Network Modeling and Control of Dynamic Disease Pathways, Review and Perspectives

Abstract

p>This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

Dynamic disease pathways are a combination of complex dynamical processes among bio-molecules in a cell that leads to diseases. Network modeling of disease pathways considers disease-related bio-molecules (e.g. DNA, RNA, transcription factors, enzymes, proteins, and metabolites) and their interaction (e.g. DNA methylation, histone modification, alternative splicing, and protein modification) to study disease progression and predict therapeutic responses. These bio-molecules and their interactions are the basic elements in the study of the misregulation in the disease-related gene expression that lead to abnormal cellular responses. Gene regulatory networks, cell signaling networks, and metabolic networks are the three major types of intracellular networks for the study of the cellular responses elicited from extracellular signals. The disease-related cellular responses can be prevented or regulated by designing control strategies to manipulate these extracellular signals. The paper reviews the regulatory mechanisms, the dynamic models, and the control strategies for each intracellular network. The applications, limitations and the prospective for modeling and control are also discussed.</p

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Network Modeling and Control of Dynamic Disease Pathways,Network Modeling and Control of Dynamic Disease Pathways,
Review and PerspectivesReview and Perspectives
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CITATION
Hsiao, Yen-Che; Dutta, Abhishek (2022): Network Modeling and Control of Dynamic Disease Pathways,
Review and Perspectives. TechRxiv. Preprint. https://doi.org/10.36227/techrxiv.21705995.v1
DOI
10.36227/techrxiv.21705995.v1

1
Network Modeling and Control of Dynamic
Disease Pathways, Review and Perspectives
Yen-Che Hsiao and Abhishek Dutta
Abstract—Dynamic disease pathways are a combination of complex dynamical processes among bio-molecules in a cell that leads to
diseases. Network modeling of disease pathways considers disease-related bio-molecules (e.g. DNA, RNA, transcription factors,
enzymes, proteins, and metabolites) and their interaction (e.g. DNA methylation, histone modification, alternative splicing, and protein
modification) to study disease progression and predict therapeutic responses. These bio-molecules and their interactions are the basic
elements in the study of the misregulation in the disease-related gene expression that lead to abnormal cellular responses. Gene
regulatory networks, cell signaling networks, and metabolic networks are the three major types of intracellular networks for the study of
the cellular responses elicited from extracellular signals. The disease-related cellular responses can be prevented or regulated by
designing control strategies to manipulate these extracellular signals. The paper reviews the regulatory mechanisms, the dynamic
models, and the control strategies for each intracellular network. The applications, limitations and the prospective for modeling and
control are also discussed.
Index Terms—Biological interaction networks, biological system modeling, biological control systems, diseases, gene expression.
✦
1 INTRODUCTION
THE study of diseases is the understanding of abnormal
cellular and molecular structure and function [1]. The
interactions of bio-molecules are essential to give a deeper
understanding of health and disease [2]. Bio-molecules in-
clude DNA, RNA, transcription factors, enzymes, proteins,
and metabolites [3]. Different cellular functions, such as in-
formation storage, processing and execution are performed
by these bio-molecules [4]. A cell can be seen as a network
of genes and proteins, which offers a doable strategy for
describing the complexity of living systems [5]. A biological
network is composed of bio-molecules and the interac-
tions or reactions between the bio-molecules [6]. Biologi-
cal networks are used to conceptually represent signaling,
gene regulation and metabolism [7]. Biological networks
are useful to disentangle biological mechanisms, to study
etiology, and to predict therapeutic responses [8]. Diseases
can be seen as certain types of network perturbation [9]. The
perturbation includes genetic and environmental perturba-
tions which lead to the rewiring of network topology [10].
The study of biological networks can help discover some
treatments for certain diseases [11].
The analysis of the complexities of health and disease
can discover the key pathways and networks involved in
disease onset, progression, and treatment [12]. The mod-
eling of networks helps to comprehend the complexity of
health, disease, and medicine [13]. The analysis of biolog-
ical network can provide clinically actionable knowledge
for disease diagnosis, prognosis, and treatment [14]. The
analysis of a network can be classified into two categories:
the static analysis of networks and the analysis of network
•Yen-Che Hsiao is with the Department of Electrical and Computer Engi-
neering, University of Connecticut, Storrs CT 06269, USA.
E-mail: yen-che.hsiao@uconn.edu
•Abhishek Dutta is with the Department of Electrical and Computer
Engineering, University of Connecticut, Storrs CT 06269, USA.
dynamic [15].
The static analysis of networks is the study of the proper-
ties of a network using the network architecture (topology)
and their initial states [16]. Graph algorithms can be used to
compute the properties of the static structure in a network,
such as the subgraphs in the network, the shortest path
length between indirectly connected nodes, or the existence
of central nodes of the network [17]. A Network motif is a
subgraph that can be found significantly more frequently in
a given network than those in randomized networks [18],
[19]. A module is a bigger subgraph that may contain more
than 100 nodes, compared to a motif which usually has
three to five nodes [20]. A network is said to be scale-free
providing that most of the nodes in the network contain
only one or two links, whereas a little number of nodes,
which are called hubs, possess many links [21]. Structure
and functions in biological networks have strong relevance
to biological processes [20]. Study of motifs in biological
network may uncover answers to many crucial biological
questions [22]. Module level analysis can be used to discover
genetic alteration and disease-related gene sets [23]. A scale-
free network is robust against random removal of scarcely
linked nodes, but susceptible to the selective removal of the
hubs [24]. A combination of structure properties can also
help identify new genes that could be linked directly to
certain diseases in genetic network [25].
The properties acquired from the static analysis cannot
describe the changes of the network properties in different
conditions [26]. The analysis of network dynamics is needed
to study the changes in the interaction of the bio-molecules
over time [27]. The stability or robustness of a biological
network can be studied from the steady-state of the network
under small perturbation [28]. Steady-state can be used to
observe the long-term behavior of a biological network [29].
Sensitivity analysis can provide information about how ro-
bust the outputs are with respect to the changes of the inputs

2
and which inputs are the key factors that affect the output
[30]. Time-dependent sensitivities can be used to rank the
most sensitive reaction steps or initial concentrations of a
biological network [31]. Bifurcation analysis can provide a
detailed illustration of dynamic behavior [32]. Singularity
theory can be applied to bifurcation analysis and it can
classify control parameters between qualitatively different
bifurcation diagrams [33]. Flux balance analysis can analyze
the flow of metabolites through a metabolic network [34].
Both the static analysis and the analysis of network
dynamics are applied to dynamic network modeling for
characterizing the network (e.g. degree distributions for
finding similar gene regulatory network structure form dif-
ferent organisms) and analyzing the network properties (e.g.
steady-state analysis for observing long term behavior in
cancer progression). These analysis methods help us build a
reliable model and evaluate the performance of the control
strategy.
2 DYNAMIC NETWO RK MODELING OF DISEASE
PATHWAYS
The examination of the topology and dynamics of cellu-
lar function can provide useful information on the under-
standing of biological systems. [32]. For disease analysis,
static modeling cannot give time information, so dynamic
modeling is crucial since it can show when cellular events
happen using ordinary differential equations, where they
arise using partial differential equations, and how often
they reappear using stochastic differential equation. [35].
Dynamic networks can describe how the connections of
biological networks change through the disease progression
[10]. This information can be further used for therapeutic
purposes.
In this section, we will first discuss the influence of
bio-molecules involved in a biological network and discuss
the various approaches used to model gene regulatory net-
works, cell signaling networks, and metabolic networks.
2.1 Bio-molecules in biological networks
Biological networks illustrate the interactions involved in
the biological reactions from DNA to proteins [36]. The role
of bio-molecules in biological networks is illustrated in Fig.
1. The processes which affect DNA include methylation,
histone modification, and transcription factors. These two
processes form a transcriptional gene regulatory network.
DNA methylation is an important mechanism in epigenetics
to modify DNA by taking proteins related in gene repres-
sion or by preventing the binding of transcription factors
to the promoter of DNA [37]. Histone modifications are
crucial for controlling chromatin structure and transcription
[38]. Histone-modifying enzymes can regulate chromatin
structure, thereby altering the transcriptional activity of a
gene [39]. Transcription factors are proteins that bind to
the promoter of DNA sequences to regulate gene transcrip-
tion [40]. Transcription factors are vital to the process of
controlling gene expression which includes normal embry-
onic development, the creation and maintenance of tissue-
specific protein synthesis, and the reaction to certain cellular
signaling pathways [41].
The elements that affect the post-transcriptional gene
regulatory network by RNA include alternative splicing,
and microRNA [36]. RNA splicing is one of the steps in-
volved in the transcription to process the initial RNA to
messenger RNA [42]. RNA splicing will remove the non-
coding sequences of genes from pre-mRNA and joins the
protein-coding sequences (exons) together [43]. Alternative
(differential) splicing is an important mechanism for the
regulation of gene expression [44]. The process of alternative
splicing will occasionally skip specific exons on a single pre-
mRNA, thereby generating multiple mRNAs from a single
pre-mRNA [45]. Alternative splicing of pre-mRNAs can lead
to quantitative control of gene expression and functional
diversification of proteins [46]. Alternative splicing can con-
tribute to several regulatory functions, such as determina-
tion and diversity of neuronal wiring or determination of
the physiological function of membrane-bound receptors in
the mammalian nervous system [47]. The disruption of the
normal splicing process can cause or modify human disease
[48]. MicroRNAs are short RNA molecules that regulate
post-transcriptional silencing of target genes [49]. MicroR-
NAs regulate their targets by inhibiting the translation and
destabilizing the mRNA [50]. Cellular activities such as
proliferation, morphogenesis, apoptosis, and differentiation
are regulated by microRNAs [51].
The biological interactions regarding proteins are sig-
naling network and metabolic network [36]. The signaling
network contains different signaling proteins to transduce
the extracellular signal received by the receptor on the
plasma membrane into the cell. Signaling pathways can
regulate important cellular components, such as metabolic
enzymes, ion channels, and the transcriptional machinery
[52]. The interaction between signaling proteins includes
ubiquitination, sumoylation, and phosphorylation.
Ubiquitination can regulate all processes in a cell using
several cellular proteins [53]. The three enzymes: ubiquitin-
activating (E1), ubiquitin-conjugating (E2), and ubiquitin-
ligating (E3) enzymes facilitate the process of ubiquitination
to the activate and transfer the ubiquitin to target proteins
[54]. A single ubiquitin or polyubiquitin chain can attach to
proteins to control gene transcription [55]. Protein sumoy-
lation is the process of attaching a sumo peptide on the
target protein [56]. Sumoylation regulates a protein mainly
by post-translational modifications to affect gene expres-
sion [57]. Protein phosphorylation and dephosphorylation
are important cellular regulatory mechanisms since many
enzymes and receptors are activated or deactivated through
the reaction with kinases and phosphatases [58].
These bio-molecules regulate the cellular function by
interacting with DNA, RNA and proteins. These mecha-
nisms should be considered in the modeling of biological
networks. For the gene regulation network, transcription
factors are widely considered as the regulators to change the
concentration of mRNAs and proteins. For the cell signaling
network, phosphorylation is commonly considered in the
process of cell signaling. For the metabolic network, it only
considers the chemical reaction between different proteins.
2.2 Modeling of gene regulatory network
A network that has been inferred from gene expression data
is called a “gene regulatory network” [59]. Studying gene

3
Fig. 1. The bio-molecules and the processes that regulate gene expression. DNA methylation can inhibit the binding of transcription factors by
blocking the promoter sites. Histone modification can modify the chromatin structure to affect transcription. Transcription factors can bind with
specific DNA to regulate gene expression. Alternative splicing selects different combinations of exons to prduce several messenger RNA. MicroRNA
can bind with messenger RNA to inhibit transcription or promote messenger RNA degradation. Protein modification diversifies protein functions to
regulate cellular process.
expression patterns and the interactions between proteins
are essential for the comprehension of cellular functions
and their dysfunctions [60]. Modeling of gene regulatory
networks is required for the dynamic network analysis to
understand how gene regulatory networks work [61]. This
section will discuss the commonly used network modeling
methods for gene regulatory networks modeling architec-
ture including Boolean networks, Bayesian networks, and
differential equations [62].
2.2.1 Boolean networks
Boolean networks are discrete networks that can show the
dynamic of the system [63]. Boolean networks model the
gene as a binary device, the binary device can only be on
or off (active or inactive) [64]. A Boolean network can be
represented by a directed graph, a set of Boolean functions,
a truth table, or a state transition graph. Each node in
Boolean networks represents a biological component such
as a gene, protein, metabolite, ion channel, or stimulus [65].
The Boolean functions in Boolean networks can be used to
describe the interactions between transcription factors [66].
The truth table shows the current states of each gene and
their next state at the next time moment. The dynamics of
Boolean network models can be depicted in state graphs
showing the transition between states [67]. The representa-
tion of a Boolean network is shown in Fig. 2.
Attractors are commonly used for analyzing a Boolean
network for certain diseases. Attractors are the steady states
to which the states in the Boolean network will eventually
converge [68]. Barbuti et al. [69] identify the attractors in
Boolean networks are important because they are often
correlated to the gene activation configurations of specific
cellular phenotypes. Fumia et al. [70] show that the attractors
related to quiescent phenotypes, apoptotic and proliferative
phenotypes control the dynamics of their cancer network.
The stochastic Boolean network proposed by Liang & Han
[71] can be applied for estimating the steady state distri-
bution. Taou et al. [72] used Boolean networks as a control
system to govern the states of other Boolean networks by
making these states flow to the desired attractor.
The first step for modeling the Boolean network is to
synthesize the network structure by extensively collecting
the relevant literature and experimental data concerning
the biological system of interest [65]. A Boolean network
requires known phenotypes in the biological system, activ-

