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1.
We have used a computational model to calculate the potential energy surface for dinucleotide steps in double helical DNA as a function of the two principal degrees of freedom, slide and shift. By using a virtual bond to model the constraints imposed by the sugar-phosphate backbone, twist, roll, tilt and rise can be simultaneously optimised for any given values of slide and shift. Thus we have been able to construct complete conformational maps for all step types. For some steps, the maps agree well with experimental data from X-ray crystal structures, but other steps appear to be strongly perturbed by the effects of context (conformational coupling with the neighbouring steps). The optimised values of twist and roll show sequence-dependent variations consistent with the crystal structure data. The conformational maps allow us to construct adiabatic paths, and hence calculate the flexibility of each step with respect to slide and shift. Again the results agree well with the available experimental assignments of flexibility: YR steps, CA/TG and CG, are the most flexible and RR steps, such as AA, the least flexible.  相似文献   

2.
Sequence dependence of DNA conformational flexibility   总被引:9,自引:0,他引:9  
A Sarai  J Mazur  R Nussinov  R L Jernigan 《Biochemistry》1989,28(19):7842-7849
By using conformational free energy calculations, we have studied the sequence dependence of flexibility and its anisotropy along various conformational variables of DNA base pairs. The results show the AT base step to be very flexible along the twist coordinate. On the other hand, homonucleotide steps, GG(CC) and AA(TT), are among the most rigid sequences. For the roll motion that would correspond to a bend, the TA step is most flexible, while the GG(CC) step is least flexible. The flexibility of roll is quite anisotropic; the ratio of fluctuations toward the major and minor grooves is the largest for the GC step and the smallest for the AA(TT) and CG steps. Propeller twisting of base pairs is quite flexible, especially of A.T base pairs; propeller twist can reach 19 degrees by thermal fluctuation. We discuss the effect of electrostatic parameters, comparison with available experimental results, and biological relevance of these results.  相似文献   

3.
The sequence-dependent DNA deformability at the basepair step level was investigated using large-scale atomic resolution molecular dynamics simulation of two 18-bp DNA oligomers: d(GCCTATAAACGCCTATAA) and d(CTAGGTGGATGACTCATT). From an analysis of the structural fluctuations, the harmonic potential energy functions for all 10 unique steps with respect to the six step parameters have been evaluated. In the case of roll, three distinct groups of steps have been identified: the flexible pyrimidine-purine (YR) steps, intermediate purine-purine (RR), and stiff purine-pyrimidine (RY). The YR steps appear to be the most flexible in tilt and partially in twist. Increasing stiffness from YR through RR to RY was observed for rise, whereas shift and slide lack simple trends. A proposed measure of the relative importance of couplings identifies the slide-rise, twist-roll, and twist-slide couplings to play a major role. The force constants obtained are of similar magnitudes to those based on a crystallographic ensemble. However, the current data have a less complicated and less pronounced sequence dependence. A correlation analysis reveals concerted motions of neighboring steps and thus exposes limitations in the dinucleotide model. The comparison of DNA deformability from this and other studies with recent quantum-chemical stacking energy calculations suggests poor correlation between the stacking and flexibility.  相似文献   

4.
A database of X-ray crystal structures of double helical DNA oligomers has been used to analyse the role of the sugar-phosphate backbone in coupling the conformational properties of neighbouring dinucleotide steps. The base step parameters which are most strongly coupled to the backbone degrees of freedom are slide and shift, and these are the two dinucleotide step parameters which show strong correlations along a sequence: the value of slide follows the values in the neighbouring steps, whereas shift tends to alternate. This conformational coupling is mediated by the shared furanose rings at the step junctions: a change in the value of slide causes a change in the mean value of the same strand 3' and 5'-chi torsion angle, and a change in the mean value of the 3' and 5' sugar pseudo-rotation phase angle, P; a change in the value of shift causes a difference between the same strand 3' and 5'-chi in A-DNA and a difference between the 3' and 5'-P in B-DNA. We have used a database of tetranucleotide X-ray crystal structures to parameterise a simple model for the coupling of slide and shift. Using this junction model together with our dinucleotide step potential energy maps described previously, we can in principle calculate the structure of any DNA oligomer. The parameterisation indicates that the rotational step parameters are accurate to within 5 degrees, and the translational step parameters are accurate to within 0.5 A. The model has been used to study the potential energy surfaces of all possible tetranucleotide sequences, and the calculations agree well with the experimental data from X-ray crystal structures. Some dinucleotide steps are context independent (AA/TT, AT and TA), because the conformational properties of all possible neighbouring steps are compatible. When the conformational properties of the neighbours are not compatible, the behaviour of a step cannot be understood at the dinucleotide level. Thus the conformations of CG, GC and GG/CC are all strongly context dependent. The remaining mixed sequence steps show weakly context-dependent behaviour. The approach allows the calculation of the relative stability and flexibility of tetranucleotide sequences, and the results indicate why TATA is used as an origin of replication. Clear predictions are made about sequences which have not yet been characterised crystallographically. In particular, poly(CCA).poly(TGG) is predicted to have an unusual structure which lies between the C and D-DNA polymorphs.  相似文献   

