types of LRRs were constructed (GALA-LRR, GL-LRR and updated CC-LRR). The probability that a match is a product of chance alone was calculated by analyzing the score distribution obtained from a profile search against a regionally randomized version of the protein database, assuming an extreme value distribution [34]. All database searches were performed with a nonredundant data set constructed from 2006 releases of non- redundant protein sequence database including GenPept, Swis- sprot, PIR, PDF, PDB and NCBI RefSeq and available on the NCBI FTP site (ftp://ftp.ncbi.nih.gov/blast/db). The sequence profiles and results of the search can be viewed on a dedicated web-page http://bioinfo.montp.cnrs.fr/profiles (Tools/Profiles/ Show Profiles). Molecular Modelling The initial template for GALA-LRRs was taken from a 24- residue LRR (residues 2211 to 2235) of the known crystal structure of human Skp2 protein [9,10] (see Results and Discussion) using the Insight II program [35]. The amino acid sequence of the template was edited in accordance with the GALA sequences using the homology modeling option of Insight II program. The structure was further refined by the energy minimization procedure based on the steepest descent algorithm implemented in the Discovery subroutine of Insight II, and tethering heavy backbone atoms to their starting conformations with force constant K = 100. The 300 steps of minimization led to a maximum RMS derivative of 0.4 kcal/(mol* A˚). The next stage of minimization was 500 steps of the conjugate gradients algorithm, tethering the backbone atoms with lower force (K = 50), and then 300 steps with K = 25. The tethering was accompanied by setting the distance constraints at K = 50, in order to improve the geometry of H-bonds. To allay the concern that these constraints generated significant tensions in the minimized structure, the last calculation was performed without any restrictions, to an RMS derivative of 0.3 kcal/(mol* A˚). The CVFF force field and the distance dependent dielectric constant were used for the energy calculations. The program PROCHECK [36] was used to check the quality of the modeled structure. In accordance with the PROCHECK results all residues of the LRR domain of the GALA4 model have backbone conformations from allowed regions of the Ramachandran plot; and G-factors of the polypeptide stereochemistry (a log-odds score based on the observed distribution of the covalent geometry) equal to 20.15. The overall average G-factors for the model is 20.49, values that would be expected for good-quality model. To examine the side-by-side packing of LRRs from different subfamilies the following procedure was used. First, fragments of the LRR domains corresponding to different LRR subfamilies were extracted from the known crystal structures (CC-LRR, pdb code 2AST; Typical LRR, pdb code 2O6Q; Bacterial LRR, pdb code 1G9U; SDS22-like LRR, pdb code 1D0B; RI-LRR, pdb code 2BNH; PS-LRR, pdb code 1OGQ). Second, each of these structures and the structural model of GALA-LRRs were superimposed with CC-LRR domain. For the superposition, the conserved b-structural parts of the LRRs were used. Two adjacent b-strands of CC-LRR and the analyzed structures were superim- posed and the side-by-side packing of the variable LRR fragments was analyzed. Tests for positive selection The selective pressure at the protein level was measured by the ratio of nonsynonymous to synonymous rates v = dN/dS, with v,1, = 1, or .1 indicating conserved, neutral or adaptive evolution respectively [37]. Selective pressure was evaluated using Evolution of GALA Proteins the probabilistic Markov models of codon substitution [27,28]. Such models describe the substitution process based on a multiple alignment tree. The transitions from one codon state to another are described by the transition probability matrix over time t as P(t) = exp(Qt). The generator matrix Q = {qij} defines the instan- taneous substitution rates at site s from codon i to codon j : qi(js)~ 8 0, > > >>> pj, > < kpj, if i and j differ by w1 nucleotides if i and j differ by one synonymous transversion if i and j differ by one synonymous transition >>> v(s)pj, if i and j differ by one nonsynonymous transversion > > >: v(s)kpj, if i and j differ by one nonsynonymous transition Here pj is the frequency of codon j, parameter k is the transition/transversion ratio, and v(s) is the v ratio for site s. The codon substitution process is assumed independent among sites, and model parameters are estimated by maximizing the log- likelihood function of sequence data X = {xs} given a phylogeny with branch lengths t and a model M: log P(X jt,M)~ X log½P(xsjt,M) : s The models used in the analysis differed by statistical distributions of the v ratio used to describe the variation of selective pressure along a sequence. Likelihood ratio test (LRT) for positive selection compares maximum log-likelihoods of two nested models, one of which allows sites under positive selection while another does not. To test that a model allowing positive selection describes data significantly better, twice the log-likelihood difference is compared to the x2-distribution with degrees of freedom equal to the difference in the number of free parameters between the two models. We performed two LRTs for positive selection, comparing models M2a and M8 that allow sites with v.1 (alternative hypotheses) with simpler models M1a and M7 respectively that do not allow sites with v.1 (null hypotheses). Model M1a (nearly-neutral) assumes two site classes in proportions p0 and p1 = 1–p0: one with v0 ratio estimated between 0 and 1, and the other with v1 fixed at 1. The alternative model M2a (positive selection) extends the model M1a by adding a proportion p2 of positively selected sites with v2.1, estimated from data. The second LRT uses the model M7 (beta) that assumes the v ratio is drawn from a beta distribution defined between 0 and 1. The alternative model M8 has an extra class of sites under positive selection with v.1. We also considered two other codon models: the most simple one-ratio model M0, where v is assumed to be constant over all sites in the sequence, and the discrete model M3 that allows three discrete classes of sites with ratios v0, v1, and v2 occurring in proportions p0, p1 and p2 = 12p02p1. Models M0 and M3 are also nested, and can be used to perform the LRT for heterogeneity of selective pressure along the sequence [38]. This test is often significant, as most coding data has significantly heterogeneous selective pressures acting on different sites of the sequence, according to their functional importance and the role in the protein folding and stability. In comparison with models M8 and M2a, model M3 better combines the algorithmic simplicity with sufficient complexity necessary to reflect heterogeneity of selection pressure in nature. This model is often used to evaluate the underlying distribution of the selective pressure across sites in a PLoS ONE | www.plosone.org 7 February 2008 | Volume 3 | Issue 2 | e1694