Activation-energy landscape for metastable RNA folding

Design of Artificial Riboswitches as Biosensors

RNA aptamers readily recognize small organic molecules, polypeptides, as well as other nucleic acids in a highly specific manner. Many such aptamers have evolved as parts of regulatory systems in nature. Experimental selection techniques such as SELEX have been very successful in finding artificial aptamers for a wide variety of natural and synthetic ligands. Changes in structure and/or stability of aptamers upon ligand binding can propagate through larger RNA constructs and cause specific structural changes at distal positions. In turn, these may affect transcription, translation, splicing, or binding events. The RNA secondary structure model realistically describes both thermodynamic and kinetic aspects of RNA structure formation and refolding at a single, consistent level of modelling. Thus, this framework allows studying the function of natural riboswitches in silico. Moreover, it enables rationally designing artificial switches, combining essentially arbitrary sensors with a broad choice of read-out systems. Eventually, this approach sets the stage for constructing versatile biosensors.

Frustration in biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their own structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of frustration in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and especially how biomolecular structure connects to function by means of localized frustration. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding mechanisms. We review here how the biological functions of proteins are related to subtle local physical frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. In this review, we also emphasize that frustration, far from being always a bad thing, is an essential feature of biomolecules that allows dynamics to be harnessed for function. In this way, we hope to illustrate how Frustration is a fundamental concept in molecular biology.

Energy-level statistics in the fine conformational resolution of RNA folding dynamics

This work is aimed at determining the energy-level statistics of the fine resolution of soft-mode dynamics warranting an adiabatically simplified structural relaxation of a folding biopolymer chain. The parameters defining the intrabasin structure relaxation are specified for RNA, so that each Watson-Crick base-pairing pattern may be treated as a quasiequilibrium ensemble of substates or torsional isomers within relevant folding time scales. The temperature-dependent threshold for energy dispersion associated with the fine structure of each superbasin is determined so as to warrant the adiabatic entrainment of the torsional dynamics.

The RNA folding problem: a variational problem within an adiabatic approximation

Biopolymer folding is an expeditious process taking place within timescales incommensurably shorter than ergodic times. Furthermore, its robustness suggests that the process must depend on a relatively coarse level of resolution of conformation space. To account for these features while focusing on the RNA context, we derive a variational principle formulated within an adiabatic approximation obtained by integrating out fast-relaxing molecular motions. Folding pathways are generated by means of a stochastic process which begets a least effort principle reflecting a stepwise minimization of the conformational entropy cost for each folding event with concurrent maximization of the base pairing. This economy of the process is found to have kinetic consequences if we treat base-pairing contact patterns (BPPs) adiabatically, that is, as quasi-equilibrium states: the probability distribution of overall folding timespans associated to the process resolved at the BPP level is maximized at the brachistochrone or overall least-time pathway for functionally-competent RNAs. In turn, this pathway is shown to yield all the phylogenetically-conserved structural features of the active conformation within biologically-relevant timescales.

The influence of a metastable structure in plasmid primer RNA on antisense RNA binding kinetics

Replication of the ColE1 group plasmids is kinetically regulated by the interaction between plasmid-encoded primer RNA II and antisense RNA I. The binding is dependent on alternative RNA II conformations, formed during the transcription, and effectively inhibits the primer function within some time interval. In this paper, the folding pathways for the wild type and copy number mutants of ColE1 RNA II are studied using simulations by a genetic algorithm. The simulated pathways reveal a transient formation of a metastable structure, which is stabilized by copy number mutations. The folding kinetics of the proposed conformational transitions is calculated using a model of a multistep refolding process with elementary steps of double-helical stem formation or disruption. The approximation shows that the lifetime of the metastable structure is relatively long and is considerably increased in the mutants, resulting in a delay of the formation of the stable RNA II structure, which is the most sensitive to the inhibition by the antisense RNA I. Thus the effect of copy number mutations can be interpreted as a compression of the time window of effective inhibition due to an increased time spent by the RNA II in the metastable state. The implications of metastable foldings in RNA functioning are discussed.

Statistical description of nucleic acid secondary structure folding

A simple statistical model describing the folding of nucleic acids is proposed. For long sequences the real configuration of the secondary structure is a quasi equilibrium state that cannot be characterised by minimal free energy. This is because the time required to achieve complete thermal equilibrium considerably exceeds the life-time of the molecule. The formation of the secondary structure is represented as a random walk process in the space of all possible molecular configurations. The quasi equilibrium structure is obtained by successive linking and disruptions of helix segments with probabilities determined by the rate constants of corresponding unimolecular reactions. The probabilities of configurations consisting of all possible compatible helices are calculated. Structures of some t-RNAs and ribosomal RNAs are analysed.

Statistics of RNA melting kinetics

We present and study the behavior of a simple kinetic model for the melting of RNA secondary structures, given that those structures are known. The model is then used as a map that assigns structure dependent overall rate constants of melting (or refolding) to a sequence. This induces a "landscape" of reaction rates, or activation energies, over the space of sequences with fixed length. We study the distribution and the correlation structure of these activation energies.