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 Treatment Arsenate (AsO4 = Asi) Competitive with Pi Asi AMP-P-As Conversion to pyruvate Release of pyruvate AMP-P +Asi Trypanosoma brucei Dependence on glycolysis inhibitor1 Treatment

Something more specific? Choice #1 Starve the cell Trypanosoma brucei Dependence on glycolysis Treatment Something more specific? Choice #1 Starve the cell Choice #2 Stuff the cell pyruvate inhibitor2 Trypanosoma brucei Test ideas for inhibitors [I]

[ATP] 0 1 5 10 25 [glucose]added We know characteristics of enzymes inhibitor1 Characteristics of enzymes Analogy of radioactivity One day (1/20) P S

32 32 How often does 32S appear? [X atoms of 32P] [32P] concentration k rate constant = 1/20 of an atom per day? 1 atom of 32S per day 20 atoms of 32P __atoms of 32S per day = d[32S] / dt

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

= d[32S] / dt rate of change Characteristics of enzymes Analogy of radioactivity One day (1/20) [32P] k = d[32S] / dt concentration rate constant rate of change One day (1/3000000) [14C] concentration

k = d[14N] / dt rate constant rate of change Characteristics of enzymes Chemical reactions AMP-P-As [32P] concentration AMP-P +Asi k = d[32S] / dt rate constant rate of change

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

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

[AMP-P-As] concentration A differential equation Its solution? Check: k = = d[AMP-P-Asi] / dt rate constant rate of change = d[S] / dt = k[S] [S] = S0 e -k(t-to) = d[S] / dt = S0 (k) e -k(t-to) = -k S0 e -k(t-to) = -k [S] Characteristics of enzymes Chemical reactions

1 [S] 0.8 [S] = S0 e -k(t-to) 0.6 0.4 = d[S] / dt = k[S] 0.2 0 0 1 2 3

t (sec) 4 5 Characteristics of enzymes Chemical reactions 1 [S] = [S] 0.8 [S] = S0 e -k(t-to) 0.6 S0 0.4

0.2 tt 0 0 1 2 3 t (sec) 4 5 Characteristics of enzymes Chemical reactions 1

[S] = S0 + tt d[S] / dt [S] 0.8 0.6 S0 0.4 0.2 = d[S] / dt = k[S] tt 0 0 1 2 3

t (sec) 4 5 Characteristics of enzymes Chemical reactions (Program) Characteristics of enzymes [S]S Chemical reactions 1 0.9 0.8 0.7 0.6 0.5 0.4

0.3 0.2 0.1 0 [S] = S0 e -k(t-to) = d[S] / dt = k[S] 0 1 2 3 t t (sec) 4 5 Characteristics of enzymes

Chemical reactions = d[S] / dt = k[S] [S] = S0 + tt d[S] / dt 1 [S] 0.8 Slope0 = -k[S0] [S1] = S0 + tt d[S] / dt Slope1 = -k[S1] Use average of Slope0 and Slope1 0.6 S0 0.4 0.2 tt

0 0 1 2 3 t (sec) 4 5 Characteristics of enzymes Chemical reactions = d[S] / dt = k[S] [S] = S0 + tt d[S] / dt 1 [S]

0.8 Slope0 = -k[S0] [S1] = S0 + tt d[S] / dt Slope1 = -k[S1] Use average of Slope0 and Slope1 Runge-Kutta method 0.6 S0 0.4 0.2 tt 0 0 1 2

3 t (sec) 4 5 Characteristics of enzymes Enzymatic reactions inhibitor1 Characteristics of enzymes Enzymatic reactions Glucose-6-phosphate [G6P] concentration Fructose-6-phosphate k = = d[G6P] / dt

rate constant k0 rate of change Characteristics of enzymes Enzymatic reactions G6P + E G6PE F6PE E-complex F6P + E Characteristics of enzymes Enzymatic reactions

