J. Phys. Chem. 1995, 99, 14418-14423
14418
Capture of Potassium Ions by Valinomycin: A Molecular Dynamics Simulation Study T. R. Forester,*,+W. Smith? and J. H. R. Clarke5 Daresbury Laboratory, Daresbury, Warrington WA4 4AD, U.K., and the Department of Chemistry, UMIST, Manchester M60 IQD, U.K. Received: March 9, 1995@
Molecular dynamics simulations of the capture of both hydrated and unhydrated potassium ions by the antibiotic valinomycin are reported. There are no explicit solvent interactions although a stochastic bath is used to simulate thermal equilibrium at ambient temperature. An “open ring” conformer has been found and, in agreement with common interpretations of experimental data, is strongly implicated in the capture process. The distant attraction of the cation to the biopolymer is dominated by the dipole-charge interaction, and as the cation approaches, conformational changes are induced in the biopolymer to enhance its dipole moment. These changes involve both amide and ester carbonyl groups aligning toward the approaching cation. Initial coordination is via amide carbonyls, although this is eventually overtaken by ester carbonyl coordination on a time scale of about 30 ps. When cation water of hydration is included in the simulations, the time scale of the capture process is lengthened by approximately 3 orders of magnitude. The presence of the hydrated cation is sufficient to induce the conformational change from the twisted-bracket form of valinomycin to the open ring structure. The valinomycin rapidly changes shape in the early part of the capture, but displacement of water molecules by (mainly) ester carbonyls is a slow process. One water molecule remained firmly attached to the complex after 18 ns. This raises the question as to whether water is transported with the complex through membranes in vivo.
1. Introduction As a cation carrier for potassium transport across cell membranes, valinomycin is of considerable biological and technological importance and is representative of an important class of single-ring ionophores. In a previous study we showed that the experimental crystal structures of both valinomycin and its potassium complex could be reproduced to good accuracy using an adapted AMBER force field.’ In this paper we are concerned with the process of K+ capture by the uncomplexed valinomycin using the same force field. The full capture mechanism is likely to be quite complicated, so in order to approach the problem in a systematic way we have performed these initial simulations using isolated valinomycin molecules. Simulations involving both hydrated and unhydrated cations have been performed. Although there are no solvent interactions, a stochastic bath is used to simulate thermal equilibrium at ambient temperature? These simplified studies were considered a necessary preliminary to full simulations of the capture process at a model membrane interface. A schematic representation of valinomycin, cyclo(L-Val-DHyl-D-Val-L-Lac)s, a cyclodecapsipeptide, is shown in Figure 1. It contains a single 36-member ring formed by alternating amide and ester linkages. The structure of valinomycin and the K-valinomycin complex are well characterized in the solid and to a lesser extent in L J ~ v oThe . ~ ,potassium ~ complex is approximately spherical, and the cation resides in the center of the complex chelated by the carbonyls of the six ester groups. The six amide groups reside near the outside of the complex and form a bracelet of hydrogen bonds in a pattern reminiscent of a tennis ball seam. The uncomplexed valinomycin molecule exhibits a wide range of aspherical conformers, but it can be crystallized from
’ Daresbury Laboratory.
E-mail:
[email protected]. Daresbury Laboratory. E-mail:
[email protected]. 8 UMIST. E-mail:
[email protected]. Abstract published in Advance ACS Abstracts, August 15, 1995
@
Figure 1. Chemical structure of valinomycin.
apolar and medium solvents into a “twisted-bracelet’’ (TB) conformation in which both ester and amide carbonyls are involved in internal hydrogen bonds. Other crystalline forms such as an open “dish shape” can be obtained from polar solvents (e.g., DMSO5), but valinomycin does not capture potassium in these media.6 In any event, NMR and FTIR measurements in apolar solvents and in lipid membranes are not consistent with these structures as they indicate that the ester carbonyls are not involved in hydrogen bonds. Consequently it has been postulated that a prebinding “open ring” (OR) conformer predominates in the interior of the lipid membrane and is responsible for cation ~ a p t u r e . ~ , ~ , ~ Despite some conjecture in the literature,* experimentally little is actually known about the mechanism of potassium capture. Particular issues such as where the capture process takes place (in the aqueous phase, the lipid membrane, or the interphase), which valinomycin conformers are involved in the capture process, and how the cation is drawn into the center of the complex are unresolved at present. An understanding of these issues could potentially provide further valuable insights into not only the biological function of valinomycin but also the structural features important for inclusion into synthetic cation carriers with application to potassium-selective detection devices.
