Dual role of DNA intrinsic curvature and flexibility in determining nucleosome stability1

Article No. jmbi.1999.2575 available online at http://www.idealibrary.com on

J. Mol. Biol. (1999) 286, 1293±1301

COMMUNICATION

Dual Role of DNA Intrinsic Curvature and Flexibility in Determining Nucleosome Stability C. Anselmi1, G. Bocchinfuso1, P. De Santis1*, M. Savino2 and A. Scipioni1 1

Dipartimento di Chimica UniversiaÁ di Roma ``La Sapienza'', 00185 Roma Italy 2

Dipartimento di Genetica e Biologia Molecolare, Istituto Pasteur, Fondazione CenciBolognetti- UniversitaÁ di Roma ``La Sapienza'', 00185 Roma Italy

A statistical mechanistic approach to evaluate the sequence-dependent thermodynamic stability of nucleosomes is proposed. The model is based on the calculation of the DNA intrinsic curvature, obtained by integrating the nucleotide step deviations from the canonical B-DNA structure, and on the evaluation of the ®rst order elastic distortion energy to reach the nucleosomal superstructure. Literature data on the free energy of nucleosome formation as obtained by competitive nucleosome reconstitution of a signi®cant pool of different DNA sequences were compared with the theoretical results, and a satisfactorily good correlation was found. A striking result of the comparison is the emergence of two opposite roles of the DNA intrinsic curvature and ¯exibility in determining nucleosome stability. Finally, the obtained results suggest that the curvature-dependent DNA hydration should play a relevant role in the sequence-dependent nucleosome stability. # 1999 Academic Press

*Corresponding author

Keywords: nucleosome stability; competitive nucleosome reconstitution; sequence-dependent DNA curvature; sequence-dependent DNA elasticity; statistical thermodynamics of DNA superstructures

The nucleosome is the association complex of DNA (145 bp) with the histone octamer; it is the elemental unit of chromatin. The ®rst model of nucleosome was proposed by Kornberg (1977), while its structure was later determined at low resolution by Klug et al. (1980) by means of electron microscopy and by Richmond et al. (1984) by X-ray diffraction techniques. It is characterized by a ¯at solenoid-like structure where the DNA axis is wrapped on the proteic core of the histone octamer Ê with a pseudo-dyad symmetry. Recently, a 2.8 A resolution electron density map was obtained by Luger et al. (1997) which con®rms the previous structure and contains relevant details of both DNA and protein core. This nucleosome structure was obtained by using the crystals of nucleosome reconstituted in vitro with a palindromic DNA sequence which in principle could adopt the dyad symmetry of protein core. However, the experimental evidence indicates that the reconstitution of nucleosome can be obtained with any DNA sequence, although a E-mail address of the corresponding author: [email protected] 0022-2836/99/101293±09 $30.00/0

number of reports have shown the existence of preferential positioning of nucleosomes along DNA as well as the occurrence of nucleosome-free regions in chromatin. Therefore, the ability to form nucleosomes appears to be enhanced or decreased by some base sequences. Different authors have investigated the phase and the translational positioning of nucleosomes on different DNAs, obtaining some rules relating nucleosome positioning to the sequence (Drew & Travers, 1985; Satchwell et al., 1986; Travers & Klug, 1987; McGhee & Fensenfeld, 1980; van Holde, 1988; Widom, 1989; Blank & Becker, 1996; Flaus et al., 1996). Competitive nucleosome reconstitution experiments provide a quantitative estimate of differential thermodynamic nucleosome stability, indicating that nucleosome positioning along a DNA sequence occurs with different af®nity; thus, a large set of experimental data of nucleosome reconstitution free energy has been accumulating in the literature (Shrader & Crothers, 1989; Godde & Wolffe, 1996; Godde et al., 1996; Widlund et al., 1997; Lowary & Widom, 1998; Rossetti et al., 1998; Dal CornoÁ et al., 1998). The differential nucleosome stability can be due to either speci®c interactions # 1999 Academic Press

