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.

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. 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)