4
Fig. 2. The presentation of a Boolean network. (a) a directed graph. (b) a set of Boolean functions. (c) truth tables. (d) a state transition graph.
ities (activate or inactivate) of genes, and the relationship
(active or inhibit) between these genes or certain genes
and the corresponding phenotype [73]. Martin et al. [62]
used the technique including k-means and support vector
regression to cluster and discretize the gene expression data
for inferring gene regulatory networks from time series mi-
croarray data. REVerse Engineering ALgorithm (REVEAL)
[74] uses systematic mutual information analysis of Boolean
network state transition tables to extract minimal network
architectures. Akutsu et al. [75] proposed a Boolean network
model and an inference algorithm for it. Kobayasshi et
al. [76] modeled a Boolean network with the arbitrarily
assigned binary values for the concentration level of genes
and Boolean functions as the control inputs.
One of the advantages of Boolean networks is that if
the information about the biological system is not enough
to build a quantitative model, Boolean modeling can find
the missing interactions to provide a way to complete the
network [77]. Another scenario for using Boolean networks
is when we are not interested in predicting the exact concen-
trations of different substances, but only in the behaviour
of the systems such as steady states [66]. Saez-Rodriguez
et al. [78] showed that the biochemical differences in signal
transduction between tumor and normal cell types can be
discovered using Boolean modeling.
Boolean network is suitable at building large scale net-
works, since it only requires the binary expression level of
the genes and the logical relationship between two states.
However, the computational complexity of finding the at-
tractors increases for a larger networks. Other challenges of
a Boolean network is its ability to apply it to a multi-scale
model for a lager and more complex biological system.
2.2.2 Bayesian networks
Bayesian network is a probabilistic model that shows the
probability of the value for a certain state from some other
states [79], e.g. ”in Fig. 3, state A=1 and state B=0 point
to state C, and state C has 0.7 chance to be 0 and 0.3
chance to be 1 in this case”. The nodes or states in Bayesian
networks can be binary values [80] to represent if a gene is
activated or not. The edges, which are depicted as arrows,
show the relationship between the two states. If state A
can regulate another state B, an arrow will point to state
B from state A. To demonstrate the probabilistic correlation
in a Bayesian network, the edges can be thicker to show a
higher probability [81]. Unlike Boolean networks, the edges
in Bayesian networks cannot form a loop [82].
Bayesian networks can be used to discover the reg-
ulatory genes and their target such as disease types by
inserting parent nodes [85]. The research from Yu et al.
[86] employed Bayesian networks to connect genetic and
metabolic networks, and they found that controlling the
level of HIF-1A helps alleviate the effects of hypoxia in
Alzheimer’s disease for early-stage patients. Kourou et al.
[87] analyzed the dynamic Bayesian networks of oral cancer
to predict its recurrence. Bayesian networks were applied by
Chudasamaet al. [88] for modeling ovarian cancer to identify
the gene with the higher levels of regulation.
Bayesian networks can be inferred from gene expression
data. Friedman [80] showed how to use gene expression
profiles from DNA microarrays to construct regulatory net-
works. The downside of using gene expression data is that it
is hard to get sufficient data for learning the interaction be-
tween hundreds of genes [89]. Kim et al. [90] used dynamic
Bayesian networks to deal with time delay information and
build cyclic networks from time series gene expression data.

5
Fig. 3. The diagram of inferring a Bayesian network. Sets of genes which are causally interacting with each others are selected by clustering [83].
Each set of genes formed a network called a network candidate. Score and search algorithm [84] are applied to find the most possible interaction
using the information among these candidates and decide the final bayesian network. In the network, the binary value in every nodes depends on
a certain probability. The aggregation to a nodes is the conditional probability of the receiving node (C) given the binary value of the source nodes
(A,B).
Needham et al. [82] inferred Bayesian networks using ma-
chine learning to find the parameters in the networks even
if the available data is incomplete. The common method for
inferring the Bayesian network is shown in Fig. 3.
The advantage of using Bayesian networks is its capa-
bility of treating noise from gene expression data [91] due
to sampling and discretization of the data [89]. Werhli et
al. [92] showed that adding adequate noise to all nodes in
Bayesian networks can help reconstruct the networks with
higher accuracy. The accuracy of Bayesian networks can also
be improved by reconstructing the network. Hartemink et
al. [93] proposed a scoring method to assess the accuracy of
Bayesian networks, thereby aiding in the reconstruction of
the networks or offering an approach for comparing differ-
ent networks. Werhli et al. [94] combined gene expression
data with two biological prior knowledge to reconstruct the
networks for higher accuracy.
Bayesian networks are suitable at modeling a gene reg-
ulatory network through noisy and sparse gene expression
data. However, the challenge for Bayesian networks is that
the computational complexity increases as selecting the gene
regulation network through a large amount of gene expres-
sion data. The other shortcoming is the directed acyclic
nature of Bayesian network that limits the model to describe
feedback loops.
2.2.3 Systems of differential equations
The dynamics of gene regulatory networks can be modeled
by chemical reaction kinetics [69]. Chemical kinetics is a
branch of dynamics, the science of motion [95], and it is the
study of the rates of chemical reactions [96]. The chemical
reactions can be translated to ordinary differential equations
by the laws of mass-action [97]. Chen et al. [98] showed the
chemical reactions in gene expression, such as transcription,
translation, and feedback loops from product proteins to
promoters, can be modeled by differential equations. The
equation in gene regulatory networks describes the concen-
tration change of a protein or a mRNA [99]. Gene regulatory
networks based on ordinary differential equations assume
the concentration of regulators is constant or linear [100].
If ordinary differential equations don’t provide enough in-
formation, single-molecule level models can be conducted
to capture more detail [79]. A gene regulatory network
modeled by systems of differential equations is shown in
Fig. 4.
Since the model needs high-quality data on kinetic pa-
rameters, ordinary differential equations only have a few
applications on real systems [79]. Von Dassow et al. [102]
constructed a dynamical model of the segment polarity gene
network to describe the interaction among the products of
five genes in Drosophila.Liet al. [103] applied differential
equations to study the dynamics behaviors of a three genes
(lacl,tetR, and cl) regulatory network with both time delays
and disturbances. Wu et al. [104] proposed a sparse additive
ordinary differential equation to construct a gene regulatory
network for T-cell activation and discovered new regulation
effects. Barbuti et al. [69] got the systems of ordinary differ-
ential equations of the lac operon gene regulatory networks
in the E. coli.
Nonlinear ordinary differential equations of gene regu-
latory networks can be simplified to facilitate the analysis
of the system [105]. Chen et al. [98] took the first-order
Taylor approximation to linearize the nonlinear transcrip-
tion function in their differential equations. Gebert et al.
[101] approximated the nonlinear term as a piecewise linear
function. However, simple linear systems cannot describe
the occurrence of multiple steady states, such as disease or
healthy states, or stable oscillatory states, such as calcium
oscillations and circadian rhythms [63].
The inference of gene regulatory networks can be ap-
plied both to determine the phenotype of biological regula-
tion and to design therapeutic strategies for genetic-based
diseases [106]. Cao et al. [107] proposed the generalized

6
Fig. 4. Ordinary differential equations model for transcriptional gene regulatory networks. (a) A small gene regulatory network composed of gene
S1,S2, and S3. (b) Ordinary differential equation model of the gene regulatory network adapted from [101]. [S1],[S2], and [S3]represent the mRNA
concentration of corresponding gene S1,S2, and S3. The parameters ki,j are production rate constant from mRNA ito mRNA j. The parameters γi
are the degradation rate of mRNA i.h+([Si], θi,j, mi,j )and h−([Si], θi,j , mi,j )are sigmoid functions, where θi,j represents the threshold constant
and mi,j represents the steepness constant depending on the reaction from mRNA jto mRNA i.
profiling method to estimate the parameters of ordinary
differential equations in a gene regulatory network from
microarray gene expression data. Ma et al. [108] inferred
all putative regulatory links in gene regulatory networks
using nonlinear ordinary differential equations from time-
series and steady-state data jointly. De Hoon et al. [109]
proposed a new method to infer a gene regulatory network
using linear differential equations from time course gene
expression data. Aubin-Frankowski et al. [110] offered a
new method using linear differential equations to infer gene
regulatory networks from scRNA-seq data.
Differential equations can be used if we are interested
in predicting the exact concentrations of the molecules [66].
Suarez et al. [111] described p53-Mdm2 system behavior, in
terms of the number of proteins, using ordinary differential
equations to represent the induction of p53-dependent cell
death in the scenario of Mdm2 overexpression. Verd et al.
[112] studied gap gene system of dipteran insects using
the concentrations of transcription-factor proteins (hb,Kr,
kni and gt) encoded by trunk gap genes to analyze the
sensitivity and steady states of the system. Barbier et al.
[113] studied the capability of the inducible toggle switch
circuit to affect an E. coli population exposed to different
concentrations of AHL and IPTG and their combinations.
Although the precision of the ordinary differential equa-
tions model is better than the discrete model, the required
information, and the computational resources for the quanti-
tative model are higher. The ordinary differential equations
model assumes continuous concentration changes and de-
terministic rates; however, these conditions will not hold
if the amount of molecules in the cell are low. It is still a
challenge to select the parameters for a high dimensional
ordinary differential equations model.
2.3 Modeling of cell signaling network
Modeling the behavior of cell signaling networks is im-
portant to understand cell biology in health and disease
[114]. Cell signaling is the process by which cells com-
municate with their environment and respond to external
stimuli that they sense there [115]. The overall mechanism in
cell communication is composed of signal reception, signal
transduction, and signal response [116]. The function of
communication with the environment is achieved through
several pathways that receive and process signals [117].
Signaling networks are the result of the interconnections be-
tween signaling pathways [118], [119]. Signaling networks
connect receptors to many different cellular machines, such
as biochemical molecules, mechanical functions, or electrical
signals [120]. Receptors in cell signaling are proteins either
inside a cell or on the membrane, which receive a signal
[121]. The output of signaling network is usually functional
outcomes such as proliferation, polarization of cells, or
migration [122].
Boolean modeling can be applied to those systems where
the organization of networks is more important than the
kinetic details of the individual interactions [123]. Boolean
model in cancer signaling networks can provide holis-
tic models capturing multi-scale, multi-cellular signaling
processes involved in cancer incidence and progression
[124]. Baur et al. [125] modeled different components using
Boolean networks in the growth factor signaling pathway
to study the efficacy of different drugs in cancer thera-
pies. Lee et al. [126] reconstructed a lung cancer Boolean
network model by incorporating major signaling pathways
associated with the FGFR signaling pathway to increase the
effectiveness of various targeted therapies for cancer. Sahin
et al. [127] identified c-MYC transcription factor as a novel
potential target protein in breast cancer cells using Boolean
network modeling on ERBB signaling network.
Bayesian networks describe pathway interactions in
terms of probabilistic influences of certain molecular com-
ponents upon other components [128]. Bayesian networks
can be used to revise existing knowledge or study potential
relationships in signaling pathways [129]. Agrahari et al.

