J. Mol. Biol. (1976) lOf3, 421437
Folding and Stability of Helical Proteins : Carp Myogen ARTEH WARsHELt
Laboratory
AND MICHAEL
LEVITT
M ~dicul Research C!ouncil of Molecular Biology. Hills Kond, Cambridge. GB2 2&H
(Received 25 February
1976, and in revised form 14 June 1976)
In this work we use our very simple general representation of protein structures to study the mainly helical protein carp myogen. The representation, which treats the amino acid side-chains as simple spheres, is further simplified by rigidly fixing residues in cc-helices. With this model we are able to reproduce the geometry and energetic stability of the native myogen conformation. Studies of the formation of a-helical sub-assemblies showed that the simulated folding of two and four-helix systems worked well, reaching compact native-like conformations with a good rate of success. Greater problems were encountered with the whole molecule (six helices), possibly due to the omission of entropic effects or to simulating the folding too rapidly. Finally, studies of the conformation of a pair of helices when isolated and when part of the whole molecule native conformation showed that long-range interactions have an unexpectedly strong influence on the conformation of the pair of hclicex.
1. Introduction The u-helix, predicted from model-building 25 years ago by Pauling & Corey (Pauling et al.. 1951; Pauling & Corey, 1951), has been found to be increasingly important in the tertiary structures of globular proteins. The first such protein solved by X-ray crystallography, myoglobin (Kendrew et al., 1960), is almost entirely built up from a-helices. Since then the majority of protein structures solved by crystallography contain several u-helices. Recently, large proportions of u-helix have been found in diverse structural proteins, including those in muscle like tropomyosin (Stewart & McLachlan, 1975), those in membranes like purple membrane protein (Henderson & Unwin, 1975), and those in virus coats like fd phage and tobacco mosaic virus (Marvin et al., 1974; Champness et al., 1975; Holmes et al, 1975). Apart from their clear structural role in protein conformations. a-helices have long been considered as nucleation sites in the folding of proteins from open to compact native conformat)ions (Levinthal, 1966; Anfinsen, 1972; Ptitsyn, 1973). This idea is an att’ractive one: cc-helices, which are built from consecutive residues along the sequence. could be stabilized by short-range interactions between near-neighbour residues. They could, therefore, be stable (if only for a short life-time) even when the rest of t’he molecule is still unfolded. Protein folding could then be thought of as the t On leave of absence from Departmrnt Rehovoth, Israel.
of Chemical
421
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assembly of several preformed helices. with t,he remainder of the polypeptide chain folding round and adjusting to the rigid frame-work provided by Dhe nucleus of helices. Some support for t)he belief that sc-helices are stabilized by local interactions comes from t,he reasonably good correlat,ion of the amino acid sequence with the: presence or absence of x-helix in tha,t region of the chain (cf. Schulz et al., 1974). Previous studies of the assembly of K-helices st,arted wit,h Crick’s study of the packing of two long helices into a superhelix or coiled coil (Crick. 1953). In t,hat work the helices seemed to pack best. with the side chains of one helix going into the space between the side chains of the ot)her helix, when the angle bet’ween t,he helix a,xes was about, 10”. This same angle has now been found between t)he short a-helices of the globular proteins in t,he purple membrane of Halohactrr (Henderson $ Cnwin, 1975) and in the coat of tobacco mosaic virus (Champness et al.. 1976: Holmes et al., 1975). Levint,hal and co-workers set up an ambitious project using computer graphics in a combined manual/computer study of helix interact’ions (Levint,ha,l. 1966). but, the computational requirements of their a,pproa,ch was t’oo great for it to be used widely. In the most recent, at,tempb to understand the role of a-helices in protein assembly, Ptit’syn & Rashin (1974) ha,ve used a very simple representation of the x-helix, but, they have tried, more ambitiously. to explain how sub-assemblies of helices lead to t#he native folded conformation of myoglobin. In this study. the helices are taken as rmiform cylinders which intera’ct through hydrophobic and hydrophilic patches on t,heir surfaces. Because Ptitsyn & Rashin (1974) looked for the lowest energy packing of helices (represented by plast’icine rods) by hand. it is dificult to a,ssess the signiticance of their findings: namely that’ the na,tive myoglobin conformat,ion is that which has the most stable association of helices at every step of the assrmhlp pathway. Recently, we introduced a general simplification of protein geometry and energy funct,ions that makes computation of minimum energy conformations fast,er by several orders of magnitude than the convent’ional calculations (Levitt & Warshel, 1975). The principles behind t’hat Ifork \verr (1) to consider thcb avrragr int’eraction between groups of aboms rat’her t,han the deta,iled atom-at,om interactions. and (2) t,o use the most effective variables. namely those that cause the greatest cha,nge of conformation for least change in energy. Although a few effective atoms were used in place of the many real atoms of each residue. all t tic following intera,ctions were included: van der Waals’ interactions between side chains: interactions of the sidechains with the surrounding solvent8 (i.e. wat,er); and the restrict’ion of hackbone conformations due to short-range interactions (a torsional energy t~crm). The methods. which have been described fully (Levitt. 1976). were used to simulate the folding of a small protein pancreactic trypsin inhibitor wit’h some success (Levit’t & Warahel, 1975). Here we extend the approach to a mainly helical protein. The protein chosen for the present study is carp myogen (Nockolds et ad.. 1972: Kretsinger & Nockolds. 1973). It i s smaller t)han myoglobin. the ot~her all x-helical protein whose struct,ure is known to atomic resolution. and has no haem group. The helical regions of the molecule were kept fixed as cc-helices. and we investigated the following three questions. (1) Can we represent the geometry and enegetio sta,bilit) of myogen with our simplified model and rigid heliccs! (2) Can preformed a-helices fold to give a~reasonably correct tertiary structure’! (3) How does the tertiary structure influence the conformation of pairs and larger assemblies of helices. The conclusions of this study can be summarized as follows. ( 1) The native myogen conformat,ion can bc represrmed well with t)he simplified geomctr!.. and conformations
FOLDING close
to that
of two and success, but do have a’n In particular, differs from, of the helix
OF CARP
MYOGEK
4’3
of native myogen are stable even with rigid helices. (2) Simulated foldings four helices give compact native-like conformations with a fair rate of there are greater problems with six helices. (3) Tertiary interactions unexpectedly strong influence on the conformation of a pair of helices. the conformation of a helix pair when it is part of the whole molecule and has a less favourable solvent int,erartion than tJhr stable conformation pair when isolated.
