Analyzing a series of ligands against malaria through the application of molecular docking, molecular quantum similarity, and reactivity indices

Alejandro Morales-Bayuelo; Ricardo Vivas-Reyes; Savas Kaya

doi:10.12688/f1000research.147631.1

Home Browse Analyzing a series of ligands against malaria through the application...

ALL Metrics

-

Views

-

Downloads

Get PDF

Get XML

Export

▬

✚

Research Article

Analyzing a series of ligands against malaria through the application of molecular docking, molecular quantum similarity, and reactivity indices

[version 1; peer review: 1 approved with reservations, 1 not approved]

Alejandro Morales-Bayuelo ¹, Ricardo Vivas-Reyes², Savas Kaya³

PUBLISHED 02 May 2024

Author details Author details

¹ Process Research Center of Tecnológico Comfenalco (CIPTEC), Industrial Engineering Program, Fundación Universitaria Tecnológico Comfenalco, Cartagena, Colombia
² Group of Quantum and Theoretical Chemistry, Faculty of Exacts and Naturals Sciences, University of Cartagena, Cartagena de Indias, 130001, Bolivar, Colombia
³ Faculty of Science, Department of Chemistry, Sivas Cumhuriyet University, 58140, Sivas, Turkey

Alejandro Morales-Bayuelo
Roles: Conceptualization, Data Curation, Formal Analysis, Funding Acquisition, Investigation, Methodology, Project Administration, Resources, Software, Supervision, Validation, Visualization, Writing – Original Draft Preparation, Writing – Review & Editing

Ricardo Vivas-Reyes
Roles: Formal Analysis, Writing – Review & Editing

Savas Kaya
Roles: Formal Analysis, Writing – Review & Editing

OPEN PEER REVIEW

REVIEWER STATUS

Abstract

Background

The primary goal of this research is to underscore the significance of molecular docking in the context of malaria drug discovery. Molecular docking plays a crucial role in comprehending the interactions between prospective drugs and the target proteins found in Plasmodium parasites. The study delves into the docking interactions of various compounds, emphasizing the necessity of stabilizing the active site to formulate potent and selective drugs.

Methods

The research focuses on highlighting compound-specific interactions with residues, stressing the importance of stabilizing the active site to design drugs tailored to specific target proteins. Inhibiting the function of these target proteins disrupts the life cycle of the malaria parasite. Quantum Similarity Analysis, utilizing Overlap and Coulomb operators, is employed to identify electronic similarities. The resulting quantum similarity values guide subsequent chemical reactivity analysis. Global reactivity indices such as chemical potential, hardness, softness, and electrophilicity contribute to drug design by showcasing compound-specific indices that underscore the significance of stability and electrophilicity. Fukui functions are utilized to visualize regions for stabilization, providing insights crucial for potential malaria treatment.

Results

The enhancement of drug-target binding affinity is observed through stabilizing interactions in the active site. Understanding electrophilicity at the active site emerges as a critical factor in drug design and selectivity. The rational manipulation of electrophilic interactions holds promise for developing potent and selective drugs against malaria. Consequently, the integration of molecular docking, quantum similarity analysis, and chemical reactivity indices offers a comprehensive approach to malaria drug discovery.

Conclusions

The study identifies potential lead compounds, emphasizing the crucial role of stabilizing the active site. Additionally, it sheds light on electronic considerations vital for the design of effective and resistance-resistant drugs. The insights provided by Fukui functions into regions susceptible to -H bond formation make these compounds promising candidates for malaria treatment.

Keywords

Malaria treatment, drug design, molecular docking, molecular quantum similarity, chemical reactivity indices, Density Functional Theory.

Corresponding author: Alejandro Morales-Bayuelo

Competing interests: No competing interests were disclosed.

Grant information: Tecnologico-2024-I.
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Copyright: © 2024 Morales-Bayuelo A et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

How to cite: Morales-Bayuelo A, Vivas-Reyes R and Kaya S. Analyzing a series of ligands against malaria through the application of molecular docking, molecular quantum similarity, and reactivity indices [version 1; peer review: 1 approved with reservations, 1 not approved]. F1000Research 2024, 13:435 (https://doi.org/10.12688/f1000research.147631.1) First published: 02 May 2024, 13:435 (https://doi.org/10.12688/f1000research.147631.1) Latest published: 02 May 2024, 13:435 (https://doi.org/10.12688/f1000research.147631.1)

Introduction

Malaria remains a substantial global health challenge, particularly in numerous tropical and subtropical regions. The disease is endemic in various countries, especially in sub-Saharan Africa, Southeast Asia, and parts of Central and South America,¹^–³ where it imposes the highest disease burden. Plasmodium parasites, transmitted through the bites of infected female Anopheles mosquitoes, cause malaria. Among the Plasmodium species infecting humans, P. falciparum is the most lethal. In 2020, the global tally of malaria cases, as reported by the World Health Organization (WHO), stands at approximately 241 million, with 627,000 recorded deaths, with a disproportionate impact on Africa.³^–⁶ At-risk demographics, including infants and expectant mothers, bear a significant burden, with pregnant women facing heightened risks, including maternal anemia and low birth weight. Control and prevention measures encompass the use of insecticide-treated bed nets, indoor residual spraying, antimalarial drugs, and initiatives targeting mosquito breeding sites.⁶^,⁷ While Artemisinin-based combination therapies (ACTs) are extensively employed for treating uncomplicated malaria, other antimalarial drugs may be utilized for specific cases or regions. The emergence of drug resistance, particularly in the Greater Mekong Subregion, presents a formidable challenge to malaria control efforts.⁷^–¹⁰ Additionally, concerns about insecticide resistance in mosquitoes underscore the importance of exploring new alternatives for malaria treatment.¹¹^–¹⁴

Current research is dedicated to advancing the development of novel antimalarial medications, vaccines, and inventive vector control strategies. The objective is to enhance the arsenal of tools for preventing, treating, and ultimately eradicating malaria. Global malaria control initiatives are actively supported by international organizations, governments, and non-governmental organizations, with pivotal roles played by the WHO's Global Malaria Program and the Roll Back Malaria Partnership in orchestrating collaborative endeavors to diminish the worldwide impact of malaria.¹⁵^–¹⁸

Furthermore, the challenges posed by the COVID-19 pandemic have impacted malaria control efforts, redirecting resources and straining health systems. For the most recent and accurate information, it is advisable to refer to recent reports from health organizations and institutions actively engaged in malaria control.¹⁹^–²² Protein kinases play pivotal roles in diverse cellular processes, encompassing signal transduction, cell cycle regulation, and gene expression.²³^,²⁴ Within the context of the malaria parasite, Plasmodium spp., protein kinases are indispensable for the parasite's survival and proliferation within the host.²⁵^–²⁹ Understanding the role of protein kinases in the malaria parasite holds significance for the development of targeted therapeutic strategies. Here are key insights into protein kinases in the malaria parasite:

Abundance of Protein Kinases: The genome of Plasmodium spp., including the human malaria parasite Plasmodium falciparum, encodes a multitude of protein kinases. P. falciparum, exemplarily, boasts over 80 putative protein kinases.³⁰^–³³ Diverse Functions: Protein kinases in Plasmodium participate in a spectrum of cellular processes, including signal transduction, cell cycle progression, host cell invasion, and immune evasion.³³^,³⁴ They play a crucial role in regulating the parasite's life cycle, spanning the invasion of host cells by the sporozoite stage to the replication within hepatocytes (liver stage) and erythrocytes (blood stage).³⁵^–³⁷ Unique Kinases: Some protein kinases in the malaria parasite exhibit uniqueness or distinct features compared to their counterparts in the host.³⁸^–⁴⁰ This distinctiveness presents opportunities for developing drugs that selectively target the parasite without affecting host cell kinases.⁴⁰^–⁴²

Druggability and Therapeutic Targets: Protein kinases have been identified as potential drug targets for antimalarial therapies. Inhibiting specific kinases can disrupt essential cellular processes in the parasite, leading to its demise. Ongoing efforts aim to identify and characterize specific protein kinases critical for the parasite's survival and development.⁴³ Inhibitors targeting these kinases could serve as the foundation for developing new antimalarial drugs. Examples of Protein Kinases in Plasmodium: Notable examples include PfCDPK1 (Calcium-Dependent Protein Kinase 1), involved in the invasion of host erythrocytes; PfPKA (Protein Kinase A), with a role in the regulation of the cell cycle; and PfPKG (Protein Kinase G), significant for the development of sexual stages of the parasite in the mosquito vector.⁴⁰^–⁴³

Progress in antimalarial drug discovery has been notable, but challenges such as drug resistance and the intricate life cycle of the malaria parasite persist, driving ongoing research efforts.³⁸^–⁴¹ Key aspects and approaches in antimalarial drug discovery include:

Targeting the Parasite's Life Cycle: Malaria, caused by Plasmodium parasites, involves a complex life cycle in both the mosquito vector and human host. Antimalarial drug discovery aims to target various stages, including the liver stage, blood stage, and transmission-blocking interventions to disrupt the life cycle.³⁰^–³⁵ Artemisinin-Based Combination Therapies (ACTs): Artemisinin and its derivatives are potent antimalarial drugs that rapidly reduce parasite biomass. ACTs, combining artemisinin compounds with other antimalarials, have proven highly effective in treating uncomplicated malaria.³⁹^–⁴² However, concerns arise over the emergence of artemisinin resistance in some regions. Drug Resistance Monitoring and Surveillance: The development of resistance to antimalarial drugs is a significant challenge. Ongoing efforts focus on monitoring and surveillance, utilizing molecular techniques to identify resistance markers in the parasite's genome.⁴⁰^–⁴³ New Target Identification: Researchers continually identify potential drug targets within the malaria parasite. This includes enzymes in essential metabolic pathways, proteins crucial for invasion and egress from host cells, and unique features of the parasite's biology exploitable for drug development.²⁵^–³⁰ High-Throughput Screening (HTS): HTS techniques rapidly test large compound libraries to identify molecules with antimalarial activity, expediting the drug discovery process.³⁰^–³⁵ Fragment-Based Drug Design: This methodology involves screening small molecular fragments for their ability to bind to a target, leading to the design of more potent and specific compounds.³⁵^–³⁸ Repurposing Existing Drugs: Cost-effective repurposing of drugs developed for other diseases has shown promise. Some drugs, initially designed for different purposes, exhibit antimalarial activity, expediting the development process. Vaccines and Transmission-Blocking Strategies: Malaria vaccine development, while not conventional, is integral to the broader strategy against the disease.⁴⁰^–⁴³ Additionally, transmission-blocking drugs aim to reduce mosquito transmission of the parasite, contributing to malaria control efforts. Public-Private Partnerships: Collaboration among academic institutions, pharmaceutical companies, and public health organizations is crucial for advancing antimalarial drug discovery. Public-private partnerships facilitate pooling resources, expertise, and funding to accelerate research and development.³⁸^–⁴³

In this manuscript is used an approach based in molecular docking, Molecular quantum similarity and Chemical reactivity indices. A comprehensive approach could involve integrating molecular docking, molecular quantum similarity, and chemical reactivity indices. For example, molecular docking can be used to predict the binding mode of a ligand to a target protein, while molecular quantum similarity and reactivity indices can help understand the electronic and chemical properties governing the interaction. We Started with molecular docking to identify potential ligands, validating the results using quantum similarity methods, and then analyze the reactivity indices to gain insights into the chemical behavior of the molecules.

Integrating these approaches allows us to leverage the strengths of each method, providing a more holistic understanding of molecular interactions and properties. However, it's important to note that these computational techniques are complemented by experimental validation for robust results. In this sense, the ligand studied has been analyzed by the Zhang group.⁴⁴ In this sense, in this manuscript these ligands will be analyzed using new reported protein kinases with the aim of obtaining new considerations on the antimalarial activity of these ligands.