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The Role of DNA Curvature and Flexibility in Nucleosome Stability

between amino acid residues and certain basepairs, or to an intrinsic propensity of a DNA tract to wrap over the protein core because of larger ¯exibility and/or a proper sequence-dependent curvature. Attempts to ®nd the sequence features which control the stability of nucleosomes were made by Shrader & Crothers (1989, 1990), Godde & Wolffe (1996), Godde et al. (1996), Wang et al. (1996), Wang & Grif®th (1996), Widlund et al. (1997) and Lowary & Widom (1998). Identifying strong nucleosomes can potentially provide routes to the discovery of DNA sequence elements or mechanical properties which determine their relatively high af®nity. This would be of great interest, as would the correlation of the genomic location of such sequences in the organization of chromatin. A complex pattern of evidence has been emerging from the results of these investigations, where the intrinsic curvature, ¯exibility and some consensus sequences play a relevant role in the nucleosome stability. In particular, by investigating arti®cial nucleosome sequences, Shrader & Crothers (1990) found that certain intrinsically curved DNAs show lower stability than relatively straight DNAs with similar sequences, while Godde & Wolffe (1996) and Godde et al. (1996) provided evidence that practically straight DNAs, characterized by (CTG) triplet repeats, show high af®nity in the reconstitution experiments. Widlund et al. (1997) recently isolated DNA segments in the mouse genome characterized by runs of phased three or four adenine residues, extensive CA repeats and in some cases TATA tetranucleotides, which form very stable nucleosomes in spite of their low curvature. Further, Lowary & Widom (1998) carried out a SELEX experiment with a large pool of synthetic random DNAs, and identi®ed individuals having the highest af®nity with histone octamer so far obtained. Their results also reveal new statistically signi®cant sequence rules. Besides the search of the strongest nucleosomes, investigations were carried out to identify the most unstable nucleosomes which were identi®ed in the telomeric sequences (Cacchione et al., 1997; Rossetti et al., 1998). Nevertheless, our understanding of the physicochemical origin of nucleosome stability is still unsettled or at least fragmented, and the question about the positioning and stability of nucleosome along the DNA chain seems to be still open. In fact, the results of competitive nucleosome reconstitution experiments, as represented by the free energy differences involved, show that the af®nity of the histone octamer to DNAs with different sequence, curvature and length, appears to be restricted within only a few kcal per mol of nucleosome. This could suggest that the DNA-histone recognition could be driven either by a few chemical determinants, which different authors have localized close to the nucleosome dyad axis (McGhee & Fensenfeld, 1980; Drew & Travers, 1985; Fitzgerald & Simpson, 1985; Satchwell et al.,

1986; Ramsay, 1986; Travers & Klug, 1987; van Holde, 1988; Widom, 1989; Blank & Becker, 1996; Flaus et al., 1996), or by simple elastic energy differences resulting from DNA intrinsic curvatures and ¯exibility. The success recently obtained in predicting the intrinsic sequence-dependent circularization propensity of DNAs and their writhing transitions in the framework of a statistical mechanic approach (De Santis et al., 1996; Anselmi et al., 1998), prompted us to extend the model to the evaluation of the nucleosome positioning and stability. We calculated the canonical ensemble free energy to transform the DNA intrinsic superstructure into the nucleosomal structure by adopting a simple ®rst order elasticity model to evaluate the thermodynamic equilibrium of the competitive nucleosome reconstitution experiments. Using standard torsional and bending force constants, but multiplied by the empirical normalized melting temperature for each dinucleotide step (Gotoh & Tagashira, 1981), to represent the differential ¯exibility along the sequence, we have obtained an analytical formulation for the nucleosome positioning and its differential stability in terms of the DNA sequence and length. The model appears to be capable of predicting the thermodynamic free energy difference of the competitive nucleosome reconstitution experiments made in different laboratories (Shrader & Crothers, 1989, l990; Godde & Wolffe, 1996; Godde et al., 1996; Widlund et al., l997; Cacchione et al., l997; Lowary & Widom, l998; Rossetti et al., 1998; Dal CornoÁ et al., 1998). If
Gk represents the nucleosome reconstitution free energy difference from a standard nucleosome of the kth DNA tract of l ˆ 144 bp along a sequence (Figure 1), the free energy per mol of nucleosome,
G, pertinent to the whole DNA chain with N base-pairs is: b
G ˆ ÿ ln