2. Methods (a)
Geometry
and
energy
functions
The same standard side-chain and backbone bond lengths, bond angles, and torsion a.ngles used before are used here. All side chains are treated as rigid and stick out from the flexible backbone. The backbone variable torsion angle c( (between 4 successive a carbons) was set to 45” in the rigid a-helices, and to an initial value of 180” (fully extended) between the helices. In some calculations the non-helical t( angles were randomized about 180” by a perturbation Aa chosen uniformly between -7.5” and 7.5” or between - 12.5” and 12.5”. The torsion angles of the rigid helices were excluded from the minimization and care was taken that there were enough flexible c( angles between the pairs of helices (at least 6 degrees of freedom to allow for the rigid-body motion of a helix). The helices were taken as residues 9 to 17, 26 to 32, 40 to 50, 60 to 69, 79 to 89, and 99 to 106, and are named, A, B, C, D, E, and F, respectively. The same energy parameters that were used before are used here. Hydrogen bonds were not included as the rigid helices could not collapse, and the previous studies of pancreatic trypsin inhibitor showed that hydrogen bonds do not significantly improve the simplified protein energy flmction (without hydrogen bonds the calculations are about twice as fast). Two sets of van der Waals’ energy parameters were used in addition t,o solvent and torsional energy terms: set A, which has smaller van der Weals’ radii (r’J) and weaker attraction (c) between polar side chains to allow for their more extended shape and relatively high flexibility compared to non-polar side chains; and set C, which treats all side chains on the same basis, with y” and 6 values that depend on the number of atoms in the residue. As the side chains of the set C parameters were extended to include the atoms of the peptide group, the non-polar side chains are a little bigger (larger 1.Ovalue) than in the set A parameters. We feel that set A parameters are better suited to t,he study of conformations near the native conformation, whereas set C parameters are bet,ter suited to studies of folding from an open chain conformation. In neither case were interactions calculated between pairs of peptide groups. (b) Minimization
and thermalization,
Again we used the powerfully convergent standard minimization method VAOSA (by H. Fletcher, and taken from the Harwell Subroutine Library) to minimize the energ) with respect to the non-helical OLtorsion angles (up to 52 variables). On reaching a minimum (i.e. root-mean-square gradient less than 10m5 kcal/mol radian), the conformation was perturbed by normal-mode thermalization to give a new starting point for the next pass of minimization. Uniformly distributed random numbers were used to give each normalmode an additional energy of up to nkT/2; where k is Boltzmann’s constant, T is the absolut,e temperature, and n is an integer chosen so that the thermal perturbations are &rong enough to get away from the current, local minimum. With pancreatic trypsin inhibitor n = 3 (giving an effective temperature of 450OK) worked well, but here m had to be increased to 10 for us to be able to routinely escape from local minima. In the present study the normal modes only included combinations of the variable inter-helix torsion angles. The need for a larger r~ value suggests that normal modes including only the torsion angles between helices are stiffer on average than normal modes that include all the torsion angles as variables. This is due to the strong interaction between the helices which hrhave like rigid bodies.
A. R’ARHHEI,
434
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IFIG. 1.
FOLDING
OF
CARP
MYOGEN
42.5
3. Results (a) The mtive
geom,etry
md
dzbility
A set of co-ordinates, known here as the simplified native co-ordinates or just the native co-ordinates, were calculated by averaging the X-ray co-ordinates of the myogen side chains to give a side-chain centroid and also taking the C’J co-ordinates to define the path of the backbone. (The co-ordinates of myogen were kindly provided by Professor Kretsinger through the Protein Data Bank.) This set of native coordinates serves as a reference throughout the present study. Deviations from the native co-ordinates are measured by (l/NI(rij - rpj)2}*. where rij is the separation i.j
of a pair of side-chain centroids or Ca atoms indexed i and j in the calculated conformation, and ryj is the corresponding separation in the native co-ordinates. (This deviation is small by approx. 2/2/3 than the more conventional r.m.s. deviation of optimally oriented molecules, r.m.s. {(ri - $I}.) Four different’ structures are considered in this work : the whole molecule (reiidues 1 to 108), the four-helix fragment CDEF (residues 40 to 108), the pair of helices CD (residues 40 to 74), and the pair of helices EF (residues 78 to 108). Idealized native conformations were generated for each of these structures by minimizing the above r.m.s. deviation with respect to the inter-helix torsion angles to fit a chain with idealized standard geometry to the actual native co-ordinates. This gave r.m.s. deviat,ions of about 1.8 A for fitting either the whole molecule, the four-helix fragment, or the pairs of helices. The corresponding r.m.s. deviation for the whole of pancreatic trypsin inhibitor (58 residues) was less (about’ 1.0 A)> indicating how the increased constraints of the rigid helices make it more difficult to fit the native co-ordinates. These best-fit conformations all have standard idealized geometry and are referred to here as idealized native conformations. The energy surface in the vicinity of the idealized native structures was then investigated in order to find the minimum energy conformation that deviated least from the native myogen co-ordinates. The minimization method used here tends to mimic molecular dynamics in that minimization runs which start with higher potential energies go further before finding a stable conformation. A constraining force was therefore used to hold the molecule close to the native co-ordinates until the most, severe interatomic forces had been relaxed by small changes of conformation (Levitt,, 1976). At this point the constraint was removed and further minimization gave a. near-native minimum energy conformation with idealized geometry that had r.m.s. deviations of 3.50 A for the whole molecule, 3-18 A for the helices CDEF, 3.96 A for the helix pair CD, and 3.05 a for the helix pair EF. The r.m.s. deviation of the whole myogen molecule (3.5 A) is similar to the corresponding result with pancreatic trypsin inhibitor (3.0 -8), even though myogen has FIQ. 1. Showing the conformations of the helix pair CD obtained by energy minimization with set C van der Weals’ parameters, solvent, and torsional energy terms. The first conformation (a) is the idealized native conformation, and the others, (b) to (o), were obtained starting the folding from an open conformation. The ribbon, which traces the path of the CO backbone, was drawn using a program kindly provided by Dr A. D. McLachlan and Mr P. Barber. The contact map to the right of the stereo drawing of the conformation shows which residues are close enough to interact, in that conformation. A cross at the intersection of row i and column j indicates that residue i is within 10 .+%of residue j (i increases from left to right, and j from top to bottom). In these maps, helices feature as a broadening of the diagonal (down from top left to bottom right), antiparallel p-sheet as a band perpendicular to the diagonal, and a parallel b-sheet as a band running parallel to the diagonal.
426
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could b(a obtained with clwi;\tions the set C parameters for the helix pairs and four-helix fragment. The r.m.s. deviation for the whole molecule with set C parameters (5.61 8) was worse, mainly because some of the polar side chains in the helices were too big in radius. confirming om feeling that the set A parameters are better suited to the study of near-native conformations. (b) Folding of pairs of helices from open conformations but
subsequent
studies
showtl
t)hat’ c*ompr;lt)lt~
Figures 1 and 2 and Table 1 show the conformations, energies and r.m.s. deviations obtained from four simulations of the folding of helix pair CD and helix pair EF. In every case the r.m.s. deviation of the minimum energy conformations obtained from the open chain starting conformation is less than 5 8, Folding a pair of helices, which involves only about eight variables, occurs very rapidly (less than 60 cycles) and with no stable intermediate conformations (no thermalization was needed). The angles between the helix axes show a wide range of values from 57” to 110” for CD and from 36” to 83” for EF. As the helices are joined by about ten residues of flexible chains, the angle between them is not a good measure of their overlap or energy of interaction. For example, conformations CD 2 and CD 4 have similar energies (- 7.5 kcal/ml and -7.3 kcal/mol), but very different inter-helix angles of 41” and llO”, respectively. TABLE 1 Folding pairs of helices
Total
He&es C-D Near-native minimum Open starting Open-folding minima (1) (2) (3) (4) H&ices E-F Near-native minimum Open starting Open-folding minima (1)
(2) (3) (4)
Energy van der Waals’
(kcel/mol) Solvent
Torsion
-5.6 718.2 - 7.3 -7.5 -6.2 -7.2
-- 19.6 701.0 ~~21.3 -- 21.3 -21.3 -25.1
0.8 4.9 1.2 1.1 2.5 4.8
13.3 12.3 12.7 12.7 13.6 13.0
-2,2 6.4 -4.9 -4.0 - 5.6 -2.8
-
5.8 6.5 5.4 5.4 4.4 6.6
11.8 14.4 13.0 12.4 13.4 13.2
20.0 14.4 23.4 22.6 23.5
~-.22.6
Helix angle (‘7
Deviation r.m.s.t (4
50
4.08
r:; 46 110
3 02 4.11 5.00 4.11
47
3.00
36 83 37 50
4.84 3.50 4.68 4.37
The initial values of the variable torsion angles between the rigid helices were set to 180” plus a random perturbation distributed uniformly between ~ 12.5” and 12.5”. The random numbers used for this were generated using the standard IBM subroutine RANDU that requires an initial random number called a seed, from which it generates a sequence of random numbers. The following seeds were used to generate different sequences of random numbers for runs (1) to (4), respectively: 11, 111, 1111111, 111111. t Throughout this work the r.m.s. deviation refers to the root-mean-square difference in the side-chain separations in the calculated conformation and in the actual simplified native coordinates.
