Abundance or concentration?

When writing rate laws (or constitutive relations) involving mass action kinetics, modelers have different preferences for the units of the SBML species (states, state variables).

In my lectures I expressed a preference for abundance units (molecules/cell) rather than concentration units (moles/L or Molar). Another systems biologist whose published models adopt this preference is Upinder Bhalla.

Because nearly all of the theory of biochemical kinetics was developed in well-mixed compartments like test tubes or spectrophotometer cuvettes, it became standard practice to say that the mass action rate law for a second order reaction is

flux = k [A] [B],

where [A] is the concentration of A. This is a correct and widely used rate law.

But it is NOT the only possible rate law, and in many modeling situations the abundance-based rate law has significant advantages.

In terms of abundances, the rate law for a second order reaction is

flux = k’ A B, where A is the abundance of A.

First, convince yourself that neither of these two rate laws is wrong. Perhaps the simplest way to do this is to recognize the the two volumes of distribution (Va for A and Vb for B) are lumped into the k’ of the abundance-based rate law. In other words, A is always proportional to [A] and B is always proportional to [B], so the only difference between the two rate law expressions is the constant of proportionality.

In return for this slightly unconventional approach, you gain significant advantages, especially when your model contains more than one place (or compartment) and some of your processes or reactions involve transport from one place to another.

  1. The units of all your fluxes are molecules min-1cell-1. This is helpful because mass is conserved and concentration is not conserved when you move from one volume of distribution to another.
  2. You don’t have to keep track of the changes in volume as you move from one place to another (for example, from cytosol to ER). This alone will prevent headaches.
  3. You don’t have to pretend you know the volumes of distribution of a species residing in an organelle membrane (for example, a receptor)
  4. The numerical values of all your state variables are directly comparable
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