Unstructured Kinetic Model Research Articles

Parametric adjustment of two different kinetic models with constant and variable yield coefficients. Butanol production from glycerol fermentation by Clostridium pasteurianum

The study of bioreactors, for their design and operation, is crucial for optimizing fermentation processes. This can be achieved through computational simulations based on unstructured kinetic models. Generally, unstructured kinetic models are established with yields associated with the concentrations of biomass, substrate, and product of constant type. It has been reported that variable polynomial yields can better describe these processes. Therefore, this work proposes the study of a glycerol fermentation system to produce butanol in the presence of Clostridium pasteurianum. Parametric identification of two unstructured kinetic models (Moser-Boulton and Moser-Levespiel) was performed. Three mass balances were proposed for a batch-operated reactor (biomass, glycerol, and butanol). Constant and variable yields of first, second, and third order were considered. Finally, the simulated data were validated using correlation coefficients with the corresponding experimental data.

Monitoring Ethanol Fermentation in Real Time by a Robust State Observer for Uncertainties

AbstractIn this article, the problem of real‐time estimation of the fermentative ethanol process is tackled. The considered observer is a model‐based technique that is robust regarding the model parameter uncertainties and inline noisy measurements. An unstructured kinetic model was used to describe the production of ethanol in a batch bioreactor for Saccharomyces cerevisiae. The biomass concentration was selected as the measured bioreactor´s output via an inline device, where the estimate variables were the substrate and ethanol concentrations. An experimental prototype was constructed to demonstrate the observer's real‐time performance. The experimental results show that the robust, smooth sliding mode observer performs better than the standard proportional sliding mode observer.

Kinetic growth model and metabolic effect of a bacterial consortia from a petrochemical processing plant

AbstractThis study focused on presenting the newly developed growth model for bacterial species present in a petrochemical processing plant in South Africa. The findings of the study serve as a theoretical basis for future experiments aimed at understanding the formation of bacterial metabolites as the bacteria develops. An unstructured kinetic model using AQUASIM 2.3, together with experimental spectrophotometric results, were used to evaluate the growth of Gram‐negative bacteria in a batch reactor system. Spectrophotometer results showed the absence of a stationary phase. The exponential bacterial growth phase supported the total organic carbon (TOC) results, showing that bacterial growth occurred on days 6 and 13; this is rarely reported in literature, as the growth in this system was much slower than the growth of single‐strain studies. The TOC concentration values indicated that carbon sources did not deplete in the death phase, suggesting the presence of a long‐term stationary phase and the production of acetate. The presence of Pseudomonas sp. and sulphate‐reducing bacteria (SRB) are commonly reported in industrial systems as they play a role in equipment failure in industry. However, in this multispecies study, methods using third generation sequencing together with high‐performance liquid chromatography (HPLC) have shown that the selective attachment and production of acetate by abundant Clostridium sp. has ascertained their role in equipment failures in the petrochemical environment.

Dynamic hybrid modeling of fuel ethanol fermentation process by integrating biomass concentration XGBoost model and kinetic parameter artificial neural network model into mechanism model

Fuel ethanol has drawn extensive attention as renewable energy. However, modeling the fuel ethanol batch fermentation process is still a critical task. The unstructured kinetic model (UKM) is often utilized to model the process, but it encounters two problems due to the large differences in initial glucose concentrations. First, the UKM has poor predictions of the yeast growth, which is a crucial production index. Second, the kinetic parameters of the UKM are time-varying because of the changing environmental conditions. The constant manually set kinetic parameters affect the prediction accuracy. To tackle the problems, we propose a dynamic hybrid model of the fuel ethanol fermentation process. First, a biomass concentration prediction model based on extreme gradient boosting is developed. It predicts the values of biomass concentrations and mycelium growth rate as supplementary mechanism knowledge. Then, we present an artificial neural network-based model to determine the time-varying kinetic parameters. Our model can accurately predict the time series of biomass, ethanol, and glucose concentrations, with RMSEs reaching 0.3323, 1.9295, and 3.0540. Experimental results show that the dynamic hybrid model performs with satisfactory accuracy in modeling the fuel ethanol fermentation process.

