  Due to its implication in cancer treatment, the Warburg Effect has received
extensive in silico investigation. Flux Balance Analysis (FBA), based on
constrained optimization, was successfully applied in the Warburg Effect
modelling. Yet, the assumption that cell types have one invariant cellular
objective severely limits the applicability of the previous FBA models.
Meanwhile, we note that cell types with different objectives show different
extents of the Warburg Effect. To extend the applicability of the previous
model and model the disparate cellular pathway preferences in different cell
types, we built a Nonlinear Multi-Objective FBA (NLMOFBA) model by including
three key objective terms (ATP production rate, lactate generation rate and ATP
yield) into one objective function through linear scalarization. By
constructing a cellular objective map and iteratively varying the objective
weights, we showed disparate cellular pathway preferences manifested by
different cell types driven by their unique cellular objectives, and we gained
insights about the causal relationship between cellular objectives and the
Warburg Effect. In addition, we obtained other biologically consistent results
by using our NLMOFBA model. For example, augmented with the constraint
associated with inefficient mitochondria function or limited substrate, NLMOFBA
predicts cellular pathways supported by the biology literature. Collectively,
NLMOFBA can help build a complete understanding towards the Warburg Effect in
different cell types.