Method

Approach for docking investigations

Protein preparation

During the docking experiment, the receptor structure was generated in adherence to specific protocols, drawing inspiration from the crystal structure of the co-crystallized ligand located at the core of PDB entries 1ob3 and 2pmn. Structural adjustments were implemented employing the protein preparation wizard module from the Schrödinger suite 2017-1. These adjustments included optimizing the hydrogen bond (H-bond) network and refining the protein structure. The PropKa (https://github.com/schrodinger/propka-3.1) utility was utilized to determine protonation states at physiological pH. Additionally, restrained molecular minimization was executed through the Impact Refinement (Impref, https://newsite.schrodinger.com/platform/products/maestro/) module, with heavy atoms constrained to a low root-mean-square deviation (RMSD, https://newsite.schrodinger.com/platform/products/maestro/) from the initial coordinates.⁴⁵^–⁴⁷

In contrast, the molecular structures of the compounds were fashioned using the Maestro Editor (Maestro, version 11.1, Schrödinger, LLC). Subsequently, 3D conformations were generated employing the LigPrep module, and ionization/tautomeric states were predicted under physiological pH conditions using Epik. Finally, energy minimization was carried out using the Macro model and the OPLS2005 force field.

Molecular docking considerations

For the molecular docking investigations, Glide⁴⁸^,⁴⁹ was employed with default parameters and the Standard Precision (SP) model. The docking grid was established using default settings, positioning the co-crystallized ligands from PDB entries 1ob3 and 2pmn at the center. To enhance the binding of larger ligands, a scaling factor of 0.8 for the van der Waals radii of nonpolar protein atoms was applied. Extra precision (XP) was also employed to accommodate alternate receptor conformations suitable for binding ligands with unconventional orientations through induced fit docking (IFD). This approach allows for potential side-chain, backbone, or combined movements in the protein structure upon ligand docking. Redocking was performed for all results, and subsequent RMSD calculations were conducted. The binding pocket was identified using Glide.⁴⁸^,⁴⁹

The docking procedure comprised four meticulous steps, leveraging Glide's scoring function and Prime's advanced conformational refinement for precision:

i. Initial docking was conducted using Glide on the rigid receptor to generate a set of poses.
ii. The side-chain prediction module of the Prime tool was utilized to sample the protein, followed by structural minimization for each pose of the protein/ligand complex.
iii. Redocking of the ligand into the low-energy induced-fit structures from the previous step was carried out using Glide's default parameters, without van der Waals scaling.
iv. The binding energy (IFDScore) was estimated, taking into account the docking energy (GScore), receptor strain, and solvation terms (Prime energy).

To further evaluate ligand interactions in the active site, the extent of residue movement induced by the induced-fit docking (IFD) computation was considered. For both the most and least active ligands, all poses were compared within the molecular set. Molecular dynamics calculations spanning 30 ns were employed to predict the best poses and analyze their stabilization in the active site.

Quantum similarity study

Molecular quantum similarity framework

The Molecular Quantum Similarity Measure (MQSM), represented as ZAB, is utilized to compare two systems, A and B, by evaluating molecules generated using their respective Density Functions (DFs). The DFs are multiplied and integrated over electronic coordinates, incorporating weighting by a pre-established positive operator Ω(r1, r2)⁵⁰^–⁵²:

(1)

Z_{AB} = ⟨ ρA | Ω | ρB ⟩ = \int \int ρA (r 1) Ω (r 1, r 2) ρB (r 2) dr 1 dr 2

The selection of the operator in Equation 1 holds significance, as it shapes the information under comparison and functions as a similarity measure between the two systems. For example, the Dirac delta function (Ω(r1, r2) = δ(r1 - r2)) proves effective for functions characterized by high peak values, such as electronic density, resembling a charge or point mass.

Commonly utilized similarity metrics include the overlapping Molecular Quantum Similarity Measure (MQSM) and the Coulomb operator (Ω(r1, r2) = |r1 - r2|⁻¹). Additionally, a self-similarity measure (ZAA for molecule A) can be applied, even when comparing two equivalent molecules.⁵²

For a group of N molecules, a similarity measure is computed for each molecule concerning others, resulting in a symmetric matrix. Each column in this matrix represents the similarity measurements between the molecule and every constituent in the group, generating discrete N-dimensional representations for each structure. These vectors serve as unique chemical descriptors extending beyond traditional molecular descriptors.⁵¹^–⁵⁸ They are universal, derived from any collection of molecules. They are impartial, determined solely by density functions and similarity measurements.

Carbó's similarity index

Carbó's similarity index (Equation 2) for two molecules, I and J, relies on the cosine of the angle formed by their density functions when treated as vectors. This index varies between 0 and 1, signifying the degree of similarity between the two molecules.⁵⁰^–⁵⁵

(2)

C_{IJ} (Ω) = z_{IJ} (Ω) {[z_{II} (Ω) z_{JJ} (Ω)]}^{- 1 / 2}

Carbó's similarity index between two molecules, I and J, is obtained from Equation 2. Also known as the cosine similarity index, it aligns with the cosine of the angle formed by the density functions treated as vectors. The Carbo QSI for any pair of compared molecules spans from 0 to 1, indicating the extent of similarity between the two molecules (approaching 1 when I equals J).⁵⁰^–⁵⁵

Quantum similarity using the Euclidean distance

Equation 3 introduces a similarity measure expressed as the Euclidean distance index (Equation 4). This index represents the distance or dissimilarity between two quantum objects, allowing geometric interpretation based on the norm of the differences in density functions:

(3)

D_{IJ} (k, x, Ω) = {[k (z_{II} (Ω) + z_{JJ} (Ω)) / 2 - x z_{IJ} (Ω)]}^{1 / 2}, x [0, k]

It is simplified to the so-called Euclidean distance index when k = x = 2. Index 3 of the form can also be defined as follows:

(4)

D_{IJ} (\infty, Ω) = max (z_{II} (Ω), z_{JJ} (Ω))

This Equation 4 forms the distance index of infinite order.⁵⁰^–⁵⁵

MQSM overlap considering the Equation 2

The Dirac delta distribution, Ω (r1, r2) = δ (r1, r2), stands out as the most common and intuitive option for a positively defined operator in this context. Such choices refine the broad definition of MQSM, resulting in the computation of the overlap MQSM, which gauges the volume measurements covered by both electronic density functions when superimposed.⁵⁶^–⁶⁰

(5)

z_{IJ} (Ω) = \int \int ρ_{I} (r_{1}) δ (r_{1} - r_{2}) ρ_{J} (r_{2}) d r_{1} d r_{2} = \int ρ_{I} (r) ρ_{J} (r) dr

Derived from its physical definition, the Dirac delta function is computationally manageable. The Molecular Quantum Similarity Measure (MQSM) gauges the degree of overlap in molecular comparisons by incorporating information about the electron concentration within the molecule.⁶¹^–⁶³

MQS Coulomb considering the Equation 5

When the operator (Ω) is replaced with the Coulomb operator, Ω (r₁, r₂) = $\frac{1}{│ r_{1} - r_{2} │}$ , the coulomb MQS is generated, which defines the electrostatically repellent coulomb energy between two charge densities⁶⁴^–⁶⁷:

(6)

Z_{IJ} (Ω) = \int \int ρ_{I} (r_{1}) \frac{1}{r_{1} - r_{2}} ρ_{J} (r_{2}) d r_{1} d r_{2}

The Coulomb operator plays a role in influencing the overlap of density functions. When molecular density functions are considered as electron distributions in space, this equation essentially extends the Coulomb operator for continuous charge distribution. In certain cases, it can be used as electrostatic potential descriptors. This operator is associated with electrostatic interactions and measures the electrostatic repulsion between electronic distributions.⁶⁸

Euclidean distance index considering the Equation 3

Another major transformation that can be expressed in terms of the classical distance is:

(7)

d_{ab} = {[\sum_{j = 1}^{p} {(Δ x_{j})}^{k}]}^{\frac{1}{k}}

Here $Δ x_{j} = x_{aj} - x_{bj}$ is the distance between a and b, and k = 2 is the definition of distance, respectively. Subsequently, the Euclidean distance between A and B as two quantum objects are defined by⁶⁸^–⁷⁰:

(8)

d_{ab} = \sqrt{{(x_{a} - x_{b})}^{2}} .

Occasionally it is written as: $D_{AB} = \sqrt{Z_{AA} + Z_{BB} + Z Z_{AB}}$ , where D_AB has values in the range of [0,∞) but for earlier circumstances where the compared items are identical, it converges to zero between them⁷⁰^–⁷²:

(9)

D_{AB} = 0

The norm of the differences in the density functions of the compared objects can be used to interpret this index geometrically. The distance or dissimilarity index can be used to define the Euclidean distance index, which can also be represented as⁷³:

(10)

D_{AB} = ∥ ρ_{A} - ρ_{B} ∥ = \sqrt{{(ρ_{A} - ρ_{B})}^{2}}

Alignment Method: Topo-Geometrical Superposition Algorithm (TGSA)

In this investigation, the TGSA is employed for data alignment, aligning molecules based on a common skeleton using atomic types and interatomic bonding interactions. TGSA functions through the scrutiny of atomic pairs, forming triangles, and evaluating atomic triads. This approach offers a distinctive and chemically intuitive alignment, even in cases where molecular structures exhibit limited flexibility.⁷³^–⁷⁶

Chemical reactivity context

Research in this domain has unveiled a firmly established correlation between quantum similarity and descriptors associated with chemical reactivity.⁷⁷^,⁷⁸ Both quantum similarity and Density Functional Theory (DFT) make use of the density function as a fundamental component in the analysis of similarity indices. Specifically, the Coulomb index can be correlated with electronic factors influencing chemical reactivity. In the computation of global reactivity indices, such as chemical potential (μ),⁷⁷ hardness (ɳ),⁷⁸ and electrophilicity (ω),⁷⁹^,⁸⁰ Frontier Molecular Orbitals (FMO) and the energy gap will be employed. These indices, represented by Equations 11-13, offer valuable insights into system stability. Chemical potential gauges the tendency of electrons to deviate from the equilibrium system,⁸¹ while chemical hardness assesses a chemical species' resistance to altering its electronic configuration.

(11)

μ \approx \frac{E_{LUMO} + E_{HOMO}}{2}

(12)

η \approx E_{LUMO} - E_{HOMO}

The mathematical definition of the electrophilicity index (ω) is related to the stabilization energy of a system when it becomes saturated by electrons from the external environment.³⁹^,⁴⁰:

(13)

ω = \frac{μ^{2}}{2 η}

In this study, the focal descriptors of reactivity under examination were the Fukui functions. Equation (14) depict how the electronic density of the system responds to changes in the global charge, representing the derivative of the electronic density with respect to the electron count under a uniform external field.

(14)

f^{+} (\vec{r}) \approx {| LUMO (\vec{r}) |}^{2}

f^{-} (\vec{r}) \approx {| HOMO (\vec{r}) |}^{2}

The terms $f^{+} (\vec{r})$ and $f^{-} (\vec{r})$ and are utilized to represent nucleophilic and electrophilic attacks, respectively.⁸¹^–⁸³

This approach integrates both global and local reactivity descriptors to evaluate quantum similarity within the molecular set. All calculations were conducted using the B3LYP method⁸⁴ with the 6-311xxG(d,p) basis set,⁸⁴ which represents an improvement over the 6-311G(d) basis set. This enhancement facilitates the computation of electronegativity, hardness, reactivity indices, and frontier molecular orbitals at a level of quality comparable to larger basis sets like Aug-cc-pVQZ and Aug-cc-pV5Z. The Gaussian 16 package⁸⁵ was employed in conjunction with this method/basis set combination.

Results and Discussion

Molecular docking outcomes for the ligands

Molecular docking plays a crucial role in drug discovery for malaria treatment. Malaria, caused by the Plasmodium parasites, A potentially fatal illness that impacts millions of individuals globally. Developing effective drugs to combat malaria requires a deep understanding of the interactions between potential drug molecules and target proteins within the Plasmodium parasites.

The compound 1 has interaction with the residue MET120 (-H, 1,125 Å) (Figure 1). In Figure 2 is shows the interaction with the compound 2 with the residues ASP123 (-H, 1,148 Å) and SER (-H, 1,358 Å).

Figure 1. Docking interactions for Compound 1.

Figure 2. Docking interactions for Compound 2.

In Figure 3, the compound 3 has interaction with the residue ASP123 (-H, 1,2561 Å).

Figure 3. Docking interactions for Compound 3.

Molecular docking helps identify and validate potential drug targets within the Plasmodium parasites. By simulating the interaction between small molecules and target proteins, researchers can prioritize which proteins are most promising for drug development. The three-dimensional structures of target proteins involved in the malaria-causing parasites are essential for designing drugs that specifically interact with these proteins. Molecular docking aids in the rational design of drug candidates by predicting the binding modes and affinities of small molecules to target proteins. Figure 4 has the interactions with the residues MET120 (-H, 1,1961 Å).

