CK BioC 2017
Statistical methods for single-cell RNA sequencing data
Department of Biostatistics and Medical InformaticsUniversity of Wisconsin-Madison
http://www.biostat.wisc.edu/~kendzior/
CK BioC 2017
Single-cell vs. bulk RNA-seq
Heterogeneous Homogeneous Sub-population
CK BioC 2017
Features of single-cell RNA-seq data
§ Abundance of zeros, increased variability, complex distributions
Bacher and Kendziorski, Genome Biology, 2016.Log (variance) Number of clusters
Prop
ortio
n of
zer
osD
ensi
ty
Expression Group
Cou
nt
CK BioC 2017
§ Normalization
§ Technical vs. biological zeros
§ Clustering; Identifying sub-populations
§ De-noising
§ Adjusting for technical variability
§ Adjusting for biological variability (oscillatory genes)
§ Identifying and characterizing differences in gene-specific expression distributions (aka. identifying differential distributions)
§ Pseudotime reordering
§ Network reconstruction
Challenges in scRNA-seq
CK BioC 2017
§ Normalization
§ Technical vs. biological zeros
§ Clustering; Identifying sub-populations
§ De-noising
§ Adjusting for technical variability
§ Adjusting for biological variability (oscillatory genes)
§ Identifying and characterizing differences in gene-specific expression distributions (aka. identifying differential distributions)
§ Pseudotime reordering
§ Network reconstruction
Challenges in scRNA-seq
CK BioC 2017
Variability induced by oscillatory genes is substantialin single-cell RNA-seq and can mask effects of interest
We developed an approach called Oscope to identify and characterize oscillations in single-cell RNA-seq experiments
CK BioC 2017
Oscope identifies oscillatory genes in unsynchronized single-cell RNA-seq experiments
Leng et al., Nature Methods, 2015
CK BioC 2017
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Oscope'(Oscilloscope):'A'sta0s0cal'pipeline'for'iden0fying'oscillatory'gene'sets'
Module'1:'Screening'for'candidate'oscillators'(Paired<sine'model)'
Module'3:'Recover'cell'order'within'cluster'(Extended'Nearest'Inser0on)'
Module'2:'Cluster'candidate'genes'into'clusters'(K'<'medoids'Algorithm)'
Top'genes'pairs'G1<G2'G3<G2'G1<G3'
G1'
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G3'
Recovered'order'
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Scaled
'expression'
Oscope: Identify and characterize oscillatory genes in an scRNA-seq experiment
Step 1: Paired-sine model identifies candidate oscillators
Step 2: Residuals from paired-sine model are used in clustering to group genes with similar frequency, varying phase
Step 3: Extension of the nearest insertion algorithm reconstructs one base cycle for every group
CK BioC 2017
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Oscope: Identifying oscillatory genes using scRNA-seq
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gene 1gene 2−0.5
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−1.0
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1.0Scaled_Expression
cell1
cell3
cell4
cell2
...
......
gene1
gene2
Cyclic order
Base cycle Base cycle
CK BioC 2017
§ Given a list of cities, only know distances between each pair of cities
Distance (mile)
Madison-Chicago 148
Madison-Iowa City 175
Madison-Atlanta 847
Madison-Minneapolis 273
Chicago-Iowa City 223
Chicago-Atlanta 716
… …
§ In our case, for each gene cluster, we want to find an optimal “route” through all cells and return to the first cell
§ The optimal route will minimize expression differences between observed and baseline oscillation−1.0
−0.5
0.0
0.5
1.0Scaled_Expression
cell1
cell3
cell4
cell2
...
...
...
gene1
gene2
§ Goal is to find an optimal route that visits each city exactly once and returns to the origin city
§ The optimal route will minimize overall distance travelled
Oscope: Connection to TSP
CK BioC 2017
§ Whitfield data: microarray time course of HeLa cells synchronized for cell cycle. 48 samples; one every hour (~3 cell cycles).
§ Applied Oscope on Whitfield data with permuted sample order
− Top cluster has 69 genes (65 of 69 validated as oscillating in Whitfield).
Oscope: Results from Whitfield data
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xpre
ssio
n
ENI Reconstructed Order0 10 20 30 40 50
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CK BioC 2017
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30,000
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ENI Reconstructed Order
Oscope: Results from H1 hESCs (with Thomson lab)
§ Oscope applied to 213 H1 hESCs identified a 29 gene group − 21 of 29 genes annotated as cell-cycle by GO.
§ To investigate this group, Oscope was reapplied to 460 H1 hESCs− 213 unlabeled and 247 FUCCI labeled (cell cycle phase is known).
G1G2/M
S
Cells are characterized as G1, S, G2/M
CC phase assignment is masked and Oscope is applied to the 29 genes
An accurate reconstructed order will clearly separate the three CC phases
CK BioC 2017
Oscope identifies potential artifact in Fluidigm C1 platform
ID
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01000
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0200500
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RPL13
0 50 100 150 200
01000
2500
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EIF3F
02000
5000
●
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FTH1
CK BioC 2017
Schematic of Fluidigm’s C1 platform
!
C48C47C46C45C44C43C42C41C40C39C38C37C36C35C34C33C32C31C30C29C28C27C26C25C24C23C22C21C20C19C18C17C16C15C14C13C12C11C10C09C08C07C06C05C04C03C02C01
C96C95C94C93C92C91C90C89C88C87C86C85C84C83C82C81C80C79C78C77C76C75C74C73C72C71C70C69C68C67C66C65C64C63C62C61C60C59C58C57C56C55C54C53C52C51C50C49
(P93)(P92)(P91)(P87)(P86)(P85)(P81)(P80)(P79)(P75)(P74)(P73)(P69)(P68)(P67)(P63)(P62)(P61)(P57)(P56)(P55)(P51)(P50)(P49)(P43)(P44)(P45)(P37)(P38)(P39)(P31)(P32)(P33)(P25)(P26)(P27)(P19)(P20)(P21)(P13)(P14)(P15)(P07)(P08)(P09)(P01)(P02)(P03)
(P94)(P95)(P96)(P88)(P89)(P90)(P82)(P83)(P84)(P76)(P77)(P78)(P70)(P71)(P72)(P64)(P65)(P66)(P58)(P59)(P60)(P52)(P53)(P54)(P48)(P47)(P46)(P42)(P41)(P40)(P36)(P35)(P34)(P30)(P29)(P28)(P24)(P23)(P22)(P18)(P17)(P16)(P12)(P11)(P10)(P06)(P05)(P04)
C46
C43
C40
C37
C34
C31
C28
C25
C24
C21
C18
C15
C12
C09
C06
C03
C47
C44
C41
C38
C35
C32
C29
C26
C23
C20
C17
C14
C11
C08
C05
C02
C48
C45
C42
C39
C36
C33
C30
C27
C22
C19
C16
C13
C10
C07
C04
C01
C96
C93
C90
C87
C84
C81
C78
C75
C70
C67
C64
C61
C58
C55
C52
C49
C95
C92
C89
C86
C83
C80
C77
C74
C71
C68
C65
C62
C59
C56
C53
C50
C94
C91
C88
C85
C82
C79
C76
C73
C72
C69
C66
C63
C60
C57
C54
C51
(P91)
(P85)
(P79)
(P73)
(P67)
(P61)
(P55)
(P49)
(P43)
(P37)
(P31)
(P25)
(P19)
(P13)
(P07)
(P01)
(P92)
(P86)
(P80)
(P74)
(P68)
(P62)
(P56)
(P50)
(P44)
(P38)
(P32)
(P26)
(P20)
(P14)
(P08)
(P02)
(P93)
(P87)
(P81)
(P75)
(P69)
(P63)
(P57)
(P51)
(P45)
(P39)
(P33)
(P27)
(P21)
(P15)
(P09)
(P03)
(P94)
(P88)
(P82)
(P76)
(P70)
(P64)
(P58)
(P52)
(P46)
(P40)
(P34)
(P28)
(P22)
(P16)
(P10)
(P04)
(P95)
(P89)
(P83)
(P77)
(P71)
(P65)
(P59)
(P53)
(P47)
(P41)
(P35)
(P29)
(P23)
(P17)
(P11)
(P05)
(P96)
(P90)
(P84)
(P78)
(P72)
(P66)
(P60)
(P54)
(P48)
(P42)
(P36)
(P30)
(P24)
(P18)
(P12)
(P06)
(e)
(c)
(d)
(a)
(b)
ID
qPC
R F
C0.
