Journal of Molecular Biology
The Dominance of Symmetry in the Evolution of Homo-oligomeric Proteins
Introduction
Symmetry fascinates everybody including mathematicians.1 The symmetry of protein complexes was discussed long before any structures were known.2, 3 Soon after the exact point group symmetry of associated highly asymmetric proteins was established,4 Monod et al. pointed out that this symmetry involves a multiplication of contacts that is most useful for introducing subunit cooperation and thus regulation into enzymes.5 After an early crude explanation of the molecular symmetry,6 many years passed by before Lukatsky et al. described a statistical effect that favored a symmetric association of simple asymmetric objects if the geometry with the lowest association energy can be chosen from a number of samples.7, 8 Recently, it was shown that this effect applies also to real proteins.9 In a different approach, protein engineering experiments demonstrated the crucial role of contact multiplicity for symmetric association.10 Both the multiplicity concept and the statistical effect refer to static situations. The molecular symmetry observed in nature, however, arose in a dynamical evolutionary process, as recently shown for higher symmetries that most likely developed from lower ones.11 Therefore, theoretical,5 statistical,7, 8, 9 or designed experimental studies10 cannot fully explain the prevalent symmetry. A simple evolutionary model was here constructed and analyzed in order to fill this gap. The model reveals the reason for the abundant symmetry of homo-oligomeric proteins, and it shows the relationship between the static concepts.5, 6, 7, 8, 9, 10
At present, many interfaces of interacting proteins are known in detail.12 They have been the subject of numerous analyses13, 14, 15, 16, 17, 18, 19 and engineering attempts,20, 21, 22 revealing a number of general properties. Interactions occur between different and identical proteins. Heteromeric protein–protein interactions are mostly transient and indispensable for cellular functioning.23 In contrast, homomeric interactions are generally permanent, although transient associations are known.24 Among the established structures, there exists an obvious dominance of homo-oligomers that belong to a point group symmetry.11, 14, 19, 25 This dominance is here analyzed for the simple C2 point symmetry, which is represented by a single 2-fold axis. Higher symmetries give rise to more dramatic differences,10 but do not yield further insights.
Section snippets
Dimer development
Evolution comprises random mutations and selection. For following an evolutionary process, we consider a population of identical cells (e.g., bacteria) containing protein X at concentration m0 (Fig. 1a). The cells propagate and protein X undergoes mutations. In a cell i, the monomer–dimer equilibrium follows the equation Ki = (m0 − 2·di)2/di, where di is the dimer concentration and ΔGi = RT ln Ki relates Ki to ΔGi. Figure 1b shows the amount of dimerization as a function of ΔGi for three reasonable
Discussion
As a general result, the dimer development depends strongly on the type of the functional advantage a cell derives from the dimer. This type determines the association geometry, which is here represented by four scenarios with fixed, relaxed, and unconstrained geometries. The two fixed-geometry scenarios S1-0 and S2-0 differ decisively in the drift period. The 10% lead groups of S1-0 reach the − 25-, − 30-, and − 35-AEU thresholds by factors of 30, 170, and 3700, respectively, faster than those of
Validation of the IPM
The IPM subdivides a real protein surface into a number of discrete parts (here patches) and allows to standardize the interaction between these parts so that symmetric and asymmetric interactions are distinctly separable from each other. Four conceivably natural evolutionary scenarios with unconstrained, relaxed, and fixed geometric dimerization conditions were defined in terms of the IPM and used in the simulations. Unnatural scenarios8 were not pursued (Fig. 2d). Assuming that the protein
Acknowledgements
I thank C. Schleberger and S. Schulz for technical assistance and E. I. Shakhnovich, C. Vonrhein, and O. Einsle for discussions. The project was supported by the Albert-Ludwigs-Universität and Wacker Chemie.
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