Figure 4. Docking interactions for Compound 4.

In Figure 5 is shows the interaction with the residue SER176 (-H, 1,256 Å).

Figure 5. Docking interactions for Compound 5.

The importance of stabilization on the active site of proteins involved in malaria lies in the context of drug discovery and the development of therapeutics. The active site of a protein is a region where interactions with other molecules, such as substrates or ligands, occur. In the case of proteins associated with malaria, targeting the active site is crucial for designing drugs that can disrupt or modulate the function of these proteins. The active site of a protein is often the functional region where the protein interacts with its substrates or other molecules. By stabilizing the active site, researchers can design drugs that specifically bind to and modulate the activity of the protein involved in the malaria-causing parasite. Stabilizing the active site allows for the design of drugs that are specific to the target protein. This specificity is crucial to avoid unintended interactions with other proteins in the host organism, minimizing side effects and improving the selectivity of the drug.

Many drugs work by inhibiting the function of a target protein. Stabilizing the active site facilitates the design of molecules that can bind tightly to the protein, disrupting its normal function. This inhibition is essential for interfering with the life cycle of the malaria parasite or preventing its ability to infect and survive within the host. Some proteins involved in malaria may rely on interactions with other proteins for their function. Stabilizing the active site can disrupt these protein-protein interactions, leading to the inhibition of essential pathways or processes required for the survival of the parasite. Figure 6 shows the interaction with the residues ASP123 (-H, 1,356 Å), SER124 (-H, 1,568 Å) and SER176 (-H, 1,239 Å), respectively.

Figure 6. Docking interactions for Compound 6.

Molecular docking provides insights into the strength of the interactions between drug candidates and target proteins by predicting binding affinities. This information is crucial for selecting lead compounds with high binding affinity and therapeutic efficacy. On the other hand, Malaria parasites can develop resistance to drugs over time. Molecular docking helps researchers understand the structural basis of drug resistance by predicting how mutations in target proteins might affect drug binding. This information is vital for designing drugs that are less prone to resistance.

Figure 7 shows the interaction with the residue ASP123 (-H, 1,569 Å) and PHE128 (-H, 1,4265 Å). In Figure 8, we can see the interactions with the residues ASP123 (-H, 1,4569 Å) and PHE128 (-H, 1,3569 Å).

Figure 7. Docking interactions for Compound 7.

Figure 8. Docking interactions for Compound 8.

In Figure 9, we can see the interaction with the residue ASP123 (-H, 1,319 Å).

Figure 9. Docking interactions for Compound 9.

Stabilizing the active site contributes to enhancing the binding affinity between the drug and the target protein. A strong and stable interaction is crucial for the drug to exert its therapeutic effects at lower concentrations, improving the efficacy of the drug. Malaria parasites can develop resistance to drugs over time. By targeting the active site and stabilizing interactions, researchers can design drugs that are less prone to resistance, as mutations in the active site that confer resistance may have a higher fitness cost to the parasite.

Knowledge of the three-dimensional structure of the active site is essential for structure-based drug design. Stabilizing interactions within the active site allows for the rational design of drug candidates that fit precisely into the binding pocket of the target protein. In these sense, stabilizing the active site of proteins involved in malaria is crucial for designing effective and specific drugs. This approach allows for the development of therapeutics that selectively target the parasite, disrupt essential processes, and minimize the risk of resistance. Structure-based drug design techniques, including molecular docking and computational simulations, often play a significant role in understanding and optimizing the stabilization of the active site.

Molecular quantum similarity analysis

Quantum Similarity Analysis in drug design provides a powerful tool for understanding molecular similarity at a deep, electronic level, contributing valuable insights into the development of new pharmaceutical agents. It integrates quantum mechanical principles into the drug discovery process, offering a more nuanced perspective on molecular interactions and reactivity.

In Table 1 the Higher similarity using the Overlap operator is between the compounds 3 and 4 with 0,8576 and an euclidean distance of 2,0743 (see Table 2). The lowest similarity value is between the compounds 3 and 6 with 0,2666 and an euclidean distance of 4,9818.

Table 1. Molecular Quantum Similarity using the Overlap Operator.

O_Hab	1	2	3	4	5	6	7	8	9
1	1,0000
2	0,4676	1,0000
3	0,3477	0,4125	1,0000
4	0,3920	0,4651	0,8576	1,0000
5	0,4020	0,4905	0,4939	0,4762	1,0000
6	0,3507	0,4124	0,2666	0,2975	0,6859	1,0000
7	0,4849	0,4435	0,4226	0,3835	0,4695	0,3502	1,0000
8	0,3391	0,4116	0,2462	0,2747	0,7208	0,6409	0,3204	1,0000
9	0,3893	0,3463	0,4457	0,4227	0,2698	0,2382	0,7147	0,3261	1,0000

Table 2. Molecular Quantum Similarity using the Overlap Euclidean Distance.

O_Dab	1	3	4	5	6	7	8	9
1	0,0000
2	4,1376
3	4,6775	0,0000
4	4,4362	2,0743	0,0000
5	4,8582	4,3635	4,3756	0,0000
6	4,8343	4,9818	4,7885	3,5433	0,0000
7	4,4332	4,5664	4,6419	4,7072	4,9962	0,0000
8	5,0896	5,2859	5,1046	3,4558	3,7726	5,3115	0,0000
9	4,9863	4,6415	4,6696	5,6808	5,5824	3,5063	5,4432	0,0000

In Table 3. The higher similarity using the Coulomb operator is between the compounds 5 and 6 with 0,9389 and an euclidean distance of 21,8492 (see Table 4). On the other hand, the lowest similarity value is between the compounds 4 and 8 with 0,5758 and an euclidean distance of 43,5506.

Table 3. Molecular Quantum Similarity using the Coulomb Operator.

C_Hab	1	2	3	4	5	6	7	8	9
1	1,0000
2	0,8997	1,0000
3	0,8075	0,8690	1,0000
4	0,8010	0,8865	0,9785	1,0000
5	0,7653	0,9061	0,9061	0,8892	1,0000
6	0,8247	0,8724	0,6911	0,5994	0,9389	1,0000
7	0,8424	0,8965	0,8507	0,8504	0,9002	0,8045	1,0000
8	0,8222	0,8653	0,6785	0,5758	0,9276	0,9354	0,7810	1,0000
9	0,7171	0,7294	0,8219	0,8196	0,8387	0,6380	0,9598	0,7983	1,0000

Table 4. Molecular Quantum Similarity using the Coulomb Euclidean Distance.

C_Dab	1	2	3	4	5	6	7	8	9
1	0,0000
2	18,1789	0,0000
3	26,2062	21,4141	0,0000
4	25,6349	18,9616	9,1432	0,0000
5	36,8946	27,0801	25,7364	28,3483	0,0000
6	25,4565	21,6359	34,3067	37,8537	21,8492	0,0000
7	24,9030	20,4358	24,4884	24,2102	25,5028	28,2490	0,0000
8	29,5238	26,4862	38,8713	43,5506	21,4000	18,8140	32,8284	0,0000
9	37,2469	36,4414	30,3458	30,7379	31,5926	42,2705	15,8066	33,3964	0,0000

Because the highest values of electronic quantum similarity were obtained, we have performed an analysis of chemical reactivity to obtain new electronic considerations in the molecular set.

Global and local chemical reactivity indices

Local reactivity indices guide the introduction of specific functional groups at strategic positions to enhance or modify the biological activity of a molecule. In these sense, global and local chemical reactivity indices play a crucial role in drug design by providing valuable information about the electronic structure and reactivity of molecules. These indices guide the selection of molecular modifications to optimize the pharmacological properties of drug candidates.

In Table 5, the compound with higher chemical potential is the compound 5 with μ = -5,4916 eV, Hardness, (ƞ = 4,5876 eV), Softness, (S = 0,2180 eV)⁻¹ and electrophilicity, (ω = 3,6480 eV). Another compound with good stability is the compound 3 with μ = -4,4106 eV, Hardness, (ƞ = 5,3315 eV), Softness, (S = 0,1876 eV⁻¹) and Electrophilicity, (ω = 1,8243 eV).

Table 5. Global reactivity indices for the compound.

Compound	C. Potential (μ, eV)	Hardness (ƞ, eV)	Softness (S, eV⁻¹)	Electrophilicity (ω, eV)
1	-4,1857	2,6673	0,3749	3,2842
2	-3,7835	3,9696	0,2519	4,1910
3	-4,4106	5,3315	0,1876	1,8243
4	-3,9814	3,7394	0,2674	4,5777
5	-3,3243	4,8200	0,2075	1,1464
6	-5,4916	4,5876	0,2180	3,6480
7	-4,1147	3,4118	0.2931	3,8337
8	-3,5401	5,1421	0.1944	1,2186
9	-3,8964	3,8695	0.2584	1,3568

The compound with higher electrophilicity is 4 with ω = 4,5777eV. Understanding electrophilicity at the active site of a protein is essential in drug design and medicinal chemistry. The active site is a region within a protein where specific interactions occur with ligands, substrates, or inhibitors. Electrophilicity in this context refers to the propensity of a molecule or a functional group to accept electrons, and it plays a crucial role in the binding of ligands to the protein. Certain amino acid residues in the active site of a protein may exhibit electrophilic characteristics. Common electrophilic residues include positively charged amino acids such as lysine (LYS) and arginine (ARG), which can form electrostatic interactions with negatively charged ligands.

Assessing electrophilicity in the active site of proteins is a fundamental aspect of drug design. It involves considering both the electrophilic nature of ligands and the nucleophilic properties of the protein's active site residues. Strategic control of electrophilic interactions has the potential to yield enhanced efficacy and selectivity in the creation of drugs for Malaria. In Figures 10 and 11, we can see the local regions involved in the stabilization into the protein pocket for the compound with higher experimental IC₅₀.

Figure 10. (a) $f^{-} (\vec{r}) \approx {| HOMO (\vec{r}) |}^{2}$ and (b) $f^{+} (\vec{r}) \approx {| LUMO (\vec{r}) |}^{2}$ , for the compound 2. Fukui Funtions (b) $f^{-} (\vec{r}) \approx {| HOMO (\vec{r}) |}^{2}$ and (c) $f^{+} (\vec{r}) \approx {| LUMO (\vec{r}) |}^{2}$ , for the compound 6.

Figure 11. Fukui Funtions (a) $f^{-} (\vec{r}) \approx {| HOMO (\vec{r}) |}^{2}$ and (b) $f^{+} (\vec{r}) \approx {| LUMO (\vec{r}) |}^{2}$ , for the compound 7. Fukui Funtions (c) $f^{-} (\vec{r}) \approx {| HOMO (\vec{r}) |}^{2}$ and (d) $f^{+} (\vec{r}) \approx {| LUMO (\vec{r}) |}^{2} f^{+} (\vec{r}) \approx {| LUMO (\vec{r}) |}^{2}$ , for the compound 8.

Figures 10 and 11 show good regions for the stabilization into the active site. These regions offers susceptibilities to form -H bond and consequently can be good candidates for the malaria treatment.

Conclusions

Molecular docking is an indispensable tool in malaria drug discovery, providing insights into the interaction between potential drug molecules and target proteins within Plasmodium parasites. The study focused on the docking interactions of various compounds, emphasizing their specific interactions with residues. Stabilizing the active site of proteins associated with malaria is crucial for designing effective and selective drugs. The docking results, shows interactions with specific residues. Stabilizing the active site enhances binding affinity, a critical factor for drug efficacy. The specificity achieved by targeting the active site minimizes unintended interactions, reducing side effects and improving drug selectivity.

Quantum Similarity Analysis, incorporating the Overlap and Coulomb operators, offers a deep electronic perspective on molecular interactions. The study presents tables indicating the electronic quantum similarity between different compounds. The analysis provides insights into chemical reactivity and potential resistance issues. The highest electronic quantum similarity values were observed between specific compound pairs, influencing the subsequent analysis of chemical reactivity. These findings prompted an exploration of global and local chemical reactivity indices to further guide drug design.

