as 100 chains will not “freeze” until much lower temperatures. To save computer time, a cutoff of 16 A was used in the 6-12 interaction calculations. As an additional check on reproducibility the DPPC simulation was repeated with a different random number sequence. Errors are estimated as standard deviations in the average of the averages which are calculated every 2500 passes. RESULTS The results of the MC calculations consist of plots of order parameter profiles (eq 1) versus bond number. Snapshots of single configurations of such a large number of chain molecules show very little, but much insight is gained from the profiles and the fluctuations in the numerical averages. Results for
0.015 0.004 0.004 0.008 0.024 0.011 0.004
0.0 0.0 0.0 0.0 0.0 0.0 0.046
9 10 11 12 13 14
0.015 0.010 0.011 0.018 0.010 0.010
cholesterol chains 0.0 0.056 0.011 0.081 0.055 0.038
each chain system are presented in sequence below. Since DPPC-cholesterol systems are the most commonly studied experimentally, these results are presented first. DPPC. Figure 1 is a plot of ( S n )vs n for the DPPC calculations, with profiles for the bulk chain average, the average over the chains which were in closest contact with the cholesterol, and the experimental points from deuterium NMR data (Seelig & Seelig, 1977). The experimental data have been uniformly divided by 0.5 to approximately correct for localized chain tilting not considered in tne simulations, as in earlier calculations (Scott, 1977, 1986). The close correspondence between experiment and calculation confirms our expectations that the predominant mechanisms which control the chain conformations are included in this model. The bulk chain averages shown in Figure 1 and subsequent figures are for all 99 chains and are indistinguishable from averages over the 93 or so chains which are not nearest neighbors to the cholesterol. A chain is defined to be a near neighbor to the cholesterol molecule if any portion of the chain comes within 7.4 A of any portion of the cholesterol molecule. It is apparent from the figure that the cholesterol molecule forces its neighboring chains into more ordered configurations in the uppermost few bonds (for which ( S n )= 1). Then a series of paired bond rotations of the form s f t ... tg? set in several (but not all) of the neighboring chains, which leads to the zigzags in the profile. finally, the terminal three or four bonds are more disordered than the bulk chain termini. Table I gives standard deviations in the averages obtained from variations in the intermediate averages as described earlier. The noteworthy feature is that there is no deviation in the cholesterol neighbor data for bonds 2-7 and 9 (bond 1 is held fixed in all simulations). For all the averaging run steps, these bonds did not change their conformational state from that attained in the equilibration runs. This is a strong indicator of the steric hindrance provided by the cholesterol. It is important to note that not all of these bonds are in the trans conformation, so that it is not correct to say that cholesterol forces all its neighbor chains into all-trans conformations in the upper bonds. The calculations show that changes in conformation occur rarely in the upper 8-9 DPPC C-C bonds due to the steric effect of the cholesterol. DSPC. Figure 2 shows order parameter profiles for the DSPC simulations. The bulk chain profiles are very similar to those for DPPC in Figure 1, indicating that the algorithm has generated consistent and reproducible results. The average order parameters for the cholesterol neighbors, on the other hand, are smaller than those for DPPC. In Table I1 the standard deviations are given for this system. As was the case in the DPPC calculations, the uppermost bonds (specifically bonds 2-6 and 8) do not change rotameric state during the averaging runs. The fact that the profile for the cholesterol neighbors shows more disorder in the cholesterol neighbor chains for DSPC than for DPPC is a consequence of the longer chain length; during the equilibration from the all-trans initial state the longer chains have a greater set of rotameric states
3690 Biochemistry, Vol. 28, No. 9, 1989
Scott and Kalaskar
1 2
I
"i
\
1~
02-
02L I
5
10
15
Bond Number
Order parameter vs bond number for calculated averages from C-18 simulations: (*) averages for all chains; (+) averages for chains which are nearest neighbors of the cholesterol molecule. Table 11: Standard Deviations for DSPC Data bond bulk cholesterol bond bulk no. chains chains no. chains
cholesterol chains ~~
8 9
0.002 0.006 0.003
0.001 0.002 0.009 0.007
0.014
0.0 0.0 0.0 0.0 0.0 0.055 0.0 0.047
10 11 12 13 14 15 16
17
0.006 0.007 0.017 0.006 0.012 0.018 0.012 0.004
Table 111: Standard Deviations for DMPC Data bond bulk cholesterol bond bulk no. chains chains no. chains 2 3 4 5 6
7
0.007
0.014 0.007 0.004 0.005 0.023
