Discrete state model and accurate estimation of loop entropy of RNA secondary structures

Abstract

Conformational entropy makes important contribution to the stability and folding of RNA molecule, but it is challenging to either measure or compute conformational entropy associated with long loops. We develop optimized discrete k-state models of RNA backbone based on known RNA structures for computing entropy of loops, which are modeled as self-avoiding walks. To estimate entropy of hairpin, bulge, internal loop, and multibranch loop of long length (up to 50), we develop an efficient sampling method based on the sequential Monte Carlo principle. Our method considers excluded volume effect. It is general and can be applied to calculating entropy of loops with longer length and arbitrary complexity. For loops of short length, our results are in good agreement with a recent theoretical model and experimental measurement. For long loops, our estimated entropy of hairpin loops is in excellent agreement with the Jacobson-Stockmayer extrapolation model. However, for bulge loops and more complex secondary structures such as internal and multibranch loops, we find that the Jacobson-Stockmayer extrapolation model has large errors. Based on estimated entropy, we have developed empirical formulae for accurate calculation of entropy of long loops in different secondary structures. Our study on the effect of asymmetric size of loops suggest that loop entropy of internal loops is largely determined by the total loop length, and is only marginally affected by the asymmetric size of the two loops. Our finding suggests that the significant asymmetric effects of loop length in internal loops measured by experiments are likely to be partially enthalpic. Our method can be applied to develop improved energy parameters important for studying RNA stability and folding, and for predicting RNA secondary and tertiary structures. The discrete model and the program used to calculate loop entropy can be downloaded at

Prediction of geometrically feasible three-dimensional structures of pseudoknotted RNA through free energy estimation

“…Cold Spring Harbor Laboratory Press on May 12, 2018 -Published by rnajournal.cshlp.org Downloaded from publications (Zhang et al 2003(Zhang et al , 2007Lin et al 2008a,b;Zhang et al 2008). This strategy of calculating loop entropy treats both nested and pseudoknotted loops in a unified physical framework, regardless of how complex the structures are.…”

“…Physically, the entropy of a loop of a specific length is determined to a large extent by the end-to-end distance and the spatial interference from nearby stems or loops. This is true for loops of all nature, regardless of whether or not it is a hairpin loop, an internal or bulge loop, a multibranch loop, or a pseudoknotted loop Chen 2005, 2006;Zhang et al 2008;Cao and Chen 2009). From this consideration and our previous work , we have developed an efficient and accurate method to calculate the loop entropy of RNA structures with pseudoknots.…”

RNA structure prediction: Progress and perspective

“…[44] Kinefold predicts the structures of pseudoknots with topological and geometrical constraints through a long-time-scale RNA folding simulation, [45] which follows the stochastic closing and opening of individual RNA helices . In addition, the thermodynamic parameters of pseudoknots loop can also be derived from a lattice model [40,47,48] and based on which, the Vfold predicts the free energy landscapes of pseudoknots. [40,48] …”

Quantitative Comparison of Conformational Ensembles

“…Additionally, the flexibility and associated entropy of proteins has been studied [11][12][13][14][15][16][17][18]. This includes the work by Damm and Carlson presented in [19].…”