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One pool, many targets: a conservation layer and what archival data can identify

Zahra Khodagholi, Niloofar Yousefi

arXiv:2610.00445v1cs.LG

TL;DR

Independent guide–transcript scores do not enforce conservation of a finite guide-loaded RISC pool. The paper formulates a differentiable equilibrium layer and audits archival data; those data do not establish added predictive value from coupling or identify the competition parameter.

  • Problem

    Pairwise guide–transcript scoring leaves the finite shared loaded-RISC budget unenforced, despite cellular competition for Argonaute and effects of target abundance.

    Source: §1 · p. 1

  • Method

    The paper replaces independent occupancies with a scalar conservation layer that solves for the free loaded pool and differentiates through the equilibrium solution.

    Source: §2 · p. 2

  • Results

    The paired permutation analysis does not establish added predictive value from coupling, and heterogeneous dose fits do not identify ρ.

    Source: §5 · p. 4, §6 · p. 5

  • Takeaways & Limitations

    Within-construct fixed-dose fractional-occupancy ranks cannot distinguish the two scoring approaches, so that class of rank test cannot detect coupling under the stated model.

    Source: §2.2 · p. 3, §7 · p. 5

    A decisive test needs more doses, constructs that are not variants of one another, and a better K; the proposed learned affinity head is not evaluated here.

    Source: §7 · pp. 5–6

Abstract

from arXiv · show

Pairwise guide--transcript scores do not enforce conservation of a finite guide-loaded RISC pool when they are interpreted independently as occupancies. We formulate a differentiable scalar equilibrium layer: one conservation equation with a unique positive root and exact implicit gradients. It yields a redistribution theorem, a qualified high-resource limit, an analysis of the retrieval approximation, and a conditional rank-invariance result: within one construct at one dose, rankings by fractional occupancy cannot distinguish equilibrium from independent scoring. We therefore audit the two experiments that proposition leaves open, dose and cross-context, on archival off-target data. Corrected thermodynamic affinities associate weakly with measured repression in the direction a working predictor requires, but a paired permutation test and a construct-cluster bootstrap do not establish added predictive value from the coupling: what survives their differing permutation-null baselines is \GapNet{}, a descriptive \GapNetOverSE{} of the equilibrium association's cluster standard error. The dose fits are heterogeneous and frequently violate the model-implied exponent constraint, which is superlinear rather than sublinear, so these data do not identify the competition parameter. A saturable compression of the competitor set holds both accuracy targets on held-out guide families but is not faster at the size measured. The contribution is a reusable conservation operator and the experimental information needed to test it. The code for this study is available at https://github.com/shadi97kh/One-Pool-Many-Targets.

1 Introduction

Pairwise sequence models score guide–transcript interactions independently, while cells have a finite guide-loaded RISC pool and target abundance affects activity. This paper develops a structural conservation operator and audits what archival data can identify.

1 Introduction

  • Sequence-based design tools score each guide–transcript pair independently, leaving the shared loaded-RISC budget unenforced [Huesken et al., 2005, Bai et al., 2024].Transfected siRNAs can also silence unintended transcripts through their seed [Jackson et al., 2003, Birmingham et al., 2006, Jackson et al., 2006].Source: §1 · p. 1
  • Argonaute is limited, transfected small RNAs compete with endogenous microRNAs, and target abundance dilutes activity [Wang et al., 2012, Janas et al., 2012, Khan et al., 2009, Arvey et al., 2010, Bosson et al., 2014, Denzler et al., 2014, 2016].The model isolates competition among target sites for a pool already loaded with the candidate guide; other processes enter through M.Source: §1 · p. 1
  • The contribution is a mostly structural operator, its comparative statics, and an audit of what archival data can identify, alongside existing quantitative competition and repression models [Loinger et al., 2012, Riba et al., 2017].Source: §1 · p. 1

2 A shared-resource equilibrium layer

The layer allocates a finite guide-loaded pool across retrieved transcripts by solving a scalar conservation equation. Its implications include redistribution and a qualified high-resource limit, while retrieval compression and fixed-dose rank tests have specific constraints.