Unstructured kinetic models with time-averaged growth approach in the biodegradation of triclosan by activated sludge culture

The concentration of triclosan in wastewater is expected to rise dramatically as a consequence of the COVID-19 pandemic. A modeling analysis of the growth kinetics of microbial culture during triclosan degradation was necessary in order to establish effective wastewater treatment. The kinetic parameters are used by engineers to aid in the design and process control of biological processes. Studies were conducted using triclosan-acclimated culture to examine biomass growth and associated substrate degradation at different initial substrate concentrations (0.35–4.9 mg L−1) to this end. Substrate inhibition was calculated from experimental growth parameters using unstructured kinetic models. Unlike other model studies, a time-averaged specific bacterial growth rate in the log phase was considered for kinetic models in this study. Overestimation of the conventional log phase calculation for unstructured kinetic model constants was eliminated when the slowdown growth part of the log growth phase was taken into account. The Haldane Model was more accurate to fitting experimental data in an excellent manner. In this case, the time-averaged specific growth rate, saturation constant, and inhibition constant were 0.56 h−1, 12.77 mg L−1, 0.52 mg L−1, respectively. A yield coefficient of 0.404 mgX.mgS−1 was calculated. The critical triclosan concentration was 2.57 mg L−1. Wastewater treatment plants can be more sensitive to the value of the critical triclosan concentration. The value for time-averaged critical specific growth rate was 0.051 h−1. Pre-or post-treatment requirements can be estimated using time-averaged critical growth rate values as a benchmarking tool in biological treatment systems.

Model-aided targeted volatile fatty acid production from food waste using a defined co-culture microbial community

The production of volatile fatty acids (VFA) is gaining momentum due to their central role in the emerging carboxylate platform. Particularly, the production of the longest VFA (from butyrate to caproate) is desired due to their increased economic value and easier downstream processing. While the use of undefined microbial cultures is usually preferred with organic waste streams, the use of defined microbial co-culture processes could tackle some of their drawbacks such as poor control over the process outcome, which often leads to low selectivity for the desired products. However, the extensive experimentation needed to design a co-culture system hinders the use of this technology. In this work, a workflow based on the combined use of mathematical models and wet experimentation is proposed to accelerate the design of novel bioprocesses. In particular, a co-culture consisting of Pediococcus pentosaceus and Megaphaera cerevisiae is used to target the production of high-value odd- and even‑carbon VFA. An unstructured kinetic model was developed, calibrated and used to design experiments with the goal of increasing the selectivity for the desired VFA, which were experimentally validated. In the case of even‑carbon VFA, the experimental validation showed an increase of 38 % in caproate yield and, in the case of enhanced odd‑carbon VFA experiments, the yield of butyrate and caproate diminished by 62 % and 94 %, respectively, while propionate became one of the main end products and valerate yield value increased from 0.007 to 0.085 gvalearte per gconsumed sugar. The workflow followed in this work proved to be a sound tool for bioprocess design due to its capacity to explore and design new experiments in silico in a fast way and ability to quickly adapt to new scenarios.

A simple unstructured kinetic model for anaerobic treatment of a class of agro‐industrial waste

AbstractBACKGROUNDDynamic modeling of the anaerobic treatment of agro‐industrial waste can help determine optimal operating conditions to maximize the process performance. For this, it is necessary to select an appropriate model and adapt it to the specific conditions of the substrate. In this work, a simple unstructured kinetic model for the anaerobic treatment of different agro‐industrial waste is proposed. The proposed model considers the three most relevant stages of anaerobic digestion (AD) and can be adapted for the treatment of different substrates, modes of operation (batch or continuous), and/or generated products (VFA or methane production), thus requiring a minimum of process macroscopic measurements.RESULTSTo evaluate the scope of the model, two case studies were analyzed: (i) methane production from tequila vinasse and agave hydrolysates, and (ii) volatile fatty acids (VFA) and biogas production from raw cheese whey. For each case, parameter estimations were performed using the Levenberg – Marquardt algorithm, which yielded a simplified model with high determination coefficients (R2 > 0.95). Moreover, the kinetic parameters estimated were consistent physically and statistically.CONCLUSIONNumerical results show that the proposed model can satisfactorily describe the dynamic behavior of the key variables of the three types of agro‐industrial waste evaluated. Therefore, the proposed model might be advantageous to determine the conditions that maximize performance without risking process stability. © 2022 Society of Chemical Industry (SCI).

