An implementation of the Gillespie algorithm for RNA kinetics with logarithmic time update

Design of a self-regulating mRNA gene circuit

Protein expression in vivo is predominately controlled via regulatory feedback mechanisms that adjust the level of mRNA transcription. However for positive sense single-stranded RNA viruses, protein expression is often controlled via secondary structural elements, such as internal ribosomal entry sites, that are encoded within the mRNA. The self-regulation of mRNA translation observed in this class of viruses suggests that it may be possible to design mRNAs that self-regulate their protein expression, enabling the creation of mRNAs for vaccines and other synthetic biology applications where protein levels in the cell can be tightly controlled without feedback to a transcriptional mechanism. As a proof of concept, I design a polycistronic mRNA based on bacteriophage MS2, where the upstream gene is capable of repressing synthesis of the downstream gene. Using a computational tool that simulates ribosome kinetics and the co-translational folding of the mRNA in response, I show that mutations to the mRNA can be identified which enhance the efficiency of the translation and the repression of the downstream gene. The results of this study open up the possibility of designing bespoke mRNA gene circuits in which the amount of protein synthesised in cells are self-regulated for therapeutic or antigenic purposes.

RNA-Based Sensor Systems for Affordable Diagnostics in the Age of Pandemics

In the era of the COVID-19 pandemic, the significance of point-of-care (POC) diagnostic tools has become increasingly vital, driven by the need for quick and precise virus identification. RNA-based sensors, particularly toehold sensors, have emerged as promising candidates for POC detection systems due to their selectivity and sensitivity. Toehold sensors operate by employing an RNA switch that changes the conformation when it binds to a target RNA molecule, resulting in a detectable signal. This review focuses on the development and deployment of RNA-based sensors for POC viral RNA detection with a particular emphasis on toehold sensors. The benefits and limits of toehold sensors are explored, and obstacles and future directions for improving their performance within POC detection systems are presented. The use of RNA-based sensors as a technology for rapid and sensitive detection of viral RNA holds great potential for effectively managing (dealing/coping) with present and future pandemics in resource-constrained settings.

Modelling ribosome kinetics and translational control on dynamic mRNA

The control of protein synthesis and the overall levels of various proteins in the cell is critical for achieving homoeostasis. Regulation of protein levels can occur at the transcriptional level, where the total number of messenger RNAs in the overall transcriptome are controlled, or at the translational level, where interactions of proteins and ribosomes with the messenger RNA determine protein translational efficiency. Although transcriptional control of mRNA levels is the most commonly used regulatory control mechanism in cells, positive-sense single-stranded RNA viruses often utilise translational control mechanisms to regulate their proteins in the host cell. Here I detail a computational method for stochastically simulating protein synthesis on a dynamic messenger RNA using the Gillespie algorithm, where the mRNA is allowed to co-translationally fold in response to ribosome movement. Applying the model to the test case of the bacteriophage MS2 virus, I show that the models ability to accurately reproduce experimental measurements of coat protein production and translational repression of the viral RNA dependant RNA polymerase at high coat protein concentrations. The computational techniques reported here open up the potential to examine the infection dynamics of a ssRNA virus in a host cell at the level of the genomic RNA, as well as examine general translation control mechanisms present in polycistronic mRNAs.

Similarity of extremely rare nonequilibrium processes to equilibrium processes

For system coupled to heat baths, typical nonequilibrated processes, e.g., induced by varying an external parameter without waiting for equilibration in between, are very different from the corresponding equilibrium infinitely slow processes. Nevertheless, there are connections between equilibrium and nonequilibrated behaviors, e.g., the theorems of Jarzynski and Crooks, which relate the distribution P(W) of nonequilibrium work to the free energy differences ΔF. Here we study the naturally arising question, whether those relevant but rare trajectories, which exhibit these work values, show a higher degree of similarity to equilibrium. For convenience, we have chosen a simple model of RNA secondary structures (or single-stranded DNA), here modeling a medium-size hairpin structure, under influence of a varying external force. This allows us to measure the work W during the resulting fast unfolding and refolding processes within Monte Carlo simulations, i.e., in nonequilibrium. Also we sample numerically efficiently directly in exact equilibrium, for comparison. Using a sophisticated large-deviation algorithm, we are able to measure work distributions with high precision down to probabilities as small as 10^{-46}, enabling us to verify the Crooks and Jarzynski theorems. Furthermore, we analyze force-extension curves and the configurations of the secondary structures during unfolding and refolding for typical equilibrium processes and nonequilibrated processes. We find that the nonequilibrated processes where the work values are close to those which are most relevant for applying Crooks and Jarzynski theorems, respectively, but which occur with exponential small probabilities, are most and quite similar to the equilibrium processes.

