Determination of Variable Humidity Profile for Lactic Acid Maximization in Fungal Solid-State Fermentation

Abstract

Solid-state fermentation (SSF) is the bioprocess where microorganisms are cultivated in the absence of free water under controlled conditions. Lactic acid can be produced by Rhizopus oryzae SSF of grape stalks. During the microorganism’s growth, the temperature and water content of the solid bed fluctuate, leading to areas of either dry or excessive moisture in the solid substrate. Therefore, it is crucial to control the water supply to the matrix. In this work, we obtain lactic acid through SSF of grape stalks using Rhizopus oryzae NCIM 1299. The SSF was conducted at a fixed temperature of 35 °C, with five constant relative humidity (RH) levels: 50, 57, 65, 72, and 80%RH. Mathematical models, including the Logistic and First-Order Plus Dead-Time models for fungal biomass growth and the Luedeking and Piret with Delay Time model for lactic acid production, were adjusted to kinetic curves. Growth kinetic parameters (X_max, μ_max, T_p, T₀, Y_p/x, and t_d) were determined for all conditions. These kinetic parameters were then correlated with relative humidity using a second-degree polynomial relationship. We observed a decrease in X_max with an increasing %RH, while the value of Y_p/x increased at a higher %RH. Finally, the optimal variable relative humidity profile was obtained by applying the dynamic optimization technique, resulting in a 16.63% increase in lactic acid production.

1. Introduction

The transition towards an eco-friendly world has been a topic of discussion for many years. However, efficient strategies must be implemented for a sustainable planet to become a reality in the short term. Bioeconomy suggests the development of green technologies for a sustainable production of bioproducts from agricultural wastes, emerging as a sustainable alternative to traditional linear production [1]. Agricultural wastes are residues from the growing and processing of raw materials such as fruits, vegetables, meat, poultry, dairy products, and crops [2]. Specifically, in the wine industry, different wastes are generated in the process of obtaining wine, with the grape stalk (GS) being a solid lignocellulosic waste that is obtained when the grapes are destemmed, and currently there is no process that is applied to it to add value or reduce its adverse effects on the environment [3].

In the field of research, the GS is being studied as a source of biocompounds (resveratrol, flavonoids, and tannins) for use in the cosmetic industry [4], and as a source of biosugars for use in submerged fermentation (SmF), for obtaining bioethanol [3] and lactic acid [5]. However, these SmF processes require an alkalinization step to obtain the sugars, which implies longer processing times and higher processing costs. In contrast, fungal solid-state fermentation (SSF) presents itself as an alternative for GS valorization that does not need pretreatment, since fungi, specifically Rhizopus oryzae (R. oryzae), which possess a powerful enzyme pool capable of degrading the lignocellulosic structure of GS, act with the consequent production of lactic acid (LA) [6].

Lactic acid is one of the few biobased organic acids that can be produced by fungal SSF from different inexpensive agricultural residues and food waste, such as sugarcane bagasse and juice and corn grain, among others [7]. Since a few years ago, various biotech companies have been actively investing in the commercialization of bio-based LA, such as NatureWorks LLC (Minneapolis, MN, USA), Corbion-Purac (Amsterdam, The Netherlands), and Galactic S.S (Brussels, Belgium). The most significant demands for LA in the global market come from the food, cosmetics, and pharmaceuticals industries, having gained great importance in recent years for its use as a precursor of the biopolymer polylactic acid (PLA) and also its use as a fundamental part of Natural Deep Eutectic Solvents (NADES), being a type of green solvent [8]. In 2022, the global market volume of LA was 1.5 million metric tons [9]. However, the demand for LA is growing exponentially, making it uncertain whether the actual demand can be met in the short term.

The development of biobased products, like LA, promotes a sustainable economy without dependence on petrochemical-derived fuels, representing an estimated market volume of USD 429.5 billion in 2024, with a compound annual growth rate (CAGR) of 6.96% (2024–2029) [10]. Despite the growth trend of this market, it is considered that it has not yet taken off due to the difficulty in obtaining affordable and sustainable raw materials from reliable sources that ensure good yields at larger scales and have a concrete demand from consumers [11]. Therefore, biotechnological advances are crucial to reduce production costs, improve yields, and make this market attractive to future investors.

A significant contribution that would enhance biotechnological advances is the implementation of optimization and control strategies for bioprocesses. Process control is a necessary tool to assure the stability of any system, including bioprocesses, as they are regulated by a complex interaction between the physical, chemical, and biological conditions of the fermentation environment and the biochemical processes that occur within microorganisms [12]. The performance of SSF can be affected by biological (type of microorganism, inoculum concentration, and solid substrate type), physicochemical (moisture content of the solid bed, pH, temperature, aeration, particle size, and gas composition), and mechanical factors (application or absence of mixing and type of bioreactor employed) [13]. Based on this, it is necessary to ensure that the temperature and moisture of the solid bed is maintained within an operational range that favors the growth of the microorganism and the production of the bioproduct [14].

Temperature and relative humidity (or moisture of solid substrate) tend to fluctuate significantly in SSF due to the heterogeneity present in the system (characterized by the existence of a gas phase, low moisture phase, and agro-industrial solid). This complexity adds difficulty to the phenomena of heat and mass transfer, by resulting in localized temperature increases and humidity decreases (due to water evaporation and microbial consumption), which negatively influences the growth of the microorganism and the productivity of the bioproduct [15]. Therefore, the matrix water supply should be controlled.

