Please wait a minute...
Acta Physico-Chimica Sinica  2010, Vol. 26 Issue (11): 2857-2864    DOI: 10.3866/PKU.WHXB20101129
Invited Aticle     
Simple Chemical Model for Facilitated Transport with an Application to Wyman-Murray Facilitated Diffusion
COLE Christine Lind, QIAN Hong
Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
Download:   PDF(795KB) Export: BibTeX | EndNote (RIS)       Supporting Info

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 wordsFacilitated diffusion      Transport      Chemical kinetic model      Grand canonical ensemble     
Received: 30 July 2010      Published: 11 October 2010

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

Corresponding Authors: COLE Christine Lind, QIAN Hong     E-mail:,
Cite this article:

COLE Christine Lind, QIAN Hong. Simple Chemical Model for Facilitated Transport with an Application to Wyman-Murray Facilitated Diffusion. Acta Physico-Chimica Sinica, 2010, 26(11): 2857-2864.

URL:     OR

1. Keener, J. P.; Sneyd, J. Mathematical physiology: cellular physiology, interdisciplinary applied mathematics. NewYork: Springer-Verlag, 1998
2. Fersht, A. Enzyme structure and mechanism. 2nd ed. NewYork: W. H. Freeman and Company, 1985
3. Roughton, F. Proc. R. Soc. Lond. B, 1932, 111: 1
4. Wittenberg, J. B. J. Biol. Chem., 1966, 241: 104
5. Wittenberg, J. B. Physiol. Rev., 1970, 50: 559
6. Hemmingsen, E. Comp. Biochem. Physiol., 1963, 10: 239
7. Scholander, P. Science, 1965, 149: 876
8. Murray, J. D. Proc. R. Soc. Lond. B-Biol. Sci., 1971, 178: 95
9. Wyman, J. J. Biol. Chem., 1966, 241: 115
10. Rubinow, S. I.; Dembo, M. Biophys. J., 1977, 18: 29
11. Kreuzer, F.; Hoofd, L. J. Respir. Physiol., 1970, 8: 280
12. Murray, J. D.; Wyman, J. J. Biol. Chem., 1971, 246: 5903
13. Murray, J. J. Theoret. Biol., 1974, 47: 115
14. Fletcher, J. E. Biophys. J., 1980, 29: 437
15. Meyer, R. A.; Sweeney, H. L.; Kushmerick, M. J. Am. J. Physiol., 1984, 246: C365
16. Qian, H. Annu. Rev. Phys. Chem., 2007, 58: 113
17. Hill, T. L. Linear aggregation theory in cell biology. NewYork: Springer-Verlag, 1987
18. King, E. L.; Altman, C. J. Phys. Chem., 1956, 60: 1375
19. Hill, T. L. Free energy transduction and biochemical cycle kinetics. New York: Dover Publications, 2004
20. Qi, F.; Dash, R. K.; Han, Y.; Beard, D. A. BMC Bioinformatics, 2009, 10: 238
21. Murray, J. D. Mathematical biology I: an introduction. 3rd ed. New York: Springer, 2007
22. Nedelman, J.; Rubinow, S. I. J. Math. Biol., 1981, 12: 73
23. Riveros-Moreno, V.; Wittenberg, J. B. J. Biol. Chem., 1972, 247: 895
24. Britton, N. F. Nonlinear Analysis, Theory, Methods& Applications. 1979, 3: 361
25. Kreuzer, F.; Hoofd, L. Adv. Exp. Med. Biol., 1976, 75: 207
26. Mochizuki, M.; Forster, R. E. Science, 1962, 138: 897

