Derivatives in discrete mathematics: a novel graph-theoretical invariant for generating new 2/3D molecular descriptors. I. Theory and QSPR application
In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ( ) of a molecular graph (MG) with respect to a given event ( E ), to obtain a new family of...
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| Veröffentlicht in: | Journal of computer-aided molecular design Jg. 26; H. 11; S. 1229 - 1246 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
01.11.2012
Springer Nature B.V |
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| ISSN: | 0920-654X, 1573-4951, 1573-4951 |
| Online-Zugang: | Volltext |
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| Abstract | In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the
first time
the use of the concept of
the derivative
(
)
of a molecular graph
(MG)
with respect to a given event
(
E
), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph’s theory’s traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix,
Q
, arises from the Boolean representation of
molecular sub
-
graphs
that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The
Q
matrix is a non-quadratic and unsymmetrical in nature, its columns (
n
) and rows (
m
) are
conditions
(letters) and
collection of conditions
(words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as
relations frequency matrix
,
F
, which characterizes
the participation intensity of the conditions (letters) in the events (words)
. With
F
, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei
i
, Δ
i
, can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei
i
with all the rest of the
j′s
atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical
invariants
are introduced. These invariants are applied to a vector whose components are the values Δ
i
for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating among different atoms, an atomic weighting scheme (atom-type labels) is used in the formation of the matrix
Q
or in
LOVIs
state. The obtained indices were utilized to describe the partition coefficient (Log P) and the reactivity index (Log K) of the 34 derivatives of 2-furylethylenes. In all the cases, our MDs showed better statistical results than those previously obtained using some of the most used families of MDs in chemometric practice. Therefore, it has been demonstrated to that the proposed MDs are useful in molecular design and permit obtaining easier and robust mathematical models than the majority of those reported in the literature. All this range of mentioned possibilities open “the doors” to the creation of a new family of MDs, using the graph derivative, and avail a new tool for QSAR/QSPR and molecular diversity/similarity studies. |
|---|---|
| AbstractList | In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ([Formula: see text]) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ(i), can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ(i) for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating among different atoms, an atomic weighting scheme (atom-type labels) is used in the formation of the matrix Q or in LOVIs state. The obtained indices were utilized to describe the partition coefficient (Log P) and the reactivity index (Log K) of the 34 derivatives of 2-furylethylenes. In all the cases, our MDs showed better statistical results than those previously obtained using some of the most used families of MDs in chemometric practice. Therefore, it has been demonstrated to that the proposed MDs are useful in molecular design and permit obtaining easier and robust mathematical models than the majority of those reported in the literature. All this range of mentioned possibilities open "the doors" to the creation of a new family of MDs, using the graph derivative, and avail a new tool for QSAR/QSPR and molecular diversity/similarity studies.In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ([Formula: see text]) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ(i), can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ(i) for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating among different atoms, an atomic weighting scheme (atom-type labels) is used in the formation of the matrix Q or in LOVIs state. The obtained indices were utilized to describe the partition coefficient (Log P) and the reactivity index (Log K) of the 34 derivatives of 2-furylethylenes. In all the cases, our MDs showed better statistical results than those previously obtained using some of the most used families