Entropy involved in fidelity of DNA replication

Information has an entropic character which can be analyzed within the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is performed sufficiently slowly. Structural and recent single-molecule assays have provided dynamic details of polymerase machinery with insight into information processing. We introduce a rigorous characterization of Shannon Information in biomolecular systems and apply it to DNA replication in the limit of no dissipation. Specifically, we devise an equilibrium pathway in DNA replication to determine the entropy generated in copying the information from a DNA template in the absence of friction. Both the initial state, the free nucleotides randomly distributed in certain concentrations, and the final state, a polymerized strand, are mesoscopic equilibrium states for the nucleotide distribution. We use empirical stacking free energies to calculate the probabilities of incorporation of the nucleotides. The copied strand is, to first order of approximation, a state of independent and non-indentically distributed random variables for which the nucleotide that is incorporated by the polymerase at each step is dictated by the template strand, and to second order of approximation, a state of non-uniformly distributed random variables with nearest-neighbor interactions for which the recognition of secondary structure by the polymerase in the resultant double-stranded polymer determines the entropy of the replicated strand. Two incorporation mechanisms arise naturally and their biological meanings are explained. It is known that replication occurs far from equilibrium and therefore the Shannon entropy here derived represents an upper bound for replication to take place. Likewise, this entropy sets a universal lower bound for the copying fidelity in replication.Comment: 25 pages, 5 figure

Thermodynamic framework for information in nanoscale systems with memory

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Arias-Gonzalez, J. Ricardo. 2017. Thermodynamic Framework for Information in Nanoscale Systems with Memory. The Journal of Chemical Physics 147 (20). AIP Publishing: 205101. doi:10.1063/1.5004793 and may be found at https://doi.org/10.1063/1.5004793."[EN] Information is represented by linear strings of symbols with memory that carry errors as a result of their stochastic nature. Proofreading and edition are assumed to improve certainty although such processes may not be effective. Here, we develop a thermodynamic theory for material chains made up of nanoscopic subunits with symbolic meaning in the presence of memory. This framework is based on the characterization of single sequences of symbols constructed under a protocol and is used to derive the behavior of ensembles of sequences similarly constructed. We then analyze the role of proofreading and edition in the presence of memory finding conditions to make revision an effective process, namely, to decrease the entropy of the chain. Finally, we apply our formalism to DNA replication and RNA transcription finding that Watson and Crick hybridization energies with which nucleotides are branched to the template strand during the copying process are optimal to regulate the fidelity in proofreading. These results are important in applications of information theory to a variety of solid-state physical systems and other biomolecular processes. Published by AIP Publishing.This work was supported by the Spanish Ministry of Economy and Competitiveness (Grant No. MAT2015-71806-R).Arias-Gonzalez, JR. (2017). Thermodynamic framework for information in nanoscale systems with memory. The Journal of Chemical Physics. 147(20):1-10. https://doi.org/10.1063/1.5004793S11014720Bustamante, C., Cheng, W., & Mejia, Y. X. (2011). 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Reviews of Modern Physics, 88(2). doi:10.1103/revmodphys.88.021002Arias-Gonzalez, J. R. (2016). Information management in DNA replication modeled by directional, stochastic chains with memory. The Journal of Chemical Physics, 145(18), 185103. doi:10.1063/1.4967335Bustamante, C., Liphardt, J., & Ritort, F. (2005). The Nonequilibrium Thermodynamics of Small Systems. Physics Today, 58(7), 43-48. doi:10.1063/1.2012462SantaLucia, J., & Hicks, D. (2004). The Thermodynamics of DNA Structural Motifs. Annual Review of Biophysics and Biomolecular Structure, 33(1), 415-440. doi:10.1146/annurev.biophys.32.110601.141800Andrieux, D., & Gaspard, P. (2008). Nonequilibrium generation of information in copolymerization processes. Proceedings of the National Academy of Sciences, 105(28), 9516-9521. doi:10.1073/pnas.0802049105Arias-Gonzalez, J. R. (2014). Single-molecule portrait of DNA and RNA double helices. Integr. Biol., 6(10), 904-925. doi:10.1039/c4ib00163jErie, D. A., Yager, T. 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A DNA-centered explanation of the DNA polymerase translocation mechanism

