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Journal of Biomolecular Structure and Dynamics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tbsd20

DNA-Bending on Ligand Binding; Change of DNA Persistence Length a

Holger Schü & Karl-Ernst Reinert

a

a

Institute of Microbiology and Experimental Therapy, Department of Biophysical Chemistry , Beutenbergstrasse 11, D-0-6900 , Jena , Germany Published online: 21 May 2012.

To cite this article: Holger Schü & Karl-Ernst Reinert (1991) DNA-Bending on Ligand Binding; Change of DNA Persistence Length, Journal of Biomolecular Structure and Dynamics, 9:2, 315-329, DOI: 10.1080/07391102.1991.10507915 To link to this article: http://dx.doi.org/10.1080/07391102.1991.10507915

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Journal of Biomolecular Structure & Dynamics, ISSN 0739-1102 Volume 9, Issue Number 2 (1991), '"Adenine Press (1991).

DNA-Bending on Ligand Binding; Change of DNA Persistence Length Downloaded by [University of Toronto Libraries] at 02:47 03 February 2015

Holger Schutz and Karl-Ernst Reinert Institute of Microbiology and Experimental Therapy Department of Biophysical Chemistry Beutenbergstrasse 11, D-0-6900 Jena Germany Abstract This paper simulates the helix-characteristic changes of apparent DNA persistence length caused by randomly distributed helix bends as induced, e.g., by DNA-bound ligand molecules. The parameters varied are the constant angle y of helix bending and the size a ofthe DNA drug binding site, but also the degree of DNA-ligand binding cooperativity and the helix-unwinding angle. If the size of the binding site is comparable with the helix pitch, the influence of phasing between helix bends and helix screw upon the apparent persistence length is obvious. In the accompanying paper experimental data are analyzed in terms of this theoretical background.

Introduction DNA interaction with biologically active ligands is often accompanied by DNA helix bending. This concerns protein-DNA systems of direct gene regulatory relevance (1), but also DNA interactions with many low molecular weight effectors like antibiotics, cancerostatics or dyes (2). The experimental analysis ofhelix bending is, besides that of helix elongation and helix stiffening, of interest for understanding sterochemistry and mechanism of interaction. Physical quantities being sensitive to DNA helix bending are measurable by means of hydrodynamic methods (3,1). An informative technique is advanced titration viscometry. This method permits us to determine, next to changes of DNA contour length L, also the change ofpersistence length a, both as a function of rbp• the ratio of ligand molecules bound per DNA base pair (bp). Details are given in the accompanying paper(2). For bending angles y~So, the change of persistence length is fairly sensitive to ligand-induced helix bending (4). It is the aim of this paper to present a theoretical basis for the helix-characteristic change of apparent persistence length with r due to ligand-binding induced helix bending for different constant interaction parameters. Sequence dependent effects are not directly treated in this report.

The mathematical procedure is essentially facilitated by the possibility to seperate the thermally driven flexibility, 1/a o, and the pure bending contribution 1/a which

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together constitute the total apparent DNA flexibility 1/a. It is Equation [1] below which enables us to restrict our calculations to the evaluation of the persistence length a of an isolong, originally straight and rigid helix, i.e. of a DNA helix with straight elements only between two adjacent bends. The main results of this paper, the change with rofthe apparent flexibility contribution from helix bending, 1/a(r), will be presented for different values of the size of the binding site, a, and of the bending angle y. Additionally, the influence of a potential cooperativity of ligand binding 1/cr, and also the ligand-binding mediated helix unwinding are studied. For non-cooperative DNA-ligand interaction and small a values, the 1/a(r) curves are almost symmetrical (4). Individual peculiarities are pointed out by the quantitative treatment. An elementary relation between the initial change of DNA persistence length and helix bending angle (4) is now corroborated, but restricted to non-and anti -cooperative interaction. Approaches for the influence oflocal structural changes of DNA molecules on the chain dimensions have been treated in serveral papers (6-10). Schellman, e.g., dealt with DNA bending on non-cooperative ligand binding (10). Our calculus differs from his approach (and the other ones) by considering the helix-directed change of the azimuthal bending direction. For small r values both approaches coincide. A preliminary short communication of our procedure, with results for a= 1 and a= 2 on non-cooperative DNA-ligand interaction only, has been presented previously (5). In the accompanying paper, experimental viscosity data from literature for serveral DNA-ligand systems are quantitively analyzed in terms ofchanges in both DNA persistence length and DNA contour length. The peculiarities of the bending contribution to the changes of the DNA persistence length enables us to seperate stiffening and bending increments and to estimate the helix bending angle y, at least for small r values.