0.0 0.0 0.0
8 9 10
0.01 1 0.0 0.007
11 12 13
0.011 0.015 0.030 0.011 0.032 0.025
~
0.097 0.069 0.070 0.043 0.051 0.048 0.048 0.058
~
cholesterol chains 0.123 0.025 0.076 0.025
0.080 0.060
accessible to them. However once a set of initial rotations have occurred, steric hindrances prevent further changes from occurring in the simulations, and this suggests again that such changes occur slowly (compared to bulk chain reorientations) in real systems. DMPC. The C-14 chains of DMPC do not extend below the cholesterol chain region, so one would expect that steric hindrances due to the cholesterol would affect a greater percentage of the bonds in the shorter chain system. Figure 3 shows the (Sn) vs n profiles for DMPC, and it is immediately apparent that the expectation is borne out. The profile for the cholesterol neighbors is generally above that for the bulk chains, with the exception of the terminal bond. The lack of a zigzag structure as seen in DPPC (Figure 1) is likely due to the fact that in the shorter chain system it is easier for single gauche bonds to form. This is also reflected in the standard deviations shown in Table 111. As was the case for the longer chains, there are several bonds which do not change state during the averaging runs. The fact that bonds 5 and 7 are able to occasionally undergo a trans-gauche transformation in a chain neighboring the cholesterol is due to the relative case the shorter chain has in forming single gauche rotations, rather than relying on pairs to form kinks or jogs. It is important to point out the zeros in the standard deviations in Tables 1-111 mean only that those segments did not change orientatior, during the averaging computer runs of
4
6
8
10
4-
'4
Bond Number
20
FIGURE 2:
7
0
2
0'
2 3 4 5 6
i
FIGURE 3: Order parameter vs bond number for calculated averages from C-14 simulations: (*) averages for all chains; (+) averages for chains which are nearest neighbors of the cholesterol molecule.
30 000 moves per chain. The exact location of the first bond for which motion occurs in the simulations is not significant. A shorter simulation of DPPC resulted in slightly different order parameters for the cholesterol neighbors and identical profiles for the bulk chains, and the first bond on a cholesterol neighbor chain to move during this run was number 6. In Table I the first bond to move is number 8. The significant result is that once the initially all-trans chains near the cholesterol undergo a small amount of disordering it is extremely difficult for further rotameric changes to occur in the regions of the chains in contact with the rigid sterol rings. However there is no single favored conformation which the cholesterol neighbors are forced into before this gridlock occurs. Since there are no experimental data which are capable of providing order parameter profiles for the cholesterol neighboring lipids alone in a bilayer, the data against which the results presented above should be judged are profiles for bulk chain profiles obtained from deuterium magnetic resonance experiments on model membranes with specific chain sites deuterated (Seelig & Seelig, 1977). As argued in earlier work (Scott, 1986) application of a scale factor accounts for cooperative chain tilting. If one assumes that the scale factor is -0.5-0.6, then the experimental profiles and the bulk profiles shown in Figure 1 are in good agreement. The results presented in this paper are a great improvement over earlier results calculated by the same basic algorithm (Scott, 1986) because of the 3-fold increase in the number of chains included in the simulation cell. DISCUSSION The results of our calculations provide a new view of the influence exerted by individual cholesterol molecules on lipid chains in a bilayer. The common notion that cholesterol forces the upper chain segments into all-trans states and allows the lower segments increased rotameric freedom is only partially true. The lower segments in DSPC and to a partial extent in DPPC do appear less ordered. However the calculations show that in all cases there is a t least some disorder in the upper segments as well. As the tables show, the rotameric changes in the upper segments occur quite infrequently, however. Although the MC calculations represent phase space ensemble sampling with no temporal considerations, it seems a reasonable conclusion that gauche rotations occur a t a much slower time scale in the upper segments of lipid chains which are nearest neighbors to molecules with large rigid sections such as cholesterol. The calculations presented here suggest that it is correct to say that cholesterol strongly hinders, but
Biochemistry, Vol. 28, No. 9, 1989 3691
