Quantitative Structure Property Analysis of Anti-Covid-19 Drugs
QQuantitative Structure Property Analysis ofAnti-Covid-19 Drugs
Sunilkumar M. Hosamani
Department of Mathematics, Rani Channamma UniversityBelagavi-591156, India
E-mail: [email protected]
Dedicated to Corona-Warriors around the world
Abstract
Inspired by recent work on anti-covid-19 drugs [2] here we study the Quantitative-structure property relationships(QSPR) of phytochemicals screened against SARS-CoV-2 3 CL pro with the help of topological indices like the first Zagreb index M ,second Zagreb index M , Randi´ c index R , Balban index J and sum-connectivityindex SCI ( G ). Our study has raveled that the sum-connectivity index ( SCI ) andthe first Zagreb index ( M ) are two important parameters to predict the molecularweight and the topological polar surface area of phytochemicals respectively. Keywords:
QSPR; Molecular descriptor; Zagreb indices.
AMS
Subject Classification: a r X i v : . [ q - b i o . B M ] A ug ptionsi comei fromi experiencei treatingi SARSi, MERSi ori somei otheri newi influenzaivirusi previouslyi. Thesei drugsi wouldi bei helpfuli buti thei efficacyi needsi toi beifurtheri confirmedi. Fewi COVID-19 vaccinesi arei alsoi underi clinicali trialsi suchi asiModerna’s mRNA- 1273, firsti US clinicali vaccinei fundedi byi NIH’s NIAID (NationalInstitute of Allergy and Infectious Diseases) (Tirumalaraju [18]). Thus, therei isi ani un-meti requirementi fori thei specifici anti-COVID-19 therapeuticsi toi limiti thei severityiofi thei deadlyi diseasei.Various clinicians and researchers are engaged in investigating and developing an-tivirals using different strategies combining experimental and in-silico approaches see[1, 3, 5, 7–14, 14, 16, 17, 21–23]. The replication cycle of SARS-CoV-2 can be broadly di-vided into three processes viral entry, viral RNA replication and lastly, viral assemblyand exit from the host cell which is depicted in Figure 1. Figure 1.
Replication cycle of SARS- COV-19.Recent studies revealed that the genome sequence of SARS-CoV-2 is very similar to that2f SARS-CoV. Recently, Qamar et.al [14] reported the following phytochemicals screenedagainst SARS-CoV-2 3 CL pro which are depicted in Figure 2.3 igure 2. Top ranked phytochemicals screened against SARS-CoV-2 3 CL pro . Ai moleculari graphi isi ai connectedi undirectedi graphi correspondingi toi structurali for-mulai ofi ai chemicali compoundi, soi thati verticesi ofi thei graphi correspondi toi atomsiofi thei moleculei andi edgesi ofi thei graphi correspondi toi thei bondsi betweeni theseiatoms.i Moleculari graphsi havei fundamentali applicationsi ini chemoinformaticsi, quan-titativei structure-propertyi relationships(QSPR)i, quantitativei structure-activityi rela-tionships(QSAR)i, virtuali screeningi ofi chemicali libraries,i andi computationali drugidesign. QSPRi, QSARi andi virtuali screeningi arei basedi oni thei structure-propertyiprinciplei, whichi statesi thati thei physicochemicali andi biologicali propertiesi ofi chem-icali compoundsi cani bei predictedi fromi theiri chemicali structurei. Onei ofi thei sim-plesti methodsi thati havei beeni devisedi fori correlatingi structuresi withi biologicaliactivitiesi ori physical-chemicali propertiesi involvei moleculari descriptorsi calledi topo-logicali indicesi. The example of molecular graph is depicted in Figure 3.4 igure 3.