Global reactivity indices, such as chemical potential, hardness, softness, and electrophilicity, were computed for each compound. These indices play a crucial role in guiding molecular modifications to optimize drug candidates' pharmacological properties. The results identified compounds with higher chemical potential and electrophilicity, essential considerations in drug design. Understanding electrophilicity at the active site is crucial for drug design, as shown by the compound with the highest electrophilicity. The assessment involves considering the electrophilic nature of ligands and the nucleophilic properties of the active site residues. Fukui functions were employed to visualize regions involved in stabilization within the protein pocket. Figures 10 and 11 highlight specific regions susceptible to -H bond formation, making them potential candidates for malaria treatment.

In this sense, the combination of molecular docking and quantum similarity analysis, coupled with an exploration of chemical reactivity indices, provides a comprehensive approach to drug discovery for malaria.

The research identifies prospective lead compounds, underscores the significance of stabilizing the active site, and elucidates electronic considerations crucial for designing drugs that are both effective and resistant-resistant.

Data availability

Underlying data

Harvard Dataverse: Replication Data for: Analyzing of a serie of ligand against malaria using Molecular docking, Molecular Quantum Similarity and reactivity indices whitin Density Functional Theory frame-work, https://doi.org/10.7910/DVN/DLWULB.⁸⁶

Data are available under the terms of the Creative Commons Zero (CC0 1.0 Public domain dedication).

