Lactic Acid Production from Distiller’s Dried Grains Dilute Acid Hydrolysates

Abstract

Lactic acid (LA) is an important chemical with diverse applications in various industries. LA can be produced by the fermentation of different substrates by many microorganisms such as bacteria, fungi, yeasts, and algae. Lactic acid bacteria (LAB) are generally accepted as the main producers of LA. A distinct characteristic of LAB is the complexity of the fermentation media. Distiller’s dried grains with solubles (DDGS), a by-product from bioethanol production, represent a promising substitute for costly sugars in the nutrition media for LA production. In the present paper, the possibility of using dilute acid DDGS hydrolysates as a substrate for LA fermentation was investigated. The influence of different factors (acid concentration, time, pressure, solid-to-liquid ratio) on the reducing sugars (RS) obtained was studied. Additional enzyme hydrolysis was carried out to increase RS content in the hydrolysates. LA production from hydrolysates without and with control of the pH during fermentation was monitored and compared with lactose as a substrate. Inhibition of the process was observed in both substrates in the absence of pH control which was overcome in the case of pH control. A mathematical model based on the Verhulst and Ludeking–Piret equations was proposed and tested, showing very good agreement with experimental data.

1. Introduction

Currently, the demand for lactic (2-Hydroxypropanoic) acid is increasing year by year. This increase is due to the wide application of LA in the pharmaceutical, cosmetic, food, and beverage industries, as well as for biodegradable polymers and environmentally friendly solvents. In recent years, LA has mainly been produced by the fermentation of different sugars. In view to overcome the relatively high cost of pure sugars, present research on LA production is focused on using second-generation (lignocellulosic biomass and industrial waste) feedstocks. A promising but still underestimated feedstock is a by-product from first-generation bioethanol production—distiller’s dry grains.

At present, global ethanol production is estimated to be around 120–130 billion liters annually. Bioethanol represents about 90–95% of total ethanol production. According to the data of the Renewable Fuel Association, world production of bioethanol in 2023 reached 112 billion liters [1]. The USA and Brazil are the major producers of bioethanol. The share of bioethanol produced in 2023 in the USA was 59.13 billion liters (53% of world production) and Brazil produces 31.27 billion liters per annum (28%). The dry-grind bioethanol production process is predominant in bioethanol production. Corn, wheat, barley, rye, or other grains are used for bioethanol production in a consecutive multistep process. After grinding and milling, grains undergo enzyme treatment to convert starch to glucose which is then further fermented into ethanol. Ethanol is separated by distillation and purified by rectification. The remaining fermentation broth (whole stillage) is separated into liquid (thin stillage) and solid (wet grains) fractions. Thin stillage is evaporated to yield so-called condensed solubles, which are mixed with wet grains. The resulting mixture (wet distiller’s grains with solubles, WDGS) is dried to yield the final by-product: distiller’s dried grains with solubles, DDGS.

Shad et al. [2] reviewed the production, properties, and potential uses of corn DDGS, while Chatzifragkou et al. [3] discussed the chemical composition of DDGS, various pre-treatment methods, and possibilities for the production of value-added products. Iram et al. [4] summarized the type and composition of different DDGS, their uses, pre-treatment methods, and some products obtained from DDGS through fermentation.

The chemical composition of DDGS varies depending on several factors [3,5]. The most important is the type of grain used for DDGS production. Other factors affecting the composition of DDGS are the ethanol production process and its parameters, the influence of the yeast used for fermentation, and the amount and composition of condensed solubles added to DDGS. All of these factors lead to considerable variation in the chemical composition of DDGS from different production sites and even between batches of production. However, the mean composition of DDGS is as follows: moisture—9%, lignocellulosic material—36%, protein—29%, fats—9%, fibers—7%, starch 5%, and ash—5%.

