Assay resolution governs the transfer of molecular dependence

Abstract

Background. Separate molecular assays retain within-assay coexpression when cross-modal pairing is unavailable. We ask which aspects of this structure support RNA–protein dependence prediction from a paired reference.

Results. We derive the sharp identified range and minimax predictor for a binary association given a fixed fine-scale interaction and within-assay moment constraints that determine the queried frequencies. The result applies directly when all individual marker frequencies are known; the case with only the two queried frequencies has a closed form. An exact response identity yields a local query-ranking rule that requires no recipient pairings. At the fitted interaction strength, its mean within-recipient Spearman correlation with exact model discrepancy was 0.939–0.942 across cohorts. In retrospective analyses of 24 Cambridge donors, 56 Newcastle donors, and 15 patients with pediatric T-cell acute lymphoblastic leukemia (T-ALL), covariance-preserving reconstruction retained 91–97% of the improvement from full assay patterns over individual marker frequencies. Recipient-specific coexpression reduced mean deviance by 9.2%, 17.9%, and 46.0% relative to pools of other recipients matched to the same marker frequencies (paired donor-bootstrap 95% intervals, 2.3–15.6%, 12.6–23.0%, and 35.2–55.8%). Those pools contained 14–55 times more cells. The response rule concentrated 85–90% of the observed net improvement into 27 of 81 marker pairs and outperformed ranking by direct source-interaction strength in Newcastle and T-ALL.

Conclusions. Recipient coexpression supports dependence predictions that individual marker frequencies and larger pooled samples do not recover. Reconstructing assay patterns before forming coarse queries preserves this information and identifies relationships that benefit from recipient-specific correction.

A sharp limit at the observed resolution

Let the observed RNA and protein summaries be arbitrary finite collections of within-assay means. They define convex polytopes of complete assay distributions consistent with those summaries. For each pair of assay distributions, matrix scaling gives the unique joint distribution with interaction S and those assay marginals.

The closure of compatible binary query tables is an interval whose endpoints are obtained by minimizing and maximizing the queried joint probability over these polytopes. It is the sharp identified set when all individual marker frequencies are supplied. Complete assay-profile histograms collapse both polytopes to points. Thus the theoretical constraints coincide with the means-only and full-pattern arms of the experiment.

The means-only exponential-family fit selects one member of this set by information projection. The interval records what the supplied frequencies identify without that additional selection. The unique minimax table equalizes the forward Kullback–Leibler loss from the two endpoint tables.

Individual frequencies can all agree

The ambiguity also occurs when every marker's individual frequency is known. Consider two binary RNA markers and one protein marker, coded as Z₁, Z₂, W ∈ {−1, 1}, each with mean zero. Fix the fine interaction to S = JZ₂W, with J ≠ 0. Let the recipient RNA distribution have correlation ρ = E(Z₁Z₂). Reconstruction gives

Changing ρ from negative to positive reverses the queried RNA–protein association without changing J or any individual marker frequency. Separate RNA profiles reveal ρ; their individual frequencies do not. As ρ ranges over its compatible values, the all-marker interval for Pr(Z₁ = 1, W = 1) is [(1 − |tanh J|)/4, (1 + |tanh J|)/4].

How coexpression changes the prediction

For fixed positive assay distributions on finite supports, scale a bilinear interaction as S_t(x, y) = t x^⊤B y, where B is the source interaction matrix and t sets its strength. Let Σ_x and Σ_y be the two within-assay covariance matrices. Near independence, the reconstructed cross-assay covariance satisfies

To first order, each predicted RNA–protein covariance sums source interactions weighted by recipient covariances in both assays. A source coefficient therefore need not equal the marginal association observed in a new population.

This local formula is the initial value of an exact finite-strength identity. If s_t is the score along the fixed-marginal reconstruction, the marginal constraints remove its conditional means and give

The response also predicts which queries are sensitive to replacing recipient coexpression by pooled structure. For a binary query with nonconstant marker frequencies, subtract the queried entries of Σ_xBΣ_y for the recipient and pool, square the difference, and divide by the product of the two marker variances. This is the leading coefficient of twice the KL divergence between their query distributions near independence (Additional file 1). We test whether this score identifies relationships whose empirical prediction improves with recipient-specific reconstruction.

Coexpression prioritizes recipient-specific corrections

The response score concentrated the recipient-specific gain into relatively few relationships. Its top third accounted for 87.0%, 90.1%, and 85.5% of the net deviance reduction in Cambridge, Newcastle, and T-ALL, compared with 85.0%, 60.9%, and 38.5% under direct source-interaction ranking.

In Newcastle, the mean gain per selected pair was 0.00506 under the response score and 0.00342 under direct ranking; the paired difference was 0.00164 (95% interval, 0.00085–0.00256). In T-ALL the gains were 0.02523 and 0.01135, a difference of 0.01388 (0.00906–0.01925). Both contrasts survived the six-comparison adjustment. Cambridge gave similar gains under the two rankings, 0.00168 and 0.00164 (difference, 0.00004; −0.00077 to 0.00085).

In T-ALL, the three highest cohort-mean scores were for CD7 RNA–CD4 protein, CD4 RNA–CD52 protein, and CD7 RNA–CD52 protein; their mean deviance gains were 0.04513, 0.01245, and 0.04981. The original study used CD4 and CD7 to distinguish T-cell populations and included CD52 in a leukemia expression signature. These corrections concern marker combinations associated with the cohort's cellular heterogeneity.

Discussion

The resolution at which a relationship is reported need not be the resolution at which it should be transferred. A binary RNA–protein table depends on the distribution of finer cellular profiles. Reconstructing those profiles before aggregation allowed one source interaction to predict different recipient associations using measurements made separately within each assay.

The pooled controls distinguish recipient-specific coexpression from generic population structure: more observations from other people did not replace the recipient's own assay patterns.