Thermodynamical model of mixed aggregation of ligands with caffeine in aqueous solution. Part II

A statistical-thermodynamical model of mixed association in which one component's self-association is unlimited while the second component does not self-aggregate is described. The model was tested with 4',6-diamidino-2-phenyl-indole-dihydrochloride (DAPI) and ethidium bromide (EB) using light absorption spectroscopy and calorimetry. The system is controlled by two parameters, which represent self-aggregation 'neighborhood' association constant KCC and mixed 'neighborhood' association constant KAC. Calculated, using this model, KAC = 58.2 +/- 1 M-1, KAC = 64.6 +/- 2 M-1 for DAPI and EB, respectively, are in good agreement with known values of stacking interactions. The titration microcalorimetric measurement of DAPI-CAF interaction delta H = -11.1 +/- 0.4 kcal/mol is also consistent with this type of reaction. The structures of the stacking complexes were also confirmed by semi-empirical molecular modeling in the presence of water. The data indicate that CAF forms stacking complexes with DAPI and EB, thus effectively lowering the concentration of the free ligands in the solution, and therefore, CAF can be used to modulate aromatic compound activity.     

Cis/trans heterogeneity of Gln30-Pro31 peptide bond determines whether a 79-residue fragment of staphylococcal nuclease self-associates

The self-association reaction of a 79-residue fragment of staphylococcal nuclease (SNase79) was studied by far-UV CD, size-exclusion chromatography, and heteronuclear multidimensional NMR spectroscopy. A large population of SNase79 is in self-associated state while a small population of SNase79 is essentially in a monomeric state. The sequence region Thr13-Val39 is responsible for association interface of SNase79. The trans-conformation of X-prolyl bond Gln30-Pro31 may make residues Tyr27-Gln30, serve as a folding nucleation site, and lead the segment Thr13-Val39 of SNase79 to adopt a native-like beta-sheet conformation, which results in the self-association of SNase79. The non-native conformation of the segment Thr13-Val39 of SNase79 associated with the cis-conformation of X-prolyl bond Gln30-Pro31 may preclude SNase79 from the soluble aggregates.     

Self-association of the plasma membrane-associated clathrin assembly protein AP-2

A self-association reaction involving the plasma membrane-associated clathrin assembly protein AP-2 has been detected by incubating AP-2 alone under solution conditions that would favor the assembly of complete coat structures if clathrin were present. Self-association was rapid, unaffected by nonionic detergents, readily reversible, and gave rise to sedimentable aggregates. Only the AP subtype AP-2 exhibited self-association: the structurally or functionally related assembly proteins AP-1 and AP-3 and unrelated proteins neither self-associated nor were incorporated into the AP-2 aggregate. AP-2 interactions responsible for self-association were of high affinity, with an apparent Kd of approximately 10(-8)M. By proteolytic dissection, the self-association domain was localized to the core of the molecule containing the intact 50- and 16-kDa polypeptides in association with the truncated 60-66-kDa moieties of the parent alpha/beta polypeptides. Self-association of the intact AP-2 molecule was pH-dependent, exhibiting an apparent pKa approximately 7.4. While it is unlikely that the large AP-2 aggregates formed in solution are themselves biologically relevant structures, the AP-2 interactions involved in their formation have properties consistent with their occurrence in intact cells and thus may be important in cellular functions of the plasma membrane-localized assembly protein.     

Self-association mode of a flavoenzyme D-amino acid oxidase from hog kidney. II. Stoichiometry of holoenzyme association and energetics of subunit association

