Ref HAL: hal-04279672_v1
Ref Arxiv: 2310.08477
Ref. & Cit.: NASA ADS
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We address the question of the time needed by $N$ particles, initially located on the first sites of a finite 1D lattice of size $L$, to exit that lattice when they move according to a TASEP transport model. Using analytical calculations and numerical simulations, we show that when $N \ll L$, the mean exit time of the particles is asymptotically given by $T_N(L) \sim L+\beta_N \sqrt{L}$ for large lattices. Building upon exact results obtained for 2 particles, we devise an approximate continuous space and time description of the random motion of the particles that provides an analytical recursive relation for the coefficients $\beta_N$. The results are shown to be in very good agreement with numerical results. This approach sheds some light on the exit dynamics of $N$ particles in the regime where $N$ is finite while the lattice size $L\rightarrow \infty$. This complements previous asymptotic results obtained by Johansson in \cite{Johansson2000} in the limit where both $N$ and $L$ tend to infinity while keeping the particle density $N/L$ finite.

Commentaires: 10 pages, 4 figures

Ref HAL: hal-03832368_v1
PMID 37862386
Ref Arxiv: 2208.12576
DOI: 10.1371/journal.pcbi.1011522
Ref. & Cit.: NASA ADS
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Gene expression consists in the synthesis of proteins from the information encoded on DNA. One of the two main steps of gene expression is the translation of messenger RNA into polypeptide sequences of amino acids. Here, by taking into account messenger RNA degradation, we model the motion of ribosomes along messenger RNA with a ballistic model where particles advance along a filament without excluded volume interactions. Unidirectional models of transport have previously been used to fit the average density of ribosomes obtained by the experimental ribo-sequencing (Ribo-seq) technique. In this case an inverse fit gives access to the kinetic rates: the position-dependent speeds and the entry rate of ribosomes onto messenger RNA. The degradation rate is not, however, accounted for and experimental data from different experiments are needed to have enough parameters for the fit. Here, we propose an entirely novel experimental setup and theoretical framework consisting in splitting the messenger RNAs into categories depending on the number of ribosomes from one to four. We solve analytically the ballistic model for a fixed number of ribosomes per messenger RNA, study the different regimes of degradation, and propose a criteria for the quality of the inverse fit. The proposed method provides a high sensitivity to the messenger RNA degradation rate. The additional equations coming from using the monosome (single ribosome) and polysome (arbitrary number) ribo-seq profiles enable us to determine all the kinetic rates in terms of the experimentally accessible messenger RNA degradation rate.

Ref HAL: hal-03691814_v1
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Gene expression consists in the synthesis of proteins from the information encoded on DNA. One of the two main steps of gene expression is the translation of messenger RNA (mRNA) into polypeptide sequences of amino acids. Here, by taking into account mRNA degradation, we model the motion of ribosomes along mRNA with a ballistic model where particles advance along a filament without excluded volume interactions. Unidirectional models of transport have previously been used to fit the average density of ribosomes obtained by the experimental ribosome sequencing (Ribo-Seq) technique. In this case an inverse fit gives access to the kinetic rates: the position-dependent speeds and the entry rate of ribosomes into mRNA. The degradation rate is not, however, accounted for and experimental data from differentexperiments are needed to have enough parameters for the fit. Here, we propose an entirely novel experimental setup and theoretical framework consisting in splitting the mRNAs into categories depending on the number of ribosomes from one to four. We analytically solve the ballistic model for a fixed number of ribosomes per mRNA, study the different regimes of degradation, and propose a criterion for the quality of the inverse fit. The proposed method provides a high sensitivity to the mRNA degradation rate. The additional equations coming from using the monosome (single ribosome) and polysome (arbitrary number) Ribo-Seq profiles enables us to determine all the kinetic rates in terms of the experimentally accessible mRNA degradation rate.