An appropriate unstructured kinetic model describing the batch fermentation growth of Debaryomyces hansenii for xylitol production using hydrolysis of oil palm empty fruit bunch

This study aimed to determine an appropriate unstructured kinetic model describing the growth of Debaryomyces hansenii with the hydrolysis of oil palm empty bunches as the substrate sources. We tested the well-known cell growth kinetic models for approximating the xylitol fermentation data. We modeled the extracellular process by considering the biomass as a variable, xylose as the substrate and xylitol as the product. The appropriate kinetic model was determined by fitting the models to the experimental data. The fitting process involved an optimization procedure that minimizes a least-squared error between the model solution and the experimental data using a gradient-based method. We found that the unstructured model with Monod specific kinetic growth model had the best approximating ability to describe the dynamics of the batch xylitol fermentation data. Some factors were highlighted as the key factors that influence the growth of yeast cells. One of them is the maximum growth rate of the yeast cell which had a high sensitivity to the maximum production of new cells and xylitol as the main product. As Monod was the best-approximated model, it implies that inhibitory effects by substrate and product played an important role in controlling the growth of yeast cells. There was a certain maximum growth rate for the yeast cell that generates maximum production of new cells and xylitol within a relatively short fermentation time. This result indicates that the growth rate parameter played an important role in adjusting the fermentation process for optimality purposes.

Kinetic modeling of biosurfactant production from crude oil using Bacillus subtilis cells

Crude oil and its derivatives have high application in different industries, and unforeseen spills or over-exploitation generate a significant threat in ecosystems, causing negative impacts on soil, water, and air. There are microorganisms capable of metabolizing hydrocarbons through the bioremediation process with biosurfactant production, but large-scale culturing and technification are still a significant challenge due to their high costs and optimization stage requirement. An unstructured kinetic model provides crucial information regarding improvements and process optimization at the first stages. Thereof prediction of bioprocess kinetic behavior is expected from mathematical expressions. Considering the above, biosurfactants' bioprocess modeling tends to be an essential tool to increasingly focus on the efficiency and profitability of oil industries. That is why biosurfactant kinetics production from Bacillus subtilis is investigated in this research, implementing a mathematical model. Previous studies refereed experimental data to integrate into Monod, Contois, Haldane, Moser, Powell, Tessier, Aiba-Edward, Luong, Yano-Koga, and Chen-Hashimoto equations. Therefore, a nonlinear regression parameterization procedure is applied using the Matlab Fmincon Function. The best accuracy found between experimental and simulated data was achieved using the Chen-Hashimoto kinetic model with μmax, kd and ks values of 2.3239 d−1, 0.3748 d−1 and 1.1619 g/L, respectively. This research suggests that biosurfactant production occurs under anaerobic conditions where hydrolysis controls microbial growth. These research results are a promising aim related to industrial biotechnology since computational modeling is essential for process efficiency from a technical and economic perspective.