01.
02.
0
0 50 100 150 200
!!!!!!!!!!!!!!!!!!!
!!!!!
!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!
!!!!!!
!
!
!!!!!
!!!
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!!!!
!!
!
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MIF0.0
1.0
2.0
!
!
!!!!!!
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!!!!!!!!
!!
!!
!!!
!
!!
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!!
!
!!!
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!!!!
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!
PFN1
ID
FPKM
0100
300
0 100 200 300
!
!!
!!!
!!
!
!
!
!!
!
!
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!
!!!!!!!!!!!!
!
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COX5A
010002500
!
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RPL13
0100250
!
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MIF
0400800
!
!
!
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!!!!
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!
!!!
!!!
!
!!!!!!!!!!!!!!
!
!!!!!!!!!!!!!!!!!!!!!!!
!
!!!!
!
!!!!!!!!!!!
!
!!!!!!!!
PFN1
ID
FPKM
0100
300
0 20 40 60 80 100
!
!
!!!
!
!!
!
!!
!
!!!!!
!
!
!
!!!
!!
!!!!!!!
!!!!
!!!!!
!
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!
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!!
!!
!!!!!!!
!
!!
!
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!!!
!!
!
!
COX5A
050100
!
!
!
!
!
!
!!
!
!
!!
!
!!!!!!!!!!!!
!!!!!!!!!
!!
!
!!
!
!!!!
!
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!!!
!!
!
!!!!!
!!
!
!
!!
!!
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!!
!
!!!!
!!
!
!
!
!!
RPL13
020
60
!
!
!
!
!
!
!
!
!
!
!!
!
!
!
!!!
!
!!!
!
!
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!
!
!!
!
!
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!!!!
!
!!!!!!!!!!
!!
!!!!!!
!!
!!
!
!
!
!
!
!
!
MIF
0200
500
!
!!!
!!
!
!
!
!
!
!!
!!!!!!!!!!!!
!!!!!!!!!
!!!!!!
!!!!
!
!
!
!
!
!
!
!
!!!
!!!
!!
!
!!!!!
!!!
!!!!!!!
!!!!!!!!
!
!!!!!!!
!
!
!!
PFN1
ID
Norm
alize
d Ex
pect
ed C
ount
020
00
0 50 100 150 200
!
!
!!
!!
!
!
!!!!!!!!
!!!!!!!!!
!
!
!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!
!
!
!!
!!
!
!
!!
!
!
!
!!
!!
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!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!!!!!!!!!!!!
!!!!!!!!!!
!
!
!
!
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!
!
!
!
!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!
COX5A
010
0025
00
!
!
!!!!
!
!
!!!
!!!!
!
!!
!!!!!!
!
!
!!!!
!!!!!
!!!!!!!!!!!!!!!!!
!
!!!!!
!
!!!
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!
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!!!
!
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!
!
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!!!!!!!!!
!!!!!!!!!!!!!
!!
!!!
!!!!!!!!!
!!
!!
!
!
!
!
!!
RPL13
010
0025
00
!
!
!!!!
!
!
!!!
!!!!
!
!!
!!!!!!
!
!
!!!!
!!!!!
!!!!!!!!!!!!!!!!!
!
!!!!!
!
!!!
!
!
!!
!
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!!!
!
!!!!!!
!
!!!
!
!!!!
!
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!
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!!!
!!!!!!!
!!!!!
!
!!!
!
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!
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!
!
!!!!
!!
!!!!!!!!!
!!!!!!!!!!!!!
!!
!!!
!!!!!!!!!
!!
!!
!
!
!
!
!!
MIF
020
00
!
!
!!
!!
!
!
!!!!!!!!
!!!!!!!!!
!
!
!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!
!
!
!!
!!
!
!
!!
!
!
!
!!
!!
!!
!!
!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!!!!!!!!!!!!
!!!!!!!!!!
!
!
!
!
!!
!
!
!
!
!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!
PFN1
CK BioC 2017
!
C48C47C46C45C44C43C42C41C40C39C38C37C36C35C34C33C32C31C30C29C28C27C26C25C24C23C22C21C20C19C18C17C16C15C14C13C12C11C10C09C08C07C06C05C04C03C02C01
C96C95C94C93C92C91C90C89C88C87C86C85C84C83C82C81C80C79C78C77C76C75C74C73C72C71C70C69C68C67C66C65C64C63C62C61C60C59C58C57C56C55C54C53C52C51C50C49
(P93)(P92)(P91)(P87)(P86)(P85)(P81)(P80)(P79)(P75)(P74)(P73)(P69)(P68)(P67)(P63)(P62)(P61)(P57)(P56)(P55)(P51)(P50)(P49)(P43)(P44)(P45)(P37)(P38)(P39)(P31)(P32)(P33)(P25)(P26)(P27)(P19)(P20)(P21)(P13)(P14)(P15)(P07)(P08)(P09)(P01)(P02)(P03)
(P94)(P95)(P96)(P88)(P89)(P90)(P82)(P83)(P84)(P76)(P77)(P78)(P70)(P71)(P72)(P64)(P65)(P66)(P58)(P59)(P60)(P52)(P53)(P54)(P48)(P47)(P46)(P42)(P41)(P40)(P36)(P35)(P34)(P30)(P29)(P28)(P24)(P23)(P22)(P18)(P17)(P16)(P12)(P11)(P10)(P06)(P05)(P04)
C46
C43
C40
C37
C34
C31
C28
C25
C24
C21
C18
C15
C12
C09
C06
C03
C47
C44
C41
C38
C35
C32
C29
C26
C23
C20
C17
C14
C11
C08
C05
C02
C48
C45
C42
C39
C36
C33
C30
C27
C22
C19
C16
C13
C10
C07
C04
C01
C96
C93
C90
C87
C84
C81
C78
C75
C70
C67
C64
C61
C58
C55
C52
C49
C95
C92
C89
C86
C83
C80
C77
C74
C71
C68
C65
C62
C59
C56
C53
C50
C94
C91
C88
C85
C82
C79
C76
C73
C72
C69
C66
C63
C60
C57
C54
C51
(P91)
(P85)
(P79)
(P73)
(P67)
(P61)
(P55)
(P49)
(P43)
(P37)
(P31)
(P25)
(P19)
(P13)
(P07)
(P01)
(P92)
(P86)
(P80)
(P74)
(P68)
(P62)
(P56)
(P50)
(P44)
(P38)
(P32)
(P26)
(P20)
(P14)
(P08)
(P02)
(P93)
(P87)
(P81)
(P75)
(P69)
(P63)
(P57)
(P51)
(P45)
(P39)
(P33)
(P27)
(P21)
(P15)
(P09)
(P03)
(P94)
(P88)
(P82)
(P76)
(P70)
(P64)
(P58)
(P52)
(P46)
(P40)
(P34)
(P28)
(P22)
(P16)
(P10)
(P04)
(P95)
(P89)
(P83)
(P77)
(P71)
(P65)
(P59)
(P53)
(P47)
(P41)
(P35)
(P29)
(P23)
(P17)
(P11)
(P05)
(P96)
(P90)
(P84)
(P78)
(P72)
(P66)
(P60)
(P54)
(P48)
(P42)
(P36)
(P30)
(P24)
(P18)
(P12)
(P06)
(e)
(c)
(d)
(a)
(b)
ID
qPC
R F
C0.
01.
02.
0
0 50 100 150 200
!!!!!!!!!!!!!!!!!!!
!!!!!
!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!
!!!!!!
!