7
[130] applied Bayesian network to classify acute myeloid
leukemia and myelodysplastic syndrome from microarray
data. Vundavilli et al. [131] developed a Bayesian net-
work to deduce the significant genes in the breast cancer
signaling network, including the JAK/STAT pathway, the
MAPK (mitogen-activated protein kinase) pathway, and the
PI3K/mTOR pathway. Azad et al. [132] proposed a method
called ’PathTurbEr’ (Pathway Perturbation Driver) to iden-
tify the breast cancer bio-markers in 13 perturbed signaling
pathways modeled by Bayesian networks.
Cell signaling networks can be described by a set of
ordinary differential equations [133]. The model of cell
signaling networks is shown in Fig. 5. Arkun et al. [134]
studied the overall effect of the autocrine feedback loop
on ERK (extracellular signal-regulated kinase) signaling
pathway using 46 ordinary differential equations and 17
algebraic equations. Dessauges et al. [135] studied ERK
dynamics in MAPK network with different perturbations
by a mathematical model consisting of the RAS GTPase
and the RAF/MEK/ERK network using ordinary differ-
ential equations. Sapega et al. [136] found that PI3K-Akt-
mTOR signaling cascade in MAPK signaling pathway can
be in metastable stationary state and the signaling cascade
can be triggered by exogenous stimuli (light, magnetism,
ultrasound, electrical pulses) [137].
Ordinary differential equations are the most common
models for cell signaling networks. Boolean networks are
Bayesian networks are applied to avoid the problems in
parameter estimation for differential equations models.
Bayesian networks are used for finding the significant genes
for diseases in a cell signaling network.
2.4 Modeling of metabolic network
Metabolism describes the series of biochemical reactions
that produce energy for the body to maintain biological
functions [139]. These biochemical reactions can be orga-
nized into several metabolic pathways based on a cer-
tain function or functions [140], [141]. Different pathways
share the same metabolic intermediates such that pathways
become interdependent and connected with one another,
whereby metabolism forms a highly branched, highly con-
nected network [142]. Metabolic networks are formed by a
collection of chemical compounds (metabolites), biochemi-
cal reactions, enzymes, and genes and the relations among
them [143]. Mathematical models can be constructed to
study the formation and adaptation of metabolic networks
[144].
Boolean networks is computationally efficient to study
large networks [145]. Kaleta et al. [146] applied Boolean net-
work on an E. coli metabolic network to predict growth phe-
notype on different carbon sources in the growth medium.
Boolean network can be used to find novel drug targets or
crucial genes for diseases [147]. Tamura et al. [148] applied a
Boolean model of genome-scale human metabolic networks
to selection of influential genes using gene expression data
from healthy and diseased (head and neck cancer) samples.
Tamura et al. [149] used integer linear programming (ILP)-
based method to study how to prohibit acetate and ethanol
production in an E. coli metabolic network modeled by
a Boolean network. Bayesian networks can be used for
the identification of novel metabolic biomarkers or for the
assessment of the predictive ability of a metabolic network
[150]. Kim et al. [151] applied Bayesian network on E. coli
metabolic network to study how the genetic perturbation,
lpdA gene knockout, affects E. coli metabolism. Zhang et
al. [152] considered the metabolic network of N-linked
glycosylations as a Bayesian network for the prediction of
glycoproteins produced by mammalian cells. Myte et al.
[153] applied learning-based Bayesian network approach in
one-carbon metabolic network and found that the plasma
concentration of folate, vitamin B6, and vitamin B2 may be
the important components for colorectal tumorigenesis.
Differential equations can be used to simulate the contin-
uous time dependent behavior of a metabolic system quan-
titatively [154]. The modeling of metabolic network through
ordinary differential equations is shown in Fig. 6. Shene et al.
[155] used ordinary differential equations in the metabolic
network model of the green microalga Chlamydomonas rein-
hardtii to predict the growth curve and starch production
of the Chlamydomonas reinhardtii. Woller et al. [156] ap-
plied ordinary differential equations in the modeling of the
metabolic network composed of the glucose-insulin module
and the βcell circadian oscillator to investigate the effect
of restricting food access to the normal rest phase. Luo et
al. [157] utilized ordinary differential equations to simulate
the dynamics of the arachidonic acid metabolic network
in human polymorphonuclear leukocytes for the study of
screening drug targets combinations.
Differential equations models are the most common
methods to model metabolic networks. Other simplified
models were applied to metabolic networks when the de-
tailed information is not needed. Boolean networks were
applied to analyze the impact of adding or deleting of
enzyme in a metabolic network. Bayesian networks were
applied to some large-scale metabolic networks to avoid
the problem of finding parameters in differential equations
models. The resources that are used for the modeling of the
three intracellular networks are listed in Table 1.
3 NE TWORK CON TRO L OF DISEASE PATHWAYS
In this section, we will focus on the control of the three
biological networks: gene regulatory network, cell signaling
network, and metabolic network.
For the gene regulatory networks, we first provide the
application focused on studying the behavior of a biological
system. Next, we will discuss the application of a melanoma
gene network for preventing disease phenotypes. In the
third paragraph, the studies focus on a class of gene reg-
ulatory networks with time delay. In the last paragraph,
we give some applications of controlling gene regulatory
networks using synthetic circuits.
For the cell signaling networks, the studies focus on
designing drug dosage strategies that can reach the desired
therapeutic result. For the metabolic networks, the control
objectives aim at maximizing the desired byproduct under
different conditions or restrictions.
3.1 Control of gene regulatory network
The study of gene regulatory networks provided insights
into the systems-level mechanisms of gene regulation that

8
Fig. 5. The ordinary differential equations model of cell signaling networks (adapted from [138]). (a)A cell signaling network consisting of two
signaling pathway with receptor P1and PA.P1to P3represent the the signaling proteins in the P1pathway. PAto PDrepresent the the signaling
proteins in the PApathway. (b)A hypothetical detailed illustration of the signaling network in (a). The pon the right of the protein notation P
represent the corresponding phosphoprotein. The phosphoproteins can be the catalyst for the dephosphorylation process. The ion the right of the
protein notation Prepresent the corresponding inactivated protein. The number on the arrows represent the number of the reaction and the letter
on the left denotes the reaction types. The reactions without the letter refer to the phosphorylation processes. The dephosphorylation processes
are denoted by the letter c. The protein synthetic processes are denoted by the letter s and the protein degradation processes are denoted by the
letter d. (c)The reaction rate vand the concentration rate d[P]/dt in the signaling network. (d)The building box of different reactions with their
corresponding reaction rate. [·]denotes the concentration of the protein in it. Vi,Kmi,kic ,kica ,Kmia ,kicb ,K mib ,kisf ,kisr ,and kid are
constant determined by experiments.
control growth, development, physiology, and stress re-
sponses [172]. Stamov et al. [173] proposed an impulsive
control strategy to a class of gene regulatory networks mod-
eled by fractional order differential equations by adding

9
Fig. 6. The ordinary differential equation model of a metabolic network. (a)A hypothetical metabolic network. (b)The intracellular reaction rates
and their chemical reactions in the metabolic network. (c)The extracellular reaction rates and their chemical reactions in the metabolic network.
(d)The ordinary differential equations model described by reaction rates and the rate of change of the metabolites concentration
TABLE 1
Resources for network modeling
Application Database and software Description Access Reference
Gene regulatory network Cell signaling gateway A database provides proteins informa-
tion based on their functional states and
the parameters associated with each sig-
naling function.
Free [62], [158]
Gene regulatory network Saccharomyces genome
database
A sequence database organizes Saccha-
romyces cerevisiae genomic sequence into
datasets for molecular biologists.
Free [159], [160]
Gene regulatory network iRegulon A software detects the transcription fac-
tors, the targets and the motifs from
a co-expressed gene set to reverse-
engineer a gene regulatory network.
Free [161], [162]
Gene regulatory network Kyoto Encyclopedia of
Genes and Genomes
A collection of databases consists of ge-
nomic, chemical, and network informa-
tion.
Free [86], [163],
[164]
Gene regulatory network
Cell signaling network
NCBI Gene Expression Om-
nibus
A database provides high throughput
gene expression data.
Limited
free
[88], [130],
[131], [132]
[165]
Gene regulatory network Yeast Search for Transcrip-
tional Regulators and Con-
sensus Tracking
A database provides regulatory associa-
tions between transcription factors and
target genes in Saccharomyces cerevisiae.
Free [166], [167]
Cell signaling network Genomics of Drug Sensitiv-
ity in Cancer
A database provides information on
drug sensitivity in cancer cells and
molecular markers of drug response.
Free [126], [168]
Cell signaling network
Metabolic network
BioModels Database A database provides access to quantita-
tive models of dynamic models of bio-
logical processes.
Free [169], [170],
[171]
impulsive changes in the concentration of mRNAs and pro-
teins as control input to improve the stability behavior of the
network and applied it to a repressilator, a cyclic negative-
feedback loop composed of lacl,tetR or cl and their corre-
sponding promoters in E. coli. Pezzotta et al. [174] applied
optimal control theory to a gene regulatory network that
captures the patterning dynamics in the ventral region of
the developing neural tube to make the set of concentrations
of the components in the network reach the desired states
corresponding to a certain cell-fate decision during tissue
patterning in embryo development by choosing the control
inputs: morphogen activator Gli-A and repressor Gli-R. In-

10
stead of studying the behavior of a biological system, more
researches have focused on the control of certain diseases.
A gene regulatory network can be used to design
different control strategies for affecting network dynam-
ics to avoid disease phenotypes [175], [176]. Datta et al.
[177] formulated the optimal control problem for a general
Markovian genetic regulatory network and applied it to a
melanoma gene network using pirin gene as the control
input for the prevention of metastasis by down-regulating
the WNT5A gene. Datta et al. [178] designed an optimal
control strategy that can be implemented in the imperfect
information case where perfect information about the ex-
pression level of each gene in the melanoma gene network
is not available. Pal et al. [179] designed an optimal infinite-
horizon control for the same melanoma gene network to
prevent in the case that there is no terminal state which may
lead to infinite total cost. Faryabi et al. [180] proposed an
approximate stochastic control method based on reinforce-
ment learning that mitigates the curses of dimensionality
and eliminates the impediment of model estimation in the
melanoma gene network. Bouaynaya et al. [181] proposed
an inverse perturbation control that minimizes the overall
energy of change between the original and controlled (per-
turbed) melanoma gene regulatory networks and showed
that the undesirable high metastatic states can be shifted to
the chosen healthy states. Imani et al. [182] applied the par-
tially observable Boolean dynamical system (POBDS) model
with the Gaussian process and reinforcement learning for
control of partially observed melanoma gene regulatory
networks through Gaussian gene expression measurements
at each time point to prevent WNT5A gene to be upregu-
lated using RET1 gene as a control input with uncertainty
modeled by Bernoulli distribution. Imani et al. [183] applied
the Boolean Kalman filter to simultaneously monitor and
control the same melanoma gene regulatory network and
found that RET1 gene is a better control input for reducing
the activation of WNT5A. Imani et al. [184] developed a
Bayesian Inverse Reinforcement Learning (BIRL) approach
to estimate the undesirable state for the level of the genes
in the melanoma gene regulatory network from gene ex-
pression data and used a state-feedback controller to shift
the dynamics of the network away from states associated
with metastasis for investigating the performance of their
proposed methodology. Imani et al. [185] applied optimal
control strategy with estimated undesirable state obtained
from BIRL approach to down-regulate the WNT5A gene in
the melanoma gene regulatory network using RET1 gene as
the control input. The optimal control strategies has been
improved to control the undesired states in gene regulatory
network in different constraints, but the way to actually
manipulate the control gene hasn’t been proposed to make
these methods applicable.
Time delays, which exist in transcription, translation,
and translocation processes, is the key factors affecting the
stability of a gene regulatory network model [186]. Huang et
al. [187] adjusted the fractional order and feedback gain of
their proposed hybrid controller to suppress the oscillatory
dynamics in the change of the concentration of mRNA,
protein, and sRNA for a two-gene regulatory network,
adopted from a Hes1 gene network [188], mediated by
sRNAs with multiple delays. Liao et al. [189] designed a
state feedback controller that is globally robustly stable for
their proposed gene regulatory network model considering
the transcriptional time delay with uncertain parameters
using the concentration of all the mRNAs to design the
control inputs and applied it to an E. coli system. Zeng et
al. [190] designed a H∞feedback controllers to regulate the
noise influences arising from random variation of the con-
centration of mRNAs and proteins using the general model
adopted from [191]. Hu et al. [192] applied an adaptive
feedback control scheme to achieve the global asymptotic
stability for a class of gene regulatory networks with mixed
delays which include both the finite distributed time delay
and the discrete time delay. Yu et al. [193] studied the mean-
square stability, robust H∞control and robust uniformly
bounded control for the delayed repressilator in E. coli with
both the parameter uncertainties and stochastic disturbance
using mRNAs of lacl,tetR or cl as control inputs. Liu et al.
[194] applied the finite-time H∞control of repressilator in E.
coli with random delays to make the concentration of all the
mRNA and proteins become stochastic bounded using the
concentrations of mRNA to design the control input. Moradi
et al. [195] redesigned a robust integral sliding mode control
for a class of perturbed delayed switched gene regulatory
networks with subsystems to guarantee robust exponential
or asymptotic stability of the network and applied it on
a repressilator in E. coli. Liu et al. [196] designed a linear
intermittent controller to exponentialy stabilize a class of
gene regulatory networks modeled by mRNAs and proteins
with mixed delays. Li et al. [197] designed a sampled-data
controller to stabilize a class of gene regulatory networks
with leakage delays that affects the negative feedback terms
in the network. Zhang et al. [198] proposed a guaranteed
cost control for a class of gene regulatory networks with
multiple time-varying discrete delays and multiple constant
distributed delays on the mRNA and protein concentrations
such that the concentrations can be restricted by an upper
bound of a defiened quadratic cost function. Xue et al.
[199] designed state-feedback controllers for a class of gene
regulatory networks with multiple delays and bounded dis-
turbances to ensure that the mRNA and protein concentra-
tions can converge to a given region. Narayanan et al. [200]
proposed a hybrid impulsive and sampled-data controller
to stabilize a class of delayed genetic regulatory networks
with the diffusion of mRNAs and proteins assuming that
the gene regulatory systems are not spatially homogeneous.
Padmaja et al. [201] designed a H∞/passive full state feed-
back controller to ensure the stability of a general delayed
gene regulatory network under disturbances modeled by
fractional-order differential equations with the concentra-
tion of mRNAs and proteins as states such that the network
can be stabilize with less control effort (smaller gains). The
strategies for overcoming the time-delay problem in the
control of the gene regulatory network has been widely
proposed. However, those methods need to be applied on
the real experiments to prove their effectiveness.
Synthetic biology refers to any use of genetic engineering
to design and build nonnative biological systems [202].
The application of control engineering to synthetic biology
focuses on the design and implementation of ‘controllers’
to engineer robust and modular biomolecular networks
carrying out desired functions in the cell [203]. Baldissera