Mass Transfer, Gas Holdup, and Kinetic Models of Batch and Continuous Fermentation in a Novel Rectangular Dynamic Membrane Airlift Bioreactor

Compared with conventional cylinder airlift bioreactors (CCABs) that produce coarse bubbles, a novel rectangular dynamic membrane airlift bioreactor (RDMAB) developed in our lab produces fine bubbles to enhance the volumetric oxygen mass transfer coefficient (kLa) and gas holdup, as well as improve the bioprocess in a bioreactor. In this study, we compared mass transfer, gas holdup, and batch and continuous fermentation for RNA production in CCAB and RDMAB. In addition, unstructured kinetic models for microbial growth, substrate utilization, and RNA formation were established. In batch fermentation, biomass, RNA yield, and substrate utilization in the RDMAB were higher than those in the CCAB, which indicates that dynamic membrane aeration produced a high kLa by fine bubbles; a higher kLa is more beneficial to aerobic fermentation. The starting time of continuous fermentation in the RDMAB was 20 h earlier than that in the CCAB, which greatly improved the biological process. During continuous fermentation, maintaining the same dissolved oxygen level and a constant dilution rate, the biomass accumulation and RNA concentration in the RDMAB were 9.71% and 11.15% higher than those in the CCAB, respectively. Finally, the dilution rate of RDMAB was 16.7% higher than that of CCAB during continuous fermentation while maintaining the same air aeration. In summary, RDMAB is more suitable for continuous fermentation processes. Developing new aeration and structural geometry in airlift bioreactors to enhance kLa and gas holdup is becoming increasingly important to improve bioprocesses in a bioreactor.

A kinetic model of heterotrophic and mixotrophic cultivation of the potential biofuel organism microalgae Chlorella sorokiniana

Better microalgal growth performance under heterotrophic and mixotrophic conditions can advance production of environmentally sustainable, lipid-based third-generation biofuels. In this study, an unstructured kinetic growth model was developed by extending a Haldane-based model to account and predict the enhancing and/or inhibitory effects of substrate (i.e. initial glucose concentration, nitrogen concentration, and light intensity) on the growth and lipid accumulation rates of the microalgae Chlorella sorokiniana during its heterotrophic and mixotrophic cultivation. The model considered a nitrogen-deprived phase of cultivation during which lipid synthesis and accumulation rates increase. Model-derived estimations for glucose and nitrogen consumption, cell growth, and lipid production under heterotrophic and mixotrophic conditions, respectively, were validated and in good agreement with experimental measurements, with R2 correlation values ranging from 0.83 to 0.99. Sensitivity analysis showed that the reaction rate constant of nitrogen consumption (KNX) has a “significant effect” on both lipid production and nitrogen consumption, suggesting that rapid depletion of nitrogen is favorable to increase lipid content instead of cell growth. The rate of cell growth declined on the 4th day during heterotrophic cultivation but remained constant after the 4th day during mixotrophic cultivation under initial glucose concentrations of 2.29, 4.32, and 6.19 g L−1. Our model further confirmed experimental observations that the best growth performance and highest lipid production are obtained under mixotrophic conditions compared to heterotrophic conditions.

Process Engineering of Biopharmaceutical Production in Moss Bioreactors via Model-Based Description and Evaluation of Phytohormone Impact.

The moss Physcomitrella is an interesting production host for recombinant biopharmaceuticals. Here we produced MFHR1, a synthetic complement regulator which has been proposed for the treatment of diseases associated to the complement system as part of human innate immunity. We studied the impact of different operation modes for the production process in 5 L stirred-tank photobioreactors. The total amount of recombinant protein was doubled by using fed-batch or batch compared to semi-continuous operation, although the maximum specific productivity (mg MFHR1/g FW) increased just by 35%. We proposed an unstructured kinetic model which fits accurately with the experimental data in batch and semi-continuous operation under autotrophic conditions with 2% CO2 enrichment. The model is able to predict recombinant protein production, nitrate uptake and biomass growth, which is useful for process control and optimization. We investigated strategies to further increase MFHR1 production. While mixotrophic and heterotrophic conditions decreased the MFHR1-specific productivity compared to autotrophic conditions, addition of the phytohormone auxin (NAA, 10 µM) to the medium enhanced it by 470% in shaken flasks and up to 230% and 260%, in batch and fed-batch bioreactors, respectively. Supporting this finding, the auxin-synthesis inhibitor L-kynurenine (100 µM) decreased MFHR1 production significantly by 110% and 580% at day 7 and 18, respectively. Expression analysis revealed that the MFHR1 transgene, driven by the Physcomitrella actin5 (PpAct5) promoter, was upregulated 16 h after NAA addition and remained enhanced over the whole process, whereas the auxin-responsive gene PpIAA1A was upregulated within the first 2 hours, indicating that the effect of auxin on PpAct5 promoter-driven expression is indirect. Furthermore, the day of NAA supplementation was crucial, leading to an up to 8-fold increase of MFHR1-specific productivity (0.82 mg MFHR1/g fresh weight, 150 mg accumulated over 7 days) compared to the productivity reported previously. Our findings are likely to be applicable to other plant-based expression systems to increase biopharmaceutical production and yields.

