Modelling Biochemical Reaction Networks Lecture 10: Glycerol - PowerPoint PPT Presentation

Modelling Biochemical Reaction Networks Lecture 10: Glycerol metabolism, Part II Marc R. Roussel Department of Chemistry and Biochemistry

SBML: Systems Biology Markup Language ◮ A standardized computer-readable format for representing biochemical models ◮ Allows a specification of rate laws, parameters and their units, compartments, chemical species, reactions, etc. ◮ Example SBML model: http://sbml.org/More_Detailed_Summary_of_SBML ◮ Many computer programs are designed to create and work with SBML models without you having to know how to do it by hand. = ⇒ data interchange format ◮ Many models available in a searchable database: http://www.ebi.ac.uk/biomodels-main ◮ This database can generate xppaut input files for an SBML model.

Borrowing from the literature ◮ For standard pathways like glycolysis, we can often find a literature (possibly SBML) model where someone else has done the work collecting parameters, working out the ODEs, etc. ◮ Strategy: Look for a model that contains as much of the relevant pathways as possible, and add whatever is necessary from there. ◮ May need to also delete irrelevant reactions

Model glycerol dihydroxyacetone glyceraldehyde glycerol 3−phosphate phosphate 3−phosphate H O CH OH CH 2 OH CH 2 OH ATP ADP NAD + + NADH + H 2 C C HO C H HO C H O H C OH glycerol glycerol triose phosphate kinase 3−phosphate isomerase 2− 2− C H O H CH 2 PO 4 dehydrogenase CH 2 PO 4 2− 2 CH 2 PO 4 1,3−bisphosphoglycerate 3−phosphoglycerate 2−phosphoglycerate 2− H O O O − O O − PO O 4 C C ADP ATP C C NAD + NADH + H + 2− C C C C H OH H OH H OH H PO 4 glyceraldehyde phosphoglycerate phosphoglycerate 3−phosphate kinase mutase 2− dehydrogenase 2− 2− CH PO CH PO C H PO HO C H 2 4 2 4 2 4 2 enolase O O − O O − C C ATP ADP 2− C O H C PO 4 pyruvate kinase C H C H 3 2 pyruvate phosphoenolpyruvate

Model of Hynne and Sørensen Biophys. Chem. 94 , 121 (2001). ◮ This model of glycolysis in Saccharomyces cerevisiae has most of the reactions we need, and several we don’t. ◮ Get xppaut code, and prune out unnecessary stuff. ◮ For species considered constant in our model, replace init (initial condition) statements by param and delete differential equation. Examples: ATP, extracellular glycerol ◮ Delete all references to sink (pyruvate). ◮ Model contains rate for “glycerol synthesis”, i.e. the reaction dihydroxyacetone phosphate + NADH → glycerol + NAD + This is the reverse of what we want. ◮ Add glycerol kinase and glycerol 3-phosphate dehydrogenase reactions.

Glycerol 3-phosphate dehydrogenase ◮ Catalyzes the reaction Gol3P + NAD + ⇋ DHAP + NADH (Gol3P=glycerol 3-phosphate; DHAP=dihydroxyacetone phosphate) ◮ The rate of the reverse reaction, which dominates under most conditions in vivo , has been studied extensively and obeys the equation v g3pd , rev = v (rev) max , g3pd [NADH][DHAP] 1 + [NAD + ] / K iq � � � �� / K b (1 + [P i ] / K P , g3pd ) [NADH] + K ia 1 + [NAD + ] / K iq � � ��� +[DHAP] [NADH] + K a Cai et al., J. Biotech. 49 , 19 (1996).

Glycerol 3-phosphate dehydrogenase ◮ Little is known about the kinetics of the forward reaction. ◮ We do however know the equilibrium constant for the reaction: K eq = [DHAP][NADH] [Gol3P][NAD + ] = 2 . 9 × 10 − 5 Cai et al., J. Biotech. 49 , 19 (1996).