DDGS have various applications: in animal and human nutrition, in energy production, and as feedstock for microbial fermentations [2,6]. Because of their high protein content (around 30%), DDGS are an excellent nutritional additive for animal feed [7,8,9,10]. If converted to flour, DDGS can be used as an additive in muffin, cookie, cake, bread, and snack production [11,12,13]. DDGS can be used for energy production by direct combustion or as a substrate for biogas [14,15] and another biofuel production [16,17]. Bokhary et al. investigated the anaerobic digestion of untreated and pretreated corn whole stillage [18]. They reported that pretreatment led to an increase in biogas production of more than 15%. Other possible applications of DDGS are as a fertilizer [19], as an adsorbent [20], as a paper additive [21], as a brick component [22], or for polymers [23] and polymer composites [24]. In recent years, the use of DDGS in some biotechnological processes has increased. They can be used as a substrate in the cultivation of mushrooms and actinobacteria or for enzyme (amylase, protease, and cellulases) production [25], as a carrier for enzyme and cell immobilization [26], or for value-added chemical production—lactic acid, ethanol, xylitol, etc. However, to be used as feedstock in the latter processes, the cellulosic part of the DDGS should be converted to fermentable sugars by a convenient pretreatment method. Usually, a combined method is used, consisting of a chemical method (acid or alkaline hydrolysis, hot water, steam explosion, or ammonia fiber expansion (AFEX)), followed by enzyme hydrolysis [27,28,29].

Dried distiller’s grains are treated by various techniques with different aims: to obtain the best conditions for maximum sugars yield, to use treated grains as a substrate for lactic acid production, or for the replacement of costly nutrient sources in the fermentation medium.

H. Noureddini and J. Byun have investigated the dilute acid hydrolysis of corn dried distiller’s grains [30]. The studied process parameters were biomass loading, sulfuric acid concentration, temperature, and reaction time. The best yield of monomeric sugars was obtained with 5% biomass loading and 1.5% sulfuric acid at 140 °C for 30 min. Iram et al. optimized three methods for DDGS pretreatment: dilute acid, soaking in aqueous ammonia, and steam explosion [31]. The highest reducing sugars yield was obtained by dilute acid treatment at 120 °C and a pressure of 15 psi.

Driessen et al. [32] treated DDGS soaked with 0.5% H₂SO₄ by steam explosion and the resulting slurry underwent enzyme hydrolysis. The obtained sugar solution was used as a substrate in an adaptive laboratory evolution of Bacillus subtilis strains with the aim of overcoming the hydrolysate’s toxicity.

There are only a few papers dealing with the making of lactic acid (LA) from by-products of ethanol production. Zaini et al. used alkali and enzyme-pretreated DDGS as a substrate for D-lactic acid production [33]. The process was carried out in separate hydrolysis and fermentation (SHF) or simultaneous saccharification and fermentation (SSF) modes. Very high degrees of conversion (about 85%) and optical purity (over 99%) were achieved. The same authors studied analogous pretreated DDGS for lactic acid production using L. coryniformis and L. pentosus separately or in simultaneous and sequential co-fermentation [34]. Better results were obtained at simultaneous co-fermentation—28.5 g/L LA (83.3% conversion).

Krull et al. demonstrated that the addition of acid or enzymatically hydrolyzed DDGS leads to up to 70% replacement of the expensive nutrient sources in the fermentation broth without significant changes in productivity and product yield [35].

Other by-products of ethanol production are also used for the production of lactic acid and other chemicals. Liu et al. investigated the possibility of using another by-product of bioethanol production-condensed distiller’s solubles (CDS) as a nutrient supplement for the fermentative production of lactic acid by Lactococcus lactis, with whey as a substrate [36]. However, a limited quantity of CDS (37 g/L) could be used, as inhibition took place at higher concentrations.

Djukić-Vukovic et al. studied the influence of some process parameters and kinetics of LA production from liquid distillery stillage using Lactobacillus rhamnosus [37]. The best conditions (41 °C, 5% (v/v) of inoculum, a shaking rate of 90 rpm, and an initial pH of 6.5 resulted in 74.3% of lactic acid yield with no addition of nitrogen or minerals to the stillage. Initial sugars in the broth (12 g/L) were adjusted to 25 g/L by adding a sterile glucose solution. In a later article, the authors immobilized L. rhamnosus by adsorption onto zeolite molecular sieves [38]. The immobilized cells were applied in a fed-batch process for LA production from liquid distillery stillage with added glucose to a final concentration of about 50 g/L. In four consecutive runs, the immobilized cells retained 39–42 g/L produced lactic acid, which was higher than that obtained with free cells.

Sen et al. utilized corn and rice-based DDGS as a substrate for sophorolipid production by a Rhodotorula babjevae strain [39].

