1. Introduction

The bond strength is an important characteristic quantity for evaluating the molecular chemical stability,reaction rate and the yield of product. The most widely used quantity of measuring the bond strength is the bond dissociation energy (BDE). However,it should be noticed that the accurate measuring of BDE is very difficult both in experiment and in theory ^{[1, 2]}. In experiment,all of these sizable and complex species tend to be extremely shortlived,especially the dissociation bond fragments and radicals. Recognized the limitations of the experimental methods,some quantum chemical methods have been developed to calculate the BDE,such as the first principle method,density functional theory (DFT),ONIOM and semi-empirical AM1 and PM3 methods. However,the BDE calculation depends very strongly upon the design of bond dissociation reaction,and one cannot apply any method mentioned in above directly and quickly to calculate the BDEs of various sizable molecules due to the limitation of computing work. As a new indicator,Yang et al.have proposed the depth of the potential acting on an electron in a molecule (PAEM) ^{[3, 4, 5]} at the saddle point along a chemical bond to predict the strength of chemical bondin situ,denoted by D_pb^[6]. However, it is difficult to apply the originalab initiomethod to calculate the D_pb of biomacromolecule because of huge computing work. Therefore,we developed an approximate method for quickly evaluating the D_pb of the potential along a chemical bond very recently ^[7].

As known,deoxyribonucleosides and ribonucleosides are the most important components of the genetic materials DNA and RNA,and may contribute to a variety of health-related problems including mutagenesis,carcinogenesis,aging,inherited disease and cell death ^{[8, 9, 10, 11, 12, 13, 14]}. However,the roles of these compounds in DNA and RNA damage cannot be properly understood in the absence of knowledge of the C-H and N-H bond strengths. In this work,as a practical application,we calculated the D_pb along the C-H and N-H bonds for deoxyribonucleosides and ribonucleosides, and predicted the strengths of all these chemical bonds. Discussions were then made about the interesting connections between our results and previously reported experimental and theoretical observations. All comparisons showed that the approximate method indicates well the strengths of chemical bonds in situ for all these molecules. This work provides a new investigation of the bond strengths for biomacromolecules.

2. Experimental

A semi-empirical formula has been proposed for quickly calculating the potential acting on an electron in a molecule (PAEM) along a chemical bond a-b,and can be expressed as the following ^[7]:

where the first term k_a-b[V_a(r)+V_b(r)] is the potential contribution of two bonded atoms,and another term -k∑_i≠a,bq_i/(r－R_i) is the interaction potential between one local electron and the rest atoms except bonded atoms.r denotes the position vector of this electron, Va-b(r) denotes the PAEM of this electron appearing atralong the axis of a-b bond,k_a-b is an important parameter,which is employed to correct the potential contributions of bonded atoms in different kinds of chemical bonds. V_a(r) and V_b(r) are the potentials acting on an electron in atomsa and bat point r respectively,k is an adjustable parameter,which is employed to correct electrostatic interactions between this electron and all rest atoms with the simple point charge. It is set to be equal to a constant (0.57) that is likeness to the atom-bond electronegativity equalization model (ABEEMsp) ^{[15, 16, 17, 18]}.q_i is the partial charge of atom i,which is calculated by using ABEEMσπ method ^{[15, 16, 17, 18]}.

According to Eq. (1),the PAEM corresponding to each electronic coordinate r along a chemical bond a-b can be obtained numerically. In the bond region,the PAEM has a local maximum from which the curve goes toward both sides. The highest point of the PAEM curve on the XZ-cross-section is just the lowest point of the PAEM curve on the vertical plane. This point is the saddle point along a-b chemical bond and the absolute value of the PAEM at the saddle point is denoted D_pb(see Fig. 1).

Remarkably,the energy contributions of bonded atoms play essential roles in the total potential. Hence,V_a(r) and V_b(r) are calculated by using the MELD ab initio method. The calculations were implemented on O300 serve (8×500 MHz MIPS R14000 CPU). In the calculations,the potential acting on an electron in atom a can be expressed as:

where Z_a is the nuclear charge of atom a ,R_a is the position vector of the nucleusa,r and r' are the position vectors of electrons,ρ(r) represents the one-electron density of an electron appearing at position r,and ρ₂(r,r') represents the two-electron density function,i.e. the probability of finding one electron at position r and at the same time finding another electron at position r'. The details have been explicitly described in the literature ^[19].

