Abstract
The MalFGK\(_2\) transporter regulates the movement of maltose across the inner membrane of E. coli and serves as a model system for bacterial ATP binding cassette (ABC) importers. Despite the wealth of biochemical and structural data available, a general model describing the various translocation pathways is still lacking. In this study, we formulate a mathematical model with the goal of determining the transporter reaction pathway, specifically looking at the order of binding events and conformation changes by which transport proceeds. Fitting our mathematical model to equilibrium binding data, we estimate the unknown equilibrium parameters of the system, several of which are key determinants of the transport process. Using these estimates along with steady-state ATPase rate data, we determine which of several possible reaction pathways is dominant, as a function of five underdetermined kinetic parameter values. Because neither experimental measurements nor estimates of certain kinetic rate constants are available, the problem of deciding which of the reaction pathways is responsible for transport remains unsolved. However, using the mathematical framework developed here, a firmer conclusion regarding the dominant reaction pathway as a function of MalE and maltose concentration could be drawn once these unknown kinetic parameters are determined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Change history
11 July 2020
The original version of this article unfortunately contained a mistake. The co-author Dr. Franck Duong Van Hoa first name and last name were misinterpreted in the original publication.
References
Bao H, Dalal K, Cytrynbaum E, Duong F (2015) Sequential action of male and maltose allows coupling atp hydrolysis to translocation in the malfgk2 transporter. J Biol Chem 290(42):25452–25460
Bao H, Duong F (2012) Discovery of an auto-regulation mechanism for the maltose ABC transporter MalFGK2. PLoS ONE 7(4):e34836
Bao H, Duong F (2013) ATP alone triggers the outward facing conformation of the maltose ATP-binding cassette transporter. J Biol Chem 288(5):3439–3448
Bao H, Duong F (2014) Nucleotide-free malk drives the transition of the maltose transporter to the inward-facing conformation. J Biol Chem 289(14):9844–9851
Bohl E, Boos W (1997) Quantitative analysis of binding protein-mediated abc transport systems. J Theor Biol 186(1):65–74. https://doi.org/10.1006/jtbi.1996.0342
Bohl E, Shuman HA, Boos W (1995) 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 172(1):83–94
Bordignon E, Grote M, Schneider E (2010) The maltose ATP-binding cassette transporter in the 21st century-towards a structural dynamic perspective on its mode of action. Mol Microbiol 77(6):1354–1366
Colquhoun D, Dowsland KA, Beato M, Plested AJ (2004) How to impose microscopic reversibility in complex reaction mechanisms. Biophys J 86(6):3510–3518
Davidson AL, Shuman HA, Nikaido H (1992) Mechanism of maltose transport in escherichia coli: transmembrane signaling by periplasmic binding proteins. Proc Natl Acad Sci 89(6):2360–2364
Fabre L, Bao H, Innes J, Duong F, Rouiller I (2017) Negative stain single-particle em of the maltose transporter in nanodiscs reveals asymmetric closure of malk2 and catalytic roles of atp, male, and maltose. J Biol Chem 292(13):5457–5464
Gould AD, Telmer PG, Shilton BH (2009) Stimulation of the maltose transporter atpase by unliganded maltose binding protein. Biochemistry 48(33):8051–8061
Locher KP (2004) Structure and mechanism of abc transporters. Curr Opin Struct Biol 14(4):426–431
Marvin JS, Hellinga HW (2001) Manipulation of ligand binding affinity by exploitation of conformational coupling. Nat Struct Biol 8(9):795–798
Merino G, Boos W, Shuman HA, Bohl E (1995) The inhibition of maltose transport by the unliganded form of the maltose-binding protein of Escherichia coli: experimental findings and mathematical treatment. J Theor Biol 177(2):171–179
Merino G, Shuman HA (1997) Unliganded maltose-binding protein triggers lactose transport in an Escherichia coli mutant with an alteration in the maltose transport system. J Bacteriol 179(24):7687–7694
Nguyen PT, Lai JY, Lee AT, Kaiser JT, Rees DC (2018) Noncanonical role for the binding protein in substrate uptake by the metni methionine atp binding cassette (abc) transporter. Proc Natl Acad Sci 115(45):E10596–E10604. https://doi.org/10.1073/pnas.1811003115
Oldham ML, Khare D, Quiocho FA, Davidson AL, Chen J (2007) Crystal structure of a catalytic intermediate of the maltose transporter. Nature 450(7169):515–521
Schirmer T, Keller TA, Wang YF, Rosenbusch JP (1995) Structural basis for sugar translocation through maltoporin channels at 3.1 A resolution. Science 267(5197):512–514
Shilton BH, Mowbray SL (1995) Simple models for the analysis of binding protein-dependent transport systems. Protein Sci 4(7):1346–1355
Silhavy TJ, Szmelcman S, Boos W, Schwartz M (1975) On the significance of the retention of ligand by protein. Proc Natl Acad Sci 72(6):2120–2124
Acknowledgements
This research was supported by grants from the National Science and Engineering Research Council of Canada (to ENC) and the Canadian Institutes of Health Research (to FD).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hiller, R.M., von Kügelgen, J., Bao, H. et al. A Mathematical Model for the Kinetics of the MalFGK\(_2\) Maltose Transporter. Bull Math Biol 82, 62 (2020). https://doi.org/10.1007/s11538-020-00737-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11538-020-00737-8