Computational procedures for multiobjective drug discovery problems.

<p>The left flowchart of the figure explains <i>a posteriori</i> 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 <i>a priori</i> 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.</p

Steady-state material balances of the intracellular dopamine.

<p>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 state.</p

A two-stage optimization procedure to discover a new drug target.

<p>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.</p

Fuzzy Decision Making Approach to Identify Optimum Enzyme Targets and Drug Dosage for Remedying Presynaptic Dopamine Deficiency

<div><p>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.</p></div

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.</p

Concentrations (relative unit) of metabolites at healthy state, their concentration fold changes and their corresponding satisfaction grades of the adverse effect in VM50 and various treatments by current prescription drugs.

<p>Concentrations (relative unit) of metabolites at healthy state, their concentration fold changes and their corresponding satisfaction grades of the adverse effect in VM50 and various treatments by current prescription drugs.</p

Number of enzyme targets for VMAT2 and TH.

<p>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 <i>u</i>_<i>t</i>, <i>u</i>_<i>l</i>, and <i>u</i>_<i>d</i> denote the external control for tyrosine, L-DOPA, and intracellular dopamine, respectively. Furthermore, α_<i>j</i> is the enzyme activity for the <i>j</i>^th reaction rate.</p

Schematic network diagram of the presynaptic dopamine metabolic pathway.

<p>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 (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164589#pone.0164589.s003" target="_blank">S1 Table</a>). 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.</p

Optimal results for the drug discovery problems with different deficient conditions.

<p>Optimal results for the drug discovery problems with different deficient conditions.</p

Optimal detected targets combined with their prescription drugs for the multiobjective drug discovery problem to remedy the most severe dopamine deficiency.

<p>Optimal detected targets combined with their prescription drugs for the multiobjective drug discovery problem to remedy the most severe dopamine deficiency.</p