model the cytoplasm as a fractal, in order to capture its limited-mobility kinetics. The resulting reaction rates predicted by the two approaches are similar, with the only difference being that the equilibrium approximation defines the constant as , whilst the quasi-steady-state approximation uses . However, each approach is founded upon a different assumption. The Michaelis–Menten equilibrium analysis is valid if the substrate reaches equilibrium on a much faster time-scale than the product is formed or, more precisely, that By contrast, the Briggs–Haldane quasi-steady-state analysis is valid if Thus it holds if the enzyme concentration is much less than the substrate concentration or or both. In both the Michaelis–Menten and Briggs–Haldane analyses, the quality of the approximation improves as decreases. However, in model building, Michaelis–Menten kinetics are often invoked without regard to the underlying assumptions. Importantly, while irreversibility is a necessary simplification in order to yield a tractable analytic solution, in the general case product formation is not in fact irreversible. The enzyme reaction is more correctly described as E{} + S <=>[\mathit{k_{f_1}}][\mathit{k_{r_1}}] ES <=>[\mathit{k_{f_2}}][\mathit{k_{r_2}}] E{} + P. In general, the assumption of irreversibility is a good one in situations where one of the below is true: 1. The concentration of substrate(s) is very much larger than the concentration of products: [S] \gg [P]. This is true under standard in vitro assay conditions, and is true for many in vivo biological reactions, particularly where the product is continually removed by a subsequent reaction. 2. The energy released in the reaction is very large, that is In situations where neither of these two conditions hold (that is, the reaction is low energy and a substantial pool of product(s) exists), the Michaelis–Menten equation breaks down, and more complex modelling approaches explicitly taking the forward and reverse reactions into account must be taken to understand the enzyme biology. Determination of constants The typical method for determining the constants and involves running a series of enzyme assays at varying substrate concentrations , and measuring the initial reaction rate . 'Initial' here is taken to mean that the reaction rate is measured after a relatively short time period, during which it is assumed that the enzyme-substrate complex has formed, but that the substrate concentration held approximately constant, and so the equilibrium or quasi-steady-state approximation remain valid. By plotting reaction rate against concentration, and using nonlinear regression of the Michaelis–Menten equation, the parameters may be obtained. Before