A Physical Origin for Functional Domain Structure in Nucleic Acids as Evidenced by Cross-linking Entropy: I

Abstract

A global strategy for estimating the entropy of long sequences of RNA is proposed to help improve the predictive capacity of RNA secondary structure dynamic programming algorithm (DPA) free energy (FE) minimization methods. These DPA strategies only consider the effects that occur in the immediate (nearest neighbor) vicinity of a given base pair (bp) in a secondary structure plot. They are therefore defined as nearest-neighbor secondary structure (NNSS) strategies. The new approach utilizes the statistical properties of the Gaussian polymer chain model to introduce both local and global contributions to the entropy of a given secondary structure. These entropic contributions are primarily a function of the persistence length of the RNA. Limits on the domain size are strongly suggested by this model and these limits are a function of both the length and the percentage of bp enclosed within a given domain. The model generalizes the penalties found in the NNSS algorithms. The approach considers the importance of flexibility in the folding and stability of RNA by considering the role of the persistence length in a biopolymer structure. The theory also suggests that molecular machinery may also take advantage of this global entropic effect to bring about catalytic effects. The applications can also be extended to protein structure calculations with some additional considerations.

A new entropy model for RNA: part I. A critique of the standard Jacobson-Stockmayer model applied to multiple cross links

“…[23][24][25][26][27][28] In the first part of this Series, we examine the use of the standard entropy model that is based on the Jacobson-Stockmayer equation. 1 The objective is to look at the subtle role of this long range entropy effect that arises in polymers and to show why it is a misconception to equate the entropy evaluation of interactions between two independent strands in dsRNA structures with apparently similar single-stranded RNA secondary structure and likewise for other polymers such as dsDNA and protein topologies.…”

“…The focus is mainly on RNA secondary structure where the JS-model has been used with considerable success in the development of prediction algorithms that employ thermodynamic evaluation methods. [2][3][4] To understand the presentation in this work, the reader needs to be familiar with the basic concept of the Gaussian polymer chain (GPC), 30,31 the CLE model, [23][24][25][26][27][28] and the basic concepts of the thermodynamics of RNA secondary structure calculations. [32][33][34][35][36][37][38] The standard model: the loop penalty model (LP-model)…”

“…Moreover, corrections for any such details are independent of the stacking free energy and, at most, influence the Kuhn length; a measure of the stiffness of a polymer and typically short in single-stranded RNA: about 5 nt for poly(A) and 3 nt for poly(U). 27,28 The Kuhn length is not an explicit property used in evaluating the loop penalty model either. Because these uncertainties are largely local in character, they are not likely in most cases to overcome the global issues discussed here.…”

“…The right hand side of Equation (25) can be modified to the following form (26) where (27) and we obtain an expression resembling Equation (15) , with (28) In general, the parameters r1 and r2 in Equations (24) and (25) correspond to states in thermodynamic equilibrium. Assuming r1>r2 for the given polymer, this would usually be a denatured state (r1 2 =x Nb 2 ) and a bound state r2>rb.…”

“…The details on how to derive the entropy loss due to the formation of structure using the CLE model are discussed in detail in Dawson et al 23,25,27 In words, the entropy loss is measured by considering the difference in the entropy for the unfolded polymer chain and the folded structure.…”