Genome-scale metabolic model (GEM) is a genome-level metabolite exchange network that targets an organism using its genomic data and combining gene annotation information (Thiele, I et al., 2010). The core of GEMs is a stoichiometry matrix containing information about all reactions and reactants in the cell. With GEMs, we can use computers to simulate the behavior of various cellular responses at the metabolic level.
Fig 1. Schematics of the predicted flux distributions in EcN(Kim, D et al., 2021)
Based on the network (Fig1), some rules, and objectives, we can make predictions about the degree (flux) of each reaction by applying some algorithms, such as conservation of mass, steady-state rules, biomass targets, and FBA algorithms (Kumar, M et al., 2019). For example, we can solve the flux of ethanol secreted by the EcN and evaluate the efficiency of fermentation theoretically.
First, we will introduce the background of the “maximum flow algorithm.”
Fig 2. Schematic diagram of the max flow algorithm
For fig 2, our goal is to make the flow to node t as large as possible, but it should be within its limit (eg. the flow from S to node ‘1’ needs to be less than 3)at the same time, which is the target and rule mentioned above. But under the GEM model, the rules we obey such as conservation of mass and algorithms we apply such as FBA are more complex.
In FBA, various compounds can be thought of as points in Fig 2, each reaction as an arrow, and the number on the arrow can be considered as the limit of the biochemical reaction (may be limited by enzyme activity, etc.). Usually, we target the model as a “biomass” reaction, which assumes that organisms are always growing in the direction of allowing themselves to grow up. The whole "biomass" reaction is not an actual reaction, but we describe the process of biological growth as a biochemical reaction.
An important step of the implementation of the algorithm is converting the metabolic network diagram (Fig1) into a stoichiometric matrix (Fig 3), and the solution of linear programming can be performed. The objective is set to the "biomass" reaction by default, and the rules are the law of conservation of mass (S*V=0, it holds that the cell reaches an equilibrium state that the transport and absorption of all substances remain balanced), and the reaction flow needs to be within the bounded range (Vmin < V< Vmax)
Fig 3 (a) constrain of the law of conservation of mass(Orth, J.D
et al., 2010)
(b) constrain of the bound of reactions
In the end, we will get a feasible region, and the highest point of our objective on it is the solution we ultimately want.
Fig 4. Spatial schematic of the solution(Orth, J.D et al., 2010)
dFBA can be considered as an extension of FBA. Its "dynamic" mainly describes the concentration of extracellular exchangeable substances dynamically through differential equations, and the upper and lower bounds (upper_bound and lower_bound) of the exchange reaction are also dynamically affected. Finally, Feedback to dynamic changes in cell growth rate. With this algorithm, we can simulate the flux changes of individual responses of cells over a period of time, and simulate the growth process of cells on a time scale. Our simulation of EcN this year is mainly based on this model and combined with the enzyme kinetic model for further expansion.
Fig 5. Schematic diagram of the dFBA algorithm
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