0022-3654/95/2099-14418$09.00/0 0 1995 American Chemical Society
Capture of Potassium Ions by Valinomycin
J. Phys. Chem., Vol. 99, No. 39, 1995 14419
2. Computational Procedures
I.
The force field used here is based on the all-atom version of the AMBER force field.9 The general potential function is of the form
Cmi i= I
C dihedrals
+ cos(n4 + s)] + C HydrogenBonds
A
B
r!?
ri?
- - -+ ‘J
In the calculations reported here all covalent bonds were kept of fixed length by use of the SHAKE algorithm,I0 so the first term in eq 1 is redundant. Hydrogen bonding is accounted for by the 12-10 potential, while other short-range nonbonded interactions are treated with the Lenndard-Jones 12-6 potential. 12-6 potential parameters for interactions between atoms of different type were generated from the standard LorentzBerthelot rules,” viz., Dab = ‘/2(Oa -k Ob),Eab = The final term of eq 1 accounts for the electrostatic interactions. The 12-6 and electrostatic parameters for valinomycin and K+ interactions are those used in a previous study.’ The SPC potential was used to represent the water molecules.I2 2.1. Molecular Dynamics Simulations. All the molecular dynamics simulations reported in this paper were carried out using the parallel-processing macromolecular simulation package DL-POLY ‘33’43’5 developed at Daresbury Laboratory and were run on Hewlett-Packard Series 9000 Model 735 workstations. The equations of motion were integrated using the Verlet leapfrog scheme coupled to a NosC-Hoover thermostat16 with a thermostat relaxation time of 0.4 ps. As in our previous work stochastic collisions were also used to simulate interaction with a heat bath; these collisions were implemented for only the sp3 hybridized carbons. This approach2 corresponds to propagation of the equations of motion in between instantaneous collisions which occur with an average frequency v and for which the incidence corresponds to a Poisson process. Each collision consists of replacing the velocities of a subset of atoms by new ones sampled from a Boltzmann distribution. The stochastic thermal bath is a particular version of Andersen’s constant temperature m e t h ~ d ’ ~and . ’ ~yields static properties corresponding to a canonical distribution at constant temperature.2 The rigid bond dynamics were handled with a parallel version of a SHAKE algorithm known as RD-SHAKEI5 with a relative tolerance in B of low6.The MD time step was 2.0 fs. A cutoff of 100 A was applied to the nonbonded atom-atom potential energy functions. 2.2. Molecular Shape Parameters. We have monitored two aspects of the global structure of the molecule. The first was the asphericity order parameter, A3, of Rudnick and GaspariI9
6.
where (...) denotes an ensemble average and the Ai are the three principle moments of inertia of the valinomycin molecule. The principal moments of inertia are obtained by diagonalization of the inertia tensor T,the components of which are given by
where a and ,8 are x, y, or z, mi is the mass of the ith particle, rp is the a component of the position vector of particle i, r:om is the a component of the center of mass of valinomycin, and X i s 168-the number of atomic sites in valinomycin. A3 is 0 for a perfectly spherical object, for a uniform, infinitely thin, circular disk, and 1.O for an infinitely thin rod. The second measure of global structure used was the mean-squared radius of gyration, defined as 1
1
(4) where M is molecular mass.
