Unifying measures of gene
function and evolution
Eugene V. Koonin, National Center for Biotechnology Information, NIH, Bethedsa
Nothing in (systems) biology makes sense except in the light of evolution
after Theodosius Dobzhansky (1970)
Wolf, Carmel, Koonin, Proc. Roy Soc. B, in press
Systems Biology and Evolution
With the advent of OMICS data…
The game of correlations began…
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?
Pairwise
correlations
Synthesis
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.
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: KOGs
Ideally, 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
Arath
Orysa
Dicdi
Enccu
Maggr
Original KOGs for
some species,
"index orthologs" for
other.
Neucr
Schpo
Sacce
Canal
Caeel
Caebr
Drome
Cioin
100 Myr
Homsa
Musmu
10058 KOGs
altogether
Variables: Gene Loss
Propensity for Gene Loss (PGL), introduced by Krylov et
al. (Genome Res. 13, 2229-2235, 2003).
Computed from KOG
phyletic pattern.
At CeDm Hs Sc Sp Ec
Gene loss
Originally an empirical
measure (Dollo parsimony
reconstruction of events;
ratio of branch lengths).
In this work – employs an
Expectation Maximization
algorithm.
Variables: Gene Duplication
Number 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
Select a taxon
Build an alignment (MUSCLE);
Compute distance matrix (PAML);
Select minimum distance
between members of the two
subtrees of the group.
Ascomycota:
Sordariomycetes vs. Yeasts
Variables: Expression Level
Expression 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 Data
Total: 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
0.405
KOG0010 0.671
1.252
0.606
0.087
1.492
KOG0011 0.905
1.698
0.428
0.073
1.547
KOG0012 2.238
0.665
0.244
KOG0013 0.355
0.014
1.343
KOG0014 1.913
4.041
0.126
2.840
KOG0015 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
0.212
1.006
0.672
1.162
1.166
0.781
1.358
0.911
0.821
0.984
0.810
1.201
1.275
3.275
0.532
0.181
0.703
2.869
2.168
1.692
1.487
1.227
0.767
0.365
0.970
5.087
-
Average
0.293
0.957
0.977
1.917
0.472
2.054
0.786
3.028
Variables
Phenotypic
• 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 correlations
NP
PPI
GI
PGL
ER
EL
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
KE
-
Two Tiers of Variables
Observation on the pattern of pairwise relationships in the
data: "phenotypic" and "evolutionary" variables behave
differently.
"phenotypic"
variables
"bigger is better"
"evolutionary"
variables
"slow is good,
fast is bad"
Two Tiers of Variables
Observation on the pattern of pairwise relationships in the
data: "phenotypic" and "evolutionary" variables behave
differently.
"phenotypic"
variables
positive
negative
"evolutionary"
variables
positive
The correlations
NP
PPI
GI
PGL
ER
EL
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
non-essential
(almost by definition)
low-expressed
relatively
fast-evolving
KE
-
PCA of the Data Space
PC.1
PC.2
PC.3
NP
0.17
0.69
0.44
PPI
0.46
0
-0.17
GI
0
0.67 -0.54
PGL
-0.33
0
0.51
ER
-0.47
0
-0.20
EL
0.48
0
0.36
KE
0.45 -0.27 -0.21
----------------------------------------% var. 25.0
15.3
14.5
Sphericity
PC7
10.0%
PC1
25.0%
PC6
10.6%
PC5
12.2%
PC2
15.3%
PC4
12.4%
PC3
14.5%
PCA of the Data Space
0.7
NP
GI
0.6
0.5
PC2
0.4
0.3
0.2
0.1
ER
PGL
PPI
0
EL
-0.1
-0.2
-0.3
-0.5
KE
-0.4
-0.3
-0.2
-0.1
0
PC1
0.1
0.2
0.3
0.4
0.5
PCA of the Data Space
0.6
PGL
NP
0.4
EL
PC3
0.2
0
PPI
-0.2
ER
KE
-0.4
GI
-0.6
-0.8
-0.3
-0.2
-0.1
0
0.1
0.2
PC2
0.3
0.4
0.5
0.6
0.7
PC1 – Gene’s “status"
0.7
NP
