The recognition and binding of proteins through the "fly-casting" mechanism are important biological processes. In this paper, a physical model for fly-casting binding is described based on the capillarity theory for protein chains. It is found that the capture radius for the fly-casting binding process is maximized at the transition temperature at which the free energy of the monomeric extended state of the protein equals that of the folded state. The factors related to the folding barrier or binding affinity do not change the condition needed to realize the optimization for fly-casting processes. These results will aid in the comprehensive understanding of binding processes.
We report a new ribonucleic acid （RNA） base discrete state model, which was first developed in our lab and designed to provide an efficient and accurate way of representing RNA structures toward RNA three-dimensional structure predictions. Since RNA free energy is largely determined by base pairs and base stackings instead of backbone trajectories, we directly model the RNA base configurations with respect to its previous one along the sequence. This is in sharp contrast with all previous works where the backbone trace was represented. To test how faithfully the discrete model can reproduce the chain trace in continuous space, we randomly select partial chains from the native structure of 23S ribosome RNA and re-grow them. The rms distance of the re-grown structures from the native ones is ～1.7 ？ for an optimized 16-state discrete model and gradually increases to ～3.3 ？ for long chains of length 50. The efficiency is also good, e.g. the program will finish within several tens of second for long loops of length 50. Our model may facilitate the RNA three-dimensional structure predictions in the near future when combined with appropriate free energy evaluation methods.
