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1.
Systems containing a base or a base pair and 25 water molecules, as well as a helical stack and 30 water molecules per base pair, have been simulated. Changes in the base hydration shell structure, after the bases have been included into the pair and then into the base pair stack, are discussed. Hydration shells of several configurations of the base pair stacks are discussed. Probabilities of formation of the hydrogen-bonded bridges of 1, 2 and 3 water molecules between hydrophilic centres have been estimated. The hydration shell structure was shown to depend on the nature of the base pair and on the stack configuration, while dependence of the global hydration shell characteristics on the stack configuration has been proved to be rather slight. The most typical structural elements of hydration shells, in the glycosidic (minor in B-like conformation) and non-glycosidic (major) grooves, for different configurations of AU and GC stacks, have been found and discussed. The number of hydrogen bonds between water molecules and bases per water molecule was shown to change upon transformation of the stack from A to B configuration. This result is discussed in connection with the reasons for B to A conformational transition and the concept of "water economy". Hydration shell patterns of NH2-groups of AU and GC helical stacks differ significantly.  相似文献   

2.
Abstract

Systems containing a base or a base pair and 25 water molecules, as well as a helical stack and 30 water molecules per base pair, have been simulated. Changes in the base hydration shell structure, after the bases have been included into the pair and then into the base pair stack are discussed. Hydration shells of several configurations of the base pair stacks are discussed. Probabilities of formation of the hydrogen-bonded bridges of 1, 2 and 3 water molecules between hydrophilic centres have been estimated. The hydration shell structure was shown to depend on the nature of the base pair and on the stack configuration, while dependence of the global hydration shell characteristics on the stack configuration has been proved to be rather slight. The most typical structural elements of hydration shells, in the glycosidic (minor in B-like conformation) and non-glycosidic (major) grooves, for different configurations of AU and GC stacks, have been found and discussed. The number of hydrogen bonds between water molecules and bases per water molecule was shown to change upon transformation of the stack from A to B configuration. This result is discussed in connection with the reasons for B to A conformational transition and the concept of “water economy”. Hydration shell patterns of NH2-groups of AU and GC helical stacks differ significantly.  相似文献   

3.
The hydration shell of several conformations of the polynucleotides poly(dA).poly(dT), poly(dA).poly(dU), and poly(dA-dI).poly(dT-dC) has been simulated using the Monte Carlo method (Metropolis sampling). Calculations have shown that the structure of the hydration shell of the minor groove greatly depends on its width. In conformations with a narrowed minor groove, the first layer of the hydration shell of this groove has only one molecule per nucleotide pair that forms H bonds with purine N3 of one pair and pyrimidine O2 of the next pair. The second layer of the hydration shell of such conformations contains molecules that form H bonds between two adjacent molecules of the first layer. The probability of formation of hydration spine is about 20% while the bridges of the first layer are formed with a probability of about 70%. In the first layer of the minor groove of the B-DNA conformation with wide minor groove there are approximately two water molecules per base pair that form H bonds with purine N3 or pyrimidine O2 and with the sugar ring oxygen of the adjacent nucleotide. The probability of simultaneous H bonding of a water molecule with N3 (or O2) and O of sugar ring is about 30%. The results of simulation suggest that hydration spine proposed for the narrowed minor groove of oligonucleotide crystals [H. R. Drew, and R. E. Dickerson (1981) Journal of Molecular Biology, Vol. 151, pp. 535-556] can be formed in fibers of poly(dA).poly(dT), poly(dA).poly(dU), and poly(dA-dI).poly(dT-dC) as well as in DNA fragments of these sequences in solution.(ABSTRACT TRUNCATED AT 250 WORDS)  相似文献   

