Thermodynamics of Molecular Information Processing

The molecular systems of the biological cell are often an inspiration for researchers imagining how low cost computational systems might be constructed. A paradigmatic example is the copying of information from a DNA template sequence into the sequence of daughter polymers (RNA and then proteins), resulting in the selective proroduction of a tiny subset of the vast number of possible RNA and protein molecules. In the cell, these product molecules are continuously created via the templates and then destroyed in a template-free fashion, resulting in a free-energy consuming cycle. We ask: given an arbitrary network of production and degradation processes, in which the templates act as catalysts, how precise (low entropy) can the distribution of output sequences be? And what sort of networks produce low entropy product distributions?

We find that for an arbitrarily catalytic templating reaction network in steady state, the specificity with which a single product sequence can dominate the product ensemble is upper bounded, and the entropy of the product ensemble lower bounded, by a function of ΔG, the difference between the maximal and minimal free-energy changes along pathways to product assembly. These simple bounds are particularly restrictive for systems with a smaller number of possible products M. Remarkably, however, although ΔG constrains the information propagated to the product distribution, the systems that saturate the bound operate in a pseudo-equilibrium fashion, with production and degradation for each product sequence largely occuring via the same pathway in forward and reverse directions, rather than through the free-energy consuming cycles observed in biology. Indeed, the larger the cyclic flux observed in the system, the worse the precision. This surprising result raises the question of why biology operates in the limit of large cyclic flux, and also suggests a possible low-energy paradigm for molecular computation.

Information propagation in far-from-equilibrium molecular templating networks is optimised by pseudo-equilibrium systems with negligible dissipation. Benjamin Qureshi, Jenny M. Poulton, Thomas E. Ouldridge. arXiv:2404.02791