The examples given above describe the significance of by-products from bioethanol production as renewable biomass, their broad possible applications, and the importance of finding optimal conditions for pretreatment as well as the process for the production of high-value chemicals.

In a previous paper, the LA production from lactose without pH control was investigated and different models describing biomass accumulation, substrate consumption, and LA production were compared [40]. The general aim of the present work is to evaluate the possibility of using DDGS hydrolysates for fermentative lactic acid production by a Lactiplantibacillus plantarum strain. This will include the optimization of reaction conditions for the hydrolysis and characterization of the hydrolysates obtained, kinetic study of lactic acid fermentation with and without pH control, and modeling of the fermentation process. To the best of our knowledge, no attempts have been made so far to model the process of LA production from DDGS hydrolysates as a substrate.

2. Materials and Methods

2.1. Distiller’s Dried Grains with Solubles

Distillery Almagest AG, Bulgaria, kindly provided corn DDGS. According to the supplier, DDGS contains protein—28.4%; fat—12.2%; starch—8.4%; and fibers—6.3%. Some other components of DDGS were determined according to Standard Biomass Analytical Methods provided by the National Renewable Energy Laboratory (NREL), Golden, CO, USA; the results are presented in

Table 1. DDGS composition.

Component	Percentage	Method
Moisture	9.2 ± 0.6	LAP-001
Total solids	90.8 ± 0.6	LAP-001
Total carbohydrates	35.6 ± 1.6	LAP-002
Acid insoluble lignin	13.2 ± 0.4	LAP-003
Acid soluble lignin	26.2 ± 0.1	LAP-004
Ash	4.7 ± 0.5	LAP-005
Extractives	15.6 ± 1.2	LAP-010

.

2.2. DDGS Pretreatment

The particular conditions for the treatment of lignocellulosic biomass vary depending on the type of biomass, the specific agent used, and the specific process requirements (desired level of delignification and hemicellulose solubilization). According to the literature reviewed [3,41], typical conditions for pretreatment are:

• Alkali treatment: concentration from 1% to 20% (w/w), temperature from 20 °C to 150 °C, solid-to-liquid ratio from 1:5 to 1:20 (w/w), and time from a few minutes to several hours;
• Dilute acid treatment: concentration from 0.5% to 5% (w/w), temperature between 120 °C and 200 °C, time from a few minutes to several hours, and solid-to-liquid ratio from 1:5 to 1:20 (w/w);
• Enzyme treatment: enzyme concentration from 10 to 50 U/g dry biomass. Biomass concentration: higher substrate concentrations usually increase productivity but may lead to enzyme inhibition from products, temperature from 45 °C to 55 °C, pH from 4.8 to 5.5, optimal for the used enzyme, and time commonly from 24 to 72 h but can be prolonged to several days for complete hydrolysis.

The specific conditions applied in this research are listed below.

2.2.1. Alkaline Pretreatment

DDGS were pretreated with NaOH and NH₄OH. Ten grams of DDGS were mixed with 100 mL (1%, 2%, and 3%) NaOH in Erlenmeyer flasks and were shaken for 70 h. Liquid and solid phases were separated by centrifugation at 3000 rpm for 30 min. The reducing sugars content in the supernatant was measured.

In the case of NH₄OH, 10 g of DDGS were soaked in 100 mL 1%, 3%, and 5% NH₄OH for 30 min at 120 rpm and then autoclaved for 30 min at 121 °C (1 atm). After cooling, the phases were separated and reducing sugars were determined in the supernatant. In both cases, 10 g DDGS wetted in 100 mL distilled water were used as a control.

2.2.2. Acid Pretreatment

For the investigation of dilute acid hydrolysis, 10 g DDGS were treated with 50 mL of 0.5, 1.0, 1.5, and 2% H₂SO₄ for 15, 30, and 60 min in autoclave at 1, and 2 atm overpressure. In another set of experiments, 10 g DDGS were treated with 30, and 60% H₂SO₄ at 37 °C for 48 h. For studying the influence of the solid-to-liquid ratio on the hydrolysis, 10 g DDGS were treated with 50, 75, 100, 125, and 150 mL 1% H₂SO₄ at 1 atm.