5.
Understanding dinucleotide sequence directed structures of nuleic acids and their variability from experimental observation remained ineffective due to unavailability of statistically meaningful data. We have attempted to understand this from energy scan along twist, roll, and slide degrees of freedom which are mostly dependent on dinucleotide sequence using ab initio density functional theory. We have carried out stacking energy analysis in these dinucleotide parameter phase space for all ten unique dinucleotide steps in DNA and RNA using DFT‐D by ωB97X‐D/6‐31G(2d,2p), which appears to satisfactorily explain conformational preferences for AU/AU step in our recent study. We show that values of roll, slide, and twist of most of the dinucleotide sequences in crystal structures fall in the low energy region. The minimum energy regions with large twist values are associated with the roll and slide values of B‐DNA, whereas, smaller twist values correspond to higher stability to RNA and A‐DNA like conformations. Incorporation of solvent effect by CPCM method could explain the preference shown by some sequences to occur in B‐DNA or A‐DNA conformations. Conformational preference of BII sub‐state in B‐DNA is preferentially displayed mainly by pyrimidine–purine steps and partly by purine–purine steps. The purine–pyrimidine steps show largest effect of 5‐methyl group of thymine in stacking energy and the introduction of solvent reduces this effect significantly. These predicted structures and variabilities can explain the effect of sequence on DNA and RNA functionality. © 2014 Wiley Periodicals, Inc. Biopolymers 103: 134–147, 2015.  相似文献   

6.
Deciphering sequence information from sugar-phosphate backbone is finely tuned through the conformational substates of DNA. BII conformation, one of the conformational substates of B-DNA, is known to play a key role in DNA-protein recognition. BI and BII are identified by the epsilon-zeta difference, which is negative in BI and positive in BII. Our analysis of MD and crystal structures shows that BII conformation is sequence specific and dinucleotides GC, CG, CA, TG, TA show high preference to take up BII conformation, while TT, TC, CT, CC dinucleotides rarely take up this conformation. Significant changes were observed in the dinucleotide parameters viz. twist, roll, and slide for the steps having BII conformation. Interestingly, the magnitude of variation in the dinucleotide parameters is seen to depend mainly on two factors, the magnitude of epsilon-zeta difference and the presence or absence of BII conformation in the second strand, across the WC base-paired dinucleotide step. Based on these two factors, the conformational substate of a dinucleotide step can be further classified as BI.BI (BI conformation in both strands), BI.BII (BI conformation in one strand and BII conformation in the other), and BII.BII (BII conformation in both strands). The occurrence of BII in both strands was found to be quite rare and thus, it can be concluded that BI.BI and BI.BII hybrid steps are more favorable than a BII.BII step. In conformity with the sequence preference seen for dinucleotides in each strand, BII.BII combination of backbone conformation was observed only for GC, CG, CA, and TG containing dinucleotide steps. We further classified BII.BII step as strong BII and weak BII depending on the magnitude of the average epsilon-zeta difference. The dinucleotide steps which belong to the category of strong BII, have large twist, high positive slide and negative roll values, while those in the weak BII group have roll, twist, and slide values similar to that of hybrid BI.BII steps. This conformational property could be contributing to the groove opening/closing and thus can modulate protein-DNA interaction.  相似文献   

