text: Computer simulations can only yield so much insight, as one would be required to run simulations on a wide range of parameter values, which can be unwieldy. A generally more powerful way to understand the properties of a model is to solve the differential equations analytically. 
  Analytical solutions are possible if simple mass-action kinetics on each reaction step are assumed:
  where  and  are the forward and reverse rate-constants, respectively.  is the substrate and  the product. If the equilibrium constant for this reaction is:
  The mass-action kinetic equation can be modified to be:
  Given the reaction rates, the differential equations describing the rates of change of the species can be described. For example, the rate of change of  will equal:
  By setting the differential equations to zero, the steady-state concentration for the species can be derived. From here, the pathway flux equation can be determined. For the three-step pathway, the steady-state concentrations of  and  are given by:
  Inserting either  or  into one of the rate laws will give the steady-state pathway flux, :
  A pattern can be seen in this equation such that, in general, for a linear pathway of  steps, the steady-state pathway flux is given by:
  Note that the pathway flux is a function of all the kinetic and thermodynamic parameters. This means there is no single parameter that determines the flux completely. If  is equated to enzyme activity, then every enzyme in the pathway has some influence over the flux.