In SSF bioreactors, it is most common to control the conditions of the inlet air, including the flow rate, relative humidity (RH), and temperature, to manage the conditions within the solid bed. This can be accomplished in two ways: either controlling the humidity of the air while keeping its temperature constant, or controlling the temperature of the air while keeping its humidity constant [16]. However, in most fungal SSF studies, the variation in the solid substrate moisture was manually studied, conditioning its humidity at the beginning of fermentation, and then keeping a constant relative humidity airflow [17,18,19,20,21]. Another alternative that has been used to control and maximize LA production is the use of a stepped temperature profile, in which a constant temperature is maintained for a certain period of time, and by producing instantaneous temperature jumps of up to 15 °C [22,23]. The disadvantage of applying such stepped temperature profiles is that they are difficult to apply practically in a bioprocess, since the instantaneous increases and decreases in temperature (or in this case RH) are physically impossible to apply in reality, so the predicted LA yield would change appreciably.

The air conditioning configurations can vary from simple systems where air enters through a blower, to a system with an air filter, followed by a humidification tank with a porous plate (humidifier); to alternatives where humidification columns are used, along with hot- and cold-water tanks with solenoid valves that allow mixing these water streams to condition the air temperature. The choice between one configuration or another will depend on criteria such as economic performance, capital cost of the devices, and operational costs (blowing the air, heating or cooling the air, producing steam, and heating water) [16]. Based on this, it would be feasible and simple to use air with a variable RH percentage throughout the SSF reactor.

This work aimed to develop a simple and innovative method that maximizes LA production by applying a variable RH profile in the SSF of grape stalks, employing Rhizopus oryzae as the fermentation agent. To achieve this, the effect of RH (50, 57, 65, 72, and 80%RH at 35 °C) was studied using a laboratory membrane culture system, which allowed collecting the dry biomass of the fungus. After acid hydrolysis of the biomass, LA production was measured. Mathematical models were fitted to the kinetic data, and after identifying the kinetic parameters for each experimental condition, polynomial relationships were established between the parameters and RH. This set of polynomials served as the input for the dynamic optimization technique, based on Fourier series and Orthogonal Polynomials.

2. Materials and Methods

The general procedure for obtaining a variable RH profile that maximizes LA production is described in Figure 1.

2.1. SSF Experimental Data

As shown in Figure 1, the workflow diagram of this study was based on experimental data from the growth kinetics of R. oryzae NCIM 1299 (from Centro de Referencia de Micología, Facultad de Ciencias Bioquímicas y Farmacéuticas, Universidad Nacional de Rosario, Rosario, Argentina) on grape stalk (from Tierra del Huarpe S.A, San Juan, Argentina). The culture membrane growth assay was employed because it mimicked the conditions in SSF, and it presented a simple manner to collect the biomass off the filter without penetrating through the structure of the GS.

Before conducting membrane growth assays, R. oryzae spore stock suspension was obtained by harvesting the fungal spores developed on potato dextrose agar (PDA). Growth experiments were conducted in Petri dishes via a membrane filter culture system, using nylon membrane (0.2 µm pore size) and culture medium with GS (0.05 gGS/mL of medium) and agar as a gelling agent. Each Petri dish was inoculated with the spore stock suspension (1.37 × 10⁸ spores/mL) and was placed under controlled RH and temperature conditions (SEMEDIC, L-291PH). Sampling was performed in duplicate every 12 h [6].

The treatment of the samples was carried out as follows: the nylon filter where the R. oryzae fungus developed was removed and placed at 80 ± 5 °C for 24 h for the determination of fungal dry biomass via gravimetry [18]. Then, each filter with the fungal dry biomass was subjected to an acid hydrolysis stage (1st step: sulfuric acid (H₂SO₄) 72% v/v at room temperature for 4 h; 2nd step: H₂SO₄ 3%v/v at 100 °C for 2 h), which enabled breaking the cell and releasing the produced LA, which was recovered with calcium carbonate (CaCO₃) and quantified with ferric chloride (FeCl₃ 6H₂O) via the spectrophotometric technique (Agilent Technology, Cary 60 UV-Vis, Santa Clara, CA, USA) at 390 nm [24].

It was chosen to work by manipulating the RH and not the moisture of the substrate, because RH is the manipulable parameter in a bioreactor through the injection of saturated air into the bioprocess, whereas the moisture of the substrate can be conditioned at the beginning of the SSF and maintained at an optimal level using humidified air [13]. Therefore, it can be assumed that the solid substrate and the fungus are at the ambient temperature RH of the air in the incubation chamber due to the following considerations:

• (a). To avoid the effect of the moisture gradient that may occur in the substrate of SSF, agar was chosen as it is a strong gelling agent with a high water retention capacity (up to 20 times its own weight) [25]. Additionally, a sufficient layer of culture medium (Agar + GS) was placed to ensure that it does not influence mass transfer effects;

• (b). The nylon filter (0.2 µm porosity) placed between the culture medium and the fungus allows it to grow under the existing ambient conditions above the nylon filter. However, at the same time, the fungus is in indirect contact with the culture medium, which contains retained water for the proper metabolic development of the fungus.

Five experiments were carried out in an incubator (SEMEDIC, L-291PH) with temperature and RH control, using a fixed temperature of 35 °C following five constant RH values: 50, 57, 65, 72, and 80%RH for 120 h. These conditions were chosen based on others’ fungal SSF work. Firstly, a study on the effect of humidity (45 to 85% w/w) on the production of LA by R. oryzae in pineapple residues was taken as a basis [20]. Also, in [21], the influence of wheat moisture on cellulase production by Aspergillus oryzae was studied using four moisture levels, 50, 60, 70, and 80%, while maintaining the temperature constant at 35 °C. Another study utilized moisture levels of 30, 40, 50, and 60%, but also varied the temperature at 20, 30, 40, and 50 °C, to evaluate the effect of humidity on enzyme production by Aspergillus niger [18].

