High-throughput sequencing reveals a simple model of nucleosome energetics

Abstract

We use genome-wide nucleosome maps to study sequence specificity of intrinsic histone-DNA interactions. In contrast with previous approaches, we employ an analogy between a classical one-dimensional fluid of finite-size particles in an arbitrary external potential and arrays of DNA-bound histone octamers. We derive an analytical solution to infer free energies of nucleosome formation directly from nucleosome occupancies measured in high-throughput experiments. The sequence-specific part of free energies is then captured by fitting them to a sum of energies assigned to individual nucleotide motifs. We have developed hierarchical models of increasing complexity and spatial resolution, establishing that nucleosome occupancies can be explained by systematic differences in mono-and dinucleotide content between nucleosomal and linker DNA sequences, with periodic dinucleotide distributions and longer sequence motifs playing a minor role. Furthermore, similar sequence signatures are exhibited by control experiments in which nucleosome-free genomic DNA is either sonicated or digested with micrococcal nuclease, making it possible that current predictions based on high-throughput nucleosomepositioning maps are biased by experimental artifacts.chromatin structure | histone-DNA interactions | nucleosome positioning | biophysical models I n eukaryotes, 75%-90% of genomic DNA is packaged into histone-DNA complexes called nucleosomes, with adjacent nucleosomes separated by stretches of linker DNA (1). Each nucleosome consists of 147 base pairs (bp) of DNA wrapped around a histone octamer in a left-handed superhelix (2). Arrays of nucleosomes fold into filamentous chromatin fibers which constitute building blocks for higher-order structures (3). DNA wrapped in a nucleosome is occluded from interacting with other DNA-binding proteins such as transcription factors, RNA polymerase, and DNA repair complexes (2). On the other hand, histone tail domains act as substrates for posttranslational modifications, providing binding sites for chromatin-associated proteins which facilitate transitions between active and silent chromatin states (4).Several distinct factors affect nucleosome positions in living cells. First of all, intrinsic histone-DNA interactions are sequence-specific: for example, polyðdA∶dTÞ tracts are well known to disfavor nucleosome formation (5, 6). In addition, nucleosome-depleted regions can be generated through the action of ATP-dependent chromatin remodeling enzymes (7) and histone acetylases (8). Finally, non-histone DNA-binding factors can alter nucleosome positions through binding their cognate sites and either displacing nucleosomes or hindering their subsequent formation (9, 10).The nucleosome code hypothesis states that DNA sequence is the primary determinant of nucleosome positions in living cells (11). This hypothesis is often contrasted with the idea of statistical positioning which asserts that most nucleosomes are ordered into regular arrays simply by steric exclusion (12, 13). In this view the nucleosoma...

A Biophysical Approach to Predicting Protein–DNA Binding Energetics

“…The zeroth species represents the background (no particle), with L 0 ¼ 1 and E 0 i ¼ 0 for all i. Likewise, we can compute the partial partition functions in the reverse direction (Segal et al 2006;Morozov et al 2009;Locke et al 2010),…”

“…The k-mer model: Another extension of the mononucleotide model adds energy contributions of longer DNA words, irrespective of where these words occur within the binding site (Locke et al 2010;Chereji and Morozov 2011). In this model, the binding energy is given by…”

“…We constrain the e j a parameters at each position j so that P a e j a ¼ 0; ensuring that the set of fitted parameters is nondegenerate (Locke et al 2010). With these constraints, the mononucleotide model has 3L þ 1 independent parameters.…”

“…For simplicity we set k B T ¼ 1; where k B is the Boltzmann constant and T is the temperature; note that chemical potentials are included implicitly into EðconfÞ: One can compute Z efficiently, using a recursive relation (Segal et al 2006;Morozov et al 2009;Locke et al 2010)…”

“…Under the assumption of thermodynamic equilibrium, these occupancies can be computed using efficient recursive techniques (Morozov et al 2009;Locke et al 2010) for an arbitrary protein-DNA interaction energy model. The parameters of the model that determine binding energies can then be fitted against the data.…”