!
!!!!!
!!!
!!!!!!!!!
!!!!!!!!
!
!!!!
!!
!
!!!!!!!!
!!!!!!!!!!!!!!
!
!
!
!!
!
!
!!!!!!
!!
!
!
!
!
!
!
!!
!!
!
!!!!
!!
!
!
!
!
!!!
!!
!
!!!!!!!
!!
!!!!!!!!!!!!!!!
!!!!!!
!!!!
!!
!
!!!
!
!!
!
!
!
MIF0.0
1.0
2.0
!
!
!!!!!!
!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!
!!
!!
!!!
!
!!
!
!!
!
!!!
!!!!!!!!
!!!
!!!!!!!
!
!!!!!
!!!!!!!!
!
!
!!!!!!!!
!
!!!
!
!
!
!!
!!!!!!!
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PFN1
ID
FPKM
0100
300
0 100 200 300
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PFN1
ID
FPKM
0100
300
0 20 40 60 80 100
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PFN1
ID
Norm
alize
d Ex
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ed C
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020
00
0 50 100 150 200
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PFN1
!
C48C47C46C45C44C43C42C41C40C39C38C37C36C35C34C33C32C31C30C29C28C27C26C25C24C23C22C21C20C19C18C17C16C15C14C13C12C11C10C09C08C07C06C05C04C03C02C01
C96C95C94C93C92C91C90C89C88C87C86C85C84C83C82C81C80C79C78C77C76C75C74C73C72C71C70C69C68C67C66C65C64C63C62C61C60C59C58C57C56C55C54C53C52C51C50C49
(P93)(P92)(P91)(P87)(P86)(P85)(P81)(P80)(P79)(P75)(P74)(P73)(P69)(P68)(P67)(P63)(P62)(P61)(P57)(P56)(P55)(P51)(P50)(P49)(P43)(P44)(P45)(P37)(P38)(P39)(P31)(P32)(P33)(P25)(P26)(P27)(P19)(P20)(P21)(P13)(P14)(P15)(P07)(P08)(P09)(P01)(P02)(P03)
(P94)(P95)(P96)(P88)(P89)(P90)(P82)(P83)(P84)(P76)(P77)(P78)(P70)(P71)(P72)(P64)(P65)(P66)(P58)(P59)(P60)(P52)(P53)(P54)(P48)(P47)(P46)(P42)(P41)(P40)(P36)(P35)(P34)(P30)(P29)(P28)(P24)(P23)(P22)(P18)(P17)(P16)(P12)(P11)(P10)(P06)(P05)(P04)
C46
C43
C40
C37
C34
C31
C28
C25
C24
C21
C18
C15
C12
C09
C06
C03
C47
C44
C41
C38
C35
C32
C29
C26
C23
C20
C17
C14
C11
C08
C05
C02
C48
C45
C42
C39
C36
C33
C30
C27
C22
C19
C16
C13
C10
C07
C04
C01
C96
C93
C90
C87
C84
C81
C78
C75
C70
C67
C64
C61
C58
C55
C52
C49
C95
C92
C89
C86
C83
C80
C77
C74
C71
C68
C65
C62
C59
C56
C53
C50
C94
C91
C88
C85
C82
C79
C76
C73
C72
C69
C66
C63
C60
C57
C54
C51
(P91)
(P85)
(P79)
(P73)
(P67)
(P61)
(P55)
(P49)
(P43)
(P37)
(P31)
(P25)
(P19)
(P13)
(P07)
(P01)
(P92)
(P86)
(P80)
(P74)
(P68)
(P62)
(P56)
(P50)
(P44)
(P38)
(P32)
(P26)
(P20)
(P14)
(P08)
(P02)
(P93)
(P87)
(P81)
(P75)
(P69)
(P63)
(P57)
(P51)
(P45)
(P39)
(P33)
(P27)
(P21)
(P15)
(P09)
(P03)
(P94)
(P88)
(P82)
(P76)
(P70)
(P64)
(P58)
(P52)
(P46)
(P40)
(P34)
(P28)
(P22)
(P16)
(P10)
(P04)
(P95)
(P89)
(P83)
(P77)
(P71)
(P65)
(P59)
(P53)
(P47)
(P41)
(P35)
(P29)
(P23)
(P17)
(P11)
(P05)
(P96)
(P90)
(P84)
(P78)
(P72)
(P66)
(P60)
(P54)
(P48)
(P42)
(P36)
(P30)
(P24)
(P18)
(P12)
(P06)
(e)
(c)
(d)
(a)
(b)
ID
qPC
R F
C0.
01.
02.
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0 50 100 150 200
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PFN1
ID
FPKM
0100
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0 100 200 300
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PFN1
ID
FPKM
0100
300
0 20 40 60 80 100
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0200
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!!!!!
!!!
!!!!!!!
!!!!!!!!
!
!!!!!!!
!
!
!!
PFN1
ID
Norm
alize
d Ex
pect
ed C
ount
020
00
0 50 100 150 200
!
!
!!
!!
!
!
!!!!!!!!
!!!!!!!!!
!
!
!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!
!
!
!!
!!
!
!
!!
!
!
!
!!
!!
!!
!!
!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!!!!!!!!!!!!
!!!!!!!!!!
!
!
!
!
!!
!
!
!
!
!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!
COX5A
010
0025
00
!
!
!!!!
!
!
!!!
!!!!
!
!!
!!!!!!
!
!
!!!!
!!!!!
!!!!!!!!!!!!!!!!!
!
!!!!!
!
!!!
!
!
!!
!
!
!!!!!
!!!
!
!!!!!!
!
!!!
!
!!!!
!
!
!!
!!
!
!
!!
!
!!
!!!!
!!!!!!!!
!!!
!!!!!!!
!!!!!
!
!!!
!
!
!!
!
!!
!
!
!
!
!
!!!!
!
!!
!!
!!
!
!
!!!!
!!
!!!!!!!!!
!!!!!!!!!!!!!
!!
!!!
!!!!!!!!!
!!
!!
!
!
!
!
!!
RPL13
010
0025
00
!
!
!!!!
!
!
!!!
!!!!
!
!!
!!!!!!
!
!
!!!!
!!!!!
!!!!!!!!!!!!!!!!!
!
!!!!!
!
!!!
!
!
!!
!
!
!!!!!
!!!
!
!!!!!!
!
!!!
!
!!!!
!
!
!!
!!
!
!
!!
!
!!
!!!!
!!!!!!!!
!!!
!!!!!!!
!!!!!
!
!!!
!
!
!!
!
!!
!
!
!
!
!
!!!!
!
!!
!!
!!
!
!
!!!!
!!
!!!!!!!!!
!!!!!!!!!!!!!
!!
!!!
!!!!!!!!!
!!
!!
!
!
!
!
!!
MIF
020
00
!
!
!!
!!
!
!
!!!!!!!!
!!!!!!!!!
!
!
!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!
!
!
!!
!!
!
!
!!
!
!
!
!!
!!
!!
!!
!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!!!!!!!!!!!!
!!!!!!!!!!
!
!
!
!
!!
!
!
!
!
!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!
PFN1
Trapnell et al., 2014
Increased expression related to capture site ID
!