2.2. Mathematical Modeling and Parametric Identification

The R. oryzae concentration (gDB/gGS) and the LA concentration (gLA/gGS) obtained at each sampling time were plotted as a function of time, for each RH. Then, mathematical models were chosen to adequately represent the kinetic behavior of R. oryzae biomass and LA production. Mathematical models were adjusted to these kinetic curves: on one hand, the Logistic (see Equation (a) from Figure 1) and First-Order Plus Dead-Time (FOPDT) (see Equation (b) from Figure 1) models were used to describe biomass generation, and, on the other hand, the Luedeking and Piret with Delay-Time model (LPwDT) (see Equation (c) from Figure 1) was applied to describe LA production [26,27]. These models have been used to predict the behavior of various systems and to tune controllers, achieving excellent results [28,29,30]. In this work, the parameter values provided by these expressions were used as a starting point for the algorithm used to improve the fit of the models.

In Equations (a)–(c) of Figure 1, the kinetic parameters highlighted in yellow (X_max, μ_max, t_p, t₀, Y_p/x, and t_d) are the ones that need to be optimized to obtain the best value of the determination coefficient (R²) for each model. To fit these parameters, a hybrid algorithm [31] that integrates a Monte Carlo random search [32] with Genetic Algorithm method [33] was applied. The first step consists in determining an initial population of individuals (parameters) using the Monte Carlo algorithm. Then, the Genetic Algorithm begins to work and, in each iteration (n = 2000), new individuals are generated using the operations of crossing and mutation; thus, a new population is created (new individuals). With all these new individuals, a new population is generated, from which the best ones are chosen to apply the process of mutation and crossing again, so this procedure continues for a certain number of iterations. Finally, the parameters converge, and the optimum is reached. The process of the described algorithm was run 50 times for each experiment, obtaining a set of kinetic parameters in each run. Therefore, there were 50 values for each of the model parameters, and the average and standard deviation of each parameter were calculated. The application of this hybrid method allowed for improvement in the adjustment of the parameters, with respect to the parameters that had been originally obtained, in the processes of obtaining biodiesel [34] and recombinant proteins production [35], among other works.

The mathematical models for each kinetic growth and LA production were fitted with Matlab R2015a software [36].

2.3. Humidity Polynomial Relationship with the Kinetic Parameters

Once the values of the kinetic parameters that maximized the R² value of each mathematical model were elucidated, they were related to the RH using a second-degree polynomial relationship:

(1)$f\left(RH\right)=a_1 R{H}^2+a_2 RH+a_3$

where f is the kinetic parameter (μ_max, X_max, t_p, t₀, and Y_p/x), a₁, a₂, and a₃ are the adjustment parameters, and RH is the relative humidity. The Matlab R2015a curve fitting tool was used to obtain the graphs, by applying a grade 2 polynomic regression.

Mathematically, polynomials can be applied to different systems under study, with no limitation on application regarding whether the substrate is liquid or solid. Our team has been working on polynomial fitting in other systems, such as the biocontrol of wine spoilage yeasts and the study of the variation of kinetic parameters obtained at different pH levels [37].

Regarding SSF, the use of polynomials was implemented to establish a relationship between the kinetic parameters of mathematical models and RH, rather than to describe the kinetics of the fermentation process.

2.4. Optimal Control Problem Statement and LA Maximization Using Dynamic Optimization

The statement of the optimal control problem (OCP) was established in Figure 1. The OCP consists in setting the objective function, in this case, maximizing the concentration of LA at the end of the fermentation (120 h), by finding the optimal profile of RH over time. To do this, clear initial conditions and equality and inequality constraints of the bioprocess were outlined (see Figure 1).

The set of polynomial kinetic parameters obtained previously were the input data to obtain the variable RH profile. This profile was obtained by applying the dynamic optimization technique, based on Fourier series and Orthogonal Polynomials. The basis of this technique is to use the first terms of the Fourier series to obtain a polynomial with a minimal number of parameters to optimize. Then, a transformation is performed from the Fourier polynomial basis to an Orthonormal basis. This results in a smooth RH profile with low frequency (from a mathematical perspective), by providing a good representation of the system with a minimum number of parameters to optimize. The complete mathematical description of this technique is sufficiently detailed in [38].

Programming was carried out using Matlab R2015a software to obtain the variable RH profile.

3. Results and Discussion

Before delving into the specific results achieved in this work, it is important to highlight the main implications of this study. As a primary contribution, a new approach to modeling experimental data of SSF is proposed. Unlike traditional methods that rely on developing complex phenomenological models of the SSF, typically involving a series of interconnected differential equations, the proposed procedure is straightforward. It utilizes well-known models, both in the scientific and process-engineering fields, making it easily transferable to the industry. Furthermore, by incorporating a variable RH profile into SSF will enable monitoring the evolution of the dynamic growth typical of fungi without having to maintain the RH at a constant value.

3.1. SSF Experimental Data, Mathematical Modeling, and Parametric Identification

Figure 2 presents the averages with their error bar of the R. oryzae experimental results at the five %RH carried out.

A small difference in the steady state of the growth kinetics can be observed at 57%RH, 65%RH, 72%RH, and 80%RH levels, but a clear difference was observed for 50%RH. This confirms that R. oryzae NCIM 1299 preferred lower humidity levels for its proper development, indicating that SSF is a suitable bioprocess for LA production with this type of microorganism. This is further confirmed by the values of the optimal kinetic parameters of the fitted models, as shown in Figure 2 and Table 1.

Regarding the adjustment of microbial growth models with the variation in RH, it is observed that the R² values were similar for the Logistic and FOPDT models, with a slight improvement in R² when applying the latter. These results, reaffirm the convenience of using the FOPDT model in the modeling of bioprocesses, due to the simplicity and wide knowledge of this model in other branches of engineering, such as chemical or electronic processes, among others [28,39].

