Salt Effects on the Thermodynamics of a Frameshifting RNA Pseudoknot under Tension

Naoto Hori; Natalia A. Denesyuk; D. Thirumalai

where the Debye length is λ D = ε(T )kBT 4πe 2 I . In the simulations, salt concentration can be varied by changing the ionic strength I = Σq 2 n ρ n , where q n is the charge of ion of type n, and ρ n is its number density. Following our earlier study [37] , we use an experimentally fitted function for the temperature-dependent dielectric constant ε(T ) [50] . The renormalized charge on the phosphate group is −q * e (q * < 1). Because of the highly charged nature of the polyanion, counterions condense onto the RNA, thus effectively reducing the effective charge per phosphate. The extent of charge reduction can be calculated using the Oosawa-Manning theory. Charge renormalization, first used in the context of RNA folding by Heilman-Miller et al. [51] and more recently incorporated into CG models for RNA by us [37] and others [52, 53] , is needed to predict accurately the thermodynamics and kinetics of RNA folding [54] . The renormalized value of the charge on the P group is approximately . CC-BY-NC-ND 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/048801 doi: bioRxiv preprint given by −q * (T )e = −be lB(T ) , where the Bjerrum length is l B (T ) = e 2 ε(T )kBT and b is the mean distance between the charges on the phosphate groups [55] . The mean distance (b) between charges on RNA is difficult to estimate (except for rod-like polyelectrolytes) because of its shape fluctuations. Therefore, it should be treated as an adjustable parameter. In our previous study, we showed that b = 4.4Å provides an excellent fit of the thermodynamics of RNA hairpins and the MMTV pseudoknot [37] . We use the same value in the present study of BWYV as well. Thus, the force field used in this study is the same as in our previous study attesting to its transferability for simulating small RNA molecules.