induced Conformational Transition of Troponin C - The Journal of

THEJOURNAL OF BIOLOGICAL CHEMISTRY 0 1986 by The American Society of Biological Chemists, Inc.

Vol. 261, No. 6, Issue of February 25, pp. 2638-2644,1986 Printed in U.S.A.

A Model for the Ca2'-induced Conformational Transition of Troponin C A TRIGGER FOR MUSCLE CONTRACTION* (Received for publication, August 15, 1985)

Osnat Herzberg, John Moult, and Michael N. G . James From the Medical ResearchCouncil of Canada Groupin Protein Structure and Function, Departmentof Biochemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2H7

The initial contractile event in muscleis the binding of the muscle whichleads to contraction (10-13). Larger scale of Cas+ ions to troponin C of the troponin complex, changes are associated with the nonphysiological removal of leading to a series of conformational changes in the metal ionsfrom the high affinity sites (14-16}. members of the thin and thick filaments. Knowledge The crystal structure of troponin C from turkey skeletal of the crystal structure of turkeyskeletal muscle tro- muscle has been determined at 2.8-A resolution in our laboponin C has provideda structural basis for the model-ratory (17). Subsequently, an a-carbon tracing of the polypeping of the first stage of this process in atomic detail. tide chain of chicken skeletal muscle troponin Cin which the This crystal structure probably represents the moleCaz+ions were replaced by MnZ+was reported at 3-A resolucule in the relaxed state of muscle, with two of the tion (18). The troponin C molecule consists of two domains maximum of 4 Cas+ions bound. The basis for the model connected by a nine-turn helix and no other direct interacpresented here is that upon binding of the additional two Cas+ ions, the regulatory domainof the molecule tions between the domains are evident (Fig. 1).The crystals of turkey troponin C were grown at pH 5 in the presence of undergoesaconformationaltransitiontobecome closely similar in structure to the domain which always an excess ofCa". In this structure, only two Ca2+ions are binds Cas' or Mg2+ underphysiological conditions. Theobserved, bound to the high affinity sites in the C-terminal domain (C-domain). The N-terminal domain (N-domain) is root mean square discrepancy in atomic coordinates between the apo and the modeled Ca2+-bound states of Ca" free. Recently it has been shown that thisis consistent the regulatory domain is 4.8 A, with some shifts as with the behavior of the molecule in solution, where only two Ca" ions per molecule can be bound at pH 5.3 (19). Examilarge as 10-15 A in the region near the linker between the two Ca2+ binding sites. It is demonstrated thatthis nation of the structure revealed the existence of three carCas+-boundconformationoftheregulatorydomain boxyl-carboxylate interactions, one of which is intramolecuconforms to accepted protein structure rules and that lar. These will only be favorable below approximately pH 6 the change in conformation can be accomplished with- (20). We suggested that such interactions play a role in outencounteringanybarrierstoohigh to be sur- trapping the N-domain in the Ca2+ free state,andthat, mounted on the physiological time scale. therefore, the structure represents troponin C in the relaxed state of muscle. Each domain of troponin C has two Ca2+-bindinghelixloop-helix motifs that are connected by a 5-residue linker The regulation of muscle contraction is associated with an peptide. However, the tertiary dispositions of the loops and M and is increase in Ca2+concentration from -lo-' to mediated through the troponin complex of the thinfilament. helices of the N-domain are markedly different from those of Troponin consists of three protein molecules of which tro- the C-domain (17). The conformation of the C-domain closely resembles that of the two Ca2+-bindingunits of parvalbumin poninC is the Ca2+-binding subunit (1). Isolated skeletal muscle troponin C binds four Ca2+ions, two with high affinity (17,21) with Ca" ions bound to each loop (the so-called Ca2+binding EF hands) and with inter-helix angles of 110 (be(K,,,, = 10' M-') and two with lower affinity (K,,,,, lo5 tween helices E and F and between G and H). In contrast, M - ~ ) (2). The high affinity sites are probably not involved in the helices of the N-domain, where there are no bound Ca2+ regulatory conformational changes because they are occupied ions, are closer to being antiparallel with interhelix angles of by a metal ion in both the relaxed and contracted states of 133 and 151 ' (between helices A and B and between C and the muscle. The low affinity sites, which are specific for Ca2+, are in the N-terminal half of the molecule and areresponsible D). In addition, residues 3-13 adopt an a-helical conformation for theregulatory function of the protein. Binding of Ca2+to and this secondary structural feature seems unique to trothese sitesis accompanied by structural changes (3-8) involv- ponin C. As a consequence of these structuraldifferences, the ing a small (8) or negligible (9) change in helical content. It last helix of the regulatory domain (designated helix D), is is the transmission of these changes to theother components surrounded by the other four helices of the domain with the result that two helical turns are completely buried in the * This research was supported by the Medical Research Council of hydrophobic core (17). Canada, an Alberta Heritage Foundation for Medical Research FelWe have suggested that one of the possible conformational lowship (to 0. H.), and an Alberta Heritage Foundation for Medical transitions that may occur when Ca" binds to theregulatory Research Visiting Scientist Fellowship (to J. M.). The costs of pub- domain is a relative shift in the helices and loops SO that it lication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertise- resembles more closely the conformation of the C-domain ment" in accordance with 18 U.S.C. Section 1734 solely to indicate (17). Support for this proposal has recently been provided by the crystal structure of calmodulin, a related protein in which this fact. O