11
et al. [204] provided a framework based on supervisory
control theory (SCT) to guide the design of synthetic genes
for a gene regulatory network modeled by Boolean network,
thereby changing the activity of the genes in the network
from initial states to desired states. Chen et al. [205] pro-
posed a systematic design method for the synthetic gene
network modeled by stochastic differential equations using
Takagi–Sugeno fuzzy method to track the desired behaviors
considering the intrinsic parameter fluctuations, uncertain
interactions with unknown molecules and environmental
disturbances and applied their method on two synthetic net-
works in E. coli to confirm the performance. Shokouhi-Nejad
et al. [206] applied a robust H∞based controller on the syn-
thetic oscillatory network for E. coli to stabilize the dynamics
of the gene regulatory networks for all admissible uncer-
tainties, nonlinearities, stochastic perturbations, and time-
varying delays. Menolascina et al. [207] designed a switched
control to regulate the amount of the CBF1 gene products in
a synthetic gene regulatory network, IRMA (In-vivo assess-
ment of Reverse-engineering and Modelling Approaches),
developed in yeast S. Cerevisiae, by modulating the amount
of galactose being fed to the network. Agrawal et al. [208]
constructed a synthetic biomolecular integral controller that
precisely regulates the protein production rate of the deGFP
reporter gene by the concentration of the P70a promoter in
an E. coli system. Shannon et al. [209] presented a new in
vivo implementation of a real-time external feedback control
scheme with a relay control strategy using the chemical
inducer Isopropyl β-D-1-thiogalactopyranoside (IPTG) as a
control input to regulate the average fluorescence output
from E. coli. The synthetic circuits can be realized on the
real biological systems; nevertheless, the performance of the
result has to be improved by advanced control strategies.
3.2 Control of cell signaling network
The control of cell signaling networks aims at investigating
the drug dosage strategies by observing the responses of the
disease related proteins through the network model. Lee et
al. [210] utilized optimal control theory for a IFN-β/JAK
induced STAT signalling network to design an optimal infu-
sion strategy of anti-cancer drugs thereby minimizing tumor
volume and the amount of the drugs: IFN-βand cisplatin.
Camacho et al. [211] proposed a bone remodeling model for
osteoporosis therapy and a bone metastasis model for bone
metastasis treatment based on transforming growth factor
β(TGFβ) pathway and Wnt pathway and they applied
optimal control to achieve the desired bone mass density
level using bisphosphonates, TGFβinhibition, and Wnt in-
put for the osteoporosis therapy and using bisphosphonates,
TGFβinhibition, Wnt inhibition, and chemotherapy for the
bone metastasis treatment. Jung et al. [212] applied optimal
control to regulate intracellular signaling networks of miR-
451–AMPK–mTOR–cell cycle dynamics with the goal of
keeping high levels of miR-451 and mTOR while minimiz-
ing glucose and drug intravenous administration infusions,
thereby preventing rapid tumor growth, hyperglycemia,
and further drug complications. Ooi et al. [213] designed an
integral feedback controller realized by a synthetic circuit
called transcription activator like effector (TALE) that can
maintain the concentration of p53 in a high constant level
(healthy state) on a p53-MDM2-miRNA network with step
input perturbation representing the effect of the disease
trying to reduce the concentration of p53 to a constant
low level (disease state). Azam et al. [214] designed a
non-linear Lyapunov controller for a p53/Mdm2 network
combined with a PID controller for a Nutlin physiological-
based kinetic (PBK) model to achieve sustained concentra-
tion of p53 using the drug Nutlin dosage. Rizwan Azam et
al. [215] designed a dynamic sliding mode controller in a
p53/Mdm2 network with input disturbance and parametric
uncertainty to achieve a sustained level of p53 using drug
Nutlin for cancer treatment. Yasin et al. [216] designed two
PID controllers for a p53/Mdm2 network to get the desired
p53 concentration using drug Nutlin for cancer therapy.
Bano et al. [217] designed a model-based chattering free
sliding mode control (CFSMC) for a p53/Mdm2 network
considering measurement noise, parametric uncertainties
and the input disturbance to track the desired concentration
of p53 protein for three levels of sustained p53 response and
an oscillatory p53 response using drug Nutlin. Although
some control strategies for drug dosage were proposed, the
validation of these results through clinical trails is needed
for practical application.
3.3 Control of metabolic network
The control of metabolic network is all focused on increas-
ing the production of the desired bio-products using less
resources. Creutzburg et al. [218] designed a gain scheduled
controller for the yeast model of the metabolic network
in Saccharomyces cerevisiae to maintain the desired biomass
concentration with disturbances in the feed concentration
and with the noise in the measurement of CO2production
by adjusting the feed rate of glucose. Hjersted et al. [219] ap-
plied an optimal control strategy that maximize ethanol pro-
ductivity and/or ethanol yield on glucose with a yeast Sac-
charomyces cerevisiae model to balance high production rates
and efficient substrate usage by adjusting glucose feed flow
rate and dissolved oxygen concentration. Kumar et al. [220]
proposed a robust economic nonlinear predictive controller
using an E. coli metabolic network to maximize the biomass
at the end of the batch biochemical processes by manipulat-
ing the feeding and perfusion (removing) rate of glucose
in the presence of process disturbances and parametric
uncertainties. Jabarivelisdeh et al. [221] applied a model
predictive control of a fed-batch bioreactor in an E. coli
metabolic-genetic network to increase ethanol productivity
by adjusting glucose feeding pattern and the regulation
time. Jabarivelisdeh et al. [222] proposed a model predictive
control algorithm on a reduced metabolic-genetic network
model of E. coli to maximize ethanol production by adjust-
ing the limited-oxygen supply to the E. coli. De Oliveira et
al. [223] proposed a model predictive controller to maxi-
mize ethanol production of Saccharomyces cerevisiae with the
model based on a consensus yeast metabolic network by
manipulating the glucose feed and the dissolved oxygen
level. Hebing et al. [224] used a robust multistage nonlinear
model predictive control in a reduced metabolic network
for Chinese Hamster Ovary (CHO) cells to maximize the
cell concentration in the beginning of the process and the
product concentration in the later phase by adjusting the

12
Fig. 7. The summary for the control of biological networks. The first row concludes the control of gene regulatory networks. Transcription factors
are the control inputs to perturb the network. The control objectives shown in the right hand side are preventing disease phenotypes, stabilize the
network, and regulate certain gene level. The second row concludes the control of cell signaling networks. Drug molecules are commonly used as
the control input and the control objective can be regulating the concentration level of certain proteins. The last row shows the control of metabolic
networks. The control inputs varies depend on the application. The control objective aims at maximizing the desired byproduct production. The
icons were adopted from Biorender.
pH value of the cell and the feed rate of the main substrate.
Murthy et al. [225] developed an optimal controller based on
iterative gradient descent algorithm using a simplified yeast
metabolic network to improve the production of ethanol
from corn in dry grind corn process under temperature
and pH disturbances with lower enzyme usage and reduced
cooling requirement. Oyarz´
un et al. [226] applied an operon
control circuit to an unbranched metabolic network in the
tryptophan pathway of E. coli thereby upregulating enzyme
production to compensate flux perturbations. Planqu´
e et al.
[227] developed an adaptive control theory called Specific
Flux (q) Optimization by Robust Adaptive Control (qORAC)
that may be applied to molecular circuits to minimize spe-
cific rates of metabolic subnetworks at fixed growth rate in
the face of varying environmental parameters. The control
of metabolic network is widely applied to the production of
bio-based products; however, the control strategies haven’t
been utilized for the human metabolic networks model. The
summary for the control of the three biological networks is
depicted in Fig. 7. The resources that are used for the control
of the three intracellular networks are listed in Table 2.
4 CONCLUSION AND OUTLOOK
A model that can accurately represent cellular functions
and that is experimentally testable is required to elucidate
the dynamical behavior of a biological system. For a large-
scale biological system, Boolean network is effective for
capturing the qualitative behavior of the system with low
complexity. However, the noise in time series data and the
lack of methods to define unknown Boolean functions is still
a challenge. Bayesian networks are suitable for expressing
causal interaction to handle noise in biological data. The
problem of Bayesian network is the computational complex-
ity for modeling large-scale networks. A biological network
described by ordinary differential equations can provide
detailed information about the time evolution of the bio-
molecules, but the computational complexity is higher than
the discrete models and the parameters are hard to infer
from gene expression data which are usually sparse and
noisy.
The control of gene regulatory networks has been widely
studied for preventing disease phenotype or producing the
desired bio-molecules; however, these methods only used

13
TABLE 2
Resources for network control
Model Software Website Access Relevant studies
Gene regulatory network MATLAB robust control
toolbox (include LMI
toolbox)
https://www.mathworks.com/
products/robust.html
Paid [190], [200], [205], [206]
Gene regulatory network YALMIP toolbox https://yalmip.github.io/ Free [198], [201]
Gene regulatory network COMSOL Multiphysics
3.5a
https://www.comsol.com/ Paid [207]
Gene regulatory network MATLAB optimization
toolbox
https://www.mathworks.com/
products/optimization.html
Paid [209]
Cell signaling network PyDSTool https://pydstool.github.io/
PyDSTool/FrontPage.html
Free [211]
Cell signaling network MATLAB numerical bi-
furcation toolbox MAT-
CONT
https://sourceforge.net/projects/
matcont/files/
Paid [212]
Metabolic network Ipopt (Interior Point Op-
timizer)
https://coin-or.github.io/Ipopt/ Free [221], [222], [223]
Metabolic network DifferentialEquations.jl https://docs.juliahub.com/
DifferentialEquations/UQdwS/
6.15.0/
Free [223]
Metabolic network High-Performance
Liquid Chromatography
(HPLC) software
(version 3.01, Waters,
Milford, MA)
https://www.waters.com/
nextgen/us/en.html
Paid [225]
numerical simulation to prove their capabilities. These con-
trol strategies should be applied to real biological systems
for validation. Synthetic biology might be a suitable way
to verify those methods. The model of the cell signaling
networks usually includes more than twenty proteins. Most
of the existing control methods simplified the models to
less than ten proteins to reduce the complexity of designing
the controller. These methods should be validated in vivo to
verify whether the simplified model is capable of meeting
the control objectives. The control of metabolic networks
has been implemented in bioreactors for producing desired
byproducts. The next step for the study of controlling the
metabolic network could be the control of human or disease
metabolic networks to design drug dosage strategies once
the model has been developed.
REFERENCES
[1] V. Kumar, A. K. Abbas, and J. C. Aster, Robbins basic pathology
e-book. Elsevier Health Sciences, 2017.
[2] X. Li, X. Wang, and M. Snyder, “Systematic investigation of
protein–small molecule interactions,” IUBMB life, vol. 65, no. 1,
pp. 2–8, 2013.
[3] P. R. Somvanshi and K. Venkatesh, “A conceptual review on
systems biology in health and diseases: from biological networks
to modern therapeutics,” Systems and synthetic biology, vol. 8,
no. 1, pp. 99–116, 2014.
[4] S. Wuchty, E. Ravasz, and A.-L. Barab ´
asi, “The architecture of
biological networks,” in Complex systems science in biomedicine,
pp. 165–181, Springer, 2006.
[5] Z. N. Oltvai and A.-L. Barab´
asi, “Life’s complexity pyramid,”
science, vol. 298, no. 5594, pp. 763–764, 2002.
[6] C. Li, M. Liakata, and D. Rebholz-Schuhmann, “Biological net-
work extraction from scientific literature: state of the art and
challenges,” Briefings in bioinformatics, vol. 15, no. 5, pp. 856–877,
2014.
[7] M. Garrido-Rodriguez, K. Zirngibl, O. Ivanova, S. Lobentanzer,
and J. Saez-Rodriguez, “Integrating knowledge and omics to
decipher mechanisms via large-scale models of signaling net-
works,” Molecular Systems Biology, vol. 18, no. 7, p. e11036, 2022.
[8] P. Zhang and Y. Itan, “Biological network approaches and ap-
plications in rare disease studies,” Genes, vol. 10, no. 10, p. 797,
2019.
[9] A. Del Sol, R. Balling, L. Hood, and D. Galas, “Diseases as
network perturbations,” Current opinion in biotechnology, vol. 21,
no. 4, pp. 566–571, 2010.
[10] J. X. Hu, C. E. Thomas, and S. Brunak, “Network biology con-
cepts in complex disease comorbidities,” Nature Reviews Genetics,
vol. 17, no. 10, pp. 615–629, 2016.
[11] X. Liu, Z. Hong, J. Liu, Y. Lin, A. Rodr´
ıguez-Pat´
on, Q. Zou,
and X. Zeng, “Computational methods for identifying the critical
nodes in biological networks,” Briefings in bioinformatics, vol. 21,
no. 2, pp. 486–497, 2020.
[12] S. Naylor and J. Y. Chen, “Unraveling human complexity and
disease with systems biology and personalized medicine,” Per-
sonalized medicine, vol. 7, no. 3, pp. 275–289, 2010.
[13] Y. Liang and A. Kelemen, “Dynamic modeling and network ap-
proaches for omics time course data: overview of computational
approaches and applications,” Briefings in bioinformatics, vol. 19,
no. 5, pp. 1051–1068, 2018.
[14] L. I. Furlong, “Human diseases through the lens of network
biology,” Trends in genetics, vol. 29, no. 3, pp. 150–159, 2013.
[15] R. Yue and A. Dutta, “Computational systems biology in disease
modeling and control, review and perspectives,” npj Systems
Biology and Applications, vol. 8, no. 1, pp. 1–16, 2022.
[16] B. H. Junker and F. Schreiber, Analysis of biological networks. John
Wiley & Sons, 2011.
[17] T. Aittokallio and B. Schwikowski, “Graph-based methods for
analysing networks in cell biology,” Briefings in bioinformatics,
vol. 7, no. 3, pp. 243–255, 2006.
[18] R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and
U. Alon, “Network motifs: simple building blocks of complex
networks,” Science, vol. 298, no. 5594, pp. 824–827, 2002.
[19] S. S. Shen-Orr, R. Milo, S. Mangan, and U. Alon, “Network motifs
in the transcriptional regulation network of escherichia coli,”
Nature genetics, vol. 31, no. 1, pp. 64–68, 2002.
[20] X. Ma and L. Gao, “Biological network analysis: insights into
structure and functions,” Briefings in functional genomics, vol. 11,
no. 6, pp. 434–442, 2012.
[21] J.-D. J. Han, “Understanding biological functions through molec-
ular networks,” Cell research, vol. 18, no. 2, pp. 224–237, 2008.
[22] E. Wong, B. Baur, S. Quader, and C.-H. Huang, “Biological
network motif detection: principles and practice,” Briefings in
bioinformatics, vol. 13, no. 2, pp. 202–215, 2012.

