1. Applications of Symbolic Logic to Gene Regulation Systems Department of Computer Science and Information Engineering of National Chi-Nan University Advisor: Professor R. C. T. Lee Speaker: Chuang Chieh Lin

2. 2 CSIE in Nation Chi-Nan University, June 4, 2004 Motivation and Idea Gene AGene BGene CGene DGene E DNA Protein P P transcription factor protein kinase catalyze protein phosphatase phosphorylated protein transcription factor Through the graph above, we know that each gene’s expression may affect other genes’ expression. Actually, such affections includes activations, inhibitions, etc.

3. 3 CSIE in Nation Chi-Nan University, June 4, 2004 Suppose we have “gene A activates gene B”, we obtain if gene A is activated, gene B will be activated and if gene A is not activated, gene B won’t be activated. Similarly, we can obtain that if gene A is activated, gene B will be inhibited and if gene A is not activated, gene B will be activated from “gene A inhibits gene B”. We say that “A is inhibited” is the same as “A is not activated”, and “A is activated” is the same as “A is not inhibited”. AB activate AB inhibit

4. 4 CSIE in Nation Chi-Nan University, June 4, 2004 Therefore, we have an idea that how a gene can regulate the other genes may be simply represented by symbolic logic. AB activate AB inhibit For example,

5. 5 CSIE in Nation Chi-Nan University, June 4, 2004 The Resolution Principle Method This method can be seen in Professor R. C. T. Lee’s classic “Symbolic Logic and Mechanical Theorem Proving”. For example,

6. 6 CSIE in Nation Chi-Nan University, June 4, 2004 Boolean Gene Regulatory Network A Boolean gene regulatory network is shown as follows. Genes A, B and C are called key regulators because no genes can affect each of them. A D B F E C G – + AND – + – – +

7. 7 CSIE in Nation Chi-Nan University, June 4, 2004 State Determination Problem Assume that we know whether the key regulators are activated or inhibited, determine that each other gene is activated or inhibited. We can determine all gene’s expression, that is, activated or inhibited by the depth-first-search method or the resolution principle method. A D B F E C G – + AND – + – – + 0 1 1 0: inhibited 1: activated

8. 8 CSIE in Nation Chi-Nan University, June 4, 2004 AA B C andDActivatedEActivated FInhibited GInhibited

9. 9 CSIE in Nation Chi-Nan University, June 4, 2004 Implicit Interaction Finding Problem The implicit interaction finding problem is to derive more interactions from a Boolean gene regulatory network A B – + D – C + A B – + D – C + A B – + D – C + – – AND

10. 10 CSIE in Nation Chi-Nan University, June 4, 2004 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (2)&(4) (1)&(3) (3)&(7) (15)      By applying the resolution principle method, we have

11. 11 CSIE in Nation Chi-Nan University, June 4, 2004 Future Work Gene Name Gene Expression ABCDEFGHIJKLMN X1X1X1X1 X2X2X2X2 Normal Condition 1011110011100111 Disruption of A 0110001110100111 Overexpression of B 1111011011100111 The identification problem is to determine whether there exists only one Boolean gene regulatory network consistent with the given data. A B G E – + – F + + I – H J – – M – K C + + D X2X2 X1X1 + + OR AND NI + Thank you.