C48C47C46C45C44C43C42C41C40C39C38C37C36C35C34C33C32C31C30C29C28C27C26C25C24C23C22C21C20C19C18C17C16C15C14C13C12C11C10C09C08C07C06C05C04C03C02C01
C96C95C94C93C92C91C90C89C88C87C86C85C84C83C82C81C80C79C78C77C76C75C74C73C72C71C70C69C68C67C66C65C64C63C62C61C60C59C58C57C56C55C54C53C52C51C50C49
(P93)(P92)(P91)(P87)(P86)(P85)(P81)(P80)(P79)(P75)(P74)(P73)(P69)(P68)(P67)(P63)(P62)(P61)(P57)(P56)(P55)(P51)(P50)(P49)(P43)(P44)(P45)(P37)(P38)(P39)(P31)(P32)(P33)(P25)(P26)(P27)(P19)(P20)(P21)(P13)(P14)(P15)(P07)(P08)(P09)(P01)(P02)(P03)
(P94)(P95)(P96)(P88)(P89)(P90)(P82)(P83)(P84)(P76)(P77)(P78)(P70)(P71)(P72)(P64)(P65)(P66)(P58)(P59)(P60)(P52)(P53)(P54)(P48)(P47)(P46)(P42)(P41)(P40)(P36)(P35)(P34)(P30)(P29)(P28)(P24)(P23)(P22)(P18)(P17)(P16)(P12)(P11)(P10)(P06)(P05)(P04)
C46
C43
C40
C37
C34
C31
C28
C25
C24
C21
C18
C15
C12
C09
C06
C03
C47
C44
C41
C38
C35
C32
C29
C26
C23
C20
C17
C14
C11
C08
C05
C02
C48
C45
C42
C39
C36
C33
C30
C27
C22
C19
C16
C13
C10
C07
C04
C01
C96
C93
C90
C87
C84
C81
C78
C75
C70
C67
C64
C61
C58
C55
C52
C49
C95
C92
C89
C86
C83
C80
C77
C74
C71
C68
C65
C62
C59
C56
C53
C50
C94
C91
C88
C85
C82
C79
C76
C73
C72
C69
C66
C63
C60
C57
C54
C51
(P91)
(P85)
(P79)
(P73)
(P67)
(P61)
(P55)
(P49)
(P43)
(P37)
(P31)
(P25)
(P19)
(P13)
(P07)
(P01)
(P92)
(P86)
(P80)
(P74)
(P68)
(P62)
(P56)
(P50)
(P44)
(P38)
(P32)
(P26)
(P20)
(P14)
(P08)
(P02)
(P93)
(P87)
(P81)
(P75)
(P69)
(P63)
(P57)
(P51)
(P45)
(P39)
(P33)
(P27)
(P21)
(P15)
(P09)
(P03)
(P94)
(P88)
(P82)
(P76)
(P70)
(P64)
(P58)
(P52)
(P46)
(P40)
(P34)
(P28)
(P22)
(P16)
(P10)
(P04)
(P95)
(P89)
(P83)
(P77)
(P71)
(P65)
(P59)
(P53)
(P47)
(P41)
(P35)
(P29)
(P23)
(P17)
(P11)
(P05)
(P96)
(P90)
(P84)
(P78)
(P72)
(P66)
(P60)
(P54)
(P48)
(P42)
(P36)
(P30)
(P24)
(P18)
(P12)
(P06)
(e)
(c)
(d)
(a)
(b)
ID
qPCR
FC
0.0
1.0
2.0
0 50 100 150 200
!!!!!!!!!!!!!!!!!!!
!!!!!
!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!
!!!!!!
!
!
!!!!!
!!!
!!!!!!!!!
!!!!!!!!
!
!!!!
!!
!
!!!!!!!!
!!!!!!!!!!!!!!
!
!
!
!!
!
!
!!!!!!
!!
!
!
!
!
!
!
!!
!!
!
!!!!
!!
!
!
!
!
!!!
!!
!
!!!!!!!
!!
!!!!!!!!!!!!!!!
!!!!!!
!!!!
!!
!
!!!
!
!!
!
!
!
MIF0.0
1.0
2.0
!
!
!!!!!!
!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!
!!
!!
!!!
!
!!
!
!!
!
!!!
!!!!!!!!
!!!
!!!!!!!
!!!!!!
!!!!!!!!
!
!
!!!!!!!!
!
!!!
!
!
!
!!
!!!!!!!
!!!!
!!
!!
!!!
!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!
PFN1
ID
FPKM
0100
300
0 100 200 300
!
!!
!!!
!!
!
!
!
!!
!
!
!!!!!
!
!!!!!!!!!!!!
!
!!!!!!!!!!!!!!!
!
!!!!
!
!!!!!
!
!
!!
!!!
!!!!
!
!!
!
!
!
!!!
!
!
!
!!!!!!!!
!
!!!
!!
!!!
!!!
!
!
!
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!
!
!
!
!!!!!!!
!
!
!!!!
!
!
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!
!!!!!!!!
!
!!!!!!!!!
!!
!!!!
!!
!
!
!
!
!!!!!
!
!
!
!!
!
!!
!
!!!!
!
!
!!
!
!
!
!
!!!!!
!!!
!!!!!!
!
!
!!
!
!!!
!
!
!
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!
!
!
!!!!!!!!
!
!!!!
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!
!
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!
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!
!!!!
!
!!!!
!
!
!!!!
!
!!
!
!
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!
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!
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!
!
!
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!
!
!
!
!
!
!
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!
!
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!
!!
!
!!
!
!!!!!!!
!!!!!!!!!!
!!!!
!
!
COX5A
010002500
!
!!
!
!
!!!
!!
!!
!
!
!
!
!!!!!
!
!
!!!!
!
!!!!
!
!
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!!!!
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!
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!
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!!!
!
!!
!!
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!
!!
!
!!
!!!
!!
RPL13
0100250
!
!
!
!!
!
!
!!!
!
!
!
!
!
!
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!
!
!
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!
!
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!
!!
!
!
!!!
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!!
!!!
!!!!!
!
!!
!
!
!
!
!
!
!!
MIF
0400800
!
!
!
!
!!
!!
!
!
!
!
!
!
!
!
!!!!
!
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!!!!
!!
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!
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!
!!
!!!!
!
!!!
!!!
!
!!!!!!!!!!!!!!
!
!!!!!!!!!!!!!!!!!!!!!!!
!
!!!!
!
!!!!!!!!!!!
!
!!!!!!!!
PFN1
ID
FPKM
0100
300
0 20 40 60 80 100
!
!
!!!
!
!!
!
!!
!
!!!!!
!
!
!
!!!
!!
!!!!!!!
!!!!
!!!!!
!
!!
!
!
!
!
!!
!!
!
!
!
!!
!
!!!!!!!!
!
!!!!
!!
!!
!!!!!!!
!
!!
!
!
!!
!!!
!!
!
!
COX5A
050100
!
!
!
!
!
!
!!
!
!
!!
!
!!!!!!!!!!!!
!!!!!!!!!
!!
!
!!
!
!!!!
!
!
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!!
!
!!
!!!
!!
!
!!!!!
!!
!
!
!!
!!
!!
!!!!!!
!!
!
!!!!
!!
!
!
!
!!
RPL13
020
60 !
!
!
!
!
!
!
!
!
!
!!
!
!
!
!!!
!
!!!
!
!
!
!!!
!!
!
!!
!!!
!
!
!
!
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!
!
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!
!
!!
!
!
!
!!!!
!
!!!!!!!!!!
!!
!!!!!!
!!
!!
!
!
!
!
!
!
!
MIF
0200
500
!
!!!
!!
!
!
!
!
!
!!
!!!!!!!!!!!!
!!!!!!!!!
!!!!!!
!!!!
!
!
!
!
!
!
!
!
!!!
!!!
!!
!
!!!!!
!!!
!!!!!!!
!!!!!!!!
!
!!!!!!!
!
!
!!
PFN1
ID
Norm
alize
d Ex
pecte
d Co
unt
020
00
0 50 100 150 200
!
!
!!
!!
!
!
!!!!!!!!
!!!!!!!!!
!
!
!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!
!
!
!!
!!
!
!
!!
!
!
!
!!
!!
!!
!!
!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!!!!!!!!!!!!
!!!!!!!!!!
!
!
!
!
!!
!
!
!
!
!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!
COX5A
010
0025
00
!
!
!!!!
!
!
!!!
!!!!
!
!!
!!!!!!
!
!
!!!!
!!!!!
!!!!!!!!!!!!!!!!!
!
!!!!!
!
!!!
!
!
!!
!
!
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!!!
!
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!
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!
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!
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!
!
!
!
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!!!!
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!!
!
!
!!!!
!!
!!!!!!!!!