7.
Abstract

The groove widths of DNA helix, especially minor groove width, are generally believed to be important for recognition of DNA by various types of ligands. It has been postulated earlier that large negative propeller twist, in the AT rich regions compresses the minor groove of duplex DNA A systematic study has now been carried out by generating models with different values of local doublet and intra-basepair parameters and calculating their minor groove widths. It is found that several local doublet parameters affect the minor groove width but it depends most strongly on the local step parameters roll and slide when each parameter is considered individually. However, a detailed analysis of the various local parameters within the B-DNA family of crystal structures indicates that propeller twist and slide are most strongly correlated with the observed values of minor groove width. The groove depth is also strongly correlated with slide. Thus the local base sequence dependent variations in slide can modify both the groove width and depth and consequently determine the ligand binding properties of DNA.  相似文献   

8.
The groove widths of DNA helix, especially minor groove width, are generally believed to be important for recognition of DNA by various types of ligands. It has been postulated earlier that large negative propeller twist, in the AT rich regions compresses the minor groove of duplex DNA. A systematic study has now been carried out by generating models with different values of local doublet and intra-basepair parameters and calculating their minor groove widths. It is found that several local doublet parameters affect the minor groove width but it depends most strongly on the local step parameters roll and slide when each parameter is considered individually. However, a detailed analysis of the various local parameters within the B-DNA family of crystal structures indicates that propeller twist and slide are most strongly correlated with the observed values of minor groove width. The groove depth is also strongly correlated with slide. Thus the local base sequence dependent variations in slide can modify both the groove width and depth and consequently determine the ligand binding properties of DNA.  相似文献   

9.
The crystal structure of the DNA dodecamer duplex CATGGGCCCATG lies on a structural continuum along the transition between A- and B-DNA. The dodecamer possesses the normal vector plot and inclination values typical of B-DNA, but has the crystal packing, helical twist, groove width, sugar pucker, slide and x-displacement values typical of A-DNA. The structure shows highly ordered water structures, such as a double spine of water molecules against each side of the major groove, stabilizing the GC base pairs in an A-like conformation. The different hydration of GC and AT base pairs provides a physical basis for solvent-dependent facilitation of the A↔B helix transition by GC base pairs. Crystal structures of CATGGGCCCATG and other A/B-DNA intermediates support a ‘slide first, roll later’ mechanism for the B→A helix transition. In the distribution of helical parameters in protein–DNA crystal structures, GpG base steps show A-like properties, reflecting their innate predisposition for the A conformation.  相似文献   

10.
Introduction of a T-A or pyrimidine-purine step into a straight and rigid A-tract can cause a positive roll deformation that kinks the DNA helix at that step. In CCTTTAAAGG, the central T-A step has an 8.6 degrees bend toward the major groove. We report the structural analysis of CCTTTAAAGG and a comparison with 25 other representative crystal structures from the NDB containing at least four consecutive A or T bases. On average, more local bending occurs at the disruptive T-A step (8.21 degrees ) than at an A-T step (5.71 degrees ). In addition, A-tracts containing an A-T step are more bent than are pure A-tracts, and hence A-A and A-T steps are not equivalent. All T-A steps examined exhibit positive roll, bending towards the major groove, while A-T steps display negative roll and bend slightly towards the minor groove. This illustrates how inherent negative and positive roll are, respectively, at A-T and T-A steps within A-tracts. T-A steps are more deformable, showing larger and more variable deformations of minor groove width, rise, cup, twist, and buckle. Standard deviations of twist, rise, and cup for T-A steps are 6.66 degrees, 0.55 A, and 15.90 degrees, versus 2.28 degrees, 0.21 A, and 2.99 degrees for A-T steps. Packing constraints determine which local values of these helical parameters an individual T-A step will adopt. For instance, with CCTTTAAAGG and three isomorphous structures, CGATTAATCG, CGATATATCG, and CGATCGATCG, crystal packing forces lead to a series of correlated changes: widened minor groove, large slide, low twist, and large rise. The difference in helical parameters between A-T steps lying within A-tracts, versus A-T steps within alternating AT sequences, demonstrates the importance of neighboring steps on the conformation of a given dinucleotide step.  相似文献   

