What kinds of problems can (mathematical) models (of biochemical systems) solve?

I think the useful applications of computer modeling to biochemistry are in the following kind of situation: You have identified a phenotype of interest, you want to know what the molecular basis is for that phenotype, you know the form of the hypothesis (“a change in the concentration of substance X causes decreased activity of enzyme Y”), but there are too many possible instantiations of the hypothesis to test all of them experimentally (there may be 100 possibilities for “substance X” and 1000 possibilities for “enzyme Y”, giving 100,000 possible hypotheses). If you have some idea of how the system works, enough to make some kind of mathematical model of the system, and some experimental data (for example omics data comparing the condition displaying the phenotype to the condition not displaying the phenotype), you can use the computer to answer questions like: What instantiations of my hypothesis are most likely to be true, based on this dataset (or based on all available datasets)?

Hopefully the computer can help you narrow down the list of reasonable hypotheses to a number that can be tested experimentally.

Lacking a specific hypothesis form, modeling becomes much trickier. So it makes sense to frame every (most?) modeling attempt in terms of hypotheses that are explicit, or can be made explicit.

To successfully use mathematical modeling in the context of biology (i.e. to use modeling in a way that advances the understanding of the physiology some organism), there are a few questions that must carefully considered:

1. What is the specific question we're trying to answer?

2. Why is modeling the ideal way to answer this question? Is it intractable to address in the laboratory? Can modeling be used to make it tractable to address in the laboratory?

3. What modeling technique can be used to address the question?

4. What experimental follow up will be used to check the results from the model?

5. Can we just skip the modeling step and go straight to the experiment? If not, why not? If so, why are we bothering with the modeling?

These questions are carefully designed to prevent two (unfortunately very common) situations from occurring. One is that biological models often make predictions that are difficult or impossible to check experimentally. The other is that it often occurs that the only way to check the predictions of a model experimentally is to perform an experiment that one could have just as easily performed (and known to perform) without having done the modeling in the first place.

It may be that some day computer simulations in biochemistry become so good that people will believe them out of hand (as engineers and architects do, if I my understanding is accurate), but it is not an exaggeration (or at least not much of one) to say that in contemporary molecular biology the only legitimate reason for modeling is to aid in experiment selection. So that is the context through which all modeling efforts should be viewed.