Composition and pretreatment factor analysis
The changes in composition of wheat straw after hydrothermal pretreatment were as expected in terms of xylose, arabinose, and glucose content (Figure 1) . Xylose and arabinose content decreased with high pretreatment-severity, whereas glucose content increased with pretreatment-severity because its recovery was not dependent on pretreatment conditions, and hence, it constituted a larger proportion of the fiber fraction when hemicellulose was solubilized. Ammonium hydroxide has a milder effect than other alkaline solutions (NaOH and KOH) on lignin , so recovery of lignin did not increase with increasing pH. As the objective of this study was to investigate the behavior of the mineral components during hydrothermal pretreatment, and to learn about their interactions with the biomass, thus retaining lignin in the fiber fraction was intended. Retention of lignin in the fiber fraction caused minimal variation between samples in terms of the structural components, so that these variations did not overshadow the variations of the less abundant mineral components.
The mineral composition of wheat straw was, in general, in agreement with literature (8850 to 17320 ppm silicon, 50 to 560 ppm aluminum, 70 to 350 ppm iron, 3090 to 4870 ppm calcium, 440 to 660 ppm magnesium, 90 to 190 ppm Na, 4120 to 20720 ppm potassium, 270 to 760 ppm phosphorus) . Some elements were above the stated ranges, but this was expected, because of seasonal and geographical variations. Potassium was the only element solubilized from the fiber fraction under all pretreatment conditions, yielding a low recovery range (Table 1, Figure 3f). This was also as expected, because potassium is exclusively present in the aqueous phase of plant cells, so it is easily leached from the biomass during pre-soaking and pretreatment. Potassium is known to be highly abundant in wheat straw, especially in the cytoplasm and aqueous environments of the vacuole, where it stabilizes the ionic strength of enzymes and osmotic pressure of the cells .
Magnesium, in spite of being 70% freely diffusible and present at fairly high concentrations in the cytoplasm,  required pre-soaking in acid before it could be solubilized from the fiber fraction (Figure 3d). The same effect of acid pre-soaking was observed for calcium (Figure 3e). Magnesium and calcium are deposited in wheat straw cell walls, where they are associated with carboxyl and phenolic hydroxyl groups of organic components, making them resistant to solubilization . Neither calcium nor magnesium was leached from the relatively intact cell walls (for example, see high recoveries at high pH and low temperatures in Figure 3d). The similarity in results from response surface modeling of calcium and magnesium (Figure 3) to some structural components of the biomass, especially arabinose but also to some degree xylose, indicates that the integrity of the cell wall influences the solubilization of calcium and magnesium.
Correlation between biomass constituents
Using PCA, it was possible to group the wheat straw constituents into two main groups: water-soluble and water-insoluble constituents (Figure 4).
In the water-insoluble group, lignin and glucose were clustered together. This was not surprising considering that these components interact strongly in lignocellulosic fibers, and are both insoluble across the range of pretreatment conditions tested in this study. Silicon formed a separate cluster, reflecting its unique properties relative to the other elements. Silicon is deposited as SiO2 · nH2O, either in intimate association with the organic components of plant cell walls or in silica bodies formed within the lumen of specialized cells -. Owing to the insoluble nature of SiO2, even releasing it from the organic material would not remove silicon from the insoluble fraction. Coupled with the high recovery range for silicon in the fiber fraction (Table 1), the implications of these findings are that the vast majority of the silicon is likely to remain associated with lignin and thus accumulate in the lignin residue stream during the further processing of the biomass. Aluminum, iron, and copper were also clustered together. These are all toxic elements for plants if they are accumulated at high concentrations in their free form ,,. The plants therefore need to control and immobilize these elements to protect themselves from the toxic effects. Aluminum is strongly bound to negatively charged groups in cell walls and is water-insoluble, hence it is not solubilized from the fiber fraction. Iron and copper are also present in an insoluble form in plants ,, and are believed to be mainly associated with insoluble cell wall components or phytate . However, some iron in plants is stored in soluble ferritin complexes . As with aluminum and copper, a fraction of the iron was solubilized during hydrothermal pretreatment, but the rest remained in the fiber fraction, regardless of the pretreatment conditions. These findings signify that in relation to biorefining, iron and copper are likely to be distributed between both the aqueous and solid fractions, and to gradually become solubilized during further processing via the enzymatic cellulose and hemicellulose hydrolysis and fermentation steps. Whether such gradual solubilization may function as a nutrient supply during the fermentation, or exert negative effects, warrants further in-depth examination.