Nÿl=2 X

exp‰ÿb
G…k†Š

…1†

kˆl=2

where b is 1/RT. The relation with the pertinent canonical partition functions allows us to write the nucleosome reconstitution free energy difference as: ÿb
G…k† ˆ ln

Qf …k† Qn …k† ÿ ln   Qf Qn

…2†

where Qn (k) ˆ j states exp[ ÿ b
Ej(k))] is the con®gurational canonical partition function of the kth nucleosomal DNA tract along the sequence; Qf(k) is that of the corresponding free DNA; Q*n and Q*f are those pertinent to a standard intrinsically straight DNA with a random sequence. The partition functions of the ¯anking DNA tracts are considered equivalent in the free form and after the kth nucleosome formation and cancel in the ratio.

1295

The Role of DNA Curvature and Flexibility in Nucleosome Stability

Figure 1. Schematic drawing of competitive nucleosome reconstitution. Each nucleosome positioning is characterized by an equilibrium constant (K1, K2, Kn). A straight random sequence DNA of 144 bp with uniform average ¯exibility is adopted as a standard. Choosing a different standard corresponds to add a constant term to the free energy difference; consequently, it does not affect the relative nucleosome stability.

This is a ®rst approximation because the ¯uctuations of the ¯anking sequences depend on the nucleosome position and favor the peripheral with respect to the central positions. This issue was raised previously to explain the different circularization propensity of DNA in the presence of CAP when settled in peripheral or central positions (De Santis et al., 1996). Such an entropic effect, which increases with the temperature, certainly in¯uences the nucleosome translational positions as experimentally found by Meersseman et al. (1992) using an oligomeric DNA, and more recently by Flaus & Richmond (1998); but plausibly it should not sensitively affect the integral nucleosome af®nity we considered here. The partition functions were ®rst evaluated taking into account the elastic terms, namely the sum of the bending,
Eb(k), and twisting,
Et(k), energies necessary to distort the kth 144 bp DNA tract in the nucleosomal form. The elastic twisting contribution can be expressed as: k‡l=2 X tT …3† ‰ n …s† ÿ of …s†Š2
Et …k† ˆ  2 T sˆkÿl=2 where t is the twisting force constant related to the torsional rigidity; n(s) ÿ of (s) is the dinucleotide twisting difference between the nucleosome and the free DNA. We have assumed for n a constant value corresponding to a DNA periodicity of 10.2 bp per turn according to the experimental evidence (Drew & Travers, 1985; Luger et al., 1997), whereas of is that corresponding to the pertinent intrinsic value (De Santis et al., 1996; Anselmi et al., 1998). T is the dinucleotide empirical melting temperature as evaluated by Gotoh & Tagashira (1981)

and T* the relative mean value assumed as standard; their ratio, averaged along the kth nucleosomal DNA modulates the force constant producing a sequence dependent ¯exibility. It should be noted that the dinucleotide melting temperatures, which has been adopted to evaluate the sequence dependent ¯exibility, show a good linear correlation with the theoretical estimates of the stacking energy (Ornstein et al., 1978; Gotoh & Tagashira, 1981) so that the latter could alternatively be adopted to modulate the elastic force constants. However the results we obtained do not change signi®cantly. The elastic bending energy contribution can be expressed as: k‡l=2 X bT  …4† jCn …s† ÿ Cof …s†j2
Eb …k† ˆ  2 T sˆkÿl=2 where b is the apparent isotropic bending force constant related to the persistence length. Cn(s) ÿ Cof (s) is the vectorial difference between the DNA curvature in the nucleosome and that of the free DNA corresponding to its intrinsic curvature. This can be expressed in terms of the differences between their Fourier transform amplitudes An(n) and Aof (n) with periodicity n: k‡l=2 X sˆkÿl=2

jCn …s† ÿ Cof …s†j2 ˆ

1X jAn …u† ÿ Aof …u†j2 l n

…5†

The summation is evaluated using the approximation successfully adopted in predicting the sequence dependent circularization propensity of DNAs, based on the Parseval equality (Spiegel, 1974):

