Welcome to Introduction to Bioinformatics Wednesday, 16 October Metabolic modeling Table of Contents First exam: Rules of the game Sep 27, SQ4: Write subroutine to print score array PS1M.8: Probability of evolution

Trypanosoma brucei Causative agent of sleeping sickness Life Cycle Central Nervous System Death

Trypanosoma brucei Dependence on glycolysis Entry of glucose Phosphorylation Breakdown to triose phosphates Conversion to pyruvate Release of pyruvate Arsenate (AsO 4 = As i ) Competitive with P i As i AMP-P-As AMP-P +As i Treatment

Trypanosoma brucei Dependence on glycolysis Something more specific? Treatment Choice #1 Starve the cell inhibitor 1

Trypanosoma brucei Dependence on glycolysis Something more specific? Treatment Choice #1 Starve the cell Choice #2 Stuff the cell inhibitor 2 pyruvate

Trypanosoma brucei Test ideas for inhibitors [glucose] added [ATP] [I] inhibitor 1 We know characteristics of enzymes

Characteristics of enzymes Analogy of radioactivity How often does 32 S appear? One day (1/20) 1/20 of an atom per day? 1 atom of 32 S 20 atoms of 32 P per day __atoms of 32 S per day [X atoms of 32 P] = [ 32 P] concentration k rate constant = d[ 32 S] / dt rate of change

Characteristics of enzymes Analogy of radioactivity Which quantity is an intrinsic characteristic? One day (1/20) [ 32 P] concentration k rate constant = d[ 32 S] / dt rate of change

Characteristics of enzymes Analogy of radioactivity [ 32 P] concentration k rate constant = d[ 32 S] / dt rate of change [ 14 C] concentration k rate constant = d[ 14 N] / dt rate of change One day (1/20)

Characteristics of enzymes Chemical reactions AMP-P-AsAMP-P +As i [ 32 P] concentration k rate constant = d[ 32 S] / dt rate of change

Characteristics of enzymes Chemical reactions [AMP-P-As] concentration k rate constant = d[AMP-P ] / dt rate of change AMP-P-AsAMP-P +As i = = d[As i ] / dt rate of change = – = d[AMP-P-As i ] / dt rate of change

Characteristics of enzymes Chemical reactions [AMP-P-As] concentration k rate constant AMP-P-AsAMP-P +As i = – = d[AMP-P-As i ] / dt rate of change [S] k = – = d[S] / dt A differential equation

Characteristics of enzymes Chemical reactions [AMP-P-As] concentration k rate constant AMP-P-AsAMP-P +As i = – = d[AMP-P-As i ] / dt rate of change = d[S] / dt A differential equation = –k[S] = S 0 e -k(t-to) [S] Its solution? = S 0 (–k) e -k(t-to) = -k S 0 e -k(t-to) = -k [S] = d[S] / dt Check:

Characteristics of enzymes Chemical reactions = d[S] / dt = –k[S] [S] = S 0 e -k(t-to)

Characteristics of enzymes Chemical reactions [S] = Δt [S] = S 0 e -k(t-to) S0S0

Characteristics of enzymes Chemical reactions Δt = d[S] / dt = –k[S] S0S0 + Δt d[S] / dt[S] =S0S0

Characteristics of enzymes Chemical reactions (Program)

Characteristics of enzymes Chemical reactions = d[S] / dt = –k[S] [S] = S 0 e -k(t-to)

Characteristics of enzymes Chemical reactions Δt = d[S] / dt = –k[S] S0S0 + Δt d[S] / dt[S] =S0S0 Slope 0 = -k[S 0 ] [S 1 ] =+ Δt d[S] / dtS0S0 Slope 1 = -k[S 1 ] Use average of Slope 0 and Slope 1

Characteristics of enzymes Chemical reactions Δt = d[S] / dt = –k[S] S0S0 + Δt d[S] / dt[S] =S0S0 Slope 0 = -k[S 0 ] [S 1 ] =+ Δt d[S] / dtS0S0 Slope 1 = -k[S 1 ] Use average of Slope 0 and Slope 1 Runge-Kutta method

inhibitor 1 Characteristics of enzymes Enzymatic reactions

[G6P] concentration k rate constant Glucose-6-phosphate Fructose-6-phosphate = – = d[G6P] / dt rate of change k  0

Characteristics of enzymes Enzymatic reactions G6P + E G6P·EF6P·EF6P + E E-complex

Characteristics of enzymes Enzymatic reactions G6P + E 1 E 1 -complexF6P + E 1 d d[G6P] / dt = d[E 1 ] / dt = d[E 1 -complex] / dt = d[F6P] / dt = -[G6P] [E 1 ] k 1 f + [E 1 -complex] k 1 r k1fk1f k1rk1r k 1 cf k 1 cr -[G6P] [E 1 ] k 1 f + [E 1 -complex] k 1 r + [E 1 -complex] k 1 cf - [F6P] [E 1 ] k 1 cr +[G6P] [E 1 ] k 1 f - [E 1 -complex] k 1 r - [E 1 -complex] k 1 cf + [F6P] [E 1 ] k 1 cr +[E 1 -complex] k 1 cf - [F6P] [E 1 ] k 1 cr

