In the top panels, we compare different physical properties for yeast (red) and drosophila (blue) chromosomes at a nucleosomal resolution of 200 <i>bp</i> (reference model).

<p>In the bottom panel, we compare the reference model (Φ₀ = 0.043) with one possible coarse-grained model (<i>CG</i> = 10 kbp, Φ = 0.97) for the drosophila case. (a,d) Individual MSD <i>g</i>₁(<i>t</i>) (top curves), and center of mass MSD <i>g</i>₃(<i>t</i>) (bottom curves) as a function of time <i>t</i>. (b,e) The average physical squared distance 〈<i>R</i>²(<i>s</i>)〉 between any two monomers as a function of their linear distance <i>s</i> along the chain (given in <i>bp</i>). (c,f) Average contact probability <i>P</i>_<i>c</i>(<i>s</i>) as a function of <i>s</i>. A contact between any two monomers is defined if the 3D distance is less than a threshold <i>d</i>_<i>c</i> (with <i>d</i>_<i>c</i> = 55 <i>nm</i> in (c) and <i>d</i>_<i>c</i> = 163 <i>nm</i> in (f)). In (e,f), averages were computed over the same real time window (100 <i>sec</i> − 30 <i>min</i>). The error bars in (a, b, c) were computed as the standard deviation of the mean. Error bars in (a) are of the similar size of the symbols. For the yeast case, we fix <i>L</i>/<i>L</i>_<i>e</i> = 0.8, <i>ρ</i> = 0.005<i>bp</i>/<i>nm</i>³, and for drosophila, <i>L</i>/<i>L</i>_<i>e</i> = 70, <i>ρ</i> = 0.009<i>bp</i>/<i>nm</i>³ (see section ‘A reference model for chromosome’).</p

Comparison of physical properties and their time evolution for two different coarse-grainings (<i>CG</i> = 5, 10 kbp) at a fixed Kuhn size of <i>N</i>_<i>k</i> = 23 kbp (top panels) or for two different Kuhn sizes (<i>N</i>_<i>k</i> = 29, 44 kbp) at a fixed coarse-graining of CG = 10 kbp (bottom panels) for the drosophila case (<i>L</i>/<i>L</i>_<i>e</i> = 70, <i>ρ</i> = 0.009<i>bp</i>/<i>nm</i>³).

<p>(a,d) Average MSDs as a function of time in <i>sec</i>, calculated from the trajectory of 10⁷ Monte Carlo steps. Time evolution of 〈<i>R</i>²(<i>s</i>)〉 (b,e) and <i>P</i>_<i>c</i>(<i>s</i>) (c,f) for different coarse-grainings (b,c) and Kuhn sizes (e,f).</p

Dynamics of interactions.

<p>(a) Predicted contact maps (<i>E</i>_<i>i</i> = −0.1 <i>kT</i>) for the region located between 15.5 and 20.5 Mbp of chromosome 3R as a function of time along the cell cycle. Same legend as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006159#pcbi.1006159.g005" target="_blank">Fig 5c</a>. (b) Time evolution of the ratio between <i>P</i>_<i>intra</i> and <i>P</i>_<i>c</i> (increasing curves) and of the ratio between <i>P</i>_<i>inter</i> and <i>P</i>_<i>c</i> (decreasing curves) averaged over genomic distances between 10 and 100 kbp, between 100 kbp and 1 Mbp and between 1 and 10 Mbp. (c) Example of the time evolution of distance between two loci in early times. The inset is the full trajectory along the cell cycle. The red dashed line represents the cut-off distance we choose to define that the two loci are in “contact” or not. From each trajectory, we define one value for the time of first encounter <i>τ</i>_<i>first</i> and several values for the contact time <i>τ</i>_<i>c</i> and the search time <i>τ</i>_<i>s</i>. (d) Probability distribution functions (p.d.f) of <i>τ</i>_<i>first</i> (left), <i>τ</i>_<i>c</i> (center) and <i>τ</i>_<i>s</i> (right) for pairs with the same (blue) or different (orange) epigenomic state separated by different genomic distance: <i>s</i> = 400 kbp (squares), 3 Mbp (circles) or 12 Mbp (triangles).</p

Simulation parameters at different coarse-grainings for a semi-flexible, self-avoiding polymer with <i>L</i>/<i>L</i>_<i>e</i> = 70 and <i>ρ</i> = 0.009 <i>bp</i>/<i>nm</i>³ (drosophila case).

