The influence of volume exclusion by chromatin on the time required to find specific DNA binding sites by diffusion.
ABSTRACT: Within the nuclei of eukaryotic cells, the density of chromatin is nonuniform. We study the influence of this nonuniform density, which we derive from microscopic images [Schermelleh L, et al. (2008) Science 320:1332-1336], on the diffusion of proteins within the nucleus, under the hypothesis that chromatin density is proportional to an effective potential that tends to exclude the diffusing protein from regions of high chromatin density. The constant of proportionality, which we call the volume exclusivity of chromatin, is a model parameter that we can tune to study the influence of such volume exclusivity on the random time required for a diffusing particle to find its target. We consider randomly chosen binding sites located in regions of low (20th-30th percentile) chromatin density, and we compute the median time to find such a binding site by a protein that enters the nucleus at a randomly chosen nuclear pore. As the volume exclusivity of chromatin increases from zero, we find that the median time needed to reach the target binding site at first decreases to a minimum, and then increases again as the volume exclusivity of chromatin increases further. Random permutation of the voxel values of chromatin density abolishes the minimum, thus demonstrating that the speedup seen with increasing volume exclusivity at low to moderate volume exclusivity is dependent upon the spatial structure of chromatin within the nucleus.
Project description:In this work, we examine how volume exclusion caused by regions of high chromatin density might influence the time required for proteins to find specific DNA binding sites. The spatial variation of chromatin density within mouse olfactory sensory neurons is determined from soft X-ray tomography reconstructions of five nuclei. We show that there is a division of the nuclear space into regions of low-density euchromatin and high-density heterochromatin. Volume exclusion experienced by a diffusing protein caused by this varying density of chromatin is modeled by a repulsive potential. The value of the potential at a given point in space is chosen to be proportional to the density of chromatin at that location. The constant of proportionality, called the volume exclusivity, provides a model parameter that determines the strength of volume exclusion. Numerical simulations demonstrate that the mean time for a protein to locate a binding site localized in euchromatin is minimized for a finite, nonzero volume exclusivity. For binding sites in heterochromatin, the mean time is minimized when the volume exclusivity is zero (the protein experiences no volume exclusion). An analytical theory is developed to explain these results. The theory suggests that for binding sites in euchromatin there is an optimal level of volume exclusivity that balances a reduction in the volume searched in finding the binding site, with the height of effective potential barriers the protein must cross during the search process.
Project description:The hallmarks of the normal heartbeat are both rapid onset of contraction and rapid relaxation as well as an inotropic response to both increased end-diastolic volume and increased heart rate. At the microscopic level, Ca(2+) plays a crucial role in normal cardiac contraction. This paper reviews the cycle of Ca(2+) fluxes during the normal heartbeat, which underlie the coupling between excitation and contraction and permit a highly synchronized action of cardiac sarcomeres. Length dependence of the response of the regulatory sarcomeric proteins mediates the Frank-Starling Law of the heart. However, Ca(2+) transport may go astray in heart disease such as in congestive heart failure, and both jeopardize systole and diastole and triggering arrhythmias. The interaction between weak and strong segments in nonuniform cardiac muscle allows partial preservation of force of contraction but may further lead to mechanoelectric feedback or reverse excitation-contraction coupling mediating an early diastolic Ca(2+) transient caused by the rapid force decrease during the relaxation phase. These rapid force changes in nonuniform muscle may cause arrhythmogenic Ca(2+) waves to propagate by the activation of neighboring sarcoplasmic reticulum by diffusing Ca(2+) ions.