11.
Basepair stacking calculations have been carried out to understand the conformational polymorphism of DNA and its sequence dependence. The recently developed self-consistent parameter set, which is specially suitable for describing irregular DNA structures, has been used to describe the geometry of a basepair doublet. While for basepairs without any propeller, the favourable stacking patterns do not appear to have very strong features, much more noticeable sequence dependent stacking patterns emerge once a propeller is applied to the basepairs. The absolute minima for most sequences occurs for a doublet geometry close to the B-DNA fibre models. Hence in the B-DNA region, no strong sequence dependent features are found, but the range of doublet geometries observed in the crystal structures generally lie within the low energy contours, obtained from stacking energy calculations. The doublet geometry corresponding to the A-DNA fibre model is not energetically favourable for the purine-pyrimidine sequences, which prefer small roll angle values when the slide has a large negative value as in A-DNA. However positive roll with large negative slide is allowed for GG, GA, AG and the pyrimidine-purine steps. This is consistent with the observed geometries of various steps in A-DNA crystals. Thus the general features of the basepair doublets predicted from these theoretical studies agree very well with the results from crystal structure analysis. However, since most sequences show an overall preference for B-type doublet geometry, the B----A transition for random sequence DNA cannot be explained on the basis of basepair stacking interactions.  相似文献   

12.
13.
A database of the structural properties of all 32,896 unique DNA octamer sequences has been calculated, including information on stability, the minimum energy conformation and flexibility. The contents of the database have been analysed using a variety of Euclidean distance similarity measures. A global comparison of sequence similarity with structural similarity shows that the structural properties of DNA are much less diverse than the sequences, and that DNA sequence space is larger and more diverse than DNA structure space. Thus, there are many very different sequences that have very similar structural properties, and this may be useful for identifying DNA motifs that have similar functional properties that are not apparent from the sequences. On the other hand, there are also small numbers of almost identical sequences that have very different structural properties, and these could give rise to false-positives in methods used to identify function based on sequence alignment. A simple validation test demonstrates that structural similarity can differentiate between promoter and non-promoter DNA. Combining structural and sequence similarity improves promoter recall beyond that possible using either similarity measure alone, demonstrating that there is indeed information available in the structure of double-helical DNA that is not readily apparent from the sequence.  相似文献   

14.
15.
Experimental X-ray crystal structures and a database of calculated structural parameters of DNA octamers were used in combination to analyse the mechanics of DNA bending in the nucleosome core complex. The 1kx5 X-ray crystal structure of the nucleosome core complex was used to determine the relationship between local structure at the base-step level and the global superhelical conformation observed for nucleosome-bound DNA. The superhelix is characterised by a large curvature (597°) in one plane and very little curvature (10°) in the orthogonal plane. Analysis of the curvature at the level of 10-step segments shows that there is a uniform curvature of 30° per helical turn throughout most of the structure but that there are two sharper kinks of 50° at ± 2 helical turns from the central dyad base pair. The curvature is due almost entirely to the base-step parameter roll. There are large periodic variations in roll, which are in phase with the helical twist and account for 500° of the total curvature. Although variations in the other base-step parameters perturb the local path of the DNA, they make minimal contributions to the total curvature. This implies that DNA bending in the nucleosome is achieved using the roll-slide-twist degree of freedom previously identified as the major degree of freedom in naked DNA oligomers. The energetics of bending into a nucleosome-bound conformation were therefore analysed using a database of structural parameters that we have previously developed for naked DNA oligomers. The minimum energy roll, the roll flexibility force constant and the maximum and minimum accessible roll values were obtained for each base step in the relevant octanucleotide context to account for the effects of conformational coupling that vary with sequence context. The distribution of base-step roll values and corresponding strain energy required to bend DNA into the nucleosome-bound conformation defined by the 1kx5 structure were obtained by applying a constant bending moment. When a single bending moment was applied to the entire sequence, the local details of the calculated structure did not match the experiment. However, when local 10-step bending moments were applied separately, the calculated structure showed excellent agreement with experiment. This implies that the protein applies variable bending forces along the DNA to maintain the superhelical path required for nucleosome wrapping. In particular, the 50° kinks are constraints imposed by the protein rather than a feature of the 1kx5 DNA sequence. The kinks coincide with a relatively flexible region of the sequence, and this is probably a prerequisite for high-affinity nucleosome binding, but the bending strain energy is significantly higher at these points than for the rest of the sequence. In the most rigid regions of the sequence, a higher strain energy is also required to achieve the standard 30° curvature per helical turn. We conclude that matching of the DNA sequence to the local roll periodicity required to achieve bending, together with the increased flexibility required at the kinks, determines the sequence selectivity of DNA wrapping in the nucleosome.  相似文献   

