Fig 1.
Schematic representation of the structure of the substrate in the model.
(a) Several cellulose microfibrils embedded in a matrix of hemicellulose reinforced by lignin. (b) Side-view of the top 50 nm of a single cellulose microfibril made of 36 polymers, and part of the surrounding matrix showing the relative arrangement of the hemicellulose and lignin polymers as well as gaps. In (a) and (b), polymer types are color-coded (cellulose: dark gray; hemicellulose: light gray; lignin: black). (c) Top-down view of the structure shown in (b). The core enclosed by the dotted line is composed of 36 polymers of cellulose (black crosses), and its structure follows that used by Ding et al. [57]. The positions in the two outer layers (gray crosses) can each either be hemicellulose or lignin polymers.
Fig 2.
Sketch (top-down view) of the accessibility of polymer bonds depending on their position within the substrate and its digestion state.
(a) Beginning of the simulation: the outer layer (gray crosses, here made entirely of hemicellulose) does not contain any gaps. None of the cellulose bonds (black crosses) are accessible for digestion by enzymes (dark gray polygons). Only the hemicellulose bonds are digestible. (b) Later stage of the simulation: some of the hemicellulose within the outer shell has been digested. The cellulose bonds highlighted by arrows are now accessible for digestion.
Fig 3.
Schematic representation of the polymer bonds that can be digested within the model.
(a) Cellulose digestion sites by endoglucanase (EG) and cellobiohydrolase (CBH). Endoglucanase may digest glucose-glucose bonds along the entire polymer, except for the two outermost bonds at each end. Cellobiohydrolase processively cuts off cellobiose from either polymer ends. (b) Cellobiose digestion site by β-glucosidase (BGL). β-glucosidase exclusively digests cellobiose into two glucose molecules. (c) Hemicellulose digestion sites by xylanase (XYL). Xylanase may digest xylose-xylose bonds at any position along the hemicellulose polymer.
Fig 4.
Sketch of the impact of Nlignols,bound (the number of monolignols involved in binding per bound enzyme) on the total number of enzymes that can be bound.
Starting at low values of Nlignols,bound in (a), many enzymes can be bound to a single lignin polymer. As Nlignols,bound increases in (b) and (c), this number steeply drops, finally reaching the limit of only a single enzyme being bindable.
Fig 5.
Sketch of the structural blocking by lignin for two different values of the covering fraction μ.
(a) For μ = 100%, every bond within each lignin polymer represents a barrier. The polymers are linear. (b) For μ = 20%, only parts of each polymer represents a barrier (showed in black) while remaining monolignols are showed as shades. The polymers are highly branched.
Table 1.
Parameters for the substrate composition, crystallinity fractions, and digestibility ratios (rc,a) at three pre-treatment severities (low, medium and high).
The composition is closely derived from experimental data: the percentages of hemicellulose and lignin are from Bura et al. [11], while the glucose percentages are adapted such that the composition percentages sum up to 1. The crystallinity fractions and digestibility ratios rc,a are determined by fitting the experimental saccharification time courses by Bura et al. [11] (see section 4.4).
Table 2.
Molecular masses of the constituents of the lignocellulose sub-units, obtained from literature and rounded to three digits.
The value for the representative monolignol was taken as the mean value of the molecular masses of the three main monolignols (coumaryl alcohol, coniferyl alcohol and sinapyl alcohol).
Fig 6.
Heatmaps depicting the dynamics over time of the distribution of cellulose polymer degrees of polymerization (DP) for a default microfibril.
Time is shown on the ordinate, DP is shown on the abscissa, and color indicates the total amount of glucose that makes up polymers of length DP divided by the total amount of glucose in the system. Present enzymes are xylanase (XYL), together with: EG in (a), CBH in (b), and EG, CBH and BGL all together in (c). In (a), cellotriose accumulates, since in the model EG alone cannot release cellobiose or glucose. In (b) cellobiose progressively accumulates. Finally, in (c), cellobiose can be digested by BGL, and in turn glucose accumulates. Each heatmap represents an average over 100 simulation runs.
Fig 7.
(a) Simulated saccharification time courses for increasing lignin percentage up to a time tend = 40 (arbitrary units). Each curve represents an average over 100 simulation runs. (b) Simulated glucan to glucose conversion at time tend versus lignin content for five different values of the overall enzyme concentration [E]. The gray lines trace the inverse logistic behavior, while the black lines indicate the approximately linear intermediate regimes. Each point represents an average over 100 simulation runs. (c) Simulated glucan to glucose conversion at time tend versus lignin content and number of monolignols involved in the binding of a single enzyme (Nlignols,bound). Enzyme concentration is: [E] = 5 μM. (d) Simulated glucan to glucose conversion at time tend versus mean polymer covering fraction and its standard deviation (see also section 2.3). The lignin content is 50%, and the enzyme concentration is [E] = 5 μM. In (c) and (d) each pixel represents an average over 10 simulation runs.
Fig 8.
Simulated final glucan to glucose conversion versus crystallinity fraction for different ratios (rc,a) between the digestibilities of the crystalline and the amorphous regions.
For each value of rc,a we observe a linear decrease in final glucan to glucose conversion percentage for increasing crystallinity fraction, whose slope becomes steeper as rc,a decreases. For rc,a = 10−3 we observe inverse proportionality in addition to linearity. Each simulated point represents an average over 100 simulations. Also shown are experimental data by Cui et al. [71] (empty squares) and Pena et al. [72] (empty circles).
Fig 9.
Experimental data (dotted lines) and best simulation fits of the saccharification time courses for three different pre-treatment severities (low: Black lines, medium: Dark grey lines, high: Light grey lines).
(a) and (d) The substrate has no structure and all polymers are freely floating within the medium. (b) and (e) The cellulose polymers form a microfibril, which is surrounded by hemicellulose and lignin. However, the crystallinity of the substrate is discarded. (c) and (f) The substrate crystallinity is additionaly included, which substantially improves the fits. Each curve represents an average over 100 simulation runs. The experimental data shown here are from Bura et al. [11].