[1] LIU Xue-Peng, KONG Fan-Tai, CHEN Wang-Chao, YU Ting, GUO Fu-Ling, CHEN Jian, DAI Song-Yuan. Application of Organic Hole-Transporting Materials in Perovskite Solar Cells[J]. Acta Physico-Chimica Sinica, 2016, 32(6): 1347-1370.
[2] XIE Fang, ZHANG Xing-Tang, FAN Zhi-Qiang, ZHANG Xiao-Jiao, YU Ji-Hai, XU Hua, CHU Yu-Fang. Effect of Rotation on the Electronic Transport Properties of a Molecular Device[J]. Acta Physico-Chimica Sinica, 2016, 32(6): 1453-1459.
[3] XIAO Gan, ZHANG Yu-Sheng, JIANG Guang-Jun. Systematic Construction and Validation of the Reduced Chemical Kinetic Model of Gasoline Multi-Component Surrogate Fuel[J]. Acta Physico-Chimica Sinica, 2016, 32(4): 879-892.
[4] ZHU Lin, MAXin-Guo, LIU Na, XU Guo-Wang, HUANG Chu-Yun. Band Structure Modulation and Carrier Transport Process of g-C3N4 Doped with Alkali Metals[J]. Acta Physico-Chimica Sinica, 2016, 32(10): 2488-2494.
[5] PEI Lei, ZHANG Gui-Ling, SHANG Yan, SUN Cui-Cui, GAN Tian. Silicon Bridge-Tuned Electronic Structures and Transport Properties of Polymetallocenes[J]. Acta Physico-Chimica Sinica, 2016, 32(10): 2495-2502.
[6] BAI Mei-Lin, WANG Ming-Lang, HOU Shi-Min. Theoretical Investigation of the Transition Voltages of Cu-Vacuum-Cu Tunneling Junctions[J]. Acta Physico-Chimica Sinica, 2015, 31(8): 1474-1482.
[7] MIAO Yan-Qin, GAO Zhi-Xiang, WU Yu-Ling, DU Xiao-Gang, LI Yuan-Hao, LIU Hui-Hui, JIA Hu-Sheng, WANG Hua, LIU Xu-Guang. Antimicrobial Drug Levofloxacin Applied to an Organic Light-Emitting Diode[J]. Acta Physico-Chimica Sinica, 2015, 31(3): 552-558.
[8] HAN Di, HONG Ze-Wen, LI Dong-Fang, ZHENG Ju-Fang, WANG Ya-Hao, ZHOU Xiao-Shun. Single-Molecule Junction Conductance of Terephthalic Acid Contacting Ag and Cu Electrodes Measured by an Electrochemical Method[J]. Acta Physico-Chimica Sinica, 2015, 31(1): 105-110.
[9] WANG Shi-Mao, DONG Wei-Wei, FANG Xiao-Dong, DENG Zan-Hong, SHAO Jing-Zhen, HU Lin-Hua, ZHU Jun. Modification of Single-Crystal TiO2 Nanorod Arrays and Its Application in Quantum Dot-Sensitized Solar Cells[J]. Acta Physico-Chimica Sinica, 2014, 30(5): 873-880.
[10] PEI Juan, HAO Yan-Zhong, SUN Bao, LI Ying-Pin, FAN Long-Xue, SUN Shuo, WANG Shang-Xin. Heterojunction Interface Modification and Its Effect on the Photovoltaic Performance of Hybrid Solar Cells[J]. Acta Physico-Chimica Sinica, 2014, 30(3): 397-407.
[11] PENG Xuan. Molecular Simulations of the Purification of Toxic Benzene Gas on Single-Walled Carbon Nanotubes[J]. Acta Physico-Chimica Sinica, 2014, 30(11): 2000-2008.
[12] ZHANG You-Fa, WU Jie, YU Xin-Quan, LIANG Cai-Hua, WU Jun. Frost and Ice Transport on Superhydrophobic Copper Surfaces with Patterned Micro- and Nano-Structures[J]. Acta Physico-Chimica Sinica, 2014, 30(10): 1970-1978.
[13] WU Qiu-Hua, ZHAO Peng, LIU De-Sheng. First-Principles Study of the Rectifying Properties of the Alkali-Metal-Atom-Doped BDC60 Molecule[J]. Acta Physico-Chimica Sinica, 2014, 30(1): 53-58.
[14] ZHU Yun-Cheng, WANG Er-Qiong, MA Guo-Lin, KANG Yan-Biao, ZHAO Lin-Hong, LIU Yang-Zhong. Interaction of C-Terminal Metal-Binding Domain of Copper Transport Protein with Ag+ and Hg2+[J]. Acta Physico-Chimica Sinica, 2014, 30(1): 1-7.
[15] PANG Bin, XIE Mao-Zhao, JIA Ming, LIU Yao-Dong. Improved Phenomenological Soot Model for Multicomponent Fuel Based on Variations in PAH Characteristics with Fuel Type[J]. Acta Physico-Chimica Sinica, 2013, 29(12): 2523-2533.