MBE Advance Access originally published online on November 23, 2006
Molecular Biology and Evolution 2007 24(2):349-351; doi:10.1093/molbev/msl181
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Letter |
Quaternary Structure Constraints on Evolutionary Sequence Divergence
* Centro de Estudios e Investigaciones, Universidad Nacional de Quilmes, Bernal, Argentina
Instituto Nacional de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, La Plata, Argentina
E-mail: jechave{at}inifta.unlp.edu.ar.
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Abstract |
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 TOP Abstract AcknowledgementsReferences |
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The structurally constrained protein evolution (SCPE) model simulates protein divergence considering protein structure explicitly. The model is based on the observation that protein structure is more conserved during evolution than the sequences encoding for that structure. In the previous work, the SCPE model considered only the tertiary structure. Here we show that the performance of the model is enhanced when the oligomeric structure is taken into account. Our results agree with recent evolutionary studies of oligomeric proteins, which show that conservation of the quaternary structure imposes additional constraints on sequence divergence. The incorporation of protein–protein interactions into protein evolution models may be important in the study of quaternary protein structures and complex protein assemblies.
Key Words: SCPE • quaternary structure • sequence divergence
A major constraint in protein sequence divergence is the conservation of protein structure. This constraint is related to the selective pressure involved in the conservation of protein cores, which involve a complex network of interresidue noncovalent interactions (Russell and Barton 1994
; Sali and Overington 1994). This network of interactions is among the predominant factors involved in the protein-folding process to obtain a stable fold (Lim and Sauer 1991; Lattman et al. 1994; Xu et al. 1998; Vendruscolo et al. 2000). These observations explain the fact that the amino acid substitution pattern for a given site depends on its structural environment and also that residue substitutions in interacting sites are correlated (Overington et al. 1990; Overington 1992; Pollock and Taylor 1997).
Noncovalent interactions between amino acid side chains are important for the correct assembly of folded chains into multichain proteins. The protein–protein interactions in these complex proteins could be permanent or transient. In the first case, proteins exist only in their complexed form, which is usually very stable. On the other hand, transient complexes associate and dissociate in vivo according to the environment or to the presence of external factors and involve proteins that also exist as independent entities (Jones and Thornton 1996; Nooren and Thornton 2003). The emerging picture suggests that the residues involved in these protein–protein interactions are evolutionarily constrained because of the selective pressure to conserve the structure of the complex to ensure the conservation of biological activity (Ofran and Rost 2003; Caffrey et al. 2004; Halperin et al. 2004; Li et al. 2004; Mintseris and Weng 2005). It was also found that for close homologues (30–40% or higher sequence identity), the protein–protein interactions are invariably the same (Aloy et al. 2003).
To study how protein structure modulates sequence divergence, we developed the structurally constrained protein evolution (SCPE) model (Parisi and Echave 2001). The SCPE model simulates sequence divergence constrained by conservation of protein structure. Recently, we successfully applied the SCPE to representatives of the main 4 classes of protein fold (alpha, beta, alpha + beta, and alpha/beta) (Parisi and Echave 2005). Using substitution matrices derived from SCPE simulations (Fornasari et al. 2002), we found that the SCPE model outperforms site-independent models such as JTT (Jones et al. 1992). In all these studies, the SCPE model considered only the tertiary structure of the protein. Here we extend the model to include protein–protein interactions and show that performance of the model improves.
We will describe briefly the algorithm of the SCPE model (a more detailed description can be found elsewhere [Parisi and Echave 2001; Fornasari et al. 2002; Parisi and Echave 2005]). In SCPE simulations, trial sequences are generated by introducing a random mutation in a reference sequence, which at the beginning of the simulation is equal to a sequence of known structure. Mutations are introduced using a amino acid mutational rate matrix Qmut derived using the HKY model of DNA evolution (Hasegawa et al. 1985) and the universal genetic code (see below). For each trial, a score 
which measures the structural perturbation, is calculated, where E
and E
are the mean-field energies of reference and trial sequences. Mean-field energies are calculated using a contact map representation of the protein structure and an empirical contact potential (Berrera et al. 2003). Trial sequences are then accepted or rejected using an acceptance probability function (P) to generate in each round a new reference sequence,
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is the only parameter of the SCPE model that must be fit to the data for each homologous set and is related to the degree of selection pressure for structural conservation.
