Pulling chromatin apart: Unstacking or Unwrapping?
© Victor et al.; licensee BioMed Central Ltd. 2012
Received: 10 August 2012
Accepted: 15 November 2012
Published: 27 November 2012
Understanding the mechanical properties of chromatin is an essential step towards deciphering the physical rules of gene regulation. In the past ten years, many single molecule experiments have been carried out, and high resolution measurements of the chromatin fiber stiffness are now available. Simulations have been used in order to link those measurements with structural cues, but so far no clear agreement among different groups has been reached.
We revisit here some of the most precise experimental results obtained with carefully reconstituted fibers.
We show that the mechanical properties of the chromatin fiber can be quantitatively accounted for by the stiffness of the DNA molecule and the 3D structure of the chromatin fiber.
In the nucleus of eukaryotic cells, chromatin is constantly under mechanical stresses due to DNA transcription and replication. In order to better understand how nucleosomal arrays can deal with such stress, several groups have used optical and magnetic tweezers to probe the response of native or reconstituted arrays to stretch and torque. In most of these studies, the only experimental read out is the extension of the array, and modelling efforts are often needed to interpret these results in term of structures. Ten years of work have revealed essential features of the mechanical response of the chromatin fiber to external stress (for two recent reviews see [1, 2]). In one of the most recent, and certainly one of the most accurate study, Kruithof and colleagues used magnetic tweezers to probe the mechanical properties of reconstituted chromatin fibers under physiological ionic conditions at an unprecedented resolution . Their study revealed that a regular nucleosome array containing linker histones (LH) is a very soft structure (a soft spring) which can be easily stretched up to three times its resting length. They interpreted these results to support a model of the 30 nm fiber in which nucleosomes are stacked in a helical structure reminiscent of the solenoid model proposed by Finch and Klug decades ago . Theses new results were reinterpreted in two consecutive modelling studies, one of which agrees with their interpretation  whereas the other one does not . Here, we propose an alternative explanation for the Kruithof et al. results which is in very good quantitative agreement with their measurements. In a first part of this paper, we will interpret their results in the geometrical framework of the zig-zag model instead of the solenoidal model of chromatin. In a second part, we will see that this alternative explanation can quantitatively account for the fiber stiffness they measure.
Results and discussion
Kruithof et al. assume that the nucleosomes in the chromatin fiber are stacked in a one-start helix. This assumption is mainly based on the spring-like behaviour of the array until it reaches an extension of 150 nm (i.e., three times the resting length of their reconstituted fiber): they reason that this extension may correspond to a fully stretched column of nucleosomes stacked upon each other. When this column is further stretched, the response is characteristic of a disruption of some contacts stabilizing the structure; this disruption is interpreted as an unstacking of the nucleosomes. In the following discussion, we will argue that the assumption of nucleosome stacking is in contradiction with some of their findings.
First, in the most compact form of the nucleosomal array (with LH and Mg2+) they observe a compaction of 5 nucleosomes(nuc)/10 nm (that is 50 nm for 25 nucleosomes) compared to the actually measured compaction of 10 nuc/10 nm based on electron microscopy for the very same construct . They propose that this difference in compaction is due to the formation of an alternate structure in which the helix gyres are not interdigitated as proposed earlier for the 10 nuc/10 nm structure seen in electron microscopy . In this respect, the structure they propose closely matches the solenoid structure in which consecutive nucleosomes in the array are stacked on top of each other . In order to achieve this stacking, the 50 bp DNA linkers joining consecutive nucleosomes have to be dramatically bent. Such bending is usually expected to be achieved through the binding of LHs (in this case H1 or H5) onto the DNA linker. Unexpectedly, Kruithof and colleagues observe a very similar mechanical behaviour of nucleosomal arrays with and without LH when the pulling force is low. They conclude that the compact structure, with bent DNA linkers, can form in the absence of LHs and attribute this possibility to the huge nucleosome stacking interaction energy they estimate from the force–extension curves. Whether or not the stacking energy can override constraints of the persistence length of naked DNA remains to be seen.
