Metabolic pathway alteration, regulation and control (5) -- Simulation of metabolic network Xi Wang...
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Transcript of Metabolic pathway alteration, regulation and control (5) -- Simulation of metabolic network Xi Wang...
Metabolic pathway alteration, regulation and control (5)
--Simulation of metabolic network
Xi Wang
02/07/2013
Spring 2013BsysE 595 Biosystems Engineering for Fuels and Chemicals
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Simulation of metabolic networkPrevious lectures: Level of metabolic pathway
• Reaction • Metabolites• Flux
• Gene--Protein--Reaction
Genome-scale metabolic network
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Simulation of metabolic network
1. Who/What controlled the reactions/flux in metabolic network?
• Enzymes• Proteins
Gene--Protein--Reaction
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Outline
1. Control of metabolic pathway• Enzyme kinetics• Single gene expression model
2. Population growth dynamics
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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(ce, cs, cp, cr)
(Stephanopoulos GN, 1998)
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Regulation of central metabolic pathway
(Covert MW et al., 2002)
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Enzyme-level metabolic regulation
Enzyme-level metabolic regulation is the main part of metabolic regulation:
1. Regulation of enzymatic activity
2. 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
fast & short response
slow & durable response
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Regulation of enzymatic activity
1. Modes of feedback inhibition/activation
(Stephanopoulos GN, 1998)
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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
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Enzyme Kinetics
• V = k3[ES]
• At steady state: d[ES]/dt = k1[E][S] - k2[ES] - k3[ES] = 0
k1[E][S] = (k2 + k3) [ES]
[ES] = k1[E][S] / (k2 + k3) , let k1 / (k2 + k3) = 1/ Km, therefore
[ES] = [E][S] / Km
• Total enzyme concentration [Et] = [E] + [ES][ES] = ([Et] - [ES]) [S] / Km
[ES] = [Et] [S] / (Km + [S])
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Michaelis-Menten Equation
V = k3 [Et] [S] / (Km + [S])
• k3 [Et] = Vmax, therefore,
V = Vmax [S] / (Km + [S]) —— Michaelis-Menten Equation
When V = ½ Vmax , [S] = Km
(Stephanopoulos GN, 1998)
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1. Low substrate concentration
[S] << Km , V = Vmax [S] / Km = K [S], first order reaction
2. High substrate concentration
[S] >> Km , V = Vmax [S] / [S] = Vmax , Zero order reaction
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Michaelis-Menten Equation
Velocity vs. substrate concentration at two enzyme concentrationsa. Michaelis-Menten Equation curveb. Double-reciprocal Lineweaver-Burk plots
(Stephanopoulos GN, 1998)
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Reversible Inhibition
1. Competitive inhibition
2. Uncompetitive inhibition
(Nelson DL and Cox MM, 2008)
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1. Competitive inhibition
Reciprocal plot of competitive inhibition
Structural similarities between substrate
(Nelson DL and Cox MM, 2008; Stephanopoulos GN, 1998)
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2. Uncompetitive inhibition
Reciprocal plot of uncompetitive inhibition
(Nelson DL and Cox MM, 2008; Stephanopoulos GN, 1998)
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Regulation of enzyme concentration
Central dogma of molecular biology
Regulation
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The structure of DNA transcription
Promoter
Ribosome binding site
Coding domain sequence
Terminator
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A model of the expression of a single gene
Deterministic rate equations description V : cell volumeSA/SR : transcription rateδM : mRNA degradation rateδP : protein degradation rateSP : 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)
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2. Cell growth
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Population Dynamics
Assume the cell grows at a condition with unlimited nutrients, spaces, and no constraints:
Logistic model of population growth:
dN / dt = r Nwhere N is the bacteria population, r is the growth rate
Solution: Nt = N0 e rt
t (0, t), N0 is the initial cell number
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Solution plotsC
ell n
umbe
r
Time
Solution plots at different N0
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Growth rate (exponential mode)
(Ye P, 2012)
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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)
Solution plots (Ye P, 2012)
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Solution plots
Assume: • K = 5 × 108 CFU ml-1
• r = 0.9 h-1
Time (h)
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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.
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Thank you for your attention!
Questions?