4.
A computational method is elaborated for studying the water environment around regular polynucleotide duplexes; it allows rigorous structural information on the hydration shell of DNA to be obtained. The crucial aspect of this Monte Carlo simulation is the use of periodical boundary conditions. The output data consists of local maxima of water density in the space near the DNA molecule and the properties of one- and two-membered water bridges as function of pairs of polar groups of DNA. In the present paper the results for poly(dG).poly(dC) and poly(dG-dC).poly(dG-dC) are presented. The differences in their hydration shells are of a purely structural nature and are caused by the symmetry of the polar groups of the polymers under study, the symmetry being reflected by the hydration shell. The homopolymer duplex hydration shell mirrors the mononucleotide repeat. The water molecules contacting the polynucleotide in the minor groove are located nearly in the plane midway between the planes of successive base pairs. One water molecule per base pair forms a water bridge facing two polar groups of bases from adjacent base pairs and on different strands making a "spine"-like structure. In contrast, the major groove hydration is stabilized exclusively by two-membered water bridges; the water molecules deepest in the groove are concentrated near the plane of the corresponding base pair. The alternating polymer is characterized by a marked dyad symmetry of the hydration shell corresponding to the axis between two successive base pairs. The minor groove hydration of the dCpdG step resembles the characteristic features of the homopolymer, but the bridge between the O2 oxygens of the other base-stacking type is formed by two water molecules. The major groove hydration is characterized by high probability of one-membered water bridges and by localization of a water molecule on the dyad axis of the dGpdC step. The found structural elements are discussed as reasonable invariants of a dynamic hydration shell.  相似文献   

5.
Polyhistidine-carboxylic acid systems are studied by ir spectroscopy. It is shown that OH ?N ? O?…H+N bonds formed between carboxylic groups and histidine residues are easily polarizable proton-transfer hydrogen bonds when the pKa of the protonated histidine residues is about 2.8 units larger than that of the carboxylic groups. From these results it bis concluded that OH ?N ? O? ?H+N bonds between glutamic or aspartic acid histidine residues in proteins may be easily polarizable proton-transfer bonds. Furthermore, it is demonstrated that water molecules shift the proton-transfer equilibria in these hydrogen bonds in favor of the polar structure, i.e., due to water or polar environments OH ?N ? O? ?H+N bonds with smaller ΔpKa values become easily polarizable proton-transfer hydrogen bonds. A consideration of the amide bands of polyhistidine shows that it can be present in five different conformations. It is shown that these conformational changes are strongly related to the degree of proton transfer. Hence, the degree of proton transfer, the degree of hydration, and conformation are not independent of each other, but are strongly coupled. Further proof for the interdependence of proton transfer and conformational changes are hysteresis effects, which are observed with studies of polyhistidine dependent on carboxylic acid, adsorption and desorption. OH ?N ? O? ?H+N bonds between aspartic and glutamic acid and histidine residues are present in hemoglobin, in ribonucleases, and in proteases, whereby this type of bond is preferentially found in the active centers of these enzymes. It is pointed out that hydrogen bonds with such interaction properties should be of great significance for structure and especially functions of proteins in which they are present.  相似文献   

6.
The nature of hydrogen bonds formed between carboxylic acid residues and histidine residues in proteins is studied by ir spectroscopy. Poly(glutamic acid) [(Glu)n] is investigated with various monomer N bases. The position of the proton transfer equilibrium OH…?N ? O?…?H+N is determined considering the bands of the carboxylic group. It is shown that largely symmetrical double minimum energy surfaces are present in the OH…?N ? O?…?H+N bonds when the pKa of the protonated N base is two values larger than that of the carboxylic groups of (Glu)n. Hence OH…?N ? O?…?H+N bonds between glutamic and aspartic acid residues and histidine residues in proteins may be easily polarizable proton transfer hydrogen bonds. The polarizability of these bonds is one to two orders of magnitude larger than usual electron polarizabilities; therefore, these bonds strongly interact with their environment. It is demonstrated that water molecules shift these proton transfer equilibria in favor of the polar proton boundary structure. The access of water molecules to such bonds in proteins and therefore the position of this proton transfer equilibrium is dependent on conformation. The amide bands show that (Glu)n is α-helical with all systems. The only exception is the (Glu)n-n-propylamine system. When this system is hydrated (Glu)n is α-helical, too. When it is dried, however, (Glu)n forms antiparallel β-structure. This conformational transition, dependent on degree of hydration, is reversible. An excess of n-propylamine has the same effect on conformation as hydration.  相似文献   