It is important to note that, in the present study, no growth morphology variation was observed in R. oryzae NCIM 1299, as it always grew in a mycelial form. In contrast, in our previous investigation, where the effect of temperature on fungal growth was examined [27], there was a change in the morphology of R. oryzae, with pellet growth observed at 40 °C and 50%RH. This could indicate that there is no direct effect of RH on fungal metabolism related to morphological changes, as is the case with temperature. Therefore, it can be said that RH would not be a parameter to manipulate when studying the improvement in LA productivity through the use of R. oryzae pellets.

Next, Figure 3 presents the averages with their error bars of the LA experimental results at the five RH levels carried out.

A slight difference in the steady state of the LA kinetics can be observed at 50%RH, 57%RH, and 65%RH, while at 72%RH and 80%RH a considerable increase in LA production was obtained. This could be due to the fact that, at 80%RH, the fungus exhibited the lowest amount of biomass produced (X_max) compared to 50%RH, 57%RH, 65%RH, and 72%RH (see Figure 2) which could be attributed to mycelium compaction due to the high humidity content. Therefore, as biomass production was restricted, the fungus dedicated itself to producing a greater quantity of the metabolite LA. This behavior was also observed in [19], where the effect of humidity on the production of antioxidant naphtho-gamma-pyrones and hydroxycinnamic acids by Aspergillus tubingensis in SSF was studied. Here, biomass production decreased, while metabolite production increased with increasing humidity.

In Table 2, the models and parameters adjusted for each %RH are presented.

When using the FOPDT model with LPwDT, an improvement in the R² value is observed under the RH conditions of 57, 65, 72, and 80%, while at 50%RH, the Logistic model with LPwDT shows a better fit. The Y_p/x values of both models clearly reflect the aforementioned suitability of working at a higher %RH to achieve higher LA productions, as shown in Figure 3. It is interesting to note that, at 80%RH (see Table 2), there is a delay of t_d = 5 h, which reflects the difficult adaptation of the fungus to high humidities, but which is later compensated with high LA yields.

3.2. Relative Humidity Polynomial Relationship with the Kinetic Parameters

On page 237 of [40], Theorem 5.1.4 is described, which states that if a system is subjected to presenting small variations in parameters, then the responses should not be very different from each other. In this sense, if the RH changes very little, it is expected that the results will be very similar to the original experience. This suggests that if the parameters change following a certain function, this function must be continuous with continuous derivatives. Although the exact form of the function representing the variation in the parameters as a function of RH is unknown, it is possible to approximate it through polynomial interpolation. Furthermore, it is possible to apply the Stone–Weierstrass Theorem (Theorem 5.6, page 21, from [41]). This theorem states that real continuous functions defined on a closed and bounded interval can be approximated as closely as desired with a polynomial. Additionally, real-coefficient polynomials are dense in the set of continuous functions over a closed interval.

Based on this, a second-degree polynomial was chosen since the considered RH interval is 30% (from 50 to 80%RH). In this interval, it is not expected that the parameters exhibit multiple local maxima and minima. What is expected is that the parameters show a maximum, a minimum, or exhibit monotonic behavior, in which case the maxima or minima will be at the limits of the considered interval. For all these reasons, a second-degree polynomial was used to fit the kinetic parameters with RH.

The need to use a higher-order polynomial would be because it is expected to obtain multiple maxima and minima. It can be seen that the P3 polynomial of Legendre polynomials, for example, has three roots in the considered interval; the P4 polynomial has four roots, and so on (Section 4.5, pages 226 to 230, from [42]). If more points were used to fit a higher-order polynomial, it means that the parameter could present, for example, two maxima and one minimum in the case of a fourth-order approximation, which does not align with the assumptions of this work. Therefore, Figure 4 shows the second-degree polynomials that related the variation of each parameter versus RH.

As shown in Figure 4a, a decrease in the value of X_max can be observed with the increase in RH, which is consistent with what was reported in [43], where they established that a higher water activity in the solid bed favors fungal sporulation, while a lower water activity favors mycelial growth. This could be due to an excess dissolution of the nutrients present in the SSF substrate, which could affect the amount of biomass obtained. Additionally, as reported in [44], in the case of aerobic fungi, the increase in water content in the substrate hinders the stretching of the mycelium in the pores of the solid substrate, since the oxygen diffusion rate in water is only 1/200,000 compared to that in air, making the water film tension a limiting factor that affects mycelial extension. However, in [18] and [45], the value of X_max increases with the increase in RH, although the humidity ranges studied went from 30 to 60% and from 45 to 65%, respectively, considerably lower than those studied in the present work, which ranged from 50% to 80%RH. Concerning the effect of RH on the μ_max parameter (Figure 4b), a behavior similar to that usually observed when evaluating the effect of temperature was noted, showing a concavity with a maximum value of μ_max at 65%RH and the μ_max value decreasing as one moves towards the extremes of the polynomial.

Regarding the FOPDT model kinetic parameters, as is shown in Figure 4c, which relates the behavior of the t_p parameter with respect to relative humidity, a convex geometric shape is evident, so that taking into account the minimum of the function, it was found that the best value of t_p was 3.22 h at 60.37%RH, being the value of RH very close to that obtained with the µmax in the Logistic model. In addition, a decrease in the value of t₀ is observed with the increase in %RH (Figure 4d), reflecting a better adaptation of the microorganism with RH increases. Despite X_max decreasing with increasing RH, contrary to the increase in t₀, it can be said that these are parameters characterizing the behavior of the microorganism in different growth stages of the fungus, with t₀ representing the adaptation phase of the fungus and X_max representing the stationary phase. Therefore, these relationships might be valid. Finally, with respect to LA production yield, a clear trend of increasing Y_p/x with increasing RH was observed (Figure 4e), an effect that has not previously been reported.

