key: cord-0055912-7f3cc2g0
authors: Rauf, Abdul; Ishtiaq, Muhammad; Siddiqui, Muhammad Kamran
title: Topological Study of Hydroxychloroquine Conjugated Molecular Structure Used for Novel Coronavirus (COVID-19) Treatment
date: 2021-01-27
journal: nan
DOI: 10.1080/10406638.2021.1873807
sha: bc4cce46d1d244a8e6e57731aeb52a9c706957c8
doc_id: 55912
cord_uid: 7f3cc2g0

The novel coronavirus disease 2019 (Covid-19) is a mutating and recombining pandemic that potentially spreading through an infected person in droplet-generated forms that have affected more than 200 countries and endanger the entire globe. There is no clear strategy for the care of COVID-19 cases. Moreover, experts across the globe are working actively to develop medicinal or anti-virus drugs. On the basis of recent clinical findings and recommendations, the study examined a variety of new medications that have shown antiviral activity against SARS-CoV-2, among other drugs, antimalarial medications Chloroquine (CQ) and Hydroxychloroquine (HCQ) have gained significant publicity to have promising effects against SARS-CoV-2. Linking a bioactive substance to a biocompatible polymer typically provides various concerns, such as improved drug solubilization, improved modification, precise restriction, and controlled discharge. An enormous number of medical analyses have confirmed that the characteristics of medical drugs have a nearby connection with their atomic structure. Medication properties can be acquired by considering the atomic structure of relating drugs. The calculation of the topological index of a medication structure empowers researchers to have a superior comprehension of the physical science and bio-organic attributes of drugs. Ev-degree and ve-degree based topological indices are two novel degrees based indices as of late defined in graph theory. Ev-degree and ve-degree based topological indices have been defined as corresponding to their relating partners. In this paper, we have computed topological indices based on ev-degree and ve-degree for the Hydroxyethyl Starch and Hydroxychloroquine (HCQ-HEC) bioconjugate molecular structure.

Over hundreds of years, viruses and contagious diseases have become the focus of research and medicine. Virology has involved some of our greatest scientific challenges and triumphs, from smallpox to HIV and so many others. Today is no different, Virology is once again at the frontline of the latest epidemic of the novel coronavirus, SARS-CoV-2, and its related infectious disease COVID-19. Following the Severe Acute Respiratory Syndrome Coronavirus (SARS-CoV) in 2003 1,2 and the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012, [3] [4] [5] COVID-19 is the third novel coronavirus to cause a large-scale epidemic in the 21st century. The first case of the novel coronavirus (2019-nCoV) was identified on 31 December 2019 in the city of networks. 18, 19 Chemicals Graph Theory have numerous applications linked to medicine, drug design, medical research and in experimental science. 20, 21 In theoretical chemistry, topological indexes are numerical functions correlated with the chemical structures for the association of chemical types form with various physical properties, reactivities of chemical or biological behaviors. These topological indexes are obtained from the structures of molecules. Numerous fascinating models have been effectively extracted when different molecular indexes have been used. Topological indices are playing an important role. In the most part, topological indices identified by the definition of vertex degrees. Topological indexes have been used to explain and improve the statistical features of drugs. The topological descriptor concept firstly given by Wiener 22 when he was working on the breaking point of paraffin. He found first topological index name as the Wiener index. The most widely used topological indices in chemical and mathematical literature are the Randic, Zareb and Wiener indices. [23] [24] [25] Zhong 26 described an index name as Harmonic index and thereafter Ediz et al., 25 described noval new Harmonic index. All of the above research was performed by using the classical definition of degrees. Chellali et al. 27 recently presented two novel definitions in the field of graph theory, namely ve-degree and ev-degree. Later Horoldagva et al. 28 explored some of ve-degree and ev-degree based mathematical concepts. The classical degree-based frameworks then have been transformed into ve-degree and ev-degree Zagreb and Randic indices in. [29] [30] [31] The ve-degree Zagreb index has been shown to have a greater predictive ability than the classic Zagreb index.

