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\begin{document}

\title{Constraint-based modeling and machine learning applications for analysis
and optimization of fermentation parameters}



\author[1]{Mohammad Karim Khaleghi}%
\author[1]{Iman Shahidi Pour Savizi}%
\author[2]{Nathan Lewis}%
\author[1]{Seyed Abbas Shojaosadati}%
\affil[1]{Tarbiat Modares University}%
\affil[2]{University of California, San Diego}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\selectlanguage{english}
\begin{abstract}
Recent noteworthy advances in the development of high-performing
microbial and mammalian strains have enabled the sustainable production
of bio-economically valuable substances such as bio-compounds, biofuels,
and biopharmaceuticals. However, to obtain an industrially viable
mass-production scheme, much time and effort are required. The robust
and rational design of fermentation processes requires analysis and
optimization of different extracellular conditions and medium
components, which have a massive effect on growth and productivity. In
this regard, knowledge- and data-driven modeling methods have received
much attention. Constraint-based modeling (CBM) is a knowledge-driven
mathematical approach that has been widely used in fermentation analysis
and optimization due to its capabilities of predicting the cellular
phenotype from genotype through high-throughput means. On the other
hand, machine learning (ML) is a data-driven statistical method that
identifies the data patterns within sophisticated biological systems and
processes, where there is inadequate knowledge to represent underlying
mechanisms. Furthermore, ML models are becoming a viable complement to
constraint-based models in a reciprocal manner when one is used as a
pre-step of another. As a result, more predictable models are produced.
This review highlights the applications of CBM and ML independently and
the combination of these two approaches for analyzing and optimizing
fermentation parameters.%
\end{abstract}%



\sloppy


\textbf{1. Introduction}

Fermentation technology is enjoying a significant moment, due to the
potential of metabolic engineering, systems biology, and synthetic
biology {[}1{]}. Various economically important compounds such as
different chemicals, fuels, and biopharmaceuticals can be obtained
through fermentation processes. With the purpose of commercialization of
any fermentation-based product, the amount of obtained product should
meet the market demand {[}2{]}. Therefore, optimization of the
fermentation parameters (e.g., temperature, pH, medium composition,
feeding strategies, etc.) is a critical factor that has an important
role in bioprocess overall yield and productivity. Furthermore,
fermentation optimization can reduce the overall cost of bioprocess
through its impact on downstream processes and purification {[}3{]}.

Various strategies have been implemented to find the optimal values of
fermentation parameters so far. Modeling has always been one of the most
popular methods due to its ability to replace expensive laboratory
experiments, or at least diminish the amount of them. In this approach,
according to the specified algorithms, the output is calculated as a
function of given inputs {[}4{]}. For instance, the inputs can be media
composition, temperature, pH, etc., then the appropriate values of these
parameters are optimized to make the desired output. Generally, three
types of models are implemented to the problems: purely
mechanistic/knowledge-driven, merely data-driven, or a combination of
the two {[}5{]}. Each of these approaches has its own advantages and
disadvantages. For example, data-driven models are black-box models,
which do not provide adequate information on the underlying mechanism
{[}6{]}. Nevertheless, large datasets may be not incorporated into a
model framework smoothly. On the other hand,
hypothesis/mechanistic-driven approaches use basic knowledge to extract
deeper information from datasets and provide valuable information on the
underlying mechanism. Nonetheless, the construction of these models is
challenging due to the rapid growth of data. However, in order to
construct the most powerful model, it is crucial for the researcher to
understand the strengths and weaknesses of these approaches. Moreover,
the hybridization of these two approaches might be the most powerful
model {[}7{]}.

Fermentation parameters have a significant effect on cellular
metabolism, thus productivity. So, mechanistic analysis of the
interaction between environmental conditions and metabolic pathways
leads us to fine-tune fermentation parameters in a comprehensive way
{[}8{]}. There are several mechanistic models for simulating metabolism
in the field of systems biology {[}9{]}. Among them, constraint-based
modeling (CBM) of metabolism is one of the most common approaches
{[}10{]}. These models are built from a genome-scale metabolic network
reconstruction to predict metabolic flux values through optimization
techniques such as flux balance analysis (FBA) {[}11, 12{]}. To date,
genome-scale metabolic models (GEMs) for diverse eukaryotic and
prokaryotic organisms and cells have been reconstructed {[}13{]} and
applied in biotechnology and human health {[}14, 15{]}. Such models have
been extensively utilized for qualitative mapping of cellular
metabolism, predicting metabolic functions, and guiding metabolic
engineering designs and bioprocess optimizations toward the desired
phenotype {[}16{]}.

In parallel, machine learning (ML) is a purely data-driven approach with
the creation and evolution of algorithms that identify patterns and
makes hypothesis or models based on learning from existing data {[}17,
18{]}. Because of the rapid increase in omics datasets, many researchers
prefer to use machine learning independently to interpret systems
biology and metabolic engineering datasets. For instance, genome
annotation, host strain selection, pathway discovery, metabolic pathway
reconstruction, metabolic flux optimization, multi-omic data
integration, and protein modeling can be obtained through machine
learning methods {[}3, 19{]}. Besides, due to the availability of the
large amounts of fermentation parameter values from empirical studies,
machine learning algorithms can be implemented directly to this
multivariate system to fine-tune the fermentation conditions {[}20,
21{]}.

Although the applications of each of the two methods separately are
constantly increasing, the unique capabilities of each have led to the
integration of models with more prediction power and accuracy. Recently,
comprehensive reviews of the integration of machine learning algorithms
and mechanistic models have been published, indicating a promising
outlook for this field of knowledge {[}22-26{]}. However, it is
worthwhile to review the capabilities of these two methods individually
or in combination for fermentation parameter optimization. The basic
idea here is that machine learning is a powerful computational tool for
analyzing omics data individually or inferring multi-omic relationships.
Moreover, as a result of CBM, an additional layer of omics data called
fluxomics is created, which can be analyzed by machine learning methods
separately or by integrating with other omics data {[}26{]}.

