Two-species totally asymmetric simple exclusion process model: From a simple description to intermittency and traveling traffic jams.

We extend the paradigmatic and versatile totally asymmetric simple exclusion process (TASEP) for stochastic 1D transport to allow for two different particle species, each having specific entry and exit rates. We offer a complete mean-field analysis, including a phase diagram, by mapping this model onto an effective one-species TASEP. Stochastic simulations confirm the results, but indicate deviations when the particle species have very different exit rates. We illustrate that this is due to a phenomenon of intermittency, and formulate a refined "intermittent" mean-field theory for this regime. We discuss how nonstationary effects may further enrich the phenomenology.

The molecular aetiology of tRNA synthetase depletion: induction of a GCN4 amino acid starvation response despite homeostatic maintenance of charged tRNA levels.

During protein synthesis, charged tRNAs deliver amino acids to translating ribosomes, and are then re-charged by tRNA synthetases (aaRS). In humans, mutant aaRS cause a diversity of neurological disorders, but their molecular aetiologies are incompletely characterised. To understand system responses to aaRS depletion, the yeast glutamine aaRS gene (GLN4) was transcriptionally regulated using doxycycline by tet-off control. Depletion of Gln4p inhibited growth, and induced a GCN4 amino acid starvation response, indicative of uncharged tRNA accumulation and Gcn2 kinase activation. Using a global model of translation that included aaRS recharging, Gln4p depletion was simulated, confirming slowed translation. Modelling also revealed that Gln4p depletion causes negative feedback that matches translational demand for Gln-tRNAGln to aaRS recharging capacity. This maintains normal charged tRNAGln levels despite Gln4p depletion, confirmed experimentally using tRNA Northern blotting. Model analysis resolves the paradox that Gln4p depletion triggers a GCN4 response, despite maintenance of tRNAGln charging levels, revealing that normally, the aaRS population can sequester free, uncharged tRNAs during aminoacylation. Gln4p depletion reduces this sequestration capacity, allowing uncharged tRNAGln to interact with Gcn2 kinase. The study sheds new light on mutant aaRS disease aetiologies, and explains how aaRS sequestration of uncharged tRNAs can prevent GCN4 activation under non-starvation conditions.

Translational control of gene expression via interacting feedback loops.

Translation is a key step in the synthesis of proteins. Accordingly, cells have evolved an intricate array of control mechanisms to regulate this process. By constructing a multicomponent mathematical framework we uncover how translation may be controlled via interacting feedback loops. Our results reveal that this interplay gives rise to a remarkable range of protein synthesis dynamics, including oscillations, step change, and bistability. This suggests that cells may have recourse to a much richer set of control mechanisms than was previously understood.

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.

Novel mRNA-specific effects of ribosome drop-off on translation rate and polysome profile.

The well established phenomenon of ribosome drop-off plays crucial roles in translational accuracy and nutrient starvation responses during protein translation. When cells are under stress conditions, such as amino acid starvation or aminoacyl-tRNA depletion due to a high level of recombinant protein expression, ribosome drop-off can substantially affect the efficiency of protein expression. Here we introduce a mathematical model that describes the effects of ribosome drop-off on the ribosome density along the mRNA and on the concomitant protein synthesis rate. Our results show that ribosome premature termination may lead to non-intuitive ribosome density profiles, such as a ribosome density which increases from the 5' to the 3' end. Importantly, the model predicts that the effects of ribosome drop-off on the translation rate are mRNA-specific, and we quantify their resilience to drop-off, showing that the mRNAs which present ribosome queues are much less affected by ribosome drop-off than those which do not. Moreover, among those mRNAs that do not present ribosome queues, resilience to drop-off correlates positively with the elongation rate, so that sequences using fast codons are expected to be less affected by ribosome drop-off. This result is consistent with a genome-wide analysis of S. cerevisiae, which reveals that under favourable growth conditions mRNAs coding for proteins involved in the translation machinery, known to be highly codon biased and using preferentially fast codons, are highly resilient to ribosome drop-off. Moreover, in physiological conditions, the translation rate of mRNAs coding for regulatory, stress-related proteins, is less resilient to ribosome drop-off. This model therefore allows analysis of variations in the translational efficiency of individual mRNAs by accounting for the full range of known ribosome behaviours, as well as explaining mRNA-specific variations in ribosome density emerging from ribosome profiling studies.

Synthetic biology routes to bio-artificial intelligence.