H2 competition between homoacetogenic bacteria and methanogenic archaea during biomethanation from a combined experimental-modelling approach

Competition for H2 between homoacetogenic bacteria and methanogenic archaea is commonly faced in biological biogas upgrading process reducing the potential for high methane production capacities. In the present work, different feeding regimes were examined using anaerobic inocula that were adapted and non-adapted to the gaseous feedstock. Adapted inoculum could compensate the increased pressure at all examined levels and especially, produced above 95% of the theoretical methane without accumulating acetate at 0.2 atm. On the contrary, acetate accumulation was detected when a non-adapted inoculum was used. Microbial adaptation to elevated pressures can be applied as a means to improve production capacities. Thermodynamic analysis showed that hydrogenotrophic methanogenesis had always lower permissive H2 partial pressures (0.43–0.85 Pa) compared to homoacetogenesis (3.20–7.46 Pa) at the examined pH (neutral vs alkaline) and pressure levels (i.e., 0.2–2.0 atm). An unstructured kinetic model was developed to study the influence of the examined variables in the hydrogenotrophic, homoacetogenesis and aceticlastic pathways. The kinetic parameters of the proposed model were estimated from experimental results and the goodness of the fitting was assessed by the coefficient of determination which indicated that the model describes efficiently the dynamics of the different compounds involved in the investigated pathways.

Incremental Model Identification of Bio-processes from Data: Application to Microbial Production of Hyaluronic Acid

The development of reliable kinetic models of bioprocesses from data is a challenging task. In this work, a systematic approach to develop a kinetic model of bioprocess involving single biomass from concentration data is proposed without imposing any kinetic model a priori. The proposed incremental model identification approach decomposes the model-building task into a set of sub-tasks such as determining the yield coefficients and maintenance coefficient, specific growth rate structure identification, and parameter estimation. It is shown that the proposed approach allows identifying the mechanism of product formation. The proposed approach is applied to the microbial production of Hyaluronic acid (HA), an important biopolymer, using a recombinant Lactococcus lactis MKG6. An unstructured kinetic model is developed for the HA production from data. It is shown that HA production is a growth-associated process. Further, the specific growth rate of HA production is identified from a set of rate candidates. It is revealed that the specific growth rate in the HA production follows the non-competitive HA inhibition model. The parameters obtained by the incremental identification are further refined to obtain statistically optimal estimates using the simultaneous model identification. Validation of the identified kinetic model of HA production on new experimental data shows that the proposed approach leads to a reliable kinetic model with the optimal parameter estimates.

Kinetic modeling and statistical optimization of submerged production of anti-Parkinson’s prodrug L-DOPA by Pseudomonas fluorescens