In the present review, first, we highlight the latest efforts in the
literature that utilize CBM as a mechanistic approach for fermentation
optimization. Next, we introduce ML as a data-driven method and
highlight its recent applications in tuning the fermentation parameters.
Finally, we present the studies in which CBM and ML combined to improve
the model accuracy for analyzing fermentation conditions.

\textbf{2. Constraint-based modeling: A mechanistic-driven approach}

Cell phenotype depends on various interlaced mechanisms such as
metabolism and transcriptional regulation. Kinetic and constraint-based
modeling are two main mechanistic approaches in analyzing the principles
governing an organism's metabolism and growth {[}27{]}. Kinetic models
help to understand the dynamic behavior of biological systems. In this
approach, the relationship between metabolites is expressed through
kinetic laws represented as the ordinary differential equations (ODE)
{[}28{]}. However, kinetic modeling requires costly and time-consuming
efforts to determine sophisticated kinetic parameters (e.g., enzymatic
constants and metabolite concentrations). Therefore, the application of
this method is limited to small-scale metabolic models for only
extremely well-studied organisms {[}29{]}. However, the advances on this
method are increasing and significant efforts have been made to build
genome-scale kinetic models {[}30{]}.

Constraint-based modeling (CBM) can overcome the limitations of the
kinetic models by reducing the need for complex kinetic parameters.
Therefore, this approach has been extensively used for understanding the
behavior of genome-wide systems {[}31{]}. The main goal of CBM is to
build models with high prediction accuracy to analyze the genome-scale
networks and shed light on relationships between genotype, phenotype,
and environmental conditions {[}32, 33{]}. In this section, we first
summarize the main concepts of CBM and next, we present recent
applications of this method in optimizing the fermentation processes.

\textbf{2.1 An overview of CBM main concepts}

Biological systems such as cellular metabolism are constrained by
physiochemical laws, genetics, and the extracellular environment
{[}34{]}. The most fundamental constraints of metabolism are the mass
balance equations for each intracellular metabolite generated from
biochemical reaction stoichiometry. Genome-scale network reconstructions
are created from all known metabolic reactions within the system of
interest. Furthermore, they are improved by additional information, such
as gene-protein-reaction (GPR) associations {[}35{]}. A valuable manual
protocol describes how to generate a high-quality genome-scale metabolic
reconstruction from genome sequencing data and how to curate the model
with empirical information {[}12{]}. A genome-scale network
reconstruction can be transformed into a mathematical format. The
mathematical representation of such reconstructed networks and
implementing further details such as GPR associations is called the
genome-scale metabolic model (GEM). This enables the quantitative and
qualitative analysis of the GEMs via computational approaches such as
constraint-based modeling {[}36{]}.

Metabolic flux analysis (MFA) and Flux balance analysis (FBA) are two
main CBM methods that aim to determine the reaction fluxes (fluxomics)
within the metabolic network (\textbf{Figure 1} ). These methods use a
stoichiometric matrix (S) with the size of m * n to calculate the
metabolic flux distribution. In the S matrix, each row represents a
metabolite (m), and each column represents a metabolic reaction (n).
Therefore, under the steady-state condition, the mass balance equation
will be as follows: S. v=0. The v vector contains metabolic fluxes, some
of which are known and some unknown. MFA is a data-driven method that
determines reaction fluxes through experimental measurements. While MFA
is useful in small-scale networks, FBA is a beneficial tool for
analyzing large-scale networks such as the genome-scale metabolic
network {[}37{]}. FBA is an optimization method that searches a solution
space and maximizes one or more objective functions such as maximum
growth rate and metabolite production via a linear programming approach
{[}11{]}. FBA calculates the single optimal flux distribution or
multiple optimal flux distributions in the GEM, which represents the
`state' of the metabolic network that relates to the physiological
function generated from the network {[}38{]}. However, mass balance
constraints alone cannot constitute a unique solution space. Therefore,
multiple optimal solutions (i.e., flux vectors) to the problem are
obtained. So, additional constraints such as flux capacity,
thermodynamic feasibility, gene expression, etc., are imposed to shrink
the solution space {[}39{]}. Moreover, MFA can combine with FBA to
determine internal metabolic fluxes to increase the prediction power
{[}40{]}. Besides, other forms of FBA and MFA, such as dynamic FBA and
MFA, can be used based on the aim of the research {[}41, 42{]}. In
addition to FBA and MFA, other CBM approaches can be used to rational
strain designs and increase product yield. These FBA-based methods aim
to determine gene deletion/addition targets, up/down regulations, data
integration, and suggest appropriate strategies to increase productivity
{[}43{]}. These computational methods also can be used in fermentation
optimization. For example, up- and down-regulation targets have been
used to identify enzyme activators and inhibitors for enhancing the
production bound in a regulatory-defined medium (RDM) {[}44{]}. COBRA
toolbox in MATLAB and COBRApy in python are two platforms for
implementing FBA and other related algorithms to GEMs {[}45, 46{]}.

Another efficient approach to increase the predictive power of the CBM
models is the integration of omics data with GEMs. Omics data can be
used both to narrow the solution space in the FBA and as a tool to
evaluate and validate the model prediction {[}6{]}. As a result of
integrating omics data with GEMs, context-specific models are created
that provide the basis for studying metabolism under different
conditions {[}47, 48{]}. Assuming that the system is steady-state,
substrate concentrations, time, and various kinetic parameters are not
taken into account to calculate the metabolic fluxes. Therefore, the
predictive accuracy of the CBMs is less than the calculated fluxes
resulting from solving ODEs in the kinetic models. As the solution space
becomes tighter, the FBA solutions approach the kinetic model solution.
Thus, the integration of omics data can overcome the limitations of the
CBM over the kinetic models. However, data integration remains a major
challenge, and existing methods do not perform at the expected level
{[}49{]}.

