INTRODUCTION
Crick proposed a “Knobs in Holes” model for the packing interface of
adjacent α-helices in the coiled-coil oligomeric assembly of keratin,
noting that an ~20° rotation of the axis of one helix
would intercalate its side chains (“knobs”) into surface cavities
(“holes”) that exist between the side chains in the other helix1,2 (Fig. 1). This interaction results in left-handed
supercoiling of the duplex, reducing the residues per turn from 3.6 to
3.5, and altering the periodic repeat of amino acids in the helix from
18 to 7. Thus, supercoiling yields a heptad repeat of amino acids
forming the coiled-coil interface. This interface is largely
solvent-excluded, and hydrophobic side chain patterning conforming to a
heptad repeat would therefore promote coiled-coil assembly. Structural
details of the knobs and holes described by Crick were limited to a
description involving simple cylindrical shapes; however, a potential
“systematic interlocking” of the knobs in holes was noted by Crick
(although it is unclear whether this referred to molecular
complementarity or steric entanglement). A model for coiled-coil
interactions was provided by Crick for a hypothetical three-stranded
coil, but indicated no obvious steric entanglement 2.
Richmond and Richards 3 undertook a geometric analysis
of α-helical packing in sperm whale myoglobin. An area of interest was
in protein unfolding; specifically, that if the reaction coordinate of
unfolding is the reverse of folding, then understanding possible
movements of interacting α-helices can identify the most plausible
folding/unfolding reaction coordinate. They reported that steric
interactions between adjacent side chains oppose shear and torsional
movement of packed helices; however, separation of helices in a
direction normal to the helix axis is not restricted by any interlocking
of side chains (such movement is opposed by non-covalent attractive
forces). Thus, the folding/unfolding reaction coordinate was postulated
to be principally associated with translational movement normal to the
helical axes.
A heptad hydrophobic repeat is the quintessential feature shared by all
proteins that adopt a coiled-coil structure 4-6. Due
to the γ-branched nature of leucine side chains Landschulz and coworkers
proposed that the leucine sidechains from one helix interdigitate with
those of the second helix, forming a “molecular zipper”7. This interdigitation of leucine was postulated to
“lock” the two helices together in a form of steric entanglement
referred to as a “leucine zipper” (Fig. 2).
Kim and coworkers 8 explored the role of electrostatic
charges in the promotion of heterodimeric coiled-coil α-helices. They
presented evidence that design of favorable heterodimeric assembly can
be achieved by destabilization of specific homodimeric interactions. The
resulting heterodimeric helices were described as “peptide Velcro”
since the “individual peptides have little self-affinity, but high
affinity for each other”. However, this study pointed out that affinity
for the heterodimeric peptides can be negatively affected by unfavorable
electrostatics. This result suggests a limited role for steric
entanglement, and a greater role for molecular complementarity and
favorable charge interactions. Thus, use of the term “Velcro” appears
inappropriate, since the basis of Velcro™ interactions is exclusively
steric entanglement and does not involve any attractive forces (Fig. 2).
Efimov 9 evaluated the knobs in holes helical
interface model using a purely mathematical perspective. Efimov used the
term “jigsaw puzzle” to describe the structural complementarity of the
hydrophobic amino acids comprising the packing interface between
helices, stating “There is an exquisite complementarity between the
hydrophobic stripes of the α-helices that fit together like pieces of a
jigsaw puzzle”. Jigsaw puzzle pieces have no attractive forces and are
sterically entangled through a dove-tail type interface (Fig. 2). The
relative contribution of non-covalent attractive interactions versus
steric entanglement intended by the jigsaw puzzle descriptor was not
provided (although it is suggestive of principally steric entanglement).
One of the original reports of “domain-swapping” protein interfaces
describes how monomeric diphtheria toxin converts to a stable dimeric
oligomer in response to freezing in acidic pH 10. The
dimer has a swapped subdomain of 15 kDa and is described as
“intertwined” and “entangled”. It was postulated that the
domain-swapped form may be less stable than the monomer, but kinetically
trapped at neutral pH due to physical entanglement. The dimerization of
bovine seminal ribonuclease involves similar swapping of a relatively
short region of 15 residues; while this may not comprise a structural
domain, it meets the definition of domain-swapping11,12. Tawfik and coworkers 13described the de novo design of β-propeller lectins by tandem
duplication of repetitive units termed “blades” (a four-stranded
antiparallel β-sheet). The repeated modules comprise three strands of
one “blade”, plus one strand of the following blade. The resulting N-
and C-termini interactions meet the definition of domain-swapping (as
defined by Eisenberg) and were described as “Velcro-like
interactions”, suggesting a steric entanglement. Tame and coworkers14 reported the computational design of a symmetric
β-propeller protein based upon the sensor domain of a protein kinase
from Mycobacterium tuberculosis. This protein architecture is a 6-bladed
propeller where the last β-strand completes the first propellor motif in
a domain-swapped arrangement that was characterized as a “Velcro
strap”.
Overall, in studies of both coiled-coil and domain-swapped protein
oligomeric assemblies, commonly utilized descriptors for the interface
include “zipper”, “Velcro”, and “jigsaw”. These terms
fundamentally describe steric entanglements (Fig. 2), which can
potentially oppose shear, rotation, and translational movement of
interacting surfaces with no reliance upon any attractive force. Despite
their widespread adoption, the precise meaning of such terms as regards
the relative importance of non-covalent attractive forces versus steric
entanglement is ambiguous. If non-covalent attractive forces could be
“switched off”, the potential role of entanglement alone could be
evaluated. However, it is not possible to experimentally eliminate
attractive forces; furthermore, the elimination of attractive forces
would promote loss of structure essential for assembly. However, 3D
printed models offer the possibility of accurate molecular models that
enable evaluation of steric entanglement in the absence of any
attractive forces.
In the present report we describe 3D printing of various coiled-coil
structures as well as different domain-swapped permutations of a de novo
designed oligomer form of a symmetric β-trefoil protein. The kinetic
energy required to dissociate these complexes is also quantified. While
the coiled-coil complexes exhibit a structural complementarity at the
interface, which opposes shear and rotation, there is minimal evidence
of steric entanglement to prevent translation normal to the axis of the
helix. In circular permutations of the oligomeric β-trefoil protein,
there are varying degrees of steric entanglement depending upon the
details of the domain-swapped region. There is evidence of an inverse
correlation between extent of entanglement, level of protein expression,
and folding cooperativity. The results suggest that the presence of
steric entanglement is a barrier to both folding and unfolding,
consistent with a kinetically trapped intermediate, and may be largely
eschewed in natural protein oligomeric interfaces.