Kolchinsky, Artemy; Corominas-Murtra, BernatISTA
In many real-world systems, information can be transmitted in two qualitatively different ways: by copying or by transformation. Copying occurs when messages are transmitted without modification, e.g. when an offspring receives an unaltered copy of a gene from its parent. Transformation occurs when messages are modified systematically during transmission, e.g. when mutational biases occur during genetic replication. Standard information-theoretic measures do not distinguish these two modes of information transfer, although they may reflect different mechanisms and have different functional consequences. Starting from a few simple axioms, we derive a decomposition of mutual information into the information transmitted by copying versus the information transmitted by transformation. We begin with a decomposition that applies when the source and destination of the channel have the same set of messages and a notion of message identity exists. We then generalize our decomposition to other kinds of channels, which can involve different source and destination sets and broader notions of similarity. In addition, we show that copy information can be interpreted as the minimal work needed by a physical copying process, which is relevant for understanding the physics of replication. We use the proposed decomposition to explore a model of amino acid substitution rates. Our results apply to any system in which the fidelity of copying, rather than simple predictability, is of critical relevance.
Journal of the Royal Society Interface
AK was supported by Grant No. FQXi-RFP-1622 from the FQXi foundation, and Grant No. CHE-1648973 from the U.S. National Science Foundation. AK would like to thank the Santa Fe Institute for supporting this research. The authors thank Jordi Fortuny, Rudolf Hanel, Joshua Garland, and Blai Vidiella for helpful discussions, as well as the anonymous reviewers for their insightful suggestions.
Kolchinsky A, Corominas-Murtra B. Decomposing information into copying versus transformation. Journal of the Royal Society Interface. 2020;17(162). doi:10.1098/rsif.2019.0623
Kolchinsky, A., & Corominas-Murtra, B. (2020). Decomposing information into copying versus transformation. Journal of the Royal Society Interface. The Royal Society. https://doi.org/10.1098/rsif.2019.0623
Kolchinsky, Artemy, and Bernat Corominas-Murtra. “Decomposing Information into Copying versus Transformation.” Journal of the Royal Society Interface. The Royal Society, 2020. https://doi.org/10.1098/rsif.2019.0623.
A. Kolchinsky and B. Corominas-Murtra, “Decomposing information into copying versus transformation,” Journal of the Royal Society Interface, vol. 17, no. 162. The Royal Society, 2020.
Kolchinsky A, Corominas-Murtra B. 2020. Decomposing information into copying versus transformation. Journal of the Royal Society Interface. 17(162), 0623.
Kolchinsky, Artemy, and Bernat Corominas-Murtra. “Decomposing Information into Copying versus Transformation.” Journal of the Royal Society Interface, vol. 17, no. 162, 0623, The Royal Society, 2020, doi:10.1098/rsif.2019.0623.