1296

The Role of DNA Curvature and Flexibility in Nucleosome Stability

2 2 Cn …s† ÿ Co …s† ˆ 1 An …m† ÿ Ao …m† f f l sˆkÿl=2 k‡l=2 X

…6†

Owing to the Parseval's theorem (Spiegel, 1974), the only necessary condition to have a nucleosome-like curvature is to constrain the Fourier term with periodicity m ˆ ÿ 0.18 to assume the value 10.9 rad leaving the maximum of the intrinsic curvature features invariant in order to minimize the elastic energy (De Santis et al., 1996; Anselmi et al., 1998). Setting jAn(m)j ˆ An ˆ 10.9 rad, jAof (m)j ˆ Aof and (bb/l)hT/T*i ˆ B:   B 2 o2 Qn …k† ˆ exp‰ÿb
Et …k†Š exp ÿ …An ‡ Af † 2 … …7† exp…BAn Aof cos f† df where f is the relative phase angle between An(m) and Aof (m). The last integral becomes equal to 2p times J0(iZ), the zero-order Bessel function of the imaginary argument Z ˆ BAnAof . Therefore: Qn …k† ˆ 2p exp‰ÿb
Eo …k†Š exp…ÿZ†J0 …iZ†

…8†

where
Eo(k) contains both the ground state bending and twisting energy contributions. For the standard nucleosome where Aof ˆ 0: 

Qn ˆ 2p exp‰ÿb
Eo Š

…9†

therefore: Qn …k† exp‰ÿb
Eo …k†Š exp…ÿZ†J0 …iZ† ˆ Qn exp‰ÿb
Eo Š

…10†

It should be stressed that only the ground states are represented in the partition function ratio of nucleosomal DNA, because the association with the histone core practically freezes the DNA superstructure in the minimum elastic energy state. On the other hand, the residual ¯uctuations around the ground states cancel in the ratio. The ratio of the canonical partition functions of the free DNAs is equal to the ratio of the bending and twisting ¯uctuation terms, as the other contributions cancel. In fact, the free DNA ¯uctuates around the ground state superstructure, which corresponds to the intrinsic curvature. Therefore, because for the standard nucleosome hT/T*i ˆ 1, the ratio of the pertinent canonical partition functions becomes practically equal to:  ÿ32l Qf …k† T ˆ  …11† T Qf where 3/2 l corresponds to the sum of bending and twisting modes. Consequently:   3 T b
Gel …k† ˆ b
Eo …k† ÿ l ln  ‡ Z ÿ ln J0 …iZ† …12† 2 T

where
Eo(k) is the minimum elastic energy required to distort the kth tract l ˆ 144 bp in the nucleosomal form; Z is equal to (bb/l)hT/T*iAnAof . An and Aof are the pertinent moduli of the Fourier amplitudes with periodicity ÿ0.18 in the nucleosome and in the free DNA respectively. Aof represents the effective curvature, namely the Fourier term of the free DNA curvature function, which coherently contributes to the nucleosomal structure; whereas ®xing An is a necessary condition to ensure that DNA assumes a nucleosome-like form. A list of de®nitions for the mathematical symbols is provided in the legend to Table 1. Using our roll, tilt and twist angles to calculate the curvature function for a given DNA (see Ê Table 1) with a persistence length equal to 450 A ÿ19 erg cm, as and a torsional rigidity of 2.1  10 successfully adopted in the theoretical predictions of the circularization propensity of DNAs (De Santis et al., 1996; Anselmi et al., 1998), we evaluated the elastic free energy difference,
Gel(k), of the competitive nucleosome reconstitution for a large set of DNAs for sequences and lengths investigated in several laboratories as reported in Table 2 (Shrader & Crothers, 1989, 1990; Godde & Wolffe, 1996; Godde et al., 1996; Wang & Grif®th, 1996; Widlund et al., 1997; Cacchione et al., 1997; Lowary & Widom, 1998; Rossetti et al., 1998; Dal CornoÁ et al., 1998). Figure 2 illustrates the differences between the experimental and theoretical (elastic) nucleosome reconstitution free energies versus the square of the intrinsic effective curvature of the free DNA represented by the pertinent average Fourier amplitude hAo2 f i. Surprisingly, the free energy differences are not the expected constant related to the choice of the standard DNA in the case of experimental data and an ideal straight DNA 144 bp in the model, but appear to be a parabolic function of the DNA curvature. This would suggest the existence of a free energy contribution directly related to the intrinsic curvature, namely to a property of the free DNA, which destabilizes the nucleosome formation. The strikingly signi®cant linear correlation (R ˆ 0.98) with the average values of hAo2 f i, strongly supports the hypothesis that DNA curvature could play two opposite roles in nucleosome stability: one favoring the nucleosome formation by reducing the elastic free energy required to distort a given DNA tract in the nucleosomal structure; the other, related to the curvature of the DNA free form, reducing the DNA af®nity for histonic octamer. The latter curvature effect can be plausibly related to the small-groove narrowing, which stabilizing the ``spine of water'' (and counterions), adds a further energy cost to the nucleosome formation which increases with the DNA curvature. This corresponds to the free energy which DNA spends to release a part of the spine of water (and counterions) when it is displaced by the histone interactions. In fact, in previous work on the theor-