The self-association pattern of D-amino acid oxidase holoenzyme in 0.1 M sodium pyrophosphate, pH 8.3, at 25 degrees C was examined by the low-angle laser light-scattering method. As to the results of nonlinear least-squares analysis of the apparent weight-average molecular weight (Mwapp) versus protein concentration (c) data, the following three models fitted equally well the data over the concentration range of 0.03-11.4 mg/ml: 1) the model of isodesmic indefinite self-association of the monomer where the dimerization constant differs from the isodesmic association constant, 2) the model which involves the dimerization of the monomer and isodesmic indefinite self-association of the dimer, and 3) the model which involves the trimerization of the monomer and isodesmic indefinite self-association of the trimer. In a more limited concentration range (0.3-11.4 mg/ml), a model of isodesmic indefinite self-association of the stable dimer where the dimer does not dissociate into the monomers cannot be excluded from the above three models. Measurements with the concentration range lowered to 0.03 mg/ml enabled us to exclude unequivocally the model involving such a stable dimer and to extrapolate the Mwapp data to the Mr of the monomer at infinite dilution as in the case of the apoenzyme. The observed sedimentation boundary profiles were qualitatively consistent with the idealized boundary profiles calculated with the model which involves the dimerization of the monomer and isodesmic indefinite self-association of the dimer, so this model is the most probable of the models examined. These results provide the first evidence that the association mode of the holoenzyme is different from that of the apoenzyme, i.e. isodesmic indefinite self-association of the monomer (Tojo, H., Horiike, K., Shiga, K., Nishina, Y., Watari, H., and Yamano, T. (1985) J. Biol. Chem. 260, 12607-12614). The overall linkage scheme, between binding of coenzyme FAD and subunit association, was considered, and the overall free energy change in each process in the scheme was calculated. The total stabilization energies of the intersubunit interaction in the holoenzyme relative to the apoenzyme were found to be -2.2 kcal/mol at the dimerization step and -0.5 kcal/mol at the step of the addition of the dimer to any 2i-mer (i = 1,2, ...).     

Self-association of some anthocyanins in neutral aqueous solution

A good contrast in optical properties caused by self-association was found between malvin and cyanin quinonoidal bases. Circular dichroism measurements of the pigments in neutral aqueous solutions show that molecules of the malvin quinonoidal base self-associate quickly and the conformational orientation of the aggregates is opposite to those formed by cyanin quinonoidal bases. Hypsochromism and hypochromism in the visible absorption also occurred on the formation of malvin aggregates. CD comparisons of malvin, hirsutin and 4′-O-methylmalvin suggest that a methoxyl group in the B-ring of the anthocyanidin strongly suppresses self-association. It is proposed that the driving forces for self-association are mainly hydrophobic interactions among the aromatic nuclei stacked parallel to each other which are surrounded by the hydrophilic glucose moieties in a suitable spatial arrangement. Furthermore, the glucose moiety at the 5-position rather than that at the 3-position plays an important role in the self-association of these anthocyanidin 3,5-diglucosides. Addition of sodium chloride promotes self-association and the greater stability of the anthocyanins in solution.     

Thermodynamics of protein self-association and unfolding. The case of apolipoprotein A-I

Protein self-association and protein unfolding are two temperature-dependent processes whose understanding is of utmost importance for the development of biological pharmaceuticals because protein association may stabilize or destabilize protein structure and function. Here we present new theoretical and experimental methods for analyzing the thermodynamics of self-association and unfolding. We used isothermal dilution calorimetry and analytical ultracentrifugation to measure protein self-association and introduced binding partition functions to analyze the cooperative association equilibria. In a second type of experiment, we monitored thermal protein unfolding with differential scanning calorimetry and circular dichroism spectroscopy and used the Zimm?Bragg theory to analyze the unfolding process. For α-helical proteins, the cooperative Zimm?Bragg theory appears to be a powerful alternative to the classical two-state model. As a model protein, we chose highly purified human recombinant apolipoprotein A-I. Self-association of Apo A-I showed a maximum at 21 °C with an association constant Ka of 5.6 × 10(5) M(?1), a cooperativity parameter σ of 0.003, and a maximal association number n of 8. The association enthalpy was linearly dependent on temperature and changed from endothermic at low temperatures to exothermic above 21 °C with a molar heat capacity ΔC(p)° of ?2.76 kJ mol(?1) K(?1). Above 45 °C, the association could no longer be measured because of the onset of unfolding. Unfolding occurred between 45 and 65 °C and was reversible and independent of protein concentration up to 160 μM. The midpoint of unfolding (T(0)) as measured by DSC was 52?53 °C; the enthalpy of unfolding (ΔH(N)(U)) was 420 kJ/mol. The molar heat capacity (Δ(N)(U)C(p)) increased by 5.0 ± 0.5 kJ mol(?1) K(?1) upon unfolding corresponding to a loss of 80?85 helical segments, which was confirmed by circular dichroism spectroscopy. Unfolding was highly cooperative with a nucleation parameter σ of 4.4 × 10(?5).     

The self-association of human spectrin at high concentration.

