Maximizing Protein Translation Rate in the Ribosome Flow Model: The Homogeneous Case

Compensating Complete Loss of Signal Recognition Particle During Co-translational Protein Targeting by the Translation Speed and Accuracy

Signal recognition particle (SRP) is critical for delivering co-translational proteins to the bacterial inner membrane. Previously, we identified SRP suppressors in Escherichia coli that inhibit translation initiation and elongation, which provided insights into the mechanism of bypassing the requirement of SRP. Suppressor mutations tended to be located in regions that govern protein translation under evolutionary pressure. To test this hypothesis, we re-executed the suppressor screening of SRP. Here, we isolated a novel SRP suppressor mutation located in the Shine–Dalgarno sequence of the S10 operon, which partially offset the targeting defects of SRP-dependent proteins. We found that the suppressor mutation decreased the protein translation rate, which extended the time window of protein targeting. This increased the possibility of the correct localization of inner membrane proteins. Furthermore, the fidelity of translation was decreased in suppressor cells, suggesting that the quality control of translation was inactivated to provide an advantage in tolerating toxicity caused by the loss of SRP. Our results demonstrated that the inefficient protein targeting due to SRP deletion can be rescued through modulating translational speed and accuracy.

Signal Recognition Particle Suppressor Screening Reveals the Regulation of Membrane Protein Targeting by the Translation Rate

The signal recognition particle (SRP) is conserved in all living organisms, and it cotranslationally delivers proteins to the inner membrane or endoplasmic reticulum. Recently, SRP loss was found not to be lethal in either the eukaryote Saccharomyces cerevisiae or the prokaryote Streptococcus mutans In Escherichia coli, the role of SRP in mediating inner membrane protein (IMP) targeting has long been studied. However, the essentiality of SRP remains a controversial topic, partly hindered by the lack of strains in which SRP is completely absent. Here we show that the SRP was nonessential in E. coli by suppressor screening. We identified two classes of extragenic suppressors-two translation initiation factors and a ribosomal protein-all of which are involved in translation initiation. The translation rate and inner membrane proteomic analyses were combined to define the mechanism that compensates for the lack of SRP. The primary factor that contributes to the efficiency of IMP targeting is the extension of the time window for targeting by pausing the initiation of translation, which further reduces translation initiation and elongation rates. Furthermore, we found that easily predictable features in the nascent chain determine the specificity of protein targeting. Our results show why the loss of the SRP pathway does not lead to lethality. We report a new paradigm in which the time delay in translation initiation is beneficial during protein targeting in the absence of SRP.IMPORTANCE Inner membrane proteins (IMPs) are cotranslationally inserted into the inner membrane or endoplasmic reticulum by the signal recognition particle (SRP). Generally, the deletion of SRP can result in protein targeting defects in Escherichia coli Suppressor screening for loss of SRP reveals that pausing at the translation start site is likely to be critical in allowing IMP targeting and avoiding aggregation. In this work, we found for the first time that SRP is nonessential in E. coli The time delay in initiation is different from the previous mechanism that only slows down the elongation rate. It not only maximizes the opportunity for untranslated ribosomes to be near the inner membrane but also extends the time window for targeting translating ribosomes by decreasing the speed of translation. We anticipate that our work will be a starting point for a more delicate regulatory mechanism of protein targeting.

Nonlinear phenotypic variation uncovers the emergence of heterosis in Arabidopsis thaliana

Heterosis describes the phenotypic superiority of hybrids over their parents in traits related to agronomic performance and fitness. Understanding and predicting nonadditive inheritance such as heterosis is crucial for evolutionary biology as well as for plant and animal breeding. However, the physiological bases of heterosis remain debated. Moreover, empirical data in various species have shown that diverse genetic and molecular mechanisms are likely to explain heterosis, making it difficult to predict its emergence and amplitude from parental genotypes alone. In this study, we examined a model of physiological dominance initially proposed by Sewall Wright to explain the nonadditive inheritance of traits like metabolic fluxes at the cellular level. We evaluated Wright's model for two fitness-related traits at the whole-plant level, growth rate and fruit number, using 450 hybrids derived from crosses among natural accessions of A. thaliana. We found that allometric relationships between traits constrain phenotypic variation in a nonlinear and similar manner in hybrids and accessions. These allometric relationships behave predictably, explaining up to 75% of heterosis amplitude, while genetic distance among parents at best explains 7%. Thus, our findings are consistent with Wright's model of physiological dominance and suggest that the emergence of heterosis on plant performance is an intrinsic property of nonlinear relationships between traits. Furthermore, our study highlights the potential of a geometric approach of phenotypic relationships for predicting heterosis of major components of crop productivity and yield.

Networks of ribosome flow models for modeling and analyzing intracellular traffic

The ribosome flow model with input and output (RFMIO) is a deterministic dynamical system that has been used to study the flow of ribosomes during mRNA translation. The input of the RFMIO controls its initiation rate and the output represents the ribosome exit rate (and thus the protein production rate) at the 3′ end of the mRNA molecule. The RFMIO and its variants encapsulate important properties that are relevant to modeling ribosome flow such as the possible evolution of “traffic jams” and non-homogeneous elongation rates along the mRNA molecule, and can also be used for studying additional intracellular processes such as transcription, transport, and more. Here we consider networks of interconnected RFMIOs as a fundamental tool for modeling, analyzing and re-engineering the complex mechanisms of protein production. In these networks, the output of each RFMIO may be divided, using connection weights, between several inputs of other RFMIOs. We show that under quite general feedback connections the network has two important properties: (1) it admits a unique steady-state and every trajectory converges to this steady-state; and (2) the problem of how to determine the connection weights so that the network steady-state output is maximized is a convex optimization problem. These mathematical properties make these networks highly suitable as models of various phenomena: property (1) means that the behavior is predictable and ordered, and property (2) means that determining the optimal weights is numerically tractable even for large-scale networks. For the specific case of a feed-forward network of RFMIOs we prove an additional useful property, namely, that there exists a spectral representation for the network steady-state, and thus it can be determined without any numerical simulations of the dynamics. We describe the implications of these results to several fundamental biological phenomena and biotechnological objectives.