O

2638

Ca2+-induced Conformational Transition

of Troponin C

2639

Crystallographic Refinement-The computer modeling described here is based on the troponin C crystal structure that has been refined at 2.2-A resolution. Intensity data (8056 unique reflections) were collected on an Enraf-Nonius CAD-4 diffractometer. A total of78 cycles of restrained-parameter least squares refinement (23) have been carried out. The startingmodel was the 2.8-A structure derived from the multiple isomorphous replacement phased electron density map (17). The agreement index R’ is 0.186 for the 8.0-2.2 A data

(6435 reflections for which the intensity I > 241)). The current model consists of 159 amino acids, 42 solvent peaks that have been interpreted as water molecules, and the two Ca2’ ions bound to the C-domain. The first 2 residues, the C-terminal residue and the side chain of Glu-67 beyond the Cpatom are too disordered to identify in the electron density map. The stereochemical indicators of the molecular geometry of troponin C are within accepted limits for wellrefined protein structures and are sufficiently good for the modeling study reported here (the root mean squFre deviations from expected stereochemical parameters are: 0.029 A for covalent bond lenghts, 0.053 A for bond angle related distances, 0.01 A for deviations from planarity of planar groups, and 2.1 ’ for deviations from 180 ’ of the w angle of trans-peptide groups). The details of the refinement will be reported elsewhere. Computational Procedures-The computer program MUTATE, written by Randy Read, was used to replace the side chains of the Cdomain with the homologous side chains of the N-domain. This replacement was done by leaving atoms common to the native and mutated residue in their original positions and building any additional atoms required in a standard conformation. Energy minimization was carried out using the GROMOS library? The potential function used is essentially that described by van Gunsteren and Karplus (24). The parameters were set 37D of GROMOS, with an 8-A cut-off. These differ from those of Ref. 24 principally in the omission of an explicit hydrogen bond function and the use of electrically neutral groups for all residues. Thus, hydrogen bonding type interactions within the protein are represented at full strength, and charge-charge and charge-dipole interactions have similar energies to these. Although popular, this treatment of charged groups is a rather gross approximation and in general probably over estimates the energy of surface salt bridges. This is a consequence of the large dielectric constant of the surrounding aqueous solution (see, for instance, Ref. 25). Since there are rather few salt bridges in troponin C compared with the number of internal hydrogen bond type interactions, and they are all on the surface, their contribution to the totalelectrostatic energy is insignificant. Of course, it is clear that charged groups play an important role in determining the precise energy balance in the troponin complex, both in interactions with Ca2+, and in inter- and intramolecular salt bridges. Further, the switching mechanism depends on the relatively small energy balance among these. We do not attempt here to perform the sort of electrostatic calculation needed to determine the exact size of this effect. Indeed, this would not be possible without a very good model of the whole complex and itsinteraction with the thin filament. Rather, we show that the terms, which could be so unfavorable as to invalidate the Ca2+-boundmodel of the N-domain or to block the conformational change between the two states, are satisfactory. These arethe internal electrostatic interactions, packing, and theextent of solvent accessible hydrophobic surface. The program was modified to include an additional energy term guiding the startingstructure towards the desired end structure.This is described in the next section. Analysis of the model building results has been carried out using programs which calculate protein solvent accessibility (26), protein core cavities, and intramolecular contacts. The structures were inspectedon theMMS-X interactive graphics system using the program M3 written by Colin Broughton (27). Construction of the Ca2+-activatedN-domain Model-We assume that upon Ca2+binding each pair of helices of the N-domain flanking the Ca2+-bindingloops change their inter-helix angle to the values found for the EF-hands in the C-domain and that thebinding loops change conformation to resemble closely the conformation of the loops there. It is possible to align the sequences of the two domains in troponin C as shown in Fig. 2. Because of the homology in the sequences of the two halves of troponin C, it seems plausible at the outset to modify the structure of the A-D helices in this manner, however it is not clear from inspection on a graphics system whether the resulting conformation will be energetically acceptable. In order to test this hypothesis, the following computer experiments were performed. 1) The C-domain structure (residues 96-159) was “mutated” such that itsside chains were replaced by the homologous side chains of the N-domain. The resulting structure now forms a new N-domain with a backbone identical to the C-domain. 2) A