The self-association of purified human spectrin has been studied at sedimentation equilibrium over a wide range of concentration (0-20 g/L) at 30 degrees C and pH 7.5. Coincidence of apparent weight average molecular weight and omega (r) plots as a function of total spectrin concentration indicated that equilibrium was attained and that no significant concentration of solute was incapable of participating in the self-association reaction. Under these conditions, no significant dissociation of the heterodimer to component polypeptide chains could be detected. The behavior of spectrin between 0 and 20 g/L can be described reasonably well by a cooperative isodesmic model, in which the protomer for association is the alpha beta heterodimer. With this model, the equilibrium constant for the heterodimer-tetramer step, K24, is 2 x 10(6) M-1, and K(iso), the equilibrium constant describing all other steps, is approximately 0.2 x 10(6) M-1. The returned value of the second virial coefficient for this model, 1.0 x 10(-7) L mol g-2, is consistent with the lower limit of values calculated for the heterodimer from the charge and Stokes radius of spectrin. On the other hand, the attenuated indefinite association model fails to describe the self-association of spectrin adequately over the range 0-20 g/L. Systematic decreases in the estimates of the second virial coefficient and the equilibrium constants for association beyond the tetramer suggest that the assumption of a single value of the second virial coefficient may not be appropriate for spectrin, and that non-ideality would best be taken into account by consideration of the detailed solution composition.     

Light-scattering studies of the alpha-ketoglutarate dehydrogenase complex from escherichia coli. I. Characterization of the self-association of the complex

The self-association of Escherichia coli alpha-ketoglutarate dehydrogenase complex (KGDC) purified by a column Chromatographic technique, was characterized by light-scattering photometry. The complex adopts a solution conformation somewhat larger than that observed in the electron microscope. The evidence suggests a nonideal indefinite self-association model for KGDC in KCl, phosphate buffer. The KGDC monomer has a molecular charge of about -3 x 10(2) at neutral pH. The self-association is promoted by increasing KCl concentrations, pH (in the range from 6.3 to 7.4) and temperature (from 20 to 30 degrees C). The effects of pH changes suggest a release of protons during the self-association and a minor 'preferential' interaction of phosphate ions. For the association of one monomer to the aggregate at neutral pH and 25 degrees C. DeltaG degrees = -7.8 kcal mol(-1). DeltaH degrees = 24 kcal mol(-1) and DeltaS degrees = 1.1 x 10(2) cal mol(-1) K(-1). These data indicate that hydrophobic interactions drive the association. Thermodynamically, the self-association of KGDC is a complex phenomenon and may serve to stabilize the enzyme complex in solution.     

Hetero-association of caffeine and aromatic drugs and their competitive binding with a DNA oligomer

NMR spectroscopy has been used to elucidate the molecular basis of the action of caffeine (CAF) on the complexation with DNA of mutagens such as ethidium bromide, propidium iodide, proflavine and acridine orange, and anticancer drugs such as actinomycin D and daunomycin. The hetero-association of CAF and each of the aromatic ligands in 0.1 mol L(-1) phosphate buffer (pD=7.1) has been investigated as a function of concentration and temperature by 500 MHz 1H NMR spectroscopy and analysed in terms of a statistical-thermodynamic model, in which molecules form indefinite aggregates for both self-association and hetero-association. The analysis leads to determination of the equilibrium constants of hetero-association and to the values of the limiting chemical shifts of the heteroassociation of CAF with each of the aromatic molecules. The hetero-association constants between CAF and each of the aromatic drugs/dyes are found to be intermediate in magnitude between those for self-association of CAF and the corresponding drug/dye. The most probable structures of the 1:1 CAF + ligand hetero-association complexes have been determined from the calculated values of the induced limiting chemical shifts of the drug protons. Knowledge of the equilibrium constants for self-association of CAF and the aromatic ligands, for their hetero-association and their complexation with a DNA fragment, the deoxytetranucleotide 5'-d(TpGpCpA), enabled the relative content of each of the CAF-ligand and CAF-ligand-d(TGCA) complexes to be calculated as a function of CAF concentration in mixed solutions. It is concluded that, on addition of CAF to the solution, the decrease in binding of drug or mutagen with DNA is due both to competition for the binding sites by CAF and the aromatic molecules, and to formation of CAF-ligand hetero-association complexes in the mixed solution; the relative importance of each process depends on the drug or mutagen being considered.     

