How total mRNA influences cell growth.

Experimental observations tracing back to the 1960s imply that ribosome quantities play a prominent role in determining a cell's growth. Nevertheless, in biologically relevant scenarios, growth can also be influenced by the levels of mRNA and RNA polymerase. Here, we construct a quantitative model of biosynthesis providing testable scenarios for these situations. The model explores a theoretically motivated regime where RNA polymerases compete for genes and ribosomes for transcripts and gives general expressions relating growth rate, mRNA concentrations, ribosome, and RNA polymerase levels. On general grounds, the model predicts how the fraction of ribosomes in the proteome depends on total mRNA concentration and inspects an underexplored regime in which the trade-off between transcript levels and ribosome abundances sets the cellular growth rate. In particular, we show that the model predicts and clarifies three important experimental observations, in budding yeast and Escherichia coli bacteria: i) that the growth-rate cost of unneeded protein expression can be affected by mRNA levels, ii) that resource optimization leads to decreasing trends in mRNA levels at slow growth, and iii) that ribosome allocation may increase, stay constant, or decrease, in response to transcription-inhibiting antibiotics. Since the data indicate that a regime of joint limitation may apply in physiological conditions and not only to perturbations, we speculate that this regime is likely self-imposed.

Optimal control of ribosome population for gene expression under periodic nutrient intake.

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.

Viro-fluidics: Real-time analysis of virus production kinetics at the single-cell level.

Real-time visualization and quantification of viruses released by a cell are crucial to further decipher infection processes. Kinetics studies at the single-cell level will circumvent the limitations of bulk assays with asynchronous virus replication. We have implemented a "viro-fluidic" method, which combines microfluidics and virology at single-cell and single-virus resolutions. As an experimental model, we used standard cell lines producing fluorescent HIV-like particles (VLPs). First, to scale the strategy to the single-cell level, we validated a sensitive flow virometry system to detect VLPs in low concentration samples (≥104 VLPs/mL). Then, this system was coupled to a single-cell trapping device to monitor in real-time the VLPs released, one at a time, from single cells under cell culture conditions. Our results revealed an average production rate of 50 VLPs/h/cell similar to the rate estimated for the same cells grown in population. Thus, the virus-producing capacities of the trapped cells were preserved and its real-time monitoring was accurate. Moreover, single-cell analysis revealed a release of VLPs with stochastic bursts with typical time intervals of few minutes, revealing the existence of limiting step(s) in the virus biogenesis process. Our tools can be applied to other pathogens or to extracellular vesicles to elucidate the dissemination mechanisms of these biological nanoparticles.

Protein degradation sets the fraction of active ribosomes at vanishing growth.

Growing cells adopt common basic strategies to achieve optimal resource allocation under limited resource availability. Our current understanding of such "growth laws" neglects degradation, assuming that it occurs slowly compared to the cell cycle duration. Here we argue that this assumption cannot hold at slow growth, leading to important consequences. We propose a simple framework showing that at slow growth protein degradation is balanced by a fraction of "maintenance" ribosomes. Consequently, active ribosomes do not drop to zero at vanishing growth, but as growth rate diminishes, an increasing fraction of active ribosomes performs maintenance. Through a detailed analysis of compiled data, we show that the predictions of this model agree with data from E. coli and S. cerevisiae. Intriguingly, we also find that protein degradation increases at slow growth, which we interpret as a consequence of active waste management and/or recycling. Our results highlight protein turnover as an underrated factor for our understanding of growth laws across kingdoms.

Unraveling Molecular Interactions in Liquid-Liquid Phase Separation of Disordered Proteins by Atomistic Simulations.

Membraneless organelles are dynamical cellular condensates formed via biomolecular liquid-liquid phase separation of proteins and RNA molecules. Multiple evidence suggests that in several cases disordered proteins are structural scaffolds that drive the condensation by forming a dynamic network of inter- and intramolecular contacts. Despite the blooming research activity in this field, the structural characterization of these entities is very limited, and we still do not understand how the phase behavior is encoded in the amino acid sequences of the scaffolding proteins. Here we exploited explicit-solvent atomistic simulations to investigate the N-terminal disordered region of DEAD-box helicase 4 (NDDX4), which is a well-established model for phase separation. Notably, we determined NDDX4 conformational ensemble at the single-molecule level, and we relied on a "divide-and-conquer" strategy, based on simulations of various protein fragments at high concentration, to probe intermolecular interactions in conditions mimicking real condensates. Our results provide a high-resolution picture of the molecular mechanisms underlying phase separation in agreement with NMR and mutagenesis data and suggest that clusters of arginine and aromatic residues may stabilize the assembly of several condensates.

