arXiv2026
Computational pathway design often focuses on evaluating selected pathways or optimizing fluxes in a fixed network, but gives less direct access to the combinatorial question of which other enzyme subsets of the network can support productive alternative pathways. A structured computational analysis of these networks can act as a valuable pre-step to the pathway design process. We present here a systematic approach for exploring biochemical pathway alternatives across enzyme subsets, using a computational methodology based on a rule-based modeling of the enzymes: for a biochemical system with enzyme set $S$, we evaluate all subsets $s \subseteq S$ by generating chemical reaction spaces, searching for integer-hyperflow pathways from prescribed inputs to target products, and organizing feasible subsets by set inclusion. This yields an inclusion-ordered landscape of pathway feasibility and carbon efficiency. We apply the approach to the non-oxidative pentose phosphate pathway, to non-oxidative glycolysis, and to glycolysis. Across these systems, feasible subsets occupy only a moderate fraction of all enzyme subsets, but the structure of this feasible region differs strongly between the systems. Larger enzyme sets do not consistently improve carbon efficiency when every enzyme in the tested subset is required to participate in the pathway. Instead, performance depends on specific enzyme combinations. The resulting subset landscapes are valuable means for identifying essential enzymes, candidate redundancies, and small high-performing enzyme subsets. By making the enzyme-subset landscape itself the object of analysis, the approach addresses the gap between detailed evaluation of individual candidate pathways and early-stage design decisions about which enzyme combinations are worth investigating at all.