Ref HAL: hal-04890444_v1
Ref Arxiv: 2307.00636
Ref. & Cit.: NASA ADS
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The cooperative binding of molecular agents onto a substrate is pervasive in living systems. To study whether a system shows cooperativity, one can rely on a fluctuation analysis of quantities such as the number of substrate-bound units and the residence time in an occupancy state. Since the relative standard deviation from the statistical mean monotonically decreases with the number of binding sites, these techniques are only suitable for small enough systems, such as those implicated in stochastic processes inside cells. Here, we present a general-purpose grand canonical Hamiltonian description of a small one-dimensional (1D) lattice gas with either nearest-neighbor or long-range interactions as prototypical examples of cooperativity-influenced adsorption processes. First, we elucidate how the strength and sign of the interaction potential between neighboring bound particles on the lattice determine the intensity of the fluctuations of the mean occupancy. We then employ this relationship to compare the theoretical predictions of our model to data from single molecule experiments on bacterial flagellar motors (BFM) of E. coli. In this way, we find evidence that cooperativity controls the mechano-sensitive dynamical assembly of the torque-generating units, the so-called stator units, onto the BFM. Furthermore, in an attempt to quantify fluctuations and the adaptability of the BFM, we estimate the stator-stator interaction potential. Finally, we conclude that the system resides in a sweet spot of the parameter space (phase diagram) with characteristics suitable for a smoothly and widely adaptive system, while minimizing fluctuations.

Ref HAL: hal-04878246_v1
DOI: 10.48550/arXiv.2310.00329
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We theoretically study the Totally Asymmetric Exclusion Process (TASEP) with quenched jumping rates disorder and finite lifetime chain. TASEP is widely used to model the translation of messenger RNAs by Ribosomes in protein synthesis. Since the exact solution of the TASEP model is analytically and computationally intractable for biologically relevant systems parameters, the canonical Mean-Field (MF) approaches of solving coupled non-linear differential equations is also computational expensive for the scale of relevant biological data analysis. In this article, we provide alternative approach to computing the MF steady state solution via a computationally efficient system of non-linear algebraic equations. We further outline a framework for including correlations progressively via the exact solution of small size TASEP system. Leading order approximation in the biologically relevant entry rate limited regime shows remarkable agreement with the full Monte-Carlo simulation result for a wide range of system parameter space. These results could be of importance to the kinetic rates inference in Ribo-Seq data analysis and other related problems.

Ref HAL: hal-04279672_v1
Ref Arxiv: 2310.08477
DOI: 10.1103/PhysRevE.109.034116
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-04252827_v2
Ref Arxiv: 2307.00636
DOI: 10.1038/s41598-025-14570-3
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

The cooperative binding of molecular agents onto a substrate is pervasive in living systems. To study whether a system shows cooperativity, one can rely on a fluctuation analysis of quantities such as the number of substrate-bound units and the residence time in an occupancy state. Since the relative standard deviation from the statistical mean monotonically decreases with the number of binding sites, these techniques are only suitable for small enough systems, such as those implicated in stochastic processes inside cells. Here, we employ a general-purpose grand canonical Hamiltonian description of a small one-dimensional (1D) lattice gas with either nearest-neighbor or long-range interactions as prototypical examples of cooperativity-influenced adsorption processes. First, building upon previous work on finite-size one-dimensional Ising-type models, we elucidate how the strength and sign of the interaction potential between neighboring bound particles on the lattice determine the intensity of the fluctuations of the mean occupancy and the nature of bound particle-particle correlations. We present our theoretical results, which extend beyond standard analysis, in a novel, physically transparent form. We explore simple limiting cases of the parameter space in greater detail, examine the complete probability distribution functions for occupation, and relate these to the shape and strength of the fluctuations. Second, we leverage these relationships to compare the theoretical predictions of our model to data from single molecule experiments on bacterial flagellar motors (BFM) of Escherichia coli. In this way, we find evidence that cooperativity controls the mechano-sensitive dynamical assembly of the torque-generating units, the so-called stator units, onto the BFM and thereby arrive at an estimate of the stator-stator interaction potential from our fluctuation analysis. Furthermore, we attempt to clarify the link between occupation fluctuations and the adaptability of the BFM. Finally, we conclude that the system resides in a sweet spot of the parameter space (phase diagram) with characteristics suitable for a smoothly and widely adaptive system, while minimizing fluctuations.

Ref HAL: hal-04901816_v1
Exporter : BibTex | endNote
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The bacterial flagellar motor is the membrane-embedded rotary motor, which turns the flagellum that provides thrust to many bacteria. This large multimeric complex, composed of a few dozen constituent proteins, is a hallmark of dynamic subunit exchange. The stator units are inner-membrane ion channels that dynamically bind to the peptidoglycan at the rotor periphery and apply torque. Their dynamic exchange is a function of the viscous load on the flagellum, allowing the bacterium to adapt to its local environment, although the molecular mechanisms of mechanosensitivity remain unknown. 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 that recapitulate the asymmetry, finding assembly dynamics to be particularly well described by a two-state catch-bond mechanism. https://doi.org/10.1126/sciadv.abl8112

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
Exporter : BibTex | endNote
Résumé:

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.