Steady-state Analysis of Gene Regulatory Networks via G-networks
Introduction Queuing Networks G-networks Parameter Estimation Simulation Study Yeast Cell Cycle Networks Discussion
Intelligent Systems & Networks GroupDept. Electrical and Electronic Engineering
Haseong Kim, Erol Gelenbe
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Introductiono Fundamental challenges of systems biology
Modeling regulatory interactions of genes by using mathematical & statistical methods
Exploring the dynamics of the gene regulatory networks (GRNs) by analyzing their long-run (steady-state) behaviors
Introduction
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Objective
Infer the steady-state probabilities of genes in GRNs
G-network Theory
Gene Regulatory Network Structures
Microarray Gene Expression
Introduction
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
A Simple Queuing System
Queue
Server
Queuing system
Customer
l: Input ratem : Service rateq : Utilization rate (Steady-state probability that a server is busy)
Queuing Networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
A Jackson Network (The Simplest Queuing Network)
Let ki be the length of ith queue.
P(K1=k1, K2=k2, K3=k3, K4=k4)
=P(K1=k1)P(K2=k2)P(K3=k3)P(K4=k4)
where P(Ki=ki)=qiki(1-qi)
James R. Jackson, 1963
Queuing Networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
G-Networks• G-networks have positive, negative customers and signals
E. Gelenbe, 1991, 1993
G-networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
G-networks for GRNs
A. Arazi et. al., 2004E. Gelenbe, 2007
G-networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
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E. Gelenbe, 2007
G-networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
The Solution of the G-networks
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E. Gelenbe, 2007
G-networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Parameter Estimation
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G-networks
P+(i,j) =P-(i,j) =Q(i,j,l) =Q(j,i,l) =1
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Parameter Estimation
Boundary of total input rate i
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Initial transcription rate without any external effects
Positive Inputs from other genes are zero and queues fully work
G-networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Parameter Estimation
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Select i* and qi* which are maximizing the Liu
G-networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Stochastic Gene Expression Model4-gene Networks
H. McAdams and A. Arkin, 1997J. Paulsson, 2005A. Riberio et al., 2006
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
4-Gene Network Example
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4-gene Networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Parameters of the Stochastic Gene Expression Model
Parameters Values References
Transcription initiation l2 0.0025sec-1 Golding, et al., 2005; Thattai and van Oudenaarden, 2001
Translation initiation l3 0.0612sec-1 Paulsson, 2005; Thattai and van Oudenaarden, 2001
mRNA degradation 2 0.00578sec-1 Thattai and van Oudenaarden, 2001
Monomer degradation 3,mono 0.00077sec-1 Thattai and van Oudenaarden, 2001; Buchler, et al., 2005
Dimer degradation 3,dimer 0.00057sec-1 Thattai and van Oudenaarden, 2001; Buchler, et al., 2005
Dimer association ka1 0.1 Buchler, et al., 2005
Dimer dissociation kd1 0.01 Buchler, et al., 2005
DNA-protein association ka2 0.189 Goeddel et al., 1977
DNA-protein dissociation kd2 0.0157 Goeddel et al., 1977
Burst size b 10 Paulsson, 2005; Thattai and van Oudenaarden, 2001
Accumulation time of pro-teins
t 0.1 Bratsun et. al., 2005
Gene ON and OFF rate is set to zero. Cell growth rate and the cell volume is fixed.
4-gene Networks
Table 1
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Data Generation• Two sets of data
– Normal vs. Abnormal – The normal set is obtained by using the parameters in Table 1– The abnormal set is the same as the normal set except the transcription
rate of GA = 0.0012 sec-1 is a half of the normal transcription rate 0.0025 sec-1
4-gene Networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Normal
Abnormal
4-gene Networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Simulation Results
20 datasets each of which have randomly selected 50 samplesCompute steady-state probabilities and p-values of t-test
4-gene Networks
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Yeast Cell Cycle
Wittenberg C. 2005Bahler J. 2005Bloom J. 2007
Yeast Cell Cycle
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Reconstructed Cell Cycle GRN
Yeast Cell Cycle
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Expression Data
• D. Olando et. al., 2008• Yeast 2.0 oligonucleotide array• To determine which transcription factors contribute to
CDKs and to global regulation of the cell cycle transitions
• Two types of groups– Wide-type (WT) (30 time points)– Cyclin-mutant (CM) (30 time points)
Yeast Cell Cycle
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
13 Genes Expression Profiles
Yeast Cell Cycle
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Steady-State Probabilities
State Cells CLN3 WHI5 SWI4 MBP1 CLB2 YOX1 YHP1 HCM1 FKH2 NDD1 SWI5 ACE2 SIC1
S1WT 0.880 0.813 0.829 0.839 0.784 0.99 0.803 0.843 0.855 0.836 0.799 0.99 0.99
CM 0.878 0.814 0.818 0.848 0.77 0.99 0.802 0.842 0.864 0.839 0.787 0.99 0.99
S2WT 0.882 0.845 0.845 0.840 0.847 0.99 0.850 0.870 0.863 0.863 0.825 0.99 0.99
CM 0.876 0.837 0.846 0.847 0.769 0.99 0.853 0.873 0.865 0.861 0.807 0.99 0.99
S3WT 0.890 0.840 0.826 0.846 0.886 0.99 0.844 0.855 0.863 0.854 0.871 0.99 0.99
CM 0.88 0.846 0.82 0.849 0.751 0.99 0.863 0.863 0.869 0.87 0.84 0.99 0.99
S4WT 0.890 0.841 0.837 0.845 0.866 0.99 0.839 0.87 0.862 0.853 0.857 0.99 0.99
CM 0.879 0.835 0.821 0.849 0.757 0.99 0.864 0.864 0.859 0.863 0.845 0.99 0.99
S5WT 0.891 0.850 0.837 0.846 0.877 0.99 0.839 0.869 0.862 0.856 0.865 0.99 0.99
CM 0.869 0.83 0.823 0.842 0.756 0.99 0.862 0.862 0.857 0.861 0.845 0.99 0.99
Introduction Queuing Networks G-networks 4-gene Network Yeast Cell Cycle
Conclusions & Discussions
• Analyze the steady-state of GRNs by using G-networks– In simulation study, our model provides more reliable measure then the t-
statistics.– Our G-networks are applied to the yeast cell cycle data
• The structure is too simple to draw the same conclusion with the original paper of the experiment data.
• More complex and large-scale networks are required
• Future works– Improve G-network model by providing proper probabilities P+(j,i), P-(j,i),
Q(i,j,l) with ensemble base GRN estimation method (H. Kim et al, 2009)– Steady-state analysis for both transcriptional and post-transcriptional
networks (E. Gelenbe., 2008)