FBApro: A fast, simple linear transformation for diverse metabolic modeling tasks

Constraint-based metabolic modeling is the predominant framework for simulating cellular metabolism. The central assumption of these models is that metabolism operates at a steady state, meaning that the production and consumption rates of each metabolite are balanced. This assumption imposes linear constraints on the fluxes of biochemical reactions. Flux Balance Analysis (FBA), a fundamental method in the field, is formulated as an optimization problem maximizing a cellular objective (e.g., growth) over the resulting linear subspace of steady state fluxes. Many other methods in the field are expressed either as a modification to FBA, or use FBA as a black box within an algorithm. Here, we propose a general alternative to optimization called FBApro. For any given vector of reference fluxes, FBApro finds the closest flux vector within the steady-state subspace, and accounts for both partially given reference fluxes and exact constraints on reactions. While FBApro is the solution to a quadratic program, we show that it can be implemented as a single linear operation using orthogonal projections to corresponding affine spaces and sets of linear equations. The overall approach is computationally efficient, does not require a cellular objective, and is easy to implement. We formally derive the closed-form expressions for FBApro and simpler variants, and validate it on both synthetic and real cancer cell line data.