3.3. Lactic Acid Maximization Using Dynamic Optimization

Once all the steps mentioned in Figure 1 have been applied, it is now possible to determine whether the application of the dynamic optimization technique achieves higher LA yields compared to those obtained in the experimental phase. The variable RH profile obtained and the LA maximized are shown in Figure 5.

It can be clearly observed in Figure 5a that applying a variable RH profile results in savings in terms of the amount of water required to humidify the SSF system. This can be estimated by graphically calculating the area under the curve for both treatments, with 50%RH as the lower limit and 80%RH as the upper limit, over the duration of the 120 h bioprocess. Thus, a 33% decrease in the amount of water required is obtained when applying the variable RH profile compared to the constant profile (80%RH). Therefore, the process with a variable RH profile would be more environmentally friendly compared to the constant RH process.

It is important to note that most of the fungal SSF studies found so far have focused on the effect of varying the initial moisture content of the solid substrate while keeping the humidified air flow static throughout the bioprocess [17,18,19,20,21]. Furthermore, in one study, a humidity control strategy was proposed based on a capillary water supply to control temperature and RH in an SSF tray bioreactor [16]. No SSF studies with RH control strategies applying a variable RH profile were found. In this regard, the present study is innovative as it proposes an alternative approach with a variable RH profile, a biotechnological aspect that has not been extensively explored so far.

Figure 5b shows the LA production obtained after applying the dynamic optimization technique compared to the LA production obtained at 80%RH. It can be observed that the optimized LA production accelerates from the beginning of the fermentation, with the parameter t_d = 0. This result indicates that the variable RH profile had a direct influence on the parameter t_d, by evidencing the disappearance of a delay time between fungal biomass and LA production. Then, there is a clear presence of an increasing ramp in LA production from 50 h, reaching at 120 h a LA concentration of 0.2111 gLA/gGS. If this concentration is compared with the 0.181 gLA/gGS obtained by applying a constant RH of 80%, an increase in LA yield of 16.63% (0.2111/0.181 = 1.1663) is evidenced.

As mentioned earlier, manipulating the RH parameter is relatively easy, as the procedure for injecting humid air is a simple technological process to implement [14]. Additionally, the humidified air injection system allows for cooling the system and provides oxygen in the case of aerobic SSF [16]. Furthermore, implementing smooth and continuous variations in bioprocess parameters is more suitable than applying step changes, as they can affect the final yield of the metabolite under study.

4. Conclusions

In this work, a dynamic optimization strategy based on Fourier series and Orthogonal Polynomials, which allowed for the obtainment of a variable RH profile (smooth, continuous, and differentiable) that maximized LA production, was presented. Under experimental conditions, the highest LA production was 0.181 gLA/gGS at 80%RH and 35 °C, while applying the variable RH profile resulted in 0.2087 gLA/gGS at the end of the bioprocess, representing a 16.63% increase. This optimized result could not have been achieved without a methodologically appropriate approach in the experimental stage, as it allowed us to fit mathematical models to the obtained data. The versatility of these models lies in their ability to accurately represent reality, with intuitive and easy-to-calculate parameters. The use of the hybrid parametric identification technique reduced the convergence time of the Matlab R2015 software compared to traditional methods. The application of second-order polynomials to relate the variation in kinetic parameters to RH was appropriate and confirmed the versatility of polynomials in describing the variability of kinetic parameters in a wide range of biological systems. The strategy proposed in this work is considered to have great potential for application in other bioprocesses, as they are generally nonlinear, highly variable, and complex systems, as is the case for SSF. Based on the results obtained, future research aims to investigate the behavior of fungal bioprocesses for LA production by applying a variable profile of both RH and temperature. The future objective will be to correlate the system’s response to the time variation in RH and temperature at the same time.

Author Contributions

Conceptualization, M.C.G., S.E.N. and G.S.; methodology, M.C.G., M.E.D.M. and L.R.; software, G.S. and B.K.; formal analysis, M.C.G. and S.E.N.; investigation, M.C.G.; writing—original draft preparation, M.C.G.; writing—review and editing, M.C.G., S.E.N. and G.S.; supervision, S.E.N. and G.S. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

This article does not contain studies with human participants or animals performed by any of the authors.

Informed Consent Statement

Informed consent was obtained from all individual participants included in this study.

Data Availability Statement

All the data are provided in this manuscript.

Acknowledgments

The authors are grateful to the staff of the Laboratorio de Control de Calidad Alberto Graffigna of the Universidad Católica de Cuyo for their collaboration and predisposition; they allowed us access to their facilities for the development of different laboratory techniques. The companies SolFrut Alimentos and the winery Tierra del Huarpe S.A. contributed by facilitating the use of some equipment and donated raw material for this research. Likewise, the authors thank the Consejo Nacional de Investigaciones Científicas y Técnicas de Argentina (CONICET), the Universidad Católica de Cuyo, the Universidad Nacional de San Juan, and the Secretaría de Ciencia, Tecnología e Innovación (SECITI, San Juan) for the financial support provided to the María Carla Groff.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Procedure applied to obtain the variable relative humidity profile of the SSF to maximize LA production, where dX/dt = R. oryzae growth rate [g dry biomass/g dry grape stalk·h, gDB/gGS·h], X = fungal biomass concentration obtained for a specific amount of time [gDB/gGS]; μmax = maximum specific growth rate [1/h]; Xmax = maximum biomass concentration [gDB/gGS]; X0 = R. oryzae inoculum [gDB/gGS], t0 = the time range in which there is no fungal biomass growth (latency phase) [h]; tp = the parameter of the bioprocess that provides information on the speed of growth up to Xmax [h]; dP/dt = the LA production rate [gLA/gGS·h]; Yp/x = the LA yield [gLA/gDB]; P0 = the initial LA concentration [gLA/gGS]; td = the time difference between when LA production and biomass generation starts [h]; and t = time [h].

