The dependence of an initial rate of reaction upon the concentration of a substrate S that is present in large excess over the concentration of an enzyme or other catalyst (or reagent) E with the appearance of saturation behaviour following the Michaelis-Menten equation: $$\nu =\frac{V\left[\text{S}\right]}{K_{\text{m}}+\left[\text{S}\right]}$$ where $\nu$ is the observed initial rate, $V$ is its limiting value at substrate saturation (i.e. $\left[\text{S}\right]\gg K_{\text{m}}$), and $K_{\text{m}}$ the substrate concentration when $\nu =\frac{V}{2}$. The definition is experimental, i.e. it applies to any reaction that follows an equation of this general form. The symbols $V_{max}$ or ${\nu }_{max}$ are sometimes used for $V$. The parameters $V$ and $K_{\text{m}}$ (the 'Michaelis constant') of the equation can be evaluated from the slope and intercept of a linear plot of ${\nu }^{-1}$ vs. ${\left[\text{S}\right]}^{-1}$ (a 'Lineweaver–Burk plot') or from slope and intercept of a linear plot of $\nu$ vs. $\frac{\nu }{\left[\text{S}\right]}$ ('Eadie–Hofstee plot'). A Michaelis–Menten equation is also applicable to the condition where E is present in large excess, in which case the concentration $\left[\text{E}\right]$ appears in the equation instead of $\left[\text{S}\right]$. The term has sometimes been used to describe reactions that proceed according to the scheme: $$\text{E}+\text{S}\stackrel{k_1}{\underset{k_{-1}}{\rightleftarrows }}\text{ES}\stackrel{k_{\text{cat}}}{\to }\text{Products}$$ in which case $K_{\text{m}}=\frac{k_{-1}+k_{\text{cat}}}{k_1}$ (Briggs–Haldane conditions). It has more usually been applied only to the special case in which $k_{-1}\gg k_{\text{cat}}$ and $K_{\text{m}}=\frac{k_{-1}}{k_1}=K_s$; in this case $K_{\text{m}}$ is a true dissociation constant (Michaelis–Menten conditions).