TheoreticalhfethodS Additivity of Contributions to DNA Flexibility DNA flexibility is proportional to the reciprocal of persistence length, 1/a. ashall be the persistence length of the worm-like helix provided with the structural modifications ofinterest, here the ligand-binding induced local helix bends, and a is the apparent persistence length of an isolong originally straight and rigid helix equipped only with the identical ligand-binding mediated helix-bending pattern. The persistence length of the undisturbed worm-like chain molecule in solution is a o (11). Different contributions to polymer flexibility of worm-like chain molecules were shown to be additive and we have to write (4)

1/a = 1/ao + 1/a

[1]

An equation of type [1] was already derived by Birshtein for the contributions from both rotational isomerism and torsional oscillations to chain flexibility (12). In

Change of Persistence Length on DNA Bending

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order to calculate the apparent persistence length a for a model of a structurally modified DNA molecule, only the apparent persistence length a of a chain with straight elements has to be evaluated by a comparably simple procedure. The quantity of experimental relevance is Lla/a o we arrive at 0

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Llakn/a

= -

=Llakn/a o

ao/a l+(a o/a)

=

(a -a

0 )

Equation [I]

[2)

For very small DNA conformational changes with -ao /a~ 1 (or a~ao) Equation [2] reduces to [2a) Our results below are presented as the dependences ofh/a on r. his the length of the DNA monomer unit (forB-DNA, h = 0.334nm), i.e., a is presented in units of the monomer length. As to be shown below, 1/a is proportional to/! The Mathematical Model

Our DNA molecule model is an orginally straight helix composed of identical elements (monomers). Between adjacent elements a sharp bend (kink) may occur or not. This event shall be correlated with the binding of a helix bending ligand. The detailed mathematical treatment is given in the Appendix. Here we outline the path. The calculus is based on the definition by Kratky and Porod of the persistence length for a worm-like chain (13). Accordingly, a is the finite value of the linear average for the projections of the end-to-end vectors of all possible conformations of the infinitely long model helix onto the direction of the first element. This projection is calculated by successive back transformations, namely of the (n + 1)st element onto the direction of the n-th element, etc. etc .. The respective 3-by3 transformation matrix strongly depends on whether or not there is a kink between the n-th and the (n+ l)st element. For averaging we need the probability for a given kink pattern. Considering a potential nearest-neighbour interaction of the bendinducing ligands (the cooperativity or nucleation parameter o being nonequal to unity) and sizes of the binding site a> 1, we have to describe those probabilities by a first-order Markoff chain (for definition of o see the Appendix). The probabilities and conditional probabilities of this Markoff chain are calculated by means of a model of cooperative binding. Finally, we reformulate the average of the power series of the transformation matrices (each series corresponds to a special kink pattern of the helix) as a power series of an "averaged" matrix. (This new matrix is a direct product of the transformation matrices and the matrix ofconditional probabilities.) The final power series [A20], the persistence length, has a finite sum [A22) for the limit of infinitely long helices.

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0

2

~=so

6

3

=,

0

0.5

ar =r /rmaiC

Figure 1: Insert: Helix-bending mediated contribution to apparent helix flexibility, h/ii, on non-cooperative binding ofligand molecules (a= 1), plotted as a function of r= r bp· ii is the apparent persistence length of a rigid helical rod equipped with the bending pattern of the original worm-like DNA molecule, and ii/h is the length of ii in units of one base pair's length. ah is the length of the binding site. The curves are labeled by their respective a value, and the helix bending angle is assumed to bey= go. For the main Figure, the abscissa is the degree of saturation, ar= r/r max• and the ordinate the quantity ah/ii. This normalization procedure does not change the local slope of all of these curves.