!!!!!!!!!!!!!
!!
!!!
!!!!!!!!!
!!
!!
!
!
!
!
!!
RPL13
010
0025
00
!
!
!!!!
!
!
!!!
!!!!
!
!!
!!!!!!
!
!
!!!!
!!!!!
!!!!!!!!!!!!!!!!!
!
!!!!!
!
!!!
!
!
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!
!
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!!!
!
!!!!!!
!
!!!
!
!!!!
!
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!!
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!!!!
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!!!
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!!!!!
!
!!!
!
!
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!
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!
!
!
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!
!!!!
!
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!!
!!
!
!
!!!!
!!
!!!!!!!!!
!!!!!!!!!!!!!
!!
!!!
!!!!!!!!!
!!
!!
!
!
!
!
!!
MIF
020
00
!
!
!!
!!
!
!
!!!!!!!!
!!!!!!!!!
!
!
!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!
!
!
!!
!!
!
!
!!
!
!
!
!!
!!
!!
!!
!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!
!!!!!!!!!!!!!
!!!!!!!!!!
!
!
!
!
!!
!
!
!
!
!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!
PFN1
!
C48C47C46C45C44C43C42C41C40C39C38C37C36C35C34C33C32C31C30C29C28C27C26C25C24C23C22C21C20C19C18C17C16C15C14C13C12C11C10C09C08C07C06C05C04C03C02C01
C96C95C94C93C92C91C90C89C88C87C86C85C84C83C82C81C80C79C78C77C76C75C74C73C72C71C70C69C68C67C66C65C64C63C62C61C60C59C58C57C56C55C54C53C52C51C50C49
(P93)(P92)(P91)(P87)(P86)(P85)(P81)(P80)(P79)(P75)(P74)(P73)(P69)(P68)(P67)(P63)(P62)(P61)(P57)(P56)(P55)(P51)(P50)(P49)(P43)(P44)(P45)(P37)(P38)(P39)(P31)(P32)(P33)(P25)(P26)(P27)(P19)(P20)(P21)(P13)(P14)(P15)(P07)(P08)(P09)(P01)(P02)(P03)
(P94)(P95)(P96)(P88)(P89)(P90)(P82)(P83)(P84)(P76)(P77)(P78)(P70)(P71)(P72)(P64)(P65)(P66)(P58)(P59)(P60)(P52)(P53)(P54)(P48)(P47)(P46)(P42)(P41)(P40)(P36)(P35)(P34)(P30)(P29)(P28)(P24)(P23)(P22)(P18)(P17)(P16)(P12)(P11)(P10)(P06)(P05)(P04)
C46
C43
C40
C37
C34
C31
C28
C25
C24
C21
C18
C15
C12
C09
C06
C03
C47
C44
C41
C38
C35
C32
C29
C26
C23
C20
C17
C14
C11
C08
C05
C02
C48
C45
C42
C39
C36
C33
C30
C27
C22
C19
C16
C13
C10
C07
C04
C01
C96
C93
C90
C87
C84
C81
C78
C75
C70
C67
C64
C61
C58
C55
C52
C49
C95
C92
C89
C86
C83
C80
C77
C74
C71
C68
C65
C62
C59
C56
C53
C50
C94
C91
C88
C85
C82
C79
C76
C73
C72
C69
C66
C63
C60
C57
C54
C51
(P91)
(P85)
(P79)
(P73)
(P67)
(P61)
(P55)
(P49)
(P43)
(P37)
(P31)
(P25)
(P19)
(P13)
(P07)
(P01)
(P92)
(P86)
(P80)
(P74)
(P68)
(P62)
(P56)
(P50)
(P44)
(P38)
(P32)
(P26)
(P20)
(P14)
(P08)
(P02)
(P93)
(P87)
(P81)
(P75)
(P69)
(P63)
(P57)
(P51)
(P45)
(P39)
(P33)
(P27)
(P21)
(P15)
(P09)
(P03)
(P94)
(P88)
(P82)
(P76)
(P70)
(P64)
(P58)
(P52)
(P46)
(P40)
(P34)
(P28)
(P22)
(P16)
(P10)
(P04)
(P95)
(P89)
(P83)
(P77)
(P71)
(P65)
(P59)
(P53)
(P47)
(P41)
(P35)
(P29)
(P23)
(P17)
(P11)
(P05)
(P96)
(P90)
(P84)
(P78)
(P72)
(P66)
(P60)
(P54)
(P48)
(P42)
(P36)
(P30)
(P24)
(P18)
(P12)
(P06)
(e)
(c)
(d)
(a)
(b)
ID
qPC
R F
C0.
01.
02.
0
0 50 100 150 200
!!!!!!!!!!!!!!!!!!!
!!!!!
!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!
!!!!!!
!
!
!!!!!
!!!
!!!!!!!!!
!!!!!!!!
!
!!!!
!!
!
!!!!!!!!
!!!!!!!!!!!!!!
!
!
!
!!
!
!
!!!!!!
!!
!
!
!
!
!
!
!!
!!
!
!!!!
!!
!
!
!
!
!!!
!!
!
!!!!!!!
!!
!!!!!!!!!!!!!!!
!!!!!!
!!!!
!!
!
!!!
!
!!
!
!
!
MIF0.0
1.0
2.0
!
!
!!!!!!
!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!
!!
!!
!!!
!
!!
!
!!
!
!!!
!!!!!!!!
!!!
!!!!!!!
!
!!!!!
!!!!!!!!
!
!
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PFN1
Wu et al., 2014
CK BioC 2017
§ Normalization
§ Technical vs. biological zeros
§ De-noising
§ Clustering; Identifying sub-populations
§ Identifying oscillatory genes
§ Identifying and characterizing differences in gene-specific expression distributions (aka. identifying differential distributions)
§ Pseudotime reordering
§ Network reconstruction
Challenges in scRNA-seq
CK BioC 2017
SCnorm: A quantile-regression based approach for robust normalization of single-cell RNA-seq data
Bacher, Chu et al., Nature Methods, 2017
CK BioC 2017
§ Goal: correct for technical artifacts and/or gene-specific features
- Sequencing depth
- Length, GC content
- Amplification and other technical biases
§ Without UMIs/spike-ins, most single-cell methods calculate global scale factors as in bulk RNA-seq
- One scale factor is calculated per sample and applied to all genes in that sample.
Background
CK BioC 2017
Bulk: Global scale-factor normalization for sequencing depth1 Plots
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Figure 1
1
CK BioC 2017
Expression vs. depth varies with expression in scRNA-seq1 Plots
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14.0 14.5 15.0 15.5 16.00
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(d)
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(h)
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Figure 1
1
CK BioC 2017
We see the count-depth relationship varying with expression in many datasets
CK BioC 2017
§ Identify gene groups based on the count-depth relationship.
§ Quantile polynomial regression is used to quantify the group-specific relationship between expression and sequencing depth. The quantile is chosen iteratively.
§ Predicted values are used to calculate group-specific scale factors for each cell.
Overview of SCnorm
Within each group,
CK BioC 2017
SCnorm
12
regression. Since the median might not best represent the full set of genes within the
group, and since multiple genes allow for estimation of somewhat subtle effects, in this
step SCnorm considers multiple quantiles τ and multiple degrees d:
)23,43 -.|0. = $*23 + $'
230. + ⋯+$4230.
43. (1)
The specific values of 67 and 87, 67∗ and 87∗ , are those that minimize :'23 − $<,'%
=>4? ,
where :'23represents the count-depth relationship among the predicted expression values
as estimated by median quantile regression using a first degree polynomial:
)*., -.23|0. = :*
23 + :'230.. Scale factors for each cell are defined as @A. =
?BCD3∗ ,E3
∗
?BD3∗
where -23∗ is the τ*th quantile of expression counts in the kth group. Normalized counts
-%,.F are given by ?BG,H
IJH .
