First of all lets have a look, what these guys want to accomplish: They want to use bacteria to make certain products. To do so, they want to exploit the bacterial metabolism at steps where no alternative pathways are available. One of these steps is the first step of glycolysis, when Glucose gets phosphorylated to glucose-6-phosphate (G6P). In bacteria the phosphorylation is done during the import of glucose into the cell by the "phosphoenolpyruvate (PEP):carbohydrate phosphotransferase system", which uses Phosphorenolpyruvate as a phosphate source. This has the disadvantage, that there is almost no free glucose inside the cell, but mostly G6P.
To overcome this problem, the group expressed alternative transporters (which transport glucose into the cell) and Glucokinase (Glk) to allow the cells to survive. This steps decoupled import and phosphorylation of the glucose and resulted in free glucose inside the cell. This free glucose can now be used by different proceses. It also allows glycolysis, since the Glk phosphorylates the glucose which then enters the glycolysis pathway. The Glk was put under different promoters to make different mutants in order to test how the different expression of Glk affects the cells viability.
To bring in another enzyme which also metabolizes glucose, they used glucose dehydrogenase (Gdh) which was expressed from a plasmid with a strong, IPTG inducible promoter. They then used different concentrations of IPTG to test the effect on the production of gluconate and cell viability (I am not going into this).
The figure above is figure 5 from the paper and shows the effect of the three different IPTG concentrations used to induce the expression of the Gdh. For 10 and 25uM IPTG the yield of gluconate is getting smaller, the higher the Glk activity gets. Only the smalled activity shows a lower yield. This is complete different for the highest concentration, but here the cells get probably messed up by the high expression of the Gdh (which also consumes a lot of energy).
In the paper they give no explanation or at least discuss the behaviour of the gluconate yield at the smallest Glk activity (I would like to read the reviewers comments on that). From the data I would expect a higher production. It is possible that the lower energy production (low amounts of G6P means little glycolysis) has negative side effects on the cells. It is also possible, that the Gdh is inhibited at lower Glk activities by some other substances in the cell. Gdh activity is for example inhibited by higher concentrations of nucleotidtriphosphates (ATP and so on), see here. Since Glk needs ATP as a cofactor it would be possible that the ATP concentration at lower Glk activities has a negative effect on the Gdh activity (my own speculation).
Or it is simply some artefact from the experiment. This has some points which can be critisized (I would like to see the reviewers comments here as well). First the error bars are pretty big, so this can also be somewhat different. In the text they mention that the data was acquired by
at least 2 parallel cultures in a representative experiment
I would expect some more repetitions (at least three independent experiments), which would make the data more reliable. Then (and this point is much more important) they can not measure the activity of Glk and Gdh in the same culture due to restrictions in the detection system. Glk activity measurements use a coupled system which in the end measure the concentration change in NADH, while Gdh uses NADPH as a co-factor. Both versions can not be differentiated by measuring a spectrum, so activity measurements of Glk can only take place in untransfected cells. Since the expression changes conditions in the cell (and we don't know how), I would expect at least some discussion about it, but it is missing.