of MDs in chemometric practice. Therefore, it has been demonstrated to that the proposed MDs are useful in molecular design and permit obtaining easier and robust mathematical models than the majority of those reported in the literature. All this range of mentioned possibilities open "the doors" to the creation of a new family of MDs, using the graph derivative, and avail a new tool for QSAR/QSPR and molecular diversity/similarity studies. In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ([Formula: see text]) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ(i), can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ(i) for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating among different atoms, an atomic weighting scheme (atom-type labels) is used in the formation of the matrix Q or in LOVIs state. The obtained indices were utilized to describe the partition coefficient (Log P) and the reactivity index (Log K) of the 34 derivatives of 2-furylethylenes. In all the cases, our MDs showed better statistical results than those previously obtained using some of the most used families of MDs in chemometric practice. Therefore, it has been demonstrated to that the proposed MDs are useful in molecular design and permit obtaining easier and robust mathematical models than the majority of those reported in the literature. All this range of mentioned possibilities open "the doors" to the creation of a new family of MDs, using the graph derivative, and avail a new tool for QSAR/QSPR and molecular diversity/similarity studies. (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative (...) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ^sub i^, can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ^sub i^ for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating among different atoms, an atomic weighting scheme (atom-type labels) is used in the formation of the matrix Q or in LOVIs state. The obtained indices were utilized to describe the partition coefficient (Log P) and the reactivity index (Log K) of the 34 derivatives of 2-furylethylenes. In all the cases, our MDs showed better statistical results than those previously obtained using some of the most used families of MDs in chemometric practice. Therefore, it has been demonstrated to that the proposed MDs are useful in molecular design and permit obtaining easier and robust mathematical models than the majority of those reported in the literature. All this range of mentioned possibilities open "the doors" to the creation of a new family of MDs, using the graph derivative, and avail a new tool for QSAR/QSPR and molecular diversity/similarity studies.[PUBLICATION ABSTRACT] In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ( ) of a molecular graph (MG) with respect to a given event ( E ), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph’s theory’s traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q , arises from the Boolean representation of molecular sub - graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns ( n ) and rows ( m ) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix , F , which characterizes the participation intensity of the conditions (letters) in the events (words) . With F , we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i , Δ i , can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j′s atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ i for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating among different atoms, an atomic weighting scheme (atom-type labels) is used in the formation of the matrix Q or in LOVIs state. The obtained indices were utilized to describe the partition coefficient (Log P) and the reactivity index (Log K) of the 34 derivatives of 2-furylethylenes. In all the cases, our MDs showed better statistical results than those previously obtained using some of the most used families of MDs in chemometric practice. Therefore, it has been demonstrated to that the proposed MDs are useful in molecular design and permit obtaining easier and robust mathematical models than the majority of those reported in the literature. All this range of mentioned possibilities open “the doors” to the creation of a new family of MDs, using the graph derivative, and avail a new tool for QSAR/QSPR and molecular diversity/similarity studies. In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ( $$ \partial $$ ) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Delta sub( )i can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Delta sub( )ifor