Proc. NatI. Acad. Sci. USA
Vol. 86, pp. 6592-6596, September 1989
Topological distribution of four-a-helix bundles
(folding motif/solvent accessibility/helix dipole)
SCOTT R. PRESNELL* AND FRED E. COHEN*t
Departments of *Pharmaceutical Chemistry and tMedicine, University of California, San Francisco, San Francisco, CA 94143-0446
Communicated by Frederic M. Richards, June 19, 1989
ABSTRACT The four-a-helix bundle, a common struc- suggest a set of bundle structures beyond those initially
tural motif in globular proteins, provides an excellent forum for reviewed by Weber and Salemme (8). Further, we will
the examination of predictive constraints for protein backbone describe robust topological characterizations and categori-
topology. An exhaustive examination of the Brookhaven Crys- zations of the discovered structures. In light of our catego-
tallographic Protein Data Bank and other literature sources has rization scheme, the past and current topological constraints
lead to the discovery of 20 putative four-a-helix bundles. used for the prediction of protein structures containing four-
Application of an analytical method that examines the differ- a-helix bundles are reevaluated.
ence between solvent-accessible surface areas in packed and
partially unpacked bundles reduced the number of structures METHODS
to 16. Angular requirements further reduced the list of bundles
to 13. In 12 of these bundles, all pairs of neighboring helices To locate putative four-a-helix bundles, two independent
were oriented in an anti-parallel fashion. This distribution is in observers employed the graphical display program MIDAS
accordance with structure types expected if the helix macro (11) to inspect more than 300 globular protein structures from
dipole effect makes a substantial contribution to the stability of the Brookhaven Protein Data Bank (12) (November 14, 1988).
the native structure. The characterizations and classifications Particularly flexible inspection criterion suggested 14 poten-
made in this study prompt a reevaluation of constraints used in tial four-a-helix bundles from 12 proteins. To discriminate
structure prediction efforts. compact bundles from within the list of putative structures,
a quantitative determination of helix-to-helix packing was
Specification of the code that translates primary to tertiary developed. This method is based on the algorithm of Lee and
structure remains unresolved. It has proven difficult to Richards (13) for surface area determination. For each pu-
predict which features in an amino acid sequence will provide tative four-a-helix bundle, the solvent-accessible surface
the basis for the three-dimensional structure or function of a area was determined for the entire helix bundle and for each
given protein. However, proteins with only 10% identity at of the four possible sets of one helix separated from the other
comparable positions in a polypeptide can have notably three. Comparing the sum of the surface areas of the one- and
similar structures (1). Indeed, an individual tertiary structure three-helical substructures to the original bundle structure
will often fall into one of a limited number of structural produced a quantitative value for the amount of surface area
classes (2). Tertiary-structure prediction systems incorporat- lost on burying each helix in the bundle. The typical surface
ing combinatorial methods (3-5) and template methods (6, 7) area of a four-a-helix bundle is approximately 2000 A2. If one
target known structural classes in an attempt to reduce the assumes an energetic conversion value of 24 cal mold A-2
number of structures created and examined. Therefore, to (14), then a loss of 200 A2 in surface area upon burying the last
effectively predict tertiary structures, we must determine as helix into a bundle provides a hydrophobic stabilization of 4.8
many constraints describing the individual structural classes kcal mol' (1 cal = 4.184J). Accordingly, if the surface area
as possible. lost on burying any individual helix was less than 10% of the
Among the structural class containing those proteins con- entire bundle's solvent-accessible surface area, then that
structed predominantly from a-helical structures, a highly group of four helices was not considered a four-a-helix
recurrent- motif is the collection of (anti)parallel a-helices bundle. Loop regions between the helices were not included
known as the four-a-helix bundle. Four-a-helix bundles are in the surface area calculations.
found in proteins covering a wide range of structure and Interhelical angles were determined for each pair of helices
function, but they display some common characteristics. along the perimeter of the bundle. Helix vectors were deter-
Weber and Salemme (8) were among the first to examine and mined using the adaptive helix parameter method (15) to
characterize four-a-helix bundles as a class of super- minimize the propagation axis variability. Ideal helices were
secondary structure. Initially, their work suggested a com- generated in a known manner from three primary helical
mon, right-handed, connective topology for all four-a-helix parameters: radius, pitch, and number of residues per turn.