Project description:Eukaryotic cells condense their genetic material in the nucleus in the form of chromatin, a macromolecular complex made of DNA and multiple proteins. The structure of chromatin is intimately connected to the regulation of all eukaryotic organisms, from amoebas to humans, but its organization remains largely unknown. The nucleosome repeat length (NRL) and the concentration of linker histones (?LH) are two structural parameters that vary among cell types and cell cycles; the NRL is the number of DNA basepairs wound around each nucleosome core plus the number of basepairs linking successive nucleosomes. Recent studies have found a linear empirical relationship between the variation of these two properties for different cells, but its underlying mechanism remains elusive. Here we apply our established mesoscale chromatin model to explore the mechanisms responsible for this relationship, by investigating chromatin fibers as a function of NRL and ?LH combinations. We find that a threshold of linker histone concentration triggers the compaction of chromatin into well-formed 30-nm fibers; this critical value increases linearly with NRL, except for long NRLs, where the fibers remain disorganized. Remarkably, the interaction patterns between core histone tails and chromatin elements are highly sensitive to the NRL and ?LH combination, suggesting a molecular mechanism that could have a key role in regulating the structural state of the fibers in the cell. An estimate of the minimized work and volume associated with storage of chromatin fibers in the nucleus further suggests factors that could spontaneously regulate the NRL as a function of linker histone concentration. Both the tail interaction map and DNA packing considerations support the empirical NRL/?LH relationship and offer a framework to interpret experiments for different chromatin conditions in the cell.
Project description:Signaling by surface receptors often relies on tethered reactions whereby an enzyme bound to the cytoplasmic tail of a receptor catalyzes reactions on substrates within reach. The overall length and stiffness of the receptor tail, the enzyme, and the substrate determine a biophysical parameter termed the molecular reach of the reaction. This parameter determines the probability that the receptor-tethered enzyme will contact the substrate in the volume proximal to the membrane when separated by different distances within the membrane plane. In this work, we develop particle-based stochastic reaction-diffusion models to study the interplay between molecular reach and diffusion. We find that increasing the molecular reach can increase reaction efficacy for slowly diffusing receptors, whereas for rapidly diffusing receptors, increasing molecular reach reduces reaction efficacy. In contrast, if reactions are forced to take place within the two-dimensional plasma membrane instead of the three-dimensional volume proximal to it or if molecules diffuse in three dimensions, increasing molecular reach increases reaction efficacy for all diffusivities. We show results in the context of immune checkpoint receptors (PD-1 dephosphorylating CD28), a standard opposing kinase-phosphatase reaction, and a minimal two-particle model. The work highlights the importance of the three-dimensional nature of many two-dimensional membrane-confined interactions, illustrating a role for molecular reach in controlling biochemical reactions.
Project description:How the nuclear lamina (NL) impacts on global chromatin architecture is poorly understood. Here, we show that NL disruption in Drosophila S2 cells leads to chromatin compaction and repositioning from the nuclear envelope. This increases the chromatin density in a fraction of topologically-associating domains (TADs) enriched in active chromatin and enhances interactions between active and inactive chromatin. Importantly, upon NL disruption the NL-associated TADs become more acetylated at histone H3 and less compact, while background transcription is derepressed. Two-colour FISH confirms that a TAD becomes less compact following its release from the NL. Finally, polymer simulations show that chromatin binding to the NL can per se compact attached TADs. Collectively, our findings demonstrate a dual function of the NL in shaping the 3D genome. Attachment of TADs to the NL makes them more condensed but decreases the overall chromatin density in the nucleus by stretching interphase chromosomes.
Project description:As a cell squeezes its nucleus through adjacent tissue, penetrates a basement membrane, or enters a small blood capillary, chromatin density and nuclear factors could in principle be physically perturbed. Here, in cancer cell migration through rigid micropores and in passive pulling into micropipettes, local compaction of chromatin is observed coincident with depletion of mobile factors. Heterochromatin/euchromatin was previously estimated from molecular mobility measurements to occupy a volume fraction f of roughly two-thirds of the nuclear volume, but based on the relative intensity of DNA and histones in several cancer cell lines drawn into narrow constrictions, f can easily increase locally to nearly 100%. By contrast, mobile proteins in the nucleus, including a dozen that function as DNA repair proteins (e.g., BRCA1, 53BP1) or nucleases (e.g., Cas9, FokI), are depleted within the constriction, approaching 0%. Such losses-compounded by the occasional rupture of the nuclear envelope-can have important functional consequences. Studies of a nuclease that targets a locus in chromosome-1 indeed show that constricted migration delays DNA damage.
