has reached equilibrium, which may be a very slow process for inhibitors with sub-nanomolar dissociation constants. In these cases, the inhibition becomes effectively irreversible, hence it is more practical to treat such tight-binding inhibitors as irreversible (see below). The effects of different types of reversible enzyme inhibitors on enzymatic activity can be visualised using graphical representations of the Michaelis–Menten equation, such as Lineweaver–Burk, Eadie-Hofstee or Hanes-Woolf plots. An illustration is provided by the three Lineweaver–Burk plots depicted in the Lineweaver–Burk diagrams figure. In the top diagram, the competitive inhibition lines intersect on the y-axis, illustrating that such inhibitors do not affect Vmax. In the bottom diagram, the non-competitive inhibition lines intersect on the x-axis, showing these inhibitors do not affect Km. However, since it can be difficult to estimate Ki and Ki' accurately from such plots, it is advisable to estimate these constants using more reliable nonlinear regression methods. Special cases Partially competitive The mechanism of partially competitive inhibition is similar to that of non-competitive, except that the EIS complex has catalytic activity, which may be lower or even higher (partially competitive activation) than that of the enzyme–substrate (ES) complex. This inhibition typically displays a lower Vmax, but an unaffected Km value. Substrate or product Substrate or product inhibition is where either an enzymes substrate or product also act as an inhibitor. This inhibition may follow the competitive, uncompetitive or mixed patterns. In substrate inhibition there is a progressive decrease in activity at high substrate concentrations, potentially from an enzyme having two competing substrate-binding sites. At low substrate, the high-affinity site is occupied and normal kinetics are followed. However, at higher concentrations, the second inhibitory site becomes occupied, inhibiting the enzyme. Product inhibition (either the enzyme's own product, or a product to an enzyme downstream in its metabolic pathway) is often a regulatory feature in metabolism and can be a form of negative feedback. Slow-tight Slow-tight inhibition occurs when the initial enzyme–inhibitor complex EI undergoes conformational isomerism (a change in shape) to a second more tightly held complex, EI*, but the overall inhibition process is reversible. This manifests itself as slowly increasing enzyme inhibition. Under these conditions, traditional Michaelis–Menten kinetics give a false value for Ki, which is time–dependent. The true value of Ki can be obtained through more complex analysis of the on (kon) and off (koff) rate constants for inhibitor association with kinetics similar to irreversible inhibition. Multi-substrate