Mathematical Treatment of Transport Data of Bacterial Transport Systems to Estimate Limitation in Diffusion through the Outer Membrane

Bacterial transport systems are traditionally treated as enzymes exhibiting a saturable binding site giving rise to an apparent Kmof transport, whereas the maximal rate of transport is regarded equivalent to the Vmaxof enzymatic reactions. Thus, the Michaelis–Menten theory is usually applied in the analysis of transport data and Kmand Vmaxare derived from the treatment of data obtained from the rate of transport at varying substrate concentrations. Such an analysis tacitly assumes that the substrate recognition site of the transport system is freely accessible to substrate. However, this is not always the case. In systems endowed with high affinity in the μ M range or those recognizing large substrates or those exhibiting high Vmax, the diffusion through the outer membrane may become rate determining, particularly at low external substrate concentrations. In such a situation the dependence of the overall rate of transport (from the medium into the cytoplasm) on the substrate concentration in the medium will no longer follow Michaelis–Menten kinetics. By analysing the deviation of transport data from the corresponding ideal Michaelis–Menten plot we developed a method that allows us to determine diffusion limitation through the outer membrane. The method allows us to find the correctKm of the transport system functioning at the inner membrane even under conditions of strong diffusion limitation through the outer membrane. The model was tested and validified with the Escherichia coli binding protein-dependent ABC transporter for maltose. The corresponding systems for sn -glycerol-3-phospate of Escherichia coli and the α -cyclodextrin transport of Klebsiella oxitoca were used as test systems.