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Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via calculation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases, the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN: decoys are able to block binding sites on PTEN mRNAs, thereby reducing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations. [ABSTRACT FROM AUTHOR]

Activated escape of a Brownian particle from the domain of attraction of a stable focus over a limit cycle exhibits non-Kramers behavior: it is non-Poissonian. When the attractor is moved closer to the boundary, oscillations can be discerned in the survival probability. We show that these oscillations are due to complex-valued higher-order eigenvalues of the Fokker-Planck operator, which we compute explicitly in the limit of small noise. We also show that in this limit the period of the oscillations is the winding number of the activated stochastic process. These peak probability oscillations are not related to stochastic resonance and should be detectable in planar dynamical systems with the topology described here. [ABSTRACT FROM AUTHOR]

Translation of proteins is a fundamental part of gene expression that is mediated by ribosomes. As ribosomes significantly contribute to both cellular mass and energy consumption, achieving efficient management of the ribosome population is also crucial to metabolism and growth. Inspired by biological evidence for nutrient-dependent mechanisms that control both ribosome-active degradation and genesis, we introduce a dynamical model of protein production, that includes the dynamics of resources and control over the ribosome population. Under the hypothesis that active degradation and biogenesis are optimal for maximizing and maintaining protein production, we aim to qualitatively reproduce empirical observations of the ribosome population dynamics. Upon formulating the associated optimization problem, we first analytically study the stability and global behaviour of solutions under constant resource input, and characterize the extent of oscillations and convergence rate to a global equilibrium. We further use these results to simplify and solve the problem under a quasi-static approximation. Using biophysical parameter values, we find that optimal control solutions lead to both control mechanisms and the ribosome population switching between periods of feeding and fasting, suggesting that the intense regulation of ribosome population observed in experiments allows to maximize and maintain protein production. Finally, we find some range for the control values over which such a regime can be observed, depending on the intensity of fasting.

Antibody microarray data provides a powerful and high-throughput tool to monitor global changes in cellular response to perturbation or genetic manipulation. However, while collecting such data has become increasingly accessible, a lack of specific computational tools has made their analysis limited. Here we present CAT PETR, a user friendly web application for the differential analysis of expression and phosphorylation data collected via antibody microarrays. Our application addresses the limitations of other GUI based tools by providing various data input options and visualizations. To illustrate its capabilities on real data, we show that CAT PETR both replicates previous findings, and reveals additional insights, using its advanced visualization and statistical options., (© 2023 Walter de Gruyter GmbH, Berlin/Boston.)

Conventional dimensionality reduction methods like Multidimensional Scaling (MDS) are sensitive to the presence of orthogonal outliers, leading to significant defects in the embedding. We introduce a robust MDS method, called DeCOr-MDS (Detection and Correction of Orthogonal outliers using MDS), based on the geometry and statistics of simplices formed by data points, that allows to detect orthogonal outliers and subsequently reduce dimensionality. We validate our methods using synthetic datasets, and further show how it can be applied to a variety of large real biological datasets, including cancer image cell data, human microbiome project data and single cell RNA sequencing data, to address the task of data cleaning and visualization., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Li, Mirone, Prasad, Miolane, Legrand and Dao Duc.)

Recent advances in Cryo-EM led to a surge of ribosome structures deposited over the past years, including structures from different species, conformational states, or bound with different ligands. Yet, multiple conflicts of nomenclature make the identification and comparison of structures and ortholog components challenging. We present RiboXYZ (available at https://ribosome.xyz), a database that provides organized access to ribosome structures, with several tools for visualisation and study. The database is up-to-date with the Protein Data Bank (PDB) but provides a standardized nomenclature that allows for searching and comparing ribosomal components (proteins, RNA, ligands) across all the available structures. In addition to structured and simplified access to the data, the application has several specialized visualization tools, including the identification and prediction of ligand binding sites, and 3D superimposition of ribosomal components. Overall, RiboXYZ provides a useful toolkit that complements the PDB database, by implementing the current conventions and providing a set of auxiliary tools that have been developed explicitly for analyzing ribosome structures. This toolkit can be easily accessed by both experts and non-experts in structural biology so that they can search, visualize and compare structures, with various potential applications in molecular biology, evolution, and biochemistry., (© The Author(s) 2022. Published by Oxford University Press on behalf of Nucleic Acids Research.)

