Evolutionary diversification of the multimeric states of proteins

Abstract

One of the most striking features of proteins is their common assembly into multimeric structures, usually homomers with even numbers of subunits all derived from the same genetic locus. However, although substantial structural variation for orthologous proteins exists within and among major phylogenetic lineages, in striking contrast to patterns of gene structure and genome organization, there appears to be no correlation between the level of protein structural complexity and organismal complexity. In addition, there is no evidence that protein architectural differences are driven by lineage-specific differences in selective pressures. Here, it is suggested that variation in the multimeric states of proteins can readily arise from stochastic transitions resulting from the joint processes of mutation and random genetic drift, even in the face of constant directional selection for one particular protein architecture across all lineages. Under the proposed hypothesis, on a long evolutionary timescale, the numbers of transitions from monomers to dimers should approximate the numbers in the opposite direction and similarly for transitions between higher-order structures.

Keywords: complex adaptation; oligomer; quaternary structure.

Fig. 1.

The types of multimeric structures observed for enzymes of glycolysis and of the citric-acid cycle, obtained from information at the Braunschweig Enzyme Database (BRENDA) (17) and Protein Interfaces, Surfaces and Assemblies (PISA) (18) databases. Data are shown only for enzymes with structures known in at least four of the major groups (note that the unicellular eukaryotes are not monophyletic, but distributed over several major lineages). There has been no attempt to weight the observations according to the frequency observed, as the data are not evenly distributed within major groupings. Because protein structural data are very limited for plants, the paucity of variation with this lineage may simply be a sampling artifact. The lack of structural variation for glucose 6-phosphate isomerase is likely due to the fact that the active site of this enzyme is formed at the dimeric interface.

Fig. 2.

Variation in the area of binding interfaces in different taxa as a function of the overall surface area of monomeric subunits. The data, given for enzymes of glycolysis and the citric-acid cycle, are derived from the PISA database (18) and are distributed over a broad range of prokaryotic and eukaryotic taxa. The average fraction of a multimer covered by the sum of its interfaces is 0.165, with a SD of 0.061 (sample size = 159). Diagonal lines denote points with equivalent proportions of the surfaces of monomeric subunits associated with interfaces.

Fig. 3.

(Upper) A general model for a linear array of oligomeric states. Class 1 represents the most extreme monomeric state, with all other classes denoting classes with increasing interface stability. The transition coefficient denotes the rate at which a population makes a change from state i to state j. (Lower) Under neutrality, the expected probability distribution of allelic states is Poisson, with a form that is independent of the size of the population. The mean allelic state is equal to and the SD is , where u and v denote the mutation rates in the upward and downward directions (the former being per molecule and the latter per relevant interfacial residue). This same relationship applies with selection promoting or opposing dimerization if or is substituted for .

Fig. 4.

A 2D array of oligomeric states, allowing for transitions to dimeric and tetrameric structures with increasing levels of interfacial stability. Only the first three columns are included in the model discussed in the text.

Fig. 5.

The equilibrium probabilities of dimeric and tetrameric states in a lineage, as a function of the joint upward and downward pressures from mutation and selection. The probability of a monomeric state is equal to 1.0 minus the sum of probabilities of dimers and tetramers. Here it is assumed that there is positive selection for multimerization.

Fig. 6.

The consequences of isologous and heterologous interfaces for the production of closed multimers with even and odd numbers of subunits. Note the mismatched interface in trimers when interfacial binding is isologous.

Fig. 7.

Flow diagram for the situation in which dimers or trimers can evolve from a monomeric ancestral state. The mutation rates between alternative allelic states are given on the arrows, and the selection coefficients are denoted below the diagram. The two potential paths to a trimeric structure simply differ in the order of occurrence of the two mutations necessary for complexation.