2.2.3. Enzyme Pretreatment

Ten grams of untreated DDGS and the solid phase remaining after treatment with 1% NaOH were used for further hydrolysis with different enzymes. Both solid phases were pretreated with 100 mL 1% H₂SO₄ for 30 min at 1 atm. After solid phase separation and multiple washing with distilled water to pH about 3.5 they were placed in 100 mL of phosphate buffer of pH 5.5. Amylolytic enzymes (50 µL α-amylase–Fuelzyme-Verenium Corporation, San Diego, CA, USA, and 150 µL glucoamylase, Deltazym GA L-E5-Verenium Corporation, San Diego, CA, USA) were added and the solution was incubated at 60 °C for 24 h. After separation, the solid phase was placed in 100 mL buffer with pH 4.6 and was hydrolyzed with 20 µg cellulase–Onozuca R-10-Yakult Pharmaceutical Industries Co., Ltd., Tokyo, Japan, at 45 °C for 24 h.

2.2.4. Microorganism

Lactiplantibacillus plantarum strain AC11 S, isolated from a sample of homemade white-brined cheese that was prepared, according to a traditional recipe, from non-pasteurized fresh sheep milk, was used in the study.

The strain was identified by molecular and classical phenotypic methods [42] and is part of the collection of the Laboratory of Lactic Acid Bacteria and Probiotics of the Institute of Microbiology-BAS. The strain was stored at −80 °C in MRS broth (HiJMedia Mumbai, India) co-plated with 20% sterile glycerol until the time of the experiments. For the experiments, the strain was pre-cultured in MRS broth with lactose (pH 6.5) twice at 30 °C for 48 h. An exponential culture of the strain was used for inoculum—10% in the fermentation broth.

2.2.5. Lactose and DDGS Hydrolysates Fermentation

An MRS medium was used, with the following composition g/L: yeast extract 5.5, peptone 12.5, KH₂PO₄ 0.25, K₂HPO₄ 0.25, CH₃COONa 10.0, MgSO₄·7H₂O 0.1, MnSO₄·4H₂O 0.05, FeSO₄·7H₂O 0.05, distilled water 1000 mL, pH 6.5.

Four series of experiments were performed with L. plantarum AC11 S with lactose and DDGS hydrolysates as substrates with or without pH control at 30 °C.

In the first set of experiments, lactose was used as the substrate in three different concentrations 10, 20, and 30 g/L. In the second set of experiments, DDGS hydrolysates containing 10, 20, and 30 g/L of reducing sugars were used. The experiments for lactic acid production without pH adjustment were performed in 300 mL Erlenmeyer flasks with a working volume of 100 mL. The experiments with pH control were carried out in a Bioflo New Brunswick Scientific fermentor (Edison, NJ, USA), with a working volume of 300 mL, at static conditions, at 30 °C.

The reducing sugars used as substrates were obtained by consecutive dilute acid and enzyme hydrolysis of DDGS as follows: 500 mL solution (20% w/v dry material) was hydrolyzed in an autoclave with 1% H₂SO₄ at 2 atm for 1 h. The resulting hydrolysate was treated with cellulase “Onozuka R-10” (Yakult Pharmaceutical Industries Co., Ltd., Tokyo, Japan) at pH 4.6 and 45 °C (40 U/g substrate) for 24 h. Aliquots were taken for fermentation with an appropriate concentration of reducing sugars.

All experiments for DDGS pretreatment were triplicated, and fermentations were duplicated. Each sample was analyzed in triplicate and the results were expressed as the mean value ± the standard deviation (SD).

2.3. Analysis

An HPLC system consisting of a Smartline S-100 pump (Knauer GmbH, Berlin, Germany), a refractometric detector-Perkin-Elmer LC-25RI (PerkinElmer, Waltham, MA, USA), and specialized EuroChrom software v. 3.05 were used. Aminex HPX-87H, 300 × 7.8 mm column, and AminexHPX-87C, both from Bio-Rad (Hercules, CA, USA), were used for lactic acid and sugar determination in isocratic mode at 70 °C. The mobile phase used was 0.01 N H₂SO₄ at a flow rate of 0.6 mL/min. Before injection, the samples were centrifuged and filtered through a 0.22 µm filter. The biomass concentration was determined by optical density measurements at 620 nm with a spectrophotometer VWR UV-1600 PC (VWR International, San Francisco, CA, USA). A calibration curve for biomass concentration determination was made after measuring the absorbance of a biomass suspension with a precisely defined concentration (mg/mL). The concentrations of reducing sugars in the DDGS hydrolysates were measured according to a modified Bertrand’s method, described previously [43].