2 A shared-resource equilibrium layer

  • The equilibrium layer solves for free loaded pool f from conservation over retrieved transcripts, with a unique root bracketed by [0, M] and gradients from the implicit function theorem.For the omitted set, β represents a linear, unsaturated reservoir; each transcript's sites are combined as mutually exclusive, with at most one complex per transcript.Source: §2 · p. 2

2.1 What the layer implies

  • Weakening one transcript's affinity frees pool for every other transcript, while the fractional-occupancy gap is O(M^-2) as M grows when β = 0.Under the stated conditions, equilibrium contains independent scoring as its high-resource limit.Source: §2.1 · pp. 2–3

2.2 Compressing the competitor set

  • The compression test compares discarding omitted transcripts, a linear reservoir, and 100 saturable groups at R = 100, after fixing configuration on eight guide families and testing 54 cases from seven disjoint families.The linear reservoir has constant slope in f and therefore misrepresents the derivative once omitted mass saturates; the compressed system's residual alone does not establish accuracy against the original conservation law.Source: §2.2 · p. 3, Figure 2 · p. 3
  • Only saturable bins meet both compression accuracy targets on held-out guide families, but the method is slower than the full reference at the measured size.At R = 100, worst gradient error is 0.0047 for saturable bins, versus 1.00 for discarding and 1.8 × 10^4 for a linear reservoir; forward times are 15.3 ms and 7.3 ms, respectively.Source: §2.2 · p. 3, Figure 2 · p. 3
  • The rank-invariance result disqualifies within-construct fixed-dose fractional-occupancy rank tests as a way to detect coupling; the layer can reorder only across constructs, doses, or transcriptomes.Source: §2.2 · pp. 3–4
  • Within one construct at one dose, fractional-occupancy rankings are identical under equilibrium and independent scoring because both are strictly decreasing in K_j.This result assumes one effective binding state per transcript and does not cover absolute occupancy or simultaneously occupiable sites.Source: §2.2 · p. 3

3 Data

The study uses archival off-target microarrays and derives abundance and thermodynamic affinity inputs from experiment-matched controls and transcript sequences. No new measurements are made.

3 Data

  • Four archival accessions provide off-target data, including a dose series and a cross-context study, with D1 and D2 supplying most of the guide-family split.D1 has 24 scored constructs; D2 has 12 guides and shares no exact guides or seeds (positions 2–8) with D1; D3 measures constructs at multiple doses; D4 covers two liver lines.Source: §3 · p. 4
  • Transcript abundance comes from control measurements in the same experiment as the response, while affinity is a ViennaRNA-based thermodynamic quantity anchored on measured seed-match K_d values.The affinity construction combines duplex energy with the cost of opening the site; K is not fitted to expression.Source: §3 · p. 4

4 Where a real transfected cell sits

The estimated cellular competition parameter depends on an unmeasured loaded fraction and literature-based copy-number assumptions, so these datasets do not determine where real transfected cells fall in the scenario range.

4 Where a real transfected cell sits

  • The literature-based scenario range for ρ_cell is [1.9 × 10^-4, 2.1], and the contour below which τ < 0.9 lies at ρ ≈ 0.044.The range sweeps the unmeasured loaded fraction α over three decades and spans a further decade in Argonaute copy-number figures; the mRNA count was not measured on these arrays.Source: §4 · p. 4

5 What the affinity scores predict

Thermodynamic affinities associate weakly with measured repression in the required direction, but the analysis does not establish that coupling improves prediction. The per-dose affinity scores order transcripts only coarsely.

5 What the affinity scores predict

  • At ρ = 0.100, equilibrium scores -0.0746 versus -0.0530 for independent scoring, a weak association in the required direction.Both scores are 11.5 to 10.5 standard deviations from their respective permutation nulls.Source: §5 · p. 4
  • At ρ = 0.100, the raw gap (-0.0216) is below the paired-null gap (-0.0242); 0.0026 survives, or 0.22 of the equilibrium association’s cluster standard error.The analysis does not establish that coupling improves prediction.Source: §5 · p. 4
  • Per dose, correlation is at most 0.079 in absolute value, so this K orders transcripts only coarsely.The affinity also misses the t1-pocket contribution associated with stronger repression of 7mer-A1 than 7mer-m8 sites.Source: §5 · p. 4

6 A dose-series identifiability audit

The dose-series audit does not identify the competition parameter: fitted exponents vary across estimators and constructs, and the model-implied bound depends on proportional loading.

