Regulation of DNA replication within the immunoglobulin heavy-chain locus during B cell commitment.

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.

Modeling inhomogeneous DNA replication kinetics.

In eukaryotic organisms, DNA replication is initiated at a series of chromosomal locations called origins, where replication forks are assembled proceeding bidirectionally to replicate the genome. The distribution and firing rate of these origins, in conjunction with the velocity at which forks progress, dictate the program of the replication process. Previous attempts at modeling DNA replication in eukaryotes have focused on cases where the firing rate and the velocity of replication forks are homogeneous, or uniform, across the genome. However, it is now known that there are large variations in origin activity along the genome and variations in fork velocities can also take place. Here, we generalize previous approaches to modeling replication, to allow for arbitrary spatial variation of initiation rates and fork velocities. We derive rate equations for left- and right-moving forks and for replication probability over time that can be solved numerically to obtain the mean-field replication program. This method accurately reproduces the results of DNA replication simulation. We also successfully adapted our approach to the inverse problem of fitting measurements of DNA replication performed on single DNA molecules. Since such measurements are performed on specified portion of the genome, the examined DNA molecules may be replicated by forks that originate either within the studied molecule or outside of it. This problem was solved by using an effective flux of incoming replication forks at the model boundaries to represent the origin activity outside the studied region. Using this approach, we show that reliable inferences can be made about the replication of specific portions of the genome even if the amount of data that can be obtained from single-molecule experiments is generally limited.

Defects and DNA replication.

We introduce a rate-equation formalism to study DNA replication kinetics in the presence of defects resulting from DNA damage and find a crossover between two regimes: a normal regime, where the influence of defects is local, and an initiation-limited regime. In the latter, defects have a global impact on replication, whose progress is set by the rate at which origins of replication are activated, or initiated. Normal, healthy cells have defect densities in the normal regime. Our model can explain an observed correlation between interorigin separation and rate of DNA replication.

Computational methods to study kinetics of DNA replication.

New technologies such as DNA combing have led to the availability of large quantities of data that describe the state of DNA while undergoing replication in S phase. In this chapter, we describe methods used to extract various parameters of replication--fork velocity, origin initiation rate, fork density, numbers of potential and utilized origins--from such data. We first present a version of the technique that applies to "ideal" data. We then show how to deal with, a number of real-world complications, such as the asynchrony of starting times of a population of cells, the finite length of fragments used in the analysis, and the finite amount of DNA in a chromosome.

Control of DNA replication by anomalous reaction-diffusion kinetics.

We propose a simple model for the control of DNA replication in which the rate of initiation of replication origins is controlled by protein-DNA interactions. Analyzing recent data from Xenopus frog embryos, we find that the initiation rate is reaction limited until nearly the end of replication, when it becomes diffusion limited. Initiation of origins is suppressed when the diffusion-limited search time dominates. To fit the experimental data, we find that the interaction between DNA and the rate-limiting protein must be subdiffusive.

Nondriven polymer translocation through a nanopore: computational evidence that the escape and relaxation processes are coupled.

Most of the theoretical models describing the translocation of a polymer chain through a nanopore use the hypothesis that the polymer is always relaxed during the complete process. In other words, models generally assume that the characteristic relaxation time of the chain is small enough compared to the translocation time that nonequilibrium molecular conformations can be ignored. In this paper, we use molecular dynamics simulations to directly test this hypothesis by looking at the escape time of unbiased polymer chains starting with different initial conditions. We find that the translocation process is not quite in equilibrium for the systems studied, even though the translocation time tau is about 10 times larger than the relaxation time tau{r}. Our most striking result is the observation that the last half of the chain escapes in less than approximately 12% of the total escape time, which implies that there is a large acceleration of the chain at the end of its escape from the channel.

A Monte Carlo algorithm to study polymer translocation through nanopores. II. Scaling laws.

In the first paper of this series, we developed a new one-dimensional Monte Carlo approach for the study of flexible chains that are translocating through a small channel. We also presented a numerical scheme that can be used to obtain exact values for both the escape times and the escape probabilities given an initial pore-polymer configuration. We now present and discuss the fundamental scaling behaviors predicted by this Monte Carlo method. Our most important result is the fact that, in the presence of an external bias E, we observe a change in the scaling law for the translocation time tau as function of the polymer length N: In the general expression tau approximately N(beta)E, the exponent changes from beta=1 for moderately long chains to beta=1+nu or beta=2nu for very large values of N (for Rouse and Zimm dynamics, respectively). We also observe an increase in the effective diffusion coefficient due to the presence of entropic pulling on unbiased polymer chains.

Sequence effects on the forced translocation of heteropolymers through a small channel.

