Unifying measures of gene function and evolution
Wolf, Carmel, Koonin, Proc. Roy Soc. B, in press
Nothing in (systems) biology makes sense except in the light of evolutionafter Theodosius Dobzhansky (1970)
Eugene V. Koonin, National Center for Biotechnology Information, NIH, Bethedsa
With the advent of OMICS data…
The game of correlations began…
Systems Biology and Evolution
Evolutionary systems biology:• In principle, we address the classical problem: the
relationship between the (largely neutral?) evolution of the genome and the (largely adaptive) evolution of the phenotype
• In practice, the progress of genomics + other OMICS allows us to measure, on whole-genome scale, the effects of all kinds of molecular phenotypic characteristics (expression level, protein-protein interactions etc etc) on evolutionary rates – this typically yields weak, even if significant, correlations
• Can we synthesize these measurements to produce a coherent picture of the links between phenomic and genomic evolution?
The Cautionary Tale
"It was six men of Indostan / To learning much inclined, Who went to see the Elephant / (Though all of them were blind), That each by observation / Might satisfy his mind "
(J.G. Saxe)
The Cautionary Tail
"…each was partly in the right / And all were in the wrong"(J.G. Saxe)
Different Faces of the Hypercube?
Synthesis
Pairwisecorrelations
Analysis of Multidimensional Data
Analysis of Multidimensional Data
"fair world" model "unfair world" model
Analysis of Multidimensional Data
Principal Components Analysis (PCA) introduces a new orthogonal coordinate system where axes are ranked by the fraction of original variance accounted for.
PC1
PC2PC3
PCA• PCA takes a set of variables and defines new variables that are linear
combinations of the initial variables. • PCA expects the variables you enter to be correlated (as is the case in the correlation game of Systems Biology). • PCA returns new, uncorrelated variables, the principal components or
axes, that summarize the information contained in the original full set of variables.
• PCA does not test any hypotheses or predict values for dependent variables; it is more of an exploratory technique.
• The data entered represent a cloud of points, in n-space. • The cloud is, typically, longer in one direction than another, and that
longest dimension is where the points are the most different; that's where PCA draws a line called the first principal component.
• The first principal component is guaranteed to be the line that places your sample points the farthest apart from each other, in that way, PCA "extracts the most variance" from your data. This process is repeated to get multiple components, or axes.
The Data Set: KOGsIdeally, we would like to obtain and synthesize the data on individual genes in precise space-time coordinates (e.g., instant evolutionary rates)
However:• some of the variables are not easily measurable (if defined at
all) for genes in extant species [e.g. rate of evolution];• other variables are measurable in principle but, in practice, are available only for a few species [e.g., expression level]• much of the data are inherently noisy, either due to technical
problems or true biological variation [e.g. fitness effect of gene disruption].
Thus, we analyze orthologous protein sets, using the proteins from different species to derive complementary data and smooth out variations in other.
Practically, this means using the KOG dataset (with additions): 10058 KOGs from 15 species (Koonin et al. 2004, Genome Biol).
The Data Set: KOGs
100 Myr
Arath
Orysa
Dicdi
Enccu
Maggr
Neucr
Schpo
Sacce
Canal
Caeel
Caebr
Drome
Cioin
Homsa
Musmu
Original KOGs for some species, "index orthologs" for other.
10058 KOGs altogether
Variables: Gene LossPropensity for Gene Loss (PGL), introduced by Krylov et al. (Genome Res. 13, 2229-2235, 2003).
At CeDm Hs Sc Sp Ec
Gene loss
Computed from KOG phyletic pattern.
Originally an empirical measure (Dollo parsimony reconstruction of events; ratio of branch lengths).
In this work – employs an Expectation Maximization algorithm.
Variables: Gene DuplicationNumber of Paralogs, average number observed for a given KOG.
Example: KOG0417 (Ubiquitin-protein ligase) and KOG0424 (Ubiquitin-protein ligase).
At1g16890 At1g36340 At1g64230 At1g78870 At2g16740 At2g32790 At3g08690 At3g08700 At3g13550 At4g27960 At5g25760 At5g41700 At5g53300 At5g56150
CE03482 CE09712 CE10824 CE28997
7292764 7292948 7295708_2 7296089 7297757 7298165 7299919
Hs17476541 Hs22043797 Hs22054779 Hs22064361 Hs4507773 Hs4507775 Hs4507777 Hs4507779 Hs4507793 Hs5454146 Hs7661808 Hs8393719
YBR082c YDR059c YDR092w YGR133w
SPAC11E3.04c SPAC1250.03 SPBC119.02 SPBC1198.09
ECU10g0940 ECU11g1990
At3g57870 CE01332 CE09784
7296195 Hs4507785 YDL064w SPAC30D11.13 ECU01g0940
Variables: Evolution Rate
Ascomycota:Sordariomycetes vs. Yeasts
Select a taxon
Build an alignment (MUSCLE);
Compute distance matrix (PAML);
Select minimum distance between members of the two subtrees of the group.