Ethanole and its molecular graph.Since physical properties or bioactivities are expressed in numbers whereas chemical struc-tures are discrete graphs, in order to associate graphs with numbers one has to rely ongraph-theoretical invariants such as local vertex invariants, e.g. vertex degree, distancesum, etc. Hundreds of topological indices have been introduced so far.The main aim of this study is to develop a quantitative structure property relationshipbetween two-dimensional(2D) topological indices, calculated physicochemical parametersof phytochemicals screened against SARS-CoV-2 3 CL pro . Experimental data used in thisstudy were taken from [14]. In this paper we have considered five topological indicesviz., the first Zagreb index M ( G ) [6], the second Zagreb index M ( G ) [6], Randi´ c index R ( G ) [15], Balban index J ( G ) [2, 3] and the sum-connectivity index SCI ( G ) [25]. Theformulae for these topological indices are give below: M ( G ) = (cid:88) u ∈ V ( G ) deg ( u ) (1) M ( G ) = (cid:88) uv ∈ E ( G ) deg ( u ) · deg ( v ) (2) R ( G ) = (cid:88) uv ∈ E ( G ) (cid:112) d G ( u ) d G ( v ) (3) J ( G ) = mm + n − (cid:88) uv ∈ E ( G ) (cid:112) w ( u ) w ( v ) (4)where w ( u ) (resp. w ( v )) denotes the sum of distances from u (resp. v ) to all the othervertices of G . 5 CI ( G ) = (cid:88) uv ∈ E ( G ) d u ( G ) + d G ( v ) (5)The productivity of the above mentioned topological indices were tested using a dataset of phytochemical, found at [2] and https://pubchem.ncbi.nlm.nih.gov/. The dataset consists of the following data: docking score, binding affinity, molecular weight andtopological polar surface, which is given in Table 1. Table 1.
The physicochemical properties of phytochemicals.PubChem Phytochemical Docking Binding Molecular TopologicalIDs Name score affinity Weight Polar(kcal/mol) Surface11610052 5,7,30,40- Tetrahydroxy -16.35 -29.57 354.40 107.00- 2-(3,3-dimethylallyl)isoflavone5281673 Myricitrin -15.64 -22.13 464.40 207.006479915 Methyl rosmarinate -15.44 -20.62 374.30 134.00NPACT00105 3,5,7,30,40,50- hexahydroxy -14.42 -19.10 .00 .00flavanone-3-Obeta- Dglucopyranoside10930068 (2S)-Eriodictyol -14.41 -19.47 602.50 253.007-O-(600-Ogalloyl)- beta-Dglucopyranoside5273567 Calceolarioside B -14.36 -19.87 478.40 186.005318606 Myricetin -13.70 -18.42 480.40 227.003-Obeta- Dglucopyranoside11111496 Licoleafol -13.63 -19.64 372.40 127.006123095 Amaranthin -12.67 -18.14 726.60 346.0064143 Nelfinavir -12.20 -17.31 567.80 127.0065947 Prulifloxacin -11.32 -15.40 461.50 125.005311054 Colistin -13.73 -18.57 1155.40 491.00
Note:
The molecular weight and topological polar surface of NPACT00105 could notfind. Therefore, we do not include this molecule for QSPR-analysis.The topological indices values of phytochemical structures ate given in Table 2.
Table 2.
Topological indices calculated for phytochemicals used in the present study6 hytochemical Name Molecular Descriptors M M R B SCI
The following regression models have been used for the study: • Linear Model: P = a ( T I ) + b • Quadratic Model : P = a ( T I ) + b ( T I ) + c • Logarithmic Model: P = a + b ln( T I ) • Multiple Linear Model: P = a ( T I ) + b ( T I ) + c ( T I ) + d ( T I ) + e ( T I ) + f where P is a physical property, T I is the topological index, a, b and c are constants.Next we present the regression models for docking score (DS) of phytochemical withthe above mentioned topological indices. Linear Model:
DS = 0 . M − .
429 (6)DS = 0 . M − .
602 (7)7S = 0 . R − .
007 (8)DS = 0 . J − .
399 (9)DS = 0 . SCI − .
138 (10)
Quadratic Model:
DS = 0 . M − .
256 (11)DS = 0 . M − (9 . E − M − .
310 (12)DS = 0 . R − . R − .
064 (13)DS = 0 . J − . J − .
841 (14)DS = 0 . SCI − . SCI − .