14
[23] X. Wang, E. Dalkic, M. Wu, and C. Chan, “Gene module level
analysis: identification to networks and dynamics,” Current opin-
ion in biotechnology, vol. 19, no. 5, pp. 482–491, 2008.
[24] I. Tavassoly, J. Goldfarb, and R. Iyengar, “Systems biology primer:
the basic methods and approaches,” Essays in biochemistry, vol. 62,
no. 4, pp. 487–500, 2018.
[25] A. Al-Aamri, K. Taha, Y. Al-Hammadi, M. Maalouf, and D. Ho-
mouz, “Analyzing a co-occurrence gene-interaction network to
identify disease-gene association,” BMC bioinformatics, vol. 20,
no. 1, pp. 1–15, 2019.
[26] C. Klein, A. Marino, M.-F. Sagot, P. Vieira Milreu, and M. Brilli,
“Structural and dynamical analysis of biological networks,” Brief-
ings in functional genomics, vol. 11, no. 6, pp. 420–433, 2012.
[27] P. Villoslada, L. Steinman, and S. E. Baranzini, “Systems biol-
ogy and its application to the understanding of neurological
diseases,” Annals of Neurology: Official Journal of the American
Neurological Association and the Child Neurology Society, vol. 65,
no. 2, pp. 124–139, 2009.
[28] R. J. Prill, P. A. Iglesias, and A. Levchenko, “Dynamic properties
of network motifs contribute to biological network organization,”
PLoS biology, vol. 3, no. 11, p. e343, 2005.
[29] F. Ay, F. Xu, and T. Kahveci, “Scalable steady state analysis of
boolean biological regulatory networks,” PloS one, vol. 4, no. 12,
p. e7992, 2009.
[30] Z. Zi, “Sensitivity analysis approaches applied to systems biology
models,” IET systems biology, vol. 5, no. 6, pp. 336–346, 2011.
[31] D. Hu and J.-M. Yuan, “Time-dependent sensitivity analysis of
biological networks: coupled mapk and pi3k signal transduction
pathways,” The journal of physical chemistry A, vol. 110, no. 16,
pp. 5361–5370, 2006.
[32] H. Kitano, “Systems biology: a brief overview,” science, vol. 295,
no. 5560, pp. 1662–1664, 2002.
[33] H. Song, P. Smolen, E. Av-Ron, D. A. Baxter, and J. H. Byrne,
“Bifurcation and singularity analysis of a molecular network for
the induction of long-term memory,” Biophysical journal, vol. 90,
no. 7, pp. 2309–2325, 2006.
[34] J. D. Orth, I. Thiele, and B. Ø. Palsson, “What is flux balance
analysis?,” Nature biotechnology, vol. 28, no. 3, pp. 245–248, 2010.
[35] B. J. Daigle, B. S. Srinivasan, J. A. Flannick, A. F. Novak, and
S. Batzoglou, “Current progress in static and dynamic modeling
of biological networks,” Systems Biology for Signaling Networks,
pp. 13–73, 2010.
[36] E. Liu, L. Li, and L. Cheng, “Gene regulatory network review,”
in Encyclopedia of Bioinformatics and Computational Biology, 2019.
[37] L. D. Moore, T. Le, and G. Fan, “Dna methylation and its basic
function,” Neuropsychopharmacology, vol. 38, no. 1, pp. 23–38,
2013.
[38] D. Molina-Serrano, D. Kyriakou, and A. Kirmizis, “Histone mod-
ifications as an intersection between diet and longevity,” Frontiers
in genetics, vol. 10, p. 192, 2019.
[39] J. L. Miller and P. A. Grant, “The role of dna methylation and
histone modifications in transcriptional regulation in humans,”
Epigenetics: Development and Disease, pp. 289–317, 2013.
[40] G. Wang, F. Wang, Q. Huang, Y. Li, Y. Liu, and Y. Wang, “Un-
derstanding transcription factor regulation by integrating gene
expression and dnase i hypersensitive sites,” BioMed research
international, vol. 2015, 2015.
[41] D. S. Latchman, “Transcription factors: an overview,” The interna-
tional journal of biochemistry & cell biology, vol. 29, no. 12, pp. 1305–
1312, 1997.
[42] S. Clancy et al., “Rna splicing: introns, exons and spliceosome,”
Nature Education, vol. 1, no. 1, p. 31, 2008.
[43] D. Most, L. Ferguson, and R. A. Harris, “Molecular basis of
alcoholism,” Handbook of clinical neurology, vol. 125, pp. 89–111,
2014.
[44] M. L. Hastings and A. R. Krainer, “Pre-mrna splicing in the new
millennium,” Current opinion in cell biology, vol. 13, no. 3, pp. 302–
309, 2001.
[45] M. R. Green, “Pre-mrna splicing,” Annual review of genetics,
vol. 20, no. 1, pp. 671–708, 1986.
[46] A. J. Lopez, “Alternative splicing of pre-mrna: developmental
consequences and mechanisms of regulation,” Annual review of
genetics, vol. 32, p. 279, 1998.
[47] Y. Lee and D. C. Rio, “Mechanisms and regulation of alternative
pre-mrna splicing,” Annual review of biochemistry, vol. 84, p. 291,
2015.
[48] N. A. Faustino and T. A. Cooper, “Pre-mrna splicing and human
disease,” Genes & development, vol. 17, no. 4, pp. 419–437, 2003.
[49] T. X. Lu and M. E. Rothenberg, “Microrna,” Journal of allergy and
clinical immunology, vol. 141, no. 4, pp. 1202–1207, 2018.
[50] N. Bushati and S. M. Cohen, “microrna functions,” Annu. Rev.
Cell Dev. Biol., vol. 23, pp. 175–205, 2007.
[51] R. W. Carthew, “Gene regulation by micrornas,” Current opinion
in genetics & development, vol. 16, no. 2, pp. 203–208, 2006.
[52] S. R. Neves, P. T. Ram, and R. Iyengar, “G protein pathways,”
Science, vol. 296, no. 5573, pp. 1636–1639, 2002.
[53] A. M. Weissman, N. Shabek, and A. Ciechanover, “The predator
becomes the prey: regulating the ubiquitin system by ubiqui-
tylation and degradation,” Nature reviews Molecular cell biology,
vol. 12, no. 9, pp. 605–620, 2011.
[54] K. Husnjak and I. Dikic, “Ubiquitin-binding proteins: decoders of
ubiquitin-mediated cellular functions,” Annual review of biochem-
istry, vol. 81, pp. 291–322, 2012.
[55] K. Haglund and I. Dikic, “Ubiquitylation and cell signaling,” The
EMBO journal, vol. 24, no. 19, pp. 3353–3359, 2005.
[56] A. M. Andreou and N. Tavernarakis, “Sumoylation and cell
signalling,” Biotechnology Journal: Healthcare Nutrition Technology,
vol. 4, no. 12, pp. 1740–1752, 2009.
[57] J. Zhao, “Sumoylation regulates diverse biological processes,”
Cellular and molecular life sciences, vol. 64, no. 23, pp. 3017–3033,
2007.
[58] F. Ardito, M. Giuliani, D. Perrone, G. Troiano, and L. Lo Muzio,
“The crucial role of protein phosphorylation in cell signaling
and its use as targeted therapy,” International journal of molecular
medicine, vol. 40, no. 2, pp. 271–280, 2017.
[59] F. Emmert-Streib, M. Dehmer, and B. Haibe-Kains, “Gene regu-
latory networks and their applications: understanding biological
and medical problems in terms of networks,” Frontiers in cell and
developmental biology, vol. 2, p. 38, 2014.
[60] L. Chen, D. Kulasiri, and S. Samarasinghe, “A novel data-driven
boolean model for genetic regulatory networks,” Frontiers in
physiology, vol. 9, p. 1328, 2018.
[61] H. Bolouri and E. H. Davidson, “Modeling transcriptional regu-
latory networks,” BioEssays, vol. 24, no. 12, pp. 1118–1129, 2002.
[62] S. Martin, Z. Zhang, A. Martino, and J.-L. Faulon, “Boolean dy-
namics of genetic regulatory networks inferred from microarray
time series data,” Bioinformatics, vol. 23, no. 7, pp. 866–874, 2007.
[63] M. Hecker, S. Lambeck, S. Toepfer, E. Van Someren, and
R. Guthke, “Gene regulatory network inference: data integration
in dynamic models—a review,” Biosystems, vol. 96, no. 1, pp. 86–
103, 2009.
[64] S. A. Kauffman, “Metabolic stability and epigenesis in randomly
constructed genetic nets,” Journal of theoretical biology, vol. 22,
no. 3, pp. 437–467, 1969.
[65] R.-S. Wang, A. Saadatpour, and R. Albert, “Boolean modeling in
systems biology: an overview of methodology and applications,”
Physical biology, vol. 9, no. 5, p. 055001, 2012.
[66] T. Schlitt and A. Brazma, “Current approaches to gene regulatory
network modelling,” BMC bioinformatics, vol. 8, no. 6, pp. 1–22,
2007.
[67] J. D. Schwab, S. D. K ¨
uhlwein, N. Ikonomi, M. K ¨
uhl, and H. A.
Kestler, “Concepts in boolean network modeling: What do they
all mean?,” Computational and structural biotechnology journal,
vol. 18, pp. 571–582, 2020.
[68] P. Bloomingdale, V. A. Nguyen, J. Niu, and D. E. Mager, “Boolean
network modeling in systems pharmacology,” Journal of pharma-
cokinetics and pharmacodynamics, vol. 45, no. 1, pp. 159–180, 2018.
[69] R. Barbuti, R. Gori, P. Milazzo, and L. Nasti, “A survey of gene
regulatory networks modelling methods: from differential equa-
tions, to boolean and qualitative bioinspired models,” Journal of
Membrane Computing, vol. 2, no. 3, pp. 207–226, 2020.
[70] H. F. Fumia and M. L. Martins, “Boolean network model for
cancer pathways: predicting carcinogenesis and targeted therapy
outcomes,” PloS one, vol. 8, no. 7, p. e69008, 2013.
[71] J. Liang and J. Han, “Stochastic boolean networks: an efficient
approach to modeling gene regulatory networks,” BMC systems
biology, vol. 6, no. 1, pp. 1–21, 2012.
[72] N. S. Taou, D. W. Corne, and M. A. Lones, “Investigating the use
of boolean networks for the control of gene regulatory networks,”
Journal of computational science, vol. 26, pp. 147–156, 2018.
[73] N. Le Novere, “Quantitative and logic modelling of molecular
and gene networks,” Nature Reviews Genetics, vol. 16, no. 3,
pp. 146–158, 2015.