References

1. Consulted 20-12-2023. http
2. Griffith KS, Lewis LS, Mali S, et al.: Treatment of Malaria in the United States: A Systematic Review. JAMA. 2007; 297(20): 2264–2277. Publisher Full Text
3. Lalloo DG, Shingadia D, Bell DJ, et al.: UK malaria treatment guidelines. J. Infect. 2016; 72(6): 635–649. PubMed Abstract | Publisher Full Text | Free Full Text
4. Cathcart SJ, Lawrence J, Grant A, et al.: Estimating unreported malaria cases in England: a capture-recapture study. Epidemiol. Infect. 2010 Jul; 138(7): 1052–1058. PubMed Abstract | Publisher Full Text
5. Smith AD, Bradley DJ, Smith V, et al.: Imported malaria and high risk groups: observational study using UK surveillance data 1987–2006.
6. Nic FC, Hughes H, Armstrong M, et al.: Falciparum malaria as a cause of fever in adult travellers returning to the United Kingdom: observational study of risk by geographical área. QJM. 2008 Aug; 101(8): 649–656. Publisher Full Text
7. Committee to Advise on Tropical Medicine and Travel (CATMAT) Canadian recommendations for the prevention and treatment of malaria among international travellers–2009. Can. Commun. Dis. Rep. 2009 Jul; 35(Suppl. 1): 1–82.
8. Debash H, Erkihun Y, Bisetegn H: Malaria Threatens to Bounce Back in Abergele District, Northeast Ethiopia: Five-Year Retrospective Trend Analysis from 2016-2020 in Nirak Health Center. Biomed. Res. Int. 2022; 2022: 6388979.
9. Phillips MA, Burrows JN, Manyando C, et al.: Malaria. Nat. Rev. Dis. Prim. 2017; 3(1): 17050. Publisher Full Text
10. World Health Organisation: World Malaria Report Geneva. Switzerland: WHO; 2021.
11. Gujjari L, Kalani H, Pindiprolu SK, et al.: Current challenges and nanotechnology-based pharmaceutical strategies for the treatment and control of malaria. Parasite Epidemiol. Control. 2022; 17: e00244. PubMed Abstract | Publisher Full Text | Free Full Text
12. Boualam MA, Pradines B, Drancourt M, et al.: Malaria in Europe: A Historical Perspective. Front. Med (Lausanne). 2021; 8: 691095. PubMed Abstract | Publisher Full Text | Free Full Text
13. Talapko J, Škrlec I, Alebić T, et al.: Malaria: The Past and the Present. Microorganisms. 2019; 7(6). PubMed Abstract | Publisher Full Text | Free Full Text
14. Cox FE: History of the discovery of the malaria parasites and their vectors. Parasit. Vectors. 2010; 3(1): 5. PubMed Abstract | Publisher Full Text | Free Full Text
15. Ross RJ: On some peculiar pigmented cells found in two mosquitos fed on malarial blood. BMJ. 1929; 2(2): 1786–1788. Publisher Full Text
16. Giribaldi G, D’Alessandro S, Prato M, et al.: Etiopathogenesis and Pathophysiology of Malaria: Human and Mosquito Lysozymes.2014 Sep 22; pp. 1–18. Publisher Full Text
17. Ménard R: Medicine: knockout malaria vaccine? Nature. 2005; 433(7022): 113–114. Publisher Full Text
18. Ejigiri I, Sinnis P: Plasmodium sporozoite-host interactions from the dermis to the hepatocyte. Curr. Opin. Microbiol. 2009; 12(4): 401–407. PubMed Abstract | Publisher Full Text | Free Full Text
19. Cowman AF, Healer J, Marapana D, et al.: Malaria: Biology and Disease. Cell. 2016; 167(3): 610–624. Publisher Full Text
20. Teo A, Feng G, Brown GV, et al.: Functional antibodies and protection against blood-stage malaria. Trends Parasitol. 2016; 32(11): 887–898. Publisher Full Text
21. Kwiatkowski D, Hill AV, Sambou I, et al.: TNF concentration in fatal cerebral, non-fatal cerebral, and uncomplicated Plasmodium falciparum malaria. Lancet. 1990; 336(8725): 1201–1204. PubMed Abstract | Publisher Full Text
22. Chugh M, Sundararaman V, Kumar S, et al.: Protein complex directs hemoglobin-to-hemozoin formation in Plasmodium falciparum. Proc. Natl. Acad. Sci. USA. 2013; 110(14): 5392–5397. PubMed Abstract | Publisher Full Text | Free Full Text
23. Vaughan AM, Kappe SHI: Malaria Parasite Liver Infection and Exoerythrocytic Biology. Cold Spring Harb Perspect. Med. 2017; 7(6).
24. Tavares J, Formaglio P, Thiberge S, et al.: Role of host cell traversal by the malaria sporozoite during liver infection. J. Exp. Med. 2013; 210(5): 905–915. PubMed Abstract | Publisher Full Text | Free Full Text
25. Ishino T, Yano K, Chinzei Y, et al.: Cell-passage activity is required for the malarial parasite to cross the liver sinusoidal cell layer. PLoS Biol. 2004; 2(1): e4. PubMed Abstract | Publisher Full Text | Free Full Text
26. Risco-Castillo V, Topçu S, Marinach C, et al.: Malaria sporozoites traverse host cells within transient vacuoles. Cell Host Microbe. 2015; 18(5): 593–603. PubMed Abstract | Publisher Full Text
27. Bhanot P, Schauer K, Coppens I, et al.: A surface phospholipase is involved in the migration of Plasmodium sporozoites through cells. JoBC. 2005; 280(8): 6752–6760. Publisher Full Text
28. Rodrigues CD, Hannus M, Prudêncio M, et al.: Host scavenger receptor SR-BI plays a dual role in the establishment of malaria parasite liver infection. Cell Host Microbe. 2008; 4(3): 271–282. PubMed Abstract | Publisher Full Text
29. Sturm A, Amino R, Van de Sand C, et al.: Manipulation of host hepatocytes by the malaria parasite for delivery into liver sinusoids. Science. 2006; 313(5791): 1287–1290. PubMed Abstract | Publisher Full Text
30. Weiss GE, Gilson PR, Taechalertpaisarn T, et al.: Revealing the sequence and resulting cellular morphology of receptor-ligand interactions during Plasmodium falciparum invasion of erythrocytes. PLoS Pathog. 2015; 11(2): e1004670. PubMed Abstract | Publisher Full Text | Free Full Text
31. Cowman AF, Tonkin CJ, Tham WH, et al.: The Molecular Basis of Erythrocyte Invasion by Malaria Parasites. Cell Host Microbe. 2017; 22(2): 232–245. PubMed Abstract | Publisher Full Text
32. Egan ES, Jiang RH, Moechtar MA, et al.: A forward genetic screen identifies erythrocyte CD55 as essential for Plasmodium falciparum invasion. Science. 2015; 348(6235): 711–714. PubMed Abstract | Publisher Full Text | Free Full Text
33. Zheng H, Tan Z, Xu W: Immune evasion strategies of pre-erythrocytic malaria parasites. Mediat. Inflamm. 2014; 2014: 362605.
34. Cowman AF, Crabb BS: Invasion of Red Blood Cells by Malaria Parasites. Cell. 2006; 124(4): 755–766. Publisher Full Text
35. Crosnier C, Bustamante LY, Bartholdson SJ, et al.: Basigin is a receptor essential for erythrocyte invasion by Plasmodium falciparum. Nature. 2011; 480(7378): 534–537. PubMed Abstract | Publisher Full Text | Free Full Text
36. Volz JC, Yap A, Sisquella X, et al.: Essential Role of the PfRh5/PfRipr/CyRPA Complex during Plasmodium falciparum Invasion of Erythrocytes. Cell Host Microbe. 2016; 20(1): 60–71. PubMed Abstract | Publisher Full Text
37. Paul AS, Egan ES, Duraisingh MT: Host-parasite interactions that guide red blood cell invasion by malaria parasites. Curr. Opin. Hematol. 2015; 22(3): 220–226. PubMed Abstract | Publisher Full Text | Free Full Text
38. Zenonos ZA, Dummler SK, Müller-Sienerth N, et al.: Basigin is a druggable target for host-oriented antimalarial interventions. J. Exp. Med. 2015; 212(8): 1145–1151. PubMed Abstract | Publisher Full Text | Free Full Text
39. Srinivasan P, Beatty WL, Diouf A, et al.: Binding of Plasmodium merozoite proteins RON2 and AMA1 triggers commitment to invasion. Proc. Natl. Acad. Sci. USA. 2011; 108(32): 13275–13280. PubMed Abstract | Publisher Full Text | Free Full Text
40. Remarque EJ, Faber BW, Kocken CH, et al.: Apical membrane antigen 1: a malaria vaccine candidate in review. Trends Parasitol. 2008; 24(2): 74–84. PubMed Abstract | Publisher Full Text
41. Boddey JA, Cowman AF: Plasmodium nesting: remaking the erythrocyte from the inside out. Ann. Rev. Microbiol. 2013; 67: 243–269. PubMed Abstract | Publisher Full Text
42. Spillman NJ, Beck JR, Goldberg DE: Protein export into malaria parasite-infected erythrocytes: mechanisms and functional consequences. Annu. Rev. Biochem. 2015; 84: 813–841. PubMed Abstract | Publisher Full Text
43. Yuthavong Y, Tarnchompoo B, Vilaivan T, et al.: Malarial dihydrofolate reductase as a paradigm for drug development against a resistance-compromised target. Proc. Natl. Acad. Sci. USA. 2012; 109(42): 16823–16828. PubMed Abstract | Publisher Full Text | Free Full Text
44. Zhang VM, Chavchich M, Waters NC: Targeting Protein Kinases in the Malaria Parasite: Update of an Antimalarial Drug Target. Curr. Top. Med. Chem. 2012; 12: 456–472. PubMed Abstract | Publisher Full Text
45. Burley SK, Berman HM, Bhikadiya C, et al.: RCSB Protein Data Bank: Biological macromolecular structures enabling research and education in fundamental biology, biomedicine, biotechnology and energy. Nucleic Acids Res. 2019; 47(D1): D464–D474. PubMed Abstract | Publisher Full Text | Free Full Text
46. Halgren JJ, Klicic DT, Mainz MP, et al.: Glide: A New Approach for Rapid, Accurate Docking and Scor- ing. 1. Method and Assessment of Docking Accuracy. J. Med. Chem. 2004; 47: 1739–1749. Publisher Full Text
47. Friesner RA, Banks JL, Murphy RB, et al.: Glide: A New Approach for Rapid, Accurate Docking and Scor- ing. 1. Method and Assessment of Docking Accuracy. J. Med. Chem. 2004; 47: 1739–1749. PubMed Abstract | Publisher Full Text
48. Madhavi Sastry G, Adzhigirey M, Day T, et al.: Protein and ligand preparation: parameters, protocols, and influence on virtual screen- ing enrichments. J. Comput. Aided Mol. Des. 2013; 27: 221–234. PubMed Abstract | Publisher Full Text
49. Jorgensen WL, Maxwell DS, Tirado-Rives J: Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996; 118: 11225–11236. Publisher Full Text
50. [(a)] Carbó-Dorca R, Amat L, Besalú E, et al.: Quantum Similarity. Adv. Molec. Simil. 1998; 2: 1–42. JAI Press. 0-7623-0258-5. Publisher Full Text [(b)] Carbó-Dorca RE: Besalú A general survey of Molecular Quantum Similarity Huzinaga symposium, Fukuoka. J. Mol. Struct. (THEOCHEM). 1998; 451: 11–23. Publisher Full Text [(c)] Solá M, Mestres J, Carbó R, et al.: A Comparative analysis by means of Quantum Molecular Similarity Measures of Density Distributions derived from conventional ab initio and Density Functional Methods. J. Chem. Phys. 1996; 104: 636–647. Publisher Full Text [(d)] Carbó R, Besalú E: Theoretical Foundation of Quantum Similarity in “Molecular Similarity and Reactivity: From Quantum Chemical to Phenomenological Approaches”.Carbó R, editor. Understanding Chemical Reactivity. Amsterdam: Kluwer Academic Publishers; 1995; Vol. 14. , pp. 3–30.
51. [(a)] Morales-Bayuelo A, Matute RA, Caballero J: Understanding the comparative molecular field analysis (CoMFA) in terms of molecular quantum similarity and DFT-based reactivity descriptors. J. Mol. Model. 2015; 21: 156. PubMed Abstract | Publisher Full Text [(b)] Morales-Bayuelo A: Ricardo Vivas-Reyes. J. Quant. Chem. 2014; 2014: 1–12. Article ID 850163. Publisher Full Text [(c)] Morales-Bayuelo A: Ricardo Vivas-Reyes. J. Math. Chem. 2013; 51: 125–143. Publisher Full Text [(d)] Morales-Bayuelo A, Vivas-Reyes R: Theoretical model for the polarization molecular and Hückel treatment of PhosphoCyclopentadiene in an external electric field: Hirschfeld study. J. Math. Chem. 2013; 51: 1835–1852. Publisher Full Text [(e)] Morales-Bayuelo A: Verónica Valdiris, Ricardo Vivas-Reyes. J. Theor. Chem. 2014; 14: 1–13. [(f)] Morales-Bayuelo A, Torres J, Baldiris R, et al.: Theoretical study of the chemical reactivity and molecular quantum similarity in a series of derivatives of 2‐adamantyl‐thiazolidine‐4‐one using density functional theory and the topo‐geometrical superposition approach. Int. J. Quantum Chem. 2012; 112: 2681–2687. Publisher Full Text [(g)] Morales-Bayuelo A, Torres J, Vivas-Reyes R: Quantum molecular similarity analysis and quantitative definition of catecholamines with respect to biogenic monoamines associated: Scale alpha and beta of quantitative convergence. Int. J. Quantum Chem. 2012; 112: 2637–2642. Publisher Full Text [(h)] Morales-Bayuelo A, Baldiris R, Vivas-Reyes R: J. Theor. Chem. 2013; 13: 1–13.
52. Te Velde G, te Velde G , Bickelhaupt FM, et al.: Chemistry with ADF. J. Comput. Chem. 2001; 22: 931–967. Publisher Full Text
53. Van Lenthe E: Relativistic total energy using regular approximations. J. Chem. 1994; 101: 9783–9792. Publisher Full Text
54. Perdew JP, Wang Y: Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B. 1992; 45: 13244–13249. PubMed Abstract | Publisher Full Text
55. Pye CC, Ziegler T, van Lenthe E , et al.: An implementation of the conductor-like screening model of solvation within the Amsterdam density functional package — Part II. COSMO for real solvents. Can. J. Chem. 2009; 87: 790–797. Publisher Full Text
56. Schipper PRT, Gritsenko OV, van Gisbergen SJA , et al.: Molecular calculations of excitation energies and (hyper)polarizabilities with a statistical average of orbital model exchange-correlation potentials. J. Chem. Phys. 2000; 112: 1344–1352. Publisher Full Text
57. Carbó-Dorca R, Leyda L, Arnau M: How similar is a molecule to another? An electron density measure of similarity between two molecular structures. Int. J. Quantum Chem. 1980; 17: 1185–1189. Publisher Full Text
58. Carbó-Dorca R, Gironés X: Foundation of quantum similarity measures and their relationship to QSPR: Density function structure, approximations, and application examples. Int. J. Quantum Chem. 2005; 101: 8–20. Publisher Full Text
59. Bultinck P, Gironés X, Carbó-Dorca R: Molecular Quantum Similarity: Theory and Applications. Rev. Comput. Chem. 2005; 21: 127. Publisher Full Text
60. Constans P, Amat L, Carbó-Dorca R: Toward a global maximization of the molecular similarity function: Superposition of two molecules. J. Comput. Chem. 1997; 18: 826–846. Publisher Full Text
61. Carbó-Dorca R, Mercado LD: Commentaries on quantum similarity (1): Density gradient quantum similarity. J. Comb. Chem. 2010; 31: 2195–2212. Publisher Full Text
62. Gironés X, Carbó-Dorca R: Modelling Toxicity using Molecular Quantum Similarity Measures. QSAR Combinator. Sci. 2006; 25: 579–589. Publisher Full Text
63. Carbó-Dorca R, Besalú E, Mercado LD: Communications on quantum similarity, part 3: A geometric‐quantum similarity molecular superposition algorithm. J. Comb. Chem. 2011; 32: 582–599. Publisher Full Text
64. Carbó-Dorca R, Gironés X: Foundation of quantum similarity measures and their relationship to QSPR: Density function structure, approximations, and application examples. Int. J. Quantum Chem. 2005; 101: 8–20. Publisher Full Text
65. Carbó-Dorca R, Besalú E: Communications on quantum similarity (2): A geometric discussion on holographic electron density theorem and confined quantum similarity measures. J. Comput. Chem. 2010; 31: 2452–2462. PubMed Abstract | Publisher Full Text
66. Morales-Bayuelo A, Ayazo H, Vivas-Reyes R: Europ. J. Med. Chem. 2010; 45: 4509.
67. Morales-Bayuelo A, Torres J, Vivas-Reyes R: Quantum molecular similarity analysis and quantitative definition of catecholamines with respect to biogenic monoamines associated: Scale alpha and beta of quantitative convergence. Int. J. Quantum Chem. 2012; 112: 2637–2642. Publisher Full Text
68. Morales-Bayuelo A, Torres J, Baldiris R, et al.: Theoretical study of the chemical reactivity and molecular quantum similarity in a series of derivatives of 2‐adamantyl‐thiazolidine‐4‐one using density functional theory and the topo‐geometrical superposition approach. Int. J. Quantum Chem. 2012; 112: 2681–2687. Publisher Full Text
69. Morales-Bayuelo A, Torres J, Vivas-Reyes R: HÜCKEL TREATMENT OF PYRROLE AND PENTALENE AS A FUNCTION OF CYCLOPENTADIENYL USING LOCAL QUANTUM SIMILARITY INDEX (LQSI) AND THE TOPO-GEOMETRICAL SUPERPOSITION APPROACH (TGSA). J. Theo. Comp. Chem. 2012; 11: 223–239. Publisher Full Text
70. Morales-Bayuelo A, Vivas-Reyes R: Topological model to quantify the global reactivity indexes as local in Diels–Alder reactions, using density function theory (DFT) and local quantum similarity (LQS). J. Math. Chem. 2013; 51: 125–143. Publisher Full Text
71. Morales-Bayuelo A: Quantifying the distortion by spin–orbit and spin–spin coupling in molecular clusters using Molecular Quantum Similarity. J. Math. Chem. 2024; 62: 591–605. Publisher Full Text
72. Morales-Bayuelo A, Baldiris R, Vivas-Reyes R: Scale Alpha and Beta of Quantitative Convergence and Chemical Reactivity Analysis in Dual Cholinesterase/Monoamine Oxidase Inhibitors for the Alzheimer Disease Treatment using Density Functional Theory (DFT). J. Theor. Chem. 2013; 13: 1.
73. Morales-Bayuelo A, Vivas-Reyes R: Theoretical Calculations and Modeling for the Molecular Polarization of Furan and Thiophene under the Action of an Electric Field Using Quantum Similarity. J. Quant. Chem. 2014; 2014: 1–10. Article ID 585394. Publisher Full Text
74. Morales-Bayuelo A, Vivas-Reyes R: Topological Model on the Inductive Effect in Alkyl Halides Using Local Quantum Similarity and Reactivity Descriptors in the Density Functional Theory. J. Quant. Chem. 2014; 2014: 1–12. Article ID 850163. Publisher Full Text
75. Morales-Bayuelo A, Valdiris V, Vivas-Reyes R: Mathematic analysis on a series of 4-Acetylamino-2-(3,5-dimethylpyrazol-1-yl)-6-pyridylpyrimidines: a simple way to relate quantum similarity with local chemical reactivity using the Gaussian orbitals localized theory. J. Theor. Chem. 2014; 14: 1–13.
76. Morales-Bayuelo A, Vivas-Reyes R: Understanding the Polar Character Trend in a Series of Diels-Alder Reactions Using Molecular Quantum Similarity and Chemical Reactivity Descriptors. J. Quant. Chem. 2014; 2014: 1–19. Article ID 239845. Publisher Full Text
77. Parr RG, Pearson RG: Absolute hardness: companion parameter to absolute electronegativity. J. Am. Chem. Soc. 1983; 105: 7512–7516. Publisher Full Text
78. Geerlings P, De Proft F, Langenaeker W: Conceptual density functional theory. Chem. Rev. 2003; 103: 1793–1874. Publisher Full Text
79. Chattaraj PK, Sarkar U, Roy DR: Electrophilicity index. Chem. Rev. 2006; 106: 2065–2091. Publisher Full Text
80. Parr RG, Szentpaly L v, Liu S: Electrophilicity Index. J. Am. Chem. Soc. 1999; 121: 1922–1924. Publisher Full Text
81. Galván M, Pérez P, Contreras R, et al.: Condensed-to-atoms electronic Fukui functions within the framework of spin-polarized density-functional theory. Chem. Phys. Lett. 1999; 30: 405.
82. Mortier WJ, Yang W: The use of global and local molecular parameters for the analysis of the gas-phase basicity of amines J. Am. Chem. Soc. 1986; 108: 5708–5711. PubMed Abstract | Publisher Full Text | Free Full Text
83. Fuentealba P, Pérez P, Contreras R: On the condensed Fukui function. J. Chem. Phys. 2000; 113: 2544–2551. Publisher Full Text
84. Zhao Y, Truhlar DG: The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, non-covalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Accounts. 2008; 120: 215–241. Publisher Full Text
85. Frisch MJ, Trucks GW, Schlegel HB, et al.: Gaussian Inc., Wallingford CT.2009.
86. Morales-Bayuelo A: Replication Data for: Analyzing of a serie of ligand against malaria using Molecular docking, Molecular Quantum Similarity and reactivity indices whitin Density Functional Theory framework. [dataset]. Harvard Dataverse. 2023; 123. Publisher Full Text

Comments on this article Comments (0)

Version 1

VERSION 1 PUBLISHED 02 May 2024

Author details Author details

¹ Process Research Center of Tecnológico Comfenalco (CIPTEC), Industrial Engineering Program, Fundación Universitaria Tecnológico Comfenalco, Cartagena, Colombia
² Group of Quantum and Theoretical Chemistry, Faculty of Exacts and Naturals Sciences, University of Cartagena, Cartagena de Indias, 130001, Bolivar, Colombia
³ Faculty of Science, Department of Chemistry, Sivas Cumhuriyet University, 58140, Sivas, Turkey

Alejandro Morales-Bayuelo
Roles: Conceptualization, Data Curation, Formal Analysis, Funding Acquisition, Investigation, Methodology, Project Administration, Resources, Software, Supervision, Validation, Visualization, Writing – Original Draft Preparation, Writing – Review & Editing

Ricardo Vivas-Reyes
Roles: Formal Analysis, Writing – Review & Editing

Savas Kaya
Roles: Formal Analysis, Writing – Review & Editing

Competing interests

No competing interests were disclosed.