\textbf{2.2 Instances of CBM applications in fermentation optimization}

The culture medium is one of the most significant factors affecting cell
growth and productivity in bio-based products {[}4, 50, 51{]}.
Optimization of culture medium and development of proper feeding
strategies has always been a critical factor in bioprocess development
{[}2, 52{]}. Since medium components, nutritional supplements, and
culture additives directly affect cellular metabolism {[}53{]}, CBM can
be a suitable approach to analyze the effect of medium components on
cell growth and productivity. CBM-based methods have been extensively
used to analyze and optimize the culture medium and develop appropriate
feeding strategies to overproduce a wide range of products such as
recombinant proteins {[}54-58{]}, biofuels {[}59-61{]}, lipids {[}62,
63{]}, chemicals {[}64-66{]}, and foods {[}36{]}. For a more detailed
example, Swayambhu et al. used FBA and its derivatives to identify gene
deletion/overexpression targets and culture medium components to enhance
the production of siderophore compounds in recombinant \emph{Escherichia
coli} . First, they used minimization of metabolic adjustment (MoMA) and
OptForce algorithms to identify the gene deletion and overexpression
targets, respectively. Then, they combined the FBA with Plackett Burman
(PB) in silico to identify the amino acids and carbon sources that had a
major impact on productivity. Also, it was observed that by changing the
rate of nutrient uptake, the priorities of some candidates for gene
deletion or overexpression have changed {[}67{]}. Fouladiha et al. used
a genome-scale metabolic model of the Chinese hamster ovary (CHO) to
design feeding strategies to increase the production of a monoclonal
antibody. In this study, CBM has been used as pre-step of the design of
experiment (DoE) methods to decrease the number of variables and
experiments. First, they set the objective function to maximize antibody
production and used flux variability scanning based on enforced
objective flux (FVSEOF) algorithm to detect reactions whose boundaries
had changed. Fifteen exchange reactions were identified related to
various media supplements, including three vitamins, seven amino acids,
and five other metabolites. PB was then applied to screen for these 15
metabolites, of which threonine and arachidonic acid were identified as
the most effective supplements for the culture medium. A more than
two-fold increase in protein production was observed through this
strategy {[}68{]}. In another study, Sarkandy et al. developed a
stoichiometric model to predict the most efficient amino acids for
enhancing the production of interleukin-2 in fed-batch culture of
recombinant \emph{Escherichia coli} . The results showed that the
mixture of leucine, aspartic acid, and glycine improves protein
productivity by almost two-fold {[}69{]}. Recently, Shahidi et al. have
comprehensively reviewed the applications of systems biology approaches,
including CBM, in chemically defined media formulations for the
overproduction of recombinant proteins {[}70{]}. FBA has also been used
to investigate the effect of glucose, glycerol, and glucose-glycerol
dual mixtures on the internal carbon flux distribution in simultaneous
ethanol and butanol production {[}71{]}.

Fermentation conditions also can directly affect the cellular metabolism
toward the growth and productivity. Therefore, CBM methods are a
convenient and low-cost approach to optimize fermentation conditions.
For example, Calic et al. used the MFA method to investigate the effect
of pH on the intracellular metabolic network of \emph{Bacillus
licheniformis} , a \selectlanguage{greek}β-\selectlanguage{english}lactamase-producing bacterium. In this study, the
values of metabolic fluxes related to cell growth, by-products, and
desired product production at pH = 6.5, 7, 7.5 were studied. The results
show that in the period of cell growth, the by-product fluxes have the
highest value at pH = 7 and the lowest value at pH = 7.5, while the
change in pH in this period does not have a significant effect on the
production of \selectlanguage{greek}β-\selectlanguage{english}lactamase. On the other hand, it has been observed that
in the stationary phase and the product formation period, the flux value
of the desired product is maximum, and the flux values of by-products
are minimum at pH = 7. Finally, this article proposes a pH operation
strategy to improve \selectlanguage{greek}β-\selectlanguage{english}lactamase production as follows: First, the
initial pH should be set to pH = 7.5 and allowed to decrease to pH = 7
during fermentation, and then kept constant at this value {[}8{]}. In
another study, Ivarsson et al. manipulated lactate consumption and
production by pH alteration during mammalian cell cultivation. They used
FBA to see how pH changes affect lactate metabolism. The results show
that by lowering the pH from the standard pH = 7.2 to pH = 6.8, lactate
consumption increases, the cell becomes more energy-efficient, and
antibody production increases. Moreover, they found that gluconeogenic
enzymes regulated the TCA cycle at undesirable pH levels {[}72{]}. FBA
method constrained by experimentally measured extracellular fluxes has
been developed by Sou et al. to investigate the effect of mild
hypothermia conditions on antibody glycosylation in the late exponential
of a CHO cell. Flux distribution values showed that during the
stationary phase at 32 \selectlanguage{ngerman}°C, more energy and metabolites are expended to
increase cell productivity, which limits most of the resources necessary
for antibody glycosylation {[}73{]}. The overall overview of CBM
applications for fermentation parameters highlighted in this review is
presented in \textbf{Table 1} .

\textbf{3. Machine learning: A data-driven approach}

Fermentation is a multivariate system in which any number of involved
parameters can influence the process outcome {[}24{]}. As outlined in
the previous section, mechanistic models (e.g., CBM in this review) can
lead to fine-tuning some fermentation parameters such as medium
composition. Nevertheless, we cannot investigate the effect of all
fermentation parameters on productivity through mechanistic approaches.
On the other hand, strictly experimental trial-and-error methods are
time-intensive and commonly high-priced. Despite the difficulties of
such traditional techniques, the large amount of data generated from
worthwhile previously fermentation studies provide an appropriate space
for data-driven modeling approaches to find the optimal sets of
fermentation parameters. Moreover, a rational analysis of large and
complex datasets generated from experiments, measurements, and
simulations can significantly contribute to an in-depth understanding of
the system of interest {[}74{]}.