15
[74] S. Liang, S. Fuhrman, and R. Somogyi, “Reveal, a general reverse
engineering algorithm for inference of genetic network architec-
tures,” in Biocomputing, vol. 3, 1998.
[75] T. Akutsu, S. Miyano, and S. Kuhara, “Inferring qualitative
relations in genetic networks and metabolic pathways,” Bioin-
formatics, vol. 16, no. 8, pp. 727–734, 2000.
[76] K. Kobayashi and K. Hiraishi, “Optimal control of gene regula-
tory networks with effectiveness of multiple drugs: A boolean
network approach,” BioMed research international, vol. 2013, 2013.
[77] R. Albert, “Boolean modeling of genetic regulatory networks,” in
Complex networks, pp. 459–481, Springer, 2004.
[78] J. Saez-Rodriguez, L. G. Alexopoulos, M. Zhang, M. K. Mor-
ris, D. A. Lauffenburger, and P. K. Sorger, “Comparing sig-
naling networks between normal and transformed hepatocytes
using discrete logical modelscomparative networks of normal
and transformed hepatocytes,” Cancer research, vol. 71, no. 16,
pp. 5400–5411, 2011.
[79] G. Karlebach and R. Shamir, “Modelling and analysis of gene
regulatory networks,” Nature reviews Molecular cell biology, vol. 9,
no. 10, pp. 770–780, 2008.
[80] N. Friedman, “Inferring cellular networks using probabilistic
graphical models,” Science, vol. 303, no. 5659, pp. 799–805, 2004.
[81] N. Friedman, M. Linial, I. Nachman, and D. Pe’er, “Using
bayesian networks to analyze expression data,” Journal of com-
putational biology, vol. 7, no. 3-4, pp. 601–620, 2000.
[82] C. J. Needham, J. R. Bradford, A. J. Bulpitt, and D. R. Westhead,
“A primer on learning in bayesian networks for computational
biology,” PLoS computational biology, vol. 3, no. 8, p. e129, 2007.
[83] P. Spirtes, C. Glymour, R. Scheines, S. Kauffman, V. Aimale, and
F. Wimberly, “Constructing bayesian network models of gene
expression networks from microarray data.” 2000.
[84] P. Larranaga, H. Karshenas, C. Bielza, and R. Santana, “A review
on evolutionary algorithms in bayesian network learning and
inference tasks,” Information Sciences, vol. 233, pp. 109–125, 2013.
[85] E. Peeling, A. Tucker, and P. A. t’Hoen, “Discovery of local
regulatory structure from microarray gene expression data using
bayesian networks,” in Proceedings of the annual workshop on Intel-
ligent Data Analysis in bioMedicine And Pharmacology (IDAMAP),
2007.
[86] H. Yu and R. H. Blair, “Integration of probabilistic regulatory
networks into constraint-based models of metabolism with appli-
cations to alzheimer’s disease,” BMC bioinformatics, vol. 20, no. 1,
pp. 1–12, 2019.
[87] K. Kourou, G. Rigas, K. P. Exarchos, C. Papaloukas, and D. I.
Fotiadis, “Prediction of oral cancer recurrence using dynamic
bayesian networks,” in 2016 38th Annual International Conference
of the IEEE Engineering in Medicine and Biology Society (EMBC),
pp. 5275–5278, IEEE, 2016.
[88] D. Chudasama, V. Bo, M. Hall, V. Anikin, J. Jeyaneethi, J. Gregory,
G. Pados, A. Tucker, A. Harvey, R. Pink, et al., “Identification
of cancer biomarkers of prognostic value using specific gene
regulatory networks (grn): a novel role of rad51ap1 for ovarian
and lung cancers,” Carcinogenesis, vol. 39, no. 3, pp. 407–417, 2018.
[89] D. Husmeier, “Sensitivity and specificity of inferring genetic reg-
ulatory interactions from microarray experiments with dynamic
bayesian networks,” Bioinformatics, vol. 19, no. 17, pp. 2271–2282,
2003.
[90] S. Y. Kim, S. Imoto, and S. Miyano, “Inferring gene networks from
time series microarray data using dynamic bayesian networks,”
Briefings in bioinformatics, vol. 4, no. 3, pp. 228–235, 2003.
[91] L. E. Chai, S. K. Loh, S. T. Low, M. S. Mohamad, S. Deris,
and Z. Zakaria, “A review on the computational approaches for
gene regulatory network construction,” Computers in biology and
medicine, vol. 48, pp. 55–65, 2014.
[92] A. V. Werhli, M. Grzegorczyk, and D. Husmeier, “Comparative
evaluation of reverse engineering gene regulatory networks with
relevance networks, graphical gaussian models and bayesian
networks,” Bioinformatics, vol. 22, no. 20, pp. 2523–2531, 2006.
[93] A. J. Hartemink, D. K. Gifford, T. S. Jaakkola, and R. A. Young,
“Bayesian methods for elucidating genetic regulatory networks,”
IEEE Intelligent Systems, vol. 17, no. 2, pp. 37–43, 2002.
[94] A. V. Werhli and D. Husmeier, “Reconstructing gene regulatory
networks with bayesian networks by combining expression data
with multiple sources of prior knowledge,” Statistical applications
in genetics and molecular biology, vol. 6, no. 1, 2007.
[95] R. J. Field, “Chemical reaction kinetics,” Scholarpedia, vol. 3,
no. 10, p. 4051, 2008.
[96] K. J. Laidler, “Chemical kinetics and the origins of physical
chemistry,” Archive for History of Exact Sciences, pp. 43–75, 1985.
[97] H. El-Samad and M. Khammash, “Modelling and analysis of
gene regulatory network using feedback control theory,” Inter-
national journal of systems science, vol. 41, no. 1, pp. 17–33, 2010.
[98] T. Chen, H. L. He, and G. M. Church, “Modeling gene expression
with differential equations,” in Biocomputing’99, pp. 29–40, World
Scientific, 1999.
[99] H. De Jong, “Modeling and simulation of genetic regulatory
systems: a literature review,” Journal of computational biology,
vol. 9, no. 1, pp. 67–103, 2002.
[100] B. Ristevski, “A survey of models for inference of gene regulatory
networks,” Nonlinear Analysis: Modelling and Control, vol. 18, no. 4,
pp. 444–465, 2013.
[101] J. Gebert, N. Radde, and G.-W. Weber, “Modeling gene regulatory
networks with piecewise linear differential equations,” European
Journal of Operational Research, vol. 181, no. 3, pp. 1148–1165, 2007.
[102] G. Von Dassow, E. Meir, E. M. Munro, and G. M. Odell, “The
segment polarity network is a robust developmental module,”
Nature, vol. 406, no. 6792, pp. 188–192, 2000.
[103] P. Li and J. Lam, “Disturbance analysis of nonlinear differ-
ential equation models of genetic sum regulatory networks,”
IEEE/ACM transactions on computational biology and bioinformatics,
vol. 8, no. 1, pp. 253–259, 2010.
[104] H. Wu, T. Lu, H. Xue, and H. Liang, “Sparse additive ordi-
nary differential equations for dynamic gene regulatory network
modeling,” Journal of the American Statistical Association, vol. 109,
no. 506, pp. 700–716, 2014.
[105] H. De Jong and J. Geiselmann, “Modeling and simulation of
genetic regulatory networks by ordinary differential equations,”
Genomic Signal Processing and Statistics, p. 201239, 2005.
[106] L. Qian, H. Wang, and E. R. Dougherty, “Inference of noisy
nonlinear differential equation models for gene regulatory net-
works using genetic programming and kalman filtering,” IEEE
Transactions on Signal Processing, vol. 56, no. 7, pp. 3327–3339,
2008.
[107] J. Cao and H. Zhao, “Estimating dynamic models for gene
regulation networks,” Bioinformatics, vol. 24, no. 14, pp. 1619–
1624, 2008.
[108] B. Ma, M. Fang, and X. Jiao, “Inference of gene regulatory
networks based on nonlinear ordinary differential equations,”
Bioinformatics, vol. 36, no. 19, pp. 4885–4893, 2020.
[109] M. J. De Hoon, S. Imoto, K. Kobayashi, N. Ogasawara, and
S. Miyano, “Inferring gene regulatory networks from time-
ordered gene expression data of bacillus subtilis using differential
equations,” in Biocomputing 2003, pp. 17–28, World Scientific,
2002.
[110] P.-C. Aubin-Frankowski and J.-P. Vert, “Gene regulation inference
from single-cell rna-seq data with linear differential equations
and velocity inference,” Bioinformatics, vol. 36, no. 18, pp. 4774–
4780, 2020.
[111] O. Suarez, C. Vega, E. Sanchez, A. G. Santiago, O. R. Jorge,
and A. P. Garcia, “Degradaci´
on anormal de p53 e inducci´
on
de apoptosis en la red p53-mdm2 usando la estrategia de con-
trol tipo pin,” REVISTA COLOMBIANA DE TECNOLOGIAS DE
AVANZADA (RCTA), vol. 2, no. 32, pp. 1–7, 2018.
[112] B. Verd, N. A. Monk, and J. Jaeger, “Modularity, criticality, and
evolvability of a developmental gene regulatory network,” Elife,
vol. 8, p. e42832, 2019.
[113] I. Barbier, R. Perez-Carrasco, and Y. Schaerli, “Controlling spa-
tiotemporal pattern formation in a concentration gradient with a
synthetic toggle switch,” Molecular systems biology, vol. 16, no. 6,
p. e9361, 2020.
[114] P. F. Gherardini and M. Helmer-Citterich, “Experimental and
computational methods for the analysis and modeling of signal-
ing networks,” New biotechnology, vol. 30, no. 3, pp. 327–332, 2013.
[115] R. A. Bradshaw and E. A. Dennis, Handbook of cell signaling.
Academic press, 2009.
[116] P. Sundaram, Mechanotransduction: Cell Signaling to Cell Response.
Academic Press, 2020.
[117] J. D. Jordan, E. M. Landau, and R. Iyengar, “Signaling networks:
the origins of cellular multitasking,” Cell, vol. 103, no. 2, pp. 193–
200, 2000.
[118] G. Weng, U. S. Bhalla, and R. Iyengar, “Complexity in biological
signaling systems,” Science, vol. 284, no. 5411, pp. 92–96, 1999.