In this paper we have explored the ve-degree and ev-degree-based topological characteristics of Hydroxyethyl starch conjugated with Hydroxychloroquine (HCQ-HEC). We have evaluated the Zagreb (M ev ) and the Randic (R ev ) indexes based on ev-degree, first Zagreb a-index (M ave

, atom-bond connectivity (ABC ve ) index, harmonic (H ve ) index, geometric-arithmetic (GA ve ) index and sum-connectivity (v ve ) index based on ve-degrees to predict some physicochemical properties for molecular structure of Hydroxyethyl starch conjugated with Hydroxychloroquine (HCQ-HEC). The functions of topological indices in pharmaceutical research has been improved. Topological indices catch molecular structure stability and offer a statistical framework for predicting properties such as viscosity, boiling points, gyration distance, etc. In all situations where the IUPAC suggestions are relevant for terminology used in molecular biology and computational drug discovery. For more about these topological indices and formulas see. [32] [33] [34] [35] [36] [37] [38] [39] 

Throughout this section, we present few initial ideologies. A connected graph denoted by G ¼ ðV, EÞ with edges set E and of vertices set V. The degree of the v vertex, denoted by K, is the amount of specific edges that may be incident to the v vertex. The open neighborhood of the v vertex, denoted by N(v), is a collection of all vertices adjacent to the v vertex. closed neighborhood of v, denoted by N½v, describes as the union of v vertex with open neighborhood N(v) of v vertex. The ev-degree, denoted by K ev ðeÞ, of any edge e ¼ uv 2 E is the total vertices quantity of the closed neighborhoods union of u and v vertex. The ve-degree, denoted by K ve ðvÞ, of any vertex v 2 V is the number of different edges that appears to any vertex in the closed neighborhood of v.

The Bioconjugate in chemistry is the study of linking one molecule to another by means of chemical and biological strategy.

The ev-degree and ve-degree based topological descriptor are defined below (see Table 1 ). In this paper, we will compute the below given topological descriptor for molecular structure of Hydroxyethyl starch conjugated with Hydroxychloroquine (HCQ-HEC).

In this paper we discussed the M ev , M ave 1 , M bve 1 , M ve 2 , R ve , R ev , ABC ve , GA ve , H ve and v ve : We also covered the closed formulas for molecular structure of Hydroxyethyl starch conjugated with Hydroxychloroquine (HCQ-HEC) to compute all given indices.

For calculation, we have utilized the combinatorial processing strategy, edge partition technique, vertex partition strategy, analytic procedures, graph hypothetical tools, techniques of counting degrees and entirety techniques of degree neighbors. Moreover, Matlab programming have been utilized for the numerical computations and checks. We likewise utilized the maple for plotting these numerical outcomes.

The COVID-19 pandemic proceeds to grasp the world in both transparent and hidden ways from almost unseen yet mysterious adversaries swapping capacities. Currently, there is no FDAapproved COVID-19 medication but high-level initiatives and investigations are underway. However, on 28 March 2020, the FDA permitting for the emergency use of chloroquine (CQ) and hydroxychloroquine (HCQ) in COVID-19. 14 Hydroxychloroquine is chloroquine derivatives, was developed in 1955 and approved for malaria treatment. Hydroxychloroquine is included in the list of the World Health Organization's important drugs with a better safety profile, especially with sustained usage. Hydroxychloroquine has expanded over the years to include autoimmune diseases such as rheumatoid arthritis, Sjogren syndrome, systemic lupus erythematosus, and post-Lyme disease arthritis. 40,41

As a particular group of biomolecules, smart polymers manifest an amazing reaction to physicochemical and biological shift when their circumstances have a minor intervention, such as shifts in PH interest, ion disruption, magnetization, light and temperature. These polymers are therefore also defined as environmentally sustainable systems or responsive stimulation. As good drug delivery mechanisms, such frameworks have broad applications in the medical field, for example, smart nucleic acid polymers or intracellular protein distribution, much like nucleus or ribosome in tissue regeneration. A special type of smart polymer or polymeric hydroxychloroquine (HCQ) conjugated with hydroxyethyl starch (HES) is commonly utilized in the production of anticancer medicines. The development of QSARs utilizing basic molecular techniques seems to be a powerful and The Zagreb index based on ev-degree

The first Zagreb a-index based on ve-degree

The atom-bond connectivity index based on ve-degree

The geometric-arithmetic index based on ve-degree

The harmonic index based on ve-degree The sum-connectivity index based on ve-degree

complementary tool for drug-protein, high-throughput screening, docking and computational chemistry. All QSAR techniques are focused on the use of molecular/topological descriptors that are mathematical tools to codify useful chemical knowledge and allow for similarities between antioxidant and statistical processes. The uses of molecular/topological descriptors in medicinal chemistry has been a rational approach to huge synthesis and screening of compounds. QSAR models estimate biological behavior by using different types of structural molecular parameters as inputs. Among such parameters, topological indices (TIs) are a very fascinating class.

