2.1 | Solution and Optimization of the Kinetic Model
Our models consist of systems of rate equations and mass balances. We solved them by using the MATLAB solver ode15s with relative and absolute error tolerances of 10-6 and a vectorization step to reduce solve time. We parameterized the initial model by using parameters reported in experimental studies of purified enzymes or prior modeling analyses, and we adjusted these parameters by using the MATLAB function fminsearch (a derivative-free minimization function) to carry out the fitting routines described below.
We optimized our newly refined model of fatty acid biosynthesis by using a series of objective functions. To incorporate the contributions of FabF and FabZ to unsaturated fatty acid synthesis, we added reactions identical to those used for FabB and FabA, respectively (Tables S1-S2), and we adjusted values of kcat for FabA, FabB, FabZ, and FabF by using Obj1, where
Obj1 = SSE1 (Eq. 1)
SSE1 is the sum of squared errors between measured and predicted unsaturated fractions generated by experimentally reconstituted FASs lacking each enzyme (i.e., we normalized unsaturated fractions by the unsaturated fraction generated by the complete FAS; Tables S3-S4; (Ruppe et al., 2020)). To incorporate the contributions of FabF and FabB to initiation, we used optimization routines that include SSE2, SSE3, and SSE4, the respective sums of squared errors
Obj2 = SSE2·SSE3·SSE4 (Eq. 2) Obj3 = (1+SSE2)·(1+SSE3)·(1+SSE4) (Eq. 3) Obj4 = (1+SSE­2)·(1+SSE3)2·(1+SSE4) (Eq. 4)
for the time course, product distribution, and initial rates of fatty acid synthesis between modeled and reconstituted FASs. Our optimization process included three steps carried out in series: (i) We removed the production of C20 fatty acids, which are not observed experimentally, and used Obj2 to fit the 18 scaling parameters described in our prior work (Table S5; (Mains et al., 2022)). (ii) Our initial fit caused an overaccumulation of FabB·acetyl-CoA (Fig. S2). To address this issue, we replaced scaling parameters for the dissociation of FabF·acetyl-ACP and the reversal of FabB activation by acetyl-CoA with parameters that scale FabF binding to malonyl-ACP and FabB binding to acetyl-CoA. We used Obj3 to optimize these two parameters and two that scale FabF- and FabB-catalyzed decarboxylation of malonyl-ACP (Table S1). (iii) We improved the fit for the product profile by using Obj4 to fit the same four parameters. Figure S1 shows the results of our optimization. Hereafter, we refer to this model as our “base model”. We used it to build the oleochemical-specific models, which used similar optimization routines (SI Methods)