2.4. Mathematical Modeling

The specificity of biotechnological process modeling is the large number of parameters in the mathematical description. The identification of model parameters in these cases is difficult to perform, owing to the multi-extremal least squares function or because some minima are of the ravine type. The solution to this problem requires very good initial parameter values (in the global minimum area) for the minimum search procedure.

Maximum product yield with full substrate utilization is the main objective of the fermentation process. An appropriate mathematical model and a correct determination of the model parameters will allow the fermentation to be conducted under optimal conditions. The bacterial growth rate can be described with the following equation:

$$\begin{array}{l}{\displaystyle \frac{dX}{dt}}=\mu X-k_{d}X\\ t=0,\hspace{1em}X=X_0\end{array}$$

(1)

where X is the cell concentration, g/L; t is time; μ is the specific growth rate, h⁻¹; and k_d is the specific cell death rate. In many cases, the term for cell death can be omitted.

We used the Verhulst equation to describe the specific growth rate as a function of substrate concentration [44]:

$$\mu ={\mu }_{\max }{\left(1-{\displaystyle \frac{X}{X_{\max }}}\right)}^n$$

(2)

where μ_max is the maximum specific growth rate, h⁻¹; X—biomass concentration, g/L; X_max—maximum biomass concentration, g/L; n is a power term defining the degree of inhibition by biomass.

To describe the formation of lactic acid, the Luedeking–Piret equation [45] was used. It considers the fact that the rate of product accumulation dP/dt is a function of the bacterial growth rate dX/dt as well as the bacterial density X:

$$\begin{array}{l}{\displaystyle \frac{dP}{dt}}=\alpha {\displaystyle \frac{dX}{dt}}+\beta X\\ t=0,\hspace{1em}P=P_0\end{array}$$

(3)

α and β are coefficients related to growth and non-growth product formation.

The substrate consumption is usually presented by the following equation rate of

$$\begin{array}{l}{\displaystyle \frac{dS}{dt}}=-{\displaystyle \frac{1}{Y_{X/S}}}{\displaystyle \frac{dX}{dt}}-{\displaystyle \frac{1}{Y_{P/S}}}{\displaystyle \frac{dP}{dt}}-m_{s}X \\ t=0,\hspace{1em}S=S_0\end{array}$$

(4)

where Y_X/S and Y_P/S are yield coefficients for biomass on substrate and product on substrate, respectively, g/g, while m_s is the biomass maintenance energy coefficient, g/g·h. In many cases, the latter was neglected. The utilization of the substrate is closely related to the cell’s growth rate and the rate of product formation.

2.5. Statistical Analysis

Statistical analyses were performed using ANOVA (SigmaPlot v.13.0, Systat Software Inc., Palo Alto, CA, USA). The statistical significance was defined as p < 0.05. The residual sum of squares (RSS), the total sum of squares (TSS), the root mean square error (RMSE), and the coefficient of determination (R²) were calculated as follows:

$$RSS={{\displaystyle \sum _i^N\left(X_i^{\exp }-X_i^{\mathrm{mod}}\right)}}^2+{{\displaystyle \sum _i^N\left(S_i^{\exp }-S_i^{\mathrm{mod}}\right)}}^2+{{\displaystyle \sum _i^N\left(P_i^{\exp }-P_i^{\mathrm{mod}}\right)}}^2$$

$$TSS={{\displaystyle \sum _i\left(X_i^{\exp }-\overline{X}\right)}}^2+{{\displaystyle \sum _i\left(S_i^{\exp }-\overline{S}\right)}}^2+{{\displaystyle \sum _i\left(P_i^{\exp }-\overline{P}\right)}}^2,$$

where $\overline{X}, \hspace{0.17em}\overline{S},\hspace{0.17em}\overline{P}$ are the mean of the observed data:

$$\overline{X}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{X}_i}, \hspace{0.33em}\overline{S}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{S}_i},\hspace{0.17em}\hspace{0.33em}\overline{P}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{P}_i}.$$

