1. Metabolic pathway alteration, regulation and control (5) -- Simulation of metabolic network Xi Wang 02/07/2013 Spring 2013 BsysE 595 Biosystems Engineering for Fuels and Chemicals

2. Simulation of metabolic network Previous lectures: Level of metabolic pathway Reaction Metabolites Flux Gene--Protein--Reaction 2 Genome-scale metabolic network

3. Simulation of metabolic network 1.Who/What controlled the reactions/flux in metabolic network? Enzymes Proteins Gene--Protein--Reaction 3

4. Outline 1.Control of metabolic pathway Enzyme kinetics Single gene expression model 2. Population growth dynamics 4

5. Control of metabolic pathway In living systems, control of biological function occurs at the molecular and cellular levels. These controls are implemented by the regulation of concentrations of species taking part in biochemical reactions, including concentrations of enzymes (E), substrates (S), products(P), and regulatory molecules (R) The rate of an enzymatic reaction can be generally expressed as v = v(c e, c s, c p, c r ) 5 (Stephanopoulos GN, 1998)

6. Regulation of central metabolic pathway 6 (Covert MW et al., 2002)

7. Enzyme-level metabolic regulation Enzyme-level metabolic regulation is the main part of metabolic regulation: 1.Regulation of enzymatic activity 1.Regulation of enzyme concentration Example: E. coli grows at 20 and 37 °C: 2-D protein gel has no difference (Ingraham, 1987). It indicated that the adjustments of cell at different environment occurred on enzyme activities 7 fast & short response slow & durable response

8. Regulation of enzymatic activity 1.Modes of feedback inhibition/activation 8 (Stephanopoulos GN, 1998)

9. Enzyme Kinetics Assumptions: A reversible enzymatic reaction: The simplest enzyme-catalyzed reaction involves a single substrate(S) converted to a single product (P) via a central complex (ES). Steady state: the synthesis rate of ES = the degradation rate of ES 9

10. Enzyme Kinetics V = k 3 [ES] At steady state: d[ES]/dt = k 1 [E][S] - k 2 [ES] - k 3 [ES] = 0 k 1 [E][S] = (k 2 + k 3 ) [ES] [ES] = k 1 [E][S] / (k 2 + k 3 ), let k 1 / (k 2 + k 3 ) = 1/ K m, therefore [ES] = [E][S] / K m Total enzyme concentration [E t ] = [E] + [ES] [ES] = ([E t ] - [ES]) [S] / K m [ES] = [E t ] [S] / (K m + [S]) 10

11. Michaelis-Menten Equation V = k 3 [E t ] [S] / (K m + [S]) k 3 [E t ] = V max, therefore, V = V max [S] / (K m + [S]) —— Michaelis-Menten Equation When V = ½ V max, [S] = K m 11 (Stephanopoulos GN, 1998)

12. 1.Low substrate concentration [S] << K m, V = V max [S] / K m = K [S], first order reaction 2.High substrate concentration [S] >> K m, V = V max [S] / [S] = V max, Zero order reaction 12

13. Michaelis-Menten Equation 13 Velocity vs. substrate concentration at two enzyme concentrations a. Michaelis-Menten Equation curve b. Double-reciprocal Lineweaver-Burk plots (Stephanopoulos GN, 1998)

14. Reversible Inhibition 1.Competitive inhibition 2.Uncompetitive inhibition 14 (Nelson DL and Cox MM, 2008)

15. 1. Competitive inhibition 15 Reciprocal plot of competitive inhibition Structural similarities between substrate (Nelson DL and Cox MM, 2008; Stephanopoulos GN, 1998)

16. 2. Uncompetitive inhibition 16 Reciprocal plot of uncompetitive inhibition (Nelson DL and Cox MM, 2008; Stephanopoulos GN, 1998)

17. Regulation of enzyme concentration 17 Central dogma of molecular biology Regulation

18. The structure of DNA transcription 18 Promoter Ribosome binding site Coding domain sequence Terminator

19. A model of the expression of a single gene 19 Deterministic rate equations description V : cell volume S A /S R : transcription rate δ M : mRNA degradation rate δ P : protein degradation rate S P : protein translation rate kon/(koff + kon), koff /(kon + koff) : the fraction of time that the gene spends in the active and repressed states, respectively (Karn M et al., 2005)

20. 2. Cell growth 20

21. Population Dynamics Assume the cell grows at a condition with unlimited nutrients, spaces, and no constraints: Logistic model of population growth: dN / dt = r N where N is the bacteria population, r is the growth rate Solution: N t = N 0 e rt t  (0, t), N 0 is the initial cell number 21

22. Solution plots 22 Cell number Time Solution plots at different N 0

23. Growth rate (exponential mode) 23 (Ye P, 2012)

24. Logistic model of single cell growth Because spaces and resources are not unlimited, cell cannot be supported in an unlimited number. Assume: K is the upper limit of cell number (carrying capacity), thus dN / dt = r N (1 – N/K) 24 Solution plots (Ye P, 2012)

25. Solution plots 25 Assume: K = 5 × 10 8 CFU ml -1 r = 0.9 h -1 Time (h)

26. Reference Covert MW, Palsson B. Transcriptional Regulation in Constraints- based Karn M, et al. Stochasticity in gene expression: from theories to phenotypes. Nature Reviews Genetics. 2005, 6:451-464. Koffas M, Roberge C, Lee K, Stephanopoulos G. Metabolic engineering. Annu. Rev. Biomed. Eng. 1999, 01: 535–557. Metabolic Models of Escherichia coli. The Journal of Biological Chemistry. 2002, 277 (31): 28058-28064. Nelson DL, Cox MM. Lehninger principles of biochemistry (Fifth edition). W.H. freeman and company, New York. 2008. Stephanopoulos GN, Aristidou AA, Nielsen J. Metabolic Engineering, Principles and Methodologies. Academic Press, 1998. 26

27. Thank you for your attention! Questions? 27