383 (15)
Logarithmic Model:
DS = 1 .
951 ln( M ) − .
213 (16)DS = 0 .
057 ln( M ) − .
114 (17)DS = 1 .
704 ln( R ) − .
519 (18)DS = 0 .
822 ln( J ) − .
818 (19)DS = 1 .
726 ln(
SCI ) − .
93 (20)8 able 3.
Correlation coefficient, F and S values.Model No R F S
Model 6 0.127 1.449 0.256Model 11 0.177 2.147 0.174Model 16 0.309 2.011 0.190Model 7 0.151 1.772 0.213Model 12 0.198 2.463 0.148Model 17 0.306 1.984 0.193Model 8 0.081 0.882 0.370Model 13 0.130 1.500 0.249Model 18 0.276 1.714 0.234Model 9 0.019 0.199 0.665Model 14 0.084 0.915 0.361Model 19 0.081 0.394 0.685Model 10 0.094 1.037 0.333Model 15 0.145 1.698 0.222Model 20 0 .288 1.821 0.217Among all the topological indices used to predict docking score of phytochemicals, model16 and model 17 were found to correlate well with correlation coefficient value r = 0 . r = 0 .
306 respectively. In fact, the predicting power for topological indices consideredhere are too low for binding affinity of phytochemicals. Therefore, next we present theregression models for binding affinity (BA) of phytochemical with the above mentionedtopological indices.
Linear Model:
BA = 1 . M − .
971 (21)BA = 1 . M − .
095 (22)BA = 15 . R − .
402 (23)BA = 46 . J + 51 .
247 (24)BA = 15 . SCI − .
051 (25)
Quadratic Model:
BA = 0 . M + 0 . M + 21 .
323 (26)BA = − . M + 0 . M + 103 .
085 (27)BA = 19 . R − . R − .
998 (28)BA = − . J + 14 . J + 258 .
086 (29)BA = 14 . SCI + 0 . SCI − .
554 (30)
Logarithmic Model:
BA = 4 .
591 ln( M ) − .
904 (31)BA = 353 .
161 ln( M ) − .
138 (32)BA = 339 .
535 ln( R ) − .
752 (33)BA = 99 .
187 ln( J ) + 94 .
221 (34)BA = 346 .
307 ln(
SCI ) − .
856 (35)10 able 4.
Correlation coefficient, F and S values.11odel No R F S
Model 21 0.127 1.449 0.256Model 26 0.177 2.147 0.174Model 31 0.309 2.011 0.190Model 22 0.132 1.519 0.246Model 27 0.171 2.061 0.182Model 32 0.261 1.585 0.257Model 23 0.095 1.046 0.331Model 28 0.146 1.710 0.220Model 33 0.258 1.561 0.262Model 24 0.160 1.899 0.198Model 29 0.433 7.635 0.020Model 34 0.493 4.374 0.047Model 25 0.105 1.174 0.304Model 30 0.157 1.866 0.202Model 35 0.268 1.650 0.245Among all the topological indices used to predict binding affinity of phytochemicals,model 29 and model 34 were found to correlate well with correlation coefficient value r = 0 .
433 and r = 0 .
493 respectively. In fact, the predicting power for topological indicesconsidered here are too low for binding affinity of phytochemicals. Therefore, next wepresent the regression models for molecular weight (MW) of phytochemical with the abovementioned topological indices.
Linear Model:
MW = 3 . M − .
709 (36)MW = 1 . M − .
095 (37)MW = 32 . R − .
898 (38)MW = 98 . J + 203 .
707 (39)MW = 32 . SCI − .
191 (40)
Quadratic Model:
MW = 0 . M + 0 . M + 168 .
241 (41)MW = − . M + 0 . M + 103 .
085 (42)MW = 33 . R − . R − .
420 (43)MW = − . J + 34 . J + 702 .
219 (44)MW = 25 . SCI + 0 . SCI − .
663 (45)12 ogarithmic Model:
MW = 730 .
933 ln( M ) − .
378 (46)MW = 704 .
988 ln( M ) − .
779 (47)MW = 714 .
373 ln( R ) − .