Machine learning (ML) is a data-driven approach that uses statistics and
probability science to analyze a dataset and discover the hidden
relationships between existing data to justify a phenomenon and build a
predictive model based on the patterns it learned. In the past,
researchers did not distinguish between ML and artificial intelligence
(AI), but nowadays, ML is recognized as a subfield of AI {[}75{]}.
Actually, AI is the industry of developing tools and techniques for ML,
while ML uses these tools in various fields such as engineering and
science {[}76{]}. In the ML process, a problem is first defined on a
dataset. Then, a set of preprocessing operations is performed on the
dataset based on the defined problem. In the next step, the ML model is
created by a user-defined estimator. Finally, the model is validated and
evaluated by standard techniques. \textbf{Figure 2} shows the general
scheme of the machine learning workflow.

\textbf{3.1 ML process}

\textbf{3.1.1 Dataset preparation}

The first step in any machine learning process is to define the desired
dataset. These datasets are sometimes called big data {[}77{]}. Volume,
velocity, variety, veracity, variability, value, and visualization are
seven common traits of big data. Therefore, contrary to popular belief,
big data is any dataset with at least one of these seven traits, and
high-volume datasets are not always required for ML models {[}78{]}.
However, the greater the amount of appropriate data provided, the more
accurate the model built {[}79{]}. Each dataset consists of rows and
columns, which rows are called samples, and each column can represent a
feature or a target value. Features are also called
dimensions.\textbf{Figure 3} shows an overview of a dataset. Each
dataset may contain unknown or outlier values for a variety of reasons,
such as high-volume data. Therefore, to prevent modeling errors, it is
necessary to perform a primary dataset inspection and identify unusual
or missing values. Various machine learning algorithms for missing data
imputation and outlier detection have been proposed so far {[}80{]}.
Input data can be divided into labeled or unlabeled data. While there
are one or more target values in labeled data, unlabeled data have no
target values. For example, in a labeled dataset, fermentation
parameters are features, and productivity is the target value. In these
datasets, usually, the aim is to find the relationship between the data
and make predictions on new data {[}77{]}. In unlabeled datasets, the
goal is finding hidden relationships, clustering, or detecting outliers.

\textbf{3.1.2 Preprocessing}

The preprocessing operation must be performed based on the defined
problem on the dataset. In this step, using statistical methods, the
input data is prepared in such a form that it is desirable for the
estimator in the modeling stage {[}81{]}. Data transformation is one of
the most common preprocessing operations. Various tools and techniques
can be implemented for data transformation based on the size,
complexity, and structure of the dataset. For instance, data
standardization is a transformation method in which the data of each
column are transmitted in a specified range (usually between zero and
one) {[}82{]}. Dimensionality reduction is another beneficial
preprocessing method in which data is transferred from a high-dimension
space to a low-dimension one preserving some key properties of the
original dataset. Principal component analysis (PCA) is the most widely
used dimensionality reduction approach that increases data
interpretability by constructing new uncorrelated variables summarizing
maximize variance {[}83{]}. Another prominent preprocessing operation is
feature selection which tremendously affects the performance of the ML
model. Feature selection is a method that manually or automatically
selects only a subset of features that are aligned with the target value
in the problem {[}84{]}.

\textbf{3.1.3 Modeling}

By preparing data in an appropriate format, one can create a model for
analyzing and making accurate predictions. First, the original dataset
should be divided into training and test sets by specific methods. In
the modeling step, the training dataset enters an algorithm, and the
algorithm uses statistical and mathematical tools, which are called
estimators, to learn and develop predictions. In ML, the process of
creating the desired model is called training. Usually, the most
challenging part of ML is choosing the right estimator based on
different types of data and problems. The scikit-learn library provides
a broad range of estimators along with a procedure on how to select the
best estimator among them (www.scikit-learn.org). Some important machine
learning estimators including linear regression, k-nearest neighbors,
support vector machines (SVMs), decision trees, random forest, Gaussian
process (GP), fuzzy logic, and artificial neural networks (ANNs) are
defined in \textbf{Table 2} . Moreover, ensemble methods aim to fuse the
prediction of several single estimators to improve the precision and
accuracy of the model {[}85{]}. For example, the random forest is an
ensemble modeling method in which several decision trees are used to
predict the outcome {[}86{]}. It is worth noting that each estimator has
its tunable parameters depending on the type of data and the problem.

\textbf{3.1.4 Validation and evaluation}

Model evaluation is first conducted on the training dataset to measure
how well the model can predict previously unseen data {[}87{]}. For
instance, k-fold cross-validation is a standard method that evaluates
the estimator's performance by randomly splitting the training dataset
into training and test sets. For better understanding, in this method,
the training dataset is divided randomly into k equal parts, called k
folds. Then, the model runs k times, and in each round, one particular
fold is used as the test set and k-1 folds as training ones {[}88{]}.
The accuracy of the model is computed for each test fold. When k-fold
cross-validation is operated, one can see how sensitive the model is to
the training dataset. Next, by evaluating the accuracy, the model's
parameters can be tuned to improve its generalization performance for
unseen data {[}89, 90{]}. The final evaluation of the model is conducted
with test data, and the predictive ability of the model is quantified by
different evaluation metrics such as accuracy, sensitivity, specificity,
precision, and recall {[}91, 92{]}. \textbf{Figure 4} shows how
evaluation methods can help to improve the model's performance.

\textbf{3.2 ML categories}

ML methods are broadly divided into supervised, unsupervised, and
semi-supervised learning {[}93{]}. Unsupervised learning aims to uncover
the hidden patterns and deduce the structures of unlabeled training data
{[}18{]}. Unsupervised learning approaches cluster subgroups of data
with similar properties or features into separate categories. Moreover,
dimensionality reduction methods mentioned earlier as preprocessing
operations are unsupervised learning methods that reduce the number of
old features and create new principal features with minimum information
loss {[}94{]}. However, because there are no target values in
unsupervised learning methods, they cannot build an independent
predictive model {[}95{]}. On the other hand, supervised learning is
applied to learn and discover associations relationships between
features and target values in a labeled dataset {[}96{]}. Therefore, the
built model can be used as a predictive one to test previously unseen
data. Two main supervised methods are classification for discrete class
labels and regression for numerical quantities {[}97{]}. It is
noteworthy that the output of unsupervised learning methods (e.g.,
low-dimension space features) can be used as the input of supervised
learning algorithms. For semi-supervised learning, there are both
labeled and unlabeled data in the training set; But usually, the amount
of unlabeled data is more. In this method, one can use labeled data to
create labels for unlabeled ones {[}98{]}.