bundles. This characterization, derived from a limited data By using the Kabsch method (16) for calculating the rms fit
base of bundle topologies, proved too restrictive to be between the ideal and observed helical coordinates, the
correct. The "handedness" constraint obscured further at- matrix required to transform the actual coordinates to lie
tempts to characterize the topology of previously known and along the x axis is produced. The three helical parameters can
newly discovered structures (9, 10). Incorporation of all the be extracted from this matrix and adjusted in an iterative
presently known four-a-helix bundle structures requires a fashion until an ideal helix fits the observed helix as nearly as
different categorization scheme. possible. The interhelical angle (fl) was defined as the
The purpose of this study is to describe and present a arc-cosine of the dot product of the two helix vectors. The
thorough examination of the literature for four-a-helix bun- cross product of the helix vectors was used to determine the
dles using generalized determination criteria. These criteria sign of the interhelical angle. Because we were interested in
perpetuating the classical definition of a four-a-helix bundle,
The publication costs of this article were defrayed in part by page charge we chose to eliminate from further consideration those bun-
payment. This article must therefore be hereby marked "advertisement" dles containing an absolute value of acute interhelical angles
in accordance with 18 U.S.C. §1734 solely to indicate this fact. greater than 400. A review of the recent literature and a
Biochemistry: Presnell and Cohen Proc. Natl. Acad. Sci. USA 86 (1989) 6593
Table 1. Definition of the putative four-a-helix bundles investigated
Protein PDB code Ref. Helix A Helix B Helix C Helix D
Cytochrome b5 2b5c 18 32-39 43-49 54-61 64-75
Cytochrome b-562 156b 19 2-19 24-45 62-85 88-108
Catalase 8cat 20 177-188 451-467 470-483 485-500
Cytochrome c' 2ccy 21 5-30 40-58 79-102 104-125
Cytochrome P-450cam 2cpp 22 127-145 149-169 234-267 359-378
Citrate synthase (a) 4cts 23 136-152 163-195 274-291 390-416
Citrate synthase (b) 4cts 23 221-236 237-341 344-365 373-386
Cytochrome c peroxidase 2cyp 24 42-54 103-119 165-177 255-272
Methemerythrin lhmq 25 19-37 41-64 70-85 91-109
T4 lysozyme 2lzm 26 92-106 116-124 125-138 144-156
p-Hydroxybenzoate hydroxylase lphh 27 12-24 53-57 102-114 299-318
Phospholipase C (a) * 28 12-28 33-55 105-125 206-242
Phospholipase C (b) * 28 85-104 105-125 171-187 206-242
Thermolysin 3tln 29 230-246 260-274 280-2% 300-312
Individual helices were defined according to the HELIX records of the data bank files. PDB, Protein Data Base. The
following proteins contained four-a-helix bundles that were evaluated but could not be analyzed by the numerical method
because of a lack of crystal coordinates: ferritin (30), interleukin 2 (31), human complement component C3a (although the
crystal structure reveals disorder in the N terminus, homology modeling with complement component C5a strongly suggests
a helical N-terminal region (32, 33), human complement CSa (33, 34), tobacco mosaic virus coat protein (35), and human
growth hormone (9).
*Phospholipase C coordinates were obtained directly from E. Hough (University of Tr0mso).
personal communication produced reports of six other four- group of related structures with absolute acute interhelical
a-helix bundles; these were also examined for handedness angles greater than 400 that will form the subject of future
and backbone topologies. study. The angular requirements further reduced the list of
The AMBER program suite (17) was used to determine bundles to the final 13.