6 A dose-series identifiability audit

  • The audit fits one pool per dose with affinity fixed, assuming guide-specific loaded pool is proportional to administered dose; constant-duplex dosing makes this plausible but does not establish it.Four constructs have measurements at 1, 10, and 25 nM; a fifth has 1 and 10 nM, each against matched 0 nM arrays.Source: §6 · p. 5
  • Conservation implies an exponent of at least 1 for loaded pool against loaded amount; the same bound applies against dose only under proportional loading.Thus an exponent below 1 challenges the combined equilibrium-and-loading specification, not equilibrium alone.Source: §6 · p. 5
  • The thermodynamic-K pooled exponent is 1.02 (95% CI [-0.15, 1.81]), with 3 of 5 per-construct exponents negative.Those negative exponents conflict with the fixed-input model when loaded pool is nondecreasing in dose.Source: §6 · p. 5
  • The dose audit does not identify ρ: site-class estimates vary widely under leave-one-construct-out checks, and 3 of 5 construct intervals lie below 1.Four of five intervals also exclude the assumed unit slope for loaded pool per dose; unconstrained per-dose pools beat proportional pools on AIC and held-out genes in all five constructs.Source: §6 · p. 5

7 Limitations and conclusion

The paper concludes that fixed-dose fractional-occupancy ranks cannot test coupling under its one-effective-K model, while archival dose and cross-context data leave key effects unresolved. Its pipeline combines matched archival measurements and computed affinities in a differentiable shared-pool model.

7 Limitations and conclusion

  • Within-construct fixed-dose fractional-occupancy rank statistics cannot detect coupling under the one-effective-K model; archival data show weak association, no established added predictive value, and dose fits too heterogeneous to identify ρ.The proposed decisive experiment needs more doses, non-variant constructs, and a better K.Source: §7 · p. 5
  • A learned, strictly positive affinity head trained through the conservation equation and evaluated on held-out guides and cell lines is proposed but not evaluated.The proposed comparison tests the head with and without the layer.Source: §7 · p. 6

A Pipeline overview

  • The pipeline pairs same-experiment control abundances with ViennaRNA-derived affinities, then applies a conservation equation with a unique root and exact implicit gradients.At fixed construct and dose, rank invariance blocks the comparison; dose and transcriptomic-context comparisons remain open, while proportional intracellular loading is an assumption.Source: A Pipeline overview · p. 8, Figure 4 · p. 8

B Code and data availability

The study’s datasets are archival and public, and its code and result-generation materials are described as traceable to their sources. The released materials also include an unreported held-out test of a site-class affinity correction.

B Code and data availability

  • The equilibrium layer, acquisition scripts, per-experiment result files, and figure code are slated for public release after review, with printed numbers mechanically traceable to result files.Retrieved bytes carry provenance records including URL, checksum, and retrieval status.Source: B Code and data availability · p. 8
  • All datasets used are archival and already public under their cited accessions..Source: B Code and data availability · p. 9
  • Released materials include a held-out external-family test of a site-class correction to K; it reduced performance and is not reported in the paper..Source: B Code and data availability · p. 9

C Proofs

The proofs establish monotone redistribution when one transcript’s affinity is weakened and validate the implicit gradients against central differences. They also report the measured high-resource gap decay and caution that retrieval compression is not necessarily faster.

C Proofs

  • The measured relative gap between the two scorings decays with exponent −2.00 ± 0.002, matching the predicted −2 over 9 decades.Source: Figure 7 · p. 10
  • The worst gradient error measured against the gradient norm is 2.3 × 10−7.Across 35 coordinates, median relative disagreement with central differences is 2.3 × 10−9; the worst relative disagreement is 1.6 × 10−4 on a near-zero gradient coordinate.Source: C Proofs · pp. 9–10
  • Raising one transcript’s Kt raises the free pool and every other transcript’s occupancy, while lowering the swept transcript’s occupancy.The proof assumes M > 0, xj ≥ 0, Kj > 0 and β ≥ 0, under which the root is unique.Source: C Proofs · p. 10

D Binned background at shallow retrieval

  • At R = 25, restoring 1% accuracy requires 125 scored terms under either binning rule, versus 501 at untruncated R = 500, but compression is slower at this size.The passage cautions that fewer terms do not imply a speed-up.Source: D Binned background at shallow retrieval · p. 10

E Compressed solve: selection, gradients and timing

The compressed-solve configuration was selected on development families and then evaluated on disjoint held-out families. The supplied results describe the gradient checks and workload-specific timing, while Table 1 specifies the occupancy-error comparison being measured.

