The identifiability boundary of composition attribution in bulk transcriptomics: a methodological study

Bulk transcriptomic differences between groups reflect both altered cell composition and altered expression within cells. Methods such as csSAM, TOAST and CIBERSORTx separate the two, but all require additional information: measured per-sample proportions, anchor genes, or an external reference. We examine what can be established under a pure-bulk paired design in which none of this information is available. We formalise the decomposition obs = comp + resid and test three propositions: whether resid can be interpreted as within-cell regulation; how closely comp tracks obs, and what that agreement depends on; and whether the number of cell compartments is a well-defined model-complexity variable. Data comprise four abdominal aortic aneurysm cohorts, one lung cohort and the HLCA normal lung atlas (584,944 cells × 27,402 genes). Deconvolution uses a self-implemented Lawson–Hanson non-negative least squares validated on three problems with known answers. comp + resid = obs is an algebraic identity (same-source R² = 1.000000000000000). resid cannot be interpreted as within-cell regulation: apart from a degenerate case, the control cell-type-specific profile is not point-identifiable, and swapping reference profiles in a zero-regulation construction drives resid to −5.4654. Pearson r between comp and obs is 0.7335 (0.7001–0.8041) under platform-matched pseudo-bulk conditions, 0.2379–0.3791 across four aorta cohorts, and 0.1675–0.3019 for lung UIP/IPF; regression slopes are 0.078–0.801. A fully crossed 3 × 3 design with four aggregation weights shows that with six reference compartments r ranges from 0.2674 to 0.8417 (SD 0.239) and is not identifiable. comp is an approximate index of compositional change; resid carries no inferable information about within-cell regulation; and the number of compartments is not a well-defined model-complexity variable. --- 群体间 bulk 转录组差异同时反映细胞组成的改变与细胞内表达的改变。csSAM、TOAST、CIBERSORTx 等方法可将两者分开,但都需要额外信息:测得的逐样本比例、锚定基因,或外部参考。本文考察在上述信息全部不可得的纯 bulk 配对设计下,这一归因能做到什么程度、边界在哪里。我们形式化分解 obs = comp + resid,并检验三个命题:resid 能否解释为细胞内调控;comp 与 obs 的一致性能达到多少、依赖什么;以及「细胞区室数」是否为良定义的模型复杂度变量。数据包括四个腹主动脉瘤队列、一个肺队列,以及 HLCA 正常肺图谱(584,944 细胞 × 27,402 基因)。解卷积用自实现的 Lawson–Hanson 非负最小二乘,在三个已知答案问题上验证。comp + resid = obs 是代数恒等式(同源 R² = 1.000000000000000)。resid 不能解释为细胞内调控:除退化情形外,对照组细胞类型特异谱不可点识别;在零调控构造中对调参考谱可使 resid 达到 −5.4654。comp 与 obs 的 Pearson r:平台匹配伪 bulk 为 0.7335(0.7001–0.8041);主动脉四队列 0.2379–0.3791;肺 UIP/IPF 0.1675–0.3019。回归斜率 0.078–0.801。完全交叉的 3 × 3 设计配合四种聚合权重显示:参考区室数为 6 时 r 在 0.2674–0.8417 间摆动(SD 0.239),不可识别。comp 可作为组成变化的近似指标;resid 不承载可推断的细胞内调控信息;区室数不是良定义的模型复杂度变量。 --- This record contains the English and the Chinese version of the manuscript, both as PDF and as editable source, together with the companion manuscript on six failure modes (files 03 and 04). This is a preprint. It has not been peer reviewed.