3. Simulation Studies 3.1. “Open Ring’Conformtion. To unravel the mechanism of complexation, we first investigated the relaxation of the isolated complexed molecule to the uncomplexed state. The potassium ion was removed from an equilibrated configuration of the isolated potassium-valinomycin complex, and the resultant structure (with P = 29 A2, A3 = 0.07, p = 3.6 D) was used as the starting configuration for a 1 ns simulation at 310 K. Remarkably, within a few picoseconds the molecule relaxed into a conformation which was a relatively flat OR conformation with (P) = 34 A2, (A3) = 0.19, p = 5.3 D. There is a noticeable pore in the center of the structure (Figure 2). This structure is apparently metastable since when the temperature was raised to 330 K the OR conformer converted spontaneously to the more symmetric TB conformer (with (P) = 29.6 A2, (A3) = 0.12, p = 3.6 D) after a further 500 ps of the simulation. At no point in any TB simulation did we see evidence of sustained (re)opening of the structure. The contributions to the configurational energy of the two conformers are given in Table 1. Both conformers exist with little internal torsion strain, which, in part, explains the long-lived metastability of the OR conformer. The persistence of the OR conformer at 3 10 K is significant since, as mentioned in the Introduction, it has been postulated that such a structure is dominant in apolar solvents and lipid membranes6.’ and is responsible for the in vivo complexation of p o t a ~ s i u m . ~ . ~ 3.2. Isolated Potassium Ion Capture. A series of simulations were performed starting from the OR structure of Figure 2. In each case a potassium ion was placed 20 8, away from the center-of-mass of the valinomycin and assigned a null initial velocity. Thirty simulations of 50 ps in length were carried out at a simulation temperature of 310 K. The initial cation positions were chosen to uniformly sample the surface of a sphere around the valinomycin, as indicated in Figure 3. The simulations were repeated for the TB conformer with a smaller number of starting positions. The “success” of each capture experiment was determined by the mean number of potassium carbonyl ligands over the final 20 ps of simulation. Complete “success” corresponds to simulations which resulted in configurations with structural parameters within statistical uncertainty of those for the equilibrated potassium complex. A “failure” occurs when the cation remains uncoordinated to the biopolymer or is repelled
14420 J. Phys. Chem., Vol. 99, No. 39, 1995
Forester et al.
a
b
Figure 2. Stereoviews of the open ring conformation used in the potassium capture experiments. Oxygen atoms are shown in black, nitrogen in dark grey, carbon in mid grey, and hydrogens as light grey: (a) viewed along the inertial axis perpendicular to the “ring”; (b) viewed along an inertial axis in the plane of the “ring”.
;&+&
TABLE 1: Configurational Energy E and Component Energies (kJ/mol) of the Twisted-Bracelet (TB) and Open Ring (OR) Conformers at 310 K TB OR
277.3 286.0
-44.3 -51.4
-102.0 -83.3
327.5 324.3
96.2 96.3
from it. Intermediate successes corresponds to partial chelation. In no case did a structure persist with only one carbonyl coordinated. The OR simulations produced a high proportion of successes and highly coordinated structures while the TB simulations showed only 1 success, 2 “5-6 ligand encounters”, and 13 “failures”. From Figure 3 it is evident that the most successful captures occur for cations placed along directions close to that of the dipole vector of the valinomycin starting configuration. This correlation between the direction of cation approach and the alignment of the dipole vector is also demonstrated in Figure 4 where the cosine of the angle 8 between the dipole moment and the vector connecting potassium and the valinomycin center of mass is plotted against R, the distance of the cations from the valinomycin center of mass. This function shows a maximum at around R = 6 A, corresponding to the potassium being coordinated to two or three carbonyl groups. Additionally however there is strong evidence for a dynamic correlation between the cation trajectory and the magnitude of the dipole moment. The capture process appears to involve a positive feedback mechanism in which the cation induces conformational changes in the biopolymer such that the dipole moment of valinomycin is enhanced in the direction of the cation. The enhanced dipole moment results in an even stronger dipole-charge interaction with the cation. This effect also can be seen in Figure 4 where the mean dipole moment, p, of the valinomycin is plotted as a function of R. The data are averaged over the nine most “successful” OR capture simulations. The dipole moment is also a maximum around R = 6 A, and the strong correlation with the direction of approach is clearly evident. The same pattern was observed in the one successful
5
5
____ _____ 3
&v-03 2
0
Figure 3. Distribution of initial positions of Kf ions relative to the inertial axes and center of mass of the starting open ring conformation of valinomycin. The numbers indicate, to the nearest integer, the mean number of carbonyl groups coordinated to the ion during the final 20 ps of the 50 ps simulation. “S” indicates a final mean structure indistinguishable from the equilibrated K-valinomycin complex. The arrow gives the direction of the dipole moment of the valinomycin at the start of each simulation.