E Compressed solve: selection, gradients and timing

  • The frozen configuration was selected on 8 guide families and applied unchanged to 7 disjoint families, covering 54 cases.The families, not the cases, are the independent units.Source: E Compressed solve: selection,… · pp. 10–11
  • Table 1 reports maximum relative on-target occupancy error against the full 952-transcript reference across ρ values, comparing the linear rule with saturable-bin counts.The B = 1 saturable bin is distinct from the no-bin linear rule.Source: Table 1 · p. 11
  • Central-difference checks covered 17 coordinates, including omitted competitors; the worst relative error was 0.0433, or 0.00144 among 13 coordinates with analytic gradients above 10−9.Both error figures are reported because neither replaces the other.Source: E Compressed solve: selection,… · p. 11
  • The timing comparison used 4,919 competitors and matched outputs; adding a reduction pass made the linear and binned backgrounds unable to beat the full solve on this workload.With preparation charged to both sides, truncation was cheaper from the first solve, while the binned configuration never broke even.Source: E Compressed solve: selection,… · p. 11

F The site-class hierarchy is not the canonical one

The site-class data reverse the expected ordering of the two 7mer classes, while the archival tests do not establish added predictive value from coupling. The dose and cross-context analyses expose important assumptions and limits on what these data can identify.

F The site-class hierarchy is not the canonical one

  • 7mer-A1 is more repressed than 7mer-m8 by 0.00305 under strongest-class assignment and by 0.00280 under lowest-∆Geff assignment.The exchange appears in 16 of 24 constructs under the first rule and 17 of 24 under the alternative; the authors link it to the t1-adenosine pocket, which duplex-pairing-only energies omit.Source: F The site-class hierarchy is not the… · pp. 11–12

G How the association is tested

  • No evaluated ρ meets the requirement that the null-centred predictive gap reach one construct-cluster standard error of the equilibrium association.At ρ = 0.100, the cluster interval on the raw gap excludes zero, but the null-centred difference is 0.0026; the raw-gap interval is not the quantity used for the claim.Source: G How the association is tested · p. 13

H Estimator validation; I The dose likelihood as implemented

  • The site-class estimator recovers the expected ordering in 5 of 5 constructs, while dose fitting identifies the absolute pool through curvature under a shared-amplitude assumption.Simulations recover parameters under the assumed generative models but do not rule out misspecification, confounding, or weak identifiability in archival data.Source: H Estimator validation · p. 13, I The dose likelihood as implemented · p. 14

J Why the pool exponent in M cannot fall below one

  • Under proportional loading, equilibrium predicts a free-pool exponent against dose of at least 1, versus exactly 1 for independent scoring.A measured exponent below 1 diagnoses failure of at least one element of the combined specification, not equilibrium alone.Source: J Why the pool exponent in M cannot… · p. 14

K Approach to the independent limit

  • Over 9 transcriptome decades, the median-transcript slope is −2.00 ± 0.002, while worst-transcript and aggregate-load slopes are −1.00 ± 0.001 and −0.99 ± 0.00.The pointwise fractional-occupancy gap is O(M^-2) asymptotically for β = 0, but worst-transcript and aggregate-load errors decay only as O(M^-1) over practical ranges.Source: K Approach to the independent limit · pp. 14–15

L The cross-context test (exploratory)

  • The exploratory HUH7-to-PLC/PRF/5 fitted-pool ratio is 0.44, but circular seed recovery, outcome-based selection, and unverified equal loading prevent a conclusion.Only 3 of 7 constructs survive exact agreement between the two seed recoveries.Source: L The cross-context test (exploratory) · p. 16

M The affinity scale; N Standing assumptions

  • The affinity calibration fixes a common scale rather than an absolute biochemical scale, and one-state, static-equilibrium, and fixed-abundance assumptions remain possible explanations for weak affinity performance.Within-construct rank statistics are invariant to rescaling every K_j, but pooled statistics and ρ are not exactly invariant.Source: M The affinity scale · p. 16, N Standing assumptions · p. 16

O Further limitations

The dose and cross-context analyses have limited identifying power because key assumptions and measurements remain uncertain. The archival datasets also required guide-sequence recovery and other data-specific processing.

O Further limitations

  • The dose-series lines differ between the STAT3 and HK2 arms, and three dose points per construct—two for one—leave per-construct exponents wide.The bootstrap resamples transcripts rather than doses, so it does not represent uncertainty about the dose grid; proportional loading and equal total loaded complex across contexts are also unverified.Source: O Further limitations · pp. 16–17

P Datasets and what had to be recovered

  • Guide sequences were absent from two archival deposits, requiring recovery from other sources or response data, and one GSE28786 construct's conflicting dose labels were resolved using its on-target measurement.The archives also use platform-specific expression summaries, including two-colour log ratios and single-channel RMA summaries.Source: P Datasets and what had to be recovered · p. 17
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