Fuzzy Decision Making Approach to Identify Optimum Enzyme Targets and Drug Dosage for Remedying Presynaptic Dopamine Deficiency
Fuzzy Decision Making Approach to Identify Optimum Enzyme Targets and Drug Dosage for Remedying Presynaptic Dopamine Deficiency
Kai-Cheng Hsu 0 1
Feng-Sheng Wang 0 1
0 Department of Chemical Engineering, National Chung Cheng University , Chiayi 62102 , Taiwan
1 Editor: Quan Zou, Tianjin University , CHINA
Model-based optimization approaches are valuable in developing new drugs for human metabolic disorders. The core objective in most optimal drug designs is positive therapeutic effects. In this study, we considered the effects of therapeutic, adverse, and target variation simultaneously. A fuzzy optimization method was applied to formulate a multiobjective drug design problem for detecting enzyme targets in the presynaptic dopamine metabolic network to remedy two types of enzymopathies caused by deficiencies of vesicular monoamine transporter 2 (VMAT2) and tyrosine hydroxylase (TH). The fuzzy membership approach transforms a two-stage drug discovery problem into a unified decision-making problem. We developed a nested hybrid differential evolution algorithm to efficiently identify a set of potential drug targets. Furthermore, we also simulated the effects of current clinical drugs for Parkinson's disease (PD) in this model and tried to clarify the possible causes of neurotoxic and neuroprotective effects. The optimal drug design could yield 100% satisfaction grade when both therapeutic effect and the number of targets were considered in the objective. This scenario required regulating one to three and one or two enzyme targets for 50%±95% and 50%±100% VMAT2 and TH deficiencies, respectively. However, their corresponding adverse and target variation effect grades were less satisfactory. For the most severe deficiencies of VMAT2 and TH, a compromise design could be obtained when the effects of therapeutic, adverse, and target variation were simultaneously applied to the optimal drug discovery problem. Such a trade-off design followed the no free lunch theorem for optimization; that is, a more serious dopamine deficiency required more enzyme targets and lower satisfaction grade. In addition, the therapeutic effects of current clinical medications for PD could be enhanced in combination with new enzyme targets. The increase of toxic metabolites after treatment might be the cause of neurotoxic effects of some current PD medications.
Data Availability Statement: All relevant data are
within the paper and its Supporting Information
Funding: This work was financially supported by
the Ministry of Science of Technology, Taiwan,
ROC (https://www.most.gov.tw/) through grants
MOST104-2627B-194-001, and MOST105-2627-M-194-001, grant
recipient Prof. Feng-Sheng Wang. The funders had
no role in study design, data collection and
analysis, decision to publish, or preparation of the
Parkinson's disease (PD) is a chronic and progressive neurodegenerative disorder and is the most
common movement disorder, affecting more than 1% of the population aged more than 65 years
]. PD is mainly characterized by a progressive loss of dopamine neurons in the
pars compacta of the substantia nigra, and a loss of dopamine neurons in the extrapyramidal
system contributes to the motor symptoms of PD. Consequently, the treatment options for PD have
been focused on restoring the dopamine function by replacing dopamine precursors and agonist
or inhibiting dopamine degradation. Several drugs affecting enzymes involved in dopamine
metabolism have been used for treating PD. For many years, L-3,4-dihydroxyphenylalanine
(L-DOPA) has been administered for treating PD symptoms. However, whether L-DOPA
exacerbates PD because of L-DOPA oxidation and side products has been debated . By contrast,
the deprenyl and tocopherol antioxidative therapy of Parkinsonism (DATATOP) study and
other follow-up trials have demonstrated that monoamine oxidase inhibitor (MAOI) delays the
use of L-DOPA [
] and reduces the rate of motor fluctuations . Such observations indicate
that the treatment of PD has to consider therapeutic and adverse effects simultaneously.
The process of making a new medicine is a challenging and endurance task [
advances in molecular medicine and powerful tools to enhance computational capacity are
enabling researchers to better understand the inner workings of human disease at the molecular
level. Model-based optimization methods are recently applied to the early drug discovery process
]. This study introduces a fuzzy decision-making approach to screen candidate targets in
the early stage of drug discovery process. The approach is a model-based optimization method
which can include multiple objectives in the optimization problem. Such a drug discovery process
may involve conflicting specifications, making it a challenging multiobjective optimization
problem where numerous pharmaceutically crucial objectives must adequately be satisfied [
drug discovery problem is characterized by vast, complex solution spaces further perplexed by
the presence of conflicting objectives. Mathematical modeling and optimization are the emerging
technologies in drug development for human metabolic disorders [
]. Most optimal drug
designs consider yielding positive therapeutic effects as the design specification; however,
production of toxic metabolites after drug usage causes adverse effects. Therefore, achieving positive
therapeutic effects and avoiding adverse effects must be simultaneously considered in drug design
problems. Moreover, using the systems approach, identifying drug targets with high enzyme
activities and low drug doses to minimize adverse effects is essential. The minimum effective
dose (MED) is the lowest dose level of a pharmaceutical product that provides a clinically
significant response with average efficacy that is significantly superior to the response provided by a
]. In this study, minimizing the variations of the identified enzymes, equivalent to
MED, is considered a representative of the low-dose objective.