By using a recently developed Monte Carlo algorithm and an exact numerical method, we calculate the translocation probability and the average translocation time for charged heterogeneous polymers driven through a nanopore by an external electric field. The heteropolymer chains are composed of two types of monomers (A and B) which differ only in terms of their electric charge. We present an exhaustive study of chains composed of eight monomers by calculating the average translocation time associated with the 256 possible arrangements for various ratios of the monomer charges (lambda(A)lambda(B)) and electric field intensities E. We find that each sequence leads to a unique value of the translocation probability and time. We also show that the distribution of translocation times is strongly dependent on the two forces felt by the monomers ( approximately lambda(A)E and approximately lambda(B)E). Finally, we present results that highlight the effect of having repetitive patterns by studying the translocation times of various block copolymer structures for a very long chain composed of N=2(18) monomers (all with the same number of A and B monomers).

A Monte Carlo algorithm to study polymer translocation through nanopores. I. Theory and numerical approach.

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.

Biased random walks on a lattice: exact numerical method to study the effect of alternating fields in disordered and asymmetric systems of obstacles.

The migration of a particle in a system of obstacles under the action of an external field is often modeled using lattice Monte Carlo algorithms. For example, such simulation methods have been used to study the electrophoresis of charged molecules in sieving gels and the separation of particles using ratchet systems. In the case of constant fields or low-frequency alternating fields, the Monte Carlo simulation method can be mapped onto a numerical or algebraic matrix problem that can be solved exactly. In this Rapid Communication, we generalize this matrix approach to treat periodic time-dependent fields. The evolution of the spatial distribution function during a period is computed using a sequence of transfer matrices, and a steady-state closure relation allows us to calculate the exact mean velocity of the particle during a complete cycle. As an example, we examine the properties of a simple spatially asymmetric ratchet system in the presence of periodic alternating fields (symmetric and asymmetric) as well as random telegraph signals.

Effective molecular diffusion coefficient in a two-phase gel medium.

We derive a mean-field expression for the effective diffusion coefficient of a probe molecule in a two-phase medium consisting of a hydrogel with large gel-free solvent inclusions, in terms of the homogeneous diffusion coefficients in the gel and in the solvent. Upon comparing with exact numerical lattice calculations, we find that our expression provides a remarkably accurate prediction for the effective diffusion coefficient, over a wide range of gel concentration and relative volume fraction of the two phases. Moreover, we extend our model to handle spatial variations of viscosity, thereby allowing us to treat cases where the solvent viscosity itself is inhomogeneous. This work provides robust grounds for the modeling and design of multiphase systems for specific applications, e.g., hydrogels as novel food agents or efficient drug-delivery platforms.

Building reliable lattice Monte Carlo models for real drift and diffusion problems.

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.

The theory of DNA separation by capillary electrophoresis.

The Human Genome has been sequenced in large part owing to the invention of capillary electrophoresis. Although this technology has matured enough to allow such amazing achievements, the physical mechanisms at play during separation have yet to be completely understood and optimized. Recently, new separation regimes and new physical mechanisms have been investigated. The use of free-flow electrophoresis and new modes of pulsed-field electrophoresis have been suggested, while we have observed a shift towards single nucleotide polymorphism analysis and microchip technologies. A strong theoretical basis remains essential for the efficient development of new methods.

An exactly solvable Ogston model of gel electrophoresis: X. Application to high-field separation techniques.

Recently, we generalized our lattice model of gel electrophoresis to study the net velocity of particles being pulled by a high-intensity electric field through an arbitrary distribution of immobile obstacles (Gauthier, M. G., Slater, G. W., J. Chem. Phys. 2002, 117, 6745-6756). In this article, we show how the high-field version of our model can be used to compare the velocity of particles with different electric charges and/or physical sizes. We then investigate specific two-dimensional distributions of obstacles that can be used to separate particles, e.g., in a microfluidic device. More precisely, we compare the velocity of differently charged or sized analytes in sieving, trapping and deflecting systems to model various electrophoretic separation techniques. In particular, we study the nonlinear effects present in ratchet systems and how they can be combined with time-asymmetric pulsed fields to provide new modes of separation.

Theory of DNA electrophoresis (approximately 1999-2002(1/2)).

Over the last two decades, the introduction of new methods such as pulsed-field gel electrophoresis and capillary array electrophoresis has made it possible to map and sequence entire genomes, including our own. The development of these experimental methods has been helped by the progress of theoretical and computational sciences, and the interactions between these three modi operandi of modern science are still pushing the limits of our technologies. We now see a clear trend towards proteomics and microfluidic (even nanofluidic!) devices. In this review, we take a look at the progress of the field over the last 3 years using the glasses of the theoretical scientist and focusing mostly on new ideas and concepts. About a dozen different subfields are discussed and reviewed. We conclude by giving a commented list of some of the best review articles published over the last 2-3 years.