L-DOPA, a precursor of dopamine, is the drug of choice for Parkinson’s disease, which persists due to decreased levels of dopamine in the brain. Present study emphasis the microbial production of L-DOPA rather than the biotransformation of L-DOPA by L-tyrosine. The production of L-DOPA by bacterial isolates had gained more acceptance due to its more straightforward extraction and downstream processes. Pseudomonas fluorescens was used to produce the L-DOPA in a bioreactor system under submerged condition. The design of experiment-based Taguchi orthogonal array method was adopted for the optimization of production. L-9 orthogonal array using the analysis of mean approach was used to study the effect of different factors viz NaCl, lactose, tryptone, and inducer on the microbial production of L-DOPA. The method mentioned above is less time consuming and does not require any harsh chemicals, proving it to be an eco-friendly process. After optimizing selected factors, i.e., NaCl (1.2 g/l), lactose (1.5 g/l), tryptone (4 g/l), and inducer (0.1 g/l), 16.9 % of enhancement in L-DOPA production with 66.6% of process cost saving was observed. The production of L-DOPA was increased from 3.426 ± 0.08 g/l to 4.123 ± 0.05 g/l after optimization. Subsequently, unstructured kinetic models were adopted to simulate the fermentation kinetics and understand the metabolic process. Fisher’ F test and determination coefficients (R 2) confirmed that the Velhurst–Pearl logistic equation, Luedeking–Piret equation, and modified Luedeking–Piret equation was best fitted with the biomass production, product formation, and substrate utilization, respectively.

Strategies for improvement of microbial fuel cell performance via stable power generation from real dairy wastewater

The microbial fuel cells (MFCs) are one of the emerging sustainable power sources, that are being effectively used for the simultaneous treatment of wastewater with concomitant generation of electricity. The present study develops a fed-batch process with an optimized level of two microorganisms for concurrent treatment of real dairy wastewater (RDW) and stable power generation using a single-chamber MFC. The MFC exhibits a maximum open circuit voltage of 652 mV at 264 h of fed-batch operation. The unstructured kinetic model suggests that the value of saturation constant (Ks) is 41.67 mg COD/L, indicating mixed culture has a higher affinity towards the utilization of RDW. The fed-batch mode achieves maximum COD removal efficiency of 95.31%, columbic efficiency of 31.58%, a maximum current density of 263 mA/m2, and power density (62.27 mW/m2). The optimum cell voltage and internal resistance of MFC are 0.48 V and 340 Ω, respectively. The study suggests that a fed-batch operation with mixed culture is suitable for the treatment of RDW and able to generate stable power from MFC.

Mathematical modeling and simulation of newly isolated bacillus cereus M1GT for tannase production through semi-solid state fermentation with agriculture residue triphala

In this present research, tannase producing bacteria were isolated from the samples of the gastrointestinal tract of a Goat. The liquid enrichment and spread plate technique were adopted and 6 distinct bacterial colonies were isolated on a nutrient agar plate. Based on qualitative and quantitative methods of screening, one isolate among six was found promising and identified as Bacillus cereus M1GT by using 16S rRNA gene sequencing technique. The cost-effective substrate Triphala was used as a tannin and energy source for tannase production through solid-state fermentation in shake flask independently. Process factors were screened by a two-step optimization process i.e. one factor at a time method and central composite design. The study of statistical experimental design with Triphala at optimized conditions showed 6.1-fold (0.116 U/gds) higher in tannase activity than that obtained in submerged fermentation. Further, the kinetics of Bacillus cereus M1GT under optimum process conditions were studied. The Logistic equation (growth, ‘µ’), Luedeking Piret equation (Tannase, ‘α’, and ‘β’) and Substrate utilization equation (Tannic acid, ‘m’ and ‘n’) of unstructured kinetic models were evaluated with the MATLAB program. The experimental and simulated values exhibited a good correspondence, indicating that models will define tannase production process.

Dynamics of microbial competition, commensalism, and cooperation and its implications for coculture and microbiome engineering.