3. Results and discussion 3.1. The ascertaining and evaluation of the parameters k_C-H and k _N-H

In this section,we chose 21 kinds of ring molecules as models to ascertain and evaluate the parameters k_C-H and k_N-H,including some small fragments of both the nucleobase and sugar (see Fig. S1 in Supporting information). All geometries were optimized at MP2/ 6-311++G (3df,3pd) level of theory. Take the C-H bond of C₄H₈O molecule for instance. We put the atom C at the origin of the coordinate system and the atom H at theX-axis for a C-H bond in C₄H₈O. First,we calculated the D_pb values of the PAEM at the saddle point along the C-H bond by using the original MELD ab initio method ^{[3, 4, 5]} at SDCI/6-311++G (d,p) level of theory,with D_pb (1.326,0.0,0.0) = 1.8598 hartree. Then,we have also computed the potentials acting on an electron in atoms C and H when the electron was local at the point (x= 1.326 a.u.,y= 0.0 a.u., z= 0.0 a.u.),with V_C(1.326,0.0,0.0) =-1.4407 hartree and V_H(1.326,0.0,0.0) =-1.3223 hartree,respectively. The interaction potential between this electron and the rest atoms except bonded atoms C and H corresponding to this point can be calculated according to the second term in Eq. (1),with V_rest = 0.0310 hartree. According to the reverse deduction method,the k_C-H for C₄H₈O is equal to 0.6839. In a similar way,the parameters k_C-H and k_N-H of all these molecules can be obtained. During the calculations,it can be found that the atoms adjacent to the bonded atoms must be considered and the further atoms have little effect for the parameters, i.e.,if the neighboring atoms are different,the parameters are different. After repetitious simulations,the parameters k_C-H and k_N-H for some familiar C-H and N-H bonds were determined and listed in Table 1.

The D_pb values of 79 bonds for these model molecules have been calculated for evaluating the accuracy of the parameters and approximate method. The results have been listed in Table S1 (Supporting information). Comparing with the original ab initio calculations,a lot of data showed that the average deviation of the D_pb is only 0.27%.

3.2. The D_pb of deoxyribonucleosides and ribonucleosides 3.2.1. Geometries

As known,the B form of DNA,i.e.,the deoxyribose pseudorotational state = S-type,C2' -endo,is considered the most important one for biological system,and the A form of RNA,i.e.,the ribose pseudorotational state = N-type,C3'-endo,is the most important one for biological system. Furthermore,since the previous studies have suggested that the anti conformation should be favored for both deoxyribonucleosides and ribonucleosides,we considered the anti conformation only in this work ^{[20, 21, 22, 23, 24, 25, 26, 27, 28]}. Li et al.have suggested that all these compounds favor the +sc conformation by comparing the energies of +sc,ap and -sc conformations,which is in agreement with the previous experiments ^{[29, 30, 31]}. As a result, we chose the C2-endo/anti/+sc conformation for deoxyribonucleosides and the C3-endo/anti/+sc conformation for ribonucleosides as starting geometries. All geometries were optimized at MP2/6-311++G (d,p) level of theory (see Fig. 2). The results are very close to the results of Li et al.^[29],Gelbin et al.^[20],Leulliot et al.^[21] and Hocquet et al.^[22].

3.2.2. D_pb values and discussions

Utilizing the approximate method,we calculated the C-H and N-H D_pb values for full deoxyribonucleosides and ribonucleosides at MP2/6-311++G (d,p) level. Take the C1' -H bond of deoxyadenosine as an example for a detailed exposition. We put the atom C1'at the origin of the coordinate system and the atom H at the X-axis,and the coordinate of atom H is x= 2.069 a.u.,y= 0.000 a.u. and z= 0.000 a.u. First,250 points of the local electronic coordinates were taken along the C1'-H bond from x=-4.000 a.u. to x= 6.000 a.u. Then,the PAEMs corresponding to these points were calculated by using the approximate method. Special attention should be paid where along the C1'-H bond there is a point x= 1.315 a.u. at which the PAEM takes its local maximum value. We make a straight line perpendicular to the C1'-H bond and pass through the point x= 1.315 a.u. With this line x= 1.315 a.u. andybeing a variable,the PAEM curve showed a local minimum value at the point x= 1.315 a.u.,y= 0.000 a.u. and z= 0.000 a.u. This implied that this point is a saddle point along the C1'-H bond,and the depth of the PAEM at this point is defined D_pb (1.8345 hartree).

In a similar way,the D_pb values of all deoxyribonucleosides and ribonucleosides have been listed in Table 2. It is worth noting that at the present time there are no experimental BDEs available for full deoxyribonucleosides and ribonucleosides. Nonetheless,we can also now understand many previous experimental observations by comparing with the BDEs reported by theoretical computations.

First,it is clear that the C-H D_pb of the sugar moieties (~1.84- 1.90 hartree) are about 18 kcal/mol lower than the C-H D_pb of the nucleosides (~1.87-1.93 hartree). The result is in agreement with the BDE deviation (10-20 kcal/mol) reported by Li et al.^[29]. Thus, the hydrogen abstraction reaction of nucleosides by the intracellular oxidants with free-radical character usually occurs at the carbohydrate moieties. Noticeably,according to our calculations, the C7-H bond of nucleobase for deoxythymidine has a lower D_pb value of 1.8738 hartree than the C-H D_pb of others nucleobases. Therefore,the C7-H bond should be also a sensitive site for DNA damage. Indeed,Li et al.^[29] have predicted that the C-H bond of deoxythymidine is a potential site for DNA damage via the hydrogen abstraction reaction with a very low C-H BDE. Very recently,Schoneich et al. ^[32] discovered that the hydrogen abstraction from C5-CH₃(i.e.the C7-H bond in this work) by thiol radicals occurs with rate constants similar to the hydrogen abstraction from the carbohydrate moieties.