FOLDING
OF
CARP
MPOGEN
Native
EF I
e-
F
,_. /‘: ‘\2 i
EF 2 2
E
EF3
Cd)
FIG. 2. Showing the conformations of the helix pair EF obtained by energy minimization with set C van der Waalx’ parameters, solvent, and torsional energy terms. The first conformation (a) is the idealized native conformation, and the others, (b) to (c’), were obtained starting the folding from an open conformation.
42s
Native
i !
_. ‘.
d CDEF I
(b )/
CDEF 2
CDEF 3
POLDlh-G
OF
CARP
MYOQES
CDEF
6
CDEF
9
‘5;
r,
!’
FJO. 3. Showing the conformations of the I-helix fragment CDEF obtained by energy minimizawith set C vsn der Wasls’ parameters, solvent, and torsional energy terms. The first conformetion (a) is the idealized native conformation, and the others, (b) to (j), were obtained starting t,hq folding from an open conformation. tion
4x1,
i\.
WARSHEL
AND
M. LEVITT
(c) Folding four he&es from an open conformatio?l. Figure 3 and Table 2 show the conformations, energies, and r.m.s. deviations from the native co-ordinates of the results of nine folding simulations of the C-terminal four helices CDEF. Before discussing the features of the individual conformations we make some general points. All tJhe conformations have reasonably low energies. with the most compacb conformations (smallest radius of gyration) having t,he lowest energies. Several conformations have lower total energies than that of thr near-native minimum (-22.0 kcal/mol). Of the nine runs. five result in conformations whose r.m.s. deviation is less than 7.0 A. root-mean-square, and the lowest r.m.s. deviation is 4.91 A, which is similar to t#hat obtained for the best folding simulation of pancreatic trypsin inhibitor, 5.3 A (Levitt & Warshel. 1975). TABLE 2 Folding
the four-helix
Total
Near-native minimum Open starting Open-folding minima (1)
(2) (3) (4) (4 (6) (7) (8) (9)
~ 22.0 757.6 - 27.6 -- 14.1 - 22.0 - 14.8 - 20.7 - 13.7 - 18.6 - 27.3 - 25.6
fragment
Energy der WaalS
van
-~ 56.0 718.0 -~ 56.6 - 49.2 -~ 69.0 -51.7 --. 56.1 49.6 -- 49.4 -- 59.6 -~ 55.5
CDEF
(kcal/mol) Solvent
Torsion
6.6 12.9 3.5 8.1 10.6 9.74 7.8 11.4 2.7 4.8 2.1
27.0 25.7 25.6 26.4 26.3 27.0 26.5 24.4 28.0 27.5 27.7
Deviation r.m.s. (4 3.31 4.91 10.7 6.19 9.56 8.10 6.92 9.25 6.09 6.93
The following random number seeds were used in t,he thermal&&ion and starting conformation randomization of the 4 helices: 11111,111, 1111, 111111, 1111111, 11, 111, 1111, 1111111. In the first 5 cases there was no randomization of the starting conformation, in the other 4 cases the maximum amplitude of the initial randomization was 7.5”.
The lowest energy conformation of four helices obtained by folding from an open conformation (CDEF 1) also has the least r.m.s. deviation (energy -27.6 kcal/mol, r.m.s. deviation 4.91 8). This conformation has a very similar arrangement of helices to that in the native protein (Fig. 3(a) and (b)), except that helix C is not close to helix D. The conformations of the loops between the helices are also similar, in particular, the doubling back of the loop between helices E and F is reproduced well. The next best folded conformation (CDEF 8) also has a low energy (-27.3 kcal/ mol) but deviates more from the native co-ordinates (6.09 A). In this conformation the helices interlock well and the association between a pair of adjacent helices is no stronger than the association between more distantly connected helices. The contact map shows some symmetry with an imperfect mirror plane running between the bottom left and top right corners of the map. The molecule itself has an approximate inversion centre near its centroid that reflects helix C into F, and D into E. The other folded conformation (CDEF 3) with a small r.m.s. deviation (6.19 A) has a higher energy (-22.0 kcal/mol) and, in particular, a much less favourable solvent
FOl,I)ING
OF CARP
bfYOGEN
13 I
interaction energy (10.6 kcal/mol for conformations CDEF 1 and CDEF 8 discussed above). In this case the conformation looks like an approximate mirror image of the native conformation (ignoring details like the hand of the helices); helices D and F have switched positions relative to the native conformation. The contact map of conformation CDEF 3 is very like that of the native conformation, as the contacts are not affected by reflection of the whole molecule. The fourth conformation that is similar to the native conformation, CDEF 9, has a,n energy of -25.6 kcal/mol and an r.m.s. deviation of 6.93 A. Its solvent energy term is the lowest of the conformations obtained in these folding simulations. The trouble with this conformation is that helix F seems to be trapped behind helix E, preventing it from moving forward to pack bett,er against helix C. These rather minor changes in conformation would reduce the r.m.s. deviation of this conformation substantially and make it much more like the native protein. The fifth conformation (CDEF 6) that is similar to the native conformation (r.m.s. deviation of 6.92 A) has a higher energy than for those discussed above (-13.7 kcal/mol). In it helix D has turned back-to-front and now packs against the flexible chain between helices C and D rather than against helix C itself. It is interestming to discover what went wrong with the other four less successful folding simulations of four helices. In two cases, CDEF 2 and CDEF 4, the chain remains open and the energy, including the solvent contribution, is higher than for the more compact conformations. The strong helix associations in both are between helices C and D and between E and F, with lit,tle interaction between the resulting helix pairs CD and EF; helices C and E are anti-parallel to D and F, respectively. in CDEF 2, and parallel to D and F, respectively, in CDEF 4. In another case, CDEF 5, the energy is lower and, although adjacent pairs of helices pack well, the overall conformat’ion is not sufficiently compact. The one conformation that is compact has a low energy (including solvent in the interaction) of -18.6 kcal/mol. yet deviat,es by 9.25 A r.m.s. from native myogen is CDEF 7. Here the problem is helix E. which should be in contact wibh helices D and F. but now is moved upwards (see Fig. 3(j)) to pack tightly against helix C. The folding simulations with four helices differ in several respects from those with only t’wo helices. In the case of the four-helix simulations. the r.m.s. deviation of the near-native minimum is significantly better than the deviations obtained when In the case of the two-helix simulations, the folding from an open conformat,ion. r.m.s. deviations are the same whether one starts at the native conformation or at the open conformation. The energies of the four-helix conformations correlate well with the r.m.s. deviations from the native conformation. with higher energy conformations generally deviating more. (The lowest’ r.m.s. deviation is 4.91 A.) The energies of the two-helix conformations do not, correlate at a.11well with the r.m.s. devia,tions. (d) Folding
the whole m.oleculu f.siz holicPs)
Figure 4 and Table 3 show some of the conformat’ions, energies and r.m.s. deviations obtained from ten simulated foldings of the whole myogen molecule, consisting of six rigid helices, from an open chain conformation. Out of the ten runs, only three gave conformations that had r.m.s. deviations less than 8.5 A from the native co-ordinates. Although the conformations obtained are compact and of reasonably low energy (i.e. well patoked), the arrangement of helices is much less ordered than usually found
No
3’ .