Materials and Methods
Most of optimal drug discovery problems use the therapeutic effect as the key criterion. A
twostage procedure shown in Fig 1 is a common approach to discover a new target, such as the
optimization program for drug design (OPDD) to identify enzyme targets for remedying
]. The first stage in Fig 1 is that a designer assigns a specification, e.g. therapeutic
effect, and then such a specification is applied to formulate an optimization problem with
constraints. An optimization solver is then applied to solve the single objective problem to obtain an
optimal solution. The design is then altered a series of requirements, and then the problem is
resolved repeatedly in order to obtain a set of targets. The second stage is a decision-making
2 / 18
Fig 1. A two-stage optimization procedure to discover a new drug target. In the first stage, a designer
assigns the therapeutic effect as the single objective in the optimization problem to obtain an optimal candidate
target, and then to alter series requirements to be repeatedly resolved the problem to obtain a set of candidate
targets. In the second stage, the designer considers some additional requirements to carry out a decision-making
procedure for selecting a desired drug target among the candidates.
procedure wherein the designer uses some additional criteria, such as adverse effect and lower
drug dose, to make a decision for selecting a desired drug target among the candidates.
The criteria in the first stage and second stage can be combined together to formulate as a
multiobjective drug discovery problem shown in Fig 2. The mathematical formulation of the
Fig 2. Computational procedures for multiobjective drug discovery problems. The left flowchart of the figure
explains a posteriori decision-making method. A generating method is applied to yield a Pareto front of the MOO
problem. For instance, the Pareto front for a two objective optimization problem is shown as the red curve. Some
additional requirements are applied to make a decision for selecting a desired drug target from the candidate
targets of the Pareto front. The green block diagram of the figure explains a priori decision-making design that the
drug target discovery problem is formulated as a fuzzy multiobjective optimization problem. The decision-making
conditions, such as a membership function for each objective, are included into the problem, and then a
preference-based method is applied to obtain the desired drug target.
3 / 18
multiobjective drug discovery problem is a type of multiobjective optimization (MOO) problems.
Many methods are available for solving MOO problems, and each method has advantages and
16, 17, 24, 25
]. These methods are classified into two categories: generating and
preference-based methods. Generating methods are applied for yielding a Pareto front of the
MOO problem (left-hand side of Fig 2), where each point of the Pareto front is an optimal
candidate of the MOO problem. Designers use decision-making criteria for performing a trade-off
procedure to obtain the desired optimal target. Such methods are referred as a posteriori
decision-making method. Preference-based methods are applied to solve problem wherein designers
have certain expectations of the optimal solution; in this scenario, a priori condition can be
implemented along with the preference-based method. Such a trade-off procedure is then applied
in the priori decision-making method to obtain the desired target.
This study introduces a fuzzy decision-making method for formulating the aforementioned
preference-based method into a fuzzy multiobjective drug discovery (FMDD) problem as
shown in the green box of Fig 2. The mathematical formulation of the FMDD problem is
expressed as follows:
(Equality constraints :
Kinetic model :
k 1nvgjkyk; j 2 Orxn
Fuzzy equal xi
Fuzzy min xj; j 2 OAE
Fuzzy equal ak
Fuzzy equal uk
Fuzzy min ul; l 2 OVE
xiHS; i 2 OTE
abasal; k 2 OVE
ubasal; k 2 OVE
j 1nuBijuj 0; i 2 OSpecies
Disease restriction :
a^j a^jDS; j 2 ODS
I(nequality constraints :
xiUB; i 2 OSpecies
zja^jbasal; j 2 OVE
zkukbasal; k 2 OVE
The first objective in Eq (1) uses a fuzzy equal operation to evaluate therapeutic effects,
where OTE is the set of metabolites to be evaluated. For example, this study is to consider the
dopamine level is as close to the healthy level as possible. Fuzzy minimization is applied in the
second objective to evaluate the adverse effects of a set of metabolites OAE that the targets can
achieve to lower side effects. The third fuzzy equal is used to evaluate variation effects for the
regulated enzyme targets, and the fourth and fifth objectives use fuzzy equal and fuzzy
minimization to compute variation effects of external controls, where OVE is the set of target enzymes
and external controls excluding a set of disease enzymes ODS. The variation effect is applied to
evaluate that the targets are regulated as small perturbation to their normal levels as possible.