In the water-soluble group, arabinose and xylose were located close together in the loadings plot, which was meaningful because in wheat straw they are associated in arabinoxylan. Magnesium and potassium belonged to the same cluster as xylose and arabinose. These two mineral elements are present at relatively high concentrations in the cytoplasm , and as the straw matures, they may become loosely bound to negatively charged components within the straw matrix. The present results indicate that magnesium and potassium are unlikely to accumulate in the insoluble fiber streams or in the lignin residue after fermentation in lignocellulose to ethanol processing. The remaining elements (calcium, phosphorus, manganese, zinc) in the water-soluble group belonged to another cluster; their common denominator is that they are all restricted in their movement in plant cells. Calcium and phosphorus interact in calcium-phosphate, calcium-phospholipid, and calcium-phytate complexes , and this could explain their similar behavior. Manganese and zinc were found to be present in the fiber fraction at very low concentrations. The low concentrations of manganese and zinc were either due to their low initial abundance in wheat straw, or because they were solubilized during pretreatment, as they exist either as free ions or bound in protein complexes . Manganese and zinc were clustered together with calcium and phosphorus, because the remaining manganese and zinc left in the fiber fraction during hydrothermal pretreatment can interact with the cell wall matrix in a similar fashion to calcium and phosphorus.
Optimization of cpH for prediction of fiber fraction composition
It is desirable to be able to predict the composition of the fiber fraction based on the severity of hydrothermal pretreatment. The temperature and time dependency of the composition of the fiber fraction was expected to follow the classic pretreatment-severity equation , where 14.75 is an arbitrary empirical constant based on the activation energy . The pH dependency varied according to the constituent. Therefore, including pH in pretreatment-severity merely by subtracting pH in the classic method  did not result in satisfactory fits; in other words, an additional factor, cpH, was needed.
We assumed that there was an underlying dependency of a given constituent on the combined pretreatment-severity, which was linear at low pretreatment-severity, but when pretreatment-severity was increased to a level where most of the constituent was solubilized, leaving no or only strongly restricted residual constituents in the fiber fraction, the dependency was assumed to attain an exponentially decaying nature. Not knowing if the range of pretreatment conditions chosen in this study were in the linear or exponential range for the constituents, we had to fit both a linear and exponential function to the data and choose which of the two gave the best fit (highest R2) for each constituent.
As shown in Figure 7b, an exponential function yielded the best fit for arabinose. This was because the pretreatment effectively solubilized arabinose from the fiber fraction, so at high pretreatment-severity the arabinose content approached zero. By contrast, for xylose (Figure 7a), higher pretreatment-severity was needed before an exponential decay could be expected. The magnesium and potassium contents also exhibited an exponential decay, although to a lesser degree than arabinose. Magnesium and potassium were clustered together with arabinose and xylose (Figure 5), and are both elements that occur at high concentrations in the cytoplasm . The remaining magnesium (~10%) and potassium (~4%) recovered in the fiber fraction after hydrothermal pretreatment at high pretreatment-severity might be more recalcitrant to solubilization than the rest, causing exponential decay of their contents at increasing pretreatment-severity. For potassium in Figure 8b, removing the point of low pretreatment-severity, which appeared to be an outlier, still resulted in an exponential decaying function.
The pH dependencies of carbohydrates, lignin, and potassium were lower than those of the other mineral elements, as observed by comparing cpH factors (Figures 7 and 8); cpH values of xylose and arabinose were low. As pH constituted merely a contribution to the severity of pretreatment by opening up the cell wall, it had no direct implications on solubilization of xylose and arabinose. For elements with high cpH (phosphorus, magnesium, calcium, zinc, manganese), low pH could, in addition to opening up the cell wall, increase the solubility of the elements. The solubility of calcium phytate, for example, increases significantly below pH 4 .
As seen in Figure 7, contents of glucose and lignin increased with higher pretreatment-severity, because the relative proportion of glucose and lignin increased when xylose and arabinose contents decreased. Variations in glucose and lignin recoveries in the fiber fraction did not depend on the severity of pretreatment, so any change in content must have been governed by removal of other main constituents of the fiber fraction, namely hemicellulose. This explains why the cpH of glucose and lignin were in the range of those of xylose and arabinose.