Growing Too Big

We discuss the scale of biochemical networks inside cells and the difficulties involved in making differential equation models at the scale of entire cells. These difficulties are primarily due not to mathematical or computational complexity but to the absence of biochemical knowledge about the enzyme kinetics. We next take a detour into systems of linear equations that are the multidimensional extensions of the y = mx + b problems many of us studied in secondary school. We introduce matrix-vector notation for representing such problems. We then return to metabolic modeling by asking if the whole-cell modeling effort can be made tractable by assuming that the metabolite concentrations in the cell are unchanging in time. Working with a toy example, we find that under this assumption the problem can be reduced to a problem in linear algebra. Adding the assumptions of a fixed set of nutrients and an evolutionary goal of maximizing cell growth from a fixed amount of those nutrients, we represent the problem as one of flux-balance analysis , and we use the QBio website to analyze a full-cell model. Exploring the idea of computationally “knocking out” reactions, we find that many of the reactions in the cell can be removed and the biochemical flux routed through other reactions. We note that this kind of biochemical robustness is different than that seen in the previous chapter and is also not due to duplicated genetic material.