Acta Phys. -Chim. Sin. ›› 2010, Vol. 26 ›› Issue (11): 2857-2864.doi: 10.3866/PKU.WHXB20101129

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Simple Chemical Model for Facilitated Transport with an Application to Wyman-Murray Facilitated Diffusion

COLE Christine Lind, QIAN Hong   

  1. Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
  • Received:2010-07-30 Revised:2010-09-13 Published:2010-10-29
  • Contact: COLE Christine Lind, QIAN Hong,
  • Supported by:

    The project was supported in part by NSF grants, USA(DMS9810726, DGE0338322AM07).


A simple chemical kinetic model is developed which describes the behavior of small ligands that can bind reversibly with large carrier molecules with slower intrinsic rates of transport. Under certain conditions, which we describe, the presence of the slower carriers in fact enhances the transport of the ligand. This is the chemical version of Wyman-Murray's facilitated diffusion. The simple model illuminates the driven nature of the enhancement of the transport by the carrier molecules: we show that the facilitated transport depends crucially on a“grand canonical” setting in which the free ligand concentrations are kept constant in the presence of the facilitating protein, in contrast to a canonical setting with constant total ligand concentrations. Results from the simple model are compared to previous experimental and theoretical results for Wyman-Murray facilitated diffusion of oxygen and carbon monoxide in muscle. A relation is established between the association-dissociation rates and the down-stream ligand concentration, or back pressure for oxygen, required for the facilitation effect to occur.


Key words: Facilitated diffusion, Transport, Chemical kinetic model, Grand canonical ensemble