Signal decomposition

When several antibodies land on the same bead, SAgA shares the signal between them — its central strength.

Chapter 3 — Signal decomposition

3.1 · Alpha + beta on DQ

SAgA's core strength is decomposing a single bead's MFI into the several antibodies behind it. DQ is the clearest example: each molecule pairs an alpha chain (the DQA1 gene) with a beta chain (the DQ serogroup), so a bead can carry two antibody targets at once.

Using the masking rule from Chapter 1, some beads are left with a single surviving target, which pins down its level: a bead left with only its beta target reveals the pure beta contribution, and one left with only its alpha target reveals the pure alpha. The bead carrying both is then their sum.

The top bead shows a single undecomposed MFI of 5000 — The top bead reads 5000 as a single value — but it carries both an alpha and a beta target.

The 5000 MFI bead decomposed into DQA1*02 at 2000 plus DQ2 at 3000 — That 5000 is the sum of its two targets: 2000 from the alpha chain (DQA1*02) and 3000 from the beta serogroup (DQ2). SAgA returns both antibodies separately.

3.2 · A full DQ panel

The same logic scales to a realistic panel with several antibodies at once. SAgA excludes the negative beads, strikes the attributes they carry from every bead, identifies each surviving antibody, then decomposes each positive MFI into its contributions — some beads carrying two antibodies at once.

A larger DQ panel decomposed into three antibodies — A serum with three antibodies (anti-DQA1*02, anti-DQ2, anti-DQ7). DQ9 and DQA1*03:01 are excluded because their bead is negative. Each positive MFI then splits into its surviving contributions, and SAgA returns DQA1*02 = 2000, DQ2 = 3000 and DQ7 = 3500.

3.3 · Noisy MFI & best fit

Those clean sums are the ideal. In practice, the same antibody binds with slightly different intensities on every bead — real MFI are noisy, and two beads carrying the same antibody no longer agree exactly on its level.

SAgA then looks for the single set of antibody levels that, together, best reproduces every bead at once — a best fit that minimises the residuals between observed MFI and the summed antibody contributions.

With noisy MFI, SAgA finds the antibody levels that best reproduce all beads — With noisy inputs, SAgA returns DQA1*02, DQ2 and DQ7 at levels close to the true ones — the combination that best explains the whole panel.

Cases for this part