R is the standardcrystallographic index defined as Z 11 F, I - IF, (1 / 2 I F, I, where 1 F, I and I F, I are theobserved and calculated structure factors, respectively.

GROMOS is distributed by W. F. van Gunsteren and H. J. C. Berendsen, Laboratory of Physical Chemistry, University of Groningen, Nijenborgh 16,9747 AG Groningen, The Netherlands.

FIG. 1. A ribbon representation of the polypeptide chain of turkey skeletal muscle troponin C, adapted from Ref. 17.The upper domain is the calcium regulatory domain (N-domain); the lower domain is the high-affinity Ca2+/Mg2+binding domain (C-domain). The eight helices involved in thefour supersecondary helix-loop-helix motifs are labeled A-H sequentially. There is an additional helical segment at the beginning of the N-domain sequence. The segments of polypeptide chain forming the Ca2+-bindingloops are labeled I to IV sequentially. Ca2+ions are found in the crystal structure only in sites 111 and IV.

all four Ca2+-bindingsites are occupied by Ca2’ ions and the two domains have very similar conformations (22). Our purpose here is to demonstrate that Ca2+binding to the N-domain can be accompanied by relative shifts of the helices to resemble the conformation of the C-domain, that these shifts do not necessitate passing through a high energy intermediate, and that this can be achieved such that the resulting structure does not contradict the known principles of protein stability. That is to say, the resulting model has to have favorable side chain interactions, hydrophilic residues should be exposed to solvent while hydrophobic ones should be buried, and thereshould not be large cavities in theinterior of the structure. MATERIALS AND METHODS

Ca2+-induced Conformational Transition of Troponin C

2640 N-terminal helix 5 10 ( T S A M ) D Q Q A E A R A F

helix A

25

20

I1

15 L S

I

*

loop I

*

*

35

*

*

helix F 120

loop I l l

*

c

110

*

*

helix B 45

T K E L G T V M R M L

E E M I A E F K A A F D K F D A30 D G G G D I S helix E 100

40

*

*

115

125

I E E L G E I L R A T

N-linker 50 G Q N P T

C-linker 130 G E H V T

75

K E E L D A I I E E V l D E D G S G T I D helix G 135

>\

*

*

*

15C

*

85

F E E F L V M M V R Q H

loop IV

*

helix D 80

*

helix H 155

FDEFLKflflE

G V Q

mutating Val-129 to Pro-53. In addition, all bond lengths and angles were optimized to fit the potential used in the energy minimization. The overall root mean square discrepancy between the mutated model and that after energy minimization was 0.56 A and the total energy drop was from f0.51 X lo5 to -0.41 X lo4 kJ/mol. For comparison, the root mean square discrepancy for the N-domain as seen in the refined crystal structure before and after 1000 steps of energy minimization was 0.45 A and the energy dropped from +0.94 X lo4 to -0.42 X lo4 kJ/mol. At the termination of the energy minimization, the root mean square potential energy gradient for both the modeled domain and the crystal structure was 0.5 kJ mol" A-'. Further minimization wouldbe expected to produce only small additional atomic shifts and so was not considered necessary. Simulation of the Conformational Transition-The conformational change from the N-domain apo-state to themodel of the Ca2+-bound form was induced by continuing the energy minimization of the crystal structure with an additional energy term Eg of the form: Eg = Z a [ xij - x i t [ , where x i are the coordinates of atom '5" for the the target structure current step'y", xit are the coordinates of atom i in "t", "a" is a constant determining the relative contribution of this term to the total energy, and the sum is over all atoms of the Ndomain. A value of a = 6 kJ mol" A" was usedhere. This expression gives a constant contribution to the force driving the structure towards the desired end point. In order to' reduce the influence of the guide force as this is reached, its contribution to the energy was smoothly scaled down with a switching function (33) over the last 1A approach to thetarget for each atom. RESULTS AND DISCUSSION