\textbf{3.3 Applications of ML algorithms for fermentation analysis and
optimization}

ANNs have been used successfully in several studies in the field of
fermentation prediction and optimization (\textbf{Table 3} ). The
predictive capacity comparison of ANN and RSM has been studied by
Nelofer et al. for the lipase production process by a
recombinant\emph{Escherichia coli} {[}99{]}. In this study, fermentation
parameters were optimized based on experimental lipase production data.
As a result, ANN showed better performance over RSM for both R2 and
adjusted-R2 values. Moreover, absolute average deviation (AAD) and root
mean square error (RMSE) in the ANN model gave lower values, indicating
the high accuracy of ANN. Instead of comparing ANN and RSM, integration
of these two strategies has also attracted much attention in recent
years. For instance, in a recent study, Wang et al. proposed an ANN-RSM
methodology to overcome the pure RSM failure in predicting complex
nonlinear systems. They used original experimental datasets to train and
validate an ANN model and produce response surface models to analyze the
effect of critical parameters in dark hydrogen fermentation. The
constructed model showed good and reliable results for this nonlinear
and noisy process {[}100{]}. Genetic algorithm (GA) is a global search
optimization method inspired by natural selection theory. GA usually has
been coupled with ANN to find the optimum values of fermentation
parameters used in model training. Recently, Unni et al. employed ANN
together with GA to optimize medium composition for the production of
human interferon-gamma (hIFN\selectlanguage{english}-\selectlanguage{greek}γ\selectlanguage{english}) using a recombinant \emph{Kluyveromyces
lactis} {[}101{]}. Recently, an on-line \selectlanguage{greek}μ-\selectlanguage{english}stat strategy was proposed for
controlling methanol feeding in a fed-batch process of
Recombinant\emph{Pichia pastoris} . In this study, Tavasoli et al.
employed MLP3 neural network (a class of ANNs) to reconstruct and adjust
the controller's performance. Consequently, a significant enhancement
was observed in the production of human recombinant alpha 1-antitrypsin
(A1AT) {[}102{]}.

SVMs are another popular method for training experimental fermentation
data and predicting the process outcome. One specific advantage that
SVMs have over ANNs is that they always find the global optimum
solution, while ANNs may fall into the local optimum. Moreover, SVMs are
effective for problems with a small number of samples. The predictive
capabilities of SVM and ANN were compared recently by Zhang et al. In
this investigation, SVM and ANN were used to build models for predicting
biomass yield, lipid production, and COD removal rate in a microbial
lipid fermentation. The results demonstrated that the SVM linked with
the genetic algorithm performed better over ANN with a small number of
samples {[}103{]}. In another study, the least-square SVM (LS-SVM), a
modified SVM, was coupled with orthogonal experimental design (OED) to
map the relationship between process parameters as inputs and cumulative
biogas production (CBP) as the output for corn stalks anaerobic
fermentation with only nine samples. In this study, the LS-SVM
parameters were optimized by the grid search method. The results showed
that using this optimization method as an alternative to pure OED
increases CBP by 14.13\% {[}104{]}.

Other ML methods also have shown reliable results in fermentation
prediction and optimization. Kennedy et al. investigated the
capabilities of fuzzy logic as a tool for media formulation. They found
that this method can save 63\% of the experiments and the remaining
experiments are adequate for media design. They found that the selection
of correct number of fuzzy logic rules is critical for enhancing model
accuracy {[}105{]}. In another study, Melcher et al. utilized random
forest and ANN for biomass and recombinant protein modeling in a
fed-batch \emph{Escherichia coli} process. Online fermentation
parameters and two-dimensional (2D) fluorescence spectroscopy were used
for dry cell mass and productivity prediction. The hybrid model accuracy
reached about \selectlanguage{ngerman}±4\% for dry cell mass and ±12\% for protein concentration
{[}106{]}. Masampally et al. employed Gaussian process regression (GPR)
in fed-batch fermentation of yeast \emph{saccharomyces cerevisiae} to
predict biomass concentration. In this study, three cascade sub-models
were developed to predict gas hold-up, dissolved oxygen (DO), and
biomass storage, respectively. Validation experiments were eventually
performed {[}107{]}. Recently, using the k-nearest-neighbor (KNN)
method, a 1.64-fold improvement in \emph{Penicillium
brevicompactum}fermentation producing mycophenolic acid (MPA) has been
obtained {[}108{]}.

\textbf{4. Incorporation of constraint-based modeling and machine
learning}

In recent years, the advances in high-throughput devices and the rapid
growth of omics data provide a unique opportunity to depict biological
samples at multiple layers. Omics data generated from high-throughput
technologies are big data that can be analyzed individually or inferred
as multi-omic relationships through ML algorithms to gain more
biological insight {[}109-111{]}. Common omics datasets include
genomics, transcriptomics, proteomics, and metabolomics produced from
DNA sequencing, RNA sequencing and microarrays, and mass spectrometry,
respectively {[}112{]}. Furthermore, fluxomics is an additional layer of
omics generated from CBM approaches and includes metabolic flux
distribution values, thus representing the metabolic phenotype
{[}113{]}. Consequently, the integration of ML (for omics and
multi-omics analysis) and CBM (for generating fluxomics) looks promising
for analyzing a biological system such as cellular metabolism. However,
the capabilities of this hybrid approach are just now being explored,
and more research in this area is needed. In this section, first, we
briefly summarize the ways that ML and CBM can be coupled. Next, the
most prominent studies aiming at analysis and optimization of
fermentation parameters by ML-CBM approaches are reviewed.

