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?