TB simulation where the maximum dipole moment was 10 D-approximately 3 times the mean value of uncomplexed TB conformer. The role of the various carbonyl groups in the chelation process can be monitored through a plot of potassium coordination number as a function of time, as shown in Figure 5, where the data are averaged over the nine most successful OR simulations. t = 0 is taken to be when the potassium first comes within 3.5 8, of a valinomycin site. The figure indicates that initially it is the amide carbonyls that coordinate to the cation. The number of coordinated amide groups reaches a peak between 5 and 10 ps, after which some amide coordination is lost in favor of the ester carbonyls. The figure is strongly suggestive of a key role for the amide groups in the initial stages of capture although ultimately it is the ester groups that dominate the coordination. Ester coordination takes longer to develop, but by the end of the simulation (50 ps in all), the amounts of ester and amide coordination are close to that seen in extended simulations of the isolated potassium complex. In every event of potassium coordinating to the valinomycin, we observed that the first coordination site of the potassium was always an amide carbonyl. Often this was accompanied
J. Phys. Chem., Vol. 99, No. 39, 1995 14421 Hydrated Potassium capture
0.6
pi
0.4
I
AJA3(t=O)
z
v
-----*
1
"
I
o
i
I d-
" " " " " " " '
10
15
"
"
20
"
"
"
25
"
30
Time I ps
Figure 5. The mean number of carbonyl oxygens within 3.5 A of the potassium as a function of time in the in uacuo OR capture experiments. As In Figure 4, results are averaged over the nine most successful simulations. t = 0 coaesponds to the time when a valinomycin site first comes within 3.5 A of the ion. The data have been recorded over 2 ps intervals. Data for both amide carbonyls (0)and ester carbonyls (0)are shown. The dashed lines on the right of the diagram indicate the final coordination numbers in the simulations.
by coordination to a neighboring ester group andor a neighboring amide group and typifies the coordination pattern both in the "2-3 ligand encounters" and at short tinme in the more highly coordinated encounters. This initial coordination pattern can be achieved with only modest conformational changes from the uncomplexed biopolymer. It is the coordination of the next two or so carbonyls that draws the cation into the "center" of the molecule and results in the valinomycin adopting near spherical symmetry around the ion. It was this step which proved difficult in many of the TB simulations. Examination of the structure showed the cation attached to the edge of the molecule, but the molecule was unable to "unravel" to complete the capture process because of twisting of the molecular ring. 3.3. Capture of Hydrated Potassium Ions. The studies so far are limited in that they do not incorporate solvent molecules. One process that is expected to accompany in vivo chelation of the cation is the displacement of water molecules from the first coordination sphere. As a precursor to a full simulation of the capture process at the apolar/aqueous interface,
"
"
"
'
"
"
'
'
"
10
amide40 water
~
15
Time I ns
Figure 6. Changes in the structure and coordination which take place during the capture of a hydrated potassium ion. The data were obtained from just one 18 ns simulation so the data are rather coarse grained in time and only give a qualitative indication of the sequence of events. Points are time averages over the following periods: 0-0.4, 0.4-0.7, 0.7-1.3, 1.3-3.5, and 3.5-18 ns. Note the rapid changes in valinomycin structure as it prepares to coordinate the hydrated potassium ion and the gradual displacement of water by valinomycin ligands.
