Quantifying thermodynamic bottlenecks of metabolic pathways. Elad Noor TAU, October 2012

Transcription

1 Quantifying thermodynamic bottlenecks of metabolic pathways Elad Noor TAU, October 2012

2 Hulda S. Haraldsdóttir Ronan M. T. Fleming Wolfram Liebermeister Ron Milo Arren Bar-Even Avi Flamholz

3 Why are there multiple pathways that have the same function? Glycolysis: glucose => lactate Carbon fixation: CO2 => carbohydrate Carbon oxidation: carbohydrate => CO2

4 How can we select the best candidate for synthetic metabolism? Stoichiometry alone gives multiple options Bar-Even, Noor, Lewis, Milo PNAS, 2010

5 Optimizing the design of pathways

6 From above, all rivers look similar Iceland Israel

7 A closer look shows how different they can be Gullfoss (32m) Iceland Jordan "river" (~0m) Israel

8 The flow speed increases with the slope v1 large difference in potential v2 small difference in potential

9 The flux is the cross-section times the flow speed v1 A2 v2 A1 large motive force small motive force J1 = A 1 v 1 J2 = A2 v2

10 Small motive forces are generally a bad thing large motive force small motive force GOOD BAD

11 G6P From rivers to biochemical pathways F6P FBP G3P DHAP BPG 2PG 3PG PEP PYR

12 ΔG' is the equivalent of height Second law of thermodynamics: ΔG' < 0

13 ΔG' is affected by reactant concentrations Second law of thermodynamics: ΔG' < 0 Thermodynamic feasibility: A B ΔG' = ΔG' + RT ln ([B] / [A]) < 0 concentrations

14 Pathways viewed from the side [A] [B] [C] [D] [E] size represents concentration

15 In 1M concentrations some reactions are unfavorable ΔG' [A] [B] [C] [D] [E] [x] = 1M

16 Any pathway is feasible if concentrations are unbounded ΔG' [A] [B] [C] [D] [E] no constraints on [x]

17 Some pathways are infeasible under physiological bounds ΔG' [A] [B] [C] [D] [E] ΔG' > 0 1 μm < [x] < 10 mm

18 Previous works focused on feasibility "... pinpoint the pathway segment that causes thermodynamic difficulties."

19 Is there a difference between ΔG' = kj/mol and ΔG' = -20 kj/mol?

20 Every reaction is a balance between forward and backward fluxes A J+ J- B The fluxes (J+ and J-) are functions of: kinetics amount of enzyme [E] concentrations of [A] and [B]

21 The forward-backward flux ratio is a function of ΔG' alone A J+ J- B The flux-force relationship*: Beard & Qian PLoS one, 2007

22 This has been known for years...

23 The closer ΔG' is to 0 the less efficient the reaction If ΔG' approaches 0, J- approaches J+

24 The closer ΔG' is to 0 the less efficient the reaction If ΔG' approaches 0, J- approaches J+ For example: ΔG' = -0.1RT ΔG' = -2.3RT backward flux is 90% of forward flux J- = 0.9 J+ J- = 0.1 J+

25 Small motive forces translate to a higher cost in enzyme production large motive force small motive force low enzyme levels high enzyme levels

26 Relevant when all we have is ΔG' Often, the kinetic parameters are missing: Genome-scale models Not measured in this organism Not Michaelis-Menten Promiscuous activity Synthetic enzyme Theoretical pathway

27 Using flux efficiency to compare pathways

28 Some pathways are infeasible under physiological bounds ΔG' [A] [B] [C] [D] [E] ΔG' > 0 1 μm < [x] < 10 mm

29 But feasible pathways can still have a "bottleneck" of low efficiency ΔG' [A] [B] [C] [D] [E] low motive force, low efficiency 1 μm < [x] < 10 mm

30 Optimized Bottleneck Energetics score quantifies the overall efficiency ΔG' [A] [B] [C] [D] [E] OBE 1 μm < [x] < 10 mm

31 Mathematical definition of OBE Solution for the following linear problem: maximize B cmin < [xi ] < cmax ΔG' + RT ST ln(c) < -B