1297

The Role of DNA Curvature and Flexibility in Nucleosome Stability Table 1. De®nitions of functions and variables A. Nucleotide step orientational parameters

B. Roll (r), tilt (p), and twist ( ) matrices d,

A T A C G

(8,0, 0.0), (ÿ5.4, 0.5), (6.8, ÿ0.4), (2.0, 1.7),

34.5 36.0 34.1 34.6

T

G

(ÿ5.4, ÿ0.5), (ÿ7.3, 0.0), (1.0, ÿ1.6), (ÿ2.5, ÿ2.7),

36.0 35.3 34.4 33.7

(6.8, (1.0, (4.6, (1.3,

0.4), 1.6), 0.0), 0.6),

C 34.1 34.4 33.5 33.1

(2.0, ÿ1.7), (ÿ2.5, 2.7), (1.3, ÿ0.6), (ÿ3.7, 0.0),

34.6 33.7 33.1 33.3

d ˆ (r, ÿit) and in degrees. Cof …s† ˆ 2p=3600

s‡5 X

d…n† exp…2pin=v†

nˆsÿ4

is the intrinsic curvature function of the free DNA in radiant per bp. d…n† ˆ …r ÿ it†nthbp

v;

DNA local periodicity ˆ

3600 s‡5 X

…n† nˆsÿ4

Qy …k† ˆ

X

exp‰ÿb
Ej …k†Š

j states

is the con®gurational canonical partition function of the kth DNA tract. Ay …v† ˆ

k‡l=2 X

C…s† exp…2pisv†

sˆkÿl=2

is the Fourier transform amplitude of the curvature function with periodicity v pertinent to the generic kth DNA tract with l ˆ 144 bp. Ê is the average persistence length adopted and r ˆ 3.38 A Ê b (the average bending force constant per bp) ˆ PRT/r; where P ˆ 450 A is the monomer repeat of B-DNA, so that b ˆ 79 kcal/bp radÿ2. t (the average twisting force constant per bp) ˆ CN/(r4.19  102), where C ˆ 2.1  10ÿ19 ergcm is the torsional rigidity adopted, N the Avogadro number and the scale factor 4.19  102 provides t ˆ 89 kcal/bp radÿ2. The index y ˆ n or f indicates the nucleosomal or the free DNA tract respectively. … iÿn 2p Jn…z† ˆ exp…iz cos f† exp…inf†df 2p 0 is the integral representation of the Bessel function of n-th order of the complex argument z.

etical prediction of the sequence dependent circularization propensity, we obtained a striking agreement with the experimental results without taking into account such an energy contribution (De Santis et al., 1996). The problem of sequence-dependent DNA hydration has been investigated by several authors in relation to its role in protein binding and speci®city (Teplukhin et al., 1991; Berman, 1994; Sprous et al., 1995; Jacobson et al., 1996; Duan et al., 1997; Robinson & Sligar, 1998). All the investigations provide evidence of differential hydration and stability of DNA sequences related to the minor groove width in agreement with the Drew & Dickerson (1981) model of the spine of water.

