Gene perturbation and intervention in probabilistic Boolean networks

1. Gene perturbation and intervention in probabilistic Boolean networks Ilya Shmulevich, Edward R. Dougherty and Wei Zhang 2004. 4. 23 Seoul National Univ. BIBS Lab. Kim Ha Seong

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9. PBN G = (V, F), given function table: Since there are 2 functions for x1, 1 for x2, 2 for x3, so there are N = 4 possible networks for matrix K

10. Second Row of K (1,1,2) means that the predictors (f1(1), f2(1) , f3(2) ) will be used. K matrix: lexicographically ordered row Since there are • 2 functions for node x1 • 1 functions for node x2 • 2 functions for node x3 N = 2 * 1 * 2 = 4 N = 4 # of genes

11. Consider Pr{(1,1,0) -> (1,0,0)} with corresponds to entry A7,5 . In the functions table, we can see there are two combinations give (1,0,0). • f1(1)=1,f1(2)=0,f2(3)=0 (1,1,2) or • f2(1)=1,f1(2)=0,f2(3)=0 (2,1,2) And we can know the path (1,1,2) or (2,1,2) in the K matrix. The row indices of path( 1,1,2) and (2,1,2) of the K matrix are 2 and 4 , respectively. So we can know that A(7,5) transition probability is Pr{(1,1,0)->(1,0,0) } = P2 + P4

12. 000 001 010 011 100 101 110 111

13. Results:

14. If D0=[ 1/8,1/8,…,1/8 ] of uniform distribution, the limiting probabilities are = [ 0.15, 0,0,0,0,0,0, 0.85 ] • This means that in the long run, all three genes will be either OFF or ON , which are called absorbing. • This concept corresponds to the attractor in Boolean networks

17. x1 X(2,0) =000 001 100 101 X(2,1) =010 011 110 111 x2 0 1 XOR x1 0 0 1 0 x3 1 1 1 1 0 1 0 1 0 1 1 1 1 0 We want to compute the influence of variable x2 on variable x1. The influence of gene x2 on f1(1) So, (1+1) /4 = 0.5

18. Remind: We can calculate other Influences by the same way. The influence of gene x2 on f2(1) The total predictors of gene x1 consist of f1(1) and f2(1), so we can obtain From x1 x2 x3 To x1 x2 x3

24. X1 X2 X3 V V’ X’1 X’2 X’3 K(1) = 2 K(2) = 1 K(3) = 2

26. x1 X(2,0) =000 001 100 101 X(2,1) =010 011 110 111 x2 0 1 XOR x1 0 0 1 0 x3 1 1 1 1 0 1 0 1 0 1 1 1 1 0 We want to compute the influence of variable x2 on variable x1. The influence of gene x2 on f1(1) So, (1+1) /4 = 0.5

27. Remind: We can calculate other Influences by the same way. The influence of gene x2 on f2(1) The total predictors of gene x1 consist of f1(1) and f2(1), so we can obtain From x1 x2 x3 To x1 x2 x3

28. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 I2(x3) I2(x2) I2(x1) 0 10 20 30 40 50 60 70 80 90 100

32. 0.25 0.2 0.15 0.1 0.05 0 (011) (101) (110) 0 2 4 6 8 10 12 14 16 18 20 There are several possibilities: Find the gene that Minimizes the mean first passage time Maximizes the probability of reaching a particular state before a certain fixed time Minimizes the time needed to reach a certain state with a given fixed probability for k0=1,...,20, for starting states(011),(101), and (110) corresponding to perturbations of first, second, and third genes, respectively.

37. Cell cycle checkpoints Several checkpoints function to ensure that complete genomes are transmitted to daughter cells. One major checkpoint arrests cells in G2 in response to damaged or unreplicated DNA. The presence of damaged DNA also leads to cell cycle arrest at a checkpoint in G1. Another checkpoint, in M phase, arrests mitosis if the daughter chromosomes are not properly aligned on the mitotic spindle. Role of p53 in G1 arrest induced by DNA damage DNA damage, such as that resulting from irradiation, leads to rapid increases in p53 levels. The protein p53 then signals cell cycle arrest at the G1 checkpoint.