Ref HAL: hal-03351194_v1
DOI: 10.1126/sciadv.abl8112
WoS: WOS:000772464300015
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The bacterial flagellar motor (BFM) is the membrane-embedded rotary molecular motor which turns the flagellum that provides thrust to many bacterial species. This large multimeric complex, composed of a few dozen constituent proteins, has emerged as a hallmark of dynamic subunit exchange. The stator units are inner-membrane ion channels which dynamically bind and unbind to the peptidoglycan at the rotor periphery, consuming the ion motive force (IMF) and applying torque to the rotor when bound. The dynamic exchange is known to be a function of the viscous load on the flagellum, allowing the bacterium to dynamically adapt to its local viscous environment, but the molecular mechanisms of exchange and mechanosensitivity remain to be revealed. Here, by actively perturbing the steady-state stator stoichiometry of individual motors, we reveal a stoichiometry-dependent asymmetry in stator remodeling kinetics. We interrogate the potential effect of next-neighbor interactions and local stator unit depletion and find that neither can explain the observed asymmetry. We then simulate and fit two mechanistically diverse models which recapitulate the asymmetry, finding stator assembly dynamics to be particularly well described by a two-state catch-bond mechanism.

Ref HAL: hal-03237857_v1
DOI: 10.1140/epje/s10189-021-00061-6
WoS: WOS:000644646200001
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erratum

Ref HAL: hal-03438826_v1
PMID 33861734
DOI: 10.1371/journal.pcbi.1008869
WoS: 000641474200004
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ParAB S , the most widespread bacterial DNA segregation system, is composed of a centromeric sequence, parS , and two proteins, the ParA ATPase and the ParB DNA binding proteins. Hundreds of ParB proteins assemble dynamically to form nucleoprotein parS -anchored complexes that serve as substrates for ParA molecules to catalyze positioning and segregation events. The exact nature of this ParB S complex has remained elusive, what we address here by revisiting the Stochastic Binding model (SBM) introduced to explain the non-specific binding profile of ParB in the vicinity of parS . In the SBM, DNA loops stochastically bring loci inside a sharp cluster of ParB. However, previous SBM versions did not include the negative supercoiling of bacterial DNA, leading to use unphysically small DNA persistences to explain the ParB binding profiles. In addition, recent super-resolution microscopy experiments have revealed a ParB cluster that is significantly smaller than previous estimations and suggest that it results from a liquid-liquid like phase separation. Here, by simulating the folding of long (≥ 30 kb) supercoiled DNA molecules calibrated with realistic DNA parameters and by considering different possibilities for the physics of the ParB cluster assembly, we show that the SBM can quantitatively explain the ChIP-seq ParB binding profiles without any fitting parameter, aside from the supercoiling density of DNA, which, remarkably, is in accord with independent measurements. We also predict that ParB assembly results from a non-equilibrium, stationary balance between an influx of produced proteins and an outflux of excess proteins, i.e., ParB clusters behave like liquid-like protein condensates with unconventional “leaky” boundaries.

Ref HAL: hal-03052753_v1
DOI: 10.1016/j.isci.2020.101861
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Bacterial ParB partitioning proteins involved in chromosomes and low-copy-number plasmid segregation are CTP-dependent molecular switches. CTP-binding converts ParB dimers to DNA clamps, allowing unidimensional diffusion along the DNA. This sliding property has been proposed to explain the ParB spreading over large distances from parS centromere sites where ParB is specifically loaded. We modeled such a ‘Clamping & sliding’ mechanism as a typical reaction-diffusion system, compared it to the F-plasmid ParB DNA binding pattern, and found that it can account neither for the long range of ParB binding to DNA, nor for the rapid assembly kinetics observed in vivo after parS duplication. Also, it predicts a strong effect on the F-plasmid ParB binding pattern from the presence of a roadblock that is not observed in ChIP-seq. We conclude that although ‘Clamping & sliding’ can occur at short distances from parS, another mechanism must apply for ParB recruitment at larger genomic distances.