Camelina straw (CS) was supplied by the AAFC Research Farm (Saskatoon Research and Development Centre, SK, Canada). Camelina was a replicated trial that mixed 17 different breeding lines plus the cultivars Midas, Cypress, Sonny, Dolly, Calena, and AAC 10CS0046. The camelina was seeded in May and harvested in September 2021. The straw was left to dry on the field and collected manually into the cloth bags. Switchgrass (SG) used in this study was the “Cave-in-rock” variety. SG was harvested in October 2021 in Nappan, Nova Scotia using a disk mower. It remained in a swath in the field for at least a week. The feedstock was randomly gathered from the swath and spread in a storage building for 2 months to dry. The initial moisture content of CS and SG were examined by following ASABE (2016). The feedstocks were dried at 40°C for 72 h and then ground to pass through 3-mm and 1-mm sieve using a laboratory knife mill (SM1, Retsch Technology GmbH, Haan, Germany) for microbial pretreatment and compositional analysis, respectively. The ground feedstock (about 5% moisture content) was stored in zip lock bags at −20°C before use.

The white-rot fungi used in this study were 1) T. versicolor m4D, a cellobiose dehydrogenase (CDH)-deficient strain (mutant) of T. versicolor (Canam et al., 2011); 2) T. versicolor 52J (ATCC 96186); and 3) P. chrysosporium. These three strains were kept as glycerol stocks frozen at −80°C and were cultivated on Difco malt extract agar (MEA) (Benton Dickenson, Sparks, MD). Ten agar plugs (5 mm in diameter) were removed from the edge of the colony grown on the malt extract agar plate and put into 250 ml of a 2% malt extract broth (MEB) by using the wide end of a sterilized Pasteur pipette. This mixture was blended in a sterilized Eberbach blender cup (Eberbach, Charter Township, MI, USA) at full speed on a Waring blender base (Waring Lab, USA) (3 pulses of 10 s), and then the blended mixture was poured into a 500 ml cotton-plugged Erlenmeyer flask and incubated at 28°C with 150 rpm of rotating shaking for 7 d. Before being used for inoculum, the liquid culture was again homogenized using a sterilized Eberbach blender cup on a Waring blender base for three consecutive 10-s cycles.

The experiment used in this study is illustrated in Figure 1. The experimental setup consisted of 21 units. Each unit contained three 250-ml Erlenmeyer flasks sealed with customized rubber stoppers supporting gas inlet and outlet ports with clips and inline 0.33 μm sterile gas filters. The gas inlet port was connected to the main distribution tube via a stop valve. The main distribution tube was connected to an oxygen tank via a 0.2 μm sterile filter, a control valve, and a gas flowmeter. All flask units were submerged in a water bath using copper flanges. The water temperature was maintained by a refrigerated/heating bath circulator (RW-0525G model, Jeiotech Lab Companion, Yuseong-gu, Daejeon, Korea). Three grams of the substrate (dry basis) was moisturized by a predetermined amount of distilled water in a 250-ml Erlenmeyer flask to achieve a final moisture content of 75% (wet basis) and then the flask was autoclaved at 121°C for 30 min. The cool moist substrate in the flask was inoculated with 2 ml of blended fungal liquid pre-culture (prepared as in Section 2.2) in a biological safety cabinet. Controls (no fungal inoculum) were prepared by adding 2 mL of sterile distilled water instead of the blended fungal liquid culture. The pretreatment was carried out in the water bath at 28°C for 30 d. Every 24 h, the headspace gas of the flask was collected and all the flasks were flushed with pure oxygen with a flow rate of 125 ml min⁻¹ for 5 min. The flasks were also sampled at days 0, 2, 4, 6, 8, 10, 12, 14, 18, 22, 26, and 30 to collect the substances for the determination of fungal biomass, holocellulose, and lignin content.

