Producing proteins costs energy, and producing longer proteins costs more energy than shorter proteins. Producing proteins which have no function, would therefore presumably negatively impact the fitness of a bacteria in culture. So my question is this:
Is there a way of modeling how much a nonfunctional protein would impact fitness relative to the wild-type which doesn't produce this protein? In other words, what is the cost — in terms of fitness — of just producing a protein, if you ignore all the other effects of the protein inside the cell?
How much would the length of the protein effect it? would the impact on fitness vary linearly with the length of the protein?
This would probably depend on many different parameters, I'm just not sure what all of them are and how each of them would factor into the final result. For instance, it would probably depend on the level of expression of the gene (which sigma factor would impact this especially).
I posted a similar question a while ago, but I've reworded it based on feedback from last time. If it helps you to think of a specific organism to answer the question, by all means, do so. Let me know if there is any literature already on a question related to this one!