7.
We studied films of poly(L -tyrosine) with hydrogen phosphate (residue/phosphate, 1:1) by ir spectroscopy. The influences of the alkali cations (Li+, Na+, K+) and of the degree of hydration were clarified. If Li+ ions are present, the OH ??OP hydrogen bonds formed in the dried films between the tyrosine OH groups and hydrogen phosphate are asymmetrical. The formation of hydrogen phosphate–hydrogen phosphate hydrogen bonds is prevented by the presence of the Li+ ions. With an increase in the degree of hydration, the tyrosine–phosphate bonds are not broken but become slightly stronger. Completely different behaviour is found if K+ ions are present. In dry films, the OH ??OP ? O? ?HOP hydrogen bonds formed between tyrosine and hydrogen phosphate show large proton polarizability. The tyrosine proton has a noticeable residence time at the acceptor O atom of the phosphate. The difference in the behaviour of the system with K+ ions when compared to the system with Li+ ions can be explained, since the hydrogen acceptor O atom of phosphate ions is more negatively charged due to the weaker influence of the K+ ions. Furthermore, POH ??OP hydrogen bonds between hydrogen phosphate molecules are formed. With an increase in the degree of hydration, the tyrosine–hydrogen phosphate hydrogen bonds are broken, all tyrosine protons are found at the tyrosine residues, and the -PO3? groupings are in a symmetrical environment, indicating that the K+ ions are removed from these groupings. If the degree of hydration increases further, hydrogen-bonded systems such as hydrogen phosphate–water–hydrogen phosphate are formed that show large proton polarizability due to collective proton motion. When Na+ ions are present, the OH ??OP ? O? ?HOP hydrogen bonds formed in dry films still show proton polarizability, but the residence time of the tyrosine proton at the phosphate is very short.  相似文献   

8.
Abstract

To compare the hydration pattern of the cytidine (Cyd) and 2′-deoxycytidine (dCyd) in the aqueous solutions at the level of microscopic interactions, Molecular Dynamics (MD) computer simulations have been undertaken. The results indicate that the hydration of the heterocyclic base moiety in cytidine and 2′-deoxycytidine has a hydrophobic character. None of the three potential Watson—;Crick base pair centres hydrogen bonds with the water molecules and the formation of something akin to a clathrate cage structure of water around base moieties of nucleosides in the aqueous solution is suggested. In contrast, the hydration of Cyd and dCyd sugar moieties shows a hydrophilic character and the three-dimensional networks of H-bonds involving all hydrophilic centres are formed differently around the ribose and 2′-deoxyribose. The sugar hydroxyl groups participate in the hydrogen bonding with water both as H-donor and as H-acceptor. Their donor-acceptor abilities have been evaluated and compared. The coordination numbers, the geometrical data of the first hydration shell, and the number of hydrogen bonds have been calculated. The changes in the pattern of hydration with the increased concentration of nucleosides and upon nucleoside protonation are discussed. The analysis of the pairwise interaction energies are also presented.  相似文献   

9.
Structure of DNA hydration shells studied by Raman spectroscopy   总被引:1,自引:0,他引:1  
N J Tao  S M Lindsay  A Rupprecht 《Biopolymers》1989,28(5):1019-1030
We have used Raman scattering to study the water O-H stretching modes at approximately 3450 and approximately 3220 cm-1 in DNA films as a function of relative humidity (r.h.). The intensity of the 3220-cm-1 band vanishes as the r.h. is decreased from 98% to around 80%, which indicates that the hydrogen-bond network of water is disrupted in the primary hydration shell (which therefore cannot have an "ice-like" structure). The number of water molecules in the primary hydration shell was determined from the intensity of the approximately 3200-cm-1 band as about 30 water molecules per nucleotide pair. The approximately 3400-cm-1 O-H stretch band was used for determining the total water content, and this band persists at 0% r.h., implying that 5-6 tightly bound water molecules per nucleotide pair remain. The frequency of the approximately 3400-cm-1 O-H stretch mode is lower by 30 to 45 cm-1 in the primary hydration shell compared to free water. The water content as a function of r.h. obtained from these experiments agrees with gravimetric measurements. The disappearance of the approximately 3200-cm-1 band and the shift of the approximately 3400-cm-1 O-H stretch band provide a reliable way of measuring the hydration number of DNA.  相似文献   