$$RMSE=\sqrt{RSS/N}$$

where N is the number of experimental data points

$$R^2=1-{\displaystyle \frac{RSS}{TSS}}$$

3. Results and Discussion

3.1. Alkaline Treatment

Alkaline treatment is usually applied to partially dissolve the lignin in the lignocellulosic materials. The method is considered to yield better delignification compared to acid treatment. Lignocellulose is affected to different degrees, depending on the severity of treatment, whereas the cellulose remains mostly intact [46]. The results of alkali treatment of DDGS are presented in Figure 1. Statistical analyses were made using two-way ANOVA, with the factors being the type and concentration of alkali. There is not a statistically significant difference between the types of alkali (p = 0.195), but there is significant difference between the control and all concentration levels (1, 2 and 3% for NaOH and 1, 3 and 5% for NH₄OH) (p = 0.001). To isolate which group(s) differ from the others, All Pairwise Multiple Comparison Procedures (Holm–Sidak method) were conducted. The results of this procedure are summarized in

Table 2. Results from All Pairwise Multiple Comparison Procedures (Figure 1 data).

Comparisons for Factor Type of Alkali
	Diff of Means	t	p	p < 0.050
NH4OH vs. NaOH	0.495	1.664	0.195	No
Comparisons for concentration
3.000 vs. Control	7.060	16.783	0.003	Yes
2.000 vs. Control	6.635	15.773	0.003	Yes
1.000 vs. Control	5.995	14.252	0.003	Yes
3.000 vs. 1.000	1.065	2.532	0.235	No
2.000 vs. 1.000	0.640	1.521	0.4	No
3.000 vs. 2.000	0.425	1.010	0.387	No

. The alkali treatment had a positive effect on the RS concentration compared to the control. On the other hand, the concentration of the alkali agent did not lead to significant differences in the obtained RS concentrations. RS concentrations after treatment in all cases are in the range of 8.0 ± 1.0 g/L.

3.2. Acid Hydrolysis

The first set of experiments studied the influence of sulfuric acid concentration and pressure on the hydrolysis of DDGS. For this purpose, 10 g of DDGS were treated according to the procedure described in Section 2.2.2. The results are presented in Figure 2. The obtained results were statistically analyzed by three-way ANOVA with the factors being pressure (1 and 2 atm), time (15, 30 and 60 min), and acid concentration (0.5, 1.0, 1.5 and 2.0%). The difference in the mean values among the different levels of pressure, time and concentration are greater than would be expected by chance. There is a statistically significant difference (p < 0.001). To isolate which group(s) differ from the others, All Pairwise Multiple Comparison Procedures (Holm–Sidak method) were conducted. The comparison showed that for all levels of each factor there was a significant difference (see

Table 3. Results from All Pairwise Multiple Comparison Procedures (Figure 2 data).

Comparisons for Factor Pressure
	Diff of Means	t	p	p < 0.050
2.000 vs. 1.000	14.903	5.446	<0.001	Yes
Comparisons for factor time
60.000 vs. 15.000	20.149	6.013	<0.001	Yes
60.000 vs. 30.000	12.424	3.707	0.003	Yes
30.000 vs. 15.000	7.725	2.305	0.034	Yes
Comparisons for factor concentration
2.000 vs. 0.500	30.873	7.978	<0.001	Yes
1.500 vs. 0.500	27.291	7.053	<0.001	Yes
2.000 vs. 1.000	15.786	4.080	0.003	Yes
1.000 vs. 0.500	15.786	3.899	0.003	Yes
1.500 vs. 1.000	12.205	3.154	0.012	Yes
2.000 vs. 1.500	3.581	0.926	0.368	No

). As expected, the increase in time, acid concentration, and pressure lead to an increase in RS obtained. Depending on the reaction conditions, the amount of reducing sugars varied from 18.8 g/L to 80.7 g/L.