Rational programming of history-dependent logic in cellular populations.

Genetic programs operating in a history-dependent fashion are ubiquitous in nature and govern sophisticated processes such as development and differentiation. The ability to systematically and predictably encode such programs would advance the engineering of synthetic organisms and ecosystems with rich signal processing abilities. Here we implement robust, scalable history-dependent programs by distributing the computational labor across a cellular population. Our design is based on standardized recombinase-driven DNA scaffolds expressing different genes according to the order of occurrence of inputs. These multicellular computing systems are highly modular, do not require cell-cell communication channels, and any program can be built by differential composition of strains containing well-characterized logic scaffolds. We developed automated workflows that researchers can use to streamline program design and optimization. We anticipate that the history-dependent programs presented here will support many applications using cellular populations for material engineering, biomanufacturing and healthcare.

Inferring efficiency of translation initiation and elongation from ribosome profiling.

One of the main goals of ribosome profiling is to quantify the rate of protein synthesis at the level of translation. Here, we develop a method for inferring translation elongation kinetics from ribosome profiling data using recent advances in mathematical modelling of mRNA translation. Our method distinguishes between the elongation rate intrinsic to the ribosome's stepping cycle and the actual elongation rate that takes into account ribosome interference. This distinction allows us to quantify the extent of ribosomal collisions along the transcript and identify individual codons where ribosomal collisions are likely. When examining ribosome profiling in yeast, we observe that translation initiation and elongation are close to their optima and traffic is minimized at the beginning of the transcript to favour ribosome recruitment. However, we find many individual sites of congestion along the mRNAs where the probability of ribosome interference can reach $50\%$. Our work provides new measures of translation initiation and elongation efficiencies, emphasizing the importance of rating these two stages of translation separately.

An equilibrium model for ribosome competition.

The number of ribosomes in a cell is considered as limiting, and gene expression is thus largely determined by their cellular concentration. In this work we develop a toy model to study the trade-off between the ribosomal supply and the demand of the translation machinery, dictated by the composition of the transcript pool. Our equilibrium framework is useful to highlight qualitative behaviours and new means of gene expression regulation determined by the fine balance of this trade-off. We also speculate on the possible impact of these mechanisms on cellular physiology.

Driven transport on a flexible polymer with particle recycling: A model inspired by transcription and translation.

Many theoretical works have attempted to coarse grain gene expression at the level of transcription and translation via frameworks based on exclusion processes. Usually in these models the three-dimensional conformation of the substrates (DNA and mRNA) is neglected, and particles move on a static unidimensional lattice in contact to an infinite reservoir. In this work we generalize the paradigmatic exclusion process and study the transport of particles along a unidimensional polymerlike flexible lattice immersed in a three-dimensional particle reservoir. We study the recycling of particles in the reservoir, how the transport is influenced by the global conformation of the lattice, and, in turn, how particle density dictates the structure of the polymer.

Power series solution of the inhomogeneous exclusion process.

We develop a power series method for the nonequilibrium steady state of the inhomogeneous one-dimensional totally asymmetric simple exclusion process (TASEP) in contact with two particle reservoirs and with site-dependent hopping rates in the bulk. The power series is performed in the entrance or exit rates governing particle exchange with the reservoirs, and the corresponding particle current is computed analytically up to the cubic term in the entry or exit rate, respectively. We also show how to compute higher-order terms using combinatorial objects known as Young tableaux. Our results address the long outstanding problem of finding the exact nonequilibrium steady state of the inhomogeneous TASEP. The findings are particularly relevant to the modeling of mRNA translation in which the rate of translation initiation, corresponding to the entrance rate in the TASEP, is typically small.

Deciphering mRNA Sequence Determinants of Protein Production Rate.

One of the greatest challenges in biophysical models of translation is to identify coding sequence features that affect the rate of translation and therefore the overall protein production in the cell. We propose an analytic method to solve a translation model based on the inhomogeneous totally asymmetric simple exclusion process, which allows us to unveil simple design principles of nucleotide sequences determining protein production rates. Our solution shows an excellent agreement when compared to numerical genome-wide simulations of S. cerevisiae transcript sequences and predicts that the first 10 codons, which is the ribosome footprint length on the mRNA, together with the value of the initiation rate, are the main determinants of protein production rate under physiological conditions. Finally, we interpret the obtained analytic results based on the evolutionary role of the codons' choice for regulating translation rates and ribosome densities.

Gene length as a regulator for ribosome recruitment and protein synthesis: theoretical insights.

Protein synthesis rates are determined, at the translational level, by properties of the transcript's sequence. The efficiency of an mRNA can be tuned by varying the ribosome binding sites controlling the recruitment of the ribosomes, or the codon usage establishing the speed of protein elongation. In this work we propose transcript length as a further key determinant of translation efficiency. Based on a physical model that considers the kinetics of ribosomes advancing on the mRNA and diffusing in its surrounding, as well as mRNA circularisation and ribosome drop-off, we explain how the transcript length may play a central role in establishing ribosome recruitment and the overall translation rate of an mRNA. According to our results, the proximity of the 3' end to the ribosomal recruitment site of the mRNA could induce a feedback in the translation process that would favour the recycling of ribosomes. We also demonstrate how this process may be involved in shaping the experimental ribosome density-gene length dependence. Finally, we argue that cells could exploit this mechanism to adjust and balance the usage of its ribosomal resources.

Identification of the mRNA targets of tRNA-specific regulation using genome-wide simulation of translation.

tRNA gene copy number is a primary determinant of tRNA abundance and therefore the rate at which each tRNA delivers amino acids to the ribosome during translation. Low-abundance tRNAs decode rare codons slowly, but it is unclear which genes might be subject to tRNA-mediated regulation of expression. Here, those mRNA targets were identified via global simulation of translation. In-silico mRNA translation rates were compared for each mRNA in both wild-type and a [Formula: see text] sup70-65 mutant, which exhibits a pseudohyphal growth phenotype and a 75% slower CAG codon translation rate. Of 4900 CAG-containing mRNAs, 300 showed significantly reduced in silico translation rates in a simulated tRNA mutant. Quantitative immunoassay confirmed that the reduced translation rates of sensitive mRNAs were [Formula: see text] concentration-dependent. Translation simulations showed that reduced [Formula: see text] concentrations triggered ribosome queues, which dissipated at reduced translation initiation rates. To validate this prediction experimentally, constitutive gcn2 kinase mutants were used to reduce in vivo translation initiation rates. This repaired the relative translational rate defect of target mRNAs in the sup70-65 background, and ameliorated sup70-65 pseudohyphal growth phenotypes. We thus validate global simulation of translation as a new tool to identify mRNA targets of tRNA-specific gene regulation.

Stepping and crowding of molecular motors: statistical kinetics from an exclusion process perspective.

Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These macromolecules, nowadays investigated with advanced experimental techniques to unveil their molecular mechanisms and the properties of their kinetic cycles, are implicated in many biological processes, ranging from biopolymerization (e.g., RNA polymerases and ribosomes) to intracellular transport (motor proteins such as kinesins or dyneins). Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics still remains unclear. Advances in this direction will improve our comprehension of transport process in the natural intracellular medium, where processive motor enzymes might operate in crowded conditions. In this work, we therefore extend contemporary statistical kinetic analysis to study collective transport phenomena of motors in terms of lattice gas models belonging to the exclusion process class. Via numerical simulations, we show how to interpret and use the randomness calculated from single particle trajectories in crowded conditions. Importantly, we also show that time fluctuations and non-Poissonian behavior are intrinsically related to spatial correlations and the emergence of large, but finite, clusters of comoving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.

Motor protein traffic regulation by supply-demand balance of resources.

In cells and in in vitro assays the number of motor proteins involved in biological transport processes is far from being unlimited. The cytoskeletal binding sites are in contact with the same finite reservoir of motors (either the cytosol or the flow chamber) and hence compete for recruiting the available motors, potentially depleting the reservoir and affecting cytoskeletal transport. In this work we provide a theoretical framework in which to study, analytically and numerically, how motor density profiles and crowding along cytoskeletal filaments depend on the competition of motors for their binding sites. We propose two models in which finite processive motor proteins actively advance along cytoskeletal filaments and are continuously exchanged with the motor pool. We first look at homogeneous reservoirs and then examine the effects of free motor diffusion in the surrounding medium. We consider as a reference situation recent in vitro experimental setups of kinesin-8 motors binding and moving along microtubule filaments in a flow chamber. We investigate how the crowding of linear motor proteins moving on a filament can be regulated by the balance between supply (concentration of motor proteins in the flow chamber) and demand (total number of polymerized tubulin heterodimers). We present analytical results for the density profiles of bound motors and the reservoir depletion, and propose novel phase diagrams that present the formation of jams of motor proteins on the filament as a function of two tuneable experimental parameters: the motor protein concentration and the concentration of tubulins polymerized into cytoskeletal filaments. Extensive numerical simulations corroborate the analytical results for parameters in the experimental range and also address the effects of diffusion of motor proteins in the reservoir. We then propose experiments for validating our models and discuss how the 'supply-demand' effects can regulate motor traffic also in in vivo conditions.

Ribosome traffic on mRNAs maps to gene ontology: genome-wide quantification of translation initiation rates and polysome size regulation.

To understand the complex relationship governing transcript abundance and the level of the encoded protein, we integrate genome-wide experimental data of ribosomal density on mRNAs with a novel stochastic model describing ribosome traffic dynamics during translation elongation. This analysis reveals that codon arrangement, rather than simply codon bias, has a key role in determining translational efficiency. It also reveals that translation output is governed both by initiation efficiency and elongation dynamics. By integrating genome-wide experimental data sets with simulation of ribosome traffic on all Saccharomyces cerevisiae ORFs, mRNA-specific translation initiation rates are for the first time estimated across the entire transcriptome. Our analysis identifies different classes of mRNAs characterised by their initiation rates, their ribosome traffic dynamics, and by their response to ribosome availability. Strikingly, this classification based on translational dynamics maps onto key gene ontological classifications, revealing evolutionary optimisation of translation responses to be strongly influenced by gene function.

Transport on a lattice with dynamical defects.

Many transport processes in nature take place on substrates, often considered as unidimensional lanes. These unidimensional substrates are typically nonstatic: Affected by a fluctuating environment, they can undergo conformational changes. This is particularly true in biological cells, where the state of the substrate is often coupled to the active motion of macromolecular complexes, such as motor proteins on microtubules or ribosomes on mRNAs, causing new interesting phenomena. Inspired by biological processes such as protein synthesis by ribosomes and motor protein transport, we introduce the concept of localized dynamical sites coupled to a driven lattice gas dynamics. We investigate the phenomenology of transport in the presence of dynamical defects and find a regime characterized by an intermittent current and subject to severe finite-size effects. Our results demonstrate the impact of the regulatory role of the dynamical defects in transport not only in biology but also in more general contexts.

A yeast tRNA mutant that causes pseudohyphal growth exhibits reduced rates of CAG codon translation.

In Saccharomyces cerevisiae, the SUP70 gene encodes the CAG-decoding tRNA(Gln)(CUG). A mutant allele, sup70-65, induces pseudohyphal growth on rich medium, an inappropriate nitrogen starvation response. This mutant tRNA is also a UAG nonsense suppressor via first base wobble. To investigate the basis of the pseudohyphal phenotype, 10 novel sup70 UAG suppressor alleles were identified, defining positions in the tRNA(Gln)(CUG) anticodon stem that restrict first base wobble. However, none conferred pseudohyphal growth, showing altered CUG anticodon presentation cannot itself induce pseudohyphal growth. Northern blot analysis revealed the sup70-65 tRNA(Gln)(CUG) is unstable, inefficiently charged, and 80% reduced in its effective concentration. A stochastic model simulation of translation predicted compromised expression of CAG-rich ORFs in the tRNA(Gln)(CUG)-depleted sup70-65 mutant. This prediction was validated by demonstrating that luciferase expression in the mutant was 60% reduced by introducing multiple tandem CAG (but not CAA) codons into this ORF. In addition, the sup70-65 pseudohyphal phenotype was partly complemented by overexpressing CAA-decoding tRNA(Gln)(UUG), an inefficient wobble-decoder of CAG. We thus show that introducing codons decoded by a rare tRNA near the 5' end of an ORF can reduce eukaryote translational expression, and that the mutant tRNA(CUG)(Gln) constitutive pseudohyphal differentiation phenotype correlates strongly with reduced CAG decoding efficiency.

Mixed population of competing totally asymmetric simple exclusion processes with a shared reservoir of particles.

We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths and entry and exit rates, competing for a finite reservoir of particles. We present relations for the partitioning of particles between the reservoir and the lattices: These relations allow us to show that competition for particles can have nontrivial effects on the phase behavior of individual lattices. For a system with nonidentical lattices, we find that when a subset of lattices undergoes a phase transition from low to high density, the entire set of lattice currents becomes independent of total particle number. We generalize our approach to systems with a continuous distribution of lattice parameters, for which we demonstrate that measurements of the current carried by a single lattice type can be used to extract the entire distribution of lattice parameters. Our approach applies to populations of TASEPs with any distribution of lattice parameters and could easily be extended beyond the mean-field case.