10.
F Eisenhaber  J H Mannik  V G Tumanyan 《Biopolymers》1990,29(10-11):1453-1464
Being interested in possible effects of sequence-dependent hydration of B-DNA with mixed sequence in fibers, we performed a series of Monte Carlo calculations of hydration of polydeoxyribonucleotides in B form, considering all sequences with dinucleotide repeat. The computational results allow the ten base-stacking types to be classified in accordance with their primary hydration in the minor groove. As a rule, the minor groove is occupied by two water molecules per base pair in the depth of the groove, which are located nearly midway between the planes of successive base pairs and symmetrically according to the dyad there. The primary hydration of the major groove depends on the type of the given base pair. The coordinates of 3 water molecules per base pair in the depth of the major groove are determined by the type of this pair together with its position and orientation in the helix, and are practically independent on the adjacent base pairs. A/T-homopolymer tracts do not fit into this hydration pattern; the base pair edges are hydrated autonomously in both grooves. Analysis of the Li-B-DNA x-ray diffraction intensities reveals those two water positions in the minor groove. In the major groove, no electronic density peaks in sufficient distance from the base edges were found, thus confirming the absence of any helical invariance of primary hydration in this region. With the help of the rules proposed in this paper it is possible to position the water molecules of the first hydration shell in the grooves of canonical B-DNA for any given sequence.  相似文献   

11.
Nanoscale α-hemolysin pores can be used to analyze individual DNA or RNA molecules. Serial examination of hundreds to thousands of molecules per minute is possible using ionic current impedance as the measured property. In a recent report, we showed that a nanopore device coupled with machine learning algorithms could automatically discriminate among the four combinations of Watson–Crick base pairs and their orientations at the ends of individual DNA hairpin molecules. Here we use kinetic analysis to demonstrate that ionic current signatures caused by these hairpin molecules depend on the number of hydrogen bonds within the terminal base pair, stacking between the terminal base pair and its nearest neighbor, and 5′ versus 3′ orientation of the terminal bases independent of their nearest neighbors. This report constitutes evidence that single Watson–Crick base pairs can be identified within individual unmodified DNA hairpin molecules based on their dynamic behavior in a nanoscale pore.  相似文献   

12.
The residence times of individual hydration water molecules in the major and minor grooves of DNA were measured by nuclear magnetic resonance (NMR) spectroscopy in aqueous solutions of d-(CGCGAATTCGCG)2 and d-(AAAAATTTTT)2. The experimental observations were nuclear Overhauser effects (NOE) between water protons and the protons of the DNA. The positive sign of NOEs with the thymine methyl groups shows that the residence times of the hydration water molecules near these protons in the major groove of the DNA must be shorter than about 500 ps, which coincides with the behavior of surface hydration water in peptides and proteins. Negative NOEs were observed with the hydrogen atoms in position 2 of adenine in both duplexes studied. This indicates that a 'spine of hydration' in the minor groove, as observed by X-ray diffraction in DNA crystals, is present also in solution, with residence times significantly longer than 1 ns. Such residence times are reminiscent of 'interior' hydration water molecules in globular proteins, which are an integral part of the molecular architecture both in solution and in crystals.  相似文献   

13.
U Burget  G Zundel 《Biopolymers》1987,26(1):95-108
(L -His)n- dihydrogen phosphate systems are studied by ir spectroscopy in the presence of various cations and as a function of the degree of hydration. Ir continua indicate that (I) OH … N ? O?…H+N (IIR) hydrogen bonds are formed and that these bonds show high proton polarizability, which increases from the Li+ to the K+ system. In the K+?system, His-Pi-Pi chains are formed, showing particularly high proton polarizability due to collective proton motion within both hydrogen bonds. The OH N ? O?…H?N equilibria are determined from ir bands. With the Li+ system, 55% of the protons are present at the histidine residues; this percentage is smaller with the Na+ system (41%), and amounts to only 32% with the K+ system. With the increasing degree of hydration the removal of the degeneracy of νas?PO2?3 vanishes, indicating loosening of the cations from the phosphates. Nevertheless, the hydrogen bond acceptor O atom becomes more negative; a shift of the equilibrium to the right is observed in the OH… N ? O?…H+N bond. This is explained by the strong interaction of the dipole of the hydrogen bonds with the water molecules. All these results show that protons can be shifted easily in these hydrogen bonds due to their high proton polarizability. The transfer equilibria can be controlled easily by local electrical fields. In addition, these results may be of significance when phosphates interact with proteins.  相似文献   

