text: The simplest example of receptor–ligand kinetics is that of a single ligand L binding to a single receptor R to form a single complex C
  The equilibrium concentrations are related by the dissociation constant K
  where k and k are the forward and backward rate constants, respectively.  The total concentrations of receptor and ligand in the system are constant
  Thus, only one concentration of the three ([R], [L] and [C]) is independent; the other two concentrations may be determined from R, L and the independent concentration.
  This system is one of the few systems whose kinetics can be determined analytically. Choosing [R] as the independent concentration and representing the concentrations by italic variables for brevity (e.g., ), the kinetic rate equation can be written
  Dividing both sides by k and introducing the constant 2E = R - L - K, the rate equation becomes
  where the two equilibrium concentrations  are given by the quadratic formula and  D is defined
  However, only the  equilibrium has a positive concentration, corresponding to the equilibrium observed experimentally.
  Separation of variables and a partial-fraction expansion yield the integrable ordinary differential equation
  whose solution is
  or, equivalently,
  for association, and
  for dissociation, respectively; where the integration constant φ is defined
  From this solution, the corresponding solutions for the other concentrations  and  can be obtained.