38. Properties of S. cerevisiae cdc28 mutants The temperature-sensitive cdc28 mutant replicates normally at the permissive temperature. At the nonpermissive temperature, however, progression through the cell cycle is blocked at START.

39. Accumulation and degradation of cyclins in sea urchin embryos The cyclins were identified as proteins that accumulate throughout interphase and are rapidly degraded toward the end of mitosis Complexes of cyclins and cyclin-dependent kinases In yeast, passage through START is controlled by Cdc2 in association with G1 cyclins (Cln1, Cln2, and Cln3). Complexes of Cdc2 with distinct B-type cyclins (Clb's) then regulate progression through S phase and entry into mitosis. In animal cells, progression through the G1 restriction point is controlled by complexes of Cdk4 and Cdk6 with D-type cyclins. Cdk2/cyclin E complexes function later in G1 and are required for the G1 to S transition. Cdk2/cyclin A complexes are then required for progression through S phase, and Cdc2/cyclin B complexes drive the G2 to M transition.

40. Structure of MPF MPF is a dimer consisting of cyclin B and the Cdc2 protein kinase. MPF regulation Cdc2 forms complexes with cyclin B during S and G2. Cdc2 is then phosphorylated on threonine-161, which is required for Cdc2 activity, as well as on tyrosine-15 (and threonine-14 in vertebrate cells), which inhibits Cdc2 activity. Dephosphorylation of Thr14 and Tyr15 activates MPF at the G2 to M transition. MPF activity is then terminated toward the end of mitosis by proteolytic degradation of cyclin B.

41. Mechanisms of Cdk regulation The activities of Cdk's are regulated by four molecular mechanisms. Induction of D-type cyclins Growth factors regulate cell cycle progression through the G1 restriction point by inducing synthesis of D-type cyclins via the Ras/Raf/ERK signaling pathway.

42. Control of the G2 checkpoint A complex of checkpoint proteins recognizes unreplicated or damaged DNA and activates the protein kinase Chk1, which phosphorylates and inhibits the Cdc25 protein phosphatase. Inhibition of Cdc25 prevents dephosphorylation and activation of Cdc2.

43. The SV40 genome The genome is divided into early and late regions. Large and small T antigens are produced by alternative splicing of early-region pre-mRNA Interaction of Rb with oncogene proteins of DNA tumor viruses The oncogene proteins of several DNA tumor viruses (e.g., SV40 T antigen) induce transformation by binding to and inactivating Rb protein.

44. cdk7 cdk2 Rb Cycin H Cyclin E p21/WAF1 DNA synthesis • Process of Cells move from G1 phase to S phase: • Cyclin E and cdk2 work together to phosphorylate the Rb protein and inactivate it • Cdk2/Cyclin E is regulated by two switches: • Positive switch complex called CAK; • Negative switch P21/WAF1; • The CAK complex can be composed of two gene products: • Cyclin H; • Cdk7 • When cyclin H and cdk7 are present, the complex can activate cdk2/cyclin E. CAK cdk7 cdk2 cyclin H cyclin E Rb p21/WAF1

45. Cell cycle regulation of Rb and E2F In its underphosphorylated form, Rb binds to members of the E2F family, repressing transcription of E2F-regulated genes. Phosphorylation of Rb by Cdk4, 6/cyclin D complexes results in its dissociation from E2F in late G1. E2F then stimulates expression of its target genes, which encode proteins required for cell cycle progression.

46. Induction of p21 by DNA damage DNA damage results in the elevation of intracellular levels of p53, which activates transcription of the gene encoding the Cdk inhibitor p21. In addition to inhibiting cell cycle progression by binding to Cdk/cyclin complexes, p21 may directly inhibit DNA synthesis by interacting with PCNA (a subunit of DNA polymerase d).

48. Proof. P=0 P>0 (Theorem2)