<p>(A) The combined host-viral form of the integrated FBA problem is a stoichiometric matrix (Stoich.) that can be considered as blocks: left, the independent host stoichiometric matrix; right, viral reactions consuming host metabolites. The combined matrix may be further organized by host metabolites that do not supply viral reactions (rows of the matrix in the upper right) and host metabolites that are consumed by viral reactions (rows at the bottom aligned with Host-Viral Stoich). The vector of fluxes contains host reaction rates at the top and viral reaction fluxes at the bottom to multiply properly with the host-left and viral-right organization of reactions in the stoichiometric matrix. Accumulation is allowed at the intersections of host viral metabolism (Met. Accumulation; right), but the steady-state assumption is enforced for host-only metabolites (0). A simplified flowchart (B) of the algorithm for integrated simulations, where Initialize indicates the definition of media nutritional conditions and the start of iterations across time, simulating at each integration time point the individual T7 ODEs and <i>E. coli</i> FBA, then reconciling the viral rate metabolite demand with host network state supply (Allocate). Both models are then recalculated to incorporate information on their mutual constraint (Revised Viral Demand, and Infected Host Fluxes). Update of environmental information and regulatory constraints at the initiation of each integration step (not specifically denoted on figure) further constrains the host-viral system.</p