<p>Lattice volumic fraction Φ, Kuhn size <i>N</i>_<i>k</i> ≡ <i>νl</i>_<i>k</i>/<i>b</i> (in kbp), bond length of the polymer <i>b</i> (in <i>nm</i>) and Kuhn length <i>l</i>_<i>k</i> (in <i>nm</i>) at different coarse-grainings (CG) of <i>ν</i> = 0.2, 2, 5, and 10 kbp. Each fifth subcolumn represents the time in <i>msec</i> equivalent to one Monte-Carlo steps (MCS). Similar tables for the yeast and mammalian cases are given in the supplementary text.</p

Comparison between experimental and predicted data.

<p>(a) Experimental Hi-C map for a 10 Mbp region of chromosome 3R. Corresponding epigenome is shown on top. (b) Average experimental contact frequency as a function of the genomic distance <i>s</i> between any pair of monomers (pink), between pairs of monomers having the same (orange) or different (cyan) epigenomic state. Grey lines represent scaling laws. (c, d) Predicted (<i>E</i>_<i>i</i> = −0.1 <i>kT</i>) vs experimental contact maps for a 10 Mbp and a 2 Mbp region. Predicted data were multiplied by a factor 2500 to adjust scale with experiments.</p

How epigenome drives chromatin folding and dynamics, insights from efficient coarse-grained models of chromosomes

<div><p>The 3D organization of chromosomes is crucial for regulating gene expression and cell function. Many experimental and polymer modeling efforts are dedicated to deciphering the mechanistic principles behind chromosome folding. Chromosomes are long and densely packed—topologically constrained—polymers. The main challenges are therefore to develop adequate models and simulation methods to investigate properly the multi spatio-temporal scales of such macromolecules. Here, we proposed a generic strategy to develop efficient coarse-grained models for self-avoiding polymers on a lattice. Accounting accurately for the polymer entanglement length and the volumic density, we show that our simulation scheme not only captures the steady-state structural and dynamical properties of the system but also tracks the same dynamics at different coarse-graining. This strategy allows a strong power-law gain in numerical efficiency and offers a systematic way to define reliable coarse-grained null models for chromosomes and to go beyond the current limitations by studying long chromosomes during an extended time period with good statistics. We use our formalism to investigate in details the time evolution of the 3D organization of chromosome 3R (20 Mbp) in drosophila during one cell cycle (20 hours). We show that a combination of our coarse-graining strategy with a one-parameter block copolymer model integrating epigenomic-driven interactions quantitatively reproduce experimental data at the chromosome-scale and predict that chromatin motion is very dynamic during the cell cycle.</p></div

CPU time (given in hours) required to simulate 30 <i>min</i> of real dynamics for the drosophila case on a 3.20 GHz processor, (a) as a function of coarse graining where Kuhn sizes are fixed at three different values and, (b) as a function of Kuhn size at three different coarse grainings.

<p>The reference model is represented by <i>N</i>_<i>k</i> = 1 kbp and <i>CG</i> = 0.2 kbp.</p

Schematic of a lattice polymer configuration on a 2D projection of a 3D fcc lattice.

<p>Solid line with beads represents the polymer chain, and the dotted lines represent the underlying lattice. Each lattice site is allowed to contain a maximum of two beads if and only if they are consecutive to each other along the chain. Semicircular arcs indicate doubly occupied lattice sites. Some of the allowed and forbidden moves are shown in green and red respectively.</p

Acidic pH-Triggered Release of Doxorubicin from Ligand-Decorated Polymeric Micelles Potentiates Efficacy against Cancer Cells

Current chemotherapeutic strategies against various intractable cancers are futile due to inefficient delivery, poor bioavailability, and inadequate accumulation of anticancer drugs in the diseased site with toxicity caused to the healthy neighboring cells. Drug delivery systems aiming to deliver effective therapeutic concentrations to the site of action have emerged as a promising approach to address the above-mentioned issues. Thus, as several receptors have been identified as being overexpressed on cancer cells including folate receptor (FR), where up to 100–300 times higher overexpression is shown in cancer cells compared to healthy cells, approximately 1–10 million receptor copies per cancer cell can be targeted by a folic acid (FA) ligand. Herein, we developed FA-decorated and doxorubicin-conjugated polymeric micelles of 30 nm size. The hydrophilic block comprises poly(ethylene glycol) units, and the hydrophobic block contains aspartic acid. Decoration of FA on the micelle surface induces ligand–receptor interaction, resulting in enhanced internalization into the cancer cell and inside the endolysosomal compartment. Under acidic pH, the micelle structure is disrupted and the hydrazone bond is cleaved, which covalently binds the doxorubicin with the hydrophobic backbone of the polymer and release the drug. We observed that the cellular uptake and nuclear colocalization of the targeted micelle are 2–4 fold higher than the control micelle at various incubation times in FR-overexpressed various cancer cell lines (KB, HeLa, and C6). These results indicate significant prospects for anticancer therapy as an effective and translational treatment strategy