Thermodynamic framework for information in nanoscale systems with memory

Abstract

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.

Writing, Proofreading and Editing in Information Theory

“…The interactions, which determine a memory, between subunits in a material chain, as for example in polynucleotide biopolymers [19], may be naturally imposed by the physics of the systems [3]. In these chains, the energy plays the role of the correctness (C → −E), and parameter R is associated with the thermal energy level, namely R → kT, where k is the Boltzmann constant and T the temperature.…”

“…The action of a human being in text composition is analogous to those of the DNA and RNA polymerases in replication and transcription, respectively. These nanomachines introduce non-equilibrium protocols with energy dissipation, which adds to the hybridization free energies of the resulting nucleic acids base-pairs [3,19].…”

“…In contrast, if we do not restrict how to access each final configuration [3,19], the probability of a certain sequence reads:…”

“…The appropriate introduction of operational rules to construct bit strings is linked to the use of the concept of proofreading and, more importantly, to the establishment of conditions for useful editing [3]. These concepts appear together in biomolecular processes associated with information management [4][5][6].…”

“…We previously formulated a thermodynamic framework for physical systems that carry information in the presence of memory effects [3] with general non-Markovian reach [18]. In this paper, we expand this framework to general systems, both symbolic and physical, conveying information, that is to systems where information content is not determined by thermodynamic laws, but able to respond to ad hoc, imposed operational rules, as is the case for human languages.…”