internal energies of native protein structures. Crystal struc- Helix-Bundle Categorization. Fig. 1 exemplifies the set of
ture coordinates were taken directly from the Brookhaven topological descriptors for helix bundles developed in the
Protein Data Bank (12) (release dated, November 14, 1988). current study: (i) the polypeptide chain connectivity, (ii) the
unit direction vectors of the individual helices, and (iii) the
RESULTS AND DISCUSSION overall bundle handedness or macroscopic chirality. Two
general types of connectivities exist between helical seg-
Structural Evaluation of Putative Helix Bundles. Table 1 ments. The first type is a plain or adjacent connection, where
specifies the structures evaluated in this study. Table 2 the C terminus of one helix is adjacent in space to the N
presents a summary of the evaluation of surface area loss terminus of the next helix, but the direction vector changes
upon burying the last helix of a four-a-helix bundle. Although orientation by 1800 within the connecting loop of polypeptide
all of the previously recognized helix bundles pack well backbone. The second category is referred to as an "over-
according to this criterion, a number of the more recently hand" connection. Here, the chain must pass back over the
described structures inferred by visual observation to be length of the first helix to enter the second helix with
helix bundles did not appear to be well packed. Application approximately the same directional vector as the entry to the
of the analytical method reduced the number of structures first helix. As a corollary to this aspect of the helix-bundle
from the 20 putative four-a-helix bundles to 16. Table 3 definition, we only consider helix bundles in which all
presents a summary of the interhelical angle determinations. constituent helices are found on the same polypeptide. Spe-
Notable was the range of acute interhelical angles: from -40° cifically, this excludes structures like uteroglobin (36) and
to +370 (mean = 5.0°, SD = 24.30). Previous efforts had
suggested that the interhelical angles were tightly clustered Table 3. Interhelical angles in 14 putative four-a-helix bundles
around + 18° (8). The data further suggest the possibility of a f1
Protein 02 Q3 Q4
Table 2. Percentage of surface area lost upon burying last helix Cytochrome b5 147.0 151.9 151.4 148.3
in 14 putative four-a-helix bundles Cytochrome b-562 -164.1 -164.9 -172.7 -149.2
Protein Helix A Helix B Helix C Helix D Catalase* 123.6 156.6 157.2 160.5
Cytochrome c' -153.3 -169.1 -165.8 -146.0
Cytochrome b5 19 16 11 15 Cytochrome P-450 152.6 153.0 -30.9 -34.2
Cytochrome b-562 23 28 26 20 Citrate synthase (a) 142.8 20.1 163.6 32.6
Catalase* 9 20 18 19 Citrate synthase (b) 172.7 151.9 162.4 163.2
Cytochrome c' 22 27 22 14 Cytochrome c peroxidase* -138.1 172.2 -99.2 -146.0
Cytochrome P-450cam 20 24 20 21 Methemerythrin -157.8 -170.7 -165.8 -170.0
Citrate synthase (a)* 15 20 8 21 T4 lysozyme -166.4 -158.9 165.9 -155.3
Citrate synthase (b)* 10 24 7 18 p-Hydroxybenzoate
Cytochrome c peroxidase 21 16 16 20 hydroxylase 44.1 19.5 26.5 28.2
Methemerythrin 23 26 16 22 Phospholipase C (a)* 172.1 -69.4 139.7 -51.6
T4 lysozyme 16 17 25 24 Phospholipase C (b) -158.3 -139.7 163.5 143.4
p-Hydroxybenzoate Thermolysin* 130.8 114.9 166.1 142.5
hydroxylase* 12 4 8 8
Phospholipase C (a) 21 24 23 19 Helix assignments for the determination of interhelical angle (fQ)
Phospholipase C (b) 23 20 20 22 started at the first helix in the sequence and proceeded sequentially
Thermolysin 15 23 21 17 around the perimeter of the bundle according to the handedness of
*Structure fails this evaluation. *Structure fails this evaluation.
6594 Biochemistry: Presneli and Cohen Proc. Natl. Acad Sci. USA 86 (1989)
.. .. ..
............................ ..... ....
................ .............. ......
FIG. 1. Two left-handed bundles (side view). Three specific attributes fully describe the topology of a four-a-helix. bundle. These are (i) the
polypeptide backbone connectivity between helices, (ii) the unit direction vectors of the individual helices, and Qff) the bundle handedness. In
the first bundle there are no overhand connections, and in the second bundle there is one overhand connection. The handedness of a particular
bundle is determined using the "right hand rule" of physics. To determine if a helix bundle is of a particular handedness, orient the thumb of
one hand parallel to the first helix or helix A where the positive unit vector stems from N terminus to C terminus. Helix B should be oriented
to the left if it is a left-handed bundle or to the right if it is a right-handed bundle. In the case where helix B is diagonally opposed to helix A,
the handedness is then based on the position of helix C relative to helices A and B.
