JAMES LINDSAY1

ION MANDOIU1

CRAIG NELSON2

Towards Whole-Transcriptome

Deconvolution with Single-cell Data

UNIVERSITY OF CONNECTICUT1DEPARTMENT OF COMPUTER SCIENCE AND

ENGINEERING2DEPARTMENT OF MOLECULAR AND CELL BIOLOGY

Mouse Embryo

Somites

POSTERIOR / TAIL

ANTERIOR / HEAD

Node

Neural

tube

Primitive streak

Unknown Mesoderm Progenitor

• What is the expression profile of the progenitor cell type?

NSB=node-streak border; PSM=presomitic mesoderm; S=somite; NT=neural tube/neurectoderm; EN=endoderm

Characterizing Cell-types

• Goal: Whole transcriptome expression profiles of individual cell-types

• Technically challenging to measure whole transcriptome expression from single-cells

• Approach: Computational Deconvolution of cell mixtures• Assisted by single-cell qPCR

expression data for a small number of genes

Modeling Cell Mixtures

Mixtures (X) are a linear combination of signature matrix (S) and concentration matrix (C)

𝑋𝑚𝑥𝑛=𝑆𝑚𝑥𝑘∙𝐶𝑘𝑥𝑛

mixtures

gene

s

cell typesge

nes

mixtures

cell

type

s

Previous Work

1. Coupled Deconvolution• Given: X, Infer: S, C

• NMF Repsilber, BMC Bioinformatics, 2010• Minimum polytope Schwartz, BMC Bioinformatics, 2010

2. Estimation of Mixing Proportions• Given: X, S Infer: C

• Quadratic Prog Gong, PLoS One, 2012• LDA Qiao, PLoS Comp Bio, 2o12

3. Estimation of Expression Signatures• Given: X, C Infer: S

• csSAM Shen-Orr, Nature Brief Com, 2010

Single-cell Assisted Deconvolution

Given: X and single-cells qPCR data Infer: S, C Approach:1. Identify cell-types and estimate reduced

signature matrix using single-cells qPCR data

• Outlier removal • K-means clustering followed by averaging

2. Estimate mixing proportions C using • Quadratic programming, 1 mixture at a time

3. Estimate full expression signature matrix S using C

• Quadratic programming , 1 gene at a time

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Step 1: Outlier Removal + Clustering

unfiltered filtered

Remove cells that have maximum Pearson correlation to other cells below .95

Step 1: PCA of Clustering

Step 2: Estimate Mixture Proportions

min (‖�̂�𝑐−𝑥‖¿¿2) ,𝑠 . 𝑡 .{ ∑𝑐=1𝑐 𝑙≥0 ∀ 𝑙=0…𝑘

¿

𝑐=𝐶𝑙 ,𝑖 ∀ 𝑙=1…𝑘𝑥=𝑋 𝑗 , 𝑖∀ 𝑗=1…𝑚

For a given mixture i:

Reduced signature matrix.Centroid of k-means clusters

Step 3: Estimating Full Expression Signatures

s: new gene to estimate signatures

mixtures

gene

s

cell types

gene

s

mixtures

cell

type

smin (‖𝑠𝐶−𝑥‖¿¿2)¿Now solve:

C: known from step 2x: observed signals from new gene

Experimental Design

Simulated Concentrations• Sample uniformly at

random [0,1]• Scale column sum to 1.

Simulated Mixtures• Choose single-cells

randomly with replacement from each cluster

• Sum to generate mixture

Single Cell Profiles• 92 profiles• 31 genes

Data: RT-qPCR

• CT values are the cycle in which gene was detected

• Relative Normalization to house-keeping genes

• HouseKeeping genes • gapdh, bactin1• geometric mean• Vandesompele, 2002

• dCT(x) = geometric mean – CT(x)• expression(x) = 2^dCT(x)

Accuracy of Inferred Mixing Proportions

Concentration Matrix: Concordance

Concentration by # Genes: Random

Concentration by # Genes: Ranked

Leave-one-out: Concentration: 50 mixR

MSE

2^dC

T

Missing Gene

Leave-one-out: Signature: 10 mixR

MSE

2^dC

T

Missing Gene

Leave-one-out: Signature: 50 mixR

MSE

2^dC

T

Missing Gene

Future Work

• Bootstrapping to report a confidence interval of each estimated concentration and signature• Show correlation between large CI and poor accuracy

• Mixing of heterogeneous technologies• qPCR for single-cells, RNA-seq for mixtures• Normalization (need to be linear)

• Whole-genome scale• # genes to estimate 10,000+ signatures• Data!

Conclusion

Special Thanks to:• Ion Mandoiu• Craig Nelson• Caroline Jakuba• Mathew Gajdosik

James.Lindsay@engr.uconn.edu