The exit tunnel is the subcompartment of the ribosome that contains the nascent polypeptide chain and, as such, is involved in various vital functions, including regulation of translation and protein folding. As the geometry of the tunnel shows important differences across species, we focus on key geometrical features of eukaryote and prokaryote tunnels. We used a simple coarse-grained molecular dynamics model to study the role of the tunnel geometry in the post-translational escape of short proteins (short open reading frames [sORFs]) with lengths ranging from 6 to 56 amino acids. We found that the probability of escape for prokaryotes is one for all but the 12-mer chains. Moreover, proteins of this length have an extremely low escape probability in eukaryotes. A detailed examination of the associated single trajectories and energy profiles showed that these variations can be explained by the interplay between the protein configurational space and the confinement effects introduced by the constriction sites of the ribosome exit tunnel. For certain lengths, either one or both of the constriction sites can lead to the trapping of the protein in the "pocket" regions preceding these sites. As the distribution of existing sORFs indicates some bias in length that is consistent with our findings, we finally suggest that the constraints imposed by the tunnel geometry have impacted the evolution of sORFs., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2022 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Ribosome profiling is a powerful technique which maps the distribution of ribosomes along mRNAs to analyze translation genome-wide. Ribosome density can be affected by multiple factors, such as changes to translation initiation or elongation rates. We describe the application of a metric for identifying genes rate-limited by these rates by analyzing the relative distribution of ribosome footprints along transcripts. This protocol also details two sample analyses comparing gene translation efficiencies and the distribution of ribosome densities on downloadable datasets. For complete details on the use and execution of this protocol, please refer to Flanagan et al. (2022)., Competing Interests: The authors declare no competing interests., (© 2022 The Author(s).)

Mutations in FMR1 are the most common heritable cause of autism spectrum disorder. FMR1 encodes an RNA-binding protein, FMRP, which binds to long, autism-relevant transcripts and is essential for normal neuronal and ovarian development. In contrast to the prevailing model that FMRP acts to block translation elongation, we previously found that FMRP activates the translation initiation of large proteins in Drosophila oocytes. We now provide evidence that FMRP-dependent translation is conserved and occurs in the mammalian brain. Our comparisons of the mammalian cortex and Drosophila oocyte ribosome profiling data show that translation of FMRP-bound mRNAs decreases to a similar magnitude in FMRP-deficient tissues from both species. The steady-state levels of several FMRP targets were reduced in the Fmr1 KO mouse cortex, including a ∼50% reduction of Auts2, a gene implicated in an autosomal dominant autism spectrum disorder. To distinguish between effects on elongation and initiation, we used a novel metric to detect the rate-limiting ribosome stalling. We found no evidence that FMRP target protein production is governed by translation elongation rates. FMRP translational activation of large proteins may be critical for normal human development, as more than 20 FMRP targets including Auts2 are dosage sensitive and are associated with neurodevelopmental disorders caused by haploinsufficiency., (© The Author(s) 2022. Published by Oxford University Press on behalf of Genetics Society of America.)

The totally asymmetric simple exclusion process (TASEP), which describes the stochastic dynamics of interacting particles on a lattice, has been actively studied over the past several decades and applied to model important biological transport processes. Here, we present a software package, called EGGTART (Extensive GUI gives TASEP-realization in Real Time), which quantifies and visualizes the dynamics associated with a generalized version of the TASEP with an extended particle size and heterogeneous jump rates. This computational tool is based on analytic formulas obtained from deriving and solving the hydrodynamic limit of the process. It allows an immediate quantification of the particle density, flux, and phase diagram, as a function of a few key parameters associated with the system, which would be difficult to achieve via conventional stochastic simulations. Our software should therefore be of interest to biophysicists studying general transport processes and can in particular be used in the context of gene expression to model and quantify mRNA translation of different coding sequences., (Copyright © 2021 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Motivation: Cryogenic electron microscopy (cryo-EM) offers the unique potential to capture conformational heterogeneity, by solving multiple three-dimensional classes that co-exist within a single cryo-EM image dataset. To investigate the extent and implications of such heterogeneity, we propose to use an optimal-transport-based metric to interpolate barycenters between EM maps and produce morphing trajectories., Results: While standard linear interpolation mostly fails to produce realistic transitions, our method yields continuous trajectories that displace densities to morph one map into the other, instead of blending them., Availability and Implementation: Our method is implemented as a plug-in for ChimeraX called MorphOT, which allows the use of both CPU or GPU resources. The code is publicly available on GitHub (https://github.com/kdd-ubc/MorphOT.git), with documentation containing tutorial and datasets., Supplementary Information: Supplementary data are available at Bioinformatics online., (© The Author(s) 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

The extent of ribosomal heterogeneity has caught increasing interest over the past few years, as recent studies have highlighted the presence of structural variations of the ribosome. More precisely, the heterogeneity of the ribosome covers multiple scales, including the dynamical aspects of ribosomal motion at the single particle level, specialization at the cellular and subcellular scale, or evolutionary differences across species. Upon solving the ribosome atomic structure at medium to high resolution, cryogenic electron microscopy (cryo-EM) has enabled investigating all these forms of heterogeneity. In this review, we present some recent advances in quantifying ribosome heterogeneity, with a focus on the conformational and evolutionary variations of the ribosome and their functional implications. These efforts highlight the need for new computational methods and comparative tools, to comprehensively model the continuous conformational transition pathways of the ribosome, as well as its evolution. While developing these methods presents some important challenges, it also provides an opportunity to extend our interpretation and usage of cryo-EM data, which would more generally benefit the study of molecular dynamics and evolution of proteins and other complexes.

Translation of mRNA into protein is a fundamental yet complex biological process with multiple factors that can potentially affect its efficiency. Here, we study a stochastic model describing the traffic flow of ribosomes along the mRNA and identify the key parameters that govern the overall rate of protein synthesis, sensitivity to initiation rate changes, and efficiency of ribosome usage. By analyzing a continuum limit of the model, we obtain closed-form expressions for stationary currents and ribosomal densities, which agree well with Monte Carlo simulations. Furthermore, we completely characterize the phase transitions in the system, and by applying our theoretical results, we formulate design principles that detail how to tune the key parameters we identified to optimize translation efficiency. Using ribosome profiling data from S. cerevisiae, we show that its translation system is generally consistent with these principles. Our theoretical results have implications for evolutionary biology, as well as for synthetic biology., Competing Interests: Declaration of Interests The authors declare no competing interests., (Copyright © 2019 Elsevier Inc. All rights reserved.)

The ribosome exit tunnel is an important structure involved in the regulation of translation and other essential functions such as protein folding. By comparing 20 recently obtained cryo-EM and X-ray crystallography structures of the ribosome from all three domains of life, we here characterize the key similarities and differences of the tunnel across species. We first show that a hierarchical clustering of tunnel shapes closely reflects the species phylogeny. Then, by analyzing the ribosomal RNAs and proteins, we explain the observed geometric variations and show direct association between the conservations of the geometry, structure and sequence. We find that the tunnel is more conserved in the upper part close to the polypeptide transferase center, while in the lower part, it is substantially narrower in eukaryotes than in bacteria. Furthermore, we provide evidence for the existence of a second constriction site in eukaryotic exit tunnels. Overall, these results have several evolutionary and functional implications, which explain certain differences between eukaryotes and prokaryotes in their translation mechanisms. In particular, they suggest that major co-translational functions of bacterial tunnels were externalized in eukaryotes, while reducing the tunnel size provided some other advantages, such as facilitating the nascent chain elongation and enabling antibiotic resistance., (© The Author(s) 2019. Published by Oxford University Press on behalf of Nucleic Acids Research.)

Previous studies have shown that translation elongation is regulated by multiple factors, but the observed heterogeneity remains only partially explained. To dissect quantitatively the different determinants of elongation speed, we use probabilistic modeling to estimate initiation and local elongation rates from ribosome profiling data. This model-based approach allows us to quantify the extent of interference between ribosomes on the same transcript. We show that neither interference nor the distribution of slow codons is sufficient to explain the observed heterogeneity. Instead, we find that electrostatic interactions between the ribosomal exit tunnel and specific parts of the nascent polypeptide govern the elongation rate variation as the polypeptide makes its initial pass through the tunnel. Once the N-terminus has escaped the tunnel, the hydropathy of the nascent polypeptide within the ribosome plays a major role in modulating the speed. We show that our results are consistent with the biophysical properties of the tunnel.