16
[119] S. S. Bajikar and K. A. Janes, “Multiscale models of cell signal-
ing,” Annals of biomedical engineering, vol. 40, no. 11, pp. 2319–
2327, 2012.
[120] E. U. Azeloglu and R. Iyengar, “Signaling networks: information
flow, computation, and decision making,” Cold Spring Harbor
perspectives in biology, vol. 7, no. 4, p. a005934, 2015.
[121] E. J. Miller and S. L. Lappin, “Physiology, cellular receptor,” in
StatPearls [Internet], StatPearls Publishing, 2021.
[122] N. J. Eungdamrong and R. Iyengar, “Modeling cell signaling
networks,” Biology of the Cell, vol. 96, no. 5, pp. 355–362, 2004.
[123] R. Albert and R.-S. Wang, “Discrete dynamic modeling of cellular
signaling networks,” Methods in enzymology, vol. 467, pp. 281–306,
2009.
[124] S. Sherekar and G. A. Viswanathan, “Boolean dynamic model-
ing of cancer signaling networks: Prognosis, progression, and
therapeutics,” Computational and Systems Oncology, vol. 1, no. 2,
p. e1017, 2021.
[125] F. Baur, S. L. Nietzer, M. Kunz, F. Saal, J. Jeromin, S. Matschos,
M. Linnebacher, H. Walles, T. Dandekar, and G. Dandekar, “Con-
necting cancer pathways to tumor engines: A stratification tool
for colorectal cancer combining human in vitro tissue models
with boolean in silico models,” Cancers, vol. 12, no. 1, p. 28, 2019.
[126] J. Lee, S. R. Choi, and K.-H. Cho, “Network dynamics caused
by genomic alteration determine the therapeutic response to fgfr
inhibitors for lung cancer,” Biomolecules, vol. 12, no. 9, p. 1197,
2022.
[127] ¨
O. Sahin, H. Fr¨
ohlich, C. L¨
obke, U. Korf, S. Burmester, M. Majety,
J. Mattern, I. Schupp, C. Chaouiya, D. Thieffry, et al., “Modeling
erbb receptor-regulated g1/s transition to find novel targets for
de novo trastuzumab resistance,” BMC systems biology, vol. 3,
no. 1, pp. 1–20, 2009.
[128] P. K. Kreeger and D. A. Lauffenburger, “Cancer systems biology:
a network modeling perspective,” Carcinogenesis, vol. 31, no. 1,
pp. 2–8, 2010.
[129] K. Sachs, D. Gifford, T. Jaakkola, P. Sorger, and D. A. Lauffen-
burger, “Bayesian network approach to cell signaling pathway
modeling,” Science’s STKE, vol. 2002, no. 148, pp. pe38–pe38,
2002.
[130] R. Agrahari, A. Foroushani, T. R. Docking, L. Chang, G. Duns,
M. Hudoba, A. Karsan, and H. Zare, “Applications of bayesian
network models in predicting types of hematological malignan-
cies,” Scientific reports, vol. 8, no. 1, pp. 1–12, 2018.
[131] H. Vundavilli, A. Datta, C. Sima, J. Hua, R. Lopes, and M. Bittner,
“Bayesian inference identifies combination therapeutic targets in
breast cancer,” IEEE Transactions on Biomedical Engineering, vol. 66,
no. 9, pp. 2684–2692, 2019.
[132] A. Azad and S. A. Alyami, “Discovering novel cancer bio-
markers in acquired lapatinib resistance using bayesian meth-
ods,” Briefings in Bioinformatics, vol. 22, no. 5, p. bbab137, 2021.
[133] O. Wolkenhauer, P. Wellstead, K.-H. Cho, P. Rangamani, and
R. Iyengar, “Modelling cellular signalling systems,” Essays in
Biochemistry, vol. 45, pp. 83–94, 2008.
[134] Y. Arkun and M. Yasemi, “Dynamics and control of the erk
signaling pathway: Sensitivity, bistability, and oscillations,” PloS
one, vol. 13, no. 4, p. e0195513, 2018.
[135] C. Dessauges, J. Mikelson, M. Dobrzy ´
nski, M.-A. Jacques, A. Fris-
mantiene, P. A. Gagliardi, M. Khammash, and O. Pertz, “Op-
togenetic actuator–erk biosensor circuits identify mapk network
nodes that shape erk dynamics,” Molecular systems biology, vol. 18,
no. 6, p. e10670, 2022.
[136] T. Sapega and G. T. Guria, “Stability analysis of the pi3k–akt–
mtor signaling pathway,” Biophysics, vol. 65, no. 2, pp. 259–267,
2020.
[137] A. S. H. Makhlouf and N. Y. Abu-Thabit, Stimuli Responsive
Polymeric Nanocarriers for Drug Delivery Applications: Volume 1:
Types and Triggers. Woodhead Publishing, 2018.
[138] T. M. Varusai and L. K. Nguyen, “Dynamic modelling of the
mtor signalling network reveals complex emergent behaviours
conferred by deptor,” Scientific reports, vol. 8, no. 1, pp. 1–14, 2018.
[139] R. D. Evans and L. C. Heather, “Metabolic pathways and abnor-
malities,” Surgery (Oxford), vol. 34, no. 6, pp. 266–272, 2016.
[140] L.-L. Hu, C. Chen, T. Huang, Y.-D. Cai, and K.-C. Chou, “Pre-
dicting biological functions of compounds based on chemical-
chemical interactions,” PloS one, vol. 6, no. 12, p. e29491, 2011.
[141] M. D. Rosenthal and R. H. Glew, Medical biochemistry: human
metabolism in health and disease. John Wiley & Sons, 2011.
[142] L. J. Sweetlove and A. R. Fernie, “Regulation of metabolic
networks: understanding metabolic complexity in the systems
biology era,” New Phytologist, vol. 168, no. 1, pp. 9–24, 2005.
[143] V. Lacroix, L. Cottret, P. Th´
ebault, and M.-F. Sagot, “An intro-
duction to metabolic networks and their structural analysis,”
IEEE/ACM transactions on computational biology and bioinformatics,
vol. 5, no. 4, pp. 594–617, 2008.
[144] K. Takemoto, “Current understanding of the formation and adap-
tation of metabolic systems based on network theory,” Metabo-
lites, vol. 2, no. 3, pp. 429–457, 2012.
[145] M. D. Martin, A computational model of the line-1 retrotransposon life
cycle and visualization of metabolic networks in 3-dimensions. PhD
thesis, University of Louisville, 2022.
[146] C. Kaleta, F. Centler, P. S. di Fenizio, and P. Dittrich, “Phenotype
prediction in regulated metabolic networks,” BMC systems biol-
ogy, vol. 2, no. 1, pp. 1–15, 2008.
[147] T. Tamura, W. Lu, and T. Akutsu, “Computational methods for
modification of metabolic networks,” Computational and structural
biotechnology journal, vol. 13, pp. 376–381, 2015.
[148] T. Tamura, T. Akutsu, C.-Y. Lin, and J.-M. Yang, “Finding influ-
ential genes using gene expression data and boolean models of
metabolic networks,” in 2016 IEEE 16th International Conference on
Bioinformatics and Bioengineering (BIBE), pp. 57–63, IEEE, 2016.
[149] T. Tamura, W. Lu, J. Song, and T. Akutsu, “Computing mini-
mum reaction modifications in a boolean metabolic network,”
IEEE/ACM transactions on computational biology and bioinformatics,
vol. 15, no. 6, pp. 1853–1862, 2017.
[150] A. J. Rogers, M. McGeachie, R. M. Baron, L. Gazourian, J. A.
Haspel, K. Nakahira, L. E. Fredenburgh, G. M. Hunninghake,
B. A. Raby, M. A. Matthay, et al., “Metabolomic derangements
are associated with mortality in critically ill adult patients,” PloS
one, vol. 9, no. 1, p. e87538, 2014.
[151] H. U. Kim, T. Y. Kim, and S. Y. Lee, “Framework for network
modularization and bayesian network analysis to investigate the
perturbed metabolic network,” in BMC systems biology, vol. 5,
pp. 1–12, Springer, 2011.
[152] L. Zhang, M. Wang, A. Castan, H. Hjalmarsson, and V. Chotteau,
“Probabilistic model by bayesian network for the prediction of
antibody glycosylation in perfusion and fed-batch cell cultures,”
Biotechnology and Bioengineering, vol. 118, no. 9, pp. 3447–3459,
2021.
[153] R. Myte, B. Gylling, J. H ¨
aggstr¨
om, J. Schneede, P. Magne Ueland,
G. Hallmans, I. Johansson, R. Palmqvist, and B. Van Guelpen,
“Untangling the role of one-carbon metabolism in colorectal can-
cer risk: a comprehensive bayesian network analysis,” Scientific
reports, vol. 7, no. 1, pp. 1–12, 2017.
[154] N. Tomar and R. K. De, “Comparing methods for metabolic
network analysis and an application to metabolic engineering,”
Gene, vol. 521, no. 1, pp. 1–14, 2013.
[155] C. Shene, J. A. Asenjo, and Y. Chisti, “Metabolic modelling and
simulation of the light and dark metabolism of chlamydomonas
reinhardtii,” The Plant Journal, vol. 96, no. 5, pp. 1076–1088, 2018.
[156] A. Woller and D. Gonze, “Modeling clock-related metabolic syn-
drome due to conflicting light and food cues,” Scientific reports,
vol. 8, no. 1, pp. 1–10, 2018.
[157] M. Luo, J. Jiao, and R. Wang, “Screening drug target combina-
tions in disease-related molecular networks,” BMC bioinformatics,
vol. 20, no. 7, pp. 129–138, 2019.
[158] A. R. Dinasarapu, B. Saunders, I. Ozerlat, K. Azam, and S. Sub-
ramaniam, “Signaling gateway molecule pages—a data model
perspective,” Bioinformatics, vol. 27, no. 12, pp. 1736–1738, 2011.
[159] I. A. Maraziotis, A. Dragomir, and D. Thanos, “Gene regulatory
networks modelling using a dynamic evolutionary hybrid,” BMC
bioinformatics, vol. 11, no. 1, pp. 1–17, 2010.
[160] J. M. Cherry, E. L. Hong, C. Amundsen, R. Balakrishnan, G. Bink-
ley, E. T. Chan, K. R. Christie, M. C. Costanzo, S. S. Dwight, S. R.
Engel, et al., “Saccharomyces genome database: the genomics
resource of budding yeast,” Nucleic acids research, vol. 40, no. D1,
pp. D700–D705, 2012.
[161] S. Aibar, C. B. Gonz´
alez-Blas, T. Moerman, V. A. Huynh-Thu,
H. Imrichova, G. Hulselmans, F. Rambow, J.-C. Marine, P. Geurts,
J. Aerts, et al., “Scenic: single-cell regulatory network inference
and clustering,” Nature methods, vol. 14, no. 11, pp. 1083–1086,
2017.
[162] R. Janky, A. Verfaillie, H. Imrichov´
a, B. Van de Sande,
L. Standaert, V. Christiaens, G. Hulselmans, K. Herten,
M. Naval Sanchez, D. Potier, et al., “iregulon: from a gene list to a