This objective means that we would like to find smaller change of the identified enzyme activity
in order to achieve the therapeutic and adverse effect minimization goals. The external controls
are considered as the regulable independent variables in the metabolic network. In general, we
are difficult to use only one target to achieve all objectives as mentioned above. Some
combinations of targets can be used to fulfill the requirements. The last objective is to consider the total
number of the identified targets as less as possible.
The material balance model in Eq (2) can be generically governed by a set of nonlinear
differential equations with the following structure:
x; α Bu
where x ∊ Rn is a vector of n-dimensional metabolite concentrations or pools, α ∊ Rr is a vector
of the r-dimensional enzyme activities, v ∊ Rr is a vector of reaction rates, N ∊ Rn×r is the
stoichiometric matrix describing the interconnecting fluxes, u ∊ Rm is a vector of m-dimensional
external controls, and B ∊ Rn×m is the connectivity matrix describing the interaction between a
metabolite and its corresponding control. The connectivity matrix is similar to the
stoichiometric property of a network. The model in Eq (4) with the external controls is a more general
formulation, which differs from our previous study [
]. The reaction rate in this study is
expressed according to the power law function described in Eq (5).
where αk is the rate constant or enzyme activity for the kth reaction rate and gkl is the kinetic
order. The power law function is based on the law of mass action in chemistry and
biochemistry to express a mathematical model of a reaction rate [
]. It has several benefit to
formulate a biological system [
], but is a nonconvex constraint in the MOO problem (2) that
may result in a computational failure when the concentration approaches zero. We use the
logarithmic expression for each rate, wk, and for each rate constant, a^k, in Eq (2) to prevent this
numerical problem. The reaction rate and concentration are computed through the
exponential operation. The advantage of this formulation is that the equality and inequality
constraints in the optimization problem form a convex domain.
To solve the FMDD framework, we defined a membership function for each fuzzy equal
objective and fuzzy minimizing objective for quantifying each corresponding satisfaction grade. The
generalized membership function for each fuzzy equal objective is described in Eq (6) as
>>>8 0; xi xiLB
>><> dixL; xiLB
The left-hand side membership function is a strictly monotonically increasing function, dixL,
whereas the right-hand side is a strictly monotonically decreasing function, dixR. A membership
function is similar to assess the effects of inaccuracies in control variables and independent
]. Monte Carlo simulation is generally applied to assess such an experimental
imprecision. However, a designer can define a membership function for fuzzy optimization problems
in advance. Sakawa [
] proposed five types of membership functions, namely linear,
exponential, hyperbolic, inverse, and piecewise linear functions, for quantifying the behavior of fuzzy
objectives or the constraints. Here, xiLB and xiUB are the lower and upper bounds of the ith
metabolite concentration or enzyme activity provided by the designer. The satisfaction grade is
zero when the metabolite concentration or enzyme activity is beyond its lower or upper
bounds. The satisfaction grade or membership function value is equal to one when the
corresponding metabolite concentration or enzyme activity is between the lower and upper bounds
of the basal value, represented as xibasal;LB, xibasal;UB, and xibasal, respectively. The satisfaction grade
is between zero and one when the metabolite concentration or enzyme activity is within its
range on the left- or right-hand side membership function. For each fuzzy minimizing
objective, the membership function is defined as a strictly monotonically decreasing function on the
xj >: dixR; xibasal
According to the membership functions expressed in Eqs (6) and (7), we conclude that the
intersection for these membership functions is zero when either the fuzzy equal objective
functions are outside the corresponding lower and upper bounds or the fuzzy minimizing objectives
are greater than the corresponding upper bounds. By contrast, when all objectives are within
their corresponding bounds, the intersection for all membership functions should show a
certain degree of satisfaction. For each membership function being introduced by the designer,
the FMDD problem is designed for determining a maximum intersection for all membership
functions between the desired bounds. The FMDD framework is then transferred to the
maximizing decision framework, which is a discontinuous function. The detailed procedures have
been discussed previously [
26, 30, 31
]. Thus, the maximizing decision problem can be rewritten
as an equivalent optimization problem on the solving domain to avoid a discontinuous
computation, as follows:
l; i 2 OTE
l; j 2 OAE
l; k 2 OVE
l; l 2 OVE
where the crisp feasible domain ψ includes the kinetic model and inequality constraints
described in Eqs (2) and (3), respectively. The total number of the identified enzyme targets is
the crisp objective so that it is transformed to a normalized value as expressed in Eq (8), where
ZUB is the upper bound. The advantage of this method is that the optimal membership grade
corresponds to the satisfaction level for each objective, and the optimal decision λ represents
the overall satisfaction grade (equivalent to the lower bound) of the problem.