Variables: Expression LevelExpression Level data for S. cerevisiae, D. melanogaster and H. sapiens were downloaded from UCSC Table Browser (hgFixed).
Organism Table No. exp. No. prob. No. KOGs
Sacce yeastChoCellCycle 17 6602 3030
Drome arbFlyLifeAll 162 4921 2617
Homsa gnfHumanAtlas2All 158 10197 3872
Standardized (=0; =1) log values; median expression level among paralogs was used to represent a KOG.
Variables: Interactions
Protein Protein and Genetic Interactions (PPI and GI) data for S. cerevisiae, C. elegans and D. melanogaster were downloaded from GRID Web site.
Median number of interaction partners among paralogs was used to represent a KOG.
Variables: Lethality
Lethality of Gene Knockout data for S. cerevisiae were downloaded from MIPS FTP site (0/1 values).
Embryonic Lethality of RNAi Interference data for C. elegans were taken from Kamath et al., 2003 (0/1 values).
Missing DataTotal: 38 variables in 10058 KOGs – lots of missing data.
Complete data (all 38 variabless available): 23 KOGs – too few.
Combined data: 7 variables, 1482 KOGs with complete data; 4124 with at most one missing point; 3912 KOGs after removal of outliers.
Example: evolution rate.At.Os Sc.Ca Mg.Nc Hs.Mm. Pl.MF
KOG0009 - 0.168 0.300 - 0.405KOG0010 0.671 1.252 0.606 0.087 1.492KOG0011 0.905 1.698 0.428 0.073 1.547KOG0012 - 2.238 0.665 0.244 -KOG0013 0.355 - - 0.014 1.343KOG0014 1.913 4.041 - 0.126 2.840KOG0015 - 2.286 0.400 0.027 -KOG0016 - - 0.506 0.380 -
0.667 1.864 0.521 0.075 1.910
At.Os Sc.Ca Mg.Nc Hs.Mm. Pl.MF- 0.090 0.575 - 0.2121.006 0.672 1.162 1.166 0.7811.358 0.911 0.821 0.984 0.810- 1.201 1.275 3.275 -0.532 - - 0.181 0.7032.869 2.168 - 1.692 1.487- 1.227 0.767 0.365 -- - 0.970 5.087 -
Average0.2930.9570.9771.9170.4722.0540.7863.028
VariablesPhenotypic
• EL – expression level
• PPI – protein-protein interactions
• GI – genetic interactions
• KE – knockout effect
• NP – number of paralogs
Evolutionary
• ER – (sequence) evolution rate
• PGL – propensity for gene loss
The correlationsNP PPI GI PGL ER EL KE
NP -
PPI 0.057 -
GI 0.060 0.034 -
PGL 0.000 -0.125 -0.019 -
ER -0.070 -0.200 0.034 0.141 -
EL 0.129 0.199 -0.050 -0.099 -0.277 -
KE 0.027 0.234 -0.048 -0.181 -0.155 0.188 -
Two Tiers of Variables
"evolutionary"variables
"phenotypic"variables
Observation on the pattern of pairwise relationships in the data: "phenotypic" and "evolutionary" variables behave differently.
"bigger is better"
"slow is good,fast is bad"
Two Tiers of Variables
"evolutionary"variables
"phenotypic"variables
positive
positive
negative
Observation on the pattern of pairwise relationships in the data: "phenotypic" and "evolutionary" variables behave differently.
The correlations
non-essential(almost by definition)
low-expressed
relativelyfast-evolving
NP PPI GI PGL ER EL KE
NP -
PPI 0.057 -
GI 0.060 0.034 -
PGL 0.000 -0.125 -0.019 -
ER -0.070 -0.200 0.034 0.141 -
EL 0.129 0.199 -0.050 -0.099 -0.277 -
KE 0.027 0.234 -0.048 -0.181 -0.155 0.188 -
PCA of the Data SpacePC.1 PC.2 PC.3
NP 0.17 0.69 0.44PPI 0.46 0 -0.17GI 0 0.67 -0.54PGL -0.33 0 0.51ER -0.47 0 -0.20EL 0.48 0 0.36KE 0.45 -0.27 -0.21-----------------------------------------% var. 25.0 15.3 14.5
PC125.0%
PC215.3%
PC314.5%
PC412.4%
PC512.2%
PC610.6%
PC710.0%PC1
25.0%
PC215.3%
PC314.5%
PC412.4%
PC512.2%
PC610.6%
PC710.0%
Sphericity
PCA of the Data Space
PC1
PC
2
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7NPGI
PGLER
EL
PPI
KE
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7NPGI
PGLER
EL
PPI
KE
PCA of the Data Space
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
NP
GI
PGL
EL
PPI
KE
PPI
ER
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
NP
GI
PGL
EL
PPI
KE
PPI
ER
PC2
PC
3
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7NPGI
PGLER
EL
PPI
KE
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7NPGI
PGLER
EL
PPI
KE
PC1 – Gene’s “status"
"important""accessory"PC1
PC
2