All three fungi grew well on both CS and SG. Cell concentrations of those fungi reached their limits after 14–22 d. The fungal mycelia occupied the whole surface area of the substrate inside the flask after 2 weeks (Figure 2). The time courses of fungal biomass generation, holocellulose consumption and lignin degradation during 30 d of microbial pretreatment are illustrated in Figure 3. TV52J showed the highest growth capacity, which was indicated by the greatest maximum fungal biomass concentration (Figures 3A, B) and holocellulose consumption (Figures 3C, D). As expected based on its impaired ability to metabolize cellulose, the mutant strain, TVm4D, performed the best in terms of holocellulose preservation (Figures 3C, D) and lignin degradation (Figures 3E, F). Maximum fungal biomass concentration was 0.084, 0.071, and 0.053 g X (g d.b. substrate)⁻¹ for CS-TV52J, CS-PC, and CS-TVm4D, respectively, while those of SG-TV52J, SG-PC, and SG-TVm4D were 0.095, 0.074, and 0.048 g X (g d.b. substrate)⁻¹, respectively (Figures 3A, B). The estimated maximum specific growth rate (μ_max), half-saturated coefficient (K_s), and self-inhibiting factor (X_m) of each substrate-fungus combination are indicated in Table 1 and the plots of predicted values against the experimental data of the growths are shown in Figure 4.

During the linear log phase (the exponential phase), TV52J showed the highest growing speed (1.210–1.216 d⁻¹), followed by TVm4D (0.911–1.005 d⁻¹) and PC (0.788–1.005 d⁻¹). The self-inhibiting factor, representing the maximum cell concentration that the mycelium can achieve, was ranked highest for TV52J [0.084–0.094 g X (g d.b. substrate)⁻¹], followed by those of PC [0.070–0.073 g X (g d.b. substrate)⁻¹] and TVm4D [0.047–0.052 g X (g d.b. substrate)⁻¹].

The growth ceased after 14-22 d when there was no more room for the cells to develop and divide. During the exponential phase from day 0 to day 14–22 (Figures 3A, B), the hyphae branching occurred aggressively in which the length, volume, and mass of each hypha were increasing and dividing. The microbial biomass was scattered as a network of hyphae on the substrate's surfaces. The stable growth relied upon the polymers from the substrate as a carbon source, which demanded the secretion of specific enzymes (Daniel and Nilsson, 1997; Ordaz et al., 2012; Bari et al., 2016). Those enzymes hydrolyzed the substrate polymers and the soluble hydrolysates diffused through the substrate (Mitchell et al., 2006a; Ruiz-Dueñas and Martínez, 2009; Ordaz et al., 2012; Bari et al., 2016). The diffusion of oxygen from the environment through the immobile gas layer to the fungal cell was stimulated by the oxygen consumption and the substrate's internal oxygen was also transferred to the cell (Mitchell et al., 2006a). At this stage, the space, nutrients, water, and oxygen were readily available for the cell to access given the small fungal biomass concentration, low OUR, and sufficient oxygen restock by the diffusion (Mitchell et al., 2006a). It is possible that the fungal biomass formation entered a nutrient-limiting stage in which the growth solely relied on the nutrient concentration during the early phase of the growth (Xu, 2020). Therefore, the growth happening during this stage was basically biologically limited.

During the latter phase of the growth (the horizontal part of Figures 3A, B), as the hyphal biomass increased, it started to meet those from neighboring microcolonies, and the mycelium started to aggregate and clump (Fuhr et al., 2011; Liu, 2020). The contacts at the tips of the hyphae negatively affected the growth, which is reflected by changes in the direction of growth or a decrease in growth rate (Daniel et al., 1992; Riquelme et al., 1998). Each microorganism has its saturation point beyond which it cannot allow nutrients, air, and water to infiltrate into the core of the aggregate (Moreira et al., 2003; Mitchell et al., 2006a). Only the edges could access oxygen and water and keep dividing until their contact with nutrients from the substrate was terminated (Raghavarao et al., 2003). As the cell concentration increased, other rates related to its growth-associated activities such as OUR, substrate consumption, and heat production, also increased. Oxygen and nutrient concentrations diminished in the adjacent environment of the cell and these reductions were normally faster than the supplying rates toward the fungal cells. Those concentrations continued to decline to a sufficiently low point where the growth rate started to drop (Mitchell et al., 2006a). Furthermore, once the mycelial density was too high, the heat production rate surpassed the heat removal rate regardless of the air-flushing and cooling water outside of the flasks. Toxins as by-products of the growth that could not be released to the environment would be accumulated inside the core. As a result, the high temperature, toxin accumulation, and unavailability of essential substances contributed to the cessation of growth or even death of cells (Mitchell et al., 2006a). Once the cell community approached the carrying capacity of the closed fermentation system, the growth proceeded toward the self-inhibiting stage (Xu, 2020), and the process was restricted by mass transfer (Mitchell et al., 2006a).