\textbf{4.1 Approaches for CBM and ML integration}

The integration of ML and CBM can be conducted in three chief ways
{[}26{]}: (a) The output of CBM is the flux distribution that indicates
the metabolic state of the cell. This fluxomic data can be trained
directly through ML methods to obtain more biological insight into the
desired system (\textbf{Figure 5A} ). (b) ML is an effective tool for
merging and analyzing heterogeneous omics datasets beyond ML
applications to single omics. By combining these multi-omics datasets
with GEMs, context-specific models are generated. More accurate flux
values obtained from context-specific GEMs can be re-integrated with
experimental omics data for further predictions (\textbf{Figure 5B} ).
(c) CBM models and fluxomic data can be produced directly by introducing
omics or multi-omics datasets into ML algorithms. All of the three
mentioned methods might be operated by supervised or unsupervised
algorithms (\textbf{Figure 5C} ).

\textbf{4.2 Instances of CBM coupled with ML for fermentation analysis
and optimization}

Routinely, CBM uses genetic and environmental conditions as inputs to
predict metabolic flux distributions. However, Sridhara et al.
investigated whether they could infer bacterial growth conditions from
internal fluxomics in an inverse manner. For this reason, the prediction
conducted using a simple linear regression. The results showed that
using the intracellular flux values, carbon and nitrogen sources
utilized in the initial culture medium could be predicted even with a
small number of impurities {[}114{]}. In a recent study, Oyetunde et al.
extracted over 1,200 curated bioprocess datasets from \selectlanguage{english}~100 articles to
predict microbial factories' performance (yield, titer, and rate). The
authors generated additional flux-based features from a CBM model to
augment ML input data. Next, they applied ensemble methods to alleviate
data challenges such as sparse, non-standardized, and incomplete
datasets. The developed ML-CBM model could predict an
engineered\emph{Escherichia coli} performance with high accuracy
{[}115{]}. In 2016, Wu et al. developed MFlux, an online platform, for
predicting bacterial central metabolism. The authors used ML approaches
(SVM, KNN, and decision tree) to train previously experimental data,
including substrate types, bioprocess strategies, and genetic
modifications from about 100 13C-MFA articles. MFlux outputs can be used
as inputs for FBA to reduce the solution space, thus improving the
model's accuracy {[}116{]}.

Most recently, a novel CBM-ML hybridization approach for time-course
controlling nutrients availability in a fed-batch CHO cell culture has
been developed. For this reason, Schinn et al. used ML as a tool to
overcome CBM limitations, such as optimal metabolism considerations and
steady-state assumptions. In this study, cell density, product titer,
glucose, lactate, glutamine, and glutamate concentrations were used as
constraints for the FBA solution. The metabolic model calculated the
initial consumption rates of proteogenic amino acids. Next, a series of
linear regressions were used to refine the predictions. Finally, using a
sigmoid function, the refined consumption rates were fit to a
time-course dependent profile. The model was able to correctly forecast
the concentrations of 13 out of 18 amino acids {[}117{]}.

Essential genes are genes that are critical for cell viability and
growth. Gene essentiality is not an intrinsic trait of a gene. But
instead, it can be influenced by environmental and genetic contexts
{[}118{]}. Nandi et al. developed an SVM-based model named SVM-RFE to
classify \emph{Escherichia coli} genes as essential or non-essential.
The model input included a mixture of genotypic and phenotypic features,
i.e., gene and protein sequences, topological network, and gene
expression. Then, they employed flux coupling analysis (FCA) to generate
flux-based features to consider gene adaptability in different
environmental conditions. SVM-RFE was trained on 4094 reaction-gene
combinations with 64 features. The model could successfully capture the
minimal set of essential genes in various environmental conditions with
high accuracy {[}119{]}. This study shows the importance of selecting
and describing appropriate features in an ML study.

In the context of multi-omics integration, Zampieri et al. employed a
combination of CBM and ML to predict lactate production, a secondary
metabolite, in CHO cell culture. In this study, transcriptomics data
from different culture conditions were integrated with fluxomics data
from in-silico genome-scale modeling to construct a data-driven
framework. The results showed an improving performance over the
predictive power of pure transcriptomic analysis {[}120{]}. Similarly,
Vijayakumar et al. proposed a machine learning pipeline integrated with
genome-scale modeling to improve phenotypic prediction in a
lipid-producing cyanobacterium. First, they extracted RNA sequencing
data from 23 different growth conditions to develop condition-specific
GEMs via transcriptomics data integration. Then, FBA was performed to
obtain context-specific fluxomic data. The preprocessing stage was
conducted to incorporate fluxomics into experimental transcriptomics
data. PCA, k-mean clustering, and LASSO regression were used to identify
the dataset's key features. As a result, a data-driven multi-view model
was developed with a high phenotype predictive accuracy {[}121{]}. This
strategy also has been adapted to predict yeast S. cerevisiae growth
rate. In this study, fluxomics, generated from parsimonious flux balance
analysis (pFBA), were coupled with transcriptomics to train neural
networks {[}122{]}.

\textbf{5. Challenges and perspectives}

It is now clear that fermentation optimization and control are needed to
achieve more efficient and economic bioprocess. Therefore, different
holistic strategies have been developed to obtain specifically tailored
fermentation parameters. In this review, we briefly summarized the
applications of two important modeling methods for analyzing and
optimizing fermentation parameters: (a) Constraint-based modeling (CBM)
and (b) machine learning (ML). The former is a mechanistic method that
aims to get more insight into the biological system of metabolism. The
latter is a data-driven approach in which a specified algorithm can
learn from previous data and make predictions with minimal human
intervention. ML can be used to analyze fermentation parameters directly
or to infer high-dimensional omics datasets. Furthermore, recent
investigations showed that ML can be integrated with CBM to improve
predictive power and get more biological insights. However, despite the
advances in CBM, ML, and CBM-ML applications in fermentation analysis
and optimization, several limitations remain to be discussed.