Figure 2. Mathematical models adjusted to R. oryzae growth kinetic curves at 50, 57, 65, 72, and 80%RH.

Figure 3. Mathematical models adjusted to LA production kinetic curves at 50, 57, 65, 72, and 80%RH.

Figure 4. Polynomial relation between the kinetic parameters and RH. (a) Xmax vs. RH, (b) μmax vs. RH, (c) tp vs. RH, (d) t0 vs. RH, (e) Yp/x vs. RH.

Figure 5. Effect of RH profile application on LA production. (a) RH vs. time and (b) LA obtained at 80%RH and by applying a variable RH profile.

Table 1

Fungal growth kinetic parameters of mathematical models obtained at different constant RH.

Experimental Conditions			R. oryzae Growth
			Logistic Model		FOPDT Model
T	RH	X 0	Xmax	µmax	R 2	tp	t 0	R 2
35	50	0.008 ± 0.002	0.080 ± 0.002	0.270 ± 0.008	82.77	4.50 ± 0.12	7.00 ± 0.23	83.55
	57		0.0694 ± 0.001	0.329 ± 0.005	92.16	2.96 ± 0.10	4.70 ± 0.09	91.37
	65		0.065 ± 0.002	0.370 ± 0.011	91.68	3.50 ± 0.11	3.00 ± 0.08	91.67
	72		0.0628 ± 0.003	0.3498 ± 0.09	90.26	5.13 ± 0.09	2.19 ± 0.06	90.83
	80		0.059 ± 0.002	0.250 ± 0.008	98.13	8.00 ± 0.25	2.00 ± 0.05	98.31

Table 2

Lactic acid production kinetic parameters of mathematical models obtained at different constant RH.

Experimental Conditions			Lactic Acid Production
			Luedeking and Piret with Delay-Time Model
			Logistic Model		FOPDT Model		Both Models
T	RH	X 0	Yp/x	R 2	Yp/x	R 2	td
35	50	0.008 ± 0.002	0.95 ± 0.027	82.45	0.95 ± 0.027	81.09	0
	57		0.85 ± 0.022	87.84	0.85 ± 0.022	88.01	0
	65		1.40 ± 0.040	83.76	1.40 ± 0.040	96.89	0
	72		2.46 ± 0.210	94.71	2.46 ± 0.210	94.91	0
	80		3.55 ± 0.370	84.33	3.55 ± 0.370	94.52	5 ± 0.16

References

1. Alves De Oliveira, R.; Komesu, A.; Vaz Rossell, C.E.; Filho, R.M. Challenges and Opportunities in Lactic Acid Bioprocess Design—From Economic to Production Aspects. Biochem. Eng. J.; 2018; 133, pp. 219-239. [DOI: https://dx.doi.org/10.1016/j.bej.2018.03.003]

2. Obi, F.; Ugwuishiwu, B.; Nwakaire, J. Agricultural Waste Concept, Generation, Utilization and Management. Niger. J. Technol.; 2016; 35, 957. [DOI: https://dx.doi.org/10.4314/njt.v35i4.34]

3. Atatoprak, T.; Amorim, M.M.; Ribeiro, T.; Pintado, M.; Madureira, A.R. Grape Stalk Valorization for Fermentation Purposes. Food Chem. Mol. Sci.; 2022; 4, 100067. [DOI: https://dx.doi.org/10.1016/j.fochms.2021.100067] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/35415689]

4. Serra, M.; Casas, A.; Teixeira, J.A.; Barros, A.N. Revealing the Beauty Potential of Grape Stems: Harnessing Phenolic Compounds for Cosmetics. Int. J. Mol. Sci.; 2023; 24, 11751. [DOI: https://dx.doi.org/10.3390/ijms241411751] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/37511513]

5. D’ambrosio, S.; Zaccariello, L.; Sadiq, S.; D’Albore, M.; Battipaglia, G.; D’Agostino, M.; Battaglia, D.; Schiraldi, C.; Cimini, D. Grape Stalk Valorization: An Efficient Re-Use of Lignocellulosic Biomass through Hydrolysis and Fermentation to Produce Lactic Acid from Lactobacillus RHamnosus IMC501. Fermentation; 2023; 9, 616. [DOI: https://dx.doi.org/10.3390/fermentation9070616]

6. Groff, M.C.; Scaglia, G.; Gaido, M.; Kassuha, D.; Ortiz, O.A.; Noriega, S.E. Kinetic Modeling of Fungal Biomass Growth and Lactic Acid Production in RHizopus oryzae Fermentation by Using Grape Stalk as a Solid Substrate. Biocatal. Agric. Biotechnol.; 2022; 39, 102255. [DOI: https://dx.doi.org/10.1016/j.bcab.2021.102255]

7. Manandhar, A.; Shah, A. Techno-Economic Analysis of Bio-Based Lactic Acid Production Utilizing Corn Grain as Feedstock. Processes; 2020; 8, 199. [DOI: https://dx.doi.org/10.3390/pr8020199]

8. Rahim, N.A.; Luthfi, A.A.I.; Abdul, P.M.; Jahim, J.M.; Bukhari, N.A. Towards Sustainable Production of Bio-Based Lactic Acid via a Bio-Based Technical Route: Recent Developments and the Use of Palm Kernel Cakes in the Bioconversion. BioResources; 2022; 17, pp. 3781-3809. [DOI: https://dx.doi.org/10.15376/biores.17.2.Rahim]

9. Statista Market Volume of Lactic Acid Worldwide from 2015 to 2022, with a Forecast for 2023 to 2030. Available online: https://www.statista.com/statistics/1310495/lactic-acid-market-volume-worldwide/ (accessed on 22 July 2024).

10. MordorIntelligence Análisis de Participación y Tamaño Del Mercado de Productos Biológicos Tendencias de Crecimiento y Pronósticos (2024–2029). Available online: https://www.mordorintelligence.com/es/industry-reports/biologics-market (accessed on 15 June 2024).

