On the gain of entrainment in the n-dimensional ribosome flow model

The ribosome flow model (RFM) is a phenomenological model for the flow of particles along a one-dimensional chain of n sites. It has been extensively used to study ribosome flow along the mRNA molecule during translation. When the transition rates along the chain are time-varying and jointly T-periodic the RFM entrains, i.e. every trajectory of the RFM converges to a unique T-periodic solution that depends on the transition rates, but not on the initial condition. In general, entrainment to periodic excitations like the 24 h solar day or the 50 Hz frequency of the electric grid is important in numerous natural and artificial systems. An interesting question, called the gain of entrainment (GOE) in the RFM, is whether proper coordination of the periodic translation rates along the mRNA can lead to a larger average protein production rate. Analysing the GOE in the RFM is non-trivial and partial results exist only for the RFM with dimensions n = 1, 2. We use a new approach to derive several results on the GOE in the general n-dimensional RFM. Perhaps surprisingly, we rigorously characterize several cases where there is no GOE, so to maximize the average production rate in these cases, the best choice is to use constant transition rates all along the chain.

Using Mechanistic Models and Machine Learning to Design Single-Color Multiplexed Nascent Chain Tracking Experiments

mRNA translation is the ubiquitous cellular process of reading messenger-RNA strands into functional proteins. Over the past decade, large strides in microscopy techniques have allowed observation of mRNA translation at a single-molecule resolution for self-consistent time-series measurements in live cells. Dubbed Nascent chain tracking (NCT), these methods have explored many temporal dynamics in mRNA translation uncaptured by other experimental methods such as ribosomal profiling, smFISH, pSILAC, BONCAT, or FUNCAT-PLA. However, NCT is currently restricted to the observation of one or two mRNA species at a time due to limits in the number of resolvable fluorescent tags. In this work, we propose a hybrid computational pipeline, where detailed mechanistic simulations produce realistic NCT videos, and machine learning is used to assess potential experimental designs for their ability to resolve multiple mRNA species using a single fluorescent color for all species. Through simulation, we show that with careful application, this hybrid design strategy could in principle be used to extend the number of mRNA species that could be watched simultaneously within the same cell. We present a simulated example NCT experiment with seven different mRNA species within the same simulated cell and use our ML labeling to identify these spots with 90% accuracy using only two distinct fluorescent tags. The proposed extension to the NCT color palette should allow experimentalists to access a plethora of new experimental design possibilities, especially for cell signalling applications requiring simultaneous study of multiple mRNAs.

Ribosome recycling induces optimal translation rate at low ribosomal availability

During eukaryotic cellular protein synthesis, ribosomal translation is made more efficient through interaction between the two ends of the messenger RNA (mRNA). Ribosomes reaching the 3′ end of the mRNA can thus recycle and begin translation again on the same mRNA, the so-called ‘closed-loop’ model. Using a driven diffusion lattice model of translation, we study the effects of ribosome recycling on the dynamics of ribosome flow and density on the mRNA. We show that ribosome recycling induces a substantial increase in ribosome current. Furthermore, for sufficiently large values of the recycling rate, the lattice does not transition directly from low to high ribosome density, as seen in lattice models without recycling. Instead, a maximal current phase becomes accessible for much lower values of the initiation rate, and multiple phase transitions occur over a wide region of the phase plane. Crucially, we show that in the presence of ribosome recycling, mRNAs can exhibit a peak in protein production at low values of the initiation rate, beyond which translation rate decreases. This has important implications for translation of certain mRNAs, suggesting that there is an optimal concentration of ribosomes at which protein synthesis is maximal, and beyond which translational efficiency is impaired.