F
I
F
No
2
No 3
cd’),
Fro. 4. Showing the conformations of the whole myogan molacule obtained by energy minimization with set C van der Waals’ parameters, solvent, and torsional energy terms. The first conformation (a) is the idealized native conformation, and the next three, (b), (c) and (d), were obtained by folding from an open starting conformation. The final conformation (e) was obtained by setting and fixing the conformation of the last 4 helices to the best conformation obtained when isolated, and then allowing helices A and B to fold onto this fixed sub-assembly.
FOLDING
OF CARP TABLE
43.:
MYOGEN
3
Polding the whole myogen molecule
Type
Near-native minimum Open-folding minimum
(1)
(2) (3) (4H
Total
Energy (kcel/mol) van der Solvent Waals’
-81.8 ~ 52.2 - 37.1 -- 53.1 -~ 44.6
-117.8 ~~92.4 - 79.7 - 94.5 - 81.8
9.7
~ 8.1 -5.2 -5.4 -9.7
Torsion
Deviation r.m.s. (4
45.6 47.9 47.8 46.8 47.0
5.61 8.15 9.58 10.44 7.42
The following random number seeds were used in the thermalization and starting conformation randomization of the whole molecule : 11111, 11, 111. 111111. In all cases the maximum amplitude of the initial randomization was 7.5”. 7 For this simulation the conformation of the lest 4 helices was set and fixed to that found for 4 helices in isolation (CDEF, Table 2).
in helical proteins; pairs of helices adjacent in the sequence do not interact strongly and the chain between helices is often stretched out (Fig. 4(c), (d) and (e)). Only conformation no. 1 (Fig. 4(b)) bears any resemblance to the native molecule, though even here helices A and B pack too closely against C, D, and E forcing helix F away from helix E. In conformation no. 4, we tried to overcome the topological problems encountered in the simultaneous packing of six connected helices by setting and fixing the last four helixes (CDEF) to the best folded conformation obtained previously (CDEF 1, Fig. 3(b)). Although the r.m.s. deviation and energies are no better than in the simultaneous foldings of six helices (Table 3), the overall arrangement of the helices is closer to that in the native structure. In fact, conformation no. 4 could become very much more like native myogen if helices A and B could pack closer to the other four helices. This cannot happen here, as the four helices CDEF are held rigid and cannot adjust to the packing of helices A and B onto them. Generally, we feel that simulations of six-helix folding, which are computationally more expensive, have proved rather unhelpful other than to highlight the increased difficulties of folding more rigid helices simultaneously. The causes and possible cures of this problem are considered in Conclusions. (e) Stability
of the native co-ordinates and its fragments
In section (d), above, we found that the best conformation of four helices could not accommodate the additional two helices unless it changed its conformation. Clearly the necessity of fitting into the tertiary structure of the whole molecule places some constraints on the conformations of the constituent helix pairs and other sub-assemblies. Here the strength of these constraints is investigated by looking at the stable conformations of a pair of helices in the whole molecule, in the last four helices, and in isolation. In all the results described so far, the chain had idealized standard geometry that, depended in no way on the known structure of native myogen (apart from the positions of the a-helices along the sequence). In this section this requirement is relaxed and the real native side-chain centroids are used for all residues including
-rFii
:I.
\VA\HSHEI,
t)he energy
of the intemctions
between
segments
d&ant
along
the
chain.
Another way would be to use weaker van der Waals’ energy terms, so that the folding would t,hen happen more slowl,v. If combined with frequent tjhermalization. thf slower folding may tend to favour local folding first. of computing \Vc? thank the Medical Research Council for tlleil generous provision facilities at tile Cambridge University Computer Centrc. One of us (A. W.) was support,c:d by a European Molecular Biology Organisation fellowship during t.lw course of this work. REFERENCES Anfinscn, C. B. (1972). Biochem. ./. 128, 737-749. Champness, J. N., Bloomer, A. C.. Bricogne, G., Butler, I’. ,J. G. & Klug, A. (l!J75). Xatlrrc (I,ondon.), 259, 20-24. Crick, F. H. C. (1953). Acta Crystallogr. 6, 689-697. Henderson, R. & Unwin, P. N. T. (1975). IVatiure (London), 257, 28%32. Holmes, K. C., Stubbs, G. .J., Ma,r&lkow, E. & Qallu-itz, U. (1975). i2;a&re (Lor~lorc). 254, 192.--196. Kendrrw, .I. (!., Dickerson, R. E., Strandhcrg, B. E., Hart, H. G. & Davies, D. R. (1!)60). Xature (Lorulon), 185, 422-425. Kretsinger, R. H. & Nockolds, C. E. (1973). J. Biol. Chem. 248, 3313%3326. Levinthal, C. (1966). Scientijc Amer. 215, no. 6, 42.-52. Levi& M. (1976). 2. MOE. BioE. 104, 59- 708. Levitt, M. & Chothia, C. (1976). A:ature (London), 261, 552-558. Levitt, M. & Warshel, A. (1975). Nature (Lon,don), 253, 694-698. Marvin, D. E., Pigram, W. J., Wiseman, R. C., Wachtel, E. J. & Marvin, b’. J. (1974). J. Mol. Biol. 88, 581-600. Nockolds, C. E., Kretsinger, R. H., Coffee, C. .J. & Bradshaw. 1~. A. (1972). I’roc. ,X’ut. Acud. Sci., i.:.S.A. 69, 581.-584. Pauling, L. 8: Corey, R. B. (1951). Proc. Nat. Acad. Sci.. U.S.A. 37, 235 485. Pauling, L., Corey, R. B. & Branson, H. R. (1951). /‘rot. Mat. Acud. Sci., C.S.A. 37, 205-220. Ptitsyll. 0. .B. (1973). Vest&k .4cad. Nauk I1.S.S.K. 5, 67 68. Ptitsyn, 0. B. & Kaallin, A. A. (1974). Hio$y.u. Chem. 3, I-20. Schulz, (:. H., Barry, C. D., Friedman, J., Chou, P. Y., Fasman, a. D., E’inkelstein, A. V.. Lim, V. I., Ptistsyn, 0. B., Kabat, E. A., Wu, T. T., Levitt., M., Robson, B. & Nagartio, K. (1974). &a&we (London), 250, 140-142. Stewart, M. & McLachlan, A. D. (1975). Nature (London), 257, 331-333.