Grant information

Tecnologico-2024-I.
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Article Versions (1)

version 1

Published: 02 May 2024, 13:435

https://doi.org/10.12688/f1000research.147631.1

Copyright

© 2024 Morales-Bayuelo A et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Download

Export To

metrics

	Views	Downloads
F1000Research	-	-
PubMed Central Data from PMC are received and updated monthly.	-	-

Citations

0

SEE MORE DETAILS

CITE

how to cite this article

Morales-Bayuelo A, Vivas-Reyes R and Kaya S. Analyzing a series of ligands against malaria through the application of molecular docking, molecular quantum similarity, and reactivity indices [version 1; peer review: 1 approved with reservations, 1 not approved]. F1000Research 2024, 13:435 (https://doi.org/10.12688/f1000research.147631.1)

NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article.

track

receive updates on this article

Track an article to receive email alerts on any updates to this article.

Open Peer Review

Version 1

VERSION 1

PUBLISHED 02 May 2024

Views

2

Reviewer Report 23 Sep 2025

Ezekiel Adebiyi, German Cancer Research Center (DKFZ), Heidelberg, Germany; African Centre of Excellence in Bioinformatics & Data Intensive Science, Kampala, Uganda

Yagoub Adam, CUBRe, Covenant University (Ringgold ID: 59198), Ota, Ogun State, Nigeria

Approved with Reservations

https://doi.org/10.5256/f1000research.161844.r407684

This computational study aimed to discover new malaria treatments by analyzing nine compounds with three computer-based methods: molecular docking (assessing how drugs bind to proteins), quantum similarity (comparing electronic properties), and chemical reactivity analysis. Although the research tackles a significant ... Continue reading

This computational study aimed to discover new malaria treatments by analyzing nine compounds with three computer-based methods: molecular docking (assessing how drugs bind to proteins), quantum similarity (comparing electronic properties), and chemical reactivity analysis. Although the research tackles a significant health concern, it faces several fundamental issues.
- The authors do not specify which malaria proteins they are targeting or explain why they chose these nine compounds. Without this information, it's hard to assess whether the computational results apply to real drug development.
- More statistical analysis is needed to show which results are significant.
- While advanced computational methods were employed, the authors failed to link their findings to practical malaria treatment. They examined electronic properties and binding interactions but did not clarify how these aspects relate to parasite eradication or patient outcomes.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

Not applicable
Are all the source data underlying the results available to ensure full reproducibility?

Partly
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Bioinformatics

We confirm that we have read this submission and believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however we have significant reservations, as outlined above.

CITE

Report a concern

Respond or Comment

Views

13

Reviewer Report 05 Jun 2024

Tawanda Zininga, Department of Biochemistry, Stellenbosch University, Stellenbosch, Western Cape, South Africa

Not Approved

https://doi.org/10.5256/f1000research.161844.r275858

Dear Editor

The manuscript by Morales-Bayuelo on analysing the series of ligands using molecular docking, molecular quantum similarity, and reactivity indices highlights the use of these techniques in malaria drug discovery efforts. The main findings are that ... Continue reading

Dear Editor

The manuscript by Morales-Bayuelo on analysing the series of ligands using molecular docking, molecular quantum similarity, and reactivity indices highlights the use of these techniques in malaria drug discovery efforts. The main findings are that the stabilisation of active site interactions as observed through electrophilicity is a critical factor in the design of selective ligands. However, there are some adjustments that need to be made to improve the quality of this manuscript. The main issue is lack of clear interpretation of the data in the context of the focus of malaria drug design. As this study is focused on malaria, a human disease, there is a need to include screening for ligands with minimal toxicity to the host. For example, a comprehensive predictive ADMET analysis could be included, of which there are several predictive analytical tools available. The information to justify how the selectivity profiles of the ligands were confirmed is missing, which affects the impact of this study. This could be done by highlighting evidence from electronic information on current drugs that the malaria parasite has developed resistance to. I hereby provide point-by-point comments below:

Introduction
This needs to be reworked to improve coherence, be relevant to this current study, and introduce relevant concepts in a broad sense.
Page 3 minimise the use of bullet points and instead write it as one coherent body of text.

Methods
Briefly, state the principles for the protocols used, or, in short, why that procedure was conducted in this manuscript.
The molecular docking procedure should be converted to a flow diagram to replace the bullet points.
On page 4, explain how the compounds used as ligands were designed.
Increase the simulation duration to show the stability of the active site after more than 250 ns as this study is based on stability analysis.

Results and discussion
Describe the findings from each of the figures and tables in this manuscript. Increase the font size for the residue labels and specify all the bonds formed between ligand and receptor that contribute to the stated binding affinities. Add an additional table with distances and relative affinities. In all the figures, the legends should summarise the main findings from each of the figures, at times with a general description of the protocol to minimise the need to go back to the methods section/main text to understand the figure.
Page 8 second from last paragraph is a repetition from sections above.
On Page 9, add the drug like properties of these compounds, such as the drug like ADMET properties of the compounds, to justify selectivity between host and parasite and the relative binding energies.
In general, the result and discussion section should be specific to describe and interpret the findings from this study. However, as noted throughout this MS, the main text on page 9 is not relevant in addressing the findings from this study and their implications thereof.
On Page 10, add a comparison of ligand and substrate binding affinities at the active site to validate the binding and interactions predicted in this study.
Page 12, explain what the values in the table mean, both in terms of the magnitude of the value and in the context of a potential drug against malaria. This is lacking throughout the manuscript and should be done to show the relevance of this study in the fight against malaria.
On page 13, paragraph 4, explain what these values mean in the context of ligand-active site stability and how that relates to the ADMET of the ligand.
Page 13, paragraph 5, be specific and refer to the protein whose active site is being investigated.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

No
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Protein biochemistry, malaria drug discovery, and drug screening

I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above.

CITE

Report a concern

Respond or Comment

Comments on this article Comments (0)

Version 1

VERSION 1 PUBLISHED 02 May 2024

Open Peer Review

Reviewer Status

Reviewer Reports

	Invited Reviewers
	1	2
Version 1 02 May 24	read	read

Tawanda Zininga, Stellenbosch University, Stellenbosch, South Africa
Ezekiel Adebiyi, German Cancer Research Center (DKFZ), Heidelberg, Germany; African Centre of Excellence in Bioinformatics & Data Intensive Science, Kampala, Uganda

Yagoub Adam, Covenant University (Ringgold ID: 59198), Ota, Nigeria

Comments on this article

All Comments(0)

Add a comment

Sign up for content alerts

Browse by related subjects

Back to all reports

Reviewer Report

2 Views

23 Sep 2025 | for Version 1

Ezekiel Adebiyi, German Cancer Research Center (DKFZ), Heidelberg, Germany; African Centre of Excellence in Bioinformatics & Data Intensive Science, Kampala, Uganda

Yagoub Adam, CUBRe, Covenant University (Ringgold ID: 59198), Ota, Ogun State, Nigeria

2 Views Cite this report Responses(0)

Approved With Reservations

This computational study aimed to discover new malaria treatments by analyzing nine compounds with three computer-based methods: molecular docking (assessing how drugs bind to proteins), quantum similarity (comparing electronic properties), and chemical reactivity analysis. Although the research tackles a significant health concern, it faces several fundamental issues.
- The authors do not specify which malaria proteins they are targeting or explain why they chose these nine compounds. Without this information, it's hard to assess whether the computational results apply to real drug development.
- More statistical analysis is needed to show which results are significant.
- While advanced computational methods were employed, the authors failed to link their findings to practical malaria treatment. They examined electronic properties and binding interactions but did not clarify how these aspects relate to parasite eradication or patient outcomes.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

Not applicable
Are all the source data underlying the results available to ensure full reproducibility?

Partly
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Bioinformatics

We confirm that we have read this submission and believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however we have significant reservations, as outlined above.

Respond to this report

Responses (0)

Back to all reports

Reviewer Report

13 Views

05 Jun 2024 | for Version 1

Tawanda Zininga, Department of Biochemistry, Stellenbosch University, Stellenbosch, Western Cape, South Africa

13 Views Cite this report Responses(0)

Not Approved

Dear Editor

The manuscript by Morales-Bayuelo on analysing the series of ligands using molecular docking, molecular quantum similarity, and reactivity indices highlights the use of these techniques in malaria drug discovery efforts. The main findings are that the stabilisation of active site interactions as observed through electrophilicity is a critical factor in the design of selective ligands. However, there are some adjustments that need to be made to improve the quality of this manuscript. The main issue is lack of clear interpretation of the data in the context of the focus of malaria drug design. As this study is focused on malaria, a human disease, there is a need to include screening for ligands with minimal toxicity to the host. For example, a comprehensive predictive ADMET analysis could be included, of which there are several predictive analytical tools available. The information to justify how the selectivity profiles of the ligands were confirmed is missing, which affects the impact of this study. This could be done by highlighting evidence from electronic information on current drugs that the malaria parasite has developed resistance to. I hereby provide point-by-point comments below:

Introduction
This needs to be reworked to improve coherence, be relevant to this current study, and introduce relevant concepts in a broad sense.
Page 3 minimise the use of bullet points and instead write it as one coherent body of text.

Methods
Briefly, state the principles for the protocols used, or, in short, why that procedure was conducted in this manuscript.
The molecular docking procedure should be converted to a flow diagram to replace the bullet points.
On page 4, explain how the compounds used as ligands were designed.
Increase the simulation duration to show the stability of the active site after more than 250 ns as this study is based on stability analysis.

Results and discussion
Describe the findings from each of the figures and tables in this manuscript. Increase the font size for the residue labels and specify all the bonds formed between ligand and receptor that contribute to the stated binding affinities. Add an additional table with distances and relative affinities. In all the figures, the legends should summarise the main findings from each of the figures, at times with a general description of the protocol to minimise the need to go back to the methods section/main text to understand the figure.
Page 8 second from last paragraph is a repetition from sections above.
On Page 9, add the drug like properties of these compounds, such as the drug like ADMET properties of the compounds, to justify selectivity between host and parasite and the relative binding energies.
In general, the result and discussion section should be specific to describe and interpret the findings from this study. However, as noted throughout this MS, the main text on page 9 is not relevant in addressing the findings from this study and their implications thereof.
On Page 10, add a comparison of ligand and substrate binding affinities at the active site to validate the binding and interactions predicted in this study.
Page 12, explain what the values in the table mean, both in terms of the magnitude of the value and in the context of a potential drug against malaria. This is lacking throughout the manuscript and should be done to show the relevance of this study in the fight against malaria.
On page 13, paragraph 4, explain what these values mean in the context of ligand-active site stability and how that relates to the ADMET of the ligand.
Page 13, paragraph 5, be specific and refer to the protein whose active site is being investigated.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

No
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Protein biochemistry, malaria drug discovery, and drug screening

I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above.

Respond to this report

Responses (0)

[1] 1. Consulted 20-12-2023. http

[2] 2. Griffith KS, Lewis LS, Mali S, et al.: Treatment of Malaria in the United States: A Systematic Review. JAMA. 2007; 297(20): 2264–2277. Publisher Full Text

[3] 3. Lalloo DG, Shingadia D, Bell DJ, et al.: UK malaria treatment guidelines. J. Infect. 2016; 72(6): 635–649. PubMed Abstract | Publisher Full Text | Free Full Text

[4] 4. Cathcart SJ, Lawrence J, Grant A, et al.: Estimating unreported malaria cases in England: a capture-recapture study. Epidemiol. Infect. 2010 Jul; 138(7): 1052–1058. PubMed Abstract | Publisher Full Text

[5] 5. Smith AD, Bradley DJ, Smith V, et al.: Imported malaria and high risk groups: observational study using UK surveillance data 1987–2006.

[6] 6. Nic FC, Hughes H, Armstrong M, et al.: Falciparum malaria as a cause of fever in adult travellers returning to the United Kingdom: observational study of risk by geographical área. QJM. 2008 Aug; 101(8): 649–656. Publisher Full Text

[7] 7. Committee to Advise on Tropical Medicine and Travel (CATMAT) Canadian recommendations for the prevention and treatment of malaria among international travellers–2009. Can. Commun. Dis. Rep. 2009 Jul; 35(Suppl. 1): 1–82.