D/E helix linker

General Description of the Model-Fig. 3 shows an a-carbon representation of the troponin C model obtained following FIG. 2. Sequence alignment of the N- and C-domains in chicken skeletal troponin C (28).The N-terminal helix has no the above procedure, superimposed on the refined crystal 76 A long (including all atoms). analogous helix in theC-domain. The D/E helix linker is not assigned structure. Both structures are to either domain. Asterisk indicate ligands of Ca2+in the C-domain The root mean square difference between all atom coordinates loops and proposed ligands in the N-domain. The homology of the of the energy-minimized N-domain in the apo-state and in two halves of troponin C is more striking from this alignment (29, the Ca2+-activated model is 4.8 A. Fig. 4 shows the relative 30) than from the more familiar alignment by sequential order of the shifts between individual a-carbons for these two states. The Ca2+-binding sites (31, 32). The homology between pairs of helices related in this way (A-E, B-F, C-G, and D-H) is markedly greater largest differences are near to the linker between the two than thatbetween equivalent helices in other motifs, even within the binding sites (helices B and C). For example, the root mean same domain (A-C, B-D, C-G, and D-H). Some significant instances square discrepancy in position of all atoms of residues Metof this are as follows. (a) The analogous residue to Met-28 in helix A 48-Asn-52 is 12.2 A. There are three main differences between is Ile-104 in helix E, whereas in helices C and G we find in the same the two states: (a) the Ca2+-bindingloop conformations, (b) position two hydrophilic residues, Glu-64 and Asp-40. ( b ) The four the inter-helix angles of helices A and B andof helices C and phenylalanine residues (26, 29, 75, and 78) which lie on the first and last helices in the N-domain have an equivalent cluster in the C- D, and (c) the relative disposition between the pairs of helices domain. However, the second and third helices of each domain (B, C BC and AD. Helix D, which in the apo-state is completely and F, G) are occupied in the same positions by other residues, surrounded by four other helices, now interacts only with the although these are also mostly hydrophobic. There are some marked N-helix and with helix A and thus is more exposed to solvent. differences between the two domains aligned in this way, particularly There is now a concave surface between helices AD and BC, in the Ca2+-binding loops, and strikingly among the Ca" ligands. in a manner analogous to that in the C-domain. Also, valines 80 and 83on helix D in the N-domain are equivalent to Environment of Helix D-The exposures of amino acids on 2 hydrophilic residues, Lys-156 and Glu-159, in the C-domain on helix H. There are less dramatic mismatches for 5 more residues: helix D before and afterthe simulated conformational changes Ala-25, Thr-39, Met-48, Leu-49, and Val-65 in the N-domain are are listed in Table I. Note that Glu-77 isa ligand to Ca", and aligned with Cys-101, Ile-115, Ala-124, Thr-125, and Ser-141 respec- that is why the conformational change results in the burial of tively, in the C-domain. In each case, a hydrophobic residue is aligned its side chain. Out of the 6 consecutive hydrophobic residues with a residue of a polar character. Phe-78-Val-83, making up the unusual largely buried two helical turns, only Met-82 becomes significantly more exrotation matrix and a translation vector were calculated to superim- posed. The solvent accessibility of Phe-75 increases also. Such pose the main chain atoms of Glu-76-Met-82 of helix D as built in the new N-domain back on their original position in the crystal an increase in solvent exposure for hydrophobic residues is structure (root mean square discrepancy of the 28 atoms after this energetically unfavorable and thisis presumably compensated operation is 0.2 A). This transformation was then used to provide an by the new favorable interactions between the Ca" ions and initial position of the new N-domain relative to the C-domain. 3) their ligands. Two initial positions were investigated for the N-helix (which has no Residues on the long interdomain helix are involved in two homologue in the C-domain). The first, maintaining its native rela- salt bridges and one Glu-Glu interaction inthe apo-state (17): tionship to helix A, resulted in a loss of contacts to the rest of the Arg-84 with Glu-64 on helix C, Glu-76 with Arg-11 on the Ndomain. The alternative of maintaining its relationship to helix D helix, and Glu-88 with Glu-57 on helix C. In the Ca2+;bound provides a close-packed arrangement, but necessitates breaking the model, the two salt bridges are maintained, but the intramochain between the N-helix and helix A. This latter arrangement was adopted, and thechain rejoined in step 4.4)Seventeen hundred steps lecular carboxyl-carboxylate interaction is no longer possible of conjugate gradient energy minimization were carried out to relieve because of the large shift of the N-terminal part of helix C. Formation of a Hydrophobic Patch-There is a striking close van der Waals contacts, to rejoin the chain between Ile-19 and Ala-20, and to correct the inappropriate geometry obtained when change with respect to hydrophobic exposure in another re90 95 K E D A K G K S E