In this section, we review the molecular structure of hydroxychloroquine (HCQ) used in the treatment of malaria which is recently suggested for emergency used in COVID-19 and computed the novel degrees based topological descriptors such as M ev , M ave

HES is produced by chemical alteration of ethylene oxide from human products, such as waxy maize starch. Hydroxyethylation improves the solubility and decreases the enzymatic oxidation of starch by serum amylases, thereby increasing the half-life of the plasma. This improvement in biostability depends on the average substitution per anhydroglucose unit (AGU) and the substitution ratio between C 2 and C 6.

42, 43 The optimization of these combinations resulted in a sufficiently extended half-life of plasma that enabled HES to be converted into the medical setting as a polymeric blood volume splitter. 44 HES formulated with hydroxychloroquine (HCQ) as a new polymeric product capable of inhibiting the aggressive existence of pancreatic cancer cells (PCs). HES was conjugated with HCQ using a simple pairing of carbonyldiimidazole to prepare chloroquine-modified HES (CQ-HES) (see Figure 1 ). HCQ-HES has the ability to create novel antimetastatic therapies as a drug delivery mechanism ideal for future production of chemotherapeutics. Throughout tumor distribution applications, these nanoparticle systems benefit from special tumor biology by enhanced permeability and retention (EPR) effects and allow for increased tumor aggregation. [45] [46] [47] Let G¼HCQ-HES graph that containing 53n þ 2 vertices and 56n þ 2 edges (see Figure 2 ). The vertices with degree 1, 2, and 3 denoted by V 1 , V 2 , and V 3 , respectively. Where jV 1 j ¼ 9n þ 2, jV 2 j ¼ 27n, and jV 3 j ¼ 17n: On the bases of degrees the vertices partition of HA-Dox is given in Table 2 . Similarly on the bases of degrees HCQ-HES having edges partition given in Table 3 . The Zagreb index based on ev-degree. From Table 3 we compute the Zagreb index based on ev-degree:

The first Zagreb a-index based on ve-degree. From Table 4 we compute the first Zagreb a-index based on ve-degree:

The first Zagreb b-index based on ve-degree. From Table 5 we compute the first Zagreb b-index based on ve-degree:

M bve 1 ðGÞ ¼ ð5Þð1Þ þ ð6Þð4nÞ þ ð7Þð3nÞ þ ð10Þð2n þ 1Þ þ ð7ÞðnÞ þ ð8ÞðnÞ þ ð9Þð9nÞ þð10ÞðnÞ þ ð10ÞðnÞ þ ð11Þð2n þ 1Þ þ ð10Þð4nÞ þ ð11Þð2nÞ þ ð12Þð2nÞ þ ð13Þð3nÞ þð11Þð2nÞ þ ð13Þð8n À 1Þ þ ð14ÞðnÞ þ ð14Þð2Þ þ ð15Þð10n À 2Þ ¼ 618n þ 11:

The second Zagreb index based on ve-degree. From Table 5 The Randic index based on ve-degree. From Table 5 we compute The Randic index based on ve-degree:

R ve ðGÞ ¼ ð6Þ À 1 2 ð1Þ þ ð8Þ À 1 2 ð4nÞ þ ð15Þ À 1 2 ð3nÞ þ ð21Þ À 1 2 ð2n þ 1Þ þ ð12Þ À 1 2 ðnÞ þ ð16Þ À 1 2 ðnÞ þð20Þ À 1 2 ð9nÞ þ ð25Þ À 1 2 ðnÞ þ ð24Þ À 1 2 ðnÞ þ ð28Þ À 1 2 ð2n þ 1Þ þ ð25Þ À 1 2 ð4nÞ þ ð30Þ À 1 2 ð2nÞ þð35Þ À 1 2 ð2nÞ þ ð40Þ À 1 2 ð3nÞ þ ð30Þ À 1 2 ð2nÞ þ ð42Þ À 1 2 ð8n À 1Þ þ ð48Þ À 1 2 ðnÞ þ ð49Þ À 1 2 ð2Þ þ ð56Þ À 1 2 ð10n À 2Þ The Randic index based on ev-degree.

