Statistical positioning from a biological perspective

An additional mechanism by which nucleosomes may be positioned has not explicitly been discussed so far. It is known as statistical positioning and is commonly attributed to Roger

Kornberg who suggested it in 1981 [52]. Kornberg proposed that the majority of nucleosomes are found at random positions under the condition that they neither overlap with each other nor with other DNA bound molecules. This leads to a phasing of nucleosomes relative to each other, i.e., to the generation of arrays of nucleosomes. A boundary on the DNA, such as a sequence-specific binding protein, ‘anchors’ such an array. Consequently, phasing relative to the boundary is observed, which, on average, appears as a non-random organization of nucleosomes. This ordering of nucleosomes extends over the range of several nucleosomes; for an illustration and qualitative discussion see Fig. 4.2. The concept of statistical posi- tioning was able to reconcile a number of experimental findings of the time, including the puzzling observation of varying nucleosome spacing in different cell types (see Refs. [52, 54] and therein).

A couple of years later, the idea behind statistical positioning was made quantitative by Kornberg and Stryer [54]. Using combinatorial arguments, the authors explicitly computed

the probability that a site on the DNA is bare, i.e., not occupied by a nucleosome, close to one or between two boundaries. Such a quantitative discussion of statistical positioning, rephrased in terms of a much older physical model, will follow in the next section. Here, I would like to concentrate on the qualitative aspects of statistical positioning and discuss related experiments.

To test the statistical positioning hypothesis qualitatively and locally, Fedor et al. charac- terized nucleosome arrays close to a regulatory region in an early study [31]. The authors altered the DNA sequence adjacent to the regulatory region. This had little effect on nucleo- some organization indicating that the regulatory region rather than the underlying sequence was responsible for nucleosome positioning. Furthermore, the nucleosome arrays depended on the existence of a specific binding site within the regulatory region. Taken together, both observations are consistent with statistical positioning in proximity to the binding site, but not with positioning of nucleosomes by the underlying sequence.

Very recently, an innovative experiment tested statistical positioning on a small scale in vitro[82]. Milani et al.considered an approximately 600 bp long DNA fragment containing a

yeast gene. A model predicting nucleosome binding affinity based on sequence [140] revealed two nucleosome excluding regions at the end and a rather uniform region without strong pronucleosomal sequences in between. Milani et al. directly tested the statistical positioning scenario by loading either one or two nucleosomes onto the DNA fragment and determining positions of the nucleosomes using atomic force microscopy imaging. In the case of the mononucleosome construct, the nucleosome was preferentially found in the central region. In the case of the dinucleosome construct, two distinct peaks in nucleosome density were observable as expected for the predicted binding landscape with two excluding barriers at the gene’s ends. Since the in vivo nucleosome occupancy [61] has the same shape, the authors

argued that statistical positioning is responsible for the nucleosome organization in vivo.

What about the situation genome-wide? Are the majority of nucleosomes placed at random positions? Do the nucleosomes appear positioned only on average, due to a few boundaries distributed over the genome? A systematic variation of DNA sequence, as done by Fedor et al. [31] for one individual location, clearly is not applicable for testing this hypothesis genome-wide. Recognizing that the period and the decay of the oscillations depend on the average nucleosome density offers an alternative experimental test, at least for the situation

in vitro. One should vary the average nucleosome density on the genome and test whether the

spacing in the nucleosome arrays changes as expected. Kaplan et al. [47] and Zhang et al. [159] chose different nucleosome densities in their in vitro studies of nucleosome organization. A

comparison of both data sets could be the first step towards a systematic analysis of this kind. Due to the lack of systematic experimental tests and the limited practicability of changing nucleosome concentrations in vivo, the question of whether statistical positioning plays a

significant role in nucleosome organization has to be addressed indirectly with modeling. Obvious candidates for the boundaries inducing nucleosome arrays are the NFRs close to the 5’ end of genes discussed above. A number of studies focused on nucleosome organization around these NFRs and reported consistency with statistical positioning downstream of the 5’ NFRs [16,77,141]. These studies will be discussed in the context of our work in Sec.4.4.3. Having described statistical positioning and (above) the notion of a genomic code, the question arises of how both are related. At first sight, both concepts seem not to be compat- ible. A second thought, however, reveals that statistical positioning actually is one possible way for sequence to direct nucleosome positions in parts of the genome. In fact, statistical positioning is often considered to at least contributing to nucleosome organization. This also

4.4 Statistical positioning 59

Figure 4.3.: One realization of a gas of hard rods with particles at positionsx1, . . . , xN placed between

two boundary particles fixed at positionsx0 andxN+1, respectively.

holds for studies arguing that models or in vitro experiments describe the situation in vivo

well [47,140]. In conclusion, the question of whether a genomic code exists should therefore be refined: (1) Are nucleosomes mainly positioned one by one or, alternatively, for the most part organized in large arrays resulting from the presence of a few boundaries? (2) Are the individual positions and/or the boundaries mainly coded into the genome or are other factors than sequence more important?