Nested hybrid differential evolution
The maximizing decision problem (8) is a mixed-integer nonlinear programming (MINLP)
problem, which is typically difficult for solving to obtain a global solution. In general, MINLP
problems are highly nonlinear and non-differentiable because of the combinatorial nature of
the associated integer-valued variables. Conventional methods widely used to solve MINLP
problems include the cutting plane, branch-and-bound, and decomposition methods and their
]. These methods have been successfully applied to many practical problems;
however, they require a suitable starting point and gradient information. Wu et al. [
mixed-integer hybrid differential evolution (MIHDE) for identifying an enzyme intervention
problem in metabolic networks; however, it was suitable only for low-dimensional problems.
The computational time increased significantly when MIHDE was applied to a
high-dimensional MINLP problem. Wang and Wu [
] proposed a nested hybrid differential evolution
(NHDE) method for solving multilevel optimization problems derived to design mutant strain
of genome-scale metabolic networks. This study modifies the NHDE algorithm for solving the
The basic operations of MIHDE are similar to those of the modified NHDE algorithm, and
the flowchart of the modified NHDE algorithm is shown in Fig 3. The core procedure of
modified NHDE is the integer variable coding strategy and fitness evaluation operation, which
differs from that in MIHDE. The integer variable coding strategy of modified NHDE is used to
represent which enzyme targets are selected to be regulated. Each target is then applied to solve
the corresponding nonlinear programming problem and to sequentially compute the fitness of
modified NHDE. Such a procedure is a parallel process to evaluate the objective function value
of the MINLP problem. The evaluation operation in modified NHDE consists of two selection
steps. The first selection step is a one-to-one competition that selects enzyme target for the
next generation. The second step determines the best enzyme target in the population.
However, the MIHDE algorithm directly uses the objective function in the MINLP problem as a
fitness function for evaluating whether each selected target replaces its competitor or is rejected.
Moreover, the convergence rate is low when MIHDE is applied to solve high-dimensional
MINLP problems. The modified NHDE algorithm can overcome such drawbacks and is
discussed in supporting information (S1 File).
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Fig 3. Flowchart of the modified algorithm for nested hybrid differential evolution. The core procedure of
the NHDE algorithm is the evaluation and selection operation as shown in the second and third block diagram of
the flowchart. The evaluation step is to solve each nonlinear programming (NLP) problem produced from the
maximizing decision problem for each target candidate. The fitness of each NLP problem is computed for selecting
the better individuals in the population, and then to generate the next individuals.
In this study, the kinetic model of the nigrostriatal dopaminergic pathway reported in Qi et al.
] was applied to formulate the fuzzy optimal drug design problem for identifying enzyme
targets to remedy two types of enzymopathies caused by deficiencies of vesicular monoamine
transporter 2 (VMAT2) and tyrosine hydroxylase (TH). This generalized mass action (GMA)
model included 34 metabolites, 18 independent variables, and 68 target enzymes. The drug
discovery problem had three external controls exerted to tyrosine, L-DOPA, and the intracellular
dopamine, as shown in Fig 4. The detailed definition of the GMA model is expressed in
supporting information (S2 File).
Deficiencies of VMAT2
To illustrate the performance of the drug discovery problem, the first case study considered
four different severities of enzymopathies: 50%, 70%, 90%, and 95% VMAT2 deficiencies
(referred as VM50, VM70, VM90, and VM95, respectively). The enzyme activity for each
deficiency was calculated using aVDMSAT 2
1 d=100abVaMsaAlT2, where δ is the percentage deficiency
for VMAT2. The DA-e concentration was zero for deficiencies >90%. First, we considered
only the therapeutic effect objective for identifying enzyme targets for each deficiency level; the
optimal results are shown in Table 1. The therapeutic objective could achieve 100% satisfaction
8 / 18
Fig 4. Schematic network diagram of the presynaptic dopamine metabolic pathway. The extracellular dopamine (DA-e)
concentration of 400 (relative unit) under a healthy state (HS) was first obtained from the kinetic model. The concentrations of the
metabolites for various deficiencies of VMAT2 and TH are listed in supporting information (S1 Table). DA-e is the therapeutic
objective: the dopamine level as close to its healthy level as possible that the identified enzyme targets can achieve. Other
metabolites of interest included toxic species, reactive oxygen species (ROS), and reactive nitrogen species (RNS). Toxic species
considered in this model were dopaquinone (DOPA-Q), 3-methoxytyramine (3-MT), 3,4-dihydroxyphenylacetaldehyde (DOPAL),
extracellular DOPAL (DOPAL-e), 3,4-dihydroxyphenylacetate quinone (DOPAC-Q), and dopamine quinone (DA-Q). ROS included
superoxide (O2−), intracellular hydrogen peroxide (H2O2), extracellular H2O2 (H2O2-e), and hydroxyl radical (HO), whereas RNS
included peroxynitrite (HO±NO2) and nitrogen dioxide (NO2). In this study, the toxic species, ROS, and RNS were considered the
objectives for evaluating adverse effects.
