Evolution of RNA Folding Kinetics

The preimages of RNA secondary structures in sequence space are neutral networks, which are derived from the set of all sequences folding into the same secondary structure through connecting all seqeunces of Hamming distance one by an edge. The existence of neutral. networks and their intersections was postulated from the analysis of sequence-structure relations of RNA about eight years ago and, very recently, verified experimentally (Schultes & Bartel, Science 289 (2000), 448-452; see enclosure). RNA secondary structures, although being (almost always) important intermediates in RNA folding, represent only coarse grained versions of full structures and need to be refined in order to make the model more realistic. Two complementary versions of refinements are necessary in this context: (i) Extending the concept of considering structures of minimal free energy (mfe) as RNA phenotypes to an inclusion of suboptimal structures and kinetic structures (In essence such an extension corresponds to the replacement of the 0 K and infinite time, thermodynamic view by a concept of structure that accounts for finite temperatures and finite folding times), and (ii) extension of secondary structures (which can be seen as listings of Watson Crick and GU base paris) to full structures through incorporation of tertiary interactions, in particular H- type pseudoknots and co-axial stacking and others. Within the frame of this proposal the distritbution of refined properties, like folding efficiencies and folding times, on the neutral networks of sequences forming the same mfe secondary structures will be investigated by means of computer simulation. We expect the appearence of classes, which allow to group molecules according to their folding properties, and suggest that molecules with given refined properties are not confined to certain areas of sequence space, but are distributed (almost uniformly) over almost entire sequence space. This conjecture, which has direct consequences for the evolutionary design of biomolecules, will be investigated by means of extensive computer simulations and, if possible, by a yet to be specified and conceived mathematical model, which allows to derive the generic features of the sequence dependence of RNA folding kinetics (In the case of neutral networks for mfe structures, application of random graph theory turned out to be successful). Already existing algorithms conceived and implemented by our group and new developed techniques will be applied to a comprehensive study of kinetically controlled sequence-structure relations of RNA molecules. A recently developed algorithm for kinetic folding of RNA is not restricted to conventional secondary structures and has been extended already to account for pseudoknots and end-on-end stacking. Provided a sufficienly large number of empirical data are available, the algorithm can be extended to consider almost all other kinds of classifiable tertiary interactions. We plan to derive new algorithms for the consideration of other classes of pseudoknots (for example, B-type) and for base triplets. The ultimate goal is to include a sufficiently large number of tertiary interactions in order to obtain well defined 3D structures.

Software tools for the design of ribonucleic acid (RNA) switches and co-folded complexes of two or more RNA molecules were conceived, implemented, and tested. A new theoretical concept was elaborated, which allows for a unified description and modelling of evolutionary and rational design of RNA switches and other molecules with predefined kinetic properties. RNA molecules became a central topic in pure and applied research in molecular biology, bio-informatics, and systems biology. The design of RNA molecules for regulation of cellular processes and therapeutic purposes is an important issue in current academic investigations and biotechnological developments. Despite the high relevance of RNA design the software tools for structure prediction are still rather modest. In order to fill the gap we developed and implemented new algorithms for the design of sequences for predefined structures, for the computation of all possible structures in addition to the most stable ones, and for the folding process resolved on the time scale known as kinetic folding. The research within this project was focused on the relation between kinetic folding and the optimization of molecules by evolution. New software packages were developed for efficient calculation of kinetic RNA folding, a simulation tool for RNA optimization in flow reactors, and for co- folding understood as simultaneous folding of two or more RNA molecules. Kinetic folding turned out to be the key for understanding the mechanism of RNA switches, which are RNA molecules that can form two (or more) structures and which are involved in the regulation of gene activities and metabolic control. Co-folding is the basis of RNA triggered gene silencing by so-called small interfering RNA molecules. Our tools have been extensively tested and validated, and they will soon be available for public usage in academia as new modules of the Vienna RNA Package. A few companies are licensing the Vienna RNA Package in order to incorporate it into commercial bio-informatics tools. Within a co-operation with Siemens Austria a user-friendly interface is being developed. The major progress in understanding the evolution of RNA molecules was made along the lines suggested in the proposal: How can we properly imagine the evolution of molecules when the most stable structures and the kinetic properties simultaneous targets of optimization by variation and selection? We had found that many sequences form the same structure and were able to show that the underlying object called neutral network provided the basis for efficient evolution. This concept is now complemented by the multitude of structures that can be formed from a single sequence when sub-optimal foldings are included. In mathematical terms we are dealing with a kind of dual mapping that sets the stage for multiple purpose RNA optimization as required for the design of RNA switches or optimally co-folding RNA molecules.