16.
We have developed a technique of partially-restrained molecular mechanics enthalpy minimisation which enables the sequence-dependence of the DNA binding of a non-intercalating ligand to be studied for arbitrary sequences of considerable length (greater than = 60 base-pairs). The technique has been applied to analyse the binding of berenil to the minor groove of a 60 base-pair sequence derived from the tyrT promoter; the results are compared with those obtained by DNAse I and hydroxyl radical footprinting on the same sequence. The calculated and experimentally observed patterns of binding are in good agreement. Analysis of the modelling data highlights the importance of DNA flexibility in ligand binding. Further, the electrostatic component of the interaction tends to favour binding to AT-rich regions, whilst the van der Waals interaction energy term favours GC-rich ones. The results also suggest that an important contribution to the observed preference for binding in AT-rich regions arises from lower DNA perturbation energies and is not accompanied by reduced DNA structural perturbations in such sequences. It is therefore concluded that those modes of DNA distortion favourable to binding are probably more flexible in AT-rich regions. The structure of the modelled DNA sequence has also been analysed in terms of helical parameters. For the DNA energy-minimised in the absence of berenil, certain helical parameters show marked sequence-dependence. For example, purine-pyrimidine (R-Y) base pairs show a consistent positive buckle whereas this feature is consistently negative for Y-R pairs. Further, CG steps show lower than average values of slide while GC steps show lower than average values of rise. Similar analysis of the modelling data from the calculations including berenil highlights the importance of DNA flexibility in ligand binding. We observe that the binding of berenil induces characteristic responses in different helical parameters for the base-pairs around the binding site. For example, buckle and tilt tend to become more negative to the 5'-side of the binding site and more positive to the 3'-side, while the base steps at either side of the centre of the site show increased twist and decreased roll.  相似文献   

17.
DNA can adopt different conformations depending on the base sequence, solvent, electrolyte composition and concentration, pH, temperature, and interaction with proteins. Here we present a model for calculating the three-dimensional atomic structure of double-stranded DNA oligomers. A theoretical energy function is used for calculating the interactions within the base steps and an empirical backbone function is used to restrict the conformational space accessible to the bases and to account for the conformational coupling of neighboring steps in a sequence. Conformational searching on large structures or a large number of structures is possible, because each base step can be described by just two primary degrees of freedom (slide and shift). A genetic algorithm is used to search for low-energy structures in slide-shift space, and this allows very rapid optimization of DNA oligomers. The other base step parameters have been previously optimized for all possible slide-shift sequence combinations, and a heuristic algorithm is used to add the atomic details of the backbone conformation in the final step of the calculation. The structures obtained by this method are very similar to the corresponding X-ray crystal structures observed experimentally. The average RMSD is 2.24 Angstroms for a set of 20 oligomer structures. For 15 of these sequences, the X-ray crystal structure is the global energy minimum. The other 5 are bistable sequences that have B-form global energy minima but crystallize as A-DNA.  相似文献   

18.
DNA bending: the prevalence of kinkiness and the virtues of normality.   总被引:22,自引:20,他引:2       下载免费PDF全文
DNA bending in 86 complexes with sequence-specific proteins has been examined using normal vector plots, matrices of normal vector angles between all base pairs in the helix, and one-digit roll/slide/twist tables. FREEHELIX, a new program especially designed to analyze severely bent and kinked duplexes, generates the foregoing quantities plus local roll, tilt, twist, slide, shift and rise parameters that are completely free of any assumptions about an overall helix axis. In nearly every case, bending results from positive roll at pyrimidine-purine base pair steps: C-A (= T-G), T-A, or less frequently C-G, in a direction that compresses the major groove. Normal vector plots reveal three well-defined types of bending among the 86 examples: (i) localized kinks produced by positive roll at one or two discrete base pairs steps, (ii) three-dimensional writhe resulting from positive roll at a series of adjacent base pairs steps, or (iii) continuous curvature produced by alternations of positive and negative roll every 5 bp, with side-to-side zig-zag roll at intermediate position. In no case is tilt a significant component of the bending process. In sequences with two localized kinks, such as CAP and IHF, the dihedral angle formed by the three helix segments is a linear function of the number of base pair steps between kinks: dihedral angle = 36 degrees x kink separation. Twenty-eight of the 86 examples can be described as major bends, and significant elements in the recognition of a given base sequence by protein. But even the minor bends play a role in fine-tuning protein/DNA interactions. Sequence-dependent helix deformability is an important component of protein/DNA recognition, alongside the more generally recognized patterns of hydrogen bonding. The combination of FREEHELIX, normal vector plots, full vector angle matrices, and one-digit roll/slide/twist tables affords a rapid and convenient method for assessing bending in DNA.  相似文献   

