Hybrid Monte Carlo with adaptive temperature in mixed-canonical ensemble: Efficient conformational analysis of RNA

A hybrid Monte Carlo method with adaptive temperature choice is presented , which exactly generates the distribution of a mixed-canonical ensemble composed o f two canonical ensembles at low and high temperature. The analysis of resulting Mark ov chains with the reweighting technique shows an efficient sampling of the canonical distribution at low temperature, whereas the high temperature component facili tates conformational transitions, which allows shorter simulation times. The algorithm was tested by comparing analytical and numerical results for th e small n-butane molecule before simulations were performed for a triri bonucleotide. Sampling the complex multi-minima energy landscape of this small RNA segment, we observe enforced crossing of energy barriers. Introduction The efficient sampling of phase space for complex biological systems remains to be the specific problem in theoretical biochemistry. This problem can only be solved with Monte Carlo (MC) or molecular dynamics (MD) simulations, if it is possib le to overcome energy barriers, which are large compared to the thermal energy. MC algorithm s, that are based on local conformational changes of functional groups, can enforce b arrier crossing by significant distortions. Unfortunately, large local distortions are ofte n nergetically unfavourable and the corresponding MC proposals will be rejected. One way to over come this problem is to use hybrid Monte Carlo (HMC) techniques [7, 6, 16], which allow t o combine global updates in position space with reasonable acceptance rates. Another w ay is to sample in so-called generalized ensembles [12], where the canonical ensemble is re placed by a probability density, which supports an extended energy range. Higher energy regi ons will be visited more often and enable conformational changes more easily. In this case the resulting Markov chain has to be reweighted according to the canonical ensemble of inte rest. For the construction of a generalized ensemble different techniques can be applied [ 4]. The classical Ferrenberg–Swendsen scheme [8] uses results from a canonical distribution at one temperature to extrapolate to expectation value s of another distribution at a different temperature. But a small difference between the temp eratures is necessary to receive statistically reliable results. The reweighting method ca n be extended to mix data from independent runs [9]. More recently, algorithms were propose d, which sample over the whole energy range [12], like the multicanonical algorithm [3], s imulations in a 1/k-sampling [13]