GI
0.6
0.5
PC2
0.4
0.3
0.2
0.1
ER
PGL
PPI
0
EL
-0.1
-0.2
-0.3
-0.5
KE
-0.4
-0.3
-0.2
-0.1
0
"accessory"
0.1
0.2
0.3
0.4
0.5
"important"
PC1
PC2 – "Adaptability"
NP
GI
0.6
"flexible"
0.7
0.5
0.3
0.2
0.1
ER
PGL
PPI
0
EL
-0.1
-0.2
-0.3
-0.5
"rigid"
PC2
0.4
KE
-0.4
-0.3
-0.2
-0.1
0
PC1
0.1
0.2
0.3
0.4
0.5
PC2 and Expression Profile
Skew
Skew ~0
Skew >0
Status - LO
Status - HI
PC2
PC2
LO
HI p-value LO
HI p-value
S. cerevisiae
0.29 0.29 1x100 0.32 0.44 3x10-3
D. melanogaster 1.82 1.84 4x10-1 1.82 1.90 7x10-2
H. sapiens
1.75 1.94 7x10-4 1.87 2.12 <1x10-20
Omnibus test
1x10-2
<1x10-20
PC3 – "Reactivity"
0.6
PGL
NP
0.4
EL
PC3
0.2
0
PPI
-0.2
ER
KE
-0.4
GI
-0.6
-0.8
-0.3
-0.2
-0.1
0
0.1
0.2
PC2
0.3
0.4
0.5
0.6
0.7
PC3 and Expression Profile
Skew
Skew ~0
Skew >0
Status - LO
Status - HI
PC3
PC3
LO
HI p-value LO
HI p-value
S. cerevisiae
0.26 0.31 3x10-1 0.22 0.50 <1x10-20
D. melanogaster 1.77 1.88 6x10-2 1.86 1.85 9x10-1
H. sapiens
1.80 1.94 3x10-4 1.86 2.13 <1x10-20
Omnibus test
4x10-4
<1x10-20
Relationships Between Variables
"STATUS"
"ADAPTABILITY"
"REACTIVITY"
"phenotypic"
variables
"evolutionary"
variables
Adaptability
Status and Adaptability of Genes
Status
Classification of KOGs into 4 major categories
Status and Adaptability of Genes
Status
INF
CELL
Adaptability
MET
Reactivity
UNKN
Classification of KOGs into 4 major categories
Status and Adaptability of Genes
6
5
4
Adaptability
3
2
1
0
-1
-2
-3
-4
-5
-4
-3
-2
-1
0
1
2
3
4
5
Status
Cytoplasmic and Mitochondrial ribosomal proteins
Status and Adaptability of Genes
6
5
4
Adaptability
3
2
1
0
-1
-2
-3
-4
-5
-4
-3
-2
-1
0
1
2
3
4
5
Status
Vacuolar ATPase and Vacuolar Sorting proteins
Status and Adaptability of Genes
6
5
4
Adaptability
3
2
1
0
-1
-2
-3
-4
-5
-4
-3
-2
-1
0
1
2
3
4
Status
Replication Licensing Complex and Histones
5
Status and Adaptability of Genes
Core Cluster
(spliceosome and
mRNA cleavagepolyadenylation
complex)
6
5
4
Adaptability
3
2
1
0
-1
-2
-3
-4
-5
-4
-3
-2
-1
0
Status
1
2
3
RNA processing and modification
4
5
Adaptability and Reactivity of Genes
1
0.8
0.6
4
0.4
Reactivity
carbohydrate
1 transport and
metabolism
translation
and ribosome
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1
2
3
replication, RNA
processing and
modification
-0.8
-0.6
-0.4
signal
transduction
-0.2
0
0.2
Adaptability
0.4
0.6
0.8
1
Status, adaptability, and reactivity of selected multisubunit
complexes and functional classes of proteins
Major functional categories
Information storage and
processing
Cellular processes and signaling
Metabolism
Poorly characterized
Complexes
Cytoplasmic ribosome
Mitochondrial ribosome
Chaperonin complex TCP-1
Spliceosome
mRNA cleavage and
polyadenylation
Proteasome
Exosome
Nucleosome
Vesicle coat complex
Vacuolar H+-ATPase
Mitochondrial F0F1-ATP
synthase
Replication licensing complex
Aminoacyl-tRNA syntetases
No. of
KOGs
951
Average
status
0.553*
Average
adaptability
-0.164*
Average
reactivity
-0.146*
1216
692
1053
No. of
KOGs
76
40
8
50
10
0.179*
-0.057
-0.669*
Average
status
2.679*
-0.004
2.237*
1.234*
0.968*
0.201*
0.075
-0.134*
Average
adaptability
0.203
-0.527*
-0.291
-0.511*
-0.609
-0.080*
0.494*
-0.100*
Average
reactivity
1.226*
-0.089
-0.299
-0.393*
-0.705
33
12
6
19
13
13
2.158*
0.967*
1.933
1.360*
1.696*
1.110*
-0.547*
-0.660
1.875
-0.496*
-0.449
-0.427
-0.329*
-0.419
1.727
-0.049
0.345
0.083
6
33
1.475*
0.425
-1.154
-0.478*
-0.046
-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-Authors
Liran Carmel
Yuri Wolf
Eugene Koonin