DynaFit Scripting Manual

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Concentration and time scale

It is important to discuss the issue of properly scaling all concentrations in such a way that round-off errors are minimized. It is also important to remember that the time unit of all rate constants (for example reciprocal seconds or minutes) must agree with the time unit of the experimental data.

Concentration scale

Optimally all concentrations would take on numerical values that differ from unity at most by three orders of magnitude.

For example, if the typical enzyme concentration in a series of experiments is 10 nM, and the typical concentration of the substrates and inhibitors is between 10 and 100 $\mu$M, then we should choose micromolar scale for all concentrations. The reason is that $10^{-6}$ is between $10^{-8}$ M for the enzyme and $10^{-4}$ M for the substrate. In this way both the numerical value of enzyme concentration (0.01 $\mu$M) and the numerical value of the substrate concentration (100 $\mu$M) differ from unity at most by two orders of magnitude.

Once a proper scale of concentrations has been determined, it affects the nominal values of two other quantities, namely, the bimolecular association rate constants and the specific molar responses. For example, if all concentrations are expressed in $\mu$M, than all bimolecular association rate constants must be expressed in $\mu{\rm M}^{-1}{\rm sec}^{-1}$ and all molar responses in signal (e.g. absorbance) change per $\mu$M.

Example

In a series of protease assays, the concentration of the enzyme was 1 nM and the concentration of the substrate was 100 $\mu$M. The hydrolysis of a chromogenic peptide substrate was followed at spectrophotometrically. At the given wavelength, the difference molar absorption coefficient is -1,300, meaning that a complete cleavage of one mole of the substrate would produce a decrease of absorbance by 1,300 units in a one centimeter cell.

In this case the proper concentration scale is micromolar, which means that the nominal concentration of the enzyme is 0.001 (micromoles per liter), and the nominal concentration of the substrate is 100 (micromoles per liter). Assuming that the bimolecular association rate constant is $10^8$ ${\rm M}^{-1}{\rm sec}^{-1}$, the nominal value is 100 (liter per micromole per second). The nominal value of the difference absorption coefficient is -0.0013 (absorbance units per micromole per liter per centimeter).

Time scale

The time scale of the experimental data must agree with the time scale of the rate constants. Most published values of rate constants for biochemical reactions are in reciprocal seconds. Therefore it is useful to convert all progress curve data files in such a way that the readings of time are in seconds. DynaFit can convert existing data files automatically, by properly setting the option Scale in the [Filter] section of the initialization file.

Similarly, all initial velocity data should be transformed in such a way that the reaction rates are expressed in concentrations (or other units such as absorbance or fluorescence intensity) per second. If the initial velocity data were not generated by DynaFit, it might be necessary to convert the data manually. DynaFit does not have the ability to convert the time-scale of initial velocity data from minutes to seconds.

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Petr Kuzmic | Jul 12 2005