grade for all cases. The activity of dopamine transporter (α13) decreased from 3.36 (relative
unit) to the basal values of 1.57 and 0.52 for VM50 and VM70, respectively, indicating that
only one enzyme target was sufficient to completely recover to the healthy state. This outcome
also implies that α13 was downregulated to reduce the DA-e transport rate, which restores
intracellular dopamine (DA-i). In addition, we computed the satisfactory grades for both the
adverse and target variation scenarios in VM50 and VM70. The adverse effect yielded
satisfactory scores for both VM50 and VM70, but the target variation effect for VM70 required more
perturbation, indicating low satisfaction levels. For VM90 and VM95, two and three enzyme
targets were required to fulfill the therapeutic objective; however, their corresponding adverse
and target variation effect grades were less satisfactory.
9 / 18
VM50 and VM95 re¯ect 50% and 95% de®ciency of VMAT2, respectively, whereas TH50 and TH100 indicate 50% and 100% de®ciency of TH, respectively.
Furthermore, ut, ul, and ud denote the external control for tyrosine, L-DOPA, and intracellular dopamine, respectively. αj is the enzyme activity for the jth
reaction rate. T, A, and V denote the satisfaction grade for therapeutic, adverse, and variation effects, respectively.
* indicates the optimal solution.
We next considered the therapeutic and adverse effect objectives simultaneously for
identifying the set of drug targets shown in the second column of Table 1. For VM50 and VM70,
downregulation of α13 was sufficient for achieving 100% satisfaction level, which was similar to
the aforementioned case. However, three and four enzyme targets were identified for VM90
and VM95, respectively, both showing satisfaction levels; however, their corresponding target
variation effects were unsatisfactory.
Subsequently, we considered the therapeutic, adverse, and target variation effects
simultaneously. VM50 yielded overall 83.9% satisfaction level despite α13 replacement by monoamine
oxidase (α15) downregulation. Application of α13 to this case yielded 78.5%, 98.2%, and 78.5%
satisfaction levels for the therapeutic, adverse, and target variation effects, respectively,
providing an overall grade less than that observed for α15. The material balance equation on DA-i
required four influxes and seven effluxes (Fig 5) to explain the aforementioned difference. In
the case of downregulation of α13 (0.41-fold), v14 reduced the transport rate by 0.52 times, and
the other fluxes changed insignificantly. Consequently, the concentrations of DA-i, DA-Q,
H2O2, and DOPAL increased by 1.04, 1.16, 1.04, and 1.04 times, respectively. By contrast, in
the case of downregulation of α15 (0.91-fold), v14 reduced the transport rate by 0.88 times; in
addition, the other fluxes changed significantly: v17, v18, and v20 changed by a factor of 1.33,
and v19 changed by a factor of 1.27. Hence, the concentrations of DA-i, DA-Q, H2O2, and
DOPAL increased by a factor of 1.75, 2.45, 0.92, and 0.81, respectively. These different
metabolic redistributions caused by the downregulation of α13 or α15, yielded different results for
the therapeutic, adverse, and target variation effect objectives.
