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OOS 33-3
Theoretical modeling C- and N- acquiring exoenzyme activities to balance microbial demands during decomposition

**Background/Question/Methods**

** **We seek to estimate the allocation of extracellular enzymes by decomposer microorganisms between three general classes of enzymes: one that oxidizes polyphenolic compounds (C_{3}≈lignin), one that hydrolyzes polysaccharides (C_{2}≈holocellulose) and one that hydrolyzes N-containing substrates (C_{1}, e.g., proteins). Our central assumptions are that allocation (1) maximizes total C-yield from C_{2}-C_{3} complexes (lignocellulose) while (2) simultaneously matching C and N requirements for microbial growth. We then estimate allocation over a range of litter qualities, represented by lignocellulose index (LCI = C_{3}/[C_{2}+C_{3}]) values from 0 to a theoretical maximum of LCI_{max}, and for different quantities of total nitrogen content (i.e., proportional to C_{1}). Reverse Michaelis-Menten (RMM) equations estimate the proportional allocation of the total extracellular enzymes (E_{T}) to oxidative (E_{3}) and hydrolytic (E_{2} and E_{1}) pools (E_{T}=E_{1}+E_{2}+E_{3}) necessary to achieve these decay rates, i.e., dC_{i}/dt = V_{maxi}·E_{i}/(K_{Ei}+E_{i}). This is done by first setting E_{2}=ß·(E_{2}+E_{3}) and E_{3}=(1-ß)·(E_{2}+E_{3}), and solving for ß to maximize C-yield from dC_{2}/dt+dC_{3}/dt. Then we set E_{1}=ø·(E_{1}+ß·(E_{2}+E_{3})) and E_{2}=(1-ø)·(E_{1}+ß·(E_{2}+E_{3})), and solve for ø to match C-yield from dC_{1}/dt+dC_{2}/dt+dC_{3}/dt to N-yield from dC_{1}/dt, given the C:N content of C_{1}.

**Results/Conclusions **

The resulting model is consistent with generally reported patterns of enzyme activity concomitant with litter quality. For example, E_{3} > 0 only when the net yield of assimilable C from dC_{2}/dt+dC_{3}/dt > the yield from dC_{2}/dt, alone. It also demonstrates that relative N-availability associated with C_{1} (and presumably as mineral N) can reduce both E_{2} and E_{3} with respect to the balance of realized C-yield from lignocellulose decay. In other words, available N can inhibit lignin decay by shifting enzyme allocation to maximize overall carbon use efficiency, potentially mineralizing N from C_{1} even if C_{2} is available in C_{2}-C_{3} complexes. However, this mineralization threshold varies with the sizes and relative assimlation efficiencies of the substrate pools, E_{T}, and CN ratios of substrates and microorganisms.