The growth kinetics were varied in previous studies depending on the substrate formulation, the SSF conditions, and the fungal strain. The fungal cell development of T. versicolor on mixtures of sawdust, coconut fiber, soybean oil, calcium carbonate, coffee husks, and corn bran reached the stationary phase after 30 d of pretreatment time when the substrates were fully colonized, with the maximum fungal biomass concentration of 0.377 g X (g d.b. substrate)⁻¹ (Sánchez and Montoya, 2020). T. versicolor PSUWC430 and PSUWC431 yielded a maximum specific growth rate of 0.304 and 0.743 d⁻¹, respectively, on the same substrate formulations (Montoya et al., 2014, 2015). The maximum specific growth rate of P. chrysosporium was 0.411–0.877 d⁻¹ and 1.498–1.617 d⁻¹ from the growth on cotton stalk under SSF and shallow stationary cultivation, respectively (Shi et al., 2012, 2014), 0.641–0.644 d⁻¹ when growing on ground fruit peels (Olorunnisola et al., 2018), and 0.422 d⁻¹ from the growth on glucose and ammoniacal nitrogen (Zhongming et al., 2003). Wan (2011) determined that the cell concentration of C. subvermispora growing on corn stover increased exponentially between 7-14 d and then started to level off at day 22.

Holocellulose, the main carbon and energy source for fungal growth, reduced significantly until 14-22 d, after which the reduction was remarkably slowed as the fungal biomass growth ceased (Figures 3C, D). In CS, holocellulose content was reduced from 58.6 g S (g d.b. substrate)⁻¹ in untreated sterile controls to 35.1, 25.7, and 28.6 g S (g d.b. substrate)⁻¹ in treatment with TVm4D, TV52J, and PC, respectively, after 14 d, which accounted for 40.1, 56.1, and 51.2%, respectively. During the stationary phase, holocellulose only dropped by 4.5, 8.2, and 4.5% to reach the minimum of 32.4, 20.9, and 25.9 g S (g d.b. substrate)⁻¹ at day 30, respectively. Following the same trend with CS, holocellulose of SG decreased from 66.2 g S (g d.b. substrate)⁻¹ in untreated sterile controls to 38.4, 33.9, and 36.8 g S (g d.b. substrate)⁻¹ in treatment with TVm4D, TV52J, and PC, respectively, after 22, 14 and 18 d, respectively, which were equivalent to 41.9, 48.8, and 44.4%. Longer pretreatment times only decreased the holocellulose by 1.9, 7.7, and 6.3% to reach the lowest of 37.2, 28.8, and 32.6 g S (g d.b. substrate)⁻¹ at the end of the time profiles, respectively. The yield coefficient from holocellulose substrate to biomass (Y_x/s) ranked the highest in TV52J (0.249–0.296 g X (g d.b. substrate)⁻¹) followed by those of PC (0.213–0.247 g X (g d.b. substrate)⁻¹) and TVm4D (0.152-0.180 g X (g d.b. substrate)⁻¹). The yield coefficients from the substrate to biomass in this study were similar to those of previous studies. P. chrysosporium yielded Y_x/s of 0.51 g X (g d.b. substrate)⁻¹ when growing on glucose and ammoniacal nitrogen (Zhongming et al., 2003), 0.240–0.276 g X (g d.b. substrate)⁻¹ on cotton stalk under shallow stationary cultivation (Shi et al., 2012), and 0.437 g X (g d.b. substrate)⁻¹ on cotton stalk under SSF (Shi et al., 2014). Y_x/s was found at 0.577, 0.55, and 0.625 g X (g d.b. substrate)⁻¹ in C. subvermispora, Gibberella fujikuroi, and Rhizopus oligosporus, respectively (Sargantanis et al., 1993; Thibault et al., 2000; Wan, 2011). Higher cell maintenance coefficient (m_s) in TV52J compared to PC and TVm4D indicated that under oxygen enriched environment, TV52J demanded more nutrients and energy than PC and TVm4D to satisfy its metabolisms.