Ca2’-induced Conformational Transition of Troponin C

FIG. 3. A comparison between the crystal structure and the Ca2+-activated model. Stereo representation of a-carbon positions. The virtual bonds between a-carbon atoms of the crystal structure are represented by bhck, thick lines and those of the modeled N-domain by open bonds. Every fifth amino acid of the crystal structure is labeled. The two Ca2+ ions inthe C-domain are represented by larger dotted spheres.

2641

3g0

4-;

E95

E95

FIG. 4. Distance- between a-carbon coordinates (A) of the troponin C N-domain in the apo-state crystal structureandintheCa2+-bound state model. The largest peak is associated with residues in thevicinity of the linker and the two smaller peaks with residues in the two Ca2+-bindingloops.

residue number gion of the molecule. This concerns the hydrophobic residues Val-45, Met-46, Met-48, and Leu-49, located on the C-terminal part of helix B preceding the linker between the two binding sites (Fig. 2). As can be seen in Table I, in the crystal structure Val-45 and Met-46are completely buried, while Met-48 and Leu-49 are partially exposed to solvent. In our new model all four amino acids become substantially more exposed, thus creating a hydrophobic “patch” on the surface of the protein. Its presence indicates eithera possible contact surface with other members of the muscle system, or that this region should change its helical conformation upon Ca2+

binding in order to avoid such an exposure. Interactions of the inhibitory protein troponin I with troponin C are reported to occur with both domains (34). However, the sites of these interactions on troponin C have not been established. A variety of situations are found in other Ca2+-binding domains: in the C-domain of troponin C the analogous residues are Ile-121, Leu-122, Ala-124, and Thr-125, all exposed to solvent, but only two have hydrophobic side chains. Similarly, in the intestinal calcium-binding protein (ICaBP) (35) the analogous residues are on helix 11: Leu-31, Leu-32, Thr34, and Glu-35. Analysis of the coordinates deposited in the

Ca2+-induced Conformational Transition

2642

Brookhaven data bank (36) shows that in this case the two hydrophilic residues are exposed to solvent, while the two leucines are buried. Leu-32 is covered by the linker which folds in a single helical turn, in contrast to the extended conformation of the linkers in troponin C. Leu-31 appears to be shielded by interaction with helix I which is nearer to helix I1 as aconsequence of the tighter inter-helix'angles in ICaBP (121 "). In parvalbumin the equivalent residues are part of helix D: Phe-66, Leu-67, Asn-69, and Phe-70. Asn-69 is hydrophilic and exposed, but the other three side chains are buried (21). They interact either with the linker region or with the AB domain, which does not exist in troponin C or ICaBP. Thus, there is more than one way in which these two proteins adapt their conformations to accommodate the burial of hydrophobic residues. However, the fact that in the Ndomain of troponinCall4 residues are hydrophobic, in contrast to the sequences of all other Ca2+-bindingproteins (including calmodulin), may be evolutionarily significant and points at a possible attachment surface to other proteins of the muscle system. Effect on Methionine Reactiuity-Another consequence of the opening of the structure is seen in thehydrophobic interTABLE 1 Solvent accessibility for some residues of the N-domain Accessibility