For VM70, VM90, and VM95, we required two, three, and four enzyme targets, respectively,
to achieve the Pareto optimal design. From the results, we observed that Pareto optimal
solutions followed the no free lunch theorem for optimization (i.e., a more severe dopamine
deficiency requires more enzyme targets and lower satisfaction grades). Moreover, we compared
objectives, namely therapeutic effect only and therapeutic effect plus the adverse effect, that
could achieve 100% satisfaction level for the VM95 case. However, the overall satisfaction
grade of 57.4% could only be realized when all three objectives (Table 1) were considered
simultaneously. Furthermore, we compared the effects on the numbers of enzyme targets. We
fixed the number of enzyme targets to three, five, and six and applied NHDE to solve each
drug discovery problem. Optimal solutions for the aforementioned conditions are presented in
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Fig 5. Steady-state material balances of the intracellular dopamine. 50% deficiency of VMAT2 is
downregulated by α15 and α13, respectively. The first element in the parentheses indicates the fold change in the
concentration and the flux, which is downregulated by α15, and the second element is the fold change
downregulated by α13. Fold change is defined as the optimal regulated solution divided by its values in a healthy
Fig 6. The overall satisfaction grade obtained using three enzymes was less than that obtained
using four enzymes. By contrast, the optimal grade obtained using five and six enzymes were
higher than that obtained using four enzymes. Notably, the overall satisfaction grade was 64%
when five enzyme targets were used, but the adverse effect was 85.4%.
Deficiencies of TH
The second case study considered four severities of TH: 50%, 70%, 90%, and 100% deficiencies
(referred as TH50, TH70, TH90, and TH100, respectively). Despite a complete TH deficiency
(TH100), for HS, the DA-e concentration levels changed from 400 to 245.7 because DOPA
decarboxylase converts L-DOPA to DA-i and is sequentially transported to the DA-e pool.
Following the procedures discussed in the first case study, we obtained the optimal enzyme
targets for different design specifications and deficiencies (Table 1). For TH50, TH70, and
TH90, using both one and two enzyme targets fulfilled the therapeutic and adverse effects
when one or two objectives were considered in the drug discovery problem. Moreover, the
overall satisfaction grade could reach 85.1% regulating with α14 and ut when the therapeutic,
adverse, and target variation effects were considered. However, for TH100, the overall
satisfaction grade was 58.8% with five enzyme targets when the three objectives were considered
simultaneously (Table 1). Furthermore, we compared the effects on the numbers of enzyme
targets. We fixed the number of enzyme targets to four, six, and seven and applied NHDE to
solve each drug discovery problem. Each optimal solution is presented in Fig 6. Although the
therapeutic level could achieve nearly 100%, the overall satisfaction grade of 41.6% obtained
11 / 18
Fig 6. Number of enzyme targets for VMAT2 and TH. Optimal drug discovery considered with therapeutic,
adverse, and variation effects simultaneously, at the specified number of enzyme targets. The left figure (A) is the
case for 95% deficiency of VMAT2, and the right (B) for 100% deficiency of TH, whereas ut, ul, and ud denote the
external control for tyrosine, L-DOPA, and intracellular dopamine, respectively. Furthermore, αj is the enzyme
activity for the jth reaction rate.
with four enzymes was less than that obtained with five enzymes. By contrast, the optimal
grades when using six and seven enzyme targets were higher than that obtained with five
enzymes (Fig 6).
Current Parkinson's disease medications
Several prescription drugs and their corresponding enzyme targets are currently used for
treating PD. The current medication are as following. The treatment of tyrosine intake control (ut)
is a diet control. Madopar and Sinemet are a clinical remedy for providing L-DOPA (ul).
Bromocriptine, Pergolide, Pramipexole and Ropinirole the prescription drugs for dopamine
agonist (ud). Entacapone and Tolcapone are catechol-O-methyl transferase (COMT) inhibitors,
which correspond to the rate constants of α22 and α26. Selegiline and Rasagiline are prescribed
for inhibiting MAO activities (MAOI), which correspond to the rate constants of α15, α23, and
α24. These current clinical drugs were respectively applied to treat PD caused by deficiencies of
VMAT2 and TH in order to evaluate the therapeutic, adverse, and target variation effects; the
computational results for various cases were listed in supporting information (S2 and S3
Tables). We observed that the current clinical drugs were unable to remedy diseases for 90 and
95% deficiencies of VMAT2, i.e. optimal solutions in the drug discovery problem for VM90
and VM95 were unable to be found. We found that MAOIs could remedy PD with the highest
satisfaction grades among PD medications for VM50 and VM70 (S2 Table). Similarly, several
deficiencies of TH were incapable of treatment by the current clinical drugs (S3 Table).
However, for TH50, the current PD medications could achieve >90% overall satisfaction level. For
TH70, MAOIs, COMT inhibitors and tyrosine intake control yielded >80% satisfaction
In the case of VM50 (S2 Table), satisfactory therapeutic efficacy (>56%) could be achieved
with the clinical drugs examined in this model. However, the satisfaction level of adverse effects
varied from 22% to 80%. We investigated the concentrations of the neurotoxic species in
VM50, to clarify the possible causes of neurotoxic and neuroprotective effects of the current
medications for PD. Table 2 shows the concentrations of toxic, ROS and RNS species at healthy
state (HS), their fold changes and the corresponding satisfaction grades of the adverse effect in
12 / 18
HS and VM50 denote as the healthy state and 50% VMAT2 de®ciency, respectively. L-DOPA/HS, DA-AG/HS, COMT/HS and MAOI/HS are the
concentration fold changes for treating L-DOPA, dopamine agonist, MAOI, and COMT inhibitors, respectively. ηj(xj) in parentheses is the corresponding
satisfaction grade of the adverse effect.