Delignification was highest in TVm4D followed by TV52J and PC. Lignin content decreased from 37.3 g L (g d.b. substrate)⁻¹ in untreated sterile CS to the minimum of 23.6, 26.1, and 30.1 g L (g d.b. substrate)⁻¹ in CS-TVm4D, CS-TV52J, and CS-PC, which was equivalent to 36.8, 30.1, and 19.3% (Figure 3E). The delignification in SG was 24.4, 14.6, and 10.9% in TVm4D, TV52J, and PC, respectively, which decreased lignin from 26.3 to 19.9, 22.4, and 23.4 g L (g d.b. substrate)⁻¹, respectively (Figure 3F). Wan (2011) found that the delignification rate was not constant, instead, it gradually enhanced along with the pretreatment time. Delignification was found to occur even when the fungal growth approached the stationary phase suggesting that complete colonization did not reduce the lignin degradation since the enzymes oxidizing it were still being generated in significant amounts (Sánchez and Montoya, 2020). The inconstant decaying coefficient was observed in the lignocellulosic biomass substrate because of its heterogeneity, therefore, using an exponential equation to illustrate the varying delignification coefficient was appropriate. The negative values of k₂ explained the increasing rate of delignification over time monitored by the higher slope of the lignin degradation curves during the latter stage of the pretreatment. TVm4D showed the highest capability in holocellulose preservation followed by PC and TV52J which agreed well with previous observations. Canam et al. (2011) observed a vigorous growth of TV52J on canola straw in comparison with TVm4D indicated by the remarkable difference in ergosterol content after 84 d (12 weeks). T. versicolor m4D was able to colonize and grow on canola straw over 84 d but the growth appeared to slow down after 42 d (Canam et al., 2011). This is likely due to the absence of CDH activity in the mutant strain, which limited its ability to access the cellulosic substrate (Dumonceaux et al., 2001). CDH, an extracellular reductive enzyme, acts as an oxidoreductase to oxidize cellobiose and reduce a variety of substrates, producing organic radicals that can degrade lignin or cellulose, although its activity has been shown primarily to be related to cellulose catabolism (Phillips et al., 2011). The mutant strain of T. versicolor, TVm4D, which lacks cellobiose dehydrogenase (CDH), is therefore deficient in accessing and utilizing crystalline cellulose as a carbon source despite having an undamaged complement of hydrolytic cellulases, yet retains the lignin-degrading capabilities of the wild-type parent strain (Canam et al., 2011; Ramirez-Bribiesca et al., 2011). T. versicolor was found to degrade more cellulose than hemicellulose in rice straw in comparison with P. chrysosporium (Taniguchi et al., 2005). After 24 d of pretreatment, the cellulose content of rice straw reduced from 38.4% to 19.6% with P. chrysosporium and 15.8% with T. versicolor, while hemicellulose decreased from 24.7% to 13.8% and 18.6%, respectively (Taniguchi et al., 2005). T. versicolor also degraded more lignin in rice straw than P. chrysosporium did. Lignin content reduced from 25.2% in untreated rice straw to 20.3% in rice straw treated by P. chrysosporium and 17.2% in rice straw treated by T. versicolor for 24 d (Taniguchi et al., 2005).

