A kinetic model for binding protein-mediated arabinose transport

Modelling bacterial chemotaxis for indirectly binding attractants

In bacterial chemotaxis, chemoattractant molecules may bind either directly or indirectly with receptors within the cell periplasmic space. The indirect binding mechanism, which involves an intermediate periplasmic binding protein, has been reported to increase sensitivity to dilute attractant concentrations as well as range of response. Current mathematical models for bacterial chemotaxis at the population scale do not appear to take the periplasmic binding protein (BP) concentration or the indirect binding mechanics into account. We formulate an indirect binding extension to the existing Rivero equation for chemotactic velocity based on fundamental reversible enzyme kinetics. The formulated indirect binding expression accounts for the periplasmic BP concentration and the dissociation constants for binding between attractant and periplasmic BP, as well as between BP and chemoreceptor. We validate the indirect-binding model using capillary assay simulations of the chemotactic responses of E. coli to the indirectly-binding attractants maltose and AI-2. The predicted response agrees well with experimental data from a number of maltose capillary assay studies conducted in previous literature. The model is also able to achieve good agreement with AI-2 capillary assay data of one study out of two tested. The chemotactic response of E. coli towards AI-2 appears to be of higher complexity due to reports of variable periplasmic BP concentration as well as the low concentration of periplasmic BP relative to the total receptor concentration. Our current model is thus suitable for indirect binding chemotactic response systems with constant periplasmic BP concentration that is significantly larger than the total receptor concentration, such as the response of E. coli towards maltose. Further considerations may be taken into account to model the chemotactic response towards AI-2 with greater accuracy.

Mathematical modeling of the low and high affinity arabinose transport systems in Escherichia coli

A mathematical model was developed for the low and high affinity arabinose transport systems in E. coli. The model is a system of three ordinary differential equations and takes the dynamics of mRNAs for the araE and araFGH proteins and the internal arabinose into account. Special attention was paid to estimate the model parameters from the literature. Our analysis and simulations suggest that the high affinity transport system helps the low affinity transport system to respond to high concentration of extracellular arabinose faster, whereas the high affinity transport system responds to a small amount of extracellular arabinose. Steady state analysis of the model also predicts that there is a regime for the extracellular concentration of arabinose where the arabinose system can show bistable behavior.

Timing and dynamics of single cell gene expression in the arabinose utilization system

The arabinose utilization system of Escherichia coli displays a stochastic all-or-nothing response at intermediate levels of arabinose, where the population divides into a fraction catabolizing the sugar at a high rate (on-state) and a fraction not utilizing arabinose (off-state). Here we study this decision process in individual cells, focusing on the dynamics of the transition from the off- to the on-state. Using quantitative time-lapse microscopy, we determine the time delay between inducer addition and fluorescence onset of a GFP reporter. Through independent characterization of the GFP maturation process, we can separate the lag time caused by the reporter from the intrinsic activation time of the arabinose system. The resulting distribution of intrinsic time delays scales inversely with the external arabinose concentration, and is compatible with a simple stochastic model for arabinose uptake. Our findings support the idea that the heterogeneous timing of gene induction is causally related to a broad distribution of uptake proteins at the time of sugar addition.

Simple models for the analysis of binding protein-dependent transport systems

Mathematical modeling was used to evaluate experimental data for bacterial binding protein-dependent transport systems. Two simple models were considered in which ligand-free periplasmic binding protein interacts with the membrane-bound components of transport. In one, this interaction was viewed as a competition with the ligand-bound binding protein, whereas in the other, it was considered to be a consequence of the complexes formed during the transport process itself. Two sets of kinetic parameters were derived for each model that fit the available experimental results for the maltose system. By contrast, a model that omitted the interaction of ligand-free binding protein did not fit the experimental data. Some applications of the successful models for the interpretation of existing mutant data are illustrated, as well as the possibilities of using mutant data to test the original models and sets of kinetic parameters. Practical suggestions are given for further experimental design.

Escherichia coli K12 arabinose-binding protein mutants with altered transport properties

The arabinose-binding protein (ABP) of Escherichia coli binds L-arabinose in the periplasm and delivers it to a cytoplasmic membrane complex consisting of the AraG and AraH proteins, for uptake into the cell. To study the interaction between the soluble and membrane components of this periplasmic transport system, regions of the ABP surface containing the opening of the arabinose-binding cleft were subjected to site-directed mutagenesis. Thirty-eight ABP variants containing one to three amino acid substitutions were recovered. ABP variants were expressed with wild-type AraG and AraH from a plasmid, in a strain lacking the chromosomal araFGH operon, and the whole cell uptake parameters, Ven (maximum initial velocity of arabinose entry) and K(en) (concentration of arabinose yielding half-maximal entry) were determined. Twenty-four mutants had normal Ven values, 3 mutants had Ven and K(en) values twice wild type, and 11 mutants had Ven and K(en) values 20-50% of wild type. Binding proteins that had altered uptake properties were each expressed, processed, and localized to the periplasm at levels equivalent to wild type. The mutant binding proteins behaved the same as wild type during purification, and each had a Kd (dissociation constant for bound arabinose) comparable to that of wild-type ABP. Mutations that resulted in altered uptake identified nine amino acids surrounding the arabinose-binding cleft, all of which are charged in the wild-type protein, and all of whose side chains project outward from the cleft. The evidence suggests that this surface of the binding protein and these nine charged loci play a major role in ABP interactions with the membrane complex.