Lee metbolic eng synthetic bio BME 162 GuestLecture Apr2_2012

I j si s j 2 m 4 m ij n n 1 k1 shredik k1

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Unformatted text preview: matics 2008;24(16):i213-9. •  Previous work on retroac0vity –  Focused only on nearest neighbors, i.e. reac0on reversibility •  Long ­range cyclical (feedback) interac0ons –  Fundamental mo0f of biochemical networks –  Metabolic cycles, allosteric regulatory loops –  Ocen mediated by cofactor metabolites (as opposed to main reactants) •  Previous work has generally ignored cofactors 4/2/12 BME 162 Guest Lecture Stavrianeas and Silverstein. Adv Physiol Educ. 2005;29 (2):128-30 52 Graph Representa0on of Metabolic Interac0ons •  Reac0on ­centric with direc0onal interac0ons –  Goal is to iden0fy groups of enzymes, rather than groups of metabolites •  An edge from R1 to R2 exists A R1 R2 B C –  If a metabolite produced by R1 is a reactant of R2 –  If a metabolite produced by R1 regulates R2 A B R8 R4 R2 R1 4/2/12 R7 R5 R3 BME 162 Guest Lecture R6 53 Shortest Retroac0ve Distance (ShReD) •  ShReDij = shortest path length from Ri to Rj + shortest path length from Rj to Ri •  If the ShReD between a pair of reac0on nodes is small (rela0ve to average), the node pair has a 0ghtly coupled cyclical interac0on, and belongs in the same module. R8 R2 R1 4/2/12 R7 R4 R3 R5 R6 Ⱥ Ⱥ R Ⱥ 1 Ⱥ R2 Ⱥ Ⱥ R3 ShReD = Ⱥ R4 Ⱥ Ⱥ R5 Ⱥ R Ⱥ 6 Ⱥ R7 Ⱥ R Ⱥ 8 BME 162 Guest Lecture R1 0 R2 3 R3 3 R4 6 R5 6 R6 6 R7 ∞ 3 0 3 6 6 6 ∞ 3 6 3 6 0 6 6 0 6 3 6 3 ∞ ∞ 6 6 6 3 0 3 ∞ 6 ∞ 6 ∞ 6 ∞ 3 ∞ 3 ∞ 0 ∞ ∞ 0 ∞ ∞ ∞ ∞ ∞ ∞ 2 R8 Ⱥ ∞ Ⱥ Ⱥ ∞ Ⱥ Ⱥ ∞ Ⱥ ∞ Ⱥ Ⱥ ∞ Ⱥ ∞ Ⱥ Ⱥ 2 Ⱥ 0 Ⱥ Ⱥ 54 Par00on Algorithm Community detection based on connectivity Module detection based on ShReD " kk % 1 Q= Aij ! i j ' si s j ($ 2 m & 4 m ij # n "n % 1 $ !k=1 ShReDik !k=1 ShReD jk ' Pij = + ' 2$ Di Dj # & Gij = Pij ! ShReDij Q = !! Gij si s j i j Ⱥ Ⱥ R Ⱥ 1 Ⱥ R2 Ⱥ Ⱥ R3 G = Ⱥ R4 Ⱥ Ⱥ R5 Ⱥ R Ⱥ 6 Ⱥ R7 Ⱥ R Ⱥ 8 R1 0 R2...
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