The Totally Asymmetric Exclusion Process (TASEP) is a classical stochastic model for describing the transport of interacting particles, such as ribosomes moving along the messenger ribonucleic acid (mRNA) during translation. Although this model has been widely studied in the past, the extent of collision between particles and the average distance between a particle to its nearest neighbor have not been quantified explicitly. We provide here a theoretical analysis of such quantities via the distribution of isolated particles. In the classical form of the model in which each particle occupies only a single site, we obtain an exact analytic solution using the matrix ansatz. We then employ a refined mean-field approach to extend the analysis to a generalized TASEP with particles of an arbitrary size. Our theoretical study has direct applications in mRNA translation and the interpretation of experimental ribosome profiling data. In particular, our analysis of data from Saccharomyces cerevisiae suggests a potential bias against the detection of nearby ribosomes with a gap distance of less than approximately three codons, which leads to some ambiguity in estimating the initiation rate and protein production flux for a substantial fraction of genes. Despite such ambiguity, however, we demonstrate theoretically that the interference rate associated with collisions can be robustly estimated and show that approximately 1% of the translating ribosomes get obstructed.

The dynamics of neuronal networks connected by synaptic dynamics can sustain long periods of depolarization that can last for hundreds of milliseconds such as Up states recorded during sleep or anesthesia. Yet the underlying mechanism driving these periods remain unclear. We show here within a mean-field model that the residence time of the neuronal membrane potential in cortical Up states does not follow a Poissonian law, but presents several peaks. Furthermore, the present modeling approach allows extracting some information about the neuronal network connectivity from the time distribution histogram. Based on a synaptic-depression model, we find that these peaks, that can be observed in histograms of patch-clamp recordings are not artifacts of electrophysiological measurements, but rather are an inherent property of the network dynamics. Analysis of the equations reveals a stable focus located close to the unstable limit cycle, delimiting a region that defines the Up state. The model further shows that the peaks observed in the Up state time distribution are due to winding around the focus before escaping from the basin of attraction. Finally, we use in vivo recordings of intracellular membrane potential and we recover from the peak distribution, some information about the network connectivity. We conclude that it is possible to recover the network connectivity from the distribution of times that the neuronal membrane voltage spends in Up states.

Neuronal excitability relies on inward sodium and outward potassium fluxes during action potentials. To prevent neuronal hyperexcitability, potassium ions have to be taken up quickly. However, the dynamics of the activity-dependent potassium fluxes and the molecular pathways underlying extracellular potassium homeostasis remain elusive. To decipher the specific and acute contribution of astroglial Kir4.1 channels in controlling potassium homeostasis and the moment to moment neurotransmission, we built a tri-compartment model accounting for potassium dynamics between neurons, astrocytes and the extracellular space. We here demonstrate that astroglial Kir4.1 channels are sufficient to account for the slow membrane depolarization of hippocampal astrocytes and crucially contribute to extracellular potassium clearance during basal and high activity. By quantifying the dynamics of potassium levels in neuron-glia-extracellular space compartments, we show that astrocytes buffer within 6 to 9 seconds more than 80% of the potassium released by neurons in response to basal, repetitive and tetanic stimulations. Astroglial Kir4.1 channels directly lead to recovery of basal extracellular potassium levels and neuronal excitability, especially during repetitive stimulation, thereby preventing the generation of epileptiform activity. Remarkably, we also show that Kir4.1 channels strongly regulate neuronal excitability for slow 3 to 10 Hz rhythmic activity resulting from probabilistic firing activity induced by sub-firing stimulation coupled to Brownian noise. Altogether, these data suggest that astroglial Kir4.1 channels are crucially involved in extracellular potassium homeostasis regulating theta rhythmic activity.

Unlabelled: :, Background: Default activation of the spindle assembly checkpoint provides severe constraints on the underlying biochemical activation rates: on one hand, the cell cannot divide before all chromosomes are aligned, but on the other hand, when they are ready, the separation is quite fast, lasting a few minutes. Our purpose is to use these opposed constraints to estimate the associated chemical rates., Results: To analyze the above constraints, we develop a markovian model to describe the dynamics of Cdc20 molecules. We compute the probability for no APC/C activation before time t, the distribution of Cdc20 at equilibrium and the mean time to complete APC/C activation after all chromosomes are attached., Conclusions: By studying Cdc20 inhibition and the activation time, we obtain a range for the main chemical reaction rates regulating the spindle assembly checkpoint and transition to anaphase.