To determine if ! = 1 is sufficient, the gene-specific relationship between log
normalized expression and log sequencing depth is represented by the slope of a median
quantile regression using a first degree polynomial as detailed above. ! = 1 is considered
sufficient if the modes of the slopes within each of 10 equally sized gene groups (where a
gene’s group membership is determined by its median expression among non-zero un-
normalized measurements) are all less than 0.1. Any mode exceeding 0.1 is taken as
evidence that the normalization provided with ! = 1 is not sufficient to adjust for the
count-depth relationship for all genes and, consequently, K is increased by one and the
count-depth relationship is estimated within each of the K groups using equation (1). For
each increase, the K-medoids algorithm is used to cluster genes into groups based on $%,';
if a cluster has fewer than 100 genes, it is joined with the nearest cluster.
Yg = (yg1,..., ygJ )
11
ONLINE METHODS Data availability. The H1 bulk and the H1-1M, H1-4M, H9-1M, H9-4M case study
datasets will be released at the gene expression omnibus (GSE85917) upon acceptance of
the manuscript. Reviewers may access this data at:
http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?token=yrargcgavhehzez&acc=GSE8591
7
Code availability. The R/SCnorm package may be found at
http://www.biostat.wisc.edu/~kendzior/SCNORM/
Filter. Genes without at least 10 cells having non-zero expression were removed prior to
all analyses. They are not shown in plots.
SCnorm. SCnorm requires estimates of expression, but is not specific to one approach.
Estimates may be obtained via RSEM7, HTSeq9, or any method providing counts per
feature. Let Yg,j denote the log non-zero expression count for gene g in cell j for g = 1,…,
m and j = 1,…, n; Xj denote log sequencing depth for cell j. Motivation for considering
non-zero counts is provided in Supplementary Section S4.
The number of groups for which the count-depth relationship varies substantially,
K, is chosen sequentially. SCnorm begins with ! = 1. For each gene, the gene-specific
relationship between log expression and log sequencing depth is represented by
$%,'using median quantile regression with a first degree polynomial:
)*., -%,.|0. = $%,* + $%,'0.. The overall relationship between log expression and log
sequencing depth for all genes in the ! = 1 group is also estimated via quantile
12
regression. Since the median might not best represent the full set of genes within the
group, and since multiple genes allow for estimation of somewhat subtle effects, in this
step SCnorm considers multiple quantiles τ and multiple degrees d:
)23,43 -.|0. = $*23 + $'
230. + ⋯+$4230.
43. (1)
The specific values of 67 and 87, 67∗ and 87∗ , are those that minimize :'23 − $<,'%
=>4? ,
where :'23represents the count-depth relationship among the predicted expression values
as estimated by median quantile regression using a first degree polynomial:
)*., -.23|0. = :*
23 + :'230.. Scale factors for each cell are defined as @A. =
?BCD3∗ ,E3
∗
?BD3∗
where -23∗ is the τ*th quantile of expression counts in the kth group. Normalized counts
-%,.F are given by ?BG,H
IJH .
To determine if ! = 1 is sufficient, the gene-specific relationship between log
normalized expression and log sequencing depth is represented by the slope of a median
quantile regression using a first degree polynomial as detailed above. ! = 1 is considered
sufficient if the modes of the slopes within each of 10 equally sized gene groups (where a
gene’s group membership is determined by its median expression among non-zero un-
normalized measurements) are all less than 0.1. Any mode exceeding 0.1 is taken as
evidence that the normalization provided with ! = 1 is not sufficient to adjust for the
count-depth relationship for all genes and, consequently, K is increased by one and the
count-depth relationship is estimated within each of the K groups using equation (1). For
each increase, the K-medoids algorithm is used to cluster genes into groups based on $%,';
if a cluster has fewer than 100 genes, it is joined with the nearest cluster.
12
regression. Since the median might not best represent the full set of genes within the
group, and since multiple genes allow for estimation of somewhat subtle effects, in this
step SCnorm considers multiple quantiles τ and multiple degrees d:
)23,43 -.|0. = $*23 + $'
230. + ⋯+$4230.
43. (1)
The specific values of 67 and 87, 67∗ and 87∗ , are those that minimize :'23 − $<,'%
=>4? ,
where :'23represents the count-depth relationship among the predicted expression values
as estimated by median quantile regression using a first degree polynomial:
)*., -.23|0. = :*
23 + :'230.. Scale factors for each cell are defined as @A. =
?BCD3∗ ,E3
∗
?BD3∗
where -23∗ is the τ*th quantile of expression counts in the kth group. Normalized counts
-%,.F are given by ?BG,H
IJH .
To determine if ! = 1 is sufficient, the gene-specific relationship between log
normalized expression and log sequencing depth is represented by the slope of a median
quantile regression using a first degree polynomial as detailed above. ! = 1 is considered
sufficient if the modes of the slopes within each of 10 equally sized gene groups (where a
gene’s group membership is determined by its median expression among non-zero un-
normalized measurements) are all less than 0.1. Any mode exceeding 0.1 is taken as
evidence that the normalization provided with ! = 1 is not sufficient to adjust for the
count-depth relationship for all genes and, consequently, K is increased by one and the
count-depth relationship is estimated within each of the K groups using equation (1). For
each increase, the K-medoids algorithm is used to cluster genes into groups based on $%,';
if a cluster has fewer than 100 genes, it is joined with the nearest cluster.
§ Filter: genes having greater than 10% expression values nonzero and median nonzero expression greater than 2.
§ Let denote log non-zero expression for gene g in cell j ; Xj denote log sequencing depth.
§ The gene-specific count-depth relationship is estimated by:
§ Genes are split into K groups. The group specific count-depth relationship is estimated by:
§ Estimates of tk and dk minimize ; where represents the count-depth relationship among predicted values.
§ K is chosen so that the absolute value of the maximum normalized slope mode is < 0.1 within each of ten groups.
CK BioC 2017
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Figure 1
1
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Bulk Single cell
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Figure 1
1
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14.0 14.5 15.0 15.5 16.00
12
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log$Sequencing$Depth
Bulk
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Single$cell
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LCR
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Low
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log$Normalized$Expression
Figure 4
4
CK BioC 2017
TPM SCDE BASiCS
LCR Median1RatioRaw
Density
Density
Density
Density
Density
Density
Slope Slope Slope
Slope Slope Slope
−2 −1 0 1 2 3
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Figure 4: Genes in the H1pooled96 dataset are divided into 10 groups by median nonzero expression.A density curve of the slopes from median quantile regression of log nonzero expression values versussequencing depth for each gene are plotted for Raw expression, LCR normalization, Median-Ratio, TPM,SCDE, and BASiCS. Genes are filtered as those having greater than 10% nonzero expression values. LCRwas run with k = 5.
4
H1 - 1 (~ 1 million reads per cell)
SCnorm
CK BioC 2017
H1 - 4 (~4 million reads per cell)
TPM SCDE BASiCS
LCR Median1RatioRawDensity
Density
Density
Density
Density
Density
Slope Slope Slope
Slope Slope Slope
−2 −1 0 1 2 3
0.0
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Figure 3: Genes in the H1pooled24 dataset are divided into 10 groups by median nonzero expression.A density curve of the slopes from median quantile regression of log nonzero expression values versussequencing depth for each gene are plotted for Raw expression, LCR normalization, Median-Ratio, TPM,SCDE, and BASiCS. Genes are filtered as those having greater than 10% nonzero expression values. LCRwas run with k = 4.
3
SCnorm
CK BioC 2017
Implications for DE analysis
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True
Exp
ress
ionNo
rmali
zed
Expr
essio
n
Sequencing Depth (Millions)
Sequencing Depth (Millions)
Sequencing Depth (Millions)
Norm
alize
d Ex
pres
sion
SCno
rmGl
obal
Scale
Fac
tor
Un-n
orm
alize
d
(a)
(b)
(c)
CK BioC 2017
FC= H1-1/H1-4
§ H1-1: ~100 H1 cells profiles at ~1 million reads per cell
§ H1-4: Same H1 cells profiled at ~4 million reads per cell
§ Prior to normalization, H1-1/H1-4 should be about ¼
§ Post normalization, H1-1/H1-4 should be about 1
§ If over-normalization is going on, H1-1/H1-4 will be greater than 1.