Second,the N-H D_pb values of all deoxyribonucleosides and ribonucleosides are higher than these C-H D_pb values of the sugar moieties of nucleobases. This means that N-H bonds is very strong and not the injured position in DNA or RNA damage. Recently,Li et al.have also predicted the N-H BDEs of deoxyadenosine (dA), deoxycytidine (dC),deoxythymidine (dT),adenosine (rA),cytidine (rC) and uridine (rU) are over 100 kcal/mol,and are about 5-20 kcal/mol higher than the C-H BDEs of the sugar moieties. However,in their calculations,the N-H BDEs of deoxyguanosine (dG) and guanosine (rG) have a very low BDE of 90.4-95.2 kcal/mol, which are about 1-8 kcal/mol lower than the C-H BDEs of the sugar moieties ^[29]. We cannot find any experimental report for the hydrogen abstraction reaction at the guanosine N-H position. Hence,our method may be better in indicating the N-H bond strength.

Third,according to the results in Table 2,it is clear that,for each type of carbohydrate C-H bond,different deoxyribonucleosides or ribonucleosides provide very similar C-H D_pb values. In other words,there is only a very small effect of different nucleobases on the C-H D_pb values at the C1',C2',C3',C4' and C5' positions. These are in excellent agreement with Li’s findings ^[29]. They predicted that there should be low selectivity among different nucleosides in the radical-mediated DNA or RNA lesion. In experiments,some literatures have also shown that the hydrogen abstraction reactions on the DNA or RNA sugar moieties do not exhibit specificity for cleavage at a particular nucleoside ^{[33, 34]}.

Finally,further comparisons were made between our D_pb and the previous theoretical predictions. For deoxyribose,Colson and Sevilla predicted the relative stabilities of five deoxyribose centered radicals to be C1'<C4'<C5'<C3'<C2' using the ROHF/3-21 G method ^{[35, 36]}. Li et al.^[29] predicted the order for deoxyribonucleosides is C1'-H<C5'-H<C4'-H~C3'-H<C2'-H. In this work,our D_pb order for deoxyribonucleosides

is C1'-H<C2'-H<C4'-H<C5'-H<C3'-H.Theorderisroughly in agreement with Colson and Sevilla’s results. Nevertheless, Colson,Sevilla and Li et al.^[29] predicted that the C2'-H is the strongest bond in deoxyribose region,while our D_pb values showed that C3'-H is the strongest. The reason is possibly that the D_pb characterized the bond strength from the view of electron movement in a molecule. We calculated the D_pb in situ while other theoretical methods obtained BDEs by hydrogen abstraction and radicals. For ribose,Osman et al. ^{[37, 38]} predicted the C-H BDEs of ribose using the MP2/6-31 G (d) and BLYP/6-31 G (d) methods: C1'-H (81.7-82.7 kcal/mol)<C2'-H (84.9-85.4 kcal/mol)~C4'-H (85.0-85.6 kcal/mol)<C3' -H (88.2-88.6 kcal/mol). Li et al.predicted the C-H BDEs orders are irregular in different ribonucleosides. OurDpb order for ribonucleosides is C1'-H<C4'-H<C2'-H<C5'-H<C3' -H. It is cleat that our order is also roughly in agreement with Osman’s finding,and all different theoretical predictions showed that the C3'-H is the strongest bond in ribonucleosides. For nucleobases parts in deoxyribonucleosides and ribonucleosides,the C-H D_pb order accords with the order of C-H BDEs reported by Li et al.To conclude,all comparisons showed that our method may indicate the chemical bond strengths for deoxyribonucleosides and ribonucleosides.

4. Conclusion

The characteristic descriptor of PAEM in the bond region,D_pb, has been calculated for quickly predicting the strength of a chemical bond by using an approximate method. In this work,as a practical application,a full scale of C-H and N-H D_pb were obtained to indicate the bond strengths for the bonds in deoxyribonucleosides and ribonucleosides. The results are in agreement with the results of previously reported experimental and theoretical observations. This work provides a new investigation for studying the chemical bond properties for biomacromolecules.

Acknowledgment

This work is supported by the National Natural Science Foundation of China (Nos. 21073080 and 21133005).

Appendix A. Supplementary data

Supplementary data associated with this article can be found,in the online version,at http://dx.doi.org/10.1016/j.cclet.2013.06.008.