11. Arthur, D. Little Why Bio-Based Materials Market Finally Poised Growth?. Available online: https://www.adlittle.com/en/insights/prism/why-bio-based-materials-market-finally-poised-growth (accessed on 2 June 2024).

12. Baeza, J.A. Principles of Bioprocess Control. Current Developments in Biotechnology and Bioengineering: Bioprocesses, Bioreactors and Controls; Elsevier B.V.: New York, NY, USA, 2017; pp. 527-561. ISBN 9780444636744

13. Webb, C.; Manan, M.A. Design Aspects of Solid State Fermentation as Applied to Microbial Bioprocessing. J. Appl. Biotechnol. Bioeng.; 2017; 4, pp. 511-532. [DOI: https://dx.doi.org/10.15406/jabb.2017.04.00094]

14. Mitchell, D.A.; Berovič, M.; Krieger, N. Solid-State Fermentation Bioreactors; Springer: Berlin/Heidelberg, Germany, 2006; ISBN 9783540312857

15. He, Q.; Peng, H.; Sheng, M.; Hu, S.; Qiu, J.; Gu, J. Humidity Control Strategies for Solid-State Fermentation: Capillary Water Supply by Water-Retention Materials and Negative-Pressure Auto-Controlled Irrigation. Front. Bioeng. Biotechnol.; 2019; 7, pp. 1-13. [DOI: https://dx.doi.org/10.3389/fbioe.2019.00263]

16. Sentís-Moré, P.; Romero-Fabregat, M.P.; Rodríguez-Marca, C.; Guerra-Sánchez, A.J.; Ortega-Olivé, N. Design Optimization of a Tray Bioreactor for Solid-State Fermentation: Study of Process Parameters through Protein Modification of By-Products. Fermentation; 2023; 9, 921. [DOI: https://dx.doi.org/10.3390/fermentation9100921]

17. Wang, H.; Sun, C.; Yang, S.; Ruan, Y.; Lyu, L.; Guo, X.; Wu, X.; Chen, Y. Exploring the Impact of Initial Moisture Content on Microbial Community and Flavor Generation in Xiaoqu Baijiu Fermentation. Food Chem. X; 2023; 20, 100981. [DOI: https://dx.doi.org/10.1016/j.fochx.2023.100981] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/38144799]

18. Saithi, S.; Borg, J.; Nopharatana, M.; Tongta, A. Mathematical Modeling of Biomass and Enzyme Production Kinetics by Aspergillus niger in Solid-State Fermentation at Various Temperatures and Moisture Contents. J. Microb. Biochem. Technol.; 2016; 8, pp. 123-130. [DOI: https://dx.doi.org/10.4172/1948-5948.1000274]

19. Carboué, Q.; Rébufa, C.; Hamrouni, R.; Roussos, S.; Bombarda, I. Statistical Approach to Evaluate Effect of Temperature and Moisture Content on the Production of Antioxidant Naphtho-Gamma-Pyrones and Hydroxycinnamic Acids by Aspergillus tubingensis in Solid-State Fermentation. Bioprocess Biosyst. Eng.; 2020; 43, pp. 2283-2294. [DOI: https://dx.doi.org/10.1007/s00449-020-02413-6] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/32880738]

20. Zain, N.A.M.; Aziman, S.N.; Suhaimi, M.S.; Idris, A. Optimization of L(+) Lactic Acid Production from Solid Pineapple Waste (SPW) by RHizopus oryzae NRRL 395. J. Polym. Environ.; 2021; 29, pp. 230-249. [DOI: https://dx.doi.org/10.1007/s10924-020-01862-0]

21. Pirota, R.D.P.B.; Tonelotto, M.; Delabona, P.S.; Fonseca, R.F.; Paixão, D.A.A.; Baleeiro, F.C.F.; Bertucci Neto, V.; Farinas, C.S. Bioprocess Developments for Cellulase Production by Aspergillus oryzae Cultivated under Solid-State Fermentation. Braz. J. Chem. Eng.; 2016; 33, pp. 21-31. [DOI: https://dx.doi.org/10.1590/0104-6632.20160331s00003520]

22. Feng, J.; Feng, N.; Zhang, J.S.; Yang, Y.; Jia, W.; Lin, C.C. A New Temperature Control Shifting Strategy for Enhanced Triterpene Production by Ganoderma lucidum G0119 Based on Submerged Liquid Fermentation. Appl. Biochem. Biotechnol.; 2016; 180, pp. 740-752. [DOI: https://dx.doi.org/10.1007/s12010-016-2129-1] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/27272496]

23. Cheng, K.K.; Zeng, J.; Jian, J.H.; Zhu, J.F.; Zhang, G.X.; Liu, D.H. Model-Based Temperature Control for Improving Lactic Acid Production from Glycerol. RSC Adv.; 2019; 9, pp. 11614-11620. [DOI: https://dx.doi.org/10.1039/C9RA01323G] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/35517023]

24. Borshchevskaya, L.N.; Gordeeva, T.L.; Kalinina, A.N.; Sineokii, S.P. Spectrophotometric Determination of Lactic Acid. J. Anal. Chem.; 2016; 71, pp. 755-758. [DOI: https://dx.doi.org/10.1134/S1061934816080037]

25. Bermúdez, A. AGAR-AGAR, La Versatilidad de Un Ingrediente En Expansión. Available online: https://granotec.com.ar/agar-agar-la-versatilidad-de-un-ingrediente-en-expansion/ (accessed on 8 June 2024).