Folding and Stability of Helical Proteins : Carp Myogen ARTEH WARsHELt
Laboratory
AND MICHAEL
LEVITT
M ~dicul Research C!ouncil of Molecular Biology. Hills Kond, Cambridge. GB2 2&H
(Received 25 February
1976, and in revised form 14 June 1976)
In this work we use our very simple general representation of protein structures to study the mainly helical protein carp myogen. The representation, which treats the amino acid side-chains as simple spheres, is further simplified by rigidly fixing residues in cc-helices. With this model we are able to reproduce the geometry and energetic stability of the native myogen conformation. Studies of the formation of a-helical sub-assemblies showed that the simulated folding of two and four-helix systems worked well, reaching compact native-like conformations with a good rate of success. Greater problems were encountered with the whole molecule (six helices), possibly due to the omission of entropic effects or to simulating the folding too rapidly. Finally, studies of the conformation of a pair of helices when isolated and when part of the whole molecule native conformation showed that long-range interactions have an unexpectedly strong influence on the conformation of the pair of hclicex.
1. Introduction The u-helix, predicted from model-building 25 years ago by Pauling & Corey (Pauling et al.. 1951; Pauling & Corey, 1951), has been found to be increasingly important in the tertiary structures of globular proteins. The first such protein solved by X-ray crystallography, myoglobin (Kendrew et al., 1960), is almost entirely built up from a-helices. Since then the majority of protein structures solved by crystallography contain several u-helices. Recently, large proportions of u-helix have been found in diverse structural proteins, including those in muscle like tropomyosin (Stewart & McLachlan, 1975), those in membranes like purple membrane protein (Henderson & Unwin, 1975), and those in virus coats like fd phage and tobacco mosaic virus (Marvin et al., 1974; Champness et al., 1975; Holmes et al, 1975). Apart from their clear structural role in protein conformations. a-helices have long been considered as nucleation sites in the folding of proteins from open to compact native conformat)ions (Levinthal, 1966; Anfinsen, 1972; Ptitsyn, 1973). This idea is an att’ractive one: cc-helices, which are built from consecutive residues along the sequence. could be stabilized by short-range interactions between near-neighbour residues. They could, therefore, be stable (if only for a short life-time) even when the rest of t’he molecule is still unfolded. Protein folding could then be thought of as the t On leave of absence from Departmrnt Rehovoth, Israel.
of Chemical
421
Physics,
Wvizmann
Tnstitute
of Scirnw.
122
.\.
\VARSHE:I.
AXI)
>I.
I,EVI’l”L‘
assembly of several preformed helices. with t,he remainder of the polypeptide chain folding round and adjusting to the rigid frame-work provided by Dhe nucleus of helices. Some support for t)he belief that sc-helices are stabilized by local interactions comes from t,he reasonably good correlat,ion of the amino acid sequence with the: presence or absence of x-helix in tha,t region of the chain (cf. Schulz et al., 1974). Previous studies of the assembly of K-helices st,arted wit,h Crick’s study of the packing of two long helices into a superhelix or coiled coil (Crick. 1953). In t,hat work the helices seemed to pack best. with the side chains of one helix going into the space between the side chains of the ot)her helix, when the angle bet’ween t,he helix a,xes was about, 10”. This same angle has now been found between t)he short a-helices of the globular proteins in t,he purple membrane of Halohactrr (Henderson $ Cnwin, 1975) and in the coat of tobacco mosaic virus (Champness et al.. 1976: Holmes et al., 1975). Levint,hal and co-workers set up an ambitious project using computer graphics in a combined manual/computer study of helix interact’ions (Levint,ha,l. 1966). but, the computational requirements of their a,pproa,ch was t’oo great for it to be used widely. In the most recent, at,tempb to understand the role of a-helices in protein assembly, Ptit’syn & Rashin (1974) ha,ve used a very simple representation of the x-helix, but, they have tried, more ambitiously. to explain how sub-assemblies of helices lead to t#he native folded conformation of myoglobin. In this study. the helices are taken as rmiform cylinders which intera’ct through hydrophobic and hydrophilic patches on t,heir surfaces. Because Ptitsyn & Rashin (1974) looked for the lowest energy packing of helices (represented by plast’icine rods) by hand. it is dificult to a,ssess the signiticance of their findings: namely that’ the na,tive myoglobin conformat,ion is that which has the most stable association of helices at every step of the assrmhlp pathway. Recently, we introduced a general simplification of protein geometry and energy funct,ions that makes computation of minimum energy conformations fast,er by several orders of magnitude than the convent’ional calculations (Levitt & Warshel, 1975). The principles behind t’hat Ifork \verr (1) to consider thcb avrragr int’eraction between groups of aboms rat’her t,han the deta,iled atom-at,om interactions. and (2) t,o use the most effective variables. namely those that cause the greatest cha,nge of conformation for least change in energy. Although a few effective atoms were used in place of the many real atoms of each residue. all t tic following intera,ctions were included: van der Waals’ interactions between side chains: interactions of the sidechains with the surrounding solvent8 (i.e. wat,er); and the restrict’ion of hackbone conformations due to short-range interactions (a torsional energy t~crm). The methods. which have been described fully (Levitt. 1976). were used to simulate the folding of a small protein pancreactic trypsin inhibitor wit’h some success (Levit’t & Warahel, 1975). Here we extend the approach to a mainly helical protein. The protein chosen for the present study is carp myogen (Nockolds et ad.. 1972: Kretsinger & Nockolds. 1973). It i s smaller t)han myoglobin. the ot~her all x-helical protein whose struct,ure is known to atomic resolution. and has no haem group. The helical regions of the molecule were kept fixed as cc-helices. and we investigated the following three questions. (1) Can we represent the geometry and enegetio sta,bilit) of myogen with our simplified model and rigid heliccs! (2) Can preformed a-helices fold to give a~reasonably correct tertiary structure’! (3) How does the tertiary structure influence the conformation of pairs and larger assemblies of helices. The conclusions of this study can be summarized as follows. ( 1) The native myogen conformat,ion can bc represrmed well with t)he simplified geomctr!.. and conformations
FOLDING close
to that
of two and success, but do have a’n In particular, differs from, of the helix
OF CARP
MYOGEK
4’3
of native myogen are stable even with rigid helices. (2) Simulated foldings four helices give compact native-like conformations with a fair rate of there are greater problems with six helices. (3) Tertiary interactions unexpectedly strong influence on the conformation of a pair of helices. the conformation of a helix pair when it is part of the whole molecule and has a less favourable solvent int,erartion than tJhr stable conformation pair when isolated.