369 (48)MW = 196 .
542 ln( J ) + 305 .
128 (49)MW = 727 .
209 ln(
SCI ) − .
401 (50)13 able 5.
Correlation coefficient, F and S values.Model No R F S
Model 36 0.765 32.588 0.000Model 41 0.718 25.484 0.001Model 46 0.777 15.680 0.001Model 37 0.723 26.105 0.000Model 42 0.672 20.489 0.001Model 47 0.742 12.912 0.002Model 38 0.780 35.410 0.000Model 43 0.761 31.783 0.000Model 48 0.781 16.030 0.001Model 39 0.308 4.448 0.061Model 44 0.159 1.887 0.200Model 49 0.472 4.016 0.057Model 40 0.791 37.849 0.000Model 45 0.761 31.785 0.000Model 50 0.791 17.037 0.001By looking at the above table we can see that the predicting power of above mentionedtopological indices are good with respect to molecular weight of phytochemicals. Thecorrelation coefficient of the first Zagreb index ( M ) lies between 0.718 to 0.777, whereas,the range for the Zagreb index( M ) is lies between 0.672 to 0.742. For Randi´ c ( R ) indexthe r values is lies between 0.761 to 0.781 and for the Balban index J the r value rangingfrom 0.159 to 0.472. Finally for sum-connectivity index, the r value lies between 0.761 to0.791. Except, the Balban index, all T I (cid:48) s are shows good correlation coefficient. Amongall T I (cid:48) s , the sum-connectivity index SCI is a good candidate for predicting molecularweight of phytochemicals.Next we present the regression models for topological polar surface (TPA) of phyto-chemical with the above mentioned topological indices.14 inear Model:
TPA = 0 . M − .
268 (51)TPA = 0 . M − .
602 (52)TPA = 0 . R − .
007 (53)TPA = 0 . J − .
399 (54)TPA = 0 . SCI − .
138 (55)
Quadratic Model:
TPA = 0 . M − .
178 (56)TPA = 0 . M − (9 . E − M − .
310 (57)TPA = 0 . R − . R − .
064 (58)TPA = 0 . J − . bJ − .
841 (59)TPA = 0 . SCI − . SCI − .
383 (60)
Logarithmic Model:
TPA = 4 .
591 ln( M ) − .
904 (61)TPA = 0 .
057 ln( M ) − .
114 (62)TPA = 1 .
704 ln( R ) − .
519 (63)TPA = 0 .
822 ln( J ) − .
818 (64)TPA = 1 .
726 ln(
SCI ) − .
93 (65)15 able 6.
Correlation coefficient, F and S values.Model No R F S
Model 51 0.804 41.023 0.000Model 56 0.753 30.540 0.000Model 61 0.815 19.793 0.001Model 52 0.787 36.898 0.000Model 57 0.726 26.456 0.000Model 62 0.811 19.311 0.001Model 53 0.780 35.410 0.000Model 58 0.761 31.783 0.000Model 63 0.781 16.030 0.001Model 54 0.774 34.248 0.000Model 59 0.749 29.906 0.000Model 64 0.774 15.412 0.001Model 55 0.781 35.596 0.000Model 60 0.748 29.610 0.000Model 65 0.782 16.102 0.001By looking at the above table we can see that the predicting power of above mentionedtopological indices are better with respect to topological polar surface area of phyto-16hemicals. The correlation coefficient of the first Zagreb index ( M ) lies between 0.753to 0.815, whereas, the range for the Zagreb index( M ) is lies between 0.726 to 0.811. ForRandi´ c ( R ) index the r values is lies between 0.761 to 0.781 and for the Balban index J the r value ranging from 0.749 to 0.774. Finally for sum-connectivity index, the r value lies between 0.748 to 0.782. Among all T I (cid:48) s , the first Zagreb index M has betterpredicting power than other topological indices with respect to topological polar surfacearea of phytochemicals. Conclusion:
The QSPR study has revealed that the molecular descriptors are bestcandidates to predict the physicochemical properties of phyctochemicals. In particular,the sum-connectivity index (
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