Second, in order to stack nucleosomes in a helix that has both the compaction and the stiffness they measure, Kruithof and colleagues propose that the nucleosomes do not interact through their faces, as previously and repeatedly reported , but through their flexible tails. At the same time the author assume a conventional face-to-face stacking of the nucleosomes when the fiber is fully stretched into a column, in order to be able to match the size of the column. If the nature of stacking would change when pulling on the array (which seems unrealistic), one would not expect the linear force-extension dependence that has been reported. Of note, the linear force-extension dependence was the main reason for assuming nucleosome stacking in the first place .
Modelling the fiber extension using the two-angle chromatin fiber model
(ii) In the absence of LHs and in the presence of Mg2+, the angle α(and hence the array extension) will also depend on the applied force. At forces below 4 pN, α can vary from 60 o (corresponding to the crystal structure of the nucleosome) to 0 o with possible rupture of the weak contacts between DNA and the histones at the SHL 6.5 and -6.5 (in yellow and orange in Figure 2). At higher force (> 4 pN), the strong DNA/histone contacts at SHL 5.5 and -5.5 are progressively disrupted and α can decrease from 0 o to -90 o , leading to a dramatic extension of the array (in yellow and green in Figure 2).
(iii) In the absence of both LHs and Mg2+, i.e., when the electrostatic repulsion between the DNA linkers at the entry/exit site is high, α is already widely open even at low forces (green in Figure 2). In this case, the contour length of the fiber is longer than 500 nm, and, upon stretching, the array can be smoothly extended up to this length following a worm-like chain behaviour. Upon further force increase, the DNA/histone contacts at SHL -4.5 and 4.5 are eventually disrupted, resulting in further increase of the length up to 700 nm. Kruithof and colleagues propose that this extension is due to nucleosome unstacking. However, similar changes in extension were reported in the case of single nucleosomes and interpreted in terms of unwrapping of DNA from the octamer by the same authors [11, 12]. Other labs have also observed DNA unwrapping under low force conditions, both in the fiber context  and on individual nucleosomes . We believe that partial unwrapping of DNA in individual nucleosomes in the array is responsible for the observed stretching behaviour of the fiber.
The stiffness of the nucleosomal array can be explained by the DNA mechanical properties
Our calculations also confirm the three fold increase in stiffness measured for a NRL of 167 bp (see Figure 3B), which is essentially due to the rapid increase of the stretch modulus with the linker length reduction. The measured stiffness of the array (k=0.05pN/nm) is compatible with an αangle of about 30 o , suggesting that the fiber with shorter NRL has a more open conformation of the entry/exit linkers. Taken together, all these calculations strongly suggest that the mechanical properties of the fiber result from the mechanical properties of the DNA linkers only and not from nucleosome unstacking.
Extracting the unwrapping energy using our tunable spring model
are the free enthalpies of the two states. E0=F2(0)−F1(0) is the energy difference between the two states, or unwrapping energy.
In conclusion, all the data presented in the Kruithof et al. paper  can be quantitatively explained by the zig-zag model of fiber morphology. The very high resolution of the experimental data they achieved using their ingenious set up can be used together with the model proposed here to determine very accurately the physical properties of the DNA/histones interactions in chromatin.
The two angle model
To construct our 3D models of the chromatin fiber we used the two–angle model as defined on Figure 1. The 3D structures were created using Maple (http://www.maplesoft.com/). In the present analysis we only considered regular fibers.
Calculation of the fiber’s stiffness
All the details of the calculations used here can be found in . The relevant elastic constant here is the effective stretch modulus, since the nicked DNA in the construct is free to rotate. The stiffness, as measured by Kruithof and colleagues, is equal to the effective stretch modulus divided by the array length. The stiffness depends on both α and β. Since the β angle can change slightly due to the amount of supercoiling stored into the nucleosome, we were able only to provide a maximum and a minimum value for k for any given α(allowed values for k are represented by the grey area on Figure 3).
J.M. and J.Z. wish to acknowledge the organizers of the 2009 Albany’s conversation during which this work was initiated. The authors are also very grateful to J. Van Noort for stimulating discussions.
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