The design of synthetic gene networks (SGNs) has advanced to the extent that novel genetic circuits are now being tested for their ability to recapitulate archetypal learning behaviours first defined in the fields of machine and animal learning. Here, we discuss the biological implementation of a perceptron algorithm for linear classification of input data. An expansion of this biological design that encompasses cellular 'teachers' and 'students' is also examined. We also discuss implementation of Pavlovian associative learning using SGNs and present an example of such a scheme and in silico simulation of its performance. In addition to designed SGNs, we also consider the option to establish conditions in which a population of SGNs can evolve diversity in order to better contend with complex input data. Finally, we compare recent ethical concerns in the field of artificial intelligence (AI) and the future challenges raised by bio-artificial intelligence (BI).

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.

Integrative Model of Oxidative Stress Adaptation in the Fungal Pathogen Candida albicans.

The major fungal pathogen of humans, Candida albicans, mounts robust responses to oxidative stress that are critical for its virulence. These responses counteract the reactive oxygen species (ROS) that are generated by host immune cells in an attempt to kill the invading fungus. Knowledge of the dynamical processes that instigate C. albicans oxidative stress responses is required for a proper understanding of fungus-host interactions. Therefore, we have adopted an interdisciplinary approach to explore the dynamical responses of C. albicans to hydrogen peroxide (H2O2). Our deterministic mathematical model integrates two major oxidative stress signalling pathways (Cap1 and Hog1 pathways) with the three major antioxidant systems (catalase, glutathione and thioredoxin systems) and the pentose phosphate pathway, which provides reducing equivalents required for oxidative stress adaptation. The model encapsulates existing knowledge of these systems with new genomic, proteomic, transcriptomic, molecular and cellular datasets. Our integrative approach predicts the existence of alternative states for the key regulators Cap1 and Hog1, thereby suggesting novel regulatory behaviours during oxidative stress. The model reproduces both existing and new experimental observations under a variety of scenarios. Time- and dose-dependent predictions of the oxidative stress responses for both wild type and mutant cells have highlighted the different temporal contributions of the various antioxidant systems during oxidative stress adaptation, indicating that catalase plays a critical role immediately following stress imposition. This is the first model to encapsulate the dynamics of the transcriptional response alongside the redox kinetics of the major antioxidant systems during H2O2 stress in C. albicans.

Minimal model of transcriptional elongation processes with pauses.

Fundamental biological processes such as transcription and translation, where a genetic sequence is sequentially read by a macromolecule, have been well described by a classical model of nonequilibrium statistical physics, the totally asymmetric exclusion principle (TASEP). This model describes particles hopping between sites of a one-dimensional lattice, with the particle current determining the transcription or translation rate. An open problem is how to analyze a TASEP where particles can pause randomly, as has been observed during transcription. In this work, we report that surprisingly, a simple mean-field model predicts well the particle current for all values of the average pause duration, using a simple description of blocking behind paused particles.

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.

Controlling translation elongation efficiency: tRNA regulation of ribosome flux on the mRNA.

Gene expression can be regulated by a wide variety of mechanisms. One example concerns the growing body of evidence that the protein-production rate can be regulated at the level of translation elongation by controlling ribosome flux across the mRNA. Variations in the abundance of tRNA molecules cause different rates of translation of their counterpart codons. This, in turn, produces a variable landscape of translational rate across each and every mRNA, with the dynamic formation and deformation of ribosomal queues being regulated by both tRNA availability and the rates of translation initiation and termination. In the present article, a range of examples of tRNA control of gene expression are reviewed, and the use of mathematical modelling to develop a predictive understanding of the consequences of that regulation is discussed and explained. These findings encourage a view that predicting the protein-synthesis rate of each mRNA requires a holistic understanding of how each stage of translation, including elongation, contributes to the overall protein-production rate.

From START to FINISH: the influence of osmotic stress on the cell cycle.