17
gene regulatory network using large motif and track collections,”
PLoS computational biology, vol. 10, no. 7, p. e1003731, 2014.
[163] K. F. Aoki and M. Kanehisa, “Using the kegg database resource,”
Current protocols in bioinformatics, vol. 11, no. 1, pp. 1–12, 2005.
[164] M. Kanehisa and S. Goto, “Kegg: kyoto encyclopedia of genes
and genomes,” Nucleic acids research, vol. 28, no. 1, pp. 27–30,
2000.
[165] R. Edgar, M. Domrachev, and A. E. Lash, “Gene expression
omnibus: Ncbi gene expression and hybridization array data
repository,” Nucleic acids research, vol. 30, no. 1, pp. 207–210, 2002.
[166] T. Huang, L. Liu, Z. Qian, K. Tu, Y. Li, and L. Xie, “Using genereg
to construct time delay gene regulatory networks,” BMC research
notes, vol. 3, no. 1, pp. 1–10, 2010.
[167] M. C. Teixeira, P. T. Monteiro, M. Palma, C. Costa, C. P. Godinho,
P. Pais, M. Cavalheiro, M. Antunes, A. Lemos, T. Pedreira, et al.,
“Yeastract: an upgraded database for the analysis of transcription
regulatory networks in saccharomyces cerevisiae,” Nucleic acids
research, vol. 46, no. D1, pp. D348–D353, 2018.
[168] W. Yang, J. Soares, P. Greninger, E. J. Edelman, H. Lightfoot,
S. Forbes, N. Bindal, D. Beare, J. A. Smith, I. R. Thompson, et al.,
“Genomics of drug sensitivity in cancer (gdsc): a resource for
therapeutic biomarker discovery in cancer cells,” Nucleic acids
research, vol. 41, no. D1, pp. D955–D961, 2012.
[169] J. W. Locasale and A. Wolf-Yadlin, “Maximum entropy recon-
structions of dynamic signaling networks from quantitative pro-
teomics data,” PloS one, vol. 4, no. 8, p. e6522, 2009.
[170] N. Le Novere, B. Bornstein, A. Broicher, M. Courtot, M. Donizelli,
H. Dharuri, L. Li, H. Sauro, M. Schilstra, B. Shapiro, et al.,
“Biomodels database: a free, centralized database of curated,
published, quantitative kinetic models of biochemical and cellu-
lar systems,” Nucleic acids research, vol. 34, no. suppl 1, pp. D689–
D691, 2006.
[171] R. S. Costa, D. Machado, I. Rocha, and E. C. Ferreira, “Hy-
brid dynamic modeling of escherichia coli central metabolic
network combining michaelis–menten and approximate kinetic
equations,” Biosystems, vol. 100, no. 2, pp. 150–157, 2010.
[172] L. T. MacNeil and A. J. Walhout, “Gene regulatory networks and
the role of robustness and stochasticity in the control of gene
expression,” Genome research, vol. 21, no. 5, pp. 645–657, 2011.
[173] T. Stamov and I. Stamova, “Design of impulsive controllers and
impulsive control strategy for the mittag-leffler stability behavior
of fractional gene regulatory networks,” Neurocomputing, vol. 424,
pp. 54–62, 2021.
[174] A. Pezzotta and J. Briscoe, “Optimal control of gene regulatory
networks for morphogen-driven tissue patterning,” bioRxiv, 2022.
[175] A. Datta, R. Pal, A. Choudhary, and E. R. Dougherty, “Con-
trol approaches for probabilistic gene regulatory networks-what
approaches have been developed for addreassinig the issue of
intervention?,” IEEE Signal Processing Magazine, vol. 24, no. 1,
pp. 54–63, 2007.
[176] E. R. Dougherty, R. Pal, X. Qian, M. L. Bittner, and A. Datta,
“Stationary and structural control in gene regulatory networks:
basic concepts,” International Journal of Systems Science, vol. 41,
no. 1, pp. 5–16, 2010.
[177] A. Datta, A. Choudhary, M. L. Bittner, and E. R. Dougherty,
“External control in markovian genetic regulatory networks,”
Machine learning, vol. 52, no. 1, pp. 169–191, 2003.
[178] A. Datta, A. Choudhary, M. L. Bittner, and E. R. Dougherty,
“External control in markovian genetic regulatory networks: the
imperfect information case,” Bioinformatics, vol. 20, no. 6, pp. 924–
930, 2004.
[179] R. Pal, A. Datta, and E. R. Dougherty, “Optimal infinite-horizon
control for probabilistic boolean networks,” IEEE Transactions on
Signal Processing, vol. 54, no. 6, pp. 2375–2387, 2006.
[180] B. Faryabi, A. Datta, and E. Dougherty, “On approximate stochas-
tic control in genetic regulatory networks,” IET Systems Biology,
vol. 1, no. 6, pp. 361–368, 2007.
[181] N. Bouaynaya, R. Shterenberg, and D. Schonfeld, “Optimal per-
turbation control of gene regulatory networks,” in 2010 IEEE
International Workshop on Genomic Signal Processing and Statistics
(GENSIPS), pp. 1–4, IEEE, 2010.
[182] M. Imani and U. M. Braga-Neto, “Control of gene regulatory
networks with noisy measurements and uncertain inputs,” IEEE
Transactions on Control of Network Systems, vol. 5, no. 2, pp. 760–
769, 2017.
[183] M. Imani and U. M. Braga-Neto, “Point-based methodology
to monitor and control gene regulatory networks via noisy
measurements,” IEEE Transactions on Control Systems Technology,
vol. 27, no. 3, pp. 1023–1035, 2018.
[184] M. Imani and U. M. Braga-Neto, “Control of gene regula-
tory networks using bayesian inverse reinforcement learning,”
IEEE/ACM transactions on computational biology and bioinformatics,
vol. 16, no. 4, pp. 1250–1261, 2018.
[185] M. Imani and U. Braga-Neto, “Optimal control of gene regulatory
networks with unknown cost function,” in 2018 Annual American
Control Conference (ACC), pp. 3939–3944, IEEE, 2018.
[186] L. Chen and K. Aihara, “Stability of genetic regulatory networks
with time delay,” IEEE Transactions on circuits and systems I:
Fundamental Theory and Applications, vol. 49, no. 5, pp. 602–608,
2002.
[187] C. Huang, J. Cao, and M. Xiao, “Hybrid control on bifurcation
for a delayed fractional gene regulatory network,” Chaos, Solitons
& Fractals, vol. 87, pp. 19–29, 2016.
[188] N. A. Monk, “Oscillatory expression of hes1, p53, and nf-κb
driven by transcriptional time delays,” Current biology, vol. 13,
no. 16, pp. 1409–1413, 2003.
[189] C.-W. Liao and C.-Y. Lu, “Design of delay-range-dependent ro-
bust controller for uncertain genetic regulatory networks with
interval time-varying delays,” Automatic Control and Computer
Sciences, vol. 44, no. 4, pp. 234–245, 2010.
[190] J. Zeng, Y. He, M. Wu, and L. Fu, “Delay-dependent h∞control
for stochastic genetic regulatory networks with interval time-
varying delays,” in Proceedings of the 30th Chinese Control Con-
ference, pp. 2291–2296, IEEE, 2011.
[191] Q. Zhou, S. Xu, B. Chen, H. Li, and Y. Chu, “Stability analysis
of delayed genetic regulatory networks with stochastic distur-
bances,” Physics Letters A, vol. 373, no. 41, pp. 3715–3723, 2009.
[192] J. Hu, J. Liang, and J. Cao, “Stabilization of genetic regulatory net-
works with mixed time-delays: an adaptive control approach,”
IMA Journal of Mathematical Control and Information, vol. 32, no. 2,
pp. 343–358, 2015.
[193] W. Yu, J. L ¨
u, Z. Wang, J. Cao, and Q. Zhou, “Robust h∞control
and uniformly bounded control for genetic regulatory network
with stochastic disturbance,” IET Control Theory & Applications,
vol. 4, no. 9, pp. 1687–1706, 2010.
[194] A. Liu, L. Yu, D. Zhang, and W.-a. Zhang, “Finite-time h∞con-
trol for discrete-time genetic regulatory networks with random
delays and partly unknown transition probabilities,” Journal of
the Franklin Institute, vol. 350, no. 7, pp. 1944–1961, 2013.
[195] H. Moradi and V. J. Majd, “Robust control of uncertain nonlin-
ear switched genetic regulatory networks with time delays: A
redesign approach,” Mathematical Biosciences, vol. 275, pp. 10–17,
2016.
[196] Y. Liu and H. Jiang, “Exponential stability of genetic regulatory
networks with mixed delays by periodically intermittent con-
trol,” Neural Computing and Applications, vol. 21, no. 6, pp. 1263–
1269, 2012.
[197] L. Li and Y. Yang, “On sampled-data control for stabilization of
genetic regulatory networks with leakage delays,” Neurocomput-
ing, vol. 149, pp. 1225–1231, 2015.
[198] X. Zhang, Z. Zhang, Y. Wang, and C. Liu, “Guaranteed cost con-
trol of genetic regulatory networks with multiple time-varying
discrete delays and multiple constant distributed delays,” IEEE
Access, vol. 8, pp. 80175–80182, 2020.
[199] Y. Xue, M. Su, X. Yang, and X. Zhang, “State bounding and
controller design for genetic regulatory networks with multiple
delays and bounded disturbances,” International Journal of Robust
and Nonlinear Control, vol. 32, no. 14, pp. 8032–8051, 2022.
[200] G. Narayanan, M. S. Ali, H. Alsulami, B. Ahmad, and J. Trujillo,
“A hybrid impulsive and sampled-data control for fractional-
order delayed reaction–diffusion system of mrna and protein in
regulatory mechanisms,” Communications in Nonlinear Science and
Numerical Simulation, vol. 111, p. 106374, 2022.
[201] N. Padmaja and P. Balasubramaniam, “Design of h∞/passive
state feedback control for delayed fractional order gene regula-
tory networks via new improved integral inequalities,” Commu-
nications in Nonlinear Science and Numerical Simulation, vol. 111,
p. 106507, 2022.
[202] V. Hsiao, A. Swaminathan, and R. M. Murray, “Control theory
for synthetic biology: recent advances in system characterization,
control design, and controller implementation for synthetic bi-
ology,” IEEE Control Systems Magazine, vol. 38, no. 3, pp. 32–62,
2018.

18
[203] I. Ruolo, S. Napolitano, D. Salzano, M. di Bernardo, and
D. di Bernardo, “Control engineering meets synthetic biology:
Foundations and applications,” Current Opinion in Systems Biol-
ogy, vol. 28, p. 100397, 2021.
[204] F. L. Baldissera, J. E. Cury, and J. Raisch, “A supervisory control
theory approach to control gene regulatory networks,” IEEE
Transactions on Automatic Control, vol. 61, no. 1, pp. 18–33, 2015.
[205] B.-S. Chen and C.-H. Wu, “Robust optimal reference-tracking
design method for stochastic synthetic biology systems: T–s fuzzy
approach,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 6,
pp. 1144–1159, 2010.
[206] H. Shokouhi-Nejad and A. Rikhtehgar-Ghiasi, “Robust h∞
observer-based controller for stochastic genetic regulatory net-
works,” Mathematical Biosciences, vol. 250, pp. 41–53, 2014.
[207] F. Menolascina, M. Di Bernardo, and D. Di Bernardo, “Analysis,
design and implementation of a novel scheme for in-vivo control
of synthetic gene regulatory networks,” Automatica, vol. 47, no. 6,
pp. 1265–1270, 2011.
[208] D. K. Agrawal, R. Marshall, V. Noireaux, and E. D. Sontag, “In
vitro implementation of robust gene regulation in a synthetic
biomolecular integral controller,” Nature communications, vol. 10,
no. 1, pp. 1–12, 2019.
[209] B. Shannon, C. G. Zamora-Chimal, L. Postiglione, D. Salzano,
C. S. Grierson, L. Marucci, N. J. Savery, and M. Di Bernardo, “In
vivo feedback control of an antithetic molecular-titration motif in
escherichia coli using microfluidics,” ACS Synthetic Biology, vol. 9,
no. 10, pp. 2617–2624, 2020.
[210] J. Lee, D. Lee, and Y. Kim, “Mathematical model of stat sig-
nalling pathways in cancer development and optimal control
approaches,” Royal Society open science, vol. 8, no. 9, p. 210594,
2021.
[211] A. Camacho and S. Jerez, “Nonlinear modeling and control
strategies for bone diseases based on tgfβand wnt factors,”
Communications in Nonlinear Science and Numerical Simulation,
vol. 100, p. 105842, 2021.
[212] E. Jung, A. A. de los Reyes V, K. J. A. Pumares, and Y. Kim,
“Strategies in regulating glioblastoma signaling pathways and
anti-invasion therapy,” PLoS One, vol. 14, no. 4, p. e0215547, 2019.
[213] H. K. Ooi and L. Ma, “Integral control feedback circuit for
the reactivation of malfunctioning p53 pathway,” arXiv preprint
arXiv:1510.04136, 2015.
[214] M. R. Azam, S. Fazal, M. Ullah, and A. I. Bhatti, “System-based
strategies for p53 recovery,” IET systems biology, vol. 12, no. 3,
pp. 101–107, 2018.
[215] M. Rizwan Azam, V. I. Utkin, A. Arshad Uppal, and A. I. Bhatti,
“Sliding mode controller–observer pair for p53 pathway,” IET
systems biology, vol. 13, no. 4, pp. 204–211, 2019.
[216] A. Yasin, A. R. Yasin, M. R. Azam, A. Raza, R. Nazir, and R. A.
Elamin Abdalla, “Computational-model-based biopharmaceutics
for p53 pathway using modern control techniques for cancer
treatment,” Applied Sciences, vol. 12, no. 11, p. 5748, 2022.
[217] S. Bano, M. R. Azam, A. A. Uppal, S. B. Javed, and A. I.
Bhatti, “Robust p53 recovery using chattering free sliding mode
control and a gain-scheduled modified utkin observer,” Journal of
Theoretical Biology, vol. 532, p. 110914, 2022.
[218] K. Creutzburg, Optimization of metabolic networks for metabolite
overproduction. PhD thesis, Technical University of Denmark,
2000.
[219] J. L. Hjersted and M. A. Henson, “Optimization of fed-batch sac-
charomyces cerevisiae fermentation using dynamic flux balance
models,” Biotechnology progress, vol. 22, no. 5, pp. 1239–1248, 2006.
[220] D. Kumar and H. Budman, “Robust nonlinear predictive control
for a bioreactor based on a dynamic metabolic flux balance
model,” IFAC-PapersOnLine, vol. 48, no. 8, pp. 930–935, 2015.
[221] B. Jabarivelisdeh, R. Findeisen, and S. Waldherr, “Model pre-
dictive control of a fed-batch bioreactor based on dynamic
metabolic-genetic network models,” IFAC-PapersOnLine, vol. 51,
no. 19, pp. 34–37, 2018.
[222] B. Jabarivelisdeh, L. Carius, R. Findeisen, and S. Waldherr,
“Adaptive predictive control of bioprocesses with constraint-
based modeling and estimation,” Computers & Chemical Engineer-
ing, vol. 135, p. 106744, 2020.
[223] R. D. De Oliveira, M. N. Guedes, J. Matias, and G. A. Le Roux,
“Nonlinear predictive control of a bioreactor by surrogate model
approximation of flux balance analysis,” Industrial & Engineering
Chemistry Research, vol. 60, no. 40, pp. 14464–14475, 2021.
[224] L. Hebing, F. Tran, H. Brandt, and S. Engell, “Robust optimizing
control of fermentation processes based on a set of structurally
different process models,” Industrial & Engineering Chemistry
Research, vol. 59, no. 6, pp. 2566–2580, 2020.
[225] G. S. Murthy, D. B. Johnston, K. D. Rausch, M. Tumbleson, and
V. Singh, “Design and evaluation of an optimal controller for
simultaneous saccharification and fermentation process,” Applied
biochemistry and biotechnology, vol. 166, no. 1, pp. 87–111, 2012.
[226] D. A. Oyarz ´
un and G.-B. Stan, “Design constraints in an operon
circuit for engineered control of metabolic networks,” in 2012
IEEE 51st IEEE Conference on Decision and Control (CDC), pp. 3608–
3613, IEEE, 2012.
[227] R. Planqu´
e, J. Hulshof, B. Teusink, J. C. Hendriks, and F. J.
Bruggeman, “Maintaining maximal metabolic flux by gene ex-
pression control,” PLOS Computational Biology, vol. 14, no. 9,
p. e1006412, 2018.
Yen-Che Hsiao received MS and BS in electrical
engineering from the National Chi Nan Univer-
sity in 2019 and 2021, respectively. He is cur-
rently pursuing the PhD degree in electrical and
computer engineering with the University of Con-
necticut. His current research interests include
control theory and biological network control.
Abhishek Dutta received PhD in electrome-
chanical engineering from Ghent University in
2014 and masters in informatics from the Univer-
sity of Edinburgh in 2007. He was an aerospace
postdoc at the University of Illinois at Ur-
bana–Champaign till 2016. He is currently an
Assistant Professor of electrical and computer
engineering and biomedical engineering and af-
filiated to the Pratt & Whitney Institute of Ad-
vanced Systems Engineering and the Connecti-
cut Institute of Brain and Cognitive Sciences.
He directs Dutta Lab which is at the intersection of engineering and
medicine and is engaged in disease control and prevention.