There is still considerable skepticism in many quarters regarding the utility of mathematical models in molecular biology. Those of us who do model are frequently required to justify our activities. The preferred justification is the ‘you can’t argue with success’ rationale, which can be used in cases where you already have a working model on hand that’s generating accurate predictions and yielding useful insights.
Unfortunately, in cases where you have yet to build that model, it is necessary to resort to other, more long-winded justifications for modeling. This Gilman and Arkin review nicely sums up the reasons I typically give for modeling:
The detailed models we examine demonstrate the principal strength of modeling: It is a means to formulate all available knowledge about a system in as precise a manner as possible. In so doing, it allows a number of complex questions to be posed: (a) Is the available knowledge self-consistent? This question can often be answered during the formulation of a model. Contradictory information about the system needs to be resolved before a model can be completed. (b) Is the available knowledge of a system’s components and their interactions sufficient to account for all the system’s known behavior? If not, a model can often focus attention on areas that would most benefit from further investigation. (c) What are the consequences of various manipulations to the system (e.g., knocking out genes, modifying promoters, modulating various biochemical reactions with pharmaceuticals, etc.)? A model can provide predictions that are at the same level of detail as the model’s formulation. A highly detailed mechanistic model can in principle predict a wide range of quantities, from the detailed timecourses of protein and nucleic acid levels, through the activation states of genes, all the way to a final phenotypic outcome. To date, questions like these have most often been treated informally, using drawn diagrams, conceptual thought, and logical argument. An excursion to the limits of such faculties, however, may be had with a glance at, say, a chart of metabolism or any of the maps at the Alliance for Cellular Signaling (http://www.afcs.org), or the contemplation of the mechanistic bases of quantitative trait loci, mutations with partial penetrance, “susceptibility” phenotypes, and mutants that are not gain/loss of function but disturbances of control of function. Proper intellectual treatment of such things will require increasingly complex hypotheses about how the systems we study work, and the more complex a hypothesis, the more difficult it is to check for internal consistency, to assess for explanatory power, and to reason from about consequences using unaided human thought.
The Finch and Pea 
All good points. In addition, it’s often important simply to be forced to make your assumptions explicit. And to be forced to recognize the implications of the “cartoon” models we draw — once the model has more than one feedback or feedforward loop, human intuition about the behavior of the system is largely useless.
We just had a great conversation yesterday in our lab about a similar point regarding the utility of models that are amenable to mathematical abstraction, even if we do not have enough information to actually create the abstraction, because that kind of model forces us to make our assumptions and variables explicit.