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.