Protein synthesis induced by food consumption is highly overrated and is not relevant for muscle growth.
If you are truly interested in the 'science' aspect of it, you should read brad pilon's book on protein. It shows, through a review of many different researches and studies, the amount of protein needed for muscle growth and more importantly he explains how protein synthesis is not and has never been proven to lead to long term muscle growth. As he explains, this protein synthesis crap is just a surrogate endpoint that is assumed to lead to growth and is used by supplement marketers and others pushing things like bcaas.
If you really want to worry about protein synthesis, then focus on the training induced synthesis or just start up hormones.