Glycerol 3-phosphate dehydrogenase ◮ Because we’re treating NADH and NAD + as constant, the rate law for the reverse reaction reduces to v ′ max , g3pd [DHAP] / K g3pd , DHAP v g3pd , rev = 1 + [DHAP] / K g3pd , DHAP where v (rev) max , g3pd [NADH] v ′ max , g3pd = [NADH]+ K a ( 1+[NAD + ] / K iq ) K b ( 1+[P i ] / K P , g3pd )[ [NADH]+ K ia ( 1+[NAD + ] / K iq )] K g3pd , DHAP = [NADH]+ K a ( 1+[NAD + ] / K iq )

Glycerol 3-phosphate dehydrogenase ◮ Cai et al. (1996) recovered 1.5 mg of glycerol-3-phosphate dehydrogenase from 30 g of cells, with a yield of 43%. Assuming that the density of a cell is about 1 g/mL, 1 . 5 mg 1 c g3pd = 0 . 43 = 116 mg / L 30 × 10 − 3 L × ◮ Cai et al. (1996) also give a specific activity of 55 . 0 µ mol min − 1 mg − 1 , from which we calculate v (rev) max , g3pd = (116 mg / L)(55 . 0 µ mol min − 1 mg − 1 ) = 6395 µ M min − 1 ≡ 6 . 4 mM min − 1 ◮ Hynne and Sørensen’s model has [NADH] = 0.33 mM, [NAD + ] = 0 . 65 mM. K a and K iq given by Cai et al. (1996). ◮ Calculate v ′ max , g3pd = 1 . 9 mM min − 1

Glycerol 3-phosphate dehydrogenase ◮ Cai et al. (1996) also give K b , K P , g 3 pd , K ia and K iq . ◮ [P i ] = 22 mM (Albe et al., J. Theor. Biol. 143 , 163, 1990) ◮ Calculate: K g3pd , DHAP = 24 mM

Interlude: Rate law for the reversible Michaelis-Menten mechanism k − 2 k 1 ⇀ ⇀ E + S C E + P − ↽ − ↽ − − − − − − k − 1 k 2 ◮ Apply enzyme conservation and the steady-state approximation: dC dt = k 1 S ( E 0 − C ) − ( k − 1 + k − 2 ) C + k 2 P ( E 0 − C ) ≈ 0 E 0 ( k 1 S + k 2 P ) ∴ C = k 1 S + k 2 P + k − 1 + k − 2

Interlude k − 2 k 1 ⇀ ⇀ E + S − ↽ − C − ↽ − E + P − − − − k − 1 k 2 v = dP dt = k − 2 C − k 2 P ( E 0 − C ) = k 1 k − 2 E 0 S − k − 1 k 2 E 0 P k 1 S + k 2 P + k − 1 + k − 2 = v + max S / K S − v − max P / K P 1 + S K S + P K P where v + max = k − 2 E 0 K S = ( k − 1 + k − 2 ) / k 1 v − max = k − 1 E 0 K P = ( k − 1 + k − 2 ) / k 2

Back to glycerol 3-phosphate dehydrogenase ◮ Compare v = v + max S / K S − v − max P / K P 1 + S K S + P K P and v ′ max , g3pd [DHAP] / K g3pd , DHAP v g3pd , rev = 1 + [DHAP] / K g3pd , DHAP ◮ In our case, P = [DHAP], and S = [Gol3P]; v − max = v ′ max , g3pd , K P = K g3pd , DHAP . ◮ Cai et al. (1996) give K S = K Gol3P > 50 mM. Another isoform of the enzyme has K g3pd , Gol3P = 34 mM (P˚ ahlman et al., J. Biol. Chem. 277 , 27991, 2002). Use K g3pd , Gol3P = 34 mM.

Back to glycerol 3-phosphate dehydrogenase ◮ At equilibrium, v = 0, so v + max S / K S = v − max P / K P S = v + ∴ P max K P (Haldane relation) v − max K S ◮ In our case, [Gol3P] = 2 . 9 × 10 − 5 [NAD + ] [DHAP] [NADH] = 5 . 7 × 10 − 5 ◮ Solving for v + max , we get max = (5 . 7 × 10 − 5 )(1 . 9 mM / min)(34 mM) = 1 . 5 × 10 − 4 mM / min v + 50 mM

Glycerol 3-phosphate dehydrogenase Summary: v + max , g3pd [Gol3P] / K g3pd , Gol3P − v − max , g3pd [DHAP] / K g3pd , DHAP v g3pd = 1 + [Gol3P] / K g3pd , Gol3P + [DHAP] / K g3pd , DHAP with max , g3pd = 1 . 5 × 10 − 4 mM / min v + K g3pd , Gol3P = 34 mM v − max , g3pd = 1 . 9 mM / min K g3pd , DHAP = 24 mM