Here we review some of the major challenges in developing CBM and ML
models. CBM can only estimate the metabolic flux distribution relying on
an optimal steady-state assumption in which it operates well only in
ideal limited time scales. Moreover, it does not account for metabolite
concentrations, enzyme kinetics, and regulations. Therefore, CBM cannot
always predict accurate metabolic fluxes {[}11{]}. Kinetic models of
metabolism that can overcome these shortcomings have been successfully
developed to analyze the effect of genetic and environmental factors at
genome scales {[}30{]}. However, difficult and computationally expensive
methods have limited kinetic model performance in an intracellular
environment {[}123{]}. An alternative approach to kinetic models is
using omics and multi-omics datasets to generate context-specific
metabolic models and derive meaningful insights {[}49, 124{]}. To this
end, several algorithms have been developed with different assumptions
and predictive capabilities {[}125, 126{]}. Nevertheless, omics datasets
also have some limitations, such as heterogeneity of individual omics,
the necessity of intensive analysis, differences in representation
formats {[}124{]}, lack of mechanistic knowledge, and inefficient
genome-scale integration tools. Thus, the construction of
context-specific GEMs remains challenging. Therefore, many researchers
prefer to build data-driven ML models in order to analyze metabolic
networks {[}7{]}. Moreover, thanks to the significant amount of
fermentation studies and advances in measuring tools, ML methods have
been widely used to optimize fermentation media and conditions.
Nevertheless, ML models are black-box models, which use previously
experimental datasets and do not provide sufficient information on the
underlying mechanism {[}6{]}.

As described above, CBM and ML both can be used as powerful tools for
analyzing metabolic networks and fermentation parameters. However, the
remarkable capabilities of each method have shown promise for the
construction of combined CBM-ML methods. The collaboration between ML
and CBM is a reciprocal process. In other words, ML can be applied to
the CBM input datasets and increase the predictive power of the
metabolic model. Conversely, CBM is a practical tool for the generation
of a new layer of omics data called fluxomics to improve the
interpretability of a data-driven ML model {[}23{]}. However, to take
full advantage of both CBM and ML, several challenges needed to be
addressed. First, CBM-derived fluxomic data require several
preprocessing steps to integrate with multi-omic data to obtain suitable
biological data. This target is restricted due to the heterogeneous and
high-dimensional datasets {[}111{]}. Second, despite the advances in
genome-scale metabolic reconstructions, appropriate high-throughput data
are only available for a small group of microorganisms {[}19{]}. Third,
the results of the integrated models, although very accurate, are not
necessarily appropriate for large-scale industrial fermentations.
Finally, the limitations of each ML and CBM method are still not fully
addressed in the integrated models.

Recent studies represent a hopeful future for improving fermentation
processes and obtaining valuable biological products through the methods
reviewed in this article. In our view, to overcome the challenges, it is
required to enhance our biological knowledge in parallel with the
development of novel mathematical and computational tools. This is
possible through collaboration between chemical engineers, biologists,
physicists, and computer engineers. For example, the integration of
high-quality metabolic regulatory networks can improve the prediction
power of CBM models. Moreover, further developments in high-throughput
techniques and more effective methods are needed to integrate omics data
with GEMs.

\textbf{Acknowledgments}

This work was supported by Tarbiat Modares University (Grant No.
IG-39702); and generous support from the Novo Nordisk Foundation
(NNF20SA0066621).

\textbf{Conflict of interest}

The authors declare no financial or commercial conflict of interest.

