Overview

Our pathway model for diacetyl producer consists of two parts: ODE pathway analysis and parameter sensitivity analysis. ODE pathway analysis is to examine the feasibility of our pathway. It is the foundation of model analysis.

Figure 1.

Figure 2.

ODE pathway analysis

Aim: To model the feasibility of the diacetyl producer pathway.
Steps:

1. Build up the equations
2. Investigate reasonable parameter sets from previous learning and researches
3. Run the model and simulation
4. Verify the feasibility of the pathway model
5. Simulation for diacetyl producer

Background:
One of the most ambitious and challenging goals of metabolic engineering is the design of biological systems base on quantitative predictions with the aid of mathematical models. This is particularly because of the well-known difficulties in assessing enzyme kinetics under in vivo conditions as a prerequisite for a quantitative analysis of the reaction pathway.

Figure 3.

Model Structure:
The dynamic model of the Embden-Meyerhof-Parnas pathway(EMP) of Escherichia coli consists of mass balance equations for extracellular glucose and for the intracellular metabolites. These mass balances take the following form:

Where C_i denotes the concentration of metabolite i, μ is the specific growth rate, and v_ij is the stoichiometric coefficient for this metabolite in reaction j, the rate of which is r_j.

The balance equation for extracellular glucose is expressed as:

Where C_glc^feed is the glucose concentration in the feed, C_glc^{extracellular} is the extracellular glucose concentration, C_x is the biomass concentration, and ρ_x is the specific weight of the biomass. The term f_pulse provides allowance for the sudden change of glucose concentration caused by the glucose pulse.

Mass balance equations:

Estimation of Maximum Reaction Rates:
The rate of the enzyme i at steady state is given by:

Where is the parameter vector and is the steady-state concentration vector of the metabolites involved in the reaction. Steady-state concentrations are required for the estimation of the maximal rate, r_max and as initial conditions for the integration of the dynamic model. Some of concentrations are available from the measurements of intracellular metabolites.
The remaining concentrations are estimated from a near-equilibrium assumption for the reaction. The near-equilibrium constant for the jth reaction:

Where K_eq,j is the equilibrium constant of the jth reaction, is the steady-state concentration of the compound i , and v_i,j is the stoichiometric coefficient of compound i in reaction j.

Result: