On the statistical physics of chains and rods, with application to multi-scale sequence-dependent DNA modelling

The complex mechanisms involved in cellular processes have been increasingly understood this past century and the central role of the DNA molecule has been recognized. The base pair sequence along a DNA fragment is observed not only to encode the genomic information, but also to induce locally very specific physical properties, such as significantly bent or stiff regions. These variations in the molecule constitution are for instance believed to be involved in DNA-protein recognition and in nucleosomes positioning. Modelling the sequence dependent DNA mechanical properties is consequently an important step towards understanding many biological functions. However, in a cell, vastly different length scales are involved, ranging from a few base pairs to several thousands, which makes difficult the definition of \textit{one} appropriate model. A promising strategy seems then to be given by the multi-scale modeling of sequence dependent DNA mechanics. In this framework, the sequence dependent rigid base and rigid base pair models have been proposed. In these coarse grain models either each base pair or each base is described as a rigid body configuration, which leads to either a chain or a bichain representation of the DNA molecule. A sequence dependent configurational distribution has then been parametrized, either from experimental data or directly from atomistic molecular dynamic simulations, and provides an efficient and realistic description at the scale of hundreds of base pairs. Important questions that can be studied in these models are for instance the influence of the sequence on the probability of contact of two sites, which are distant along the molecule length, or on the expectation of the relative configuration of these two sites. In this thesis, we propose to approach these physical situations both from the discrete and the continuum modeling point of view, and then to discuss in which sense they actually constitute only one multi-scale point of view. In the first part, we discuss mechanical properties of heterogeneous rigid body chains and bichains, as well as continuum rod and birods, in classical statics and in equilibrium statistical physics. Equilibirum conditions, variational principles and configurational distributions are studied for single chains and rods, and then extended to bichains and birods. We have introduced in particular an original coordinate free Hamiltonian formulation in arc-length of the birod equilibrium conditions, and the notion of the persistence matrix for the configurational moment for chains and rods. We then present deterministic and stochastic exponential Cauchy-Born rules allowing to bridge the scales between the discrete and continuum representations. In the second part, we present applications of the proposed multi-scale mechanical theory for chains and rods to sequence dependent DNA modelling. We discuss the approximation using the birod model of most probable bichain configurations satisfying prescribed end conditions. Similarly, we then present the computation of the sequence dependent frame correlation matrix and the Flory persistence vector for chains using a continuum rod model. In addition, a homogenization method is proposed. These results are believed to constitute a substantial improvement in the multi-scale modeling of DNA mechanics

Sequence-Dependent Persistence Lengths of DNA

A Monte Carlo code applied to the <i>cgDNA</i> coarse-grain rigid-base model of B-form double-stranded DNA is used to predict a sequence-averaged persistence length of <i>l</i>_F = 53.5 nm in the sense of Flory, and of <i>l</i>_p = 160 bp or 53.5 nm in the sense of apparent tangent–tangent correlation decay. These estimates are slightly higher than the consensus experimental values of 150 bp or 50 nm, but we believe the agreement to be good given that the <i>cgDNA</i> model is itself parametrized from molecular dynamics simulations of short fragments of length 10–20 bp, with no explicit fit to persistence length. Our Monte Carlo simulations further predict that there can be substantial dependence of persistence lengths on the specific sequence S of a fragment. We propose, and confirm the numerical accuracy of, a simple factorization that separates the part of the apparent tangent–tangent correlation decay lp(S) attributable to intrinsic shape, from a part ld(S) attributable purely to stiffness, i.e., a sequence-dependent version of what has been called sequence-averaged dynamic persistence length <i>l̅</i>_d (=58.8 nm within the <i>cgDNA</i> model). For ensembles of both random and λ-phage fragments, the apparent persistence length lp(S) has a standard deviation of 4 nm over sequence, whereas our dynamic persistence length ld(S) has a standard deviation of only 1 nm. However, there are notable dynamic persistence length outliers, including poly­(A) (exceptionally straight and stiff), poly­(TA) (tightly coiled and exceptionally soft), and phased A-tract sequence motifs (exceptionally bent and stiff). The results of our numerical simulations agree reasonably well with both molecular dynamics simulation and diverse experimental data including minicircle cyclization rates and stereo cryo-electron microscopy images

Measurement of the muon flux for the SHiP experiment

We report the results of the measurement of the muon flux emanating from the SHiP target at the CERN SPS. A replica of the SHiP target followed by a $2.4~\rm{m}$ iron hadron absorber was installed in the H4 400 GeV/c proton beamline. To measure the momentum spectrum, a spectrometer consisting of drift tubes and resistive plate chambers (RPCs) was placed around the Goliath magnet. During a three week period a dataset for analysis corresponding to $3.27 \times 10^{11}$ protons on target (POT) was recorded. This amounts to approximatively $1\%$ of a SHiP spill. The amount of accumulated data allows us to make a validation of the results from our Pythia and Geant4 based Monte Carlo (FairShip)