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7NPGI
PGLER
EL
PPI
KE
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7NPGI
PGLER
EL
PPI
KE
PC2 – "Adaptability"
PC1
PC
2
"flex
ible
""r
igid
"
PC2 and Expression Profile Skew
Skew ~0 Skew >0
S. cerevisiae 0.29 0.291x100 0.32 0.443x10-3
D. melanogaster 1.82 1.844x10-1 1.82 1.907x10-2
H. sapiens 1.75 1.947x10-4 1.87 2.12<1x10-20
PC2 PC2LO HI p-value LO HI p-value
Status - LO Status - HI
Omnibus test 1x10-2 <1x10-20
PC3 – "Reactivity"
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
NP
GI
PGL
EL
PPI
KE
PPI
ER
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
NP
GI
PGL
EL
PPI
KE
PPI
ER
PC2
PC
3
PC3 and Expression Profile Skew
S. cerevisiae 0.26 0.313x10-1 0.22 0.50<1x10-20
D. melanogaster 1.77 1.886x10-2 1.86 1.859x10-1
H. sapiens 1.80 1.943x10-4 1.86 2.13<1x10-20
PC3 PC3LO HI p-value LO HI p-value
Status - LO Status - HI
Omnibus test 4x10-4 <1x10-20
Skew ~0 Skew >0
Relationships Between Variables
"evolutionary"variables
"ADAPTABILITY""REACTIVITY"
"phenotypic"variables
"STATUS"
Status and Adaptability of Genes
Classification of KOGs into 4 major categories
Status
Adap
tabi
lity
Status and Adaptability of Genes
Classification of KOGs into 4 major categories
Status
Adaptability
Reactivity
INF
CELL
MET
UNKN
Status and Adaptability of Genes
Cytoplasmic and Mitochondrial ribosomal proteins
-5 -4 -3 -2 -1 0 1 2 3 4 5-4
-3
-2
-1
0
1
2
3
4
5
6
Status
Ada
ptab
ility
Status and Adaptability of Genes
Vacuolar ATPase and Vacuolar Sorting proteins
-5 -4 -3 -2 -1 0 1 2 3 4 5-4
-3
-2
-1
0
1
2
3
4
5
6
Status
Ada
ptab
ility
Status and Adaptability of Genes
Replication Licensing Complex and Histones
-5 -4 -3 -2 -1 0 1 2 3 4 5-4
-3
-2
-1
0
1
2
3
4
5
6
Status
Ada
ptab
ility
-5 -4 -3 -2 -1 0 1 2 3 4 5-4
-3
-2
-1
0
1
2
3
4
5
6
Status
Ada
ptab
ility
Status and Adaptability of Genes
RNA processing and modification
Core Cluster(spliceosome and mRNA cleavage-polyadenylation
complex)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1
23
4
Adaptability
Rea
ctiv
ityAdaptability and Reactivity of Genes
translation and ribosome
replication, RNA processing and
modification
signal transduction
carbohydrate transport and metabolism
Status, adaptability, and reactivity of selected multisubunit complexes and functional classes of proteins
Major functional categories No. of KOGs
Average status
Average adaptability
Average reactivity
Information storage and processing
951 0.553* -0.164* -0.146*
Cellular processes and signaling 1216 0.179* 0.201* -0.080* Metabolism 692 -0.057 0.075 0.494* Poorly characterized 1053 -0.669* -0.134* -0.100*
Complexes No. of KOGs
Average status
Average adaptability
Average reactivity
Cytoplasmic ribosome 76 2.679* 0.203 1.226* Mitochondrial ribosome 40 -0.004 -0.527* -0.089 Chaperonin complex TCP-1 8 2.237* -0.291 -0.299 Spliceosome 50 1.234* -0.511* -0.393* mRNA cleavage and polyadenylation
10 0.968* -0.609 -0.705
Proteasome 33 2.158* -0.547* -0.329* Exosome 12 0.967* -0.660 -0.419 Nucleosome 6 1.933 1.875 1.727 Vesicle coat complex 19 1.360* -0.496* -0.049 Vacuolar H+-ATPase 13 1.696* -0.449 0.345 Mitochondrial F0F1-ATP synthase
13 1.110* -0.427 0.083
Replication licensing complex 6 1.475* -1.154 -0.046 Aminoacyl-tRNA syntetases 33 0.425 -0.478* -0.131 * - Significantly different from zero (P < 0.05), using t-test with Bonferroni correction.
Conclusions• Three composite, independent variables – "status",
"adaptability" and "reactivity" – dominate the multidimensional data space of quantitative genomics.
• The notion of status provides biologically relevant null hypotheses regarding the connections between various measures.
• Breaks in the pattern possibly indicate something nontrivial (targets for further investigation).
• Functional groups of genes show distinctive patterns of status, adaptability, and reactivity
Co-AuthorsLiran Carmel Eugene Koonin
Yuri Wolf
