Metabolic steady state

Metabolic steady state is condition of cell in which concentrations of the metabolites inside the cell do not change over time. In cells that are growing exponentially, such as microbes in their log phase of growth, the cells are in metabolic pseudo-steady state as the concentration of metabolites inside the cells in bulk, remain constant on average.

Although it might be difficult for you to accept this but we can actually do experiments to study metabolism assuming this metabolic steady state and generate data that would be observed only when this condition was true.

For any metabolite to be in steady state, the rate of formation of that metabolite should be equal to the rate of consumption of the metabolite. For example, let’s take one hypothetical metabolite “A”. For this example, “A” is produced by reactions “R1” and “R2”, and consumed by reactions “R3”, “R4” and “R5”. This can be represented by a diagram as follows:

 

 

When `A` is in metabolic steady state, i.e., when concentration of `A` remains constant, the sum of the reaction rates, i.e., the sum of fluxes of reaction that produce `A` (R1, and R2) would be equal to the sum of the fluxes of reactions that consume it (R3, R4 and R5). This can be written in the form of a simple equation.

 R1 + R2 = R3 + R4 + R5

This can also be written as:

R1 + R2 - R3 - R4 - R5 = 0

A metabolic steady state model of a cell would have similar equations for each metabolite inside the cell. They could be represented in a single matrix equation. We will cover it sometime later. However, our example model of one metabolite, `A` above, can be represented in matrix equation form as follows:

Sv = 0

which in long form is:

 

The `S` is called as the stoichiometric matrix. The `v` is called the flux vector. On the right-hand side, it is just a matrix with all values equal to zero. For our example, there is just one value in this matrix.

Note that in our example there is one metabolite and 5 reactions. Thus, the stoichiometric matrix has 1 row and 5 columns. We can construct stoichiometric matrix of whole metabolic network of a cell but that would be explained in later write-up.