In general, increasing the acid concentration, pressure, and time increases the concentration of obtained reducing sugars. Cekmecelioglu and Demirci [29] have reported nearly the same RS concentration (78.6 g/L) after DDGS treatment with 5% H₂SO₄ for 60 min at 120 °C and 20% solid load. Other authors have also obtained comparable results. For example, Nghiem et al. [40] reported 63.9 g/L RS after enzymatic hydrolysis of DDGS pretreated with 4% H₂SO₄ for 1 h at 120 °C and a 1:10 solid-to-liquid ratio. Noureddini and Byun [26] reported total sugar yields in the range of 47.5 g/L with 10% DDGS loading pretreated with 1.0% v acid at 120 °C for 60 min.

The next experimental set aimed to elucidate the influence of the solid-to-liquid ratio on the amount of reducing sugars after acid hydrolysis. Ten grams of DDGS were treated with 1% sulfuric acid in different ratios from 1:5 to 1:15 at a pressure of 1 or 2 atm for 30 min. The results obtained are shown in Figure 3. Statistical analyses were made using two-way ANOVA with the factors of pressure and ratio. The difference in the mean values among the different levels of two factors is not great enough to exclude the possibility that the difference is just due to random sampling variability after allowing for the effects of differences in concentration. There is not a statistically significant difference (p = 0.086 for pressure and p = 0.101 for solid-liquid ratio). The concentration of RS decreases by increasing the volume of the acid, whereas the total amount of sugars in grams increases. Noureddini and Byun [30] also reported maximum sugars yield at a lower solid load—5%.

3.3. Enzyme Hydrolysis

The solid phases remaining after alkali treatment and untreated DDGS were provided with 100 mL 1% H₂SO₄ at 1 atm for 30 min. After liquid separation and multiple washing, the solid phases were placed in 100 mL buffer, and enzymes were added, following the protocol described in Section 2.2.3. The results are presented in Figure 4. The amount of RS increased after each treatment step, from 7.6 g/L after alkali treatment to 40.16 g/L after enzyme hydrolysis in case of 10 g DDGS. It is worth mentioning that, in the case of alkali-treated DDGS, the RS concentration after enzyme hydrolysis is higher, due to the partial lignin removal. Doubling the amount of DDGS doubled the concentration of obtained RS, but further increase had negligible effect. Combining acid and enzyme hydrolysis of DDGS led to a sufficient amount of fermentable sugars to be used as a substrate in lactic acid production. The combination of dilute acid and enzyme hydrolysis is most employed in the pretreatment of lignocellulosic materials. The yield of reducing sugars depends on the conditions of acid pretreatment as well as on the type of cellulosic enzyme used [46].

3.4. Fermentation

Initially, the production of lactic acid by L. plantarum with lactose as substrate (10, 20, and 30 g/L) without and with pH control was investigated, and the results obtained were compared with those with DDGS hydrolysates as substrate. The results are presented in Figure 5 and Figure 6. In the case of fermentation without pH control and lactose as a substrate, complete conversion was observed only at 10 g/L lactose. Increasing the substrate concentration, inhibition of the process was observed and the yield decreased to 62% for 20 g/L and 50% for 30 g/L of lactose. Similar behavior was observed in our previous paper [41] and the initial substrate concentration at which inhibition started (15 g/L) was determined by mathematical modeling. Carrying out the fermentation under controlled pH conditions ameliorated the final yield of LA, with complete conversion for 10 and 20 g/L and 86% for 30 g/L initial lactose concentration. At the same time, the quantity of biomass obtained was higher in the case of pH-controlled fermentation.

When DDGS hydrolysates were used as substrate, the obtained final LA concentrations were very similar: 96, 64, and 52% in the case of pH-uncontrolled fermentation and 100, 100, and 82% with pH control for 10, 20, and 30 g/L RS as a substrate, respectively. Zaini et al. [33,34] investigated the lactic acid production from alkali and enzyme-treated DDGS and reported 24.7 g/L LA in case of fermentation with L. pentosus, and 28.5 g/L after sequential co-fermentation of L. coryniformis and L. pentosus.

3.5. Process Modeling

An algorithm was developed to simultaneously solve the model equations describing the fermentation process at different initial substrate concentrations. Our experimental data were used, through this algorithm, to obtain the model parameters by minimizing the least square function Q, using the fminsearch procedure of MATLAB 2013A software. A derivative-free method (fminsearch) is used to find the minimum of the target function Q of several variables on an unbounded domain. This method uses the Nelder–Mead simplex search method of Lagarias et al. [47]. The fminsearch method is a direct search method that does not use numerical or analytic gradients.

