Figure 1.
True- and False-Positive Rates on Simulated Data
(A) A receiver operating characteristic (ROC)-like curve, in which the y-axis corresponds to the true-positive rate (TPR), and the x-axis corresponds to the false-positive rate (FPR). A perfect analytical method would be located in the upper-left corner (i.e., TPR = 1, FPR = 0), whereas methods located near the diagonal (dashed line, TPR = FPR) are statistically equivalent to a random guess. Each point in the plot corresponds to the mean outcome from the corresponding model analysis (orange = the Fisher exact test, black = evolutionary-network) of ten replicate simulations of binary-state sequences evolving under various settings of the pairwise coevolution parameter, ɛ (ranging from 1 to 3; see figure labels).
(B) Boxplots corresponding to the false-positive rate (as a fraction of the total number of pairwise comparisons = 528) from the corresponding analysis (evolutionary-network [Evol-Net] or Fisher exact test [Fisher]) of simulated sequences evolving according to a null model of codon substitutions in which sites evolve independently, using parameter settings estimated from the original V3 sequence alignment. We generated 100 replicate simulations of nucleotide sequences evolving along the original neighbor-joining tree.
Figure 2.
Distribution of the Marginal Posterior Probability of Network Edges
This histogram indicates the frequency of the marginal posterior probability of the 528 possible edges, sampled from a Markov chain over the space of node orders (see Materials and Methods). The prior probability of each edge was set to the uninformative value of 0.5. Note that the vertical range of the histogram was truncated to a maximum of 50; the first bin of the histogram contained 485 edges as indicated on the figure. Individual values are indicated by tick marks along the x-axis. A red line indicates the arbitrary cutoff value of 0.95.
Figure 3.
The Consensus Network of V3 Residues
Each node corresponds to a residue in the V3 loop, numbered according to their position in the consensus sequence (identical to Korber et al. [19]) and labeled with the consensus amino acid. Dark-shaded nodes indicate residues that are connected by edges with parametric bootstrap support values exceeding 50%; each edge is labeled with its support value. Edges with support values below this threshold are indicated by dashed lines.
Figure 4.
Structural Model of the V3 Loop
A three-dimensional visualization of the structure of the V3 loop, using structural coordinates from a model comprised of the HIV-1 gp120 core protein complexed to the CD4 receptor and the X5 antibody [28]. The structure is oriented such that the host cell membrane would be positioned at the top of the figure. The cysteine residues forming a disulfide bridge that closes the loop are labeled in green. The amino acid sequence depicted here differs from our consensus sequence at five positions, such that identity would require the following substitutions: Q5N, H12R, R17Q, T21A, and E24D.
Figure 5.
A consensus network assembled from edges with marginal posterior probabilities exceeding 0.95, in which nodes represent nonsynonymous substitution events at codon sites in the V3 and C4 domains. Nodes that correspond to residues in the C4 domain are shaded blue (numbered according to their position in the consensus env gene sequence), and nodes that were connected by strongly supported edges in the V3-specific network are shaded black. We retain the same numbering scheme for residues in V3 for consistency.