we investigated the feasibility of capture in the presence of limited amounts of water which initially were placed around the cation. A single very long simulation was performed for the OR conformation with the starting position for the cation the same as that for the most successful unsolvated capture (marked with an asterisk in Figure 3). The cation was surrounded by six water molecules corresponding to approximately the first solvation shell of the ion. The simulation supports a mechanism involving the stepwise removal of water from the cation. It was found that the solvated ion moved to the pore mouth within a few picoseconds, and the resulting changes in global structure and cation coordination occurring thereafter are summarized in Figure 6. Although from a single simulation we can only obtain a rather "coarse-grained" picture of the events, it is notable that changes in the global structure of the valinomycin occur quite quickly in the absence of a surrounding medium; most of the observed changes in both A3 and $ take place within 0.5 ns. This is in marked contrast to the rather slow displacement of water molecules in the cation coordination sphere by (mainly) the ester carbonyls. The coordination sphere is defined at 3.5 A, which is the position of the first minimum of the cation oxygen pair distribution function for K+ in SPC water. After about 4 ns the situation is still quite complicated. All but two water molecules have been displaced. The ester coordination number is about 4, but the total coordination number of the potassium ion is about 7 due to additional close approach by amide
14422 J. Phys. Chem., Vol. 99, No. 39, 1995
a
5’
Forester et al.
Y
h
Figure 7. Stereoviews of water adducts obtained during the hydrated open ring capture simulation: (a) n = 6 water; (b) n = 4 waters; (c) n = 1 water. In each case the potassium is shown as a sphere. The shading on the valinomycin atoms is the same as in Figure 2.
carbonyls. As expected, the ratio of amide carbonyls to ester carbonyl coordinated to the cation approached the value found for the equilibrated in vacuo complex.* We did not observe the loss of the final water even after a total of 18 ns. As far as this simulation is concerned, this result is not totally unexpected as the configurational energy of the single water adduct is approximately 30kT lower than that of the isolated potassium complex, an effect due almost equally to more favorable electrostatic and van der Waals energies. Although this situation may well change in the presence of solvent and allow complete formation of the 6-fold coordinated potassium complex, it does however leave open the possibility that residual coordinated water is transported by the complex through membranes in vivo. Typical structures adopted at intermediate stages corresponding to approximately six, four, and one solvent molecules are shown in Figure 7. These are of interest because they suggest that the capture process takes place though the “Lac” face of the molecule as suggested from the results of a restrained simulation study of K-valinomycin in methanol.23 The isopropyl groups (associated with the “HyV” face) are on the opposite side of the molecule and form a hydrophobic cluster. These intermediate structures are suggestive that the capture process may take place with the valinomycin straddling the interface. The hydrophobic rear of the molecule is situated in the apolar phase while the cation is loaded directly from the aqueous phase through the “Lac” face.
An additional simulation was also carried out for capture of a solvated potassium ion by a twisted-bracelet conformation of valinomycin (the same conformation that produced the one and only successful unsolvated TB capture-as described earlier). As the solvated cation was attracted to the biopolymer within about 20 ps, the latter untwisted to form an OR structure (9= 34 A2). The simulation then followed a similar course to the OR simulation described above. This strongly suggests that the first stage of the complexation mechanism involves the open ring structure surrounding an essentially full solvated cation. The presence of the solvated cation is sufficient to effect the conformational transformation from TB to OR conformers. As compared to the isolated potassium ion capture, the inclusion of modest amounts of water in the capture simulations leads to some additional important differences. For example, the initial role of amide coordination to the cation is considerably reduced by inclusion of water. From direct examination of structures, it appears that a possible reason for this is that water molecules, while coordinated to the cation, may also hydrogen bond to the ester carbonyls. This holds the ester groups in a position where coordination to the cation is possible. The amide carbonyls do not participate in hydrogen bonding with water to the same extent. 4. Conclusions