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True E
xpres
sion
Norm
alized
Expre
ssion
Sequencing Depth (Millions)
Sequencing Depth (Millions)
Sequencing Depth (Millions)
Norm
alized
Expre
ssion
SCno
rmGlo
bal S
cale
Facto
rUn
-norm
alized
(a)
(b)
(c)
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Norm
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Expre
ssion
Sequencing Depth (Millions)
Sequencing Depth (Millions)
Sequencing Depth (Millions)
Norm
alized
Expre
ssion
SCno
rmGlo
bal S
cale
Facto
rUn
-norm
alized
(a)
(b)
(c)
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Expre
ssion
Sequencing Depth (Millions)
Sequencing Depth (Millions)
Sequencing Depth (Millions)
Norm
alized
Expre
ssion
SCno
rmGlo
bal S
cale
Facto
rUn
-norm
alized
(a)
(b)
(c)
CK BioC 2017
0
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−3
−2
−1
0
1
2
1 2 3 4Expression Group Expression Group
log 2
Fold
-Cha
nge
Num
ber o
f DE
gene
s
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spec
ifici
ty
NoNormLCRMedian−RatioTPMSCDEBASiCS
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spec
ifici
ty
NoNormLCRMedian−RatioTPMSCDEBASiCS
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spec
ifici
ty
NoNormLCRMedian−RatioTPMSCDEBASiCS
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spec
ifici
ty
NoNormLCRMedian−RatioTPMSCDEBASiCS
0
100
200
300
400
500
600
700
800
1 2 3 4
MRonly
SCDEonly
BASiCSonly
scranOnlyscran
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spec
ifici
ty
NoNormLCRMedian−RatioTPMSCDEBASiCS
MR
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spec
ifici
ty
NoNormLCRMedian−RatioTPMSCDEBASiCS
SCnorm
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spe
cific
ity
NoNormLCRMedian−RatioTPMSCDEBASiCS
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spe
cific
ity
NoNormLCRMedian−RatioTPMSCDEBASiCS
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spe
cific
ity
NoNormLCRMedian−RatioTPMSCDEBASiCS
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spe
cific
ity
NoNormLCRMedian−RatioTPMSCDEBASiCS
0
100
200
300
400
500
600
700
800
1 2 3 4
MRonly
SCDEonly
BASiCSonly
scranOnlyscran
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spe
cific
ity
NoNormLCRMedian−RatioTPMSCDEBASiCS
MR
0.00
0.25
0.50
0.75
1.00
1Expression Group
Spe
cific
ity
NoNormLCRMedian−RatioTPMSCDEBASiCS
SCnorm
FC= H1-1/H1-4
§ H1-1: ~100 H1 cells profiles at ~1 million reads per cell
§ H1-4: Same H1 cells profiled at ~4 million reads per cell
CK BioC 2017
Normalization via SCnorm
−2 −1 0 1 2 3
01
23
45
6
IslamES
−2 −1 0 1 2 3
01
23
45
Slope
Density
Density
Density
Density
DensitySlope
Slope Slope Slope
−2 −1 0 1 2 3
01
23
4
IslamEF
BuettnerG1 BuettnerS BuettnerG2M
−2 −1 0 1 2 3
01
23
45
−2 −1 0 1 2 3
01
23
45
Low
HighExpression
Low
HighExpression
Low
HighExpression
Low
HighExpression
Low
HighExpression
Figure 5: A density curve of the slopes from a quantile regression of log nonzero expression versus sequenc-ing depth are plotted for LCR normalization on five public datasets. Genes are divided into 10 groupsbased on nonzero median raw expression. Genes were filtered for reach dataset as those having greaterthan 10% nonzero expression. LCR was run with k = 7, 7, 5, 7, and 3 for IslamES, IslamEF, BuettnerG1,BuettnerS, and BuettnerG2, respectively.
5
CK BioC 2017
§ Normalization
§ Technical vs. biological zeros
§ De-noising
§ Clustering; Identifying sub-populations
§ Identifying oscillatory genes
§ Identifying and characterizing differences in gene-specific expression distributions (aka. identifying differential distributions)
§ Pseudotime reordering
§ Network reconstruction
Challenges in scRNA-seq
CK BioC 2017
scDD: A Dirichlet mixture model based approach for identifying differential distributions in scRNA-seq experiments
Korthauer et al., Genome Biology, to appear, 2016
CK BioC 2017
Gene-specific multi-modality
Snapshot of Population of Single Cells
Histogram of Observed Expression Level of Gene X
Number of Cells
(A)
(B) (C)
Expression States of Gene X for Individual Cells Over Time
Low Expression State: µ1 High Expression State: µ2
µ1 µ2
Time
Cell 1
Cell 2
Cell 3 !"! !
Cell J
!"! !
CK BioC 2017
Many genes show multi-modal expression distributions
Multimodality in scRNA-seq
0.0
0.2
0.4
0.6
0.8
1 2 3+Number of Modes
Prop
ortio
n of
gen
es (o
r tra
nscr
ipts
)
DatasetGE.50GE.75GE.100LC.77H1.78DEC.64NPC.86H9.87
Modality of Bulk (Reds) vs Single−cell (Blues) RNA−seq datasets
6
Number of clustersNumber of clusters
Cou
nt
Prop
ortio
n
CK BioC 2017
Opportunity to identify differences beyond traditional DE
Traditional DE
µ1 µ2
(A) Differential Proportion (DP)
µ1 µ2
(B)
Differential Modality (DM)
µ1 µ2
(C) Both DM and DE
µ1 µ3 µ2
(D)
Traditional DE
µ1 µ2
(A) Differential Proportion (DP)
µ1 µ2
(B)
Differential Modality (DM)
µ1 µ2
(C) Both DM and DE
µ1 µ3 µ2
(D)
Differential expression (DE) Differential proportions (DP)
Differential modes (DM) Both DM and DE
CK BioC 2017
scRNA-seq DE Analysis
Di↵erential Expression and scRNA-seq
⌅ Recent methods use mixture modeling to account for ‘on’ and‘o↵’ components
• Shalek et al. (2014)• SCDE (Kharchenko et al., 2014)• MAST (Finak et al., 2015)
⌅ When detected, each gene has a latent level of expressionwithin a biological condition, and measurements fluctuatearound that level due to biological and technical sources ofvariability
4
CK BioC 2017
scDD: GoalOur goals
⌅ Model expression profiles while accommodating the oftenmultimodal distributions in the detected cells
⌅ Find genes with Di↵erential Distributions (DD) of expressionacross two conditions:
• di↵erential means• di↵erential proportion within modes• di↵erential modality (number of modes)• combination thereof• di↵erential zeroes (detection rate)
7
CK BioC 2017
§ Log non-zero normalized, de-noised, expression arises out of a fixed variance Dirichlet Process Mixture of normals model.
§ For each gene, obtain maximum a posteriori (MAP) partition of the samples to components using the modalclust algorithm (Dahl 2009).
- fast and deterministic
- requires point estimate of cluster variance (obtain via mclust).
§ To evaluate evidence of DD, fit under two different hypotheses:
- ignoring condition (MED : equivalent regulation)
- separately for each condition (MDD : differential regulation)
scDD: Overview
CK BioC 2017
scDD: Overview (continued)
§ Assume that log non-zero normalized, de-noised, expression measurements for gene g in J cells arise from a conjugate
Dirichlet Process Mixture (DPM) of normals model:
§ Let K denote the number of components (unique values in {µj, tj}, j=1,.., J).Of primary interest is the posterior of (µ,t), which is intractable for moderate sample sizes.
§ Let Z = (z1, …, zJ) denote component memberships. Then is a PPM.