[EN] DNA polymerase couples chemical energy to translocation along a DNA template with a specific directionality while it replicates genetic information. According to single-molecule manipulation experiments, the polymerase-DNA complex can work against loads greater than 50 pN. It is not known, on the one hand, how chemical energy is transduced into mechanical motion, accounting for such large forces on sub-nanometer steps, and, on the other hand, how energy consumption in fidelity maintenance integrates in this non-equilibrium cycle. Here, we propose a translocation mechanism that points to the flexibility of the DNA, including its overstretching transition, as the principal responsible for the DNA polymerase ratcheting motion. By using thermodynamic analyses, we then find that an external load hardly affects the fidelity of the copying process and, consequently, that translocation and fidelity maintenance are loosely coupled processes. The proposed translocation mechanism is compatible with single-molecule experiments, structural data and stereochemical details of the DNA- protein complex that is formed during replication, and may be extended to RNA transcription.The author thanks B. Ibarra and F.J. Cao for fruitful discussion and H.Rodriguez-Rodriguez for critical reading of the manuscript. This work was supported the Spanish Ministry of Economy and Competitiveness (grant number MAT2015-71806-R).Arias-Gonzalez, JR. (2017). A DNA-centered explanation of the DNA polymerase translocation mechanism. Scientific Reports. 7:1-8. https://doi.org/10.1038/s41598-017-08038-2S187Bustamante, C., Cheng, C. & Mejia, Y. X. Revisiting the central dogma one molecule at a time. Cell 144, 480–497 (2011).van Oijen, A. M. & Loparo, J. J. Single-molecule studies of the replisome. Annu. Rev. Biophys. 39, 429–448 (2010).Wang, H.-Y., Elston, T., Mogilner, A. & Oster, G. Force generation in RNA polymerase. Biophys. 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Single-molecule portrait of DNA and RNA double helices

This is a pre-copyedited, author-produced version of an article accepted for publication in Integrative Biology following peer review. The version of record Arias-Gonzalez, J. Ricardo. 2014. Single-Molecule Portrait of DNA and RNA Double Helices. Integr. Biol. 6 (10). Oxford University Press (OUP): 904 25. doi:10.1039/c4ib00163j is available online at: https://doi.org/10.1039/c4ib00163j[EN] The composition and geometry of the genetic information carriers were described as double-stranded right helices sixty years ago. The flexibility of their sugar¿phosphate backbones and the chemistry of their nucleotide subunits, which give rise to the RNA and DNA polymers, were soon reported to generate two main structural duplex states with biological relevance: the so-called A and B forms. Double-stranded (ds) RNA adopts the former whereas dsDNA is stable in the latter. The presence of flexural and torsional stresses in combination with environmental conditions in the cell or in the event of specific sequences in the genome can, however, stabilize other conformations. Single-molecule manipulation, besides affording the investigation of the elastic response of these polymers, can test the stability of their structural states and transition models. This approach is uniquely suited to understanding the basic features of protein binding molecules, the dynamics of molecular motors and to shedding more light on the biological relevance of the information blocks of life. Here, we provide a comprehensive single-molecule analysis of DNA and RNA double helices in the context of their structural polymorphism to set a rigorous interpretation of their material response both inside and outside the cell. From early knowledge of static structures to current dynamic investigations, we review their phase transitions and mechanochemical behaviour and harness this fundamental knowledge not only through biological sciences, but also for Nanotechnology and Nanomedicine.We are sincerely indebted to S. Hormeno, F. Moreno-Herrero, B. Ibarra, J. L. Carrascosa, J. M. Valpuesta, M. Fuentes-Perez and C. Carrasco for their work throughout the years. C. Flors and A. Villasante are acknowledged for critical revision. This work was supported by Fundacion IMDEA Nanociencia.Arias-Gonzalez, JR. (2014). Single-molecule portrait of DNA and RNA double helices. Integrative Biology. 6(10):904-925. https://doi.org/10.1039/c4ib00163jS904925610Ivanov, V. I., Minchenkova, L. E., Minyat, E. E., Frank-Kamenetskii, M. D., & Schyolkina, A. K. (1974). The B̄ to Ā transition of DNA in solution. Journal of Molecular Biology, 87(4), 817-833. doi:10.1016/0022-2836(74)90086-2FRANKLIN, R. E., & GOSLING, R. G. (1953). 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Writing, Proofreading and Editing in Information Theory