The results of these simulations give support to the hypothesis that an open ring conformer of valinomycin plays an important
Capture of Potassium Ions by Valinomycin role in the capture of both isolated and hydrated potassium ions. When the cation was removed from the stable complex in a heat bath at 3 10 K, the valinomycin relaxed spontaneously to the well-defined OR structure which was stable for well over 1 ns. During the hydrated cation capture, starting with the more stable twisted-braclet (TB) conformer, there was a rapid and early transformation to the OR structure. One significant difference between the TB and OR conformers is the strongly enhanced dipble moment of the latter structure by about a factor of 50%. Strong electrostatic interaction with the distant potassium ion may be the driving force for the formation of the OR conformer as the valinomycin prepares itself for the capture process. There is a strong correlation between the changing dipole moment of the valinomycin with the trajectory of the incoming cation. Amide groups are involved in the initial stages of complexation, but ultimately it is the ester oxygen coordination which dominates. The most significant mechanistic differences in the case of hydrated potassium ions is the much longer time scale of the capture process (nanoseconds as opposed to picoseconds for the unhydrated ion). Water is squeezed out of the hydration shell of the cation only in the rather late stages when the cation is already starting to embed itself into the valinomycin. The final structure after 18 ns of simulation retained one water molecule of hydration, and for this reason we cannot be sure that the complexation process is complete in the absence of surrounding medium. The final coordination number of the potassium was 7.6. This value is in keeping with the general behavior of this cation in aqueous solution20s21and with other cyclic peptides.22
Note added in proof A very recent potential of mean force simulation of Kf -valinomycin in methanol24 predicts complexation to take place through the HyV face in preference to the Lac face.
J. Phys. Chem., Vol. 99, No. 39, I995 14423 References and Notes (1) Forester, T. R.; Smith, W.; Clarke, J. H. R. J . Phys. Chem. 1994, 98, 9422. (2) Depaepe, J. M.; Ryckaert, J. P.; Bellemans, A. Mol. Phys. 1993, 78, 1575. (3) Neupert-Laves, K.; Dobler, M. Helv. Chim. Acta 1975, 58, 432. (4) Karle, I. L. J . Am. Chem. SOC. 1975, 97, 4379. (5) Karle, I. L.; Flippen-Anderson, J. L. J . Am. Chem. SOC.1988, 110, 3253. (6) Jackson, M.; Mantsch, H. H., Biopolymers 1991, 31, 1205. (7) Feigenson, G. W.; Meers, P. R. Nature 1980, 285, 313. (8) Grell, E.; Funck, T. In Membranes; Eisemann, G., Eds.; Dekker: New York, 1975; Vol. 3, p 1 ff. (9) Weiner, S. J.; Kollman, P. A.; Nguyen, D. T.; Case, D. A. J . Comput. Chem. 1986, 7, 230. (10) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J . Comput. Phys. 1977, 23, 327. (11) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1989. (12) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Hermans, J. In Intermolecular Forces; Pullman, B., Ed.; Reidel: Dordrecht, The Netherlands; 1981; p 331. (13) Forester, T. R.; Smith, W. The DL POLY User's Manual; Daresbury Laboratory; 1994. Ref No. DLISCIIPMlOOT. (14) Smith, W.; Forester, T. R. Comput. Phys. Commun. 1994, 79, 52. (15) Smith, W.; Forester, T. R. Comput. Phys. Commun. 1994, 79, 63. (16) Hoover, W. G.; Phys. Rev. 1985, A31, 1695. (17) Andersen, C. J . Chem. Phys. 1980, 72, 2384. (18) Andrea, T. A.; Swope, W. C.; Andersen, C. J . Chem. Phys. 1983, 79, 4576. (19) Rudnick, J.; Gaspari, G. Science 1987, 237, 384. (20) Bounds, D. G. Mol. Phys. 1985, 54, 1335. (21) Impey, R. W.; Madden, P. A.; McDonald, I. R. J . Phys. Chem. 1983, 87, 5071. (22) Dobler, M.; Dunitz, J.; Kilboum, B. Helv. Chim. Acta 1969, 52, 2573. (23) Lqvist, J.; Alvarez, 0.; Eisenman, G. J. Phys. Chem. 1992, 96, 10019. (24) Marrone, T. J.; Merz, K. M., Jr. J. Am. Chem. Soc. 1995, 117, 779. JP950678E