VM50 and various treatments. Four neurotoxic species in VM50, namely DOPA-Q, DA-Q,
HO, and HO–NO2, were higher than 1.2 fold change (or less than 0.94 satisfaction grade) to
their levels in HS. L-DOPA, dopamine agonist, MAOI, and COMT inhibitors were respectively
applied to treat the disease caused by VM50. The extracellular dopamine level was remedied
from the fold change of 0.486 to 0.673 after treating L-DOPA. However, the concentrations of
DOPA-Q, DA-Q, HO, and HO–NO2, increased about 8.0, 4.4, 2.5, and 2.3-folds, respectively,
i.e. induced more neurotoxic species. We obtained the similar results by treating dopamine
agonist, MAOI, and COMT inhibitors, respectively, as shown in Table 2. MAOI could achieve
100% therapeutic satisfaction grade and 80% adverse satisfaction grade for treating VM50.
To remedy the most severe illnesses, namely VM95 and TH100, the NHDE algorithm was
then applied for identifying a new set of formulated drugs, which included each current
prescription drug with their detected targets. Table 3 lists the optimal detected targets combined
with their prescription drugs. For VM95, the COMT inhibitors combined with four enzyme
targets (α13, α15, α31, and α61) could achieve 62.6% satisfaction level, which was higher than the
previous result obtained using four targets, as shown in the first row of Table 3. Thus, targets
α13 and α15 were found in each medication. By contrast, for TH100, the MAOIs combined
with five enzyme targets (α2, α8, ut, ul, and ud) achieved 63.7% satisfaction level, which was
higher than the previous result obtained using five targets, as shown in the first row of Table 3.
Thus, targets α2 and α8 were found in each medication.
The main strategy in treating motor symptoms of PD is dopamine replacement. However,
neuronal death and adverse effects were observed despite medical treatments. Several metabolites
in the dopamine metabolism, including ROS, RNS, and toxic species, were speculated to be
neurotoxic and might cause neurodegeneration in PD. Therefore, considering the therapeutic,
adverse, and target variation effects simultaneously is essential for making a PD treatment
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The current prescription drugs for PD treatment are shown in parentheses. VM95 re¯ect 95% de®ciency of VMAT2 and TH100 indicate 100% de®ciency of
TH. Furthermore, ut, ul, and ud denote the external control for tyrosine, L-DOPA, and intracellular dopamine, respectively. αj is the enzyme activity for the jth
reaction rate. T, A, and V denote the satisfaction grade for therapeutic, adverse, and variation effects, respectively.
* indicates the optimal solution.
plan. In the study, the concentration of DA-e in VM95 was lower than that in TH100, whereas
VM95 showed high concentrations of neurotoxic metabolites, namely DOPA-Q, DA-Q, HO.,
and HO.-NO2, compared with those observed in TH100. The results are compatible with the
experimental findings that a reduction in VMAT2 levels causes a severe reduction in dopamine
levels; elicits the nigrostriatal neurodegeneration, making neurons vulnerable to various toxic
agents; and causes motor deficits [
]. When considering only the therapeutic objective,
two and three enzyme targets were detected in TH100 and VM95, respectively, to completely
restore the concentration of DA-e to the basal levels. However, after treatment, the
concentrations of neurotoxic metabolites in VM95 were still substantially higher than those in TH100.
The fuzzy multiobjective optimization approach was performed with a trade-off procedure for
obtaining a compromise design to yield reduced therapeutic effect in order to improve adverse
and target variation effects.
This study also aimed to reduce the target variation effect and minimize the number of
enzyme targets. Reducing target variation effect leads to less perturbation in the enzyme
activities, implying usage of low drug doses and subsequently minimizing the adverse effects.
Furthermore, combination therapies are frequent in current PD treatments, and the simulation
shows that multiple enzyme targets are detected in treatments for severe enzymopathies.
However, drug combination may cause unexpected effects beyond those caused by an individual
]. Consequently, the number of enzyme targets should be minimized when the
therapeutic, adverse, and target variation effects are satisfied.
