Determining the selectivity of positions in overlapping peptides

For each residue in the protein being mapped in overlapping peptides, the algorithm seeks to determine which amino acid substitutions leads to a significant change in signal intensity relative to the native amino acid. Here, the substitution values are used to generate a substitution matrix expressing substitution values of one protein residue being represented in different positions in the overlapping peptides (see Fig 1 for a schematic illustration of the procedure). Here, only peptides are included containing protein positions previously identified to be involved in the epitope.

Figure showing overlapping peptides (left) with the valine (V highlighted in bold) being analyzed for antibody selectivity. The box contains the substitution values, x_i,j, with columns representing the amino acid, i, which substitutes valine and rows representing the position, j, of the valine in the peptide (illustrated to the left) undergoing substitution. The mean substitution value, μ_i, of each replacing amino acid is shown in the bottom row. The global mean, μ_g, is calculated across all substitution values in the matrix.

A Dunnett’s multiple comparison procedure is used to test which mean, μ_i (i.e. which replacing amino acid), that are significantly different from the value 1 of no selectivity. The LSD of each column of the substitution matrix is calculated as described above for each column of the PSSM. Protein positions will be reported and visualized, where the relative change in signal of one or more amino acid substitutions exceeds the LSD value.

If SE_i is the pooled standard error of the i-th column of the substitution matrix, then t_i = (μ_i − μ_g)/SE_i is the t-statistic used to test the departure of the replacing amino acid i relative to the global mean, μ_g, of the substitution matrix. Thus, mean substitution values above μ_g yield positive t-statistics (amino acids favouring interactions), while substitution values below μ_g yield negative t-statistics (amino acids disfavouring interactions). The p-value of the t-statistic is calculated from the cumulative distribution function for the noncentral Dunnett’s test distribution with degrees of freedoms equal i) to the number of replacing amino acid (up to 19) and ii) the total number of substitution values minus the number of replacing amino acids. To visualize the selectivity profile, each protein residue is presented in a logo-plot with the corresponding amino acid substitutions scored as

and subsequently rescaled so that ∑|s_i| = (1 − μ_g), consequently making the absolute sum of logo-heights reflect the mean change caused by substitutions of the native amino acid. To illustrate this, a sample data is shown in Fig 2, exemplifying two positions with high and low selectivity, respectively. In Fig 2A, only the native amino acid E (highlighted in solid fill at μ = 1) retains complete antibody binding (μ_E ≈ 1). The majority of the remaining amino acid substitutions lead to a decrease in signal and thus lower substitution value. The p-value associated with the native amino acid E is hence low (p ≪ 1), since the departure from the global mean μ_g is high (t > 0), leading to a high positive score, s_E. The resulting logo-plot is shown in Fig 2C. The native amino acid employs the largest letter scale, but both the negatively charged amino acid D and the positively charged amino acids K, H and R employ larger letter scales due to their departure from μ_g, in opposite directions. The absolute sum of the logo-plot column corresponds to the global effect of substitution (1 − μ_g = 0.60). Fig 2B exemplifies positions with only two amino acid substitutions affecting the signal. Here, the native amino acid, which also happens to be E (highlighted in solid fill at μ = 1) will employ a high p-value (p ≈ 1), since the substitution value is close to μ_g, leading to a low score (s_E ≈ 0). The resulting logo-plot is shown in Fig 2D. The absolute sum of the logo-plot column is much smaller in this example (1 − μ_g = 0.20) and only substitutions to K and H are affecting the signal, as seen by the relatively large negative scales.

Figure showing example of selectivity of two epitope positions in overlapping peptides upon substitutions with all 19 amino acids. A and B shows illustrative density plots of substitution values taken from a substitution matrix, with the mean substitution value,.μ_i, of each replacing amino acid shown in diamond shapes. Filled diamond is the native amino acid (E in both examples). C and D show the resulting logo-plot of the positions exemplified in A and B, respectively. The logo-plots are made using Seq2Logo [16].