2. Methods (a)
Geometry
and
energy
functions
The same standard side-chain and backbone bond lengths, bond angles, and torsion a.ngles used before are used here. All side chains are treated as rigid and stick out from the flexible backbone. The backbone variable torsion angle c( (between 4 successive a carbons) was set to 45” in the rigid a-helices, and to an initial value of 180” (fully extended) between the helices. In some calculations the non-helical t( angles were randomized about 180” by a perturbation Aa chosen uniformly between -7.5” and 7.5” or between - 12.5” and 12.5”. The torsion angles of the rigid helices were excluded from the minimization and care was taken that there were enough flexible c( angles between the pairs of helices (at least 6 degrees of freedom to allow for the rigid-body motion of a helix). The helices were taken as residues 9 to 17, 26 to 32, 40 to 50, 60 to 69, 79 to 89, and 99 to 106, and are named, A, B, C, D, E, and F, respectively. The same energy parameters that were used before are used here. Hydrogen bonds were not included as the rigid helices could not collapse, and the previous studies of pancreatic trypsin inhibitor showed that hydrogen bonds do not significantly improve the simplified protein energy flmction (without hydrogen bonds the calculations are about twice as fast). Two sets of van der Waals’ energy parameters were used in addition t,o solvent and torsional energy terms: set A, which has smaller van der Weals’ radii (r’J) and weaker attraction (c) between polar side chains to allow for their more extended shape and relatively high flexibility compared to non-polar side chains; and set C, which treats all side chains on the same basis, with y” and 6 values that depend on the number of atoms in the residue. As the side chains of the set C parameters were extended to include the atoms of the peptide group, the non-polar side chains are a little bigger (larger 1.Ovalue) than in the set A parameters. We feel that set A parameters are better suited to t,he study of conformations near the native conformation, whereas set C parameters are bet,ter suited to studies of folding from an open chain conformation. In neither case were interactions calculated between pairs of peptide groups. (b) Minimization
and thermalization,
Again we used the powerfully convergent standard minimization method VAOSA (by H. Fletcher, and taken from the Harwell Subroutine Library) to minimize the energ) with respect to the non-helical OLtorsion angles (up to 52 variables). On reaching a minimum (i.e. root-mean-square gradient less than 10m5 kcal/mol radian), the conformation was perturbed by normal-mode thermalization to give a new starting point for the next pass of minimization. Uniformly distributed random numbers were used to give each normalmode an additional energy of up to nkT/2; where k is Boltzmann’s constant, T is the absolut,e temperature, and n is an integer chosen so that the thermal perturbations are &rong enough to get away from the current, local minimum. With pancreatic trypsin inhibitor n = 3 (giving an effective temperature of 450OK) worked well, but here m had to be increased to 10 for us to be able to routinely escape from local minima. In the present study the normal modes only included combinations of the variable inter-helix torsion angles. The need for a larger r~ value suggests that normal modes including only the torsion angles between helices are stiffer on average than normal modes that include all the torsion angles as variables. This is due to the strong interaction between the helices which hrhave like rigid bodies.
A. R’ARHHEI,
434
ANl)
M. I,E\‘ITl’
C .
/ ‘\ . .,’ ,t; .I, i. , ‘, ‘-:*D
CD I
(b)j
CD 2
(e) L
IFIG. 1.
FOLDING
OF
CARP
MYOGEN
42.5
3. Results (a) The mtive
geom,etry
md
dzbility
A set of co-ordinates, known here as the simplified native co-ordinates or just the native co-ordinates, were calculated by averaging the X-ray co-ordinates of the myogen side chains to give a side-chain centroid and also taking the C’J co-ordinates to define the path of the backbone. (The co-ordinates of myogen were kindly provided by Professor Kretsinger through the Protein Data Bank.) This set of native coordinates serves as a reference throughout the present study. Deviations from the native co-ordinates are measured by (l/NI(rij - rpj)2}*. where rij is the separation i.j
of a pair of side-chain centroids or Ca atoms indexed i and j in the calculated conformation, and ryj is the corresponding separation in the native co-ordinates. (This deviation is small by approx. 2/2/3 than the more conventional r.m.s. deviation of optimally oriented molecules, r.m.s. {(ri - $I}.) Four different’ structures are considered in this work : the whole molecule (reiidues 1 to 108), the four-helix fragment CDEF (residues 40 to 108), the pair of helices CD (residues 40 to 74), and the pair of helices EF (residues 78 to 108). Idealized native conformations were generated for each of these structures by minimizing the above r.m.s. deviation with respect to the inter-helix torsion angles to fit a chain with idealized standard geometry to the actual native co-ordinates. This gave r.m.s. deviat,ions of about 1.8 A for fitting either the whole molecule, the four-helix fragment, or the pairs of helices. The corresponding r.m.s. deviation for the whole of pancreatic trypsin inhibitor (58 residues) was less (about’ 1.0 A)> indicating how the increased constraints of the rigid helices make it more difficult to fit the native co-ordinates. These best-fit conformations all have standard idealized geometry and are referred to here as idealized native conformations. The energy surface in the vicinity of the idealized native structures was then investigated in order to find the minimum energy conformation that deviated least from the native myogen co-ordinates. The minimization method used here tends to mimic molecular dynamics in that minimization runs which start with higher potential energies go further before finding a stable conformation. A constraining force was therefore used to hold the molecule close to the native co-ordinates until the most, severe interatomic forces had been relaxed by small changes of conformation (Levitt,, 1976). At this point the constraint was removed and further minimization gave a. near-native minimum energy conformation with idealized geometry that had r.m.s. deviations of 3.50 A for the whole molecule, 3-18 A for the helices CDEF, 3.96 A for the helix pair CD, and 3.05 a for the helix pair EF. The r.m.s. deviation of the whole myogen molecule (3.5 A) is similar to the corresponding result with pancreatic trypsin inhibitor (3.0 -8), even though myogen has FIQ. 1. Showing the conformations of the helix pair CD obtained by energy minimization with set C van der Weals’ parameters, solvent, and torsional energy terms. The first conformation (a) is the idealized native conformation, and the others, (b) to (o), were obtained starting the folding from an open conformation. The ribbon, which traces the path of the CO backbone, was drawn using a program kindly provided by Dr A. D. McLachlan and Mr P. Barber. The contact map to the right of the stereo drawing of the conformation shows which residues are close enough to interact, in that conformation. A cross at the intersection of row i and column j indicates that residue i is within 10 .+%of residue j (i increases from left to right, and j from top to bottom). In these maps, helices feature as a broadening of the diagonal (down from top left to bottom right), antiparallel p-sheet as a band perpendicular to the diagonal, and a parallel b-sheet as a band running parallel to the diagonal.
426
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IOX N&luw
i111(1
may a~ct~ua~lly hdp wt
.A van drr Wilds
\\‘;\RSHEI,
trypsiu
tIlta
slightly
AKII)
iuhitdcw
only
u.hm swrching
para~rnetcw
ww
lwrtl
31. 1,EVI’l”I 68 rc~sitiuw:
of t,htk hrlicw
t htt rigidity
fol
a st’w hlr nrxr-uatiw for tlw initial calculation
minimum. ‘I’hc of t81itw minima.
could b(a obtained with clwi;\tions the set C parameters for the helix pairs and four-helix fragment. The r.m.s. deviation for the whole molecule with set C parameters (5.61 8) was worse, mainly because some of the polar side chains in the helices were too big in radius. confirming om feeling that the set A parameters are better suited to the study of near-native conformations. (b) Folding of pairs of helices from open conformations but
subsequent
studies
showtl
t)hat’ c*ompr;lt)lt~
Figures 1 and 2 and Table 1 show the conformations, energies and r.m.s. deviations obtained from four simulations of the folding of helix pair CD and helix pair EF. In every case the r.m.s. deviation of the minimum energy conformations obtained from the open chain starting conformation is less than 5 8, Folding a pair of helices, which involves only about eight variables, occurs very rapidly (less than 60 cycles) and with no stable intermediate conformations (no thermalization was needed). The angles between the helix axes show a wide range of values from 57” to 110” for CD and from 36” to 83” for EF. As the helices are joined by about ten residues of flexible chains, the angle between them is not a good measure of their overlap or energy of interaction. For example, conformations CD 2 and CD 4 have similar energies (- 7.5 kcal/ml and -7.3 kcal/mol), but very different inter-helix angles of 41” and llO”, respectively. TABLE 1 Folding pairs of helices
Total
He&es C-D Near-native minimum Open starting Open-folding minima (1) (2) (3) (4) H&ices E-F Near-native minimum Open starting Open-folding minima (1)
(2) (3) (4)
Energy van der Waals’
(kcel/mol) Solvent
Torsion
-5.6 718.2 - 7.3 -7.5 -6.2 -7.2
-- 19.6 701.0 ~~21.3 -- 21.3 -21.3 -25.1
0.8 4.9 1.2 1.1 2.5 4.8
13.3 12.3 12.7 12.7 13.6 13.0
-2,2 6.4 -4.9 -4.0 - 5.6 -2.8
-
5.8 6.5 5.4 5.4 4.4 6.6
11.8 14.4 13.0 12.4 13.4 13.2
20.0 14.4 23.4 22.6 23.5
~-.22.6
Helix angle (‘7
Deviation r.m.s.t (4
50
4.08
r:; 46 110
3 02 4.11 5.00 4.11
47
3.00
36 83 37 50
4.84 3.50 4.68 4.37
The initial values of the variable torsion angles between the rigid helices were set to 180” plus a random perturbation distributed uniformly between ~ 12.5” and 12.5”. The random numbers used for this were generated using the standard IBM subroutine RANDU that requires an initial random number called a seed, from which it generates a sequence of random numbers. The following seeds were used to generate different sequences of random numbers for runs (1) to (4), respectively: 11, 111, 1111111, 111111. t Throughout this work the r.m.s. deviation refers to the root-mean-square difference in the side-chain separations in the calculated conformation and in the actual simplified native coordinates.
