Theoretical Analysis Reveals the Cost and Benefit of Proofreading in Coronavirus Genome Replication

Linear-Decoupling Enables Accurate Speed and Accuracy Predictions for Copolymerization Processes

Biological processes exhibit remarkable accuracy and speed and can be theoretically explored through various approaches. The Markov-chain copolymerization theory, describing polymer growth kinetics as a Markov chain, provides an exact set of equations to solve for error and speed. Still, due to nonlinearity, these equations are hard to solve. Alternatively, the enzyme-kinetics approach, which formulates a set of linear equations, simplifies the biological processes as transitions between discrete chemical states, but generally, it might not be accurate. Here, we show that the enzyme-kinetic approach can lead to inaccurate fluxes, even for first-order polymerization processes. To address the problem, we propose a simplified linear-decoupling approximation for steady-state probabilities of higher-order copolymer chains under biologically relevant conditions. Our findings demonstrate that the stationary speed and error rate obtained from the linear-decoupling method align closely with exact values from the Markov-chain (nonlinear) approximation. Extending the technique to higher-order processes with proofreading and internal states shows that it works equally well to describe trade-offs between speed and accuracy for DNA replication and transcription elongation. Our work underscores the proposed linear-decoupling approximation's efficacy in addressing the nonlinear behavior of the Markov-chain approach and the enzyme-kinetic approach's limitations, ensuring accurate predictions for high-fidelity biological processes.

Insights into Error Control Mechanisms in Biological Processes: Copolymerization and Enzyme-Kinetics Revisited

The high fidelity observed in biological information processing ranging from replication to translation has stimulated significant research efforts to clarify the underlying microscopic picture. Theoretically, several approaches to analyze the error rates have been proposed. The copolymerization theory describes the addition and removal of monomers at the growing tip of a copolymer, leading to a closed set of nonlinear equations. On the other hand, enzyme-kinetics approaches formulate linear equations of biochemical networks, describing transitions between discrete chemical states. However, it is still unclear whether the error values computed by the two approaches agree. Moreover, there are conflicting interpretations on whether the error is under thermodynamic or kinetic discrimination control. In this work, we examine the error rate in persistent copying biochemical processes by specifically analyzing both theoretical approaches. The initial disagreement of the results between the two theories motivated us to rederive the formula for the error rate in the kinetic model. The error computed with the new method resulted in excellent agreement between both theoretical approaches and with Monte Carlo simulations. Furthermore, our theoretical analysis shows that the kinetic discrimination controls the error, even when the energy difference between adding the right and wrong products is very small. Our theoretical investigation gives important insights into the physical-chemical properties of complex biological processes by providing the quantitative framework to evaluate them.

Multimodal data fusion using sparse canonical correlation analysis and cooperative learning: a COVID-19 cohort study

Through technological innovations, patient cohorts can be examined from multiple views with high-dimensional, multiscale biomedical data to classify clinical phenotypes and predict outcomes. Here, we aim to present our approach for analyzing multimodal data using unsupervised and supervised sparse linear methods in a COVID-19 patient cohort. This prospective cohort study of 149 adult patients was conducted in a tertiary care academic center. First, we used sparse canonical correlation analysis (CCA) to identify and quantify relationships across different data modalities, including viral genome sequencing, imaging, clinical data, and laboratory results. Then, we used cooperative learning to predict the clinical outcome of COVID-19 patients: Intensive care unit admission. We show that serum biomarkers representing severe disease and acute phase response correlate with original and wavelet radiomics features in the LLL frequency channel (cor(Xu1, Zv1) = 0.596, p value < 0.001). Among radiomics features, histogram-based first-order features reporting the skewness, kurtosis, and uniformity have the lowest negative, whereas entropy-related features have the highest positive coefficients. Moreover, unsupervised analysis of clinical data and laboratory results gives insights into distinct clinical phenotypes. Leveraging the availability of global viral genome databases, we demonstrate that the Word2Vec natural language processing model can be used for viral genome encoding. It not only separates major SARS-CoV-2 variants but also allows the preservation of phylogenetic relationships among them. Our quadruple model using Word2Vec encoding achieves better prediction results in the supervised task. The model yields area under the curve (AUC) and accuracy values of 0.87 and 0.77, respectively. Our study illustrates that sparse CCA analysis and cooperative learning are powerful techniques for handling high-dimensional, multimodal data to investigate multivariate associations in unsupervised and supervised tasks.