14.
A Brillouin scattering study of the hydration of Li- and Na-DNA films   总被引:2,自引:0,他引:2  
We have used Brillouin spectroscopy to study the velocities and attenuation of acoustic phonons in wet-spun films of Na-DNA and Li-DNA as a function of the degree of hydration at room temperature. Our data for the longitudinal acoustic (LA) phonon velocity vs water content display several interesting features and reveal effects that we can model at the atomic level as interhelical bond softening and relaxation of the hydration shell. The model for interhelical softening makes use of other physical parameters of these films, which we have determined by gravimetric, x-ray, and optical microscopy studies. We extract intrinsic elastic constants for hydrated Na-DNA molecules of c11 ? 8.0 × 1010 dynes/cm2 and c33 ? 5.7 × 1010 dynes/cm2, which corresponds to a Young's modulus, E ? 1.1 × 1010 dynes/cm2 (with Poisson's ratio, σ = 0.44). The negative velocity anisotropy of the LA phonons indicates that neighboring DNA molecules are held together by strong interhelical bonds in the solid state. The LA phonon attenuation data can be understood by the relaxational model in which the acoustic phonon is coupled to a relaxation mode of the water molecules. Na-DNA undergoes the A to B phase transition at a relative humidity (rh) of 92% while Li-DNA (which remains in the B form in this range) decrystallizes at an rh of 84%. We find that our Brillouin results for Na- and Li-DNA are remarkably similar, indicating that the A to B phase transition does not play an important role in determining the acoustic properties of these two types of DNA.  相似文献   

15.
A molecular-dynamics simulation was used to carry out an introductory study of the hydration of a section of a rigid single A- or B-DNA helix with one Na+ counterion per nucleotide. Four Na+ ions and four nucleotides and periodic boundary conditions were used to mimic an infinite helix. The atoms of the helix and the Na+ ions were assumed to be Lennard-Jones spheres that also carried charges. Stillinger four-point charge model water molecules were used. We carried out five calculations, for 26 and 46 water molecules in B-DNA and 20, 32, and 46 in A-DNA fragments. The arrangements of the Na+ ions are found to have some similarities to those obtained by Clementi and Corongiu. In the calculations with 46 water molecules, we found that two Na+ ions can be bridged by about two water molecules and form a hydrated bound pair, which in turn forms a bridge between the guanine N7 and a near phosphate group. These bound pairs may be important in stabilizing the helix structure of DNA molecules.  相似文献   

16.
Natural DNAs and some polynucleotides organised in fiber present the A--B form transition at a relative humidity (r.h.) which depends on the temperature. A shift of the midpoint of that helix--helix transition to higher r.h. values is observed when the temperature is risen. It is shown that the average number of water molecules associated to a nucleotide pair is the relevant parameter for the A-B transition and that this parameter can be given a precise value by a combination of different r.h. and temperature values. The minimum number of water molecules necessary to get the B form depends on the base composition of the DNA. It is observed that AT base pairs have a higher affinity toward water molecules than GC base pairs. In the B form there are 27 water molecules per GC nucleotide pair and 44 per AT pair. Moreover, we noted that the fraction of nucleotides in the B form as a function of the average number of water molecules associated per base pair does not depend on the temperature. The A helical form is obtained with about 11 water molecules per nucleotide pair and this number is not very sensitive to the base composition of DNA.  相似文献   

17.
In the present work, molecular dynamics simulations have been carried out to study the dependence of counterion distribution around the DNA double helix on the character of ion hydration. The simulated systems consisted of DNA fragment d(CGCGAATTCGCG) in water solution with the counterions Na+, K+, Cs+ or Mg2+. The characteristic binding sites of the counterions with DNA and the changes in their hydration shell have been determined. The results show that due to the interaction with DNA at least two hydration shells of the counterions undergo changes. The first hydration shell of Na+, K+, Cs+, and Mg2+ counterions in the bulk consists of six, seven, ten, and six water molecules, respectively, while the second one has several times higher values. The Mg2+ and Na+ counterions, constraining water molecules of the first hydration shell, mostly form with DNA water-mediated contacts. In this case the coordination numbers of the first hydration shell do not change, while the coordination numbers of the second one decrease about twofold. The Cs+ and K+ counterions that do not constrain surrounding water molecules may be easily dehydrated, and when interacting with DNA their first hydration shell may be decreased by three and five water molecules, respectively. Due to the dehydration effect, these counterions can squeeze through the hydration shell of DNA to the bottom of the double helix grooves. The character of ion hydration establishes the correlation between the coordination numbers of the first and the second hydration shells.
Graphical Abstract Hydration of counterions interacting with DNA double helix
  相似文献   