FOLDING
OF
CARP
MPOGEN
Native
EF I
e-
F
,_. /‘: ‘\2 i
EF 2 2
E
EF3
Cd)
FIG. 2. Showing the conformations of the helix pair EF obtained by energy minimization with set C van der Waalx’ parameters, solvent, and torsional energy terms. The first conformation (a) is the idealized native conformation, and the others, (b) to (c’), were obtained starting the folding from an open conformation.
42s
Native
i !
_. ‘.
d CDEF I
(b )/
CDEF 2
CDEF 3
POLDlh-G
OF
CARP
MYOQES
CDEF
6
CDEF
9
‘5;
r,
!’
FJO. 3. Showing the conformations of the I-helix fragment CDEF obtained by energy minimizawith set C vsn der Wasls’ parameters, solvent, and torsional energy terms. The first conformetion (a) is the idealized native conformation, and the others, (b) to (j), were obtained starting t,hq folding from an open conformation. tion
4x1,
i\.
WARSHEL
AND
M. LEVITT
(c) Folding four he&es from an open conformatio?l. Figure 3 and Table 2 show the conformations, energies, and r.m.s. deviations from the native co-ordinates of the results of nine folding simulations of the C-terminal four helices CDEF. Before discussing the features of the individual conformations we make some general points. All tJhe conformations have reasonably low energies. with the most compacb conformations (smallest radius of gyration) having t,he lowest energies. Several conformations have lower total energies than that of thr near-native minimum (-22.0 kcal/mol). Of the nine runs. five result in conformations whose r.m.s. deviation is less than 7.0 A. root-mean-square, and the lowest r.m.s. deviation is 4.91 A, which is similar to t#hat obtained for the best folding simulation of pancreatic trypsin inhibitor, 5.3 A (Levitt & Warshel. 1975). TABLE 2 Folding
the four-helix
Total
Near-native minimum Open starting Open-folding minima (1)
(2) (3) (4) (4 (6) (7) (8) (9)
~ 22.0 757.6 - 27.6 -- 14.1 - 22.0 - 14.8 - 20.7 - 13.7 - 18.6 - 27.3 - 25.6
fragment
Energy der WaalS
van
-~ 56.0 718.0 -~ 56.6 - 49.2 -~ 69.0 -51.7 --. 56.1 49.6 -- 49.4 -- 59.6 -~ 55.5
CDEF
(kcal/mol) Solvent
Torsion
6.6 12.9 3.5 8.1 10.6 9.74 7.8 11.4 2.7 4.8 2.1
27.0 25.7 25.6 26.4 26.3 27.0 26.5 24.4 28.0 27.5 27.7
Deviation r.m.s. (4 3.31 4.91 10.7 6.19 9.56 8.10 6.92 9.25 6.09 6.93
The following random number seeds were used in t,he thermal&&ion and starting conformation randomization of the 4 helices: 11111,111, 1111, 111111, 1111111, 11, 111, 1111, 1111111. In the first 5 cases there was no randomization of the starting conformation, in the other 4 cases the maximum amplitude of the initial randomization was 7.5”.
The lowest energy conformation of four helices obtained by folding from an open conformation (CDEF 1) also has the least r.m.s. deviation (energy -27.6 kcal/mol, r.m.s. deviation 4.91 8). This conformation has a very similar arrangement of helices to that in the native protein (Fig. 3(a) and (b)), except that helix C is not close to helix D. The conformations of the loops between the helices are also similar, in particular, the doubling back of the loop between helices E and F is reproduced well. The next best folded conformation (CDEF 8) also has a low energy (-27.3 kcal/ mol) but deviates more from the native co-ordinates (6.09 A). In this conformation the helices interlock well and the association between a pair of adjacent helices is no stronger than the association between more distantly connected helices. The contact map shows some symmetry with an imperfect mirror plane running between the bottom left and top right corners of the map. The molecule itself has an approximate inversion centre near its centroid that reflects helix C into F, and D into E. The other folded conformation (CDEF 3) with a small r.m.s. deviation (6.19 A) has a higher energy (-22.0 kcal/mol) and, in particular, a much less favourable solvent
FOl,I)ING
OF CARP
bfYOGEN
13 I
interaction energy (10.6 kcal/mol for conformations CDEF 1 and CDEF 8 discussed above). In this case the conformation looks like an approximate mirror image of the native conformation (ignoring details like the hand of the helices); helices D and F have switched positions relative to the native conformation. The contact map of conformation CDEF 3 is very like that of the native conformation, as the contacts are not affected by reflection of the whole molecule. The fourth conformation that is similar to the native conformation, CDEF 9, has a,n energy of -25.6 kcal/mol and an r.m.s. deviation of 6.93 A. Its solvent energy term is the lowest of the conformations obtained in these folding simulations. The trouble with this conformation is that helix F seems to be trapped behind helix E, preventing it from moving forward to pack bett,er against helix C. These rather minor changes in conformation would reduce the r.m.s. deviation of this conformation substantially and make it much more like the native protein. The fifth conformation (CDEF 6) that is similar to the native conformation (r.m.s. deviation of 6.92 A) has a higher energy than for those discussed above (-13.7 kcal/mol). In it helix D has turned back-to-front and now packs against the flexible chain between helices C and D rather than against helix C itself. It is interestming to discover what went wrong with the other four less successful folding simulations of four helices. In two cases, CDEF 2 and CDEF 4, the chain remains open and the energy, including the solvent contribution, is higher than for the more compact conformations. The strong helix associations in both are between helices C and D and between E and F, with lit,tle interaction between the resulting helix pairs CD and EF; helices C and E are anti-parallel to D and F, respectively. in CDEF 2, and parallel to D and F, respectively, in CDEF 4. In another case, CDEF 5, the energy is lower and, although adjacent pairs of helices pack well, the overall conformat’ion is not sufficiently compact. The one conformation that is compact has a low energy (including solvent in the interaction) of -18.6 kcal/mol. yet deviat,es by 9.25 A r.m.s. from native myogen is CDEF 7. Here the problem is helix E. which should be in contact wibh helices D and F. but now is moved upwards (see Fig. 3(j)) to pack tightly against helix C. The folding simulations with four helices differ in several respects from those with only t’wo helices. In the case of the four-helix simulations. the r.m.s. deviation of the near-native minimum is significantly better than the deviations obtained when In the case of the two-helix simulations, the folding from an open conformat,ion. r.m.s. deviations are the same whether one starts at the native conformation or at the open conformation. The energies of the four-helix conformations correlate well with the r.m.s. deviations from the native conformation. with higher energy conformations generally deviating more. (The lowest’ r.m.s. deviation is 4.91 A.) The energies of the two-helix conformations do not, correlate at a.11well with the r.m.s. devia,tions. (d) Folding
the whole m.oleculu f.siz holicPs)
Figure 4 and Table 3 show some of the conformat’ions, energies and r.m.s. deviations obtained from ten simulated foldings of the whole myogen molecule, consisting of six rigid helices, from an open chain conformation. Out of the ten runs, only three gave conformations that had r.m.s. deviations less than 8.5 A from the native co-ordinates. Although the conformations obtained are compact and of reasonably low energy (i.e. well patoked), the arrangement of helices is much less ordered than usually found
No
3’ .
