Minimal and yield optimal minimal turnover rates. Idea of minimal turnover rates (MTR) and yield optimal minimal turnover rates (YMTR). If μ > 0, the MTR via the metabolite E1 has to be greater than zero. The MTR for M1 and M2 are zero, because the paths are alternatives. If the substrate uptake rate is minimal (yield optimal), the YMTR via M2 is greater than zero. The YMTR via M1 is zero because the path via M1 is less efficient than via M2.