Cotranscriptional Kinetic Folding of RNA Secondary Structures Including Pseudoknots

Computational prediction of ribonucleic acid (RNA) structures is an important problem in computational structural biology. Studies of RNA structure formation often assume that the process starts from a fully synthesized sequence. Experimental evidence, however, has shown that RNA folds concurrently with its elongation. We investigate RNA secondary structure formation, including pseudoknots, that takes into account the cotranscriptional effects. We propose a single-nucleotide resolution kinetic model of the folding process of RNA molecules, where the polymerase-driven elongation of an RNA strand by a new nucleotide is included as a primitive operation, together with a stochastic simulation method that implements this folding concurrently with the transcriptional synthesis. Numerical case studies show that our cotranscriptional RNA folding model can predict the formation of conformations that are favored in actual biological systems. Our new computational tool can thus provide quantitative predictions and offer useful insights into the kinetics of RNA folding.

An Automated Model Test System for Systematic Development and Improvement of Gene Expression Models

Gene expression models greatly accelerate the engineering of synthetic metabolic pathways and genetic circuits by predicting sequence-function relationships and reducing trial-and-error experimentation. However, developing models with more accurate predictions remains a significant challenge. Here we present a model test system that combines advanced statistics, machine learning, and a database of 9862 characterized genetic systems to automatically quantify model accuracies, accept or reject mechanistic hypotheses, and identify areas for model improvement. We also introduce model capacity, a new information theoretic metric for correct cross-data-set comparisons. We demonstrate the model test system by comparing six models of translation initiation rate, evaluating 100 mechanistic hypotheses, and uncovering new sequence determinants that control protein expression levels. We then applied these results to develop a biophysical model of translation initiation rate with significant improvements in accuracy. Automated model test systems will dramatically accelerate the development of gene expression models, and thereby transition synthetic biology into a mature engineering discipline.

Finding the direct optimal RNA barrier energy and improving pathways with an arbitrary energy model

Motivation

RNA folding kinetics plays an important role in the biological functions of RNA molecules. An important goal in the investigation of the kinetic behavior of RNAs is to find the folding pathway with the lowest energy barrier. For this purpose, most of the existing methods use heuristics because the number of possible pathways is huge even if only the shortest (direct) folding pathways are considered.

Results

In this study, we propose a new method using a best-first search strategy to efficiently compute the exact solution of the minimum barrier energy of direct pathways. Using our method, we can find the exact direct pathways within a Hamming distance of 20, whereas the previous methods even miss the exact short pathways. Moreover, our method can be used to improve the pathways found by existing methods for exploring indirect pathways.

Availability and implementation

The source code and datasets created and used in this research are available at https://github.com/eukaryo/czno.

Supplementary information

Supplementary data are available at Bioinformatics online.

A stochastic model for simulating ribosome kinetics in vivo

Computational modelling of in vivo protein synthesis is highly complicated, as it requires the simulation of ribosomal movement over the entire transcriptome, as well as consideration of the concentration effects from 40+ different types of tRNAs and numerous other protein factors. Here I report on the development of a stochastic model for protein translation that is capable of simulating the dynamical process of in vivo protein synthesis in a prokaryotic cell containing several thousand unique mRNA sequences, with explicit nucleotide information for each, and report on a number of biological predictions which are beyond the scope of existing models. In particular, I show that, when the complex network of concentration dependent interactions between elongation factors, tRNAs, ribosomes, and other factors required for protein synthesis are included in full detail, several biological phenomena, such as the increasing peptide elongation rate with bacterial growth rate, are predicted as emergent properties of the model. The stochastic model presented here demonstrates the importance of considering the translational process at this level of detail, and provides a platform to interrogate various aspects of translation that are difficult to study in more coarse-grained models.

