As you mentioned it is a method based on nitrogen content. But you refer to it is a protein quantification method.
Is there any particular reason why you want to use this method?
The thing is that you probably know that Berthelot's reagent is an alkaline solution of phenol and hypochlorite and its use is based on the fact that Ammonia reacts with this Berthelot's reagent. The reagent is often used for determining urea. In this case the urea is determined indirectly after the enzyme urease is used to catalyse the hydrolysis of urea into carbon dioxide and ammonia. It has been reported that the Phenol in the Berthelot reagent can be replaced by for example sodium salicylate, that has been used for blood urea nitrogen (BUN) determinations.
Replacement of phenol by 2-phenylphenol reduces interferences by a variety of soil and water constituents and improves color stability at slightly lower pH. Perhaps this comes close to what you are looking for.
It could be that you stumbled on some reference which did use a method based on the Berthelot reaction for this purpose. In that case it looks like the Kjeldahl method. This method measures the nitrogen in a protein sample after it’s been converted to ammonia after a number of time consuming steps. It is basically based on assumption that your original protein sample was 16% nitrogen and then back-calculate the total amount of protein.
Unless you have a very good reason to use the Berthelot method I would say try something that is usually used by others. As you probably know one of the following well-known ways to quantify protein content are:
BCA: This colorimetric assay, like the Lowry assay, uses complexation of the protein(s) with copper ions. Subsequently this protein-bound copper chelates BCA to give an intense purple color. Its tolerance to samples containing detergents and its more uniform response to different proteins than the Bradford assay are the benefits of this approach. Disadvantages are the sensitivity for tyrosine, tryptophan, and cysteine amino acids and for chemicals which interact with copper (such as ammonia).
Bradford: The Bradford method is one of the most commonly used methods because it is simple: based on the fact that the negatively-charged Coomassie brilliant blue dye binds to positively-charged proteins. The Bradford reaction is fast and easy, it is however less able to detect bigger proteins and it’s sensitive to detergents.
Folin-Lowry: Also based on an initial complexation of copper with the nitrogen in your protein and the subsequent complexed tyrosine and tryptophan react with Folin-Ciocalteu phenol reagent. Because of the fact that this is a so-called endpoint assay with a stable result it has lots of practical advantages however this assay is sensitive to a variety of chemicals like Tris, reducing agents such as DTT and potassium and magnesium ions.