The temporal order of replication of mammalian chromosomes appears to be linked to their functional organization, but the process that establishes and modifies this order during cell differentiation remains largely unknown. Here, we studied how the replication of the Igh locus initiates, progresses, and terminates in bone marrow pro-B cells undergoing B cell commitment. We show that many aspects of DNA replication can be quantitatively explained by a mechanism involving the stochastic firing of origins (across the S phase and the Igh locus) and extensive variations in their firing rate (along the locus). The firing rate of origins shows a high degree of coordination across Igh domains that span tens to hundreds of kilobases, a phenomenon not observed in simple eukaryotes. Differences in domain sizes and firing rates determine the temporal order of replication. During B cell commitment, the expression of the B-cell-specific factor Pax5 sharply alters the temporal order of replication by modifying the rate of origin firing within various Igh domains (particularly those containing Pax5 binding sites). We propose that, within the Igh C H -3′RR domain, Pax5 is responsible for both establishing and maintaining high rates of origin firing, mostly by controlling events downstream of the assembly of pre-replication complexes.

The detection of linear polymers translocating through a nanoscopic pore is a promising idea for the development of new DNA analysis techniques. However, the physics of constrained macromolecules and the fluid that surrounds them at the nanoscopic scale is still not well understood. In fact, many theoretical models of polymer translocation neglect both excluded-volume and hydrodynamic effects. We use Molecular Dynamics simulations with explicit solvent to study the impact of hydrodynamic interactions on the translocation time of a polymer. The translocation time tau that we examine is the unbiased (no charge on the chain and no driving force) escape time of a polymer that is initially placed halfway through a pore perforated in a monolayer wall. In particular, we look at the effect of increasing the pore radius when only a small number of fluid particles can be located in the pore as the polymer undergoes translocation, and we compare our results to the theoretical predictions of Chuang et al. (Phys. Rev. E 65, 011802 (2001)). We observe that the scaling of the translocation time varies from tau approximately N 11/5 to tau approximately N 9/5 as the pore size increases (N is the number of monomers that goes up to 31 monomers). However, the scaling of the polymer relaxation time remains consistent with the 9/5 power law for all pore radii.

The process during which a polymer translocates through a nanopore depends on many physical parameters and fundamental mechanisms. We propose a new one-dimensional lattice Monte Carlo algorithm that integrates various effects such as the entropic forces acting on the subchains that are outside the channel, the external forces that are pulling the polymer through the pore, and the frictional effects that involve the chain and its environment. Our novel approach allows us to study the polymer as a single Brownian particle diffusing while subjected to a position-dependent force that includes both the external driving forces and the internal entropic bias. Frictional effects outside and inside the pore are also considered. This Monte Carlo method is much more efficient than other simulation methods, and it can be used to obtain scaling laws for various polymer translocation regimes. In this first part, we derive the model and describe a subtle numerical approach that gives exact results for both the escape probability and the mean translocation time (and higher moments of its distribution). The scaling laws obtained from this model will be presented and discussed in the second part of this series.

We revisit the well-known issue of representing an overdamped drift-and-diffusion system by an equivalent lattice random-walk model. We demonstrate that commonly used Monte Carlo algorithms do not conserve the diffusion coefficient when a driving field of arbitrary amplitude is present, and that such algorithms would actually require fluctuating jumping times and one clock per Cartesian direction to work properly. Although it is in principle possible to construct valid algorithms with fixed time steps, we show that no such algorithm can be used in more than two dimensions if the jumps are made along only one axis at each time step.

Traditionally, the Ogston regime is studied solely in the limit of low field intensities. This explains why the theoretical discussion has focused until now on the relative roles of the fractional volume available to the analyte and the subtleties of the gel architecture. Over the past several years, we have developed a lattice model of gel electrophoresis that has allowed us to revisit the fundamental assumptions of the standard Ogston model. In particular, we demonstrated that the fractional free volume is not the relevant parameter for gel sieving. In this article, we continue the development of this model and we generalize our mathematical approach to treat nonvanishing electric field intensities. To do so, we must revisit the way biased random walks are normally modeled by stochastic processes. Straightforward generalizations based on standard Metropolis-like schemes fail at high field intensities. Moreover, our generalization requires the complete decoupling of the spatial directions parallel and perpendicular to the field direction. We show that our novel theoretical approach makes it possible to calculate exact mobilities in the presence of lattice obstacles. Several two-dimensional examples are then studied, including one that includes topological dead ends that act like traps. In the latter case, we recover results very similar to those reported by Serwer et al. [Biopolymers 29, 1863 (1990)] on the trapping electrophoresis of charged spheres in agarose gels. In the absence of such traps, the mobility is shown to be a very weak function of the electric field, thus validating the historical neglect of the field intensity in the development of obstruction models for the Ogston sieving regime of small analytes. Finally, we describe how the present model could be improved to treat more realistic cases and we discuss the problem of the field dependence of the diffusion coefficient during electrophoresis.