The cell cycle is a sequence of biochemical events that are controlled by complex but robust molecular machinery. This enables cells to achieve accurate self-reproduction under a broad range of different conditions. Environmental changes are transmitted by molecular signalling networks, which coordinate their action with the cell cycle. The cell cycle process and its responses to environmental stresses arise from intertwined nonlinear interactions among large numbers of simpler components. Yet, understanding of how these pieces fit together into a coherent whole requires a systems biology approach. Here, we present a novel mathematical model that describes the influence of osmotic stress on the entire cell cycle of S. cerevisiae for the first time. Our model incorporates all recently known and several proposed interactions between the osmotic stress response pathway and the cell cycle. This model unveils the mechanisms that emerge as a consequence of the interaction between the cell cycle and stress response networks. Furthermore, it characterises the role of individual components. Moreover, it predicts different phenotypical responses for cells depending on the phase of cells at the onset of the stress. The key predictions of the model are: (i) exposure of cells to osmotic stress during the late S and the early G2/M phase can induce DNA re-replication before cell division occurs, (ii) cells stressed at the late G2/M phase display accelerated exit from mitosis and arrest in the next cell cycle, (iii) osmotic stress delays the G1-to-S and G2-to-M transitions in a dose dependent manner, whereas it accelerates the M-to-G1 transition independently of the stress dose and (iv) the Hog MAPK network compensates the role of the MEN network during cell division of MEN mutant cells. These model predictions are supported by independent experiments in S. cerevisiae and, moreover, have recently been observed in other eukaryotes.

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.

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.

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.

A systems biology analysis of long and short-term memories of osmotic stress adaptation in fungi.

BACKGROUND: Saccharomyces cerevisiae senses hyperosmotic conditions via the HOG signaling network that activates the stress-activated protein kinase, Hog1, and modulates metabolic fluxes and gene expression to generate appropriate adaptive responses. The integral control mechanism by which Hog1 modulates glycerol production remains uncharacterized. An additional Hog1-independent mechanism retains intracellular glycerol for adaptation. Candida albicans also adapts to hyperosmolarity via a HOG signaling network. However, it remains unknown whether Hog1 exerts integral or proportional control over glycerol production in C. albicans. RESULTS: We combined modeling and experimental approaches to study osmotic stress responses in S. cerevisiae and C. albicans. We propose a simple ordinary differential equation (ODE) model that highlights the integral control that Hog1 exerts over glycerol biosynthesis in these species. If integral control arises from a separation of time scales (i.e. rapid HOG activation of glycerol production capacity which decays slowly under hyperosmotic conditions), then the model predicts that glycerol production rates elevate upon adaptation to a first stress and this makes the cell adapts faster to a second hyperosmotic stress. It appears as if the cell is able to remember the stress history that is longer than the timescale of signal transduction. This is termed the long-term stress memory. Our experimental data verify this. Like S. cerevisiae, C. albicans mimimizes glycerol efflux during adaptation to hyperosmolarity. Also, transient activation of intermediate kinases in the HOG pathway results in a short-term memory in the signaling pathway. This determines the amplitude of Hog1 phosphorylation under a periodic sequence of stress and non-stressed intervals. Our model suggests that the long-term memory also affects the way a cell responds to periodic stress conditions. Hence, during osmohomeostasis, short-term memory is dependent upon long-term memory. This is relevant in the context of fungal responses to dynamic and changing environments. CONCLUSIONS: Our experiments and modeling have provided an example of identifying integral control that arises from time-scale separation in different processes, which is an important functional module in various contexts.

A max-plus model of ribosome dynamics during mRNA translation.

We examine the dynamics of the translation stage of cellular protein production, in which ribosomes move uni-directionally along an mRNA strand, building amino acid chains as they go. We describe the system using a timed event graph-a class of Petri net useful for studying discrete events, which have to satisfy constraints. We use max-plus algebra to describe a deterministic version of the model, where the constraints represent steric effects which prevent more than one ribosome reading a given codon at a given time and delays associated with the availability of the different tRNAs. We calculate the protein production rate and density of ribosomes on the mRNA and find exact agreement between these analytical results and numerical simulations of the deterministic model, even in the case of heterogeneous mRNAs.

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.

The dynamics of supply and demand in mRNA translation.

We study the elongation stage of mRNA translation in eukaryotes and find that, in contrast to the assumptions of previous models, both the supply and the demand for tRNA resources are important for determining elongation rates. We find that increasing the initiation rate of translation can lead to the depletion of some species of aa-tRNA, which in turn can lead to slow codons and queueing. Particularly striking "competition" effects are observed in simulations of multiple species of mRNA which are reliant on the same pool of tRNA resources. These simulations are based on a recent model of elongation which we use to study the translation of mRNA sequences from the Saccharomyces cerevisiae genome. This model includes the dynamics of the use and recharging of amino acid tRNA complexes, and we show via Monte Carlo simulation that this has a dramatic effect on the protein production behaviour of the system.