Characteristics of enzymes Enzymatic reactions G6P + E 1 E 1 -complexF6P + E 1 d d[E 1 ] / dt = d[I] / dt = d [E 1 -I-complex] / dt = k1fk1f k1rk1r k 1 cf k 1 cr - [G6P] [E 1 ] k 1 f + [E 1 -complex] k 1 r +[E 1 -complex] k 1 cf - [F6P] [E 1 ] k 1 cr - [I] [E 1 ] k 1 if + [E 1 -I-complex] k 1 ir I + E1I + E1 k 1 if k 1 ir E 1 -I-complex

Characteristics of enzymes Enzymatic reactions G6P + E 1 E 1 -complexF6P + E 1 d d[G6P] / dt = d[E 1 ] / dt = d[E 1 -complex] / dt = d[F6P] / dt = -[G6P] [E 1 ] k 1 f + [E 1 -complex] k 1 r k1fk1f k1rk1r k 1 cf k 1 cr -[G6P] [E 1 ] k 1 f + [E 1 -complex] k 1 r + [E 1 -complex] k 1 cf - [F6P] [E 1 ] k 1 cr +[G6P] [E 1 ] k 1 f - [E 1 -complex] k 1 r - [E 1 -complex] k 1 cf + [F6P] [E 1 ] k 1 cr +[E 1 -complex] k 1 cf - [F6P] [E 1 ] k 1 cr

Characteristics of enzymes Enzymatic reactions G6P + E 1 E 1 -complexF6P + E 1 d[E 1 -complex] / dt = d[F6P] / dt = k1fk1f k1rk1r k1ck1c +[G6P] [E 1 ] k 1 f - [E 1 -complex] k 1 r - [E 1 -complex] k 1 c + [F6P] [E 1 ] k 1 cr +[E 1 -complex] k 1 c - [F6P] [E 1 ] k 1 cr 0 (steady state assumption)

Characteristics of enzymes Enzymatic reactions G6P + E 1 E 1 -complexF6P + E 1 d[E 1 -complex] / dt = d[F6P] / dt = k1fk1f k1rk1r k 1 cf +[G6P] [E 1 ] k 1 f - [E 1 -complex] k 1 r - [E 1 -complex] k 1 c + [F6P] [E 1 ] k 1 cr +[E 1 -complex] k 1 c - [F6P] [E 1 ] k 1 cr [G6P] [E 1 ] k 1 f = [E 1 -complex] k 1 c - [E 1 -complex] k 1 r [G6P] ([E total ]-[E 1 -complex]) k 1 f = [E 1 -complex] (k 1 c - k 1 r)

Characteristics of enzymes Enzymatic reactions G6P + E 1 E 1 -complexF6P + E 1 d[F6P] / dt = k1fk1f k1rk1r k 1 cf +[E 1 -complex] k 1 c - [F6P] [E 1 ] k 1 cr [G6P] [E 1 ] k 1 f = [E 1 -complex] k 1 c - [E 1 -complex] k 1 r [G6P] [E total ] k 1 f [G6P] [E total ] [G6P] + (k 1 c - k 1 r) [G6P] + (k 1 c - k 1 r)/k 1 f [G6P] ([E total ]-[E 1 -complex]) k 1 f = [E 1 -complex] (k 1 c - k 1 r) [E 1 -complex] = =

Characteristics of enzymes Enzymatic reactions G6P + E 1 E 1 -complexF6P + E 1 d[F6P] / dt = +[E 1 -complex] k 1 c k1fk1f k1rk1r k 1 cf [G6P] [E total ] k 1 c [G6P] + (k 1 c - k 1 r)/k 1 f = [G6P] [E total ] k 1 c [G6P] + K m =

Characteristics of enzymes Enzymatic reactions G6P + E 1 E 1 -complexF6P + E 1 d[F6P] / dt = +[E 1 -complex] k 1 c k1fk1f k1rk1r k 1 cf [G6P] [E total ] k 1 c [G6P] + (k 1 c - k 1 r)/k 1 f = [G6P] [E total ] k 1 c [G6P] + K m = Max d[F6P] / dt = (V max ) = [E total ] k 1 c

Characteristics of enzymes Enzymatic reactions G6P + E 1 E 1 -complexF6P + E 1 d[F6P] / dt = k1fk1f k1rk1r k 1 cf [G6P] V Max [G6P] + K m d[product] / dt = [S] V Max [S] + K m v (velocity) =