Site-specific substitution matrices are derived from a matrix of counts for each site: for i 
j, N
is half the number of mutational steps, which result in either i 
j or j i amino acid replacements at site p. N
is the number of mutational steps for which amino acid i remains constant. Then, the substitution rate matrix Qp is obtained using
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Finally, to avoid numerical problems, each Qp is recalculated using pseudocounts as described previously (Parisi and Echave 2005).
In this paper a series of position-specific Qp were calculated using 2 alternative models: one model considers only the tertiary structure of a protein (SCPEt) and the other the quaternary structure of the protein (SCPEq). Seven homooligomeric protein families were used as test systems for model comparisons. These families adopt different quaternary structures and also belong to different fold classes (table 1). As described previously (Parisi and Echave 2004, 2005), for each family a set of homologous DNA sequences were collected and a maximum parsimony (MP) topology was inferred using DNAPARS (DNA parsimony program) (Felsenstein 1993). These sequences were aligned and Hasegawa-Kishino-Yano parameters estimated using hypothesis testing using phylogenies (HYPHY)(Pond et al. 2005). This alignment was translated using the universal code to obtain a protein alignment. The alignment length was adjusted to fit the reference sequence length. With this protein alignment, a MP topology was obtained using PROTPARS (Felsenstein 1993). This protein alignment and the derived MP topology are used to evaluate the likelihood of the models, as described below.
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For each test system, we obtained, using SCPEt and SCPEq simulations, a set of Qp over a grid of
values. With maximum likelihood (ML) calculations, we obtained the ML for each in the set. Then, both models were compared using parametric bootstrapping with a likelihood ratio test statistic (see Goldman 1993). In this evaluation, the best for each model was used, and because the structural representation of the protein is not the same in SCPEt and SCPEq, the best value for both models could not be the same. All the ML optimizations were performed independently for the different sites of the protein using the program HYPHY (Pond et al. 2005) and using the protein alignment and the MP topology for each family described above.
For each representative set of sequences, the statistic 2
data = 2(ln (ML
) – ln (ML
)) was calculated, using the SCPEt as the null hypothesis and SCPEq as the alternative one. In order to assess the significance of 2data, we simulated 300 data sets (parametric bootstrapping) using the null hypothesis to obtain the 2 reference distribution. Then, the significance of 2data was evaluated calculating a Z score as follows:
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distribution obtained by parametric bootstrapping.
In the first column of table 2, we show the results of the comparison of both models using the likelihood ratio test. The SCPEq model outperforms the SCPEt model in all the cases with high statistical significance (P < 10–2). The main difference between the 2 models is that because SCPEq takes into account the interactions between the chains in the oligomeric structure, the constraints imposed on those positions involved in intermonomer interactions differ from those of the SCPEt model that does not consider these interactions. These positions, called quaternary positions (QP), are detected by the difference in the total number of contacts per position between the contact matrices obtained using the quaternary structure (SCPEq) or just the tertiary structure (SCPEt). Positions with the same number of contacts in the 2 models are called tertiary positions (TP). To study the reason for the enhanced performance of SCPEq over SCPEt, we studied the 2data distributions for QP and TP. Using the Kolmogorov–Smirnov test, we found that these distributions are significantly different for all the protein families considered. This test was chosen because it has the advantage of making no assumption about the distribution of the data. Moreover, the average of 2data for QP shows a bias toward positive values, whereas for the corresponding TP values these averages are approximately centered around 2data = 0, as can be seen in table 2. We should note, however, that in 1 family (4-oxalocrotonate tautomerase, see table 2), the average 2data for TP departs more than it would be expected from zero, probably indicating that the TPs could be influenced by contacts with quaternary sites. This hypothesis requires additional studies that will be addressed in the future.
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In summary, we have shown that the model SCPEq significantly outperforms SPCEt and that this improvement rests on the better modeling of QP when the quaternary structure is considered. This improvement shows the importance of the conservation of quaternary structure as one of the factors constraining sequence divergence during evolution. Thus, the oligomeric state of a protein should be taken into account to improve the quality of evolutionary models. Taking into account these constraints will improve our understanding of the forces involved in the formation and evolution of protein complexes.
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Acknowledgements |
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TOPAbstractAcknowledgementsReferences |
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We thank Jeff Thorne and an anonymous reviewer for their useful remarks that resulted in an improved version of the manuscript. This work was partially supported by grants from Universidad Nacional de Quilmes, Agencia Nacional de Promocion Cientifica y Tecnologica, and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). G.P and J.E are members of CONICET.
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Footnotes |
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Spencer V. Muse, Associate Editor
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References |
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