Michaelis-Menten kinetics of single enzymes

In Chapter 4 (Section 4.1.1), we derived the Lineweaver-Burk double-reciprocal relation between the steady state flux of an enzyme reaction and its substrate concentrations. (See Equation (4.5).) Furthermore, we showed in Section 4.4.1 that the same equation can be obtained from a stochastic point of view. Recalling this derivation, consider the basic mechanism 

Breaking down the overall reaction of converting one S to one P, the first step of binding of S to E takes an average time l/( i[S]). The dwell time in state ES is + k2), after which the ES complex transitions either to E + P or back to 

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