F
I
F
No
2
No 3
cd’),
Fro. 4. Showing the conformations of the whole myogan molacule obtained by energy minimization with set C van der Waals’ parameters, solvent, and torsional energy terms. The first conformation (a) is the idealized native conformation, and the next three, (b), (c) and (d), were obtained by folding from an open starting conformation. The final conformation (e) was obtained by setting and fixing the conformation of the last 4 helices to the best conformation obtained when isolated, and then allowing helices A and B to fold onto this fixed sub-assembly.
FOLDING
OF CARP TABLE
43.:
MYOGEN
3
Polding the whole myogen molecule
Type
Near-native minimum Open-folding minimum
(1)
(2) (3) (4H
Total
Energy (kcel/mol) van der Solvent Waals’
-81.8 ~ 52.2 - 37.1 -- 53.1 -~ 44.6
-117.8 ~~92.4 - 79.7 - 94.5 - 81.8
9.7
~ 8.1 -5.2 -5.4 -9.7
Torsion
Deviation r.m.s. (4
45.6 47.9 47.8 46.8 47.0
5.61 8.15 9.58 10.44 7.42
The following random number seeds were used in the thermalization and starting conformation randomization of the whole molecule : 11111, 11, 111. 111111. In all cases the maximum amplitude of the initial randomization was 7.5”. 7 For this simulation the conformation of the lest 4 helices was set and fixed to that found for 4 helices in isolation (CDEF, Table 2).
in helical proteins; pairs of helices adjacent in the sequence do not interact strongly and the chain between helices is often stretched out (Fig. 4(c), (d) and (e)). Only conformation no. 1 (Fig. 4(b)) bears any resemblance to the native molecule, though even here helices A and B pack too closely against C, D, and E forcing helix F away from helix E. In conformation no. 4, we tried to overcome the topological problems encountered in the simultaneous packing of six connected helices by setting and fixing the last four helixes (CDEF) to the best folded conformation obtained previously (CDEF 1, Fig. 3(b)). Although the r.m.s. deviation and energies are no better than in the simultaneous foldings of six helices (Table 3), the overall arrangement of the helices is closer to that in the native structure. In fact, conformation no. 4 could become very much more like native myogen if helices A and B could pack closer to the other four helices. This cannot happen here, as the four helices CDEF are held rigid and cannot adjust to the packing of helices A and B onto them. Generally, we feel that simulations of six-helix folding, which are computationally more expensive, have proved rather unhelpful other than to highlight the increased difficulties of folding more rigid helices simultaneously. The causes and possible cures of this problem are considered in Conclusions. (e) Stability
of the native co-ordinates and its fragments
In section (d), above, we found that the best conformation of four helices could not accommodate the additional two helices unless it changed its conformation. Clearly the necessity of fitting into the tertiary structure of the whole molecule places some constraints on the conformations of the constituent helix pairs and other sub-assemblies. Here the strength of these constraints is investigated by looking at the stable conformations of a pair of helices in the whole molecule, in the last four helices, and in isolation. In all the results described so far, the chain had idealized standard geometry that, depended in no way on the known structure of native myogen (apart from the positions of the a-helices along the sequence). In this section this requirement is relaxed and the real native side-chain centroids are used for all residues including
-rFii
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Another way would be to use weaker van der Waals’ energy terms, so that the folding would t,hen happen more slowl,v. If combined with frequent tjhermalization. thf slower folding may tend to favour local folding first. of computing \Vc? thank the Medical Research Council for tlleil generous provision facilities at tile Cambridge University Computer Centrc. One of us (A. W.) was support,c:d by a European Molecular Biology Organisation fellowship during t.lw course of this work. REFERENCES Anfinscn, C. B. (1972). Biochem. ./. 128, 737-749. Champness, J. N., Bloomer, A. C.. Bricogne, G., Butler, I’. ,J. G. & Klug, A. (l!J75). Xatlrrc (I,ondon.), 259, 20-24. Crick, F. H. C. (1953). Acta Crystallogr. 6, 689-697. Henderson, R. & Unwin, P. N. T. (1975). IVatiure (London), 257, 28%32. Holmes, K. C., Stubbs, G. .J., Ma,r&lkow, E. & Qallu-itz, U. (1975). i2;a&re (Lor~lorc). 254, 192.--196. Kendrrw, .I. (!., Dickerson, R. E., Strandhcrg, B. E., Hart, H. G. & Davies, D. R. (1!)60). Xature (Lorulon), 185, 422-425. Kretsinger, R. H. & Nockolds, C. E. (1973). J. Biol. Chem. 248, 3313%3326. Levinthal, C. (1966). Scientijc Amer. 215, no. 6, 42.-52. Levi& M. (1976). 2. MOE. BioE. 104, 59- 708. Levitt, M. & Chothia, C. (1976). A:ature (London), 261, 552-558. Levitt, M. & Warshel, A. (1975). Nature (Lon,don), 253, 694-698. Marvin, D. E., Pigram, W. J., Wiseman, R. C., Wachtel, E. J. & Marvin, b’. J. (1974). J. Mol. Biol. 88, 581-600. Nockolds, C. E., Kretsinger, R. H., Coffee, C. .J. & Bradshaw. 1~. A. (1972). I’roc. ,X’ut. Acud. Sci., i.:.S.A. 69, 581.-584. Pauling, L. 8: Corey, R. B. (1951). Proc. Nat. Acad. Sci.. U.S.A. 37, 235 485. Pauling, L., Corey, R. B. & Branson, H. R. (1951). /‘rot. Mat. Acud. Sci., C.S.A. 37, 205-220. Ptitsyll. 0. .B. (1973). Vest&k .4cad. Nauk I1.S.S.K. 5, 67 68. Ptitsyn, 0. B. & Kaallin, A. A. (1974). Hio$y.u. Chem. 3, I-20. Schulz, (:. H., Barry, C. D., Friedman, J., Chou, P. Y., Fasman, a. D., E’inkelstein, A. V.. Lim, V. I., Ptistsyn, 0. B., Kabat, E. A., Wu, T. T., Levitt., M., Robson, B. & Nagartio, K. (1974). &a&we (London), 250, 140-142. Stewart, M. & McLachlan, A. D. (1975). Nature (London), 257, 331-333.
