Steady-state Analysis of Gene Regulatory Networks via G-networks

1. 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 Group • Dept. Electrical and Electronic Engineering Haseong Kim, ErolGelenbe

2. Introduction Introduction • 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

3. Introduction Objective Gene Regulatory Network Structures • Infer the steady-state probabilities of genes in GRNs • G-network Theory Microarray Gene Expression

4. Queuing Networks A Simple Queuing System Server Queuing system Queue Customer l: Input rate m : Service rate q : Utilization rate (Steady-state probability that a server is busy)

5. Queuing Networks 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

6. G-networks G-Networks • G-networks have positive, negative customers and signals E. Gelenbe, 1991, 1993

7. G-networks G-networks for GRNs A. Araziet. al., 2004 E. Gelenbe, 2007

8. G-networks E. Gelenbe, 2007

9. G-networks The Solution of the G-networks E. Gelenbe, 2007

10. G-networks Parameter Estimation P+(i,j) =P-(i,j) =Q(i,j,l) =Q(j,i,l) =1 ri = number of outdegrees of gene i mi = mRNA degradation rate of gene i

11. G-networks Parameter Estimation Boundary of total input rate Li Initial transcription rate without any external effects Positive Inputs from other genes are zero and queues fully work

12. G-networks Parameter Estimation Compute qiu by solving the following equation numerically Select Li* and qi* which are maximizing the Liu

13. 4-gene Networks Stochastic Gene Expression Model H. McAdams and A. Arkin, 1997 J. Paulsson, 2005 A. Riberio et al., 2006

14. 4-gene Networks 4-Gene Network Example Gillespie Algorithm (D. Gillespie, 1977) Generalized Gillespie Algorithm (D. Bratsun, 2005)

15. 4-gene Networks Parameters of the Stochastic Gene Expression Model Table 1

16. 4-gene Networks 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

17. 4-gene Networks Normal Abnormal

18. 4-gene Networks Simulation Results 20 datasets each of which have randomly selected 50 samples Compute steady-state probabilities and p-values of t-test

19. Yeast Cell Cycle Yeast Cell Cycle Wittenberg C. 2005 Bahler J. 2005 Bloom J. 2007

20. Yeast Cell Cycle Reconstructed Cell Cycle GRN

21. 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)

22. Yeast Cell Cycle 13 Genes Expression Profiles

23. Steady-State Probabilities

24. 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)