It is noteworthy that the polyamine spermine shows higher af®nity with the curved multimeric DNA (CA4T4G)n, than for (GT4A4C)n, which has the opposite sequence polarity and also a much lower curvature (Bordin et al., 1992). Therefore, we have introduced an additive contribution (
Gw) characterized by an inverse quadratic dependence on minor groove contraction from the straight DNA, to represent the water dipole energy difference in the electrostatic ®eld of phosphates, obtaining a good agreement between experimental and theoretical nucleosome reconstitution free energy data (R ˆ 0.91) as illustrated in Figure 3. It is noteworthy that the corresponding formulation can be satisfactorily ®tted in the range

1298

The Role of DNA Curvature and Flexibility in Nucleosome Stability Table 2. The DNA fragments considered ordered by increasing value of experimental free energy,
G Sequence 618 Histone H4 gene TATA-tetrads-TATA CTG10 GT TG H4
CTG Mouse minor satellite CAG-runs-CAG H4
CTG/CGG A-tracts-A-1 ANNA KlCEN1 5S RNA gene CA-runs-CA-1 CGG74 NoSecs-1 FIN CGG13 IAT AEXT TIATR SCEN6 EXAT ANISO TTT 19 IGC 20 EXGC END 22 AOUT 34 Arabid. Thal. telomere Homo telomere Sacch. Cerev. telomere Tetrahymena telomere

References


G/RT

N (bp)

Lowary & Widom (1998) Godde & Wollfe (1996) Widlund et al. (1997) Godde et al.(1996) Shrader & Crothers (1989) Shrader & Crothers (1989) Godde & Wollfe (1996) Widlund et al. (1997) Widlund et al. (1997) Godde & Wollfe (1996) Widlund et al. (1997) Shrader & Crothers (1990) Dal CornoÁ et al. (1998) Godde & Wollfe (1996) Widlund et al. (1997) Godde et al. (1996) Widlund et al. (1991) Shrader & Crothers (1990) Godde et al. (1996) Shrader & Crothers (1990) Shrader & Crothers (1990) Shrader & Crothers (1990) Dal CornoÁ et al. (l998) Shrader & Crothers (1990) Shrader& Crothers (1990) Shrader & Crothers (1990) Shrader & Crother (1990) Shrader & Crothers (1990) Shrader & Crothers (1990) Shrader & Crothers (1990) Shrader & Crother (1990) Shrader & Crothers (1990) Shrader & Crothers (1990) Shrader & Crother Rossetti et al. (1998) Rossetti et al. (1998) Rossetti et al. (1998) Rossetti et al. (1998)

ÿ3.40 ÿ2.00 ÿ0.60 ÿ0.40 0.00 0.00 0.10 0.10 0.20 0.20 0.20 0.25 0.35 0.40 0.50 0.60 0.65 0.70 0.70 0.80 0.80 1.00 1.15 1.20 1.25 1.50 1.50 2.20 2.60 2.60 2.70 2.70 3.00 3.30 5.25 5.70 6.10 6.40

274 216 172 224 162 162 197 169 178 174 170 162 216 226 171 427 171 167 244 162 162 162 218 162 162 162 157 162 162 162 162 172 162 162 195 192 168 185

of considered curvatures by a simple harmonic o2 expression in terms of hAo2 f i (
Gw/RT ˆ 3.2 hAf i). This means that the virtual force-®eld variation acting on water (and counterions) is simply proportional to the curvature in the range of interest. The experimental data by Wang & Grif®th (1996) are not reported in Figure 3 because they were obtained using a different standard DNA (pUC19, 262 bp). However, the pUC19 DNA fragment used is predicted to form very stable nucleosome; so that the apparent resistance of CCG triplet repeats to nucleosome formation is relative only to the pUC19 DNA and not to the standard ``random sequence'' DNA. Aside the theoretical evaluation of the free energy involved in the nucleosome competitive reconstitution, the model is in principle also capable of predicting the nucleosome virtual positions which correspond to the minima of the free energy function
G(k), where k indicates the dyad position along the sequence. However, the problem of nucleosome positioning is also related to the evaluation of the free energy contributions due to the thermal ¯uctuations of the nucleosome ¯anking sequences, we already mentioned, which requires further investigations.

