Sugar Influx Sensing by the Phosphotransferase System of Escherichia coli

The phosphotransferase system (PTS) plays a pivotal role in the uptake of multiple sugars in Escherichia coli and many other bacteria. In the cell, individual sugar-specific PTS branches are interconnected through a series of phosphotransfer reactions, thus creating a global network that not only phosphorylates incoming sugars but also regulates a number of cellular processes. Despite the apparent importance of the PTS network in bacterial physiology, the holistic function of the network in the cell remains unclear. Here we used Förster resonance energy transfer (FRET) to investigate the PTS network in E. coli, including the dynamics of protein interactions and the processing of different stimuli and their transmission to the chemotaxis pathway. Our results demonstrate that despite the seeming complexity of the cellular PTS network, its core part operates in a strikingly simple way, sensing the overall influx of PTS sugars irrespective of the sugar identity and distributing this information equally through all studied branches of the network. Moreover, it also integrates several other specific metabolic inputs. The integrated output of the PTS network is then transmitted linearly to the chemotaxis pathway, in stark contrast to the amplification of conventional chemotactic stimuli. Finally, we observe that default uptake through the uninduced PTS network correlates well with the quality of the carbon source, apparently representing an optimal regulatory strategy.

The set of reactions for the above-mentioned scheme is given by Uptake of sugar Transfer of phosphate to EIIA from PEP Conversion of sugar to sugar-phosphate Transfer of phosphate to EIIBC from EIIA-P Production of energy from sugar-phosphate by metabolic protein ! and consumption of energy in uptake and metabolic enzyme production Induction of the transporter EIIBC by sugar-phosphate For the case of no induction of the transporter, !"#$%&# = 0 Induction of metabolic enzyme by sugar-phosphate The corresponding equations for the dynamics of the reactants (based on mass action kinetics) are Sugar uptake

Induction of metabolic enzymes
Production and consumption of energy Biomass production Growth of the population of cells The values of the reaction constants: Phosphotransfer reaction: Induction and dilution of enzymes: for the case of fixed maximum fold induction (i) for the case of fixed maximum induction (ii) for the case of no induction (iii) Production and consumption of energy The equations are simulated for 10 ! ∼ 100 for 5 different values of the nutritional value with three fold differences and 100 different values of the uptake rate for each value of . The biomass produced is calculated in these 100 min. The uptake rate which delivers the highest growth-rate is defined as the optimal uptake rate (transporter number multiplied by the uptake rate constant) for a particular nutritional value of a sugar. We used CVode [1] interfaced with MATLAB to solve the ODEs.

Solution of the simple model
The simple cost benefit model for the utilization and uptake of the sugar can be written as where and represent the nutritional value and the cost of uptake respectively. indicates the uptake rate.
Solving the equation for to obtain the optimal uptake rate, = 0, by taking derivative of equation (2) we obtain Taking derivative of equation (3) with respect to , Equation (4) implies that > 0 when ! > 2 ! suggesting that optimal uptake rate would increase with the nutritional value as long as energy produced during sugar uptake is much higher than the energy produced during starvation.
The optimal uptake rate corresponds to the basal uptake rate at which the biomass produced within a certain amount of time is maximal. If the basal uptake rate is below the optimum, it limits cell growth (biomass production). As the basal uptake rate is increased, the sugar-phosphate accumulates inside the cell, inducing the uptake. Consequently, high basal uptake rate leads to high induced uptake rate, ultimately resulting in the energy consumption in uptake being disproportionally high compared to the energy production by metabolism of the sugar. At an intermediate level of the basal uptake, the energy production and energetic cost are balanced, giving rise to an optimal basal uptake rate. In this scenario, for a sugar with a low metabolic efficiency the induction of uptake occurs at low basal uptake rate, since the sugar-phosphate accumulates due to low rate of its metabolism. In contrast, the same basal uptake rate would not lead to uptake induction for a sugar with high metabolic efficiency, because the corresponding sugar-phosphate would not accumulate due to its faster metabolism. As a consequence, the induction will occur at higher basal uptake rate, thus leading to higher optimal basal uptake rates for sugars with higher metabolic efficiency.

Model for sugar utilization in a mixture of PTS sugars
When more than one PTS sugar is available in the environment, E.coli can utilize both sugars simultaneously. Inside the cytoplasm, the sugars are phosphorylated by the same phosphate source.
The model is first constructed for a mixture of two sugars. We assume that the sugars can only be taken up by their specific transporters and the phosphate transfer occurs from the phosphate source EIIA-P to both the sugars. The nutritional values are only different for the two sugars. The rates of phosphotransfer reactions are assumed to be the same. The transporter and the metabolic enzymes are induced by the corresponding sugar-phosphate. The simulations are performed for 20 different values of the basal uptake rate for each of the sugars. The two uptake rates for which the growth rate is maximum indicate the optimal basal uptake rates for the two sugars in mixture. We carried out the simulation for five different mixture of two sugars by changing the nutritional value of one of the sugars, keeping the other sugar fixed and the biomass produced was calculated within 100 min with a periodic (every 20 min) resupply of sugars.
Uptake of sugar 1 Transfer of phosphate to EIIA from PEP Conversion of sugar1 to sugar-phosphate 1 Production and consumption of energy Similarly, one more sugar is added in the model to construct a mixture of 3 sugars. The three sugars differ by four fold in the nutritional values. The equations are simulated by varying the basal uptake rates of the three sugars and the three basal uptake rates are obtained which display maximum growth rate. In this case, the three sugars compete with each other for transport inside cell, since all transporters utilize the same phosphate source (PEP). However, the transcriptional activation of the transporter and the metabolic enzymes for a particular sugar is specifically induced by the corresponding sugar-phosphate. As a result, the sugar for which the metabolic efficiency is highest has the highest optimal basal uptake rate in mixture.