Association of Inosine and Cytidine

A rigorous theory for the analysis of an associating system involving two different monomer units, which may also undergo self-association, has been developed. In the present paper the application of the theory to actual data is demonstrated for the first time. The model system chosen is the interaction of inosine with cytidine, both of which self-associate strongly. Application of the theory indicates that inosine associates with cytidine and that the association constant is of a similar order of magnitude to that for the self-association of the monomers.     

Indefinite noncooperative self-association of chicken deoxy hemoglobin D

The minor tetrameric hemoglobin (Hb), Hb D, of chicken red blood cells self-associates upon deoxygenation. This self-association enhances the cooperativity of oxygen binding. The maximal Hill coefficient is greater than 4 at high Hb concentrations. Previous measurements at low Hb concentrations were consistent with a monomer-to-dimer equilibrium and an association constant of ～1.3-1.6 × 10(4) M(-1). Here, the Hb tetramer is considered as the monomer. However, new results indicate that the association extends beyond the dimer. We show by combination of Hb oligomer modeling and sedimentation velocity analyses that the data can be well described by an indefinite noncooperative or isodesmic association model. In this model, the deoxy Hb D associates noncooperatively to give a linear oligomeric chain with an equilibrium association constant of 1.42 × 10(4) M(-1) at 20°C for each step. The data are also well described by a monomer-dimer-tetramer equilibrium model with monomer-to-dimer and dimer-to-tetramer association constants of 1.87 and 1.03 × 10(4) M(-1) at 20°C, respectively. A hybrid recombinant Hb D was prepared with recombinant α(D)-globin and native β-globin to give a Hb D tetramer (α(2)(D)β(2)). This rHb D undergoes decreased deoxygenation-dependent self-association compared with the native Hb D. Residue glutamate 138 has previously been proposed to influence intertetramer interactions. Our results with recombinant Hb D show that Glu138 plays no role in deoxy Hb D intertetramer interactions.     

Self-association of sperm whale metmyoglobin

The solution behavior of sperm whale metmyoglobin in 0.15 I phosphate-chloride buffer, pH 7.2, has been examined by sedimentation equilibrium, frontal gel chromatography, and sedimentation velocity. Results obtained from all three studies are shown to be consistent with a self-association model in which dimerization of the myoglobin is governed by an association equilibrium constant of 0.068 liter/g (580 M-1) at 20 degrees C.     

Determinants of the higher order association of the restriction factor TRIM5alpha and other tripartite motif (TRIM) proteins

Many tripartite motif (TRIM) proteins self-associate, forming dimers and higher order complexes. For example, dimers of TRIM5α, a host factor that restricts retrovirus infection, assemble into higher order arrays on the surface of the viral capsid, resulting in an increase in avidity. Here we show that the higher order association of different TRIM proteins exhibits a wide range of efficiencies. Homologous association (self-association) was more efficient than the heterologous association of different TRIM proteins, indicating that specificity determinants of higher order self-association exist. To investigate the structural determinants of higher order self-association, we studied TRIM mutants and chimeras. These studies revealed the following: 1) the RING domain contributes to the efficiency of higher order self-association, which enhances the binding of TRIM5α to the human immunodeficiency virus (HIV-1) capsid; 2) the RING and B-box 2 domains work together as a homologous unit to promote higher order association of dimers; 3) dimerization is probably required for efficient higher order self-association; 4) the Linker 2 region contributes to higher order self-association, independently of effects of Linker 2 changes on TRIM dimerization; and 5) for efficiently self-associating TRIM proteins, the B30.2(SPRY) domain is not required for higher order self-association. These results support a model in which both ends of the core TRIM dimer (RING-B-box 2 at one end and Linker 2 at the other) contribute to the formation of higher order arrays.     