G6P + E1 k1f k1r E1-complex k1cf k1cr F6P + E1 dd[G6P] / dt = -[G6P] [E1] k1f + [E1-complex] k1r d[E1] / dt = -[G6P] [E1] k1f + [E1-complex] k1r + [E1-complex] k1cf - [F6P] [E1] k1cr d[E1-complex] / dt = +[G6P] [E1] k1f - [E1-complex] k1r - [E1-complex] k1cf + [F6P] [E1] k1cr d[F6P] / dt =

+[E1-complex] k1cf - [F6P] [E1] k1cr Characteristics of enzymes Enzymatic reactions G6P + E1 k1f k1r E1-complex I + E1 k1if k1ir E1-I-complex d[E1] / dt = d d[I] / dt =

k1cf k1cr - [G6P] [E1] k1f + [E1-complex] k1r +[E1-complex] k1cf - [F6P] [E1] k1cr - [I] [E1] k1if + [E1-I-complex] k1ir d [E1-I-complex] / dt = F6P + E1 Characteristics of enzymes Enzymatic reactions G6P + E1 k1f k1r E1-complex k1cf k1cr

F6P + E1 dd[G6P] / dt = -[G6P] [E1] k1f + [E1-complex] k1r d[E1] / dt = -[G6P] [E1] k1f + [E1-complex] k1r + [E1-complex] k1cf - [F6P] [E1] k1cr d[E1-complex] / dt = +[G6P] [E1] k1f - [E1-complex] k1r - [E1-complex] k1cf + [F6P] [E1] k1cr d[F6P] / dt = +[E1-complex] k1cf - [F6P] [E1] k1cr Characteristics of enzymes Enzymatic reactions G6P + E1 k1f k1r

E1-complex k1c F6P + E1 0 (steady state assumption) d[E1-complex] / dt = +[G6P] [E1] k1f - [E1-complex] k1r - [E1-complex] k1c + [F6P] [E1] k1cr d[F6P] / dt = +[E1-complex] k1c - [F6P] [E1] k1cr Characteristics of enzymes Enzymatic reactions G6P + E1 k1f k1r E1-complex

k1cf F6P + E1 [G6P] [E1] k1f = [E1-complex] k1c - [E1-complex] k1r [G6P] ([Etotal]-[E1-complex]) k1f = [E1-complex] (k1c - k1r) d[E1-complex] / dt = +[G6P] [E1] k1f - [E1-complex] k1r - [E1-complex] k1c + [F6P] [E1] k1cr d[F6P] / dt = +[E1-complex] k1c - [F6P] [E1] k1cr Characteristics of enzymes Enzymatic reactions G6P + E1 k1f k1r E1-complex

k1cf F6P + E1 [G6P] [E1] k1f = [E1-complex] k1c - [E1-complex] k1r [G6P] ([Etotal]-[E1-complex]) k1f = [E1-complex] (k1c - k1r) [E1-complex] = [G6P] [Etotal] k1f [G6P] + (k1c - k1r) d[F6P] / dt = = [G6P] [Etotal] [G6P] + (k1c - k1r)/k1f +[E1-complex] k1c - [F6P] [E1] k1cr Characteristics of enzymes Enzymatic reactions k1f k1r

G6P + E1 E1-complex d[F6P] / dt = +[E1-complex] k1c = = [G6P] [Etotal] k1c [G6P] + (k1c - k1r)/k1f [G6P] [Etotal] k1c [G6P] + Km k1cf F6P + E1 Characteristics of enzymes Enzymatic reactions G6P + E k1f

k1r 1 E1-complex k1cf d[F6P] / dt = +[E1-complex] k1c = = Max d[F6P] / dt = (Vmax) [G6P] [Etotal] k1c [G6P] + (k1c - k1r)/k1f [G6P] [Etotal] k1c [G6P] + Km [G6P] [E ] k c [G6P] + K total

1 m = [Etotal] k1c F6P + E1 Characteristics of enzymes Enzymatic reactions G6P + E 1 k1f k1r d[F6P] / dt = v (velocity) = E1-complex

k1cf [G6P] VMax [G6P] + Km d[product] / dt = [S] VMax [S] + Km F6P + E1