design of pgns for malaria parasite and cell cycle control systemsjb/lectures/genetic...
TRANSCRIPT
-
Design of PGNs for
malaria parasite and cell cycle
control systems
Junior Barrera
DCC-IME-USP / BIOINFO-USP
-
Layout
• Introduction
• Probabilistic genetic network (PGN)
• Cell cycle regulation
• Design of PGN from data
• Malaria parasite
-
Layout
• Introduction
• Probabilistic genetic network (PGN)
• Cell cycle regulation
• Design of PGN from data
• Malaria parasite
-
GENES NETWORK
Translat.Transcr.
Proteins
Pool
Pathways
Metabolic
microarray
Regulatory System
-
Layout
• Introduction
• Probabilistic genetic network (PGN)
• Cell cycle regulation
• Design of PGN from data
• Malaria parasite
-
GENE is aGENE is a
NON LINEAR STOCHASTIC GATENON LINEAR STOCHASTIC GATE
SYSTEM: SYSTEM: built by compiling these gatesbuilt by compiling these gates
Expression of a Gene Expression of a Gene depends ondepends on
Activator and Inhibitory SignalsActivator and Inhibitory Signals
-
Network dynamics:
State of the regulatory network at time t:
=
][
.
.
][
][
][
2
1
tx
tx
tx
tx
n
}1,0,1{][ +−∈txi
])[(]1[ txtx φ=+
Expression of gene i at time t:
-
φi ]1[ +txi
][tx j
][txk
=
nφ
φ
φ
φ
.
.
.
2
1
])[(]1[ txtx ii φ=+
target
predictors
-
Probabilistic Genetic Network (PGN)
φi
−−
=+
])[],[|1( 1
])[],[|0(0
])[],[|1(1
]1[
txtxp
txtxp
txtxp
tx
kj
kj
kj
i
][tx j
][txk
])[],[|(])[],[|(])[],[|(
:},1,0,1{,,
txtxwptxtxzptxtxyp
wzywzy
kjkjkj +>>
≠≠−∈∃
-
Layout
• Introduction
• Probabilistic genetic network (PGN)
• Cell cycle regulation
• Design of PGN from data
• Malaria parasite
-
Phases of the Cell CyclePhases of the Cell Cycle
(*)
-
Model: architecture and dynamicsModel: architecture and dynamics
Transition Function
aij = ag green arrow from i to j
aij = ar red arrow from i to j
Simulation parameters: ag = -ar = 1
Li, 2004.
-
Time StepsTime Steps
One single pulse of One single pulse of CSCS = 2 at = 2 at t = t = --11DeterministicDeterministic
START
G1
S
G2
M
Stationary G1
-
0000--33
0000--22
0000--11
110000
111111
111122
111133
)1( +tS j0)( =tS j 1)( =tS j
∑j
jij Sa )0(
M MM
M M M
00
00
11
22
22
22
22
00
00
00
11
22
22
22
00
00
00
00
11
22
22
--33
--22
--11
00
11
22
33
)1( +ty j
0)( =tS j 1)( =tS j∑
j
jij Sa )0(
M MM
M M M
2)( =tS j
M
M
Binary 3 Levels (0, 1, 2)00
21 →→
-
00
00
11
22
22
22
22
00
00
00
11
22
22
22
00
00
00
00
11
22
22
--33
--22
--11
00
11
22
33
)1( +ty j
0)( =tS j 1)( =tS j∑
j
jij Sa )0(
M MM
M M M
2)( =tS j
M
M
=
=
=+
=+
005.0 with
005.0 with
99.0 with )1(
)1(
Pb
Pa
Pty
tx
i
i
{ } { })1(2,1,0, where +−∈ tyba i
Stochastic Transition Function
-
PGN with PGN with P = P = 0.99 0.99 One single pulse of One single pulse of CSCS = 2 at = 2 at t = t = --11
Time StepsTime Steps
-
Total input signal driving a generic variable
: memory of the system
Driving functionDriving function forfor
: weight for variable at time
Our gene modelOur gene model
∑∑= =
−=N
j
m
k
j
k
jii ktxatd1 1
)()(
-
StochasticStochastic
TransitionTransition
FunctionFunction
Our gene modelOur gene model
<
≤≤
≥
=+
1
21
2
)(0
)(1
)(2
)1(
ii
iii
ii
i
thtdif
thtdthif
thtdif
ty
-
Our network architectureOur network architecture
G1 G1 phasephase S, G2 S, G2 andand M M phasesphases
time
Forward Forward signalsignal
Feedback to P Feedback to P
Feedback to Feedback to previousprevious
layerlayer
Trigger gene
F F : : integrationintegration ofof signalssignals fromfrom layerlayer ss
ss PP wwvv zzyyxxGene Gene LayersLayers
s1
I
s2
s5
ExternalExternal
stimulistimuli
F
P
v
w1
w2
x1
x6
y1
y2
z
.
.
.
.
.
.
