Quantify components of biological systems

Bulk tissues mix cell populations. Autoimmunity and cancer change both composition and state of those populations (Schnell et al. 2020).

Immune balance (schematic)

Complementary schematic of Figure 1:

%%{init: {"theme": "sandstone"}}%%
flowchart TB
  H["Balanced<br/>Regulation ≈ Inflammation<br/>Healthy"]
  U["Under-reaction<br/>Regulation ≫ Inflammation<br/>Cancer risk"]
  O["Over-reaction<br/>Inflammation ≫ Regulation<br/>Autoimmunity"]
  H -->|"imbalance?"| U
  H -->|"imbalance?"| O

Holistic complexity

Genes cooperate in pathways; metabolites and cell populations interact in bio-molecular networks. Deconvolution alone is not enough — we need structure on the gene side as well (Schnell et al. 2020).

Why bulk is limited for biomarkers

Shoemaker et al. (2012): the same bulk fold-change can come from

• Scenario A — activation within an existing cell type
• Scenario B — arrival of a new cell population (Figure 5)

Technical alternatives

Deconvolution recovers cell-type proportions from bulk when single-cell is impractical at scale.

The ecosystem of algorithms

Taxonomy after Shen-Orr & Gannett (2013) and reviews such as Avila Cobos et al. (2018), Gaspard-Boulinc et al. (2025):

• Partial deconvolution — estimate proportions \(p\) given signature \(X\)
• Complete deconvolution — jointly infer \(p\) and \(X\) (ill-posed without priors)

Granularity

Deconvolution targets vary:

• Mixtures of cell populations (e.g. immune fractions)
• Mixtures of tissues (e.g. tumour purity)
• Mixtures of cell-cycle phases

Reference-based principle

1. Purified cellular profiles (signature matrix \(X\))
2. Bulk mixture \(y\)
3. Estimate proportions \(p\) (often with simplex constraints)

Classic tools include DeconRNASeq (Gong and Szustakowski 2013), CIBERSORT (Newman et al. 2015), and EPIC (Racle et al. 2017).

Signature-based families

Compact survey of common reference-based tools (Table 1):

Global pipeline

1. Collect / curate cell-type datasets
2. Learn features & GRN structure
3. DeCovarT estimation of \(p\)
4. Biological exploitation

Multivariate Gaussian convolution

Cell type \(j\): \(x_j \sim \mathcal{N}_G(\mu_j, \Sigma_j)\).

Bulk observation (Equation 1):

\[ y \mid p \;\sim\; \mathcal{N}_G\!\Bigl( \mu p,\; \sum_j p_j^{2}\,\Sigma_j \Bigr). \tag{1}\]

• \(G\): number of genes (dimension of \(y\))
• \(J\): number of cell types; \(p \in \Delta^{J-1}\)
• \(\mu\): \(G \times J\) mean signature; \(\Sigma_j\): gene–gene covariance of type \(j\)

Covariance structure enters the likelihood — gene–gene dependence is first-class, not noise.

Unit-simplex constraint

Proportions live on \(\Delta^{J-1}\). DeCovarT uses an unconstrained map \(\rho \mapsto p\) (additive logistic / soft-max) that is a \(C^{2}\)-diffeomorphism, then optimises with Marquardt–Levenberg.

Toy model (2 cells × 2 genes)

Bivariate convolutions make the geometry visible: entropy of \(p\), overlap of \(\Sigma_j\), and solver behaviour (DeconRNASeq vs DeCovarT). See Figure 10 and Figure 11.

Package vignettes: synthetic scenarios and benchmark_bivariate_gaussian_convolutions().

Sjögren’s disease

Transcriptomic patient clusters and IFN modules motivate composition-aware analysis of immune infiltration (Soret et al. 2021).

DTOO / gastruloid perspectives

Digital twins and multimodal gastruloid maps need deconvolution across bulk, single-cell, and ATAC layers — composition + covariance again.

Spatial deconvolution (outlook)

Emerging toolkits mix (Gaspard-Boulinc et al. 2025):

• Graph / optimal transport pairing of cells to spots
• Bayesian count models (NB, Poisson–gamma, topic models)
• Regression with simplex / robust / ensemble constraints

Perspectives for DeCovarT

• Rare / unknown cell content and spillover
• Multi-omics and spatio-temporal resolution
• Hierarchical ontologies (coarse vs fine labels)
• Compositional statistics on \(p\)

Thanks

Take-away messages

• Bulk mixes cell types; deconvolution recovers proportions \(p\).
• Reference-based methods need a signature \(X\); unsupervised methods need strong priors (Table 1).
• DeCovarT models gene–gene covariance via multivariate Gaussian convolutions (Equation 1).
• Always validate with aliquots (bulk + FACS / scRNA-seq) when possible.