Detection of DD genes: modeling framework
⌅ Assume that the log nonzero expression measurements Y = (y1, ..., yJ)of a given gene for J cells arise out of a conjugate Dirichlet ProcessMixture (DPM) of normals model
y
j
⇠ N(µj
, ⌧j
)
µj
, ⌧j
⇠ G
G ⇠ DP(↵,G0)
G0 = NG(m0, s0, a0/2, 2/b0)
⌅ Condition posterior on a partition of samples to componentsZ = (z1, ..., zJ)
f (Y |Z) =KY
k=1
f (y (k))
/KY
k=1
�(ak
/2)
(bk
/2)ak/2s
�1/2k
Where f (y (k)) is the component-specific distribution after integratingout all other parameters, and a
k
, bk
and s
k
are cluster-specific posteriorparameters
10
Yg = (yg1,..., ygJ )
f (Y | Z )
Detection of DD genes: modeling framework
⌅ Assume that the log nonzero expression measurements Y = (y1, ..., yJ)of a given gene for J cells arise out of a conjugate Dirichlet ProcessMixture (DPM) of normals model
y
j
⇠ N(µj
, ⌧j
)
µj
, ⌧j
⇠ G
G ⇠ DP(↵,G0)
G0 = NG(m0, s0, a0/2, 2/b0)
⌅ Condition posterior on a partition of samples to componentsZ = (z1, ..., zJ)
f (Y |Z) =KY
k=1
f (y (k))
/KY
k=1
�(ak
/2)
(bk
/2)ak/2s
�1/2k
Where f (y (k)) is the component-specific distribution after integratingout all other parameters, and a
k
, bk
and s
k
are cluster-specific posteriorparameters
10
CK BioC 2017
§ To quantify the evidence of DD for gene g, obtain MAP partition estimate, , and evaluate under competing hypotheses:
ignoring condition (MED: equivalent distributions)separately within condition (MDD: differential distributions)
§ Evaluate MDD using a pseudo-Bayes Factor score:
Scoreg =
§ Assess significance via permutation.
scDD: Overview (continued)
logf Yg,Zg MDD( )f Yg,Zg MED( )
!
"##
$
%&&
Z f Y,Z( )
CK BioC 2017
scDD: Classification of DD genesClassification of DD genes
⌅ Classify DD genes into categories based on• number of components detected in each condition• whether clusters overlap
Traditional DE
µ1 µ2
(A) Differential Proportion (DP)
µ1 µ2
(B)
Differential Modality (DM)
µ1 µ2
(C) Both DM and DE
µ1 µ3 µ2
(D)
!VS!
⌅ Overlap is determined by sampling from the marginal posteriordistribution of cluster means
µk
|Y ,Z ⇠ t
a
k
⇣m
k
,b
k
a
k
s
k
⌘
12
CK BioC 2017
scDD: Evaluation via simulation studiesEvaluation: simulation setup
⌅ 8000 ED genes:• 4000 from single Negative Binomial component• 4000 from two component mixture of Negative Binomial
⌅ 2000 DD genes:• 500 DE genes• 500 DP genes (0.33/0.66 proportion di↵erence)• 500 DM genes (0.50 belong to second mode)• 500 DB genes (mean in second condition is average of means
in the first)
⌅ Sample sizes varied 2 {50, 75, 100}⌅ Component distances �µ for multimodal conditions varied
2 {2, 3, 4, 5, 6} SDs
⌅ Means, variances, and detection rates sampled empirically
13
Evaluate: Power to identify DD genesRate at which DD genes are correctly classifiedRate at which correct # components are identified
CK BioC 2017
Korthauer et al. Page 26 of 30
Table 2 Power to detect DD genes in simulated data
True Gene Category
Sample Size Method DE DP DM DB Overall (FDR)
scDD 0.893 0.418 0.898 0.572 0.695 (0.030)
50 SCDE 0.872 0.026 0.816 0.260 0.494 (0.004)
MAST 0.908 0.400 0.871 0.019 0.550 (0.026)
scDD 0.951 0.590 0.960 0.668 0.792 (0.031)
75 SCDE 0.948 0.070 0.903 0.387 0.577 (0.003)
MAST 0.956 0.632 0.942 0.036 0.642 (0.022)
scDD 0.972 0.717 0.982 0.727 0.850 (0.033)
100 SCDE 0.975 0.125 0.946 0.478 0.631 (0.003)
MAST 0.977 0.752 0.970 0.045 0.686 (0.022)
scDD 1.000 0.985 1.00 0.903 0.972 (0.034)
500 SCDE 1.000 0.858 0.998 0.785 0.910 (0.004)
MAST 1.000 0.992 1.00 0.174 0.792 (0.021)Average power to detect simulated DD genes by true category. Averages are calculated over 20
replications. Standard errors were < 0.025 (not shown).
Table 3 Correct Classification Rate in simulated data
Gene Category
Sample Size DE DP DM DB
50 0.719 0.801 0.556 0.665
75 0.760 0.732 0.576 0.698
100 0.781 0.678 0.598 0.706
500 0.814 0.552 0.580 0.646Average Correct Classification Rate for detected DD genes. Averages are calculated over 20
replications. Standard errors were < 0.025 (not shown).
Table 4 Average correct classification rates by cluster mean distance
Sample Gene Cluster mean distance �µ
Size Category 2 3 4 5 6
DP 0.02 0.20 0.78 0.94 0.98
50 DM 0.10 0.23 0.58 0.81 0.89
DB 0.08 0.22 0.59 0.80 0.80
DP 0.02 0.18 0.77 0.94 0.97
75 DM 0.08 0.27 0.69 0.86 0.90
DB 0.09 0.29 0.71 0.83 0.84
DP 0.03 0.16 0.74 0.93 0.95
100 DM 0.10 0.32 0.76 0.87 0.91
DB 0.08 0.32 0.80 0.85 0.84
DP 0.02 0.15 0.70 0.92 0.94
500 DM 0.11 0.33 0.72 0.85 0.89
DB 0.03 0.40 0.86 0.85 0.86Average Correct Classification Rates stratified by �µ. Averages are calculated over 20 replications.
Standard errors were < 0.025 (not shown).
scDD: Power to detect DD genes within each category
500
CK BioC 2017
Comparison of hESCsThomson lab hESC comparisons
Undifferentiated
Differentiated
H1
NPC DEC
H9
Number of DD genes identified in each cell type comparison
scDDComparison DE DP DM DB DZ Total SCDE MASTH1 vs NPC 1342 429 739 406 1590 4506 2938 5729H1 vs DEC 1408 404 939 345 880 3976 1581 3523NPC vs DEC 1245 449 700 298 2052 4744 1881 5383H1 vs H9 194 84 55 32 145 510 102 1091
17
scDD only: 2% 21% 38% 24% 15%
CK BioC 2017
Genes identified in H1 vs. NPC comparison
DE DP
DM DB
Condition
log(
norm
alize
d re
ad c
ount
s)
Not DE by SCDE or MAST
CK BioC 2017
§ Opportunities
scDD for identifying differential distributions in scRNA-seq data. Korthauer et al., Genome Biology, 2016.
Wavecrest for identifying cell lineage. Chu et al., Genome Biology, 2016.
§ Challenges due to zeros, increased variability, gene-specific distributionsOscope: for identifying and characterizing oscillations in
scRNA-seq experiments. Leng et al., Nature Methods, 2015.
OEFinder: for identifying genes with ordering effects due to position on IFC. Leng et al., Bioinformatics, 2016.
SCDC: for reducing the variation imposed by identified oscillators.
SCnorm: for scRNA-seq normalization. Bacher, Chu et al., Nature Methods, 2017.
Summary
CK BioC 2017
Acknowledgementscknowledgements
Jamie Thomson, VMD, PhDRon Stewart, PhDLi-Fang Chu, PhD
Scott Swanson, MS
Biomedical Computing GroupNIH R01GM076274NIH U54 AI117924
Rhonda Bacher, PhDZiyue WangYing LiJared BrownJacob MarongeZijian Ning
Ning Leng, PhDKeegan Korthauer, PhDShuyun Ye, PhD
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