NMR determination of the hetero-association of phenanthridines with daunomycin and their competitive binding to a DNA oligomer

500 MHz (1)H NMR spectroscopy has been used to determine thermodynamic and structural information on the hetero-association of daunomycin (DAU) with the phenanthridine mutagenic dyes ethidium bromide (EB) and propidium iodide (PI). The NMR complexation data have been analysed by a statistical-thermodynamic model which takes into account indefinite association for both the self-association of the drugs and their hetero-association. The results have been used to estimate the effect of the side chains of the phenanthridines on the competitive binding between DAU and the mutagens with DNA. Knowledge of the equilibrium constants for self-association of the phenanthridines and DAU, their hetero-association and their complexation with a DNA fragment, the deoxytetranucleotide 5'-d(TpGpCpA), enabled the relative content of each of the EB-DAU, PI-DAU, EB-DAU-d(TGCA) and PI-DAU-d(TGCA) complexes to be calculated as a function of drug concentration in mixed solutions. The results provide some insight into the molecular basis of the action of combinations of biologically-active molecules. When intercalating drugs are used in combination, it is found that the decrease in binding of drug or mutagen with DNA is due both to formation of drug-mutagen hetero-association complexes in the mixed solution and to competition for the binding sites by the aromatic molecules; the relative importance of each process depends on the molecular properties of the drug or mutagen molecules being considered. Thus, the longer branched side chain of PI and the electrostatic contribution of the extra positive charge of the molecule compared with the ethyl group of EB results in lower affinity for self-association of PI molecules and their hetero-association with DAU, but increases the degree of binding of PI with DNA.     

Self-aggregation of surfactant protein A

Environmental factors of physiological relevance such as pH, calcium, ionic strength, and temperature can affect the state of self-aggregation of surfactant protein A (SP-A). We have studied the secondary structure of different SP-A aggregates and analyzed their fluorescence characteristics. (a) We found that self-aggregation of SP-A can be Ca(2+)-dependent. The concentration of Ca(2+) needed for half-maximal self-association (K(a)(Ca)()2+) depended on the presence of salts. Thus, at low ionic strength, K(a)(Ca)()2+ was 2.3 mM, whereas at physiological ionic strength, K(a)(Ca)()2+ was 2.35 microM. Circular dichroism and fluorescence measurements of Ca(2+)-dependent SP-A aggregates indicated that those protein aggregates formed in the absence of NaCl are structurally different from those formed in its presence. (b) We found that self-aggregation of SP-A can be pH-dependent. Self-aggregation of SP-A induced by H(+) was highly influenced by the presence of salts, which reduced the extent of self-association of the protein. The presence of both salts and Ca(2+) attenuated even more the effects of acidic media on SP-A self-aggregation. (c) We found that self-aggregation of SP-A can be temperature-dependent. At 20 degrees C, SP-A underwent self-aggregation at physiological but not at low ionic strength, in the presence of EDTA. All of these aggregates were dissociated by either adding EDTA (a), increasing the pH to neutral pH (b), or increasing the temperature to 37 degrees C (c). Dissociation of Ca(2+)-induced protein aggregates at low ionic strength was accompanied by an irreversible loss of both SP-A secondary structure and SP-A-dependent lipid aggregation properties. On the other hand, temperature-dependent experiments indicated that a structurally intact collagen-like domain was required for either Ca(2+)- or Ca(2+)/Na(+)-induced SP-A self-aggregation but not for H(+)-induced protein aggregation.     

Self-association of collagen triple helic peptides into higher order structures

Interest in self-association of peptides and proteins is motivated by an interest in the mechanism of physiologically higher order assembly of proteins such as collagen as well as the mechanism of pathological aggregation such as beta-amyloid formation. The triple helical form of (Pro-Hyp-Gly)(10), a peptide that has proved a useful model for molecular features of collagen, was found to self-associate, and its association properties are reported here. Turbidity experiments indicate that the triple helical peptide self-assembles at neutral pH via a nucleation-growth mechanism, with a critical concentration near 1 mM. The associated form is more stable than individual molecules by about 25 degrees C, and the association is reversible. The rate of self-association increases with temperature, supporting an entropically favored process. After self-association, (Pro-Hyp-Gly)(10) forms branched filamentous structures, in contrast with the highly ordered axially periodic structure of collagen fibrils. Yet a number of characteristics of triple helix assembly for the peptide resemble those of collagen fibril formation. These include promotion of fibril formation by neutral pH and increasing temperature; inhibition by sugars; and a requirement for hydroxyproline. It is suggested that these similar features for peptide and collagen self-association are based on common lateral underlying interactions between triple helical molecules mediated by hydrogen-bonded hydration networks involving hydroxyproline.     