Multimodal Biomedical Data Fusion Using Sparse Canonical Correlation Analysis and Cooperative Learning: A Cohort Study on COVID-19

Through technological innovations, patient cohorts can be examined from multiple views with high-dimensional, multiscale biomedical data to classify clinical phenotypes and predict outcomes. Here, we aim to present our approach for analyzing multimodal data using unsupervised and supervised sparse linear methods in a COVID-19 patient cohort. This prospective cohort study of 149 adult patients was conducted in a tertiary care academic center. First, we used sparse canonical correlation analysis (CCA) to identify and quantify relationships across different data modalities, including viral genome sequencing, imaging, clinical data, and laboratory results. Then, we used cooperative learning to predict the clinical outcome of COVID-19 patients. We show that serum biomarkers representing severe disease and acute phase response correlate with original and wavelet radiomics features in the LLL frequency channel (corr(Xu1, Zv1) = 0.596, p-value < 0.001). Among radiomics features, histogram-based first-order features reporting the skewness, kurtosis, and uniformity have the lowest negative, whereas entropy-related features have the highest positive coefficients. Moreover, unsupervised analysis of clinical data and laboratory results gives insights into distinct clinical phenotypes. Leveraging the availability of global viral genome databases, we demonstrate that the Word2Vec natural language processing model can be used for viral genome encoding. It not only separates major SARS-CoV-2 variants but also allows the preservation of phylogenetic relationships among them. Our quadruple model using Word2Vec encoding achieves better prediction results in the supervised task. The model yields area under the curve (AUC) and accuracy values of 0.87 and 0.77, respectively. Our study illustrates that sparse CCA analysis and cooperative learning are powerful techniques for handling high-dimensional, multimodal data to investigate multivariate associations in unsupervised and supervised tasks.

Synergy among Pausing, Intrinsic Proofreading, and Accessory Proteins Results in Optimal Transcription Speed and Tolerable Accuracy

Cleavage of dinucleotides after the misincorporational pauses serves as a proofreading mechanism that increases transcriptional elongation accuracy. The accuracy is further improved by accessory proteins such as GreA and TFIIS. However, it is not clear why RNAP pauses and why cleavage-factor-assisted proofreading is necessary despite transcriptional errors in vitro being of the same order as those in downstream translation. Here, we developed a chemical-kinetic model that incorporates most relevant features of transcriptional proofreading and uncovers how the balance between speed and accuracy is achieved. We found that long pauses are essential for high accuracy, whereas cleavage-factor-stimulated proofreading optimizes speed. Moreover, in comparison to the cleavage of a single nucleotide or three nucleotides, RNAP backtracking and dinucleotide cleavage improve both speed and accuracy. Our results thereby show how the molecular mechanism and the kinetic parameters of the transcriptional process were evolutionarily optimized to achieve maximal speed and tolerable accuracy.

The energy cost and optimal design of networks for biological discrimination

Many biological processes discriminate between correct and incorrect substrates through the kinetic proofreading mechanism that enables lower error at the cost of higher energy dissipation. Elucidating physico-chemical constraints for global minimization of dissipation and error is important for understanding enzyme evolution. Here, we identify theoretically a fundamental error-cost bound that tightly constrains the performance of proofreading networks under any parameter variations preserving the rate discrimination between substrates. The bound is kinetically controlled, i.e. completely determined by the difference between the transition state energies on the underlying free energy landscape. The importance of the bound is analysed for three biological processes. DNA replication by T7 DNA polymerase is shown to be nearly optimized, i.e. its kinetic parameters place it in the immediate proximity of the error-cost bound. The isoleucyl-tRNA synthetase (IleRS) of E. coli also operates close to the bound, but further optimization is prevented by the need for reaction speed. In contrast, E. coli ribosome operates in a high-dissipation regime, potentially in order to speed up protein production. Together, these findings establish a fundamental error-dissipation relation in biological proofreading networks and provide a theoretical framework for studying error-dissipation trade-off in other systems with biological discrimination.

Mutation Rates, Mutation Frequencies, and Proofreading-Repair Activities in RNA Virus Genetics

The error rate displayed during template copying to produce viral RNA progeny is a biologically relevant parameter of the replication complexes of viruses. It has consequences for virus-host interactions, and it represents the first step in the diversification of viruses in nature. Measurements during infections and with purified viral polymerases indicate that mutation rates for RNA viruses are in the range of 10-3 to 10-6 copying errors per nucleotide incorporated into the nascent RNA product. Although viruses are thought to exploit high error rates for adaptation to changing environments, some of them possess misincorporation correcting activities. One of them is a proofreading-repair 3' to 5' exonuclease present in coronaviruses that may decrease the error rate during replication. Here we review experimental evidence and models of information maintenance that explain why elevated mutation rates have been preserved during the evolution of RNA (and some DNA) viruses. The models also offer an interpretation of why error correction mechanisms have evolved to maintain the stability of genetic information carried out by large viral RNA genomes such as the coronaviruses.