From Table 3 we compute The Randic index based on ev-degree: R ev ðGÞ ¼ X e2EðGÞ K ev ðeÞ À 1 2 , R ev ðGÞ ¼ ð3Þ À 1 2 ð4n þ 1Þ þ ð4Þ À 1 2 ð5n þ 1Þ þ ð4Þ À 1 2 ð12nÞ þ ð5Þ À 1 2 ð25nÞ þ ð6Þ À 1 2 ð10nÞ

The atom-bond connectivity index based on ve-degree. From Table 5 we compute The atom-bond connectivity index based on ve-degree: The goemetric-arithmetic index based on ve-degree. From Table 5 we compute the goemetric-arithmetic index based on ve-degree: The harmonic index based on ve-degree. From Table 5 we compute the harmonic index based on ve-degree: The sum-connectivity index based on ve-degree. From Table 5 we compute the sum-connectivity index based on ve-degree: v ve ðGÞ ¼ X uv2EðGÞ ðK ve ðuÞ þ K ve ðvÞÞ À 1 2 , v ve ðGÞ ¼ ð5Þ À 1 2 ð1Þ þ ð6Þ À 1 2 ð4nÞ þ ð7Þ À 1 2 ð3nÞ þ ð10Þ À 1 2 ð2n þ 1Þ þ ð7Þ À 1 2 ðnÞ þ ð8Þ À 1 2 ðnÞ þð9Þ À 1 2 ð9nÞ þ ð10Þ À 1 2 ðnÞ þ ð10Þ À 1 2 ðnÞ þ ð11Þ À 1 2 ð2n þ 1Þ þ ð10Þ À 1 2 ð4nÞ þ ð11Þ À 1 2 ð2nÞ þð12Þ À 1 2 ð2nÞ þ ð13Þ À 1 2 ð3nÞ þ ð11Þ À 1 2 ð2nÞ þ ð13Þ À 1 2 ð8n À 1Þ þ ð14Þ À 1 2 ðnÞ þð14Þ À 1 2 ð2Þ þ ð15Þ À 1 2 ð10n À 2Þ

Topological indices based QSAR models can play a significant role in reducing the expense of time, human services, physical facilities and animal studies to discover drugs or drug targets. The QSAR models based descriptor particularly used to understand the biological behavior of antiparasite medications that are being researched in significant part. Correlation of degree-based topological descriptor occurring in chemical literature has been verified for generic heat forming and usual octane isomer boiling points. The association capacity of each of these indexes is considered to be either very low or zero. In this portion, we have provided numerical results for evdegree and ve-degree related topological descriptors for the structure of Hydroxyethyl starch conjugated with Hydroxychloroquine (HCQ-HEC) to understand the similarities between statistical and biological behavior. We have used different values of n to compute numerical tables for the ev-degree and ve-degree based indices such as the Zagreb (M ev ) and the Randic (R ev ) indexes based on ev-degree, first Zagreb a-index (M ave 1 ), first Zagreb b-index (M bve 1 ), Randic index (R ve ), second Zagreb index (M ve 2 ), atom-bond connectivity (ABC ve ) index, harmonic (H ve ) index, geometric-arithmetic (GA ve ) index and sum-connectivity (v ve ) index based on ve-degrees to predict physiochemical and medication properties for the molecular structure of (HCQ-HES), (see Tables  6 ). Moreover, we have drawn the graphs 3-7 for the structure of (HCQ-HES) to review the behavior of topological descriptors computed above to predict the level of toxicity, antidotes, physiochemical and medication properties of drugs. We have provided the comparison graphs related to M ev , M ave 1 , M bve 1 and M ve 2 given in Figure 8 (a) and graph related to R ve , R ev , ABC ve , GA ve , H ve and v ve given in Figure 8 (b). We also provide all indices comparison result by graphical representation see Figure 9 It can be observed from the Figures 3-7 and Table 6 that all topological descriptors computed for the structures of (HCQ-HES) increases with the increase in n.

For the computation of the overall p-electronic energy of the molecules, the Zagreb form indices were found; 48 thus, in the case of (HCQ-HES) for higher values of n, the p-electronic energy is growing/increases.

In studying the chemical similarity of molecular compounds, the Randic index can be used, which necessary to allow for the automatic decision making. 49 The Randic index is among the most commonly employed molecular-graphic structure descriptors and is surprising to note that its alteration functions considerably better than the normal version. In addition, the Randic index used for the calculation of the Kovat constants and the boiling point of the compounds. The Randic index for the molecular structure of (HCQ-HES) increases by the increment in n.