Data on OUR and CPR is presented in Figure 5. Those two response variables were of interest since they provided the most convenient method to online monitor the growth of a filamentous fungus inside a bioreactor (Mitchell and Krieger, 2006b). It is also proportional to the heat production rate, therefore, providing a useful method for the temperature management of a SSF system (Mitchell and Krieger, 2006b). During the exponential phase of growth, OUR and CPR increased vigorously along with an increase in fungal biomass concentration. As the substrate reached its carrying capacity and fungal growth stagnated, the OUR and CPR remained constant and slightly dropped during the latter stage of the pretreatment. TV52J consumed the highest amount of oxygen and released the greatest amount of carbon dioxide per day followed by PC and TVm4D. This correlated with the higher fungal biomass concentration found in TV52J than that of PC and TVm4D. Only OUR and CPR monitored during the linear log phase of growth were used to fit with models in Equations (6), (7), and illustrated in Figure 6. The yield coefficient from oxygen to the fungal cell was inversely proportional to OUR and was the smallest in TV52J at 0.009–0.018 g X (mmol O₂)⁻¹ followed by those of PC (0.031–0.037 g X (mmol O₂)⁻¹) and TVm4D (0.078–0.080 g X (mmol O₂)⁻¹). In contrast, the maintenance coefficient (m_o) is proportional to OUR and valued highest at 19.434–20.567 mmol O₂ (g X)⁻¹ d⁻¹ in TV52J followed by those of PC (13.046–13.526 mmol O₂ (g X)⁻¹ d⁻¹) and TVm4D [9.525–9.712 mmol O₂ (g X)⁻¹ d⁻¹]. The high amount of oxygen consumption was associated with the high value of the maintenance coefficient from oxygen to fungal biomass indicating the vigorous metabolisms of fungi during the SSF. In previous studies, the yield coefficient from oxygen to the fungal biomass was 0.0061–0.0088 g X (mmol O₂)⁻¹ in P. chrysosporium growth on cotton stalk (Shi et al., 2012), 0.0055 g X (mmol O₂)⁻¹ in C. subvermispora growth on corn stover (Wan, 2011), 0.015 g X (mmol O₂)⁻¹ in G. fujikuroi growth on starch and urea (Pajan et al., 1997). The corresponding maintenance coefficient from oxygen to fungal biomass was 7.469–47.813 g X (mmol O₂)⁻¹ (Shi et al., 2012), 21.8867 g X (mmol O₂)⁻¹ (Wan, 2011), and 19.5 g X (mmol O₂)⁻¹ (Pajan et al., 1997), respectively. The ratio of carbon dioxide production to oxygen consumption (CO₂/O₂) was less than one in all substrate-fungus combinations most of the time (Figure 6) representing the simultaneous lignin oxidation-holocellulose metabolisms (Shi et al., 2014). The smaller the CO₂/O₂, the stronger the delignification activities (Shi et al., 2014). Therefore, an oxygen-enriched environment is strongly recommended for effective delignification. The plots of OUR and CPR against the fungal biomass concentration X are illustrated in Figure 7. Oxygen uptake rate could be linearly correlated to fungal biomass (X) with determination coefficient of 63.0–72.9% for TVm4D (Figures 7A, B), 74.3–81.3% for TV52J (Figures 7C, D), and 62.6–68.2% for PC (Figures 7E, F). The same linear correlations were also observed in CPR with the determination coefficient of 61.7–77.1% for TVm4D (Figures 7A, B), 68.0–76.4% for TV52J (Figures 7C, D), and 72.5–75.2% for PC (Figures 7E, F). However, the linear correlation might not represent the relationship of OUR and CPR with fungal biomass (X) very well since the data slope tended to increase along with the increase of X. Shi et al. (2012) suggested that a non-linear relationship may occur between OUR and cell concentration X. Therefore, it was necessary to explore more appropriate non-linear models to better predict fungal biomass from instantaneous and inexpensive measurements including OUR and CPR.

Enzyme production was examined to give a broader view of product formation by fungus vs. cell growth since it was not the main interest of this study regarding the microbial pretreatment of lignocellulosic substrate for biofuel production. Following the same trend with fungal growth (X), OUR, and CPR, the enzyme production rate increased during the linear log phase of growth and stagnated after that (Figure 8). The higher values of α than that of β suggested that enzyme production might be growth-associated. The growth-associated constant (α) ranked highest in TV52J [0.126–0.154 g proteins (g X)⁻¹] followed by that of PC (0.105–0.139 g proteins (g X)⁻¹) and TVm4D [0.089–0.124 g proteins (g X)⁻¹]. Cellulolytic and ligninolytic enzyme productions might be correlated to fungal biomass growth and substrate metabolisms (Shi et al., 2012). Shi et al. (2012) determined that ligninolytic enzyme production of PC growth on cotton stalk was not directly influenced by fungal growth since α and β were on the same magnitude. However, their models failed to estimate cellulase production. The enzyme production model proposed by Wan (2011) also generated a poor prediction because of the complicated enzyme systems during the SSF of C. subvermispora on corn stover. Enzyme generation was observed to be independent of metabolic energy provided by carbohydrates (Gaden, 1959), and the energy demand of PC fungus was higher than that provided by delignification (Shi et al., 2012). An overall trend of decline in enzyme production after a specific incubation time was also observed in T. versicolor, P. ostreatus, and L. edodes (Montoya et al., 2015). It was strongly recommended to monitor individual enzymes as well as provide more sophisticated models to predict each one of them.