the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating among different atoms, an atomic weighting scheme (atom-type labels) is used in the formation of the matrix Q or in LOVIs state. The obtained indices were utilized to describe the partition coefficient (Log P) and the reactivity index (Log K) of the 34 derivatives of 2-furylethylenes. In all the cases, our MDs showed better statistical results than those previously obtained using some of the most used families of MDs in chemometric practice. Therefore, it has been demonstrated to that the proposed MDs are useful in molecular design and permit obtaining easier and robust mathematical models than the majority of those reported in the literature. All this range of mentioned possibilities open "the doors" to the creation of a new family of MDs, using the graph derivative, and avail a new tool for QSAR/QSPR and molecular diversity/similarity studies. |
| Author | Torrens, Francisco Barigye, Stephen J. Marrero-Ponce, Yovani Santiago, Oscar Martínez López, Yoan Martínez |
| Author_xml | – sequence: 1 givenname: Yovani surname: Marrero-Ponce fullname: Marrero-Ponce, Yovani email: ymarrero77@yahoo.es, ymponce@gmail.com, yovanimp@uclv.edu.cu organization: Unit of Computer-Aided Molecular “Biosilico” Discovery and Bioinformatic Research (CAMD-BIR Unit), Faculty of Chemistry-Pharmacy, Central University of Las Villas, Institut Universitari de Ciència Molecular, Universitat de València – sequence: 2 givenname: Oscar Martínez surname: Santiago fullname: Santiago, Oscar Martínez organization: Unit of Computer-Aided Molecular “Biosilico” Discovery and Bioinformatic Research (CAMD-BIR Unit), Faculty of Chemistry-Pharmacy, Central University of Las Villas, Department of Chemical Science, Faculty of Chemistry-Pharmacy, Central University of Las Villas – sequence: 3 givenname: Yoan Martínez surname: López fullname: López, Yoan Martínez organization: Unit of Computer-Aided Molecular “Biosilico” Discovery and Bioinformatic Research (CAMD-BIR Unit), Faculty of Chemistry-Pharmacy, Central University of Las Villas, Department of Computer Sciences, Faculty of Informatics, Camaguey University – sequence: 4 givenname: Stephen J. surname: Barigye fullname: Barigye, Stephen J. organization: Unit of Computer-Aided Molecular “Biosilico” Discovery and Bioinformatic Research (CAMD-BIR Unit), Faculty of Chemistry-Pharmacy, Central University of Las Villas – sequence: 5 givenname: Francisco surname: Torrens fullname: Torrens, Francisco organization: Institut Universitari de Ciència Molecular, Universitat de València |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/23124489$$D View this record in MEDLINE/PubMed |
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| ContentType | Journal Article |
| Copyright | Springer Science+Business Media B.V. 2012 Springer Science+Business Media Dordrecht 2012 |
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| DOI | 10.1007/s10822-012-9591-9 |
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| ISSN | 0920-654X 1573-4951 |
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| Issue | 11 |
| Keywords | Invariant QSPR study Molecular graph Sub-graph Physicochemical property Frequency matrix Discrete mathematics Derivatives of 2-furylethylene Derivative of molecular graph Chemical graph theory Incidence matrix |
| Language | English |
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| PublicationSubtitle | Incorporating Perspectives in Drug Discovery and Design |
| PublicationTitle | Journal of computer-aided molecular design |
| PublicationTitleAbbrev | J Comput Aided Mol Des |
| PublicationTitleAlternate | J Comput Aided Mol Des |
| PublicationYear | 2012 |
| Publisher | Springer Netherlands Springer Nature B.V |
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| References | KatritzkyARPerumalSPetrukhinRKleinpeterEJ Chem Inf Comput Sci20014156910.1021/ci000099t1:CAS:528:DC%2BD3cXoslGqtro%3D TodeschiniRConsonniVHandbook of molecular descriptors2000GermanyWiley-VCH10.1002/9783527613106 Devillers J (2000) Curr Opin Drug Discovery Dev. 3 GalvezJJMol Struct (THEOCHEM)199842925510.1016/S0166-1280(97)00366-71:CAS:528:DyaK1cXitVKquro%3D RouvrayDHChemical applications of graph theory1976LondonAcademic Press RandicMHansenPJJursPCJChem Inf Comput Sci1988286010.1021/ci00058a0041:CAS:528:DyaL1cXitVeqtrY%3D RogersDHopfingerAJJChem Inf Comput Sci19943485410.1021/ci00020a0201:CAS:528:DyaK2cXkslejt7s%3D Gugisch R, Kerber A, Laue R, Meringer M, Weidinger J University of Bayreuth, D-95440 Bayreuth, Germany