Project description:Knowledge of the average density of the crust of a planet is important in determining its interior structure. The combination of high-resolution gravity and topography data has yielded a low density for the Moon's crust, yet for other terrestrial planets the resolution of the gravity field models has hampered reasonable estimates. By using well-chosen constraints derived from topography during gravity field model determination using satellite tracking data, we show that we can robustly and independently determine the average bulk crustal density directly from the tracking data, using the admittance between topography and imperfect gravity. We find a low average bulk crustal density for Mars, 2582 ± 209 kg m-3. This bulk crustal density is lower than that assumed until now. Densities for volcanic complexes are higher, consistent with earlier estimates, implying large lateral variations in crustal density. In addition, we find indications that the crustal density increases with depth.
Project description:During spermiogenesis in mammals and many other vertebrate classes, histone-containing nucleosomes are replaced by protamine toroids, which can repackage chromatin at a 10 to 20-fold higher density than in a typical somatic nucleus. However, recent evidence suggests that sperm of many species, including human and mouse retain a small compartment of nucleosomal chromatin, particularly near genes important for embryogenesis. As in mammals, spermiogenesis in the fruit fly, Drosophila melanogaster has also been shown to undergo a programmed substitution of nucleosomes with protamine-like proteins. Using chromatin immunoprecipitation (ChIP) and whole-genome tiling array hybridization (ChIP-chip), supported by immunocytochemical evidence, we show that in a manner analogous to nucleosomal chromatin retention in mammalian spermatozoa, distinct domains packaged by the canonical histones H2A, H2B, H3 and H4 are present in the fly sperm nucleus. We also find evidence for the retention of nucleosomes with specific histone H3 trimethylation marks characteristic of chromatin repression (H3K9me3, H3K27me3) and active transcription (H3K36me3). Raw and processed data from the experiments are available at GEO, accession GSE52165.
Project description:BACKGROUND:The 3-dimensional (3D) conformation of chromatin inside the nucleus is integral to a variety of nuclear processes including transcriptional regulation, DNA replication, and DNA damage repair. Aberrations in 3D chromatin conformation have been implicated in developmental abnormalities and cancer. Despite the importance of 3D chromatin conformation to cellular function and human health, little is known about how 3D chromatin conformation varies in the human population, or whether DNA sequence variation between individuals influences 3D chromatin conformation. RESULTS:To address these questions, we perform Hi-C on lymphoblastoid cell lines from 20 individuals. We identify thousands of regions across the genome where 3D chromatin conformation varies between individuals and find that this variation is often accompanied by variation in gene expression, histone modifications, and transcription factor binding. Moreover, we find that DNA sequence variation influences several features of 3D chromatin conformation including loop strength, contact insulation, contact directionality, and density of local cis contacts. We map hundreds of quantitative trait loci associated with 3D chromatin features and find evidence that some of these same variants are associated at modest levels with other molecular phenotypes as well as complex disease risk. CONCLUSION:Our results demonstrate that common DNA sequence variants can influence 3D chromatin conformation, pointing to a more pervasive role for 3D chromatin conformation in human phenotypic variation than previously recognized.
Project description:The underlying global organization of chromatin within the cell nucleus has been the focus of intense recent research. Hi-C methods have allowed for the detection of genome-wide chromatin interactions, revealing a complex large-scale organization where chromosomes tend to partition into megabase-sized "topological domains" of local chromatin interactions and intra-chromosomal contacts extends over much longer scales, in a cell-type and chromosome specific manner. Until recently, the distinct chromatin folding properties observed experimentally have been difficult to explain in a single conceptual framework. We reported that a simple polymer-physics model of chromatin, the strings and binders switch (SBS) model, succeeds in describing the full range of chromatin configurations observed in vivo. The SBS model simulates the interactions between randomly diffusing binding molecules and binding sites on a polymer chain. It explains how polymer architectural patterns can be established, how different stable conformations can be produced and how conformational changes can be reliably regulated by simple strategies, such as protein upregulation or epigenetic modifications, via fundamental thermodynamics mechanisms.