Residue

-Ca'+

6(+Ca2+ / -Ca2+)

+Ca2+

A '

7.7 -4.4

35.0 70.0

Helix D Phe-75 Glu-76 77.2 Glu-77 2.7 Phe-78 Leu-79 Val-80 Met-81 12.3 Met-82 Val-83 Arg-84 66.4 Gln-85 Met-86 Helix B Val-45 35.0 Met-46 Met-48 98.2 Leu-49 Helix A Phe-22 Phe-26 Met-28 Phe-29 9.5

10.3 49.7 36.2 0.1 0.5 0.0 9.5 4.6 0.1 10.5 70.7 50.70.1 8.938.2

41.8 0.0 0.5 11.8

37.9 11.3

31.5 27.5 -33.5 -0.1 2.3 37.8 0.8

50.9 47.1

0.0 72.6 0.1 42.3 96.2 28.2

72.7 138.5

4.1 0.0 128.6 46.2

20.1 16.5 129.9 55.7

FIG. 5. A stereo plot of the watersized empty space in the hydrophobic core of the crystal structure Ndomain. The neighboring amino acids of the crystal structureare shown by solid lines and of the modeled Ca2'-activated state by dotted lines. In this particular view, helix D is seen down its axis in thelower part of figure.

16.0 16.5 1.3

of

Troponin C

actions of helix A. In the apo-state, Phe-29 on this helix interacts with Met-48 (on helix B). According to our model, when Ca2+ binds, thisinteraction no longer exists and is replaced by one with Phe-78 on helix D following the large shift of helix B. As can be seen from Table I, Met-48 becomes more exposed to solvent. This may provide an explanation for the change in reactivity of Met-28 adjacent to Phe-29 upon Ca2+ binding detected by Johnson et al. (37). These workers found that Ca2+binding to theregulatory domain of troponin C increased the amount of diazylaziridine bound to Met-25 (the equivalent methionine in rabbit troponin C). Although Met-28 appears to be exposed to solvent in boththe apo and Ca2+-bound states (Table I), its accessibility to a larger molecule like diazylaziridine .increases as Met-28 becomes more distant from helix B. Packing Consideration+" checkon the validity of the model is provided by examination of the structure for solvent inaccesssible cavities. No cavities large enough to contain a water molecule were found in the modeled structure. In contrast, there is a water molecule-sized hole in the N-domain of the crystal structure, bothfor the refined x-ray structure and for the energy-minimized one. This cavity is completely surrounded by hydrophobic side chains belonging to theN-helix, helix A, and helix D. Fig. 5 shows this feature together with its amino acid environment. Superimposed on it is the environment of our model structure. The key residues surrounding this hydrophobic holeare: Phe-13, Leu-14,Ile-19, Phe-22, Leu-79, Met-82, Val-83, and Met-86. In the Ca2+-activated state, the closure of the space is achieved exclusively by the shift of Phe-22 towards the cavity center. Thisincludes a 1.11.4-A shift of the main chain atoms. It should be emphasized that no "hand" manipulation was performed on the structure, rather the relative main chain positions of helix A and helix D are an intrinsic property of the CaZ+/M$+ domain which is our parent structure in modeling the Ca2+-boundstate of the N-domain. This loose packing of the N-domain may be necessary to enable it toundergo the conformational changes associated with Ca2+binding. Since the N-terminal helix and helices A and D are in close proximity in both the apo-state and the modeled Ca2+-activatedstate, an imperfection of the packing may be unavoidable. Energetics of the Model-As is usual when the technique of Cartesian energy minimization is employed, there are no bad contacts in the model, and thebond lengths and bond angles are close to the ideal values used. However, this should not be taken as a sufficient condition to establish the validity of this conformation (38). With the energy function used, the total energy of the model is about 3% higher than thatof the Ca2+free structure.