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Table 1. Overview of constraint-based modeling applications for analysis
and optimization of fermentation parameters demonstrated in this review.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Parameter\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Aim\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Achievement\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Ref\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Culture medium\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Combining the FBA with Plackett Burman (PB) for a recombinant
\emph{Escherichia coli}\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Identifying the key amino acids and carbon sources for successful
improvement in siderophore production\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
{[}67{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Culture medium\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Using the FVSEOF algorithm to design feeding strategies for CHO
cells\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Suggesting threonine and arachidonate as supplements by the metabolic
model and a two-fold increase in antibody production\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
{[}68{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Culture medium\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Designing a strategy for amino acid supplementation by a stoichiometric
model\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Enhancing the production of interleukin-2 by adding a mixture of
leucine, aspartic acid, and glycine\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
{[}69{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Culture medium\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Performing FBA for \emph{C. sporogenes} NCIM on glucose, glycerol \&
their mixture\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Glucose and glucose-glycerol mixture improve the growth and the butyric
acid production. Glycerol reduces the growth and improves ethanol
yield\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
{[}71{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
pH\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
MFA used for \emph{Bacillus licheniformis} to study the effect of pH on
metabolic flux distribution\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Proposing a pH-controlled strategy to improve \selectlanguage{greek}β-\selectlanguage{english}lactamase
production\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
{[}8{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
pH\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
FBA used to gain mechanistic insight into the question of how pH affects
lactate metabolism for a mammalian cell\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Lowering the pH increases lactate consumption, antibody production and
makes the cell more energy-efficient\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
{[}72{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Temperature\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
FBA implemented to study the effect of mild hypothermia conditions on
the CHO cell behaviors\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Formation of premature glycosylated antibodies during the stationary
phase at 32 \selectlanguage{ngerman}°C\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
{[}73{]}\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Table 2. A brief introduction to the machine learning estimators
(algorithms) that considered in this review.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Estimator (Algorithm)\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Task\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Description\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Relevant studies\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Linear regressions\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Regression\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
The simplest form of regression models. Attempts to minimize the mean
squared error (MSE) between actual target values and the target values
estimated by fitting a linear equation to the training set.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
{[}114, 120, 121, 123{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
\emph{k}-nearest neighbors (KNN)\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Classification Regression\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
A simple ML algorithm that stores \emph{k} nearest neighbor samples in a
dataset (\emph{k}=1, 2, 3, \ldots{}) based on the feature
similarities.\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
{[}81, 108, 116{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Support vector machines (SVMs)\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Classification Regression\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
The objective of SVM is to transform each data in an n-dimensional space
(n: number of features) and separate data points into two categories in
a manner that maximizes the width of the gap between the nearest
observations. SVMs are divided into two main groups: Support vector
regressors (SVRs) and support vector classifiers (SVCs).\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
{[}103, 104, 115, 116, 119{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Decision trees and random forest\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Classification Regression\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Decision trees provide a tree-shaped structure, including nodes and
branches. The algorithm makes decisions based on a hierarchy of if/else
questions. Each node classifies the input depending on the question, and
the branches are the final decisions representing the output. Random
forest is an ensemble method that collects many randomly made decision
trees. This algorithm aims to overcome the limitations of each
individual decision tree and averages their results.\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
{[}106, 115, 116{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Gaussian process (GP)\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Classification Regression\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
GP is a probabilistic non-parametric method that aims to make
predictions and provide uncertainty information on the estimations based
on Bayes' rule. Gaussian process classification (GPC) and Gaussian
process regression (GPR) are two main groups of GP.\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
{[}107{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Fuzzy logic (FL)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Regression\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
FL resembles the pattern of human reasoning for solving problems
considering all available possibilities between Yes and No.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
{[}105{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Artificial neural networks (ANNs)\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Classification Regression\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
ANNs are one of the most popular ML algorithms which are inspired by the
human brain information process. ANNs are consist of interconnected
neurons arranged in an input layer, a series of hidden layers, and an
output layer. In these algorithms, each neuron makes decisions and gives
it to other neurons in the next layer. The weighted sum of the inputs is
calculated by an activation function. Then, the procedure tends to
update the weights in order to minimize the prediction errors.\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
{[}99-102, 106, 115, 117, 122{]}\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Table 3. Overview of machine learning applications for analysis and
optimization of fermentation parameters demonstrated in this review.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Host\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Aim\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Input features\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Achievement\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Ref\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\emph{Escherichia coliBL21}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Comparing RSM and ANN for optimizing lipase production\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Glucose, sodium chloride (NaCl), temperature and induction time\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
ANN showed better R\textsuperscript{2} and adjusted-R\textsuperscript{2}
values, and lower AAD and RMSE values\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
{[}99{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Sludge\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Integrating RSM and ANN for improving biohydrogen titer\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Carbon sources, metal cofactor Fe\textsuperscript{0}, pH, and sludge
concentration\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Developing a robust, cost-effective, and reliable optimization
methodology\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
{[}100{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\emph{Kluyveromyces lactis}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Using ANN coupled with GA for media optimization in hIFN-\selectlanguage{greek}γ
\selectlanguage{english}production\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Medium components (sorbitol, glycine, Na2HPO4, and MgSO4.7H2O)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Achieving maximum productivity in shake flasks level and bioreactor
level\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
{[}101{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\emph{Pichia pastoris}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
MLP3 neural network was used to optimize the controller for a novel
fed-batch production of A1AT\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Controller gain and control poles\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
The cell growth and protein titer were improved significantly in
comparison to traditional approaches\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
{[}102{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\emph{Rhodotorula glutinis}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Establishing ANN and SVM models for microbial lipid production\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Biomass, lipid yield, and COD removal rate\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
SVM performed better than ANN for small samples Fermentation parameters
were optimized by integration of SVM and GA\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
{[}103{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Sludge\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Developing a hybrid model for optimizing CBP production using LS-SVM and
OED\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Corn stalk weight, ultrasonic duration time, pretreatment time, and
dual-frequency ultrasound\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
The model increases CBP 14.13\% more than pure OED\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
{[}104{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\emph{Escherichia coli}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Using random forest and ANN for biomass and recombinant protein modeling
in a fed-batch process\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Temperature, induction strength, growth rate, soluble/insoluble product
formation\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
The accuracy reached about \selectlanguage{ngerman}±4\% for dry cell mass and ±12\% for protein
concentration\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
{[}106{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\emph{saccharomyces cerevisiae}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Employing GPR for prediction of \emph{S. cerevisiae} biomass
concentration\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Molasses feed rate\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Experimentally validation results showed high accuracy\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
{[}107{]}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\emph{Penicillium brevicompactum}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Establishing a \emph{k}-nearest-neighbor model to optimize different
independent factors in MPA production\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Ultrasound power, irradiation duration, treatment frequency and duty
cycle\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.64-fold improvement observed in MPA production\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
{[}108{]}\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\textbf{Figure Legends:}

\textbf{Figure 1: Schematic of constraint-based modeling methods.} FBA
and MFA indicate metabolic flux distributions (fluxomics). A rational
analysis of fluxomics causes the optimization of fermentation
parameters, thus enhancing the product yield and reducing the production
costs.

\textbf{Figure 2: Machine learning workflow.}

\textbf{Figure 3: An overview of the structure of a dataset.} This
figure demonstrates a labeled dataset because one or more target values
are reported. Datasets are usually prepared by data scientists. However,
the more one knows about a dataset, the easier the machine learning
process will be.

\textbf{Figure 4: The role of cross-validation in machine
learning.}First, the generalization power of the ML model is evaluated
through cross-validation. Then, hyperparameter tuning is performed
before training the model to refine the model's parameters which are
called hyperparameters. Grid search and Bayesian optimization algorithms
are the most common search-based methods to tune hyperparameters.
Finally, the curated model is used to evaluate the prediction capability
of unseen test data.

\textbf{Figure 5: Integrating constraint-based modeling and machine
learning.} CBM and ML can be integrated in different ways for analysis
and optimization of fermentation parameters. \textbf{(a)} Predicting
parameters by ML when fluxomics are used as inputs.
\textbf{(b)}Predicting parameters by ML when the integration of
fluxomics with multi-omics is used as input. \textbf{(c)} Predicting
fluxomics and constraint-based models by ML when multi-omics are used as
inputs.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 4}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 5}

\selectlanguage{english}
\FloatBarrier
\end{document}

