Journal of Nucleic Acids Investigation

A new entropy model for RNA: part V, Incorporating the Flory-Huggins model in structure prediction and folding

Wayne Dawson, Gota Kawai — Mon, 13 Jul 2015 00:00:00 +0000

The effect of solvent-biopolymer interactions is hardly negligible. Whereas the ideal (non-interacting) polymer consisting of N monomers in an ideal solvent is expected to have the terminal ends of its chain with a root-mean-squared (rms) end-to-end separation distance (rms) proportional to the square root of N, real interactions of a rms polymer both with itself and with the solvent often tend to strongly perturb rms. In rms poor solvent, the biopolymer can collapse into a small globule much smaller than the ideal rms due to excluding solvent. In good solvent, the biopolymer can swell to a size much larger than the ideal r due to favoring solvent. These effects require rms corrections to an ideal polymer equation. We have been developing the cross linking entropy (CLE) model in this series. The model attempts find the maximum entropy of a folded polymer by taking into account the correlation caused by bonding and other interactions of the structure. In RNA, this mostly occurs in the stems. Here we adapt CLE model to handle polymer swelling and collapse for RNA molecules both in good and in poor solvent. This work is intended to introduce this type of study and to allow its systematic application in problems of RNA folding and structure prediction. The current study suggests that there may be some tendency for RNA to behave as a polymer in poor solvent and that this collapse may happen in sequences longer than 50 nt.

A new entropy model for RNA: part IV, The Minimum Free Energy (mFE) and the thermodynamically most-probable folding pathway (TMPFP)

Wayne Dawson, Gota Kawai — Mon, 13 Jul 2015 00:00:00 +0000

Here we discuss four important questions (1) how can we be sure that the thermodynamically most-probable folding-pathway yields the minimum free energy for secondary structure using the dynamic programming algorithm (DPA) approach, (2) what are its limitations, (3) how can we extend the DPA to find the minimum free energy with pseudoknots, and finally (4) what limitations can we expect to find in a DPA approach for pseudoknots. It is our supposition that some structures cannot be fit uniquely by the DPA, but may exist in real biology situations when disordered regions in the biomolecule are necessary. These regions would be identifiable by using suboptimal structure analysis. This grants us some qualitative tools to identify truly random RNA sequences, because such are likely to have greater degeneracy in their thermodynamically most-probable folding-pathway.

A new entropy model for RNA: part III. Is the folding free energy landscape of RNA funnel shaped?

Wayne Dawson, Toshikuni Takai, Nobuharu Ito, Kentaro Shimizu, Gota Kawai — Mon, 03 Nov 2014 00:00:00 +0000

The concept of a free energy (FE) landscape, in which the conformations of a polymer progressively take on the structure of the native state while spiraling down a FE surface that resembles the shape of a funnel, has long been viewed as the reason why a complex protein structure forms so rapidly compared to the number of conformations available to it. On the other hand, this landscape picture is less clear with RNA due to the multiplicity of conformations and the uncertainties in the current thermodynamics. It is therefore sometimes proposed that within the ensemble of suboptimal states of the RNA molecule, the vast majority of those states all closely resemble the native state and therefore simply overwhelm the few states that represent the global minimum FE. However, calculations of the free energy of observed structures often suggest that the most frequently observed cluster of structures are far from the minimum FE, particularly in the case of long sequences. If so, then such a FE surface is unlikely to be funnel shaped. We have been developing a version of vsfold that can evaluate the suboptimal structures of the FE surface (through a modified version called vs_subopt). Here we show that the ensemble of suboptimal structures for a number of known RNA structures can actually be both close to the minimum FE and also be the dominant observed structure when a proper Kuhn length is selected. Two state aptamers known as riboswitches can show neighboring FE states in the suboptimal structures that match the observed structures and their relative difference in FE is well within the range of the binding free energy of the metabolite. For the riboswitches and other short RNA sequences (less than 250 nt), the flow of the suboptimal structures (including pseudoknots) tended to resemble a rock rolling down a hill along the reaction coordinate axis. An important insight yielded by the cross-linking entropy (CLE) model is that the global entropy limits the size of domains. Hence, based on the CLE model, Levinthal’s paradox is overcome by the funnel shape in the FE, by a reduction in the number of degrees of freedom due to Kuhn length, and by limits on the size of the domains that can form. These concepts are also applicable to calculating transition rates between different suboptimal structures.