Ca2+-induced Conformational Transition of Troponin C

2643

stable a t a pH below approximately 6 and is often observed in crystal structuresunder that condition (20). The Conformational Transition-After 12,800 steps of the guided energy minimization, the root mean square difference for all atoms from the target coordinates was 0.8 A, and for main chain atoms only, 0.2 A. The remaining deviations for 011 I side chain atoms from the target coordinates are a consef ! I quence of a few side chains nothaving passed over the barrier to rotation from one staggered conformation to another. Some of these differences in stagger between the initial and final structures are due to the standard conformation in which residues were built by MUTATE. Three of them are,however, conserved residues in both N- and C-domains that adopt different staggered conformations in thecrystal structure. Ile37 differs from the equivalent Ile-113, Ile-73 from Ile-149,and Met-81 from Met-157. Thus, in making the conformational transition, these residues must rotate. The rotations of Ile-37 t and Met-81 take place, but not thatof Ile-73: the guide force used was large enough to drive the other components of the transition, but not thisside chain rotation. The behavior of the potential energy during this process is shown in Fig. 6. Energy minimization including the guiding term will tend toincrease the size of the normal total potential energy of the molecule as a consequence of strain introduced in moving out of the local minimum near to the crystallographically observed apo-state towards the Ca” complexed state. The extent of this increase provides a measure of the height of the energy barrier which must be surmounted in making the transition by this pathway. A barrier height obtained in thisway gives an upper bound to theactual value, since some other pathway may exist involving the surmounting of a lower barrier. In this instance, essentially no barrier is observed: the potential energy never rises above the energy of the end state during the trajectory. The relatively simple step number energy function used, with reduced electrostatic interactions FIG. 6. Behavior of the potential energy of the regulatory and no solvent contribution, would nevertheless be expected domain of troponin C during the induced conformational transition. a, potential energy excluding the guide term. This is the sum to indicate such a barrier, since van der Waals clashes on the direct pathway followed would bethe dominant factor. Thus, of van der Waals, electrostatic, torsion, bond angle, and bond length terms. b, van der Waals energy term. c, electrostatic energy term. d, it seems that the opening of the inter-helix angles and the guide energy term (see text). The initial dip in a is caused by the fall rearrangement of the Ca2+-bindingloops and thelinker region in the electrostatic energy (c) as thestructure moves out of the local can be accomplished smoothly and easily. minimum reached during the initial energy minimization. There are A significant barrier height wouldbe one involving an substantial rearrangements of the polar interactions duringthe tranincrease in initial energy of the domain substantially larger sition. The rise in energy after this is caused by the increase in van der Waals energy (b),initially because of close contacts caused by the than those normally present in the form of thermal fluctuaguide term forcing the conformational transition to take place, and tions. The specific heat provides a measure of the size of these later because of the more open form of the final structure. fluctuations, and for a domain of this size the root mean square fluctuations in the total internal energy (kinetic plus This is largely a consequence of the more open form of the potential) would be expected to be approximately 54 kJ/mol Ca2+-boundstructure, resulting in fewer van der Waals inter- (39). Molecular dynamics simulations indicate that this sort actions. In reality these interactions wouldbe replaced by of fluctuation may occur on a time scale of 10 to 100 ps (40). interactions with solvent or with groups on other molecules Thus, inthe absence of any barrierof this order, the transition of the troponin complex. There would also be an additional might be expected to proceed very rapidly. There have been compensation from interactions of charged side chains with no direct measurements of the speed of this conformational transition reported, but available data indicate it is rapid (41). the Ca2+ions, not included here. Detailed calculation of the electrostatic interactionsinvolvAcknowledgments-We thank Wilfred van Gunsteren and Herman ing charged groups would require a much more elaborate Berendsen for the provision of the GROMOS package, Randy Read approach than has been in this work. However, as discussed for the use of his program MUTATE, and the Unversity of Alberta earlier, these cannot greatly perturb the total energy of the Computer Centre for the provision of computing facilities. molecule. The salt bridges in the observed crystallographic REFERENCES structure are maintained in the model. Except for Ca2+li1. Greaser, M. L., and Gergely, J. (1973) J. Biol. Chem. 248,2125gands, no charged groups become more isolated from solvent 2133 in the model, an effect which would have a large unfavorable 2. Potter, J. D., and Gergely, J. (1975) J. Biol. Chem. 2 5 0 , 4628energy associated with it. The most significant change in the 4633 electrostatic situation is the loss of the Glu-57-Glu-88 intra3. Potter, J. D., Seidel, J. C., Leavis, P., Lehrer, S. S. and Gergely, molecular interaction. This is an arrangement which is only J. (1976) J. Bid. Chem. 251, 7551-7556

ess

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