Microbial consortium is a complex adaptive system with higher‐order dynamic characteristics that are not present by individual members. To accurately predict the social interactions, we formulate a set of unstructured kinetic models to quantitatively capture the dynamic interactions of multiple microbial species. By introducing an interaction coefficient, we analytically derived the steady‐state solutions for the interacting species and the substrate‐depleting profile in the chemostat. We analyzed the stability of the possible coexisting states defined by competition, parasitism, amensalism, commensalism, and cooperation. Our model predicts that only parasitism, commensalism, and cooperation could lead to stable coexisting states. We also determined the optimal social interaction criteria of microbial coculture when sequential metabolic reactions are compartmentalized into two distinct species. Coupled with Luedeking–Piret and Michaelis–Menten equations, accumulation of metabolic intermediates in one species and formation of end‐product in another species could be derived and assessed. We discovered that parasitism consortia disfavor the bioconversion of intermediate to final product; and commensalism consortia could efficiently convert metabolic intermediates to final product and maintain metabolic homeostasis with a broad range of operational conditions (i.e., dilution rates); whereas cooperative consortia leads to highly nonlinear pattern of precursor accumulation and end‐product formation. The underlying dynamics and emergent properties of microbial consortia may provide critical knowledge for us to understand ecological coexisting states, engineer efficient bioconversion process, deliver effective gut therapeutics as well as elucidate probiotic‐pathogen or tumor‐host interactions in general.

Unstructured kinetic models to simulate an arabinose switch that decouples cell growth from metabolite production

Modeling synthetic gene circuits to implement dynamic flux balancing is crucial in teaching and exploring metabolic engineering strategies to repartition metabolic precursors and construct efficient microbial cell factories. Microbial fitness and production rates are often complex phenotypes that are governed by highly non-linear, multivariable functions which are intrinsically linked through carbon metabolism. The solution of such dynamic system can be difficult for synthetic biologists to visualize or conceptualize. Recently, researchers (Santala et al., Metab. Eng. Comm., 2018) have implemented an arabinose based genetic switch to dynamically partition the central carbon flux between cell growth and product formation. The autonomous switch allowed dynamic shift from arabinose-associated cell growth to acetate-associated product (wax ester) formation. This system clearly demonstrates the effectiveness of using a genetic switch to decouple cell growth from product formation in a one-pot bioreactor to minimize operational cost. Coupled with Michaelis-Menten kinetics, and Luedeking-Piret equations, we were able to reconstruct and analyze this metabolic switch in silica and achieved graphical solutions that qualitatively match with the experimental data. By assessing physiologically-accessible parameter space, we observed a wide range of dynamic behavior and examined the different limiting cases. Graphical solutions for this dynamic system can be viewed simultaneously and resolved in real time via buttons on the graphical user interface (GUI). Metabolic bottlenecks in the system can be accurately predicted by varying the respective rate constants. The GUI serves as a diagnosis toolkit to troubleshoot genetic circuits design constraints and as an interactive workflow of using this arabinose based genetic switch to dynamically control carbon flux, which may provide a valuable computational toolbox for metabolic engineers and synthetic biologists to simulate and understand complex genetic-metabolic system.

Analytical solution for a hybrid Logistic-Monod cell growth model in batch and continuous stirred tank reactor culture.

Monod and Logistic growth models have been widely used as basic equations to describe cell growth in bioprocess engineering. In the case of the Monod equation, the specific growth rate is governed by a limiting nutrient, with the mathematical form similar to the Michaelis–Menten equation. In the case of the Logistic equation, the specific growth rate is determined by the carrying capacity of the system, which could be growth‐inhibiting factors (i.e., toxic chemical accumulation) other than the nutrient level. Both equations have been found valuable to guide us build unstructured kinetic models to analyze the fermentation process and understand cell physiology. In this work, we present a hybrid Logistic‐Monod growth model, which accounts for multiple growth‐dependent factors including both the limiting nutrient and the carrying capacity of the system. Coupled with substrate consumption and yield coefficient, we present the analytical solutions for this hybrid Logistic‐Monod model in both batch and continuous stirred tank reactor (CSTR) culture. Under high biomass yield (Y x/s) conditions, the analytical solution for this hybrid model is approaching to the Logistic equation; under low biomass yield condition, the analytical solution for this hybrid model converges to the Monod equation. This hybrid Logistic‐Monod equation represents the cell growth transition from substrate‐limiting condition to growth‐inhibiting condition, which could be adopted to accurately describe the multi‐phases of cell growth and may facilitate kinetic model construction, bioprocess optimization, and scale‐up in industrial biotechnology.