Lipid Chains and Cholesterol in Membranes does not altogether preclude, rotameric disorder in the upper segments of neighboring chains. In the M C runs, average order parameter profiles were kept for chains which were next-nearest neighbors to the cholesterol also. These profiles agreed within the standard deviations with the bulk lipid profiles for DMPC. For DPPC and DSPC the order parameters for the next-nearest neighbor chains still, at a few segments, showed some differences from the bulk averages, suggesting a small chain-length dependence to the range of the cholesterol-induced chain perturbations. Our results have implications for the mechanism by which cholesterol affects lipid phase transitions at low cholesterol concentrations. According to the calculations we have done, each cholesterol molecule partially or wholly (depending on the chain length) hinders the ability of about six neighboring lipid chains to change their rotameric states. Thus at low concentrations cholesterol approximately removes three lipid molecules from the cooperative lipid-lipid interactions. Extrapolated to higher concentrations, this implies that at a 3:l 1ipid:cholesterolratio the lipid phase transition will disappear. However at higher concentrations there will be interactions between cholesterol-immobilized lipid chain complexes which should hinder disordering in “interstitial” chains, and the transition should actually disappear before the 3:l ratio is reached. At this point it does not appear necessary to invoke phase separations to explain the data. It should be pointed out that the experimental data apply only to very large lipid:cholesterol ratios, and at lower ratios more complex interactions may lead to phase-separated regions. The calculations do suggest that a plot of lipid phase transition enthalpy change vs cholesterol concentration should have a intercept of 1 /3 if extrapolated from low cholesterol concentration. As the concentration increases the slope should change, reducing the value of the intercept, for reasons mentioned above. The current experimental situation is that there appears to be two components to differential scanning calorimetry data: a narrow sharp component and a broad, diffuse component. The sharp component is naturally associated with the unhindered lipid chains and the diffuse component with those chains which are affected by the cholesterol (Estep et al., 1978). The data error bars are too large to allow conclusions about changes in slope of AH vs cholesterol concentration plots to be drawn. By far the majority of the experiments have been carried out on the DPPC-cholesterol system. Our results suggest that the effect of cholesterol on DMPC is more dramatic, and the effect on DSPC is less dramatic, compared to DPPC in that a greater (DMPC) or a smaller (DSPC) percentage of the C-C bonds are immobilized. In summary, the M C calculations described herein have provided some new insight into possible modes of lipid-cho-
-
lesterol interaction. It appears that one cannot simply classify chains which neighbor cholesterol as frozen in the all-trans state. However, one can classify these chains as strongly hindered in their effort to undergo conformational changes. It will be interesting to extend these calculations to systems with several cholesterol molecules. This will be carried out in the near future. ACKNOWLEDGMENTS We thank Dr. A. Chowdhury for several contributions to the computer code. Registry No. Cholesterol, 57-88-5.
REFERENCES Copeland, B. R., & McConnell, H. M. (1980) Biochim. Biophys. Acta 599, 95-109. Delmelle, M., Butler, K. W., & Smith, I. C. P. (1980)Biochemistry 19, 698-704. Demel, R. A., Bruckdorfer, K. R., & van Deenen, L. L. M. (1972)Biochim. Biophys. Acta 255, 31 1-320. Estep, T. N., Mountcastle, D. B., Biltonen, R. B., & Thompson, T. E. (1978)Biochemistry 17, 1984-1989. Hinz, H.-J., & Sturtevant, J. M.(1972)J . Biol. Chem. 247, 3697-3700. Jacobs, R., & Oldfield, E. (1979)Biochemistry 18,3280-3285. Jorgensen, W. (1982)J . Chem. Phys. 77,4156-4163. Kox, A.J., Michels, J. P. J., & Weigel, F. W. (1978)Nature (London) 287, 317-319. Mabrey, S., & Sturtevant, J. M. (1978) Methods Membr. Biol. 9,237-274. Marcelja, S . (1976)Biochim. Biophys. Acta 455, 1-7. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., & Teller, E. (1953)J . Chem. Phys. 21, 1087-1096. Mouritsen, 0.G.(1984)Computer Studies of Phase Transitions and Critical Phenomena, Springer-Verlag, Berlin and Heidelberg. Pink, D. A., & Chapman, D. (1979)Proc. Natl. Acad. Sci. U.S.A. 76, 1542-1 55 1. Presti, F. T. (1985)in Membrane Fluidity in Biology (Aloia, R. C. & Boggs, J. M., Eds.) pp 97-146,Academic Press, Boca Raton, FL. Scott, H. L. (1977)Biochim. Biophys. Acta 469,264-271. Scott, H. L. (1986)Biochemistry 25, 6122-6126. Scott, H.L.,& Cherng, S.-L. (1978)Biochim. Biophys. Acta 51 0,209-2 1 5 , Scott, H. L., & Coe, T. J. (1984)Biophys. J . 42,264-271. Seelig, A.,& Seelig, J. (1974)Biochemistry 13, 4839-4845. van der Ploeg, P., & Berendsen, H. J. C. (1 983) Mol. Phys. 49,233-256.
