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Single-cell mRNA quantification and differential analysis with Census

Last update: 05/01/2020
By: Huitian (Yolanda) Diao

Information

| ~ | Description | | — | — | | Objective | Convert TPM to relative transcript counts without spike-in standards or UMIs for differential analysis | | Environment | R | | Dependency | Monocole2 | | Development release | Github |

Algorithm

1. Cell lysate recovery

• Y_ij^l ≈ α_iY_ij^C
  
• S_ij^l ≈ β_iS_ij

Variable	Symbol
Gene	j
Cell	i
Recovery rate of RNA	α
Recovery rate of spike-in	β
Total RNA	YC
Total Spike in	S
Lysate RNA	Yl
Lysate Spike in	Sl

2. cDNA conversion

• Y_ij^d ≈ Y_ij^l * θ_i
  
• S_ij^d ≈ S_ij^l * θ_i
  

Variable	Symbol
Capture rate	θ
Endo cDNA	Yd
Spike in cDNA	*Sd*

3. Relative abundance

• cDNA: Y_ij^d / Σ_j=1ⁿ (Y_ij^d + S_ij^d )
• Spike in: S_ij^d / Σ_j=1ⁿ (Y_ij^d + S_ij^d )

4. Multinomial sampling of R reads

• R_i = γ Σ_j=1ⁿ (Y_ij^d + S_ij^d)

Variable	Symbol
Average reads per cDNA	γ

5. Read count

• cDNA: Y_ij^r ~ multinomial (Relative cDNA abundance, Multinomial sampling of cDNA)
• Spike in: Y_ij^r ~ multinomial (Relative spike in abundance, Multinomial sampling of spike in)

6. Simulator for sc-RNA-seq process

7. Estimate capture rate based on spike-in

Probability to observe at least one copy of transcript: ρ = 1 - (1 - θ)^S

Variable	Symbol
Copy number	S

…

Objective

Use a assumed value of θ to convert TPM X_ij^l to real transcript number (Y_ij^l ) with a Gaussian kernel density estimation to identify peak of distribution (with capturing probability distribution from 7.)