18.
Monte Carlo simulations [(N, V, T)-ensemble] were performed for the hydration shell of poly(dA-dT).poly(dA-dT) in canonical B form and for the hydration shell of poly(dA).poly(dT) in canonical B conformation and in a conformation with narrow minor groove, highly inclined bases, but with a nearly zero-inclined base pair plane (B' conformation). We introduced helical periodic boundary conditions with a rather small unit cell and a limited number of water molecules to reduce the dimensionality of the configuration space. The coordinates of local maxima of water density and the properties of one- and two-membered water bridges between polar groups of the DNA were obtained. The AT-alternating duplex hydration mirrors the dyad symmetry of polar group distribution. At the dApdT step, a water bridge between the two carbonyl oxygens O2 of thymines is formed as in the central base-pair step of Dickerson's dodecamer. In the major groove, 5-membered water chains along the tetranucleotide pattern d(TATA).d(TATA) are observed. The hydration geometry of poly(dA).poly(dT) in canonical B conformation is distinguished by autonomous primary hydration of the base-pair edges in both grooves. When this polymer adopts a conformation with highly inclined bases and narrow minor groove, the water density distribution in the minor groove is in excellent agreement with Dickerson's spine model. One local maximum per base pair of the first layer is located near the dyad axis between adjacent base pairs, and one local maximum per base pair in the second shell lies near the dyad axis of the base pair itself. The water bridge between the two strands formed within the first layer was observed with high probability. But the water molecules of the second layer do not have a statistically favored orientation necessary for bridging first layer waters. In the major groove, the hydration geometry of the (A.T) base-pair edge resembles the main features of the AT-pair hydration derived from other sequences for the canonical B form. The preference of the B' conformation for oligo(dA).oligo(dT) tracts may express the tendency to common hydration of base-pair edges of successive base pairs in the grooves of B-type DNA. The mean potential energy of hydration of canonical B-DNA was estimated to be -60 to -80 kJ/mole nucleotides in dependence on the (G.C) contents. Because of the small system size, this estimation is preliminary.  相似文献   

19.
Changes in the oxidation state of the DNA bases, induced by oxidation (ionization) or by reduction (electron capture), have drastic effects on the acidity or basicity, respectively, of the molecules. Since in DNA every base is connected to its complementary base in the other strand, any change of the electric charge status of a base in one DNA strand that accompanies its oxidation or reduction may affect also the other strand via proton transfer across the hydrogen bonds in the base pairs. The free energies for electron transfer to or from a base can be drastically altered by the proton transfer processes that accompany the electron transfer reactions. Electron-transfer (ET) induced proton transfer sensitizes the base opposite to the ET-damaged base to redox damage, i.e., damage produced by separation of charge (ionization) has an increased change of being trapped in a base pair. Of the two types of base pair in DNA, A-T and C-G, the latter is more sensitive to both oxidative and reductive processes than the former.

Proton transfer induced by ET does not only occur between the heteroatoms (o and N) of the base pairs (intra-pair proton transfer), but also to and from adjacent water molecules in the hydration shell of DNA (extra-pair proton transfer). These proton transfers can involve carbon and as such are likely to be irreversible. It is the A-T pair which appears to be particularly prone to such irreversible reactions.  相似文献   

20.
N Lavalle  S A Lee  A Rupprecht 《Biopolymers》1990,30(9-10):877-887
We report measurements of the water content and swelling of wet-spun films of Na-, K-, Rb-, and Cs-DNA as a function of relative humidity (rh). The water contents (number of water molecules per base pair of DNA) of these films are found to be quite similar, indicating that the identity of the counterion species is unimportant for the water content. Since the A to B transition for these DNAs occurs at different rhs, the corresponding water contents of the A to B transition are found to be quite different. These films swell as a function of rh in a very similar manner, implying that the changes in the intermolecular bonds in the different DNAs are similar. Dramatic changes are observed in the dimensions of the films above 84% rh for all types of DNA. Combining the water content and swelling measurements yields the dependence of the volume per base pair on water content. The volume per base pair is observed to be a nonlinear function of water content, indicating nonideal mixing of the water with the DNA.  相似文献   

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