Heterosis Is a Systemic Property Emerging From Non-linear Genotype-Phenotype Relationships: Evidence From in Vitro Genetics and Computer Simulations

Heterosis, the superiority of hybrids over their parents for quantitative traits, represents a crucial issue in plant and animal breeding as well as evolutionary biology. Heterosis has given rise to countless genetic, genomic and molecular studies, but has rarely been investigated from the point of view of systems biology. We hypothesized that heterosis is an emergent property of living systems resulting from frequent concave relationships between genotypic variables and phenotypes, or between different phenotypic levels. We chose the enzyme-flux relationship as a model of the concave genotype-phenotype (GP) relationship, and showed that heterosis can be easily created in the laboratory. First, we reconstituted in vitro the upper part of glycolysis. We simulated genetic variability of enzyme activity by varying enzyme concentrations in test tubes. Mixing the content of "parental" tubes resulted in "hybrids," whose fluxes were compared to the parental fluxes. Frequent heterotic fluxes were observed, under conditions that were determined analytically and confirmed by computer simulation. Second, to test this model in a more realistic situation, we modeled the glycolysis/fermentation network in yeast by considering one input flux, glucose, and two output fluxes, glycerol and acetaldehyde. We simulated genetic variability by randomly drawing parental enzyme concentrations under various conditions, and computed the parental and hybrid fluxes using a system of differential equations. Again we found that a majority of hybrids exhibited positive heterosis for metabolic fluxes. Cases of negative heterosis were due to local convexity between certain enzyme concentrations and fluxes. In both approaches, heterosis was maximized when the parents were phenotypically close and when the distributions of parental enzyme concentrations were contrasted and constrained. These conclusions are not restricted to metabolic systems: they only depend on the concavity of the GP relationship, which is commonly observed at various levels of the phenotypic hierarchy, and could account for the pervasiveness of heterosis.

A model for competition for ribosomes in the cell

A single mammalian cell includes an order of 10(4)-10(5) mRNA molecules and as many as 10(5)-10(6) ribosomes. Large-scale simultaneous mRNA translation induces correlations between the mRNA molecules, as they all compete for the finite pool of available ribosomes. This has important implications for the cell's functioning and evolution. Developing a better understanding of the intricate correlations between these simultaneous processes, rather than focusing on the translation of a single isolated transcript, should help in gaining a better understanding of mRNA translation regulation and the way elongation rates affect organismal fitness. A model of simultaneous translation is specifically important when dealing with highly expressed genes, as these consume more resources. In addition, such a model can lead to more accurate predictions that are needed in the interconnection of translational modules in synthetic biology. We develop and analyse a general dynamical model for large-scale simultaneous mRNA translation and competition for ribosomes. This is based on combining several ribosome flow models (RFMs) interconnected via a pool of free ribosomes. We use this model to explore the interactions between the various mRNA molecules and ribosomes at steady state. We show that the compound system always converges to a steady state and that it always entrains or phase locks to periodically time-varying transition rates in any of the mRNA molecules. We then study the effect of changing the transition rates in one mRNA molecule on the steady-state translation rates of the other mRNAs that results from the competition for ribosomes. We show that increasing any of the codon translation rates in a specific mRNA molecule yields a local effect, an increase in the translation rate of this mRNA, and also a global effect, the translation rates in the other mRNA molecules all increase or all decrease. These results suggest that the effect of codon decoding rates of endogenous and heterologous mRNAs on protein production is more complicated than previously thought. In addition, we show that increasing the length of an mRNA molecule decreases the production rate of all the mRNAs.

Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach

Translation is an important stage in gene expression. During this stage, macro-molecules called ribosomes travel along the mRNA strand linking amino acids together in a specific order to create a functioning protein. An important question, related to many biomedical disciplines, is how to maximize protein production. Indeed, translation is known to be one of the most energy-consuming processes in the cell, and it is natural to assume that evolution shaped this process so that it maximizes the protein production rate. If this is indeed so then one can estimate various parameters of the translation machinery by solving an appropriate mathematical optimization problem. The same problem also arises in the context of synthetic biology, namely, re-engineer heterologous genes in order to maximize their translation rate in a host organism. We consider the problem of maximizing the protein production rate using a computational model for translation-elongation called the ribosome flow model (RFM). This model describes the flow of the ribosomes along an mRNA chain of length n using a set of n first-order nonlinear ordinary differential equations. It also includes n + 1 positive parameters: the ribosomal initiation rate into the mRNA chain, and n elongation rates along the chain sites. We show that the steady-state translation rate in the RFM is a strictly concave function of its parameters. This means that the problem of maximizing the translation rate under a suitable constraint always admits a unique solution, and that this solution can be determined using highly efficient algorithms for solving convex optimization problems even for large values of n. Furthermore, our analysis shows that the optimal translation rate can be computed based only on the optimal initiation rate and the elongation rate of the codons near the beginning of the ORF. We discuss some applications of the theoretical results to synthetic biology, molecular evolution, and functional genomics.