Results and Discussion Influence of the Binding Site Size a The insert of Figure 1 reveals the simulated contribution to apparent DNA flexibility, 1/a, due to non-cooperative interaction of the orginally straight helical DNA model with helix-bending ligands. What has been plotted is the quantity 103h/a as a function of r= rbp· For all different values of the parameter a treated here, we chose the same DNA bending angle ofy=8°, arbitrarily localized between the first two base pairs of the ligand-covered binding site. The size of the binding site, a, is measured in units ofbase pairs. It is the character of Equations [2,2a] which recommends a negative direction of the ordinate for positive values of h/a. For comparison of the variations in the details of the curve, the main partofFigure 1 displays the normalized plot ah/a vs. ar. The numerical data are given in Table I. What is typical for all of these curves with a 1 and ar near to unity, the h/avaluesdifferfromthoseat(l-ar)(16).Alsoarpositionandamountoftheah/amaxima vary with a (Figure 1; cf. also Figure 5, below).

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Note also that the amplitude of the helix-bending mediated drop of a o /a and !1ada o in the insert ofFigure 1 increases with decreasing a. A smaller size ofthe binding site enables a higher number of ligand molecules to induce helix bends.

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Influence of the Bending Angle y To elucidate the dependence of the 1/a(r) curves in Figure 1 on the magnitude of the bending angle y, respective functions have been calculated for several values ofboth y and a. The data confirm the proportionallity of 1/a(r) to l. The accuracy ofthis relation upto25° or48°,proved to be better than -l%or -4% atar=0.20 and better than + 1% or 2 to 5% at ar=0.5, respectively (results not shown here). This fact evidently enables us to evaluate 1/a(r;a) curves, from the data of Table I or the 1/a plots of the Figures, for any bending angle y~ 20 .. .50° according to the relation

[3] m shall be the (negative) initial slope of the bending increment daJa!a o and, according to Equation [2a], also of -a o /a(r):

We corroborate also the relation suggested recently (4):

[4] Equation [4] is a basis for the determination of the angle y ofligand-binding induced DNA helix-bending at low r-values on non-cooperative DNA-drug interaction. Due to the quadratic relation between m andy, the relative error of an experimentally determined y value will be relatively small. On strong cooperative DNA-ligand interaction, see the next section. For very small a o /a values we have dakn/a o ~ -a o /a (Equation [2a]). With increasing y the general character of the dakn/a (r) curves, compared to the 1/a(r) functions, continually alters (Equation [2], Figure 2). 0

Influence of Cooperativity and Anti-cooperativity Some helix-bending ligands as, e.g., the anthracycline antibiotic aclacinomycin A, exhibit a significant cooperativity (cr 1, cooperativity by a< 1 (cf. Appendix). Strong deviations of a from unity cause remarkable alterations of the apparent helix flexibility, 1/a(r) (Figures 3a,b ). For strong anti-cooperative ligand binding with cr~ 1 an additional relative minimum of h/a(r) appears at

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Change of Persistence Length on DNA Bending 01

02

0.3

0.2

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0.3 0.4

-0.4

0.5

0.6

-0.6

0.7 0.8

0.8

0.9

---t-tO 1.1

1.2 Figure 2: Comparison of the r dependence of a o/a with that of ~kn/a o. For all curves a= 3. The values ofy are noted in the Figure. Contrary to a 0 /a, ~akn/ao is not proportional to l at y; 5o.

Figure 3: Influence of cooperativity (cr< 1) and anti-cooperativity(cr> 1) ofDNA-ligand interaction on h/ a(r). The curves are labeled by the respective values of cr. For all curves the helix-bending angle is y=8°. (a) a= 1, (b) a= 5. (The cooperativity parameter of McGhee and vonHippel (26) is w= 1/cr.)

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ar= a/(a+ 1): In this case, the ligand molecule avoids to bind DNA base pairs adjacent to an occupied site and the effective size of the binding site seems to be enhanced by one monomer unit ( 18). The initial slope, of interest for y determination, is not modified, even on rather high anti-cooperativity.

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On cooperative DNA-ligand interaction (cr

DNA-bending on ligand binding; change of DNA persistence length.

This paper simulates the helix-characteristic changes of apparent DNA persistence length caused by randomly distributed helix bends as induced, e.g., ...
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