EstradaEJPhys Chem A2002106908510.1021/jp026238m1:CAS:528:DC%2BD38XmsVOisr4%3D RandićMJ Math Chem1991715510.1007/BF01200821 Todeschini R, Consonni V, Mauri A, Pavan M (2005) 1.0 ed., Talete, Milano Marrero-Ponce Y (2002) version 1.0 ed., Unit of computer-aided molecular “Biosilico” Discovery and Bioinformatic Research (CAMD-BIR Unit): Santa Clara, Villa Clara DaudelRLefebreRMoserCQuantum chemistry: methods and applications1984New YorkWiley EstradaEMolinaEJ Chem Inf Comput Sci20014179110.1021/ci000156i1:CAS:528:DC%2BD3MXhvV2lurs%3D KierLBHallLHJ Mol Graph Model2001207610.1016/S1093-3263(01)00102-41:CAS:528:DC%2BD3MXntlyjtbk%3D 2.13 ed. 7204 Mullen, Shawnee, KS 66216, USA Todeschini R, Consonni V, Pavan M (2002) 2.1 ed., Milano Chemometric and QSAR Research Group, Milano, Italy EstradaEChem Phys Lett200133624810.1016/S0009-2614(01)00127-01:CAS:528:DC%2BD3MXitVOgsr4%3D RandićMTrinajstićNJMol Struct (Theochem)1993300551 KarelsonMMolecular descriptors in QSAR/QSPR2000New YorkWiley EstradaEUriarteECurr Med Chem20018157310.2174/09298670133719231:CAS:528:DC%2BD3MXosV2gtbg%3D StankevichVSkvortsovaMIZefirovNSJMol Struct (THEOCHEM)199534217310.1016/0166-1280(95)90111-61:CAS:528:DyaK2MXptlGjurY%3D Martínez Santiago O, Martínez-López Y, Marrero-Ponce Y (2010) version 1.0 ed., Unit of computer-aided molecular “Biosilico” discovery and bioinformatic research (CAMD-BIR Unit), Santa Clara, Villa Clara, Cuba EstradaERodríguezLGutierrezACommun Math Chem (MATCH)1997351451:CAS:528:DyaK2sXjsFSqsLY%3D BalabanATFrom chemical graphs to three-dimensional geometry1997New YorkPlenum Press Topological Indices and Related Descriptors in QSAR and QSPR; Devillers, J. B., A. T, Ed.; Gordon and Breach Amsterdam, The Netherlands, 1999 KierLBHallLHMolecular connectivity in structure—activity analysis1986LetchworthResearch Studies Press Marrero-PonceYCastillo-GaritJACastroEATorrensFRotondoRJMath. Chem.2008 DoreJCVielCFarmaco197530811:CAS:528:DyaE2MXktVShtrk%3D EstradaERodríguezLComm Math Chem (MATCH)1997351571:CAS:528:DyaK2sXjsFSqsLc%3D KierLBHallLHJChem Inf Comput Sci20004079210.1021/ci990135s1:CAS:528:DC%2BD3cXhslensbY%3D IvanciucOGasteigerJEd2003WeinheimWiley-VCH103 KierLBHallLHMolecular structure description. The electrotopological state1999New YorkAcademic Press GoldbergDEGenetic algorithms1989ReadingAddison Wesley Aires-de-SousaJGasteigerJJ Mol Graph Model20022037310.1016/S1093-3263(01)00136-X1:CAS:528:DC%2BD38XovFGmsg%3D%3D GolbraikhABonchevDTropshaAJ Chem Inf Comput Sci20014114710.1021/ci000082a1:CAS:528:DC%2BD3MXmtFSj SoSSKarplusMJ Med Chem199639152110.1021/jm95070351:CAS:528:DyaK28XhsVyhurY%3D EstradaEMolinaEJ Mol Graph Model2001205410.1016/S1093-3263(01)00100-01:CAS:528:DC%2BD3MXntlyjtbs%3D TodeschiniRConsonniVMATCH Commun. Math. Comput. Chem2010643591:CAS:528:DC%2BC3cXhsVeku77I Gorbátov VA (1988) Fundamentos de la Matematica discreta, Mir, Moscow, URSS LB Kier (9591_CR38) 2001; 20 E Estrada (9591_CR19) 2001; 336 Y Marrero-Ponce (9591_CR23) 2008 D Rogers (9591_CR33) 1994; 34 EJ Estrada (9591_CR40) 2002; 106 DE Goldberg (9591_CR32) 1989 M Randić (9591_CR13) 1993; 300 SS So (9591_CR34) 1996; 39 9591_CR26 M Randić (9591_CR12) 1991; 7 O Ivanciuc (9591_CR17) 2003 9591_CR24 V Stankevich (9591_CR35) 1995; 342 E Estrada (9591_CR10) 2001; 8 R Daudel (9591_CR25) 1984 JC Dore (9591_CR29) 1975; 30 LB Kier (9591_CR14) 1999 E Estrada (9591_CR28) 2001; 41 AR Katritzky (9591_CR3) 2001; 41 9591_CR30 E Estrada (9591_CR11) 1997; 35 R Todeschini (9591_CR1) 2000 9591_CR2 J Aires-de-Sousa (9591_CR21) 2002; 20 9591_CR4 9591_CR5 M Karelson (9591_CR9) 2000 JJ Galvez (9591_CR36) 1998; 429 M Randic (9591_CR39) 1988; 28 9591_CR6 9591_CR8 9591_CR31 LB Kier (9591_CR37) 2000; 40 DH Rouvray (9591_CR15) 1976 LB Kier (9591_CR16) 1986 A Golbraikh (9591_CR22) 2001; 41 E Estrada (9591_CR20) 1997; 35 R Todeschini (9591_CR7) 2010; 64 E Estrada (9591_CR27) 2001; 20 AT Balaban (9591_CR18) 1997 11410059 - J Chem Inf Comput Sci. 2001 May-Jun;41(3):791-7 11760003 - J Mol Graph Model. 2001;20(1):54-64 1123038 - Farmaco Sci. 1975 Feb;30(2):81-109 10850784 - J Chem Inf Comput Sci. 2000 May;40(3):792-5 11885960 - J Mol Graph Model. 2002 Mar;20(5):373-88 11760005 - J Mol Graph Model. 2001;20(1):76-83 11562286 - Curr Med Chem. 2001 Nov;8(13):1573-88 8691483 - J Med Chem. 1996 Mar 29;39(7):1521-30 11206367 - J Chem Inf Comput Sci. 2001 Jan-Feb;41(1):147-58 11410031 - J Chem Inf Comput Sci. 2001 May-Jun;41(3):569-74 |