[8] 8. Debash H, Erkihun Y, Bisetegn H: Malaria Threatens to Bounce Back in Abergele District, Northeast Ethiopia: Five-Year Retrospective Trend Analysis from 2016-2020 in Nirak Health Center. Biomed. Res. Int. 2022; 2022: 6388979.

[9] 9. Phillips MA, Burrows JN, Manyando C, et al.: Malaria. Nat. Rev. Dis. Prim. 2017; 3(1): 17050. Publisher Full Text

[10] 10. World Health Organisation: World Malaria Report Geneva. Switzerland: WHO; 2021.

[11] 11. Gujjari L, Kalani H, Pindiprolu SK, et al.: Current challenges and nanotechnology-based pharmaceutical strategies for the treatment and control of malaria. Parasite Epidemiol. Control. 2022; 17: e00244. PubMed Abstract | Publisher Full Text | Free Full Text

[12] 12. Boualam MA, Pradines B, Drancourt M, et al.: Malaria in Europe: A Historical Perspective. Front. Med (Lausanne). 2021; 8: 691095. PubMed Abstract | Publisher Full Text | Free Full Text

[13] 13. Talapko J, Škrlec I, Alebić T, et al.: Malaria: The Past and the Present. Microorganisms. 2019; 7(6). PubMed Abstract | Publisher Full Text | Free Full Text

[14] 14. Cox FE: History of the discovery of the malaria parasites and their vectors. Parasit. Vectors. 2010; 3(1): 5. PubMed Abstract | Publisher Full Text | Free Full Text

[15] 15. Ross RJ: On some peculiar pigmented cells found in two mosquitos fed on malarial blood. BMJ. 1929; 2(2): 1786–1788. Publisher Full Text

[16] 16. Giribaldi G, D’Alessandro S, Prato M, et al.: Etiopathogenesis and Pathophysiology of Malaria: Human and Mosquito Lysozymes.2014 Sep 22; pp. 1–18. Publisher Full Text

[17] 17. Ménard R: Medicine: knockout malaria vaccine? Nature. 2005; 433(7022): 113–114. Publisher Full Text

[18] 18. Ejigiri I, Sinnis P: Plasmodium sporozoite-host interactions from the dermis to the hepatocyte. Curr. Opin. Microbiol. 2009; 12(4): 401–407. PubMed Abstract | Publisher Full Text | Free Full Text

[19] 19. Cowman AF, Healer J, Marapana D, et al.: Malaria: Biology and Disease. Cell. 2016; 167(3): 610–624. Publisher Full Text

[20] 20. Teo A, Feng G, Brown GV, et al.: Functional antibodies and protection against blood-stage malaria. Trends Parasitol. 2016; 32(11): 887–898. Publisher Full Text

[21] 21. Kwiatkowski D, Hill AV, Sambou I, et al.: TNF concentration in fatal cerebral, non-fatal cerebral, and uncomplicated Plasmodium falciparum malaria. Lancet. 1990; 336(8725): 1201–1204. PubMed Abstract | Publisher Full Text

[22] 22. Chugh M, Sundararaman V, Kumar S, et al.: Protein complex directs hemoglobin-to-hemozoin formation in Plasmodium falciparum. Proc. Natl. Acad. Sci. USA. 2013; 110(14): 5392–5397. PubMed Abstract | Publisher Full Text | Free Full Text

[23] 23. Vaughan AM, Kappe SHI: Malaria Parasite Liver Infection and Exoerythrocytic Biology. Cold Spring Harb Perspect. Med. 2017; 7(6).

[24] 24. Tavares J, Formaglio P, Thiberge S, et al.: Role of host cell traversal by the malaria sporozoite during liver infection. J. Exp. Med. 2013; 210(5): 905–915. PubMed Abstract | Publisher Full Text | Free Full Text

[25] 25. Ishino T, Yano K, Chinzei Y, et al.: Cell-passage activity is required for the malarial parasite to cross the liver sinusoidal cell layer. PLoS Biol. 2004; 2(1): e4. PubMed Abstract | Publisher Full Text | Free Full Text

[26] 26. Risco-Castillo V, Topçu S, Marinach C, et al.: Malaria sporozoites traverse host cells within transient vacuoles. Cell Host Microbe. 2015; 18(5): 593–603. PubMed Abstract | Publisher Full Text

[27] 27. Bhanot P, Schauer K, Coppens I, et al.: A surface phospholipase is involved in the migration of Plasmodium sporozoites through cells. JoBC. 2005; 280(8): 6752–6760. Publisher Full Text

[28] 28. Rodrigues CD, Hannus M, Prudêncio M, et al.: Host scavenger receptor SR-BI plays a dual role in the establishment of malaria parasite liver infection. Cell Host Microbe. 2008; 4(3): 271–282. PubMed Abstract | Publisher Full Text

[29] 29. Sturm A, Amino R, Van de Sand C, et al.: Manipulation of host hepatocytes by the malaria parasite for delivery into liver sinusoids. Science. 2006; 313(5791): 1287–1290. PubMed Abstract | Publisher Full Text

[30] 30. Weiss GE, Gilson PR, Taechalertpaisarn T, et al.: Revealing the sequence and resulting cellular morphology of receptor-ligand interactions during Plasmodium falciparum invasion of erythrocytes. PLoS Pathog. 2015; 11(2): e1004670. PubMed Abstract | Publisher Full Text | Free Full Text

[31] 31. Cowman AF, Tonkin CJ, Tham WH, et al.: The Molecular Basis of Erythrocyte Invasion by Malaria Parasites. Cell Host Microbe. 2017; 22(2): 232–245. PubMed Abstract | Publisher Full Text

[32] 32. Egan ES, Jiang RH, Moechtar MA, et al.: A forward genetic screen identifies erythrocyte CD55 as essential for Plasmodium falciparum invasion. Science. 2015; 348(6235): 711–714. PubMed Abstract | Publisher Full Text | Free Full Text

[33] 33. Zheng H, Tan Z, Xu W: Immune evasion strategies of pre-erythrocytic malaria parasites. Mediat. Inflamm. 2014; 2014: 362605.

[34] 34. Cowman AF, Crabb BS: Invasion of Red Blood Cells by Malaria Parasites. Cell. 2006; 124(4): 755–766. Publisher Full Text

[35] 35. Crosnier C, Bustamante LY, Bartholdson SJ, et al.: Basigin is a receptor essential for erythrocyte invasion by Plasmodium falciparum. Nature. 2011; 480(7378): 534–537. PubMed Abstract | Publisher Full Text | Free Full Text

[36] 36. Volz JC, Yap A, Sisquella X, et al.: Essential Role of the PfRh5/PfRipr/CyRPA Complex during Plasmodium falciparum Invasion of Erythrocytes. Cell Host Microbe. 2016; 20(1): 60–71. PubMed Abstract | Publisher Full Text

[37] 37. Paul AS, Egan ES, Duraisingh MT: Host-parasite interactions that guide red blood cell invasion by malaria parasites. Curr. Opin. Hematol. 2015; 22(3): 220–226. PubMed Abstract | Publisher Full Text | Free Full Text

[38] 38. Zenonos ZA, Dummler SK, Müller-Sienerth N, et al.: Basigin is a druggable target for host-oriented antimalarial interventions. J. Exp. Med. 2015; 212(8): 1145–1151. PubMed Abstract | Publisher Full Text | Free Full Text

[39] 39. Srinivasan P, Beatty WL, Diouf A, et al.: Binding of Plasmodium merozoite proteins RON2 and AMA1 triggers commitment to invasion. Proc. Natl. Acad. Sci. USA. 2011; 108(32): 13275–13280. PubMed Abstract | Publisher Full Text | Free Full Text

[40] 40. Remarque EJ, Faber BW, Kocken CH, et al.: Apical membrane antigen 1: a malaria vaccine candidate in review. Trends Parasitol. 2008; 24(2): 74–84. PubMed Abstract | Publisher Full Text

[41] 41. Boddey JA, Cowman AF: Plasmodium nesting: remaking the erythrocyte from the inside out. Ann. Rev. Microbiol. 2013; 67: 243–269. PubMed Abstract | Publisher Full Text

[42] 42. Spillman NJ, Beck JR, Goldberg DE: Protein export into malaria parasite-infected erythrocytes: mechanisms and functional consequences. Annu. Rev. Biochem. 2015; 84: 813–841. PubMed Abstract | Publisher Full Text

[43] 43. Yuthavong Y, Tarnchompoo B, Vilaivan T, et al.: Malarial dihydrofolate reductase as a paradigm for drug development against a resistance-compromised target. Proc. Natl. Acad. Sci. USA. 2012; 109(42): 16823–16828. PubMed Abstract | Publisher Full Text | Free Full Text

[44] 44. Zhang VM, Chavchich M, Waters NC: Targeting Protein Kinases in the Malaria Parasite: Update of an Antimalarial Drug Target. Curr. Top. Med. Chem. 2012; 12: 456–472. PubMed Abstract | Publisher Full Text

[45] 45. Burley SK, Berman HM, Bhikadiya C, et al.: RCSB Protein Data Bank: Biological macromolecular structures enabling research and education in fundamental biology, biomedicine, biotechnology and energy. Nucleic Acids Res. 2019; 47(D1): D464–D474. PubMed Abstract | Publisher Full Text | Free Full Text

[46] 46. Halgren JJ, Klicic DT, Mainz MP, et al.: Glide: A New Approach for Rapid, Accurate Docking and Scor- ing. 1. Method and Assessment of Docking Accuracy. J. Med. Chem. 2004; 47: 1739–1749. Publisher Full Text

[47] 47. Friesner RA, Banks JL, Murphy RB, et al.: Glide: A New Approach for Rapid, Accurate Docking and Scor- ing. 1. Method and Assessment of Docking Accuracy. J. Med. Chem. 2004; 47: 1739–1749. PubMed Abstract | Publisher Full Text

[48] 48. Madhavi Sastry G, Adzhigirey M, Day T, et al.: Protein and ligand preparation: parameters, protocols, and influence on virtual screen- ing enrichments. J. Comput. Aided Mol. Des. 2013; 27: 221–234. PubMed Abstract | Publisher Full Text

[49] 49. Jorgensen WL, Maxwell DS, Tirado-Rives J: Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996; 118: 11225–11236. Publisher Full Text

[50] 50. [(a)] Carbó-Dorca R, Amat L, Besalú E, et al.: Quantum Similarity. Adv. Molec. Simil. 1998; 2: 1–42. JAI Press. 0-7623-0258-5. Publisher Full Text [(b)] Carbó-Dorca RE: Besalú A general survey of Molecular Quantum Similarity Huzinaga symposium, Fukuoka. J. Mol. Struct. (THEOCHEM). 1998; 451: 11–23. Publisher Full Text [(c)] Solá M, Mestres J, Carbó R, et al.: A Comparative analysis by means of Quantum Molecular Similarity Measures of Density Distributions derived from conventional ab initio and Density Functional Methods. J. Chem. Phys. 1996; 104: 636–647. Publisher Full Text [(d)] Carbó R, Besalú E: Theoretical Foundation of Quantum Similarity in “Molecular Similarity and Reactivity: From Quantum Chemical to Phenomenological Approaches”.Carbó R, editor. Understanding Chemical Reactivity. Amsterdam: Kluwer Academic Publishers; 1995; Vol. 14. , pp. 3–30.

[51] 51. [(a)] Morales-Bayuelo A, Matute RA, Caballero J: Understanding the comparative molecular field analysis (CoMFA) in terms of molecular quantum similarity and DFT-based reactivity descriptors. J. Mol. Model. 2015; 21: 156. PubMed Abstract | Publisher Full Text [(b)] Morales-Bayuelo A: Ricardo Vivas-Reyes. J. Quant. Chem. 2014; 2014: 1–12. Article ID 850163. Publisher Full Text [(c)] Morales-Bayuelo A: Ricardo Vivas-Reyes. J. Math. Chem. 2013; 51: 125–143. Publisher Full Text [(d)] Morales-Bayuelo A, Vivas-Reyes R: Theoretical model for the polarization molecular and Hückel treatment of PhosphoCyclopentadiene in an external electric field: Hirschfeld study. J. Math. Chem. 2013; 51: 1835–1852. Publisher Full Text [(e)] Morales-Bayuelo A: Verónica Valdiris, Ricardo Vivas-Reyes. J. Theor. Chem. 2014; 14: 1–13. [(f)] Morales-Bayuelo A, Torres J, Baldiris R, et al.: Theoretical study of the chemical reactivity and molecular quantum similarity in a series of derivatives of 2‐adamantyl‐thiazolidine‐4‐one using density functional theory and the topo‐geometrical superposition approach. Int. J. Quantum Chem. 2012; 112: 2681–2687. Publisher Full Text [(g)] Morales-Bayuelo A, Torres J, Vivas-Reyes R: Quantum molecular similarity analysis and quantitative definition of catecholamines with respect to biogenic monoamines associated: Scale alpha and beta of quantitative convergence. Int. J. Quantum Chem. 2012; 112: 2637–2642. Publisher Full Text [(h)] Morales-Bayuelo A, Baldiris R, Vivas-Reyes R: J. Theor. Chem. 2013; 13: 1–13.

