Mathematical Treatment of the Kinetics of Binding Protein Dependent Transport Systems Reveals That Both the Substrate Loaded and Unloaded Binding Proteins Interact With the Membrane Components

J Theor Biol. 1995 Jan 7;172(1):83-94. doi: 10.1006/jtbi.1995.0006.


Binding-protein-dependent transport systems in Gram-negative bacteria are multicomponent systems in which a soluble periplasmic binding protein of high substrate binding affinity establishes the major substrate recognition site. Usually, there are two membrane proteins which are thought to interact with the substrate loaded form of the binding protein to allow transport of substrate to occur. Transport is against the concentration gradient and needs energization by an ATP hydrolyzing polypeptide. Overall transport is considered mainly unidirectional owing to the high energy of ATP hydrolysis coupled to transport. We dissected the overall transport process into three individual steps: (i) reversible binding of substrate to the binding protein; (ii) reversible binding of the binding protein to the membrane components forming the translocation complex; (iii) irreversible transport of substrate through the membrane and dissociation of the binding protein from the complex. Two models were considered. In the first, only the substrate-loaded binding protein interacts with the membrane components, while in the second model both the loaded and the unloaded form of the binding protein interact with the membrane components. The mathematical analysis of the second model revealed that the substrate concentration KM at half-maximal rate of transport approaches KD of the binding protein when the last step of transport becomes low and when the concentration of binding protein in the periplasm becomes large. This is usually observed in real systems. Under the same conditions, in model 1 KM approaches zero and is hence considerably smaller than KD. This has never been observed in any real system. In addition, the dependence of the overall rate of transport on the concentration of binding protein in the periplasm follows a sigmoidal curve only when model 2 is considered. The sigmoidal behavior becomes more pronounced when the substrate concentration is low and it is less pronounced when the last step in overall transport is low. This phenomenon has been observed with the Escherichia coli maltose transport system. Thus, at least for the maltose transport system, it seems likely that both the loaded and the unloaded forms of the binding protein interact with the membrane components. We propose that this should generally be considered in binding-protein-dependent transport systems.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adenosine Triphosphate / metabolism
  • Bacterial Proteins / metabolism*
  • Biological Transport
  • Carrier Proteins / metabolism*
  • Gram-Negative Bacteria / metabolism*
  • Kinetics
  • Maltose / metabolism*
  • Mathematics


  • Bacterial Proteins
  • Carrier Proteins
  • Maltose
  • Adenosine Triphosphate