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Chem2010643591:CAS:528:DC%2BC3cXhsVeku77I – reference: KierLBHallLHMolecular connectivity in structure—activity analysis1986LetchworthResearch Studies Press – reference: Gorbátov VA (1988) Fundamentos de la Matematica discreta, Mir, Moscow, URSS – reference: DaudelRLefebreRMoserCQuantum chemistry: methods and applications1984New YorkWiley – reference: GoldbergDEGenetic algorithms1989ReadingAddison Wesley – reference: GalvezJJMol Struct (THEOCHEM)199842925510.1016/S0166-1280(97)00366-71:CAS:528:DyaK1cXitVKquro%3D – reference: IvanciucOGasteigerJEd2003WeinheimWiley-VCH103 – reference: RandićMJ Math Chem1991715510.1007/BF01200821 – reference: EstradaEMolinaEJ Chem Inf Comput Sci20014179110.1021/ci000156i1:CAS:528:DC%2BD3MXhvV2lurs%3D – reference: DoreJCVielCFarmaco197530811:CAS:528:DyaE2MXktVShtrk%3D – reference: Todeschini R, Consonni V, Mauri A, Pavan M (2005) 1.0 ed., Talete, Milano – reference: EstradaERodríguezLGutierrezACommun Math Chem (MATCH)1997351451:CAS:528:DyaK2sXjsFSqsLY%3D – reference: RogersDHopfingerAJJChem Inf Comput Sci19943485410.1021/ci00020a0201:CAS:528:DyaK2cXkslejt7s%3D – reference: 2.13 ed. 7204 Mullen, Shawnee, KS 66216, USA – reference: KierLBHallLHJChem Inf Comput Sci20004079210.1021/ci990135s1:CAS:528:DC%2BD3cXhslensbY%3D – reference: EstradaERodríguezLComm Math Chem (MATCH)1997351571:CAS:528:DyaK2sXjsFSqsLc%3D – reference: EstradaEJPhys Chem A2002106908510.1021/jp026238m1:CAS:528:DC%2BD38XmsVOisr4%3D – reference: Marrero-PonceYCastillo-GaritJACastroEATorrensFRotondoRJMath. 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T, Ed.; Gordon and Breach Amsterdam, The Netherlands, 1999 – reference: Aires-de-SousaJGasteigerJJ Mol Graph Model20022037310.1016/S1093-3263(01)00136-X1:CAS:528:DC%2BD38XovFGmsg%3D%3D – reference: Todeschini R, Consonni V, Pavan M (2002) 2.1 ed., Milano Chemometric and QSAR Research Group, Milano, Italy – reference: Devillers J (2000) Curr Opin Drug Discovery Dev. 3 – volume: 35 start-page: 145 year: 1997 ident: 9591_CR20 publication-title: Commun Math Chem (MATCH) – volume: 300 start-page: 551 year: 1993 ident: 9591_CR13 publication-title: Mol Struct (Theochem) doi: 10.1016/0022-2860(93)87047-D – volume-title: Molecular descriptors in QSAR/QSPR year: 2000 ident: 9591_CR9 – volume: 7 start-page: 155 year: 1991 ident: 9591_CR12 publication-title: J Math Chem doi: 10.1007/BF01200821 – volume: 20 start-page: 54 year: 2001 ident: 9591_CR27 publication-title: J Mol Graph Model doi: 10.1016/S1093-3263(01)00100-0 – volume: 429 start-page: 255 year: 1998 ident: 9591_CR36 publication-title: Mol Struct (THEOCHEM) doi: 10.1016/S0166-1280(97)00366-7 – start-page: 103 volume-title: Ed year: 2003 ident: 9591_CR17 – ident: 9591_CR5 – volume: 41 start-page: 147 year: 2001 ident: 9591_CR22 publication-title: J Chem Inf Comput Sci doi: 10.1021/ci000082a – volume: 41 start-page: 569 year: 2001 ident: 9591_CR3 publication-title: J Chem Inf Comput Sci doi: 10.1021/ci000099t – volume: 20 start-page: 76 year: 2001 ident: 9591_CR38 publication-title: J Mol Graph Model doi: 10.1016/S1093-3263(01)00102-4 – volume-title: Quantum chemistry: methods and applications year: 1984 ident: 9591_CR25 – volume: 40 start-page: 792 year: 2000 ident: 9591_CR37 publication-title: Chem Inf Comput Sci doi: 10.1021/ci990135s – ident: 9591_CR30 – volume-title: Chemical applications of graph theory year: 1976 ident: 9591_CR15 – ident: 9591_CR26 – year: 2008 ident: 9591_CR23 publication-title: Math. 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| Snippet | In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the... (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) In this report, we present a new mathematical approach for describing chemical... |
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| SubjectTerms | Animal Anatomy Atomic properties Atoms & subatomic particles Chemistry Chemistry and Materials Science Computer Applications in Chemistry Computer Simulation Derivatives Drug Design Graph theory Graphs Histology Incidence Invariants Mathematical models Mathematics Models, Chemical Models, Theoretical Molecular chemistry Molecular structure Morphology Nuclei Organic Chemicals - chemistry Organic Chemicals - pharmacology Physical Chemistry Quantitative Structure-Activity Relationship Three dimensional |
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| Title | Derivatives in discrete mathematics: a novel graph-theoretical invariant for generating new 2/3D molecular descriptors. I. Theory and QSPR application |
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| Volume | 26 |
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