Self-association mode of a flavoenzyme D-amino acid oxidase from hog kidney. I. Analysis of apparent weight-average molecular weight data for the apoenzyme in terms of models

The self-association of D-amino acid oxidase apoenzyme in 0.1 M sodium pyrophosphate, pH 8.3, at 25 degrees C was studied by low-angle laser light scattering. The concentration (c) dependence of the apparent weight-average molecular weight (Mwapp) was determined over a wide concentration range of 0.04 to 6.1 mg/ml. The extrapolated Mwapp value, to zero enzyme concentration, corresponded to the Mr value of the monomer. The self-association mode of the apoenzyme was systematically explored with nonlinear least-squares analysis of the Mwapp versus c data. The simplest model that fitted the data well was a model of isodesmic indefinite self-association of the monomer with the isodesmic association constant of 0.467 +/- 0.034 liter/g. The monomer-dimer model proposed previously, but only in a low enzyme concentration range of less than 0.9 mg/ml at 5-20 degrees C (Henn, S. W., and Ackers, G. K. (1969) Biochemistry 8, 3829-3838), did not fit the Mwapp versus c data either in the limited low concentration range or in the whole concentration range examined at 25 degrees C. To test the validity of the chosen model, the observed sedimentation boundary profiles were compared with the idealized boundary profiles calculated for the better-fit models. The profile calculated with the model of the isodesmic indefinite self-association mechanism was qualitatively consistent with the observed ones. The utility of the nonlinear least-squares procedure for analyzing self-associating systems was demonstrated.     

Self-association process of a peptide in solution: from beta-sheet filaments to large embedded nanotubes

Lanreotide is a synthetic octapeptide used in the therapy against acromegaly. When mixed with pure water at 10% (w/w), Lanreotide (acetate salt) forms liquid crystalline and monodisperse nanotubes with a radius of 120 A. The molecular and supramolecular organization of these structures has been determined in a previous work as relying on the lateral association of 26 beta-sheet filaments made of peptide noncovalent dimers, the basic building blocks. The work presented here has been devoted to the corresponding self-association mechanisms, through the characterization of the Lanreotide structures formed in water, as a function of peptide (acetate salt) concentration (from 2% to 70% (w/w)) and temperature (from 15 degrees C to 70 degrees C). The corresponding states of water were also identified and quantified from the thermal behavior of water in the Lanreotide mixtures. At room temperature and below 3% (w/w) Lanreotide acetate in water, soluble aggregates were detected. From 3% to 20% (w/w) long individual and monodisperse nanotubes crystallized in a hexagonal lattice were evidenced. Their molecular and supramolecular organizations are identical to the ones characterized for the 10% (w/w) sample. Heating induces the dissolution of the nanotubes into soluble aggregates of the same structural characteristics as the room temperature ones. The solubilization temperature increases from 20 degrees C to 70 degrees C with the peptide concentration and reaches a plateau between 15% and 25% (w/w) in peptide. These aggregates are proposed to be the beta-sheet filaments that self-associate to build the walls of the nanotubes. Above 20% (w/w) of Lanreotide acetate in water, polydisperse embedded nanotubes are formed and the hexagonal lattice is lost. These embedded nanotubes exhibit the same molecular and supramolecular organizations as the individual monodisperse nanotubes formed at lower peptide concentration. The embedded nanotubes do not melt in the range of temperature studied indicating a higher thermodynamic stability than individual nanotubes. In parallel, the thermal behaviors of water in mixtures containing 2-80% (w/w) in peptide have been studied by differential scanning calorimetry, and three different types of water were characterized: 1), bulk water melting at 0 degrees C, 2), nonfreezing water, and 3), interfacial water melting below 0 degrees C. The domains of existence and coexistence of these different water states are related to the different Lanreotide supramolecular structures. All these results were compiled into a binary Lanreotide-water phase diagram and allowed to propose a self-association mechanism of Lanreotide filaments into monodisperse individual nanotubes and embedded nanotubes.     

Subunit associations among chromatin particles.

The self-association of oligonucleosomal chromatin particles in solution has been studied by light scattering and sedimentation. In the absence of magnesium ions no association is observed. In the presence of 70mM sodium or 2mM magnesium ions mono, di, tri and tetranucleosomes self-associate only if they contain bound histone 1. This association leads to the formation of compact aggregates and is continuous and non-cooperative. The relevance to higher order arrangements of nucleosomes is discussed.