Is it possible to use Vmax as Kcat in a Michaelis-Menten reaction?

I am studying a biological system using ODEs. As part of my work I need to use the '$k\_\text{cat}$' version of the Michaelis-Menten reaction, which is:


$$\frac{V\_\text{max}\cdot [\ce{S}]}{(K\_\mathrm m+[\ce{S}])} = \frac{k\_\text{cat} \cdot [\ce{E}\_\text{free}] \cdot [\ce{S}]}{(K\_\mathrm m+[\ce{S}])}$$


I have found in a publication a value of a $V\_\text{max}$ for one of my reactions: 


$$V\_\text{max}=\mathrm{\frac{11.4\;pmol}{min^{-1}{\;pmol^{-1}\;enzyme}} = \frac{0.19\;nmol}{s^{-1}\;nmol^{-1}\;enzyme}}$$


My question is, since this $V\_\text{max}$ value is quoted in terms of 1 unit of enzyme (i.e. 0.19 nmol is the maximum one nmol of enzyme can catalyze in a second), can I use this $V\_\text{max}$ value as a $k\_\text{cat}$? 


here is the abstract I found the information from :



> 
> Retinoic acid (RA) is a critical signaling molecule that performs
>  multiple functions required to maintain cellular viability. It is also
>  used in the treatment of some cancers. Enzymes in the CYP26 family are
>  thought to be responsible for the elimination of RA, and CYP26A1
>  appears to serve themost critical functions in this family. In spite
>  of its importance, CYP26A1 has neither been heterologously expressed
>  nor characterized kinetically. We expressed the rCYP26A1 in
>  baculovirus-infected insect cells and purified the hexahistidine
>  tagged protein to homogeneity. Heme incorporation was determined by
>  carbon monoxide difference spectrum and a type 1 spectrum was observed
>  with RA binding to CYP26A1.We found that RA is a tight binding ligand
>  of CYP26A1 with low nM binding affinity. CYP26A1 oxidized RA
>  efficiently (depletion Km
>  9.4 3.3 nM and Vmax 11.3 4.3 pmoles min1 pmole P4501 ) when supplemented with P450 oxidoreductase and NADPH but was independent of
>  cytochrome b5. 4-Hydroxy-RA (4-OH-RA) was the major metabolite
>  produced by rCYP26A1 but two other primary products were also formed.
>  4-OH-RA was further metabolized by CYP26A1 to more polar metabolites
>  and this sequential metabolism of RA occurred in part without 4-OH-RA
>  leaving the active site of CYP26A1. The high efficiency of CYP26A1 in
>  eliminating both RA and its potentially active metabolites supports
>  the major role of this enzyme in regulating RA clearance in vivo.
>  These results provide a biochemical framework for CYP26A1 function and
>  offer insight into the role of CYP26A1 as a drug target as well as in
>  fetal development and cell cycle regulation.
> 
> 
> 




$V\_{max}=k\_{cat}[E\_0]$ where $[E\_0]$ is the total enzyme concentration and not just the free enzyme. See my answer [here](https://chemistry.stackexchange.com/a/37161/5295).


You cannot use the value of $V\_{max}$ as $k\_{cat}$ because while the latter is the property of the enzyme (actually the enzyme-substrate pair), the former is the property of the chemical sample i.e. it is a system parameter.


Obviously, the $V\_{max}$ will be same as $k\_{cat}$ for a unit-concentration of total enzyme (unit concentration does not mean [units of enzyme](http://www.wikiwand.com/en/Enzyme_unit). It means, for whatever you are using as the units of concentration in your equation, lets say unit-x, the concentration of the enzyme should be 1 unit-x)


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