The diagnostics of the nonlinear models were conducted based on 4 hypotheses including: 1) the correct mean function; 2) the correctness of the assumption of homogeneity of variances (homoscedasticity); 3) the errors of measurements were normally distributed; and 4) the errors of measurements were mutually independent (Ritz and Streibig, 2008). The normality and independence of measurement errors were reliably determined by the replication of treatments, the randomization of sampling, and the repeated final measurements (the repeatability of the analysis). In general, if the model explains the mean structure of the dataset suitably, then the predicted regression curve should follow the trend of the data. Therefore, the model could be examined visually by plotting the regression curves against the observations. The suitability of the fitness was also inspected by evaluating whether the measured data were allocated randomly (non-systematically) around the fitted curve by generating a residual plot.

With the estimated parameters indicated in Table 1, the predicted values of fungal biomass (X), holocellulose (S), and lignin content (L) were plotted against the experimental observations (Figure 4). The calculated results by the proposed hybrid logistic-Monod model agreed well with the batch culture experimental data, which was indicated by the high correlation coefficients and the random distribution of the residuals around zero (see model's normality check in Supplementary Figures 9A–C, 18A–C, 27A–C, 36A–C, 45A–C, 54A–C). The insignificance of the estimated k_LD in the case of SG-PC may have resulted from the insignificant reduction of lignin content in SG by P. chrysosporium. The predictions of OUR, CPR, and enzyme formation during the linear log phase of growth are shown in Figures 6, 8, respectively, and the regression curves also agreed well with the observations. The residuals of OUR, CPR, and enzyme models were also randomly distributed around the horizontal zero line without showing any obvious trend or pattern indicating the correctness of the models and the assumptions (see model's normality check in Supplementary Figures 9D–F, 18D–F, 27D–F, 36D–F, 45D–F, 54D–F). In addition, the standard deviation of the errors of prediction (the standard error of the estimate, σ_est) was also calculated and indicated in Supplementary Figures 9, 18, 27, 36, 45, 54. The very small values of σ_est represent the high accuracy of the predictions.

Simultaneous experimental and modeling design is recommended to develop the production scale SSF bioreactor (Mitchell et al., 2006b). Supplementary Figure 55 illustrates the strategy of using models to design and optimize the operation of SSF bioreactors. Determination of bioreactor type, modeling the growth kinetics and testing it on a laboratory scale is the very first steps of the process. In the context of biorefineries, the physiochemical quality of pellets (i.e., durability and heating value) or the structural characteristics of the substrate (i.e., the content of carbohydrates or enzymatic digestibility) are the targeted product information. After optimizing the product quality by a particular microorganism on a specific lignocellulosic substrate under lab scale, engineers and scientists will have enough data to develop large-scale process. After the bioreactor is built with the assistance of the model, data obtained from the operation can be used to enhance the model, and hence making the model more useful. The performance of the bioreactor can be tuned and significantly enhanced by enforcing the control strategy; in this case, the model is also useful in establishing those control schemes. In general, a mathematical model of an SSF bioreactor demands two sub-models including 1) the growth kinetics sub-model which represents the biological aspects of the microorganism and 2) the mass and energy balances and transport circumstance sub-model (Mitchell and Krieger, 2006a). The first model, which was developed in this study, provides essential information to develop the second model (Supplementary Figure 56). The fungal biomass equation can be used to predict the metabolic heat generation and hence assist the cooling system design. Or the headspace gas equations can be used to predict the fungal biomass content, which is cumbersome to measure, and therefore provide a quick method to determine the growth condition. They can also be used to calculate the amount of oxygen/air to be supplied to the bioreactor. The holocellulose and lignin equations can be used to forecast the product's targets and then adjust the operating condition of the reactor. It is highly recommended that the second sub-model is developed to generate data for both parts of the model.