repressor of primer (ROP) (37). Typically, helix direction covalently bonded, hydrogen-bonded, non-bonded, and elec-
vectors are described with respect to an adjacent helix, trostatic interactions over a range of values for the dielectric
referring to the pair of helices as either parallel or anti- constant (e = 1, 5, 50, r). A comparison ofthe all-anti-parallel
parallel. Entire helix bundles are referred to as anti-parallel bundle from phospholipase C and cytochrome P-450cam,
if all adjacent helix pairs are anti-parallel. which does not have an all-anti-parallel arrangement of
Table 4 shows the categorization of four-a-helix bundles. helices, produced similar results (both are right-handed struc-
There are 48 topologically distinct types of four-a-helix tures with one overhand connection). Without a model of the
bundles. Only six of these types are of the all-anti-parallel unfolded state to allow a calculation of the free energy of
topology, a ratio of 1:7 anti-parallel/non-anti-parallel (Fig. 2). stabilization, these results cannot be interpreted unambig-
From our current data, the observed ratio of anti-parallel/ uously; however, it would appear that any effect from a helix
non-anti-parallel bundles is 12:1. This marked asymmetry is macro dipole on the folded state of a four-a-helix bundle
reminiscent of the preference for right-handed crossover would have to be subtle. Moreover, the calculations of Gilson
connections between parallel (3-strands (38, 39). In that case, and Honig (40), who used the finite difference Poisson-
the uniform handedness was proposed to be a consequence Boltzmann method to calculate the work for assembling a
of chain economy, the preferred twist direction of a poly- four-a-helix bundle, suggest that the helix macro dipole effect
peptide chain during the folding of an extended chain, and the destabilizes four-a-helix bundles and, therefore, is unimpor-
inherent handedness of a-helices. tant in determining the chain topology.
Hypotheses for the Observed Bundle Distribution. The ob- On the other hand, calculations on four-a-helix bundles
served distribution of four-a-helix bundles could be rational- using point-charge or all-atom representations of the helix
ized if the helix macro-dipole effect made a substantial macro dipole with a low dielectric constant have shown that
contribution to a structure's electrostatic energy either dur- the bundle configuration with the most favorable electrostatic
ing folding or in the final structure. A comparison of the energy is that one in which all pairs of neighboring helices are
internal energies of the folded, isolated, all-anti-parallel bun- oriented anti-parallel (10, 41). Similarly, using the numbers of
dles from T4 lysozyme (a left-handed bundle) and cy- expected and observed all-anti-parallel helix bundles to arrive
tochrome c' (a right-handed bundle) using the AMBER pro- at a pseudoequilibrium value provides an enthalpic energy
gram suite indicated less than 10% difference between the value of the same order of magnitude of the model studies
two bundles in each of the internal energy terms describing (approximately -2.6 kcal mol1). These results suggest that
Table 4. Topologies of currently known four-a-helix bundles
Overhand All anti-parallel
no. Left-handed Right-handed Others (right-handed)
0 Complement C3a Cytochrome b-562
Complement C5a Cytochrome c'
Cytochrome b5 Methemerythrin
Interleukin 2 TMV coat protein
1 Ferritin Phospholipase C (b) CytochromeP-450c..
2 Human growth hormone
There are no left-handed topologies for "other" four-a-helix bundles. TMV, tobacco mosaic virus.
Biochemistry: Presnell and Cohen Proc. Natl. Acad. Sci. USA 86 (1989) 6595
Right-handed all and-parallel bundles: occur with approximately equal frequency. In a second case,
the prediction of the human growth hormone structure (45)
did not succeed partly because putative structures containing
AL D A-C long interhelical connections were considered unlikely on
l B AD D B
kinetic grounds. In this study, we have noted several exam-
ples of four-a-helix bundles that contain one or two overhand
connections (ferritin, phospholipase C, human growth hor-
mone, and cytochrome P-450cam). These findings suggest
that a predicted structure containing overhand connections
Left-handed all ant-parallel bundles:
cannot be rejected as unreasonable, kinetically or otherwise.
We thank Dr. Hough for supplying the coordinates of phospholi-
pase C. We acknowledge the support of the Computer Graphics
Laboratory at the University of California, San Francisco (Grant
RR1081 from the National Institutes of Health), the Macromolecular
Workbench project (Defense Advanced Research Projects Agency,
i- B B B D
Grant ONR N00014-86-K-0757), the National Institutes of Health
(Grant GM39900), and the Searle Family Trust.
FIG. 2. Schematic representation of the possible anti-parallel
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