One of the pathological hallmarks of PD is the loss of dopaminergic neurons in the
substantia nigra pars compacta; the hypothesis is that dopamine itself may be toxic through oxidative
stress caused by auto-oxidation [
]. Clinically, the precursor of dopamine, L-DOPA, is the
most effective therapeutic agent for symptomatic relief of PD. However, chronic L-DOPA
treatment might be harmful [
], and L-DOPA could be neurotoxic [
]. In addition,
many in vitro studies have shown that L-DOPA and dopamine are cytotoxic [
et al. [
] reported that midbrain cell death increased in wide type and PINK1 gene knockout
mice when the dopamine concentration increased. A complex of ROS production and calcium
14 / 18
signaling were proposed to be the cause of dopamine induced cell death. Contrarily, the
DATATOP study and other follow-up trials have demonstrated that MAOI delays the use of
]. The computational results (Table 3, S2 and S3 Tables) confirmed the
aforementioned clinical observations. The computation using MAOI yielded concentrations of most
neurotoxic metabolites below the basal levels; however, concentrations of several neurotoxic
metabolites elevated when using L-DOPA.
In the work of Qi et al. [
], gain analysis was used to aid the screening and selection of
pharmacological therapies. In their simulation, increasing VMAT2 and MAO inhibition could elevate
concentrations of extracellular dopamine. Furthermore, combined targeting of VMAT2 and
MAO increased the extracellular dopamine and reduced the concentrations of toxic species. This
method examined enzyme targets in turn, and failed to simulate all the combinations. In OPDD
], optimization search and decision making were separated into two stages. The first stage
of the OPDD is to enumerate each enzyme to identify a set of candidate enzyme targets that fulfill
the therapeutic objectives. The second stage of the OPDD is a posterior decision making
determining a satisfactory target from the candidate enzyme targets. This method is less competent by
reason of the manual process of decision making. In our work, we introduce a fuzzy
multi-objective optimization approach to solve the enzyme target design problem. The problem is a unified
optimization framework, in which the identification of enzyme targets is combined with
multicriteria decision-making. This proposed method can consider all the objectives simultaneously
and identify the optimal enzyme targets for drug discovery efficiently.
It should be noted that there are limitations for the simulation of human metabolic
disorders. The prediction accuracy of the computation depends on the accuracy of the mathematical
model. Currently, the models of human metabolic networks are still under construction.
According to the advances in computational biology, some algorithms, such as the machine
learning methods for identification of multi-functional enzymes [
], can be valuable for
the construction of metabolic network. The results of our simulations may become more
precise to experimental results when the models become more complete. In this work, we propose
the method to act as a computer-aided design (CAD) of the drug discovery. This method
maybe unable to identify the exact targets for new drugs but can narrow down the targets for
further trial and error method. Eventually, the results of simulation should be verified with the
results of experiment.
A model-based drug target discovery problem is a decision-making problem, which can
consider many criteria in the optimization formulation. This study introduced a fuzzy
decisionmaking method for identifying enzyme targets of model-based drug discovery problems in
presynaptic dopamine metabolic networks. This method combined several objectives in a unified
framework to perform a trade-off procedure for obtaining a compromise design. In the case
study, three fuzzy objectives, namely therapeutic, adverse, and target variation effects, and a
number of targets were applied simultaneously for identifying enzyme targets. Moreover, the
effects and adverse effects of current medications can be compared in this model to clarify the
possible causes of neuroprotective and neurotoxic effects. Although the optimization approach
is a trend in drug discovery, meaningful and exact modeling is the core facilitator of the desired
S1 File. The detailed computational procedures.
15 / 18
S2 File. List of dependent and independent variables for presynaptic dopamine metabolic
S1 Table. The steady state concentrations of metabolites in healthy condition and various
deficiencies of VMAT2 and TH.
S2 Table. The therapeutic, adverse, and target variation effects remedied by the current
clinical drugs to treat PD caused by deficiencies of VMAT2.
S3 Table. The therapeutic, adverse, and target variation effects remedied by the current
clinical drugs to treat PD caused by deficiencies of TH.
The financial support from Ministry of Science and Technology of Taiwan (Grant
MOST1032221-E-194-045-MY3, MOST104-2627-B-194-001 and MOST105-2627-M-194-001), is highly
Conceptualization: KCH FSW.
Data curation: KCH FSW.
Formal analysis: KCH FSW.
Funding acquisition: FSW.
Investigation: KCH FSW.
Methodology: KCH FSW.
Project administration: FSW.
Resources: KCH FSW.
Validation: KCH FSW.
Visualization: KCH FSW.
Writing – original draft: KCH.
Writing – review & editing: FSW.
16 / 18
17 / 18
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