26. Groff, M.C.; Scaglia, G.; Ortiz, O.A.; Noriega, S.E. Modification of the Luedeking and Piret Model with a Delay Time Parameter for Biotechnological Lactic Acid Production. Biotechnol. Lett.; 2022; 44, pp. 415-427. [DOI: https://dx.doi.org/10.1007/s10529-022-03227-0]

27. Groff, M.C.; Noriega, S.E.; Gil, R.M.; Pantano, N.; Scaglia, G. Dynamic Optimization of Lactic Acid Production from Grape Stalk Solid-State Fermentation with RHizopus oryzae Applying a Variable Temperature Profile. Fermentation; 2024; 10, 101. [DOI: https://dx.doi.org/10.3390/fermentation10020101]

28. Sardella, M.F.; Serrano, M.E.; Camacho, O.; Scaglia, G.J.E. Design and Application of a Linear Algebra Based Controller from a Reduced-Order Model for Regulation and Tracking of Chemical Processes under Uncertainties. Ind. Eng. Chem. Res.; 2019; 58, pp. 15222-15231. [DOI: https://dx.doi.org/10.1021/acs.iecr.9b01257]

29. Scaglia, G.; Serrano, M.E.; Albertos, P. Linear Algebra Based Controllers; Springer: New York, NY, USA, 2020; [DOI: https://dx.doi.org/10.1007/978-3-030-42818-1]

30. Groff, C.; Kuchen, B.; Gil, R.; Fernández, C. Scaglia Application of the Luedeking and Piret with Delay Time Model in Bioproductions with Non-Zero Kinetic Parameters. IEEE Lat. Am. Trans.; 2023; 21, pp. 882-888. [DOI: https://dx.doi.org/10.1109/TLA.2023.10246344]

31. Fernández, C.; Pantano, N.; Godoy, S.; Serrano, E.; Scaglia, G. Optimización de Parámetros Utilizando Los Métodos de Monte Carlo y Algoritmos Evolutivos. Aplicación a un Controlador de Seguimiento de Trayectoria en Sistemas no Lineales. Rev. Iberoam. Automática Informática Ind.; 2018; 16, pp. 89-99. [DOI: https://dx.doi.org/10.4995/riai.2018.8796]

32. Kroese, D.P.; Rubinstein, R.Y. Monte Carlo Methods. Wiley Interdiscip. Rev. Comput. Stat.; 2012; 4, pp. 48-58. [DOI: https://dx.doi.org/10.1002/wics.194]

33. Walbridge, C.T. Genetic Algorithms: What Computers Can Learn from Darwin. Technol. Rev.; 1989; 92, 5404766.

34. Pantano, M.N.; Fernández, M.C.; Amicarelli, A.; Scaglia, G.J.E. Evolutionary Algorithms and Orthogonal Basis for Dynamic Optimization in L2 Space for Batch Biodiesel Production. Chem. Eng. Res. Des.; 2022; 177, pp. 354-364. [DOI: https://dx.doi.org/10.1016/j.cherd.2021.11.001]

35. Pantano, M.N.; Fernandez Puchol, M.C.; Rossomando, F.G.; Scaglia, G.J.E. Open-Loop Dynamic Optimization for Nonlinear Multi-Input Systems. Application to Recombinant Protein Production. IEEE Lat. Am. Trans.; 2021; 19, pp. 1307-1314. [DOI: https://dx.doi.org/10.1109/TLA.2021.9475861]

36. Attaway, S. Matlab: A Practical Introduction to Programming and Problem Solving; Elsevier: Amsterdam, The Netherlands, 2009; ISBN 9780750687621

37. Kuchen, B.; Garay, S.A.; Gil, R.M.; Vazquez, F.; Scaglia, G.J.E. Optimization of Batch Reactors: Application to the Biocontrol of Spoilage Yeasts in Wines. IEEE Lat. Am. Trans.; 2022; 21, pp. 217-225. [DOI: https://dx.doi.org/10.1109/TLA.2023.10015214]

38. Pantano, M.N.; Fernández, M.C.; Ortiz, O.A.; Scaglia, G.J.E.; Vega, J.R. A Fourier-Based Control Vector Parameterization for the Optimization of Nonlinear Dynamic Processes with a Finite Terminal Time. Comput. Chem. Eng.; 2020; 134, 106721. [DOI: https://dx.doi.org/10.1016/j.compchemeng.2019.106721]

39. Scaglia, G.; Serrano, E.; Rosales, A.; Albertos, P. Tracking Control Design in Nonlinear Multivariable Systems: Robotic Applications. Math. Probl. Eng.; 2019; 2019, 15. [DOI: https://dx.doi.org/10.1155/2019/8643515]

40. Agarwal, R.P. Difference Equations and Inequalities: Theory, Methods, and Applications; CRC Press: Boca Raton, FL, USA, 2000.

41. John, B. Conway A Course in Functional Analysis; 2nd ed. Springer: New York, NY, USA, 2007; Volume 5, ISBN 9788578110796

42. Oliver, P.J.; Shakiban, C. Applied Linear Algebra; Springer International Publishing AG: New York, NY, USA, 2018; ISBN 9783319910406

43. Manpreet, S.; Sawraj, S.; Sachin, D.; Pankaj, S.; Banerjee, U.C. Influence of Process Parameters on the Production of Metabolites in Solid-State Fermentation. Malalaysian J. Microbiol.; 2005; 1, pp. 1-9. [DOI: https://dx.doi.org/10.21161/mjm.120501]

44. Chen, H. Modern Solid State Fermentation Theory and Practice; Springer: Amsterdam, The Netherlands, 2013; ISBN 9789400760424

45. Hamidi-Esfahani, Z.; Shojaosadati, S.A.; Rinzema, A. Modelling of Simultaneous Effect of Moisture and Temperature on A. niger Growth in Solid-State Fermentation. Biochem. Eng. J.; 2004; 21, pp. 265-272. [DOI: https://dx.doi.org/10.1016/j.bej.2004.07.007]