Computational approaches for alternative and transient secondary structures of ribonucleic acids

Transient and alternative structures of ribonucleic acids (RNAs) play essential roles in various regulatory processes, such as translation regulation in living cells. Because experimental analyses for RNA structures are difficult and time-consuming, computational approaches based on RNA secondary structures are promising. In this article, we review computational methods for detecting and analyzing transient/alternative secondary structures of RNAs, including static approaches based on probabilistic distributions of RNA secondary structures and dynamic approaches such as kinetic folding and folding pathway predictions.

A Model for Viral Assembly around an Explicit RNA Sequence Generates an Implicit Fitness Landscape

Previously, a stochastic model of single-stranded RNA virus assembly was created to model the cooperative effects between capsid proteins and genomic RNA that would occur in a packaging signal-mediated assembly process. In such an assembly scenario, multiple secondary structural elements from within the RNA, termed "packaging signals" (PS), contact coat proteins and facilitate efficient capsid assembly. In this work, the assembly model is extended to incorporate explicit nucleotide sequence information as well as simple aspects of RNA folding that would be occurring during the RNA/capsid coassembly process. Applying this paradigm to a dodecahedral viral capsid, a computer-derived nucleotide sequence is evolved de novo that is optimal for packaging the RNA into capsids, while also containing capacity for coding for a viral protein. Analysis of the effects of mutations on the ability of the RNA sequence to successfully package into a viral capsid reveals a complex fitness landscape where the majority of mutations are neutral with respect to packaging efficiency with a small number of mutations resulting in a near-complete loss of RNA packaging. Moreover, the model shows how attempts to ablate PSs in the viral RNA sequence may result in redundant PSs already present in the genome fulfilling their packaging role. This explains why recent experiments that attempt to ablate putative PSs may not see an effect on packaging. This modeling framework presents an example of how an implicit mapping can be made from genotype to a fitness parameter important for viral biology, i.e., viral capsid yield, with potential applications to theoretical models of viral evolution.

RNA folding kinetics using Monte Carlo and Gillespie algorithms

RNA secondary structure folding kinetics is known to be important for the biological function of certain processes, such as the hok/sok system in E. coli. Although linear algebra provides an exact computational solution of secondary structure folding kinetics with respect to the Turner energy model for tiny ([Formula: see text]20 nt) RNA sequences, the folding kinetics for larger sequences can only be approximated by binning structures into macrostates in a coarse-grained model, or by repeatedly simulating secondary structure folding with either the Monte Carlo algorithm or the Gillespie algorithm. Here we investigate the relation between the Monte Carlo algorithm and the Gillespie algorithm. We prove that asymptotically, the expected time for a K-step trajectory of the Monte Carlo algorithm is equal to [Formula: see text] times that of the Gillespie algorithm, where [Formula: see text] denotes the Boltzmann expected network degree. If the network is regular (i.e. every node has the same degree), then the mean first passage time (MFPT) computed by the Monte Carlo algorithm is equal to MFPT computed by the Gillespie algorithm multiplied by [Formula: see text]; however, this is not true for non-regular networks. In particular, RNA secondary structure folding kinetics, as computed by the Monte Carlo algorithm, is not equal to the folding kinetics, as computed by the Gillespie algorithm, although the mean first passage times are roughly correlated. Simulation software for RNA secondary structure folding according to the Monte Carlo and Gillespie algorithms is publicly available, as is our software to compute the expected degree of the network of secondary structures of a given RNA sequence-see http://bioinformatics.bc.edu/clote/RNAexpNumNbors .

Network Properties of the Ensemble of RNA Structures

We describe the first dynamic programming algorithm that computes the expected degree for the network, or graph G = (V, E) of all secondary structures of a given RNA sequence a = a₁, …, a_n. Here, the nodes V correspond to all secondary structures of a, while an edge exists between nodes s, t if the secondary structure t can be obtained from s by adding, removing or shifting a base pair. Since secondary structure kinetics programs implement the Gillespie algorithm, which simulates a random walk on the network of secondary structures, the expected network degree may provide a better understanding of kinetics of RNA folding when allowing defect diffusion, helix zippering, and related conformation transformations. We determine the correlation between expected network degree, contact order, conformational entropy, and expected number of native contacts for a benchmarking dataset of RNAs. Source code is available at http://bioinformatics.bc.edu/clotelab/RNAexpNumNbors.