[EN] Information is a physical entity amenable to be described by an abstract theory. The concepts associated with the creation and post-processing of the information have not, however, been mathematically established, despite being broadly used in many fields of knowledge. Here, inspired by how information is managed in biomolecular systems, we introduce writing, entailing any bit string generation, and revision, as comprising proofreading and editing, in information chains. Our formalism expands the thermodynamic analysis of stochastic chains made up of material subunits to abstract strings of symbols. We introduce a non-Markovian treatment of operational rules over the symbols of the chain that parallels the physical interactions responsible for memory effects in material chains. Our theory underlies any communication system, ranging from human languages and computer science to gene evolution.This work was supported by the Spanish Ministry of Economy and Competitiveness (MINECO, Grant MAT2015-71806-R). IMDEANanociencia acknowledges support from the 'Severo Ochoa' Programme for Centres of Excellence in R&D (MINECO, Grant SEV-2016-0686). These funds covered the costs to publish in open access.Arias-Gonzalez, JR. (2018). Writing, Proofreading and Editing in Information Theory. Entropy. 20(5):1-10. https://doi.org/10.3390/e20050368S11020

Microscopically Reversible Pathways with Memory

[EN] Statistical mechanics is a physics theory that deals with ensembles of microstates of a system compatible with environmental constraints and that on average define a thermodynamic state. The evolution of a small system is normally subjected to changing constraints, as set by a protocol, and involves a stochastic dependence on previous events. Here, we generalize the dynamic trajectories described by a realization of a physical system without dissipation to include those in which the history of previous events is necessary to understand its future. This framework is then used to characterize the processes experienced by the stochastic system, as derived from ensemble averages over the available pathways. We find that the pathways that the system traces in the presence of a protocol entail different statistics from those in its absence and prove that both types of pathways are equivalent in the limit of independent events. Such equivalence implies that a thermodynamic system cannot evolve away from equilibrium in the absence of memory. These results are useful to interpret single-molecule experiments in biophysics and other fields in nanoscience, as well as an adequate platform to describe non-equilibrium processes.Work supported by Ministerio de Ciencia e Innovacion, grant number PID2019-107391RB-I00.Arias-Gonzalez, JR. (2021). Microscopically Reversible Pathways with Memory. Mathematics. 9(2):1-21. https://doi.org/10.3390/math9020127S1219

Comment on "Information management in DNA replication modeled by directional, stochastic chains with memory" [J. Chem. Phys. 145, 185103 (2016)]

Arias-Gonzalez, JR.; Aleja, D. (2020). Comment on "Information management in DNA replication modeled by directional, stochastic chains with memory" [J. Chem. Phys. 145, 185103 (2016)]. The Journal of Chemical Physics. 152(4):1-2. https://doi.org/10.1063/1.5140055S121524Arias-Gonzalez, J. R. (2016). Information management in DNA replication modeled by directional, stochastic chains with memory. The Journal of Chemical Physics, 145(18), 185103. doi:10.1063/1.4967335The Journal of Chemical Physics14518185103201