19.
Local variability and base sequence effects in DNA crystal structures   总被引:1,自引:0,他引:1  
The importance and usefulness of local doublet parameters in understanding sequence dependent effects has been described for A- and B-DNA oligonucleotide crystal structures. Each of the two sets of local parameters described by us in the NUPARM algorithm, namely the local doublet parameters, calculated with reference to the mean z-axis, and the local helical parameters, calculated with reference to the local helix axis, is sufficient to describe the oligonucleotide structures, with the local helical parameters giving a slightly magnified picture of the variations in the structures. The values of local doublet parameters calculated by NUPARM algorithm are similar to those calculated by NEWHELIX90 program, only if the oligonucleotide fragment is not too distorted. The mean values obtained using all the available data for B-DNA crystals are not significantly different from those obtained when a limited data set is used, consisting only of structures with a data resolution of better than 2.4 A and without any bound drug molecule. Thus the variation observed in the oligonucleotide crystals appears to be independent of the quality of their crystallinity. No strong correlation is seen between any pair of local doublet parameters but the local helical parameters are interrelated by geometric relationships. An interesting feature that emerges from this analysis is that the local rise along the z-axis is highly correlated with the difference in the buckle values of the two basepairs in the doublet, as suggested earlier for the dodecamer structures (Bansal and Bhattacharyya, in Structure & Methods: DNA & RNA, Vol. 3 (Eds., R.H. Sarma and M.H. Sarma), pp. 139-153 (1990)). In fact the local rise values become almost constant for both A- and B-forms, if a correction is applied for the buckling of the basepairs. In B-DNA the AA, AT, TA and GA basepair sequences generally have a smaller local rise (3.25 A) compared to the other sequences (3.4 A) and this seems to be an intrinsic feature of basepair stacking interaction and not related to any other local doublet parameter. The roll angles in B-DNA oligonucleotides have small values (less than +/- 8 degrees), while mean local twist varies from 24 degrees to 45 degrees. The CA/TG doublet sequences show two types of preferred geometries, one with positive roll, small positive slide and reduced twist and another with negative roll, large positive slide and increased twist.(ABSTRACT TRUNCATED AT 400 WORDS)  相似文献   

20.
DNA binding with enzymes is followed by specific adaptation of the DNA structure, including partial or almost complete melting, structural changes in the sugar-phosphate backbone, stretching, compressing, bending or kinking, base flipping, etc. The set of conformational changes is individual for each enzyme and is aimed at efficiently adjusting the orbitals of the reacting groups of the enzyme and the specific DNA site to 10°–15°. The efficiency of nucleotide sequence adaptation determined by the enzyme depends on several structural characteristics. Optimal adjustment is achieved only in the case of specific DNA sequences; as a result, the reaction rate is four to eight orders of magnitude higher with specific than with nonspecific sequences. DNA topoisomerase I (Topo) is a sequence-dependent enzyme. Although less efficiently, Topo cleaves sequences which differ considerably from the optimal sequence. A method based on the analysis of conformational and physicochemical properties of the DNA helix was used to examine many nucleotide sequences cleavable by Topo. The method yields detailed information on similarity or difference of DNA structural units. The cleavable sequences proved to be similar in roll, slide, twist, and rise. In addition, all sequences had sterically disadvantageous contacts between N3 and NH2 of guanines and N3 of adenines in the minor groove, which corresponded to the presence of dinucleotides Py-Pu in the cleavage site. DNA bending towards the major groove is easier in the case of the optimal sequence. This method is promising for analyzing the efficiency of nucleic acid cleavage by various DNA- and RNA-dependent enzymes.__________Translated from Molekulyarnaya Biologiya, Vol. 39, No. 3, 2005, pp. 488–496.Original Russian Text Copyright © 2005 by Oshchepkov, Bugreev, Kolchanov, Nevinsky.  相似文献   

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