Nevertheless, the approach based on the sequence-dependent DNA elasticity advanced here, appears to be promising if one consider that we roughly predicted (Boffelli et al., 1991) the nucleosome positioning on the basis of the correlation function between the intrinsic curvature of a given DNA tract and the characteristic average curvature function deduced by the analysis of the Satchwell et al. (1986) set of nucleosomal DNAs. Furthermore, we showed that the evaluation of the elastic distortion energy of recurrent DNA tracts 144 bp along the sequence provided a ®rst order solution to the problem of nucleosome positioning (De Santis et al., 1993). Concluding remarks On the basis of the reported results, we can advance the conclusion that the DNA intrinsic curvature is the main factor which controls nucleosome stability, and as a consequence nucleosome positioning. DNA curvature plays a dual role: by decreasing the distortion free energy of the DNA tract when it assumes the nucleosomal shape, and by increasing the energy cost which the corresponding DNA free form spends to release a part

The Role of DNA Curvature and Flexibility in Nucleosome Stability

1299

Figure 2. Differences between experimental and theoretical (elastic) nucleosome-reconstitution free energy (continuous line) are reported versus the squared intrinsic effective curvatures, hAo2 f i (broken line), for a large set of synthetic and natural DNAs. DNA tracts are identi®ed by the pre®xes: SC (Shrader & Crothers, 1989, 1990); GW (Godde & Wolffe, 1996); W (Godde et al., 1996); Wd (Widlund et al., 1997); LW (Lowary & Widom, 1998); R (Rossetti et al., 1998); D (Dal CornoÁ et al., 1998).

Figure 3. Comparison between experimental (continuous line) and theoretical (broken line) nucleosome-reconstitution free energies for a large set of synthetic and natural DNAs (R ˆ 0.91). The DNAs are sorted according to increasing curvature which is expressed in terms of the intrinsic effective curvature hAo2 f i (dotted line). The experimental data (see Table 1) are related to the TG pentamer (SC TG*) (Shrader & Crothers, 1989, 1990) as a standard and are identi®ed by the pre®xes SC (Shrader & Crothers, 1989, 1990); GW (Godde & Wolffe, 1996); W (Godde et al., 1996); Wd (Widlund et al., 1997); LW (Lowary & Widom, 1998); R (Rossetti et al., 1998); D (Dal CornoÁ et al., 1998).

1300

The Role of DNA Curvature and Flexibility in Nucleosome Stability

of the spine of water (and counterions) which is displaced by histone interactions. Other factors concerning chemical recognition arising from speci®c interactions between base-pairs and amino acid residues probably play a minor role which requires further investigation. Also the ¯exibility (bendability and twistability) appears to play a dual role: by decreasing the distortion energy necessary for nucleosome formation (equations (3) and (4)), and by increasing the entropy difference between the ¯exible free form and the ®nal rigid nucleosomal structure (equation (12)). In all the cases investigated, the entropy contribution appears to be the most important. Furthermore, it is important to note that the DNAs investigated have different length, which obviously increases the number of virtual positions and therefore the histone af®nity in competitive nucleosome reconstitution. It is noteworthy in spite of the non-uniform distribution of curvature and twist along the sequence which characterizes the nucleosome crystal structure (Luger et al. 1997), the use of their average values is adequate to obtain a satisfactorily ®rst order evaluation of nucleosome stability. Finally, it is interesting that a general feature of curved DNAs is the recurrence of repeated AA sequences in phase with the double helix periodicity, faced in the bending direction of the free form, as well as toward the histone core in the nucleosome (Drew & Travers, 1985). The presence of A
T base-pair adds further stability to the spine of water as ®rst shown by X-ray crystallographic studies (Drew & Dickerson, 1981) as well as to binding of counterions (Shui et al., 1998). A signi®cant part of such water molecules (and counterions) is displaced by the histone minor groove binding, thus increasing the energy cost of nucleosome formation. Therefore AA stretches appear to control the equilibrium in stabilizing and limiting the nucleosome stability. These considerations raise the interesting possibility that in addition to elastic and conformational properties of DNA, hydration effects may signi®cantly contribute to selective nucleic acid recognition processes.

Acknowledgments This research was supported by CNR ``Progetto Strategico Biologia Strutturale'' and Murst Co®n 40% Biologia Strutturale. The computer program which allows the evaluation of the nucleosome reconstitution free energy from the sequence can be obtained from the corresponding author.

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Edited by T. Richmond (Received 28 September 1998; received in revised form 21 January 1999; accepted 21 January 1999)