DynaFit Scripting Manual

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Concentration jump experiments

In many useful experiments, a certain number of (bio)chemical reactants are first equilibrated to form various molecular complexes. Subsequently the equilibrated mixture is diluted by the addition of the last reactant.

A good example are studies of ``slow, tight'' binding enzyme inhibitors. An enzyme E is first incubated with a reversible, ``slow, tight'' binding inhibitor I, until the mixture containing E, I, and the complex EI is at equilibrium. Finally the substrate S is added to initiate the catalytic reaction $S \rightarrow P$, while at the same the enzyme - inhibitor mixture is diluted. From this kind of a study, the rate constants governing the $E \rightleftharpoons I$ binding and dissociation can be determined.

To set up the analysis of such biphasic experiments (an equilibration phase followed by a dynamic phase), the DynaFit script file must contain in the [progress] section the keywords equilibrate and dilute.

Example 1 Enzyme E and inhibitor I were incubated at 100 nM each until equilibrium was reached. The equilibrated mixture was diluted 1:50 by the addition of substrate S. The final concentration was $[S]$ = 10.0 $\mu$M.

[mechanism]
   E + S
   E + I <==> EI  :  Ki   dissoc
[progress]
   file ff
   equilibrate E = 0.1, I = 0.1, dilute 1:50
   concentration S = 10.0

   ; final concentrations:
   ;    [E] = [I] = 0.002, [S] = 10.0

A more complex example is taken from the published biochemical literature [4,5].

Example 2: Thrombin - Dehydrothrombin - Hirudin

Thrombin (178 nM) and hirudin (208 nM) were incubated until equilibrium was achieved. The total volume was 90 $\mu$l. The equilibrated mixture was then diluted with 10 $\mu$l dehydrothrombin so that the total concentration of the mutated enzyme was 165 nM. In a complementary experiment, dehydrothrombin (183 nM) and hirudin (208 nM) were incubated in 90 $\mu$l of buffer, and 10 $\mu$l thrombin was added so that the final concentration was 160 nM. Thus the final concentrations of all components were identical in both experiments, only the order of addition was different. The concentration of free thrombin was followed over time by using a kinetic assay. [4]

[task]

   data  = progress
   task  = fit
   model = compet

[mechanism]

   E + L <===> EL  :  k1   k2
   F + L <===> FL  :  k3   k4

[constants]

   k1 = 0.001 ?? , k2 = 0.00005 ??
   k3 = 0.001 ?? , k4 = 0.00005 ??

[concentrations]

   ; All concentrations specified 
   ; in [progress] section.

[response]

   E = 1

[progress]

   directory ./examples/thrombin/data
   extension txt
   delay     30

   file d1e
      equilibrate   E=178  , L=208, dilute 90:100
      concentration F=165 ?

   file d2e
      equilibrate   E=178  , L=208, dilute 90:100
      concentration F=165 ?

   file d3e
      equilibrate   E=178  , L=208, dilute 90:100
      concentration F=165 ?

   file d4e
      equilibrate   F=183  , L=208, dilute 90:100
      concentration E=160 ?

   file d5e
      equilibrate   F=183  , L=208, dilute 90:100
      concentration E=160 ?

   file d6e
      equilibrate   F=183  , L=208, dilute 90:100
      concentration E=160 ?

[end]

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Petr Kuzmic | Jul 12 2005