To this end, the experimental data were used to minimize the objective function Q, which is the sum of the squares of the differences between the measured biomass, substrate, and lactic acid concentrations and the calculated concentrations from the models:

$$\begin{array}{l}Q\left({\mu }_{max},X_{max}, n,Y_{X/S}, Y_{P/S},\alpha ,\beta \right)=\\ {\displaystyle \frac{1}{N}}{\displaystyle \sum _{j=1}^N}{\left(X_j-X_j^{exp}\right)}^2+{\displaystyle \frac{1}{N}}{\displaystyle \sum _{j=1}^N}{\left(S_j-S_j^{exp}\right)}^2+{\displaystyle \frac{1}{N}}{\displaystyle \sum _{j=1}^N}{\left(P_j-P_j^{exp}\right)}^2\to min\end{array}$$

where j is the experimental point number; X, S, and P are values of biomass and product concentration calculated by the model; X^exp, S^exp, and P^exp are experimental values; $t_j\left(j=1,\dots ,N\right)$ are the times in which the biomass (X), substrate (S), and lactic acid (P) concentrations are measured; and N is the experimental data number.

The values of the parameters obtained after solving the mathematical model simultaneously for the three initial substrate concentrations are presented in Table 2 and Table 3. The values of the maximum specific growth rate are very close but a little bit higher for the lactose as a substrate. Comparing pH-controlled and pH-uncontrolled fermentations, it may be seen that the values in controlled fermentations are slightly higher. The obtained values of µ_max are very close to these reported in the literature for LA production from lactose [48,49]. In all cases, the lactic acid fermentation was growth-related, which was confirmed by the ratio of the parameters α and β.

The results of mathematical modeling are presented in Figure 7 and Figure 8. There is not a statistically significant difference between the experimental and model data. A very good agreement between the experimental and computed results is observed. (See

Table 4. Lactic acid fermentation without pH control.

Initial Substrate Concentrations (10, 20, 30 g/L)	Model Parameters
	μmax, h−1	Xmax, g dm−3	n	YX/S [—}	YP/S [—}	α, h−1	β, h−1	Q	R2	RMSE	RSS
$S_{Lactose}^0$	0.2402	2.2447	1.7068	0.1647	4.3034	6.3202	0.0029	3.150	0.994	1.775	13.604
$S_{DDGS}^0$	0.2309	1.3693	0.9693	0.1798	5.2371	7.9996	0.0136	2.871	0.996	1.694	23.138

and

Table 5. Lactic acid fermentation with pH control.

Initial Substrate Concentrations (10, 20, 30 g/L)	Model Parameters
	μmax, h−1	Xmax, g dm−3	n	YX/S [—}	YP/S [—}	α, h−1	β, h−1	Q	R2	RMSE	RSS
$S_{Lactose}^0$	0.2539	3.7727	1.8228	0.1715	4.7211	5.6631	0.0044	3.521	0.966	1.876	52.573
$S_{DDGS}^0$	0.2415	1.906	1.2517	0.2566	2.1982	7.2765	0.0133	0.403	0.992	0.635	33.757

). The high determination coefficients (R² from 0.966 to 0.996) proved the goodness of fit of the model. To the best of our knowledge, this is the first attempt to model the process of LA from DDGS hydrolysates.

4. Conclusions

This study presents the results of using DDGS hydrolysates as a substrate for LA production. Different pretreatment methods (alkali, dilute acid, and enzyme pretreatment) were separately or consecutively applied. Depending on the experimental conditions and the pretreatment method used, different amounts of RS were obtained—from 18.8 to 80.7 g/L. Resulting sugar solutions were used for LA fermentation using L. plantarum without and with pH control. The results obtained were compared with similar results with lactose as a substrate. Both fermentations were growth-associated. Applying pH control ameliorates the LA yield for both substrates, reaching full conversion for 10 and 20 g/L initial substrate concentration, and 82–86% for 30 g/L. A mathematical model based on the Verhulst and Luedeking–Piret equations was used for modeling the experimental data, with very good agreement. The parameter values calculated by the model for all cases were of the same magnitude and were higher in the case of pH control. This is the first attempt at modeling the LA fermentation from DDGS reducing sugars.