A Thermodynamically-Consistent Non-Ideal Stochastic Hard-Sphere Fluid

A grid-free variant of the Direct Simulation Monte Carlo (DSMC) method is proposed, named the Isotropic DSMC (I-DSMC) method, that is suitable for simulating dense fluid flows at molecular scales. The I-DSMC algorithm eliminates all grid artifacts from the traditional DSMC algorithm; it is Galilean invariant and microscopically isotropic. The stochastic collision rules in I-DSMC are modified to yield a non-ideal structure factor that gives consistent compressibility, as first proposed in [Phys. Rev. Lett. 101:075902 (2008)]. The resulting Stochastic Hard Sphere Dynamics (SHSD) fluid is empirically shown to be thermodynamically identical to a deterministic Hamiltonian system of penetrable spheres interacting with a linear core pair potential, well-described by the hypernetted chain (HNC) approximation. We apply a stochastic Enskog kinetic theory for the SHSD fluid to obtain estimates for the transport coefficients that are in excellent agreement with particle simulations over a wide range of densities and collision rates. The fluctuating hydrodynamic behavior of the SHSD fluid is verified by comparing its dynamic structure factor against theory based on the Landau-Lifshitz Navier-Stokes equations. We also study the Brownian motion of a nano-particle suspended in an SHSD fluid and find a long-time power-law tail in its velocity autocorrelation function consistent with hydrodynamic theory and molecular dynamics calculations.Comment: 30 pages, revision adding some clarifications and a new figure. See also arXiv:0803.035

Stochastic Hard-Sphere Dynamics for Hydrodynamics of Non-Ideal Fluids

A novel stochastic fluid model is proposed with non-ideal structure factor consistent with compressibility, and adjustable transport coefficients. This Stochastic Hard Sphere Dynamics (SHSD) algorithm is a modification of the Direct Simulation Monte Carlo (DSMC) algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nano-particle suspended in a compressible solvent.Comment: This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (LLNL-JRNL-401745). To appear in Phys. Rev. Lett. 200

Epigenetic regulation of key developmental genes during early mouse development

In undifferentiated ES cells, many Polycomb Repressive Complex 2 (PRC2) target genes carry not only repressive H3K27me3 but are also enriched for conventional indicators of active chromatin including methylated H3K4. This so-called bivalent domain structure is thought to silence key developmental regulators while keeping them poised for future activation (or repression). Consistent with this hypothesis, bivalent genes assemble RNAP II preferentially phosphorylated on Serine 5 residues (poised RNAP II) and are transcribed at low levels. Productive expression is, however, prevented by the action of PRC1. Here, I have focused on the pre-implantation stage of mouse development to evaluate whether bivalent or poised chromatin signatures are indeed specific attributes of emerging pluripotent cells and investigate how the fate of key developmental genes is specified while the first lineage decision event (extra-embryonic lineage formation) occurs. Using blastocyst-derived stem cells and chromatin immunoprecipitation (ChIP), I have shown that lineage-inappropriate genes retain bivalent histone marking in extra-embryonic trophoblast stem (TS). However, and in contrast to ES cells, PRC1 (Ring1B) and poised RNAP II are not recruited to these loci in TS cells, indicating that gene priming is a unique hallmark of pluripotent cells in the early embryo. To investigate the intricate relationship between lineage identity and dynamic chromatin changes, I exploited the potential to convert ES cells into trophoblast-like stem (TSL) cells using a previously established artificial system dependent on doxycycline (Dox) induced repression of an Oct4 transgene. I demonstrated that Suv39h1-mediated H3K9me3 alongside DNA methylation is targeted to PRC2-bound bivalent, lineage-inappropriate genes upon trophectoderm lineage commitment. A change in chromatin conformation was observed upon differentiation of ES cells to TSL cells comparable to that seen in TS cells derived in the traditional manner from the trophectoderm (TE) of blastocyst stage embryos. Most importantly, I have begun to explore when epigenetic differences are specified, at the locus level, from 8-cell stage embryos onwards using newly designed Carrier ChIP technology. This data validated the occurrence of bivalent chromatin domains in vivo and further support the view that alternative strategies operate in the TE to silence key developmental regulators upon blastocyst lineage segregation