-
One single pulse of One single pulse of FF = 2 at = 2 at t = t = --11
Time StepsTime Steps
z
F
P
v
w1
x1
y1
PGN with PGN with P = P = 0.990.99
-
Signal Signal FF = period 50 oscillator= period 50 oscillator
Time StepsTime Steps
z
F
P
v
w1
x1
y1
PGN with PGN with P = P = 0.990.99
-
Signal Signal FF = period 10 oscillator= period 10 oscillator
Time StepsTime Steps
z
F
P
v
w1
x1
y1
PGN with PGN with P = P = 0.990.99
-
Signal Signal FF = period 3 oscillator= period 3 oscillator
Time StepsTime Steps
z
F
P
v
w1
x1
y1
PGN with PGN with P = P = 0.990.99
-
Layout
• Introduction
• Probabilistic genetic network (PGN)
• Cell cycle regulation
• Design of PGN from data
• Malaria parasite
-
Architecture
Identification.][],...,2[],1[ nxxx
target genes
-
Entropy
∑−∈
=
→−
}1,0,1{
1)(
]1,0[}1,0,1{:
y
yP
P
Distribution of Y
∑−∈
−=}1,0,1{
)(log)()(y
yPyPYH
Mutual information
0)|()(),( ≥−= XYHYHYXI
-1 0 1
P(Y)
-1 0 1
P(Y’)
)'()( YHYH > )''()'( YHYH =
-1 0 1
P(Y’’)
-
Mean mutual information estimation
∑ ∑∧∧∧∧
−= .))|(log()|()()]|([ XYPXYPXPXYHE
Mean conditional entropy
∑ ∑−= ))|(log().|()()]|([ XYPXYPXPXYHE
Mean mutual information
]]|[[)()],([ XYHEYHYXIE −=
)]|([)()],([ XYHEYHYXIE∧∧∧
−=
-
Estimation of P(Y|X)
If #(X=(a,b)) ≥ n, then
If #(X=(a,b)) < n, then is uniform)),(|(^
baXYP =
)),((#
)),()((#)),(|(
^
baX
baXcYbaXcYP
=
=∧====
Y: the taget gene at t+1, that is,
X: the predictors at t, that is, ])[],[( txtxX kj=
]1[ += txY i
For a fixed parameter n
-
Estimation of P(X) for a fixed parameter n
X
P(X)
If #(X=(a,b)) ≥ n, then
If #(X=(a,b)) < n, then
])[],[( txtxX kj=
∑∀
-
- For each target gene, rank the couples of all genes by
_their estimated mutual information and sample size;
- When two mutual information are equal, the one
_estimated from a larger sample comes first;
- Choose the best couples;
- Design the interaction graph
Buiding Interaction Graphes
-
Layout
• Introduction
• Probabilistic genetic network (PGN)
• Cell cycle regulation
• Design of PGN from data
• Malaria parasite
-
The life cycle of the malaria parasite
CAMDA, 2004
-
Back
-
Malaria parasite genes with almost
sinusoidal signals
DeRisi, 2003.
Sinousoidal
signals
-
DeRisi, 2003.
Functional Classification
-
Malaria parasite genes
Sinousoidal
signals
Non sinousoidal
signals
-
Functional Classification
-
Interaction Graph
Glycolisis Apicoplast
-
System architecture
USP datasetdetermination
USP
dataset
Scaling
and
quantization
Quantized
USPdataset
Design
of
PGN
Target
genes
Plasmo DB
MetabolicPathways
DeRisi´s
transcriptomeTable
of
predictors
GraphViz
Functional
groups
Overview
set
Output
graph
Biological Interpretation
-
System architecture
USP datasetdetermination
USP
dataset
Scaling
and
quantization
Quantized
USPdataset
Design
of
PGN
Target
genes
Plasmo DB
MetabolicPathways
DeRisi´s
transcriptomeTable
of
predictors
GraphViz
Functional
groups
Overview
set
Output
graph
Biological Interpretation
-
Good spots
Weak spots
Bad spots
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
1
.
.
.
6532
Genes
t
NO INTERPOLATION
-
System architecture
USP datasetdetermination
USP
dataset
Scaling
and
quantization
Quantized
USPdataset
Design
of
PGN
Target
genes
Plasmo DB
MetabolicPathways
DeRisi´s
transcriptomeTable
of
predictors
GraphViz
Functional
groups
Overview
set
Output
graph
Biological Interpretation
-
Scaling
For each i, estimate the mean
and standard desviation
of the spots
]][[^
txE i
]][[^
txiσ
]][[
]][[][][
^
^
tx
txEtxtn
i
iii
σ
−=
Scale normalization of the spots
-
Quantization
Let and denote, respectively, the normalized
signals greater and lower than zero at t.
][tni+ ][tni
−
1 then ]],[[][ If
0 then ]],[[][ and ]][[][ If
1 then ]],[[][ If
^
^^
^
−=<
=≤≥
+=>
−−
++−−
++
[t]xtnEtn
[t]xtnEtntnEtn
[t]xtnEtn
iii
iiiii
iii
-
System architecture
USP datasetdetermination
USP
dataset
Scaling
and
quantization
Quantized
USPdataset
Design
of
PGN
Target
genes
Plasmo DB
MetabolicPathways
DeRisi´s
transcriptomeTable
of
predictors
GraphViz
Functional
groups
Overview
set
Output
graph
Biological Interpretation
-
Architecture
Identification.]48[],...,2[],1[ xxx
target genes
-
System architecture
USP datasetdetermination
USP
dataset
Scaling
and
quantization
Quantized
USPdataset
Design
of
PGN
Target
genes
Plasmo DB
MetabolicPathways
DeRisi´s
transcriptomeTable
of
predictors
GraphViz
Functional
groups
Overview
set
Output
graph
Biological Interpretation
-
Output example
Plastid genomeIn Overview
Organelar Translation machinery
In Overview
Unknown groupIn Overview
Unknown groupNot in Overview
In Overview
Not in Overview
-
Back
-
Back
-
Back
-
Back
-
J. Barrera, R.M. Cesar Jr., C. P. Pereira, D. Martins,
R. Z. Vencio, E. F. Merino, M. M. Yamamoto
www.bioinfo.usp.br