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JAMES LINDSAY1
CAROLINE JAKUBA2
ION MANDOIU1
CRAIG NELSON2
Gene Expression 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
Neura
l 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
gen
es
cell typesg
ene
smixtures
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
�̂�
�̂�
Step 1: Outlier Removal + Clustering
unfiltered filtered
Remove cells that have maximum Pearson correlation to other cells below .95
Step 2: Estimate Mixture Proportions
min (‖�̂�𝑐−𝑥‖¿¿2) ,𝑠 . 𝑡 .{ ∑𝑐=1𝑐 𝑙≥0 ∀ 𝑙=0…𝑘
¿
𝑐=𝐶𝑙 ,𝑖 ∀ 𝑙=1…𝑘
𝑥=𝑋 𝑗 , 𝑖∀ 𝑗=1…𝑚
For a given mixture i:
Step 3: Estimating Full Expression Signatures
s: new gene to estimate signatures
mixtures
gen
es
cell types
gen
es
mixtures
cell
type
s
min (‖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
Actual Mixtures• 12 mixtures• 31 genes
Dimensions• k = 3• m = 31• n = 92, 12• # mixtures = {10…
300}
Data Processing
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
predicted
Leave-one-out Accuracy of Inferred Gene Expression Signatures
Future Work
• Apply gene signature estimation technique using more genes in mixed samples
• Identify PSM-Pr Signature• Confirm the anatomical location of the putative PSM-
Pr cell population through exhaustive ISH
Conclusion
Special Thanks to:• Ion Mandoiu• Craig Nelson• Caroline Jakuba• Mathew Gajdosik