The predictive power of the geometric-arithmetic index was found to be superior to that of the Randic connectivity index. With the rise in n, the GA index for (HCQ-HES) structure is increases.

The Atomic Bond Connectivity (ABC) index presents a very strong correlation for calculating cycloalkanes strain energy and also for the stability of linear and branched alkanes. 50 The ABC index for the (HCQ-HES) increases with increment in n. In the current research, the ABC index increases for the structure of (HCQ-HES) with the enhancement of n. The Zagreb index and the atom-bond connectivity index show the better results. Also the ev-degree Randic index and Harmonic index are correlated (see Figure 8 (b)). The recently introduced sum-connectivity index and harmonic index, while they have fairly strong correlation capacities, are outperformed than any of the older indices. The rationale for their usage in quantitative structural-property relationship/quantitative structure-activity relationship (QSPR/QSAR) is thus unclear.

The Topological Indices Technique has opened up a broad variety of potential uses for the assessment of QSAR antiparasitic products. Topological indices used to research network topologies have offered different possibilities for the identification of drug targets for parasite disease. Current QSAR studies are expected to be applied to complex issues, including the design of antiparasite drugs and the development of drug targets. The usage of technology and QSAR models in drug development analysis and medicinal chemistry has been growing in recent times. Quantitative Structure-Activity Relationship (QSAR) frameworks of Medicinal Chemistry and Pharmaceutical design are used for the development of anti-parasite medicines. Since the COVID-19 is the novel major issue of the world with continuously increasing the ratio of cases and death. Effective treatment for this COVID-19 pandemic is an essential aspect of current medical research. Chloroquine and hydroxychloroquine are a couple of old drugs used for malaria prevention and recovery are permitting for the treatment of COVID-19 in case of emergency. Studies released in February and March indicate that medications suppress the virus that triggers COVID-19 in monkey cells. A limited clinical experiment in France revealed that hydroxychloroquine helps people recover more rapidly from the infection, although another experimental test in Beijing showed no significant advantage to this medication. Many clinical studies, including one funded by the World Health Organization, are planned to carry out more stringent research on the medicines.

Chloroquine has emerged regularly over the past decade as a possible antiviral against developing pathogens. Research in 2004 and 2005 also established it as an agent of the initial coronavirus SARS. Scientists have since conducted several studies using chloroquine or hydroxychloroquine to prevent or reduce viral infections in mice, including OC43 coronavirus, avian influenza, Ebola virus, Zika virus, and MERS-CoVthe coronavirus that causes respiratory syndrome in the Middle East. However, human studies were less successful, and the drugs were never approved for the treatment of viral infections. Despite the absence of clear data in patients, many drug companies have promised to donate millions of doses in the months ahead. Hydroxychloroquine or chloroquine, sometimes in conjunction with second-generation macrolide, is commonly used for the diagnosis of COVID-19, without definitive proof of its benefit. Coupling a cytotoxic drug to a macromolecular product increases a drug's pharmacokinetic profile, prolongs the delivery of medicines and reduces time. 51,52

Topological indices methodology has opened up a broad variety of possible applications for the QSAR estimation of antiparasitic drugs. Topological indices used to study network topologies which have provided new possibilities for detecting drug targets in parasites disease. It is expected that current QSAR studies will be applied in complicated problems including the design of antiparasite drugs and the development of drug targets. To understand and then analyzing the underlying topologies through topological descriptors is important. These experimental studies have a broad range of applications in the fields of chem-informatics, bio-informatics and bio-medicine, where various graph topological based assessments are used to tackle many complicated schemes. Graphs topologies are important tools for approximating and predicting the properties of biological and chemical compounds in the analysis of the quantitative structure-property relationships (QSPRs) and the quantitative structure-activity relationships (QSARs). In this paper, we provided results related to the ev-degree and ve-degree based topological indices such as the Zagreb (M ev ) and the Randic (R ev ) indexes based on ev-degree, first Zagreb a-index (M ave 1 ), first Zagreb b-index (M bve 1 ), Randic index (R ve ), second Zagreb index (M ve 2 ), atom-bond connectivity (ABC ve ) index, harmonic (H ve ) index, geometric-arithmetic (GA ve ) index and sum-connectivity (v ve ) index based on ve-degrees for molecular structure of Hydroxyethyl starch conjugated with Hydroxychloroquine (HCQ-HEC) to study the pharmaceutical properties of drugs. All the topological descriptor are in increasing order.

There are no conflicts of interest. 

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