[52] 52. Te Velde G, te Velde G , Bickelhaupt FM, et al.: Chemistry with ADF. J. Comput. Chem. 2001; 22: 931–967. Publisher Full Text

[53] 53. Van Lenthe E: Relativistic total energy using regular approximations. J. Chem. 1994; 101: 9783–9792. Publisher Full Text

[54] 54. Perdew JP, Wang Y: Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B. 1992; 45: 13244–13249. PubMed Abstract | Publisher Full Text

[55] 55. Pye CC, Ziegler T, van Lenthe E , et al.: An implementation of the conductor-like screening model of solvation within the Amsterdam density functional package — Part II. COSMO for real solvents. Can. J. Chem. 2009; 87: 790–797. Publisher Full Text

[56] 56. Schipper PRT, Gritsenko OV, van Gisbergen SJA , et al.: Molecular calculations of excitation energies and (hyper)polarizabilities with a statistical average of orbital model exchange-correlation potentials. J. Chem. Phys. 2000; 112: 1344–1352. Publisher Full Text

[57] 57. Carbó-Dorca R, Leyda L, Arnau M: How similar is a molecule to another? An electron density measure of similarity between two molecular structures. Int. J. Quantum Chem. 1980; 17: 1185–1189. Publisher Full Text

[58] 58. Carbó-Dorca R, Gironés X: Foundation of quantum similarity measures and their relationship to QSPR: Density function structure, approximations, and application examples. Int. J. Quantum Chem. 2005; 101: 8–20. Publisher Full Text

[59] 59. Bultinck P, Gironés X, Carbó-Dorca R: Molecular Quantum Similarity: Theory and Applications. Rev. Comput. Chem. 2005; 21: 127. Publisher Full Text

[60] 60. Constans P, Amat L, Carbó-Dorca R: Toward a global maximization of the molecular similarity function: Superposition of two molecules. J. Comput. Chem. 1997; 18: 826–846. Publisher Full Text

[61] 61. Carbó-Dorca R, Mercado LD: Commentaries on quantum similarity (1): Density gradient quantum similarity. J. Comb. Chem. 2010; 31: 2195–2212. Publisher Full Text

[62] 62. Gironés X, Carbó-Dorca R: Modelling Toxicity using Molecular Quantum Similarity Measures. QSAR Combinator. Sci. 2006; 25: 579–589. Publisher Full Text

[63] 63. Carbó-Dorca R, Besalú E, Mercado LD: Communications on quantum similarity, part 3: A geometric‐quantum similarity molecular superposition algorithm. J. Comb. Chem. 2011; 32: 582–599. Publisher Full Text

[64] 64. Carbó-Dorca R, Gironés X: Foundation of quantum similarity measures and their relationship to QSPR: Density function structure, approximations, and application examples. Int. J. Quantum Chem. 2005; 101: 8–20. Publisher Full Text

[65] 65. Carbó-Dorca R, Besalú E: Communications on quantum similarity (2): A geometric discussion on holographic electron density theorem and confined quantum similarity measures. J. Comput. Chem. 2010; 31: 2452–2462. PubMed Abstract | Publisher Full Text

[66] 66. Morales-Bayuelo A, Ayazo H, Vivas-Reyes R: Europ. J. Med. Chem. 2010; 45: 4509.

[67] 67. Morales-Bayuelo A, Torres J, Vivas-Reyes R: Quantum molecular similarity analysis and quantitative definition of catecholamines with respect to biogenic monoamines associated: Scale alpha and beta of quantitative convergence. Int. J. Quantum Chem. 2012; 112: 2637–2642. Publisher Full Text

[68] 68. Morales-Bayuelo A, Torres J, Baldiris R, et al.: Theoretical study of the chemical reactivity and molecular quantum similarity in a series of derivatives of 2‐adamantyl‐thiazolidine‐4‐one using density functional theory and the topo‐geometrical superposition approach. Int. J. Quantum Chem. 2012; 112: 2681–2687. Publisher Full Text

[69] 69. Morales-Bayuelo A, Torres J, Vivas-Reyes R: HÜCKEL TREATMENT OF PYRROLE AND PENTALENE AS A FUNCTION OF CYCLOPENTADIENYL USING LOCAL QUANTUM SIMILARITY INDEX (LQSI) AND THE TOPO-GEOMETRICAL SUPERPOSITION APPROACH (TGSA). J. Theo. Comp. Chem. 2012; 11: 223–239. Publisher Full Text

[70] 70. Morales-Bayuelo A, Vivas-Reyes R: Topological model to quantify the global reactivity indexes as local in Diels–Alder reactions, using density function theory (DFT) and local quantum similarity (LQS). J. Math. Chem. 2013; 51: 125–143. Publisher Full Text

[71] 71. Morales-Bayuelo A: Quantifying the distortion by spin–orbit and spin–spin coupling in molecular clusters using Molecular Quantum Similarity. J. Math. Chem. 2024; 62: 591–605. Publisher Full Text

[72] 72. Morales-Bayuelo A, Baldiris R, Vivas-Reyes R: Scale Alpha and Beta of Quantitative Convergence and Chemical Reactivity Analysis in Dual Cholinesterase/Monoamine Oxidase Inhibitors for the Alzheimer Disease Treatment using Density Functional Theory (DFT). J. Theor. Chem. 2013; 13: 1.

[73] 73. Morales-Bayuelo A, Vivas-Reyes R: Theoretical Calculations and Modeling for the Molecular Polarization of Furan and Thiophene under the Action of an Electric Field Using Quantum Similarity. J. Quant. Chem. 2014; 2014: 1–10. Article ID 585394. Publisher Full Text

[74] 74. Morales-Bayuelo A, Vivas-Reyes R: Topological Model on the Inductive Effect in Alkyl Halides Using Local Quantum Similarity and Reactivity Descriptors in the Density Functional Theory. J. Quant. Chem. 2014; 2014: 1–12. Article ID 850163. Publisher Full Text

[75] 75. Morales-Bayuelo A, Valdiris V, Vivas-Reyes R: Mathematic analysis on a series of 4-Acetylamino-2-(3,5-dimethylpyrazol-1-yl)-6-pyridylpyrimidines: a simple way to relate quantum similarity with local chemical reactivity using the Gaussian orbitals localized theory. J. Theor. Chem. 2014; 14: 1–13.

[76] 76. Morales-Bayuelo A, Vivas-Reyes R: Understanding the Polar Character Trend in a Series of Diels-Alder Reactions Using Molecular Quantum Similarity and Chemical Reactivity Descriptors. J. Quant. Chem. 2014; 2014: 1–19. Article ID 239845. Publisher Full Text

[77] 77. Parr RG, Pearson RG: Absolute hardness: companion parameter to absolute electronegativity. J. Am. Chem. Soc. 1983; 105: 7512–7516. Publisher Full Text

[78] 78. Geerlings P, De Proft F, Langenaeker W: Conceptual density functional theory. Chem. Rev. 2003; 103: 1793–1874. Publisher Full Text

[79] 79. Chattaraj PK, Sarkar U, Roy DR: Electrophilicity index. Chem. Rev. 2006; 106: 2065–2091. Publisher Full Text

[80] 80. Parr RG, Szentpaly L v, Liu S: Electrophilicity Index. J. Am. Chem. Soc. 1999; 121: 1922–1924. Publisher Full Text

[81] 81. Galván M, Pérez P, Contreras R, et al.: Condensed-to-atoms electronic Fukui functions within the framework of spin-polarized density-functional theory. Chem. Phys. Lett. 1999; 30: 405.

[82] 82. Mortier WJ, Yang W: The use of global and local molecular parameters for the analysis of the gas-phase basicity of amines J. Am. Chem. Soc. 1986; 108: 5708–5711. PubMed Abstract | Publisher Full Text | Free Full Text

[83] 83. Fuentealba P, Pérez P, Contreras R: On the condensed Fukui function. J. Chem. Phys. 2000; 113: 2544–2551. Publisher Full Text

[84] 84. Zhao Y, Truhlar DG: The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, non-covalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Accounts. 2008; 120: 215–241. Publisher Full Text

[85] 85. Frisch MJ, Trucks GW, Schlegel HB, et al.: Gaussian Inc., Wallingford CT.2009.

[86] 86. Morales-Bayuelo A: Replication Data for: Analyzing of a serie of ligand against malaria using Molecular docking, Molecular Quantum Similarity and reactivity indices whitin Density Functional Theory framework. [dataset]. Harvard Dataverse. 2023; 123. Publisher Full Text

Analyzing a series of ligands against malaria through the application of molecular docking, molecular quantum similarity, and reactivity indices

Abstract

Background

Methods

Results

Conclusions

Keywords

Introduction

Method

Approach for docking investigations

Quantum similarity study

Molecular quantum similarity framework

(1)

Carbó's similarity index

(2)

Quantum similarity using the Euclidean distance

(3)

(4)

MQSM overlap considering the Equation 2

(5)

MQS Coulomb considering the Equation 5

(6)

Euclidean distance index considering the Equation 3

(7)

(8)

(9)

(10)

Alignment Method: Topo-Geometrical Superposition Algorithm (TGSA)

Chemical reactivity context

(11)

(12)

(13)

(14)

Results and Discussion

Molecular docking outcomes for the ligands

Figure 1. Docking interactions for Compound 1.

Figure 2. Docking interactions for Compound 2.

Figure 3. Docking interactions for Compound 3.

Figure 4. Docking interactions for Compound 4.

Figure 5. Docking interactions for Compound 5.

Figure 6. Docking interactions for Compound 6.

Figure 7. Docking interactions for Compound 7.

Figure 8. Docking interactions for Compound 8.

Figure 9. Docking interactions for Compound 9.

Molecular quantum similarity analysis

Table 1. Molecular Quantum Similarity using the Overlap Operator.

Table 2. Molecular Quantum Similarity using the Overlap Euclidean Distance.

Table 3. Molecular Quantum Similarity using the Coulomb Operator.

Table 4. Molecular Quantum Similarity using the Coulomb Euclidean Distance.

Global and local chemical reactivity indices

Table 5. Global reactivity indices for the compound.

Figure 10. (a) f−(r→)≈|HOMO(r→)|2 and (b) f+(r→)≈|LUMO(r→)|2, for the compound 2. Fukui Funtions (b) f−(r→)≈|HOMO(r→)|2 and (c) f+(r→)≈|LUMO(r→)|2, for the compound 6.

Figure 11. Fukui Funtions (a) f−(r→)≈|HOMO(r→)|2 and (b) f+(r→)≈|LUMO(r→)|2, for the compound 7. Fukui Funtions (c) f−(r→)≈|HOMO(r→)|2 and (d) f+(r→)≈|LUMO(r→)|2f+(r→)≈|LUMO(r→)|2, for the compound 8.

Conclusions

Data availability

Underlying data

References

Comments on this article Comments (0)

Open Peer Review

Comments on this article Comments (0)

Open Peer Review

Reviewer Status

Reviewer Reports

Comments on this article

Browse by related subjects

Competing Interests Policy

Stay Updated

Figure 10. (a) $f^{-} (\vec{r}) \approx {| HOMO (\vec{r}) |}^{2}$ and (b) $f^{+} (\vec{r}) \approx {| LUMO (\vec{r}) |}^{2}$ , for the compound 2. Fukui Funtions (b) $f^{-} (\vec{r}) \approx {| HOMO (\vec{r}) |}^{2}$ and (c) $f^{+} (\vec{r}) \approx {| LUMO (\vec{r}) |}^{2}$ , for the compound 6.