32 Mathematical definition of OBE Solution for the following linear problem: maximize B cmin < [xi ] < cmax ΔG' + RT ST ln(c) < -B * Note: If OBE < 0, the pathway is infeasible

33 Is there a thermodynamic difference between EMP and ED?

34 The ED pathway bypasses a bottleneck at the expense of ATP bo ck ne e ttl

35 Optimized Bottleneck Energetics [kj/mol] The thermodynamic score of the ED pathway is higher than EMP

36 Example: comparing carbon fixation pathway alternatives Natural Synthetic Calvin-Benson 3-Hydroxypropionate 3-Hydroxypropionate-4-hydroxybutyrate Dicarboxylate-4-hydroxybutyrate Bar-Even, Noor, Lewis, Milo PNAS, 2010

37 Optimized Bottleneck Energetics [kj/mol] Thermodynamic score values for all alternatives E. coli physiological conditions

38 Other reasons why being far from equilibrium is better Robustness to errors in ΔG' Embedding a synthetic pathway in a bigger network Complying with unknown concentration limitations

39 But where will we get the ΔG' from?

40 Tables of formation energies are used to calculate ΔG' ATP + H2O ADP + Pi ΔrG' = ΔfG' (ADP) + ΔfG' (Pi) - ΔfG' (ATP) - ΔfG' (H2O) Burton Thauer Alberty

41 Assuming additivity of thermodynamic properties helps estimate more ΔG Mavrovouniotis Biotech & Bioeng, 1991

42 Assuming additivity of thermodynamic properties helps estimate more ΔG Mavrovouniotis Biotech & Bioeng, 1991

43 Using group decomposition more reactions can be used ΔrG' = -ΔgrG' (-OH) - ΔgrG' (=n+<) + ΔgrG' (-n<) + ΔgrG' (=O) Mavrovouniotis Jankowski et al Noor et al.

44 Modellers choose method ad hoc Accuracy Coverage Suitable for Formation Energies + - single pathway or sub-system models Group Contribution - + genome scale models

45 Group contribution is less precise and cannot be easily combined with "known" Gibbs energies Total = -2.9 kj/mol

46 Map services were used as inspiration walking bus

47 Formation energies can be derived by linear regression derived formation energies S T stoichiometric matrix ΔfG' = -RT ln K'eq measured reaction equilibrium constants

48 S is typically rank deficient the set of reaction that are a linear sum of measured reactions range S R n there are reactions that cannot be reached by linear combination

49 Gibbs Energy of Reaction Approximation using Layered Decomposition (GERALD)

50 Gibbs Energy of Reaction Approximation using Layered Decomposition (GERALD)

51 Gibbs Energy of Reaction Approximation using Layered Decomposition (GERALD) X XR XN

52 Cross-validation shows a 20% improvement (of median error) over standard GCM CDF of the cross-validation error for observations in TECRDB

53 GERALD is being implemented as part of COBRA Open-source (python and Matlab) Integration with von Bertalanffy Automatic generation of thermodynamic models Automatic adjustment to ph and ionic strength COBRA implementation of TMFA mtow

54 Conclusions High driving forces mean less enzyme costs Optimized Bottleneck Efficiency can be used as a score to compare pathways The GERALD method provides good coverage and precision for ΔG'

55 Appendix

56

57 We can approximate J as a function of -ΔG' Define flux efficiency as:

58 We can approximate J as a function of -ΔG' Define flux efficiency as: Assume a rate law, where the total flux is constant (J+ + J- = const) so that:

59 Flux efficiency is a function -ΔG' η 100% 90% 50% 0% -ΔG' ~RT 3RT 2.7 kj/mol 7.4 kj/mol

60 Flux efficiency is a function -ΔG' η 100% 90% Concave function! 50% 0% -ΔG' ~RT 3RT 2.7 kj/mol 7.4 kj/mol

61 Flux efficiency is a function -ΔG' η 100% 90% Concave function! 50% 0% -ΔG' ~RT 3RT 2.7 kj/mol 7.4 kj/mol