Monte Carlo Energy Landscape Paving and Basin Paving simulation of RNA T-loop hairpin Pradipta Bandyopadhyay ⇑ , Hungyo Kharerin Centre for Computational Biology and Bioinformatics, School of Computational and Integrative Sciences 1 , Jawaharlal Nehru University, 110067 New Delhi, India article info Article history: Received 2 November 2010 In final form 6 December 2010 Available online 8 December 2010 abstract Conformational landscape of RNA T-loop hairpin has been investigated by Energy Landscape Paving (ELP) and Basin Paving (BP) Monte Carlo simulations. Both ELP and BP simulations use memory of the simula- tion to increase the probability of the states less visited. The unfolded structures of the RNA were obtained from the folded one by ELP method. Structures were folded from extended structures by BP method. Choice of different parameters, including the use of the end-to-end distance of RNA as a memory term, in the simulations to accelerate sampling is discussed. It has been found that both ELP and BP are highly efficient techniques for unfolding and folding RNA T-loop hairpin. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Determination of energy landscape of molecules can give infor- mation about structure, dynamics and thermodynamics of the sys- tem [1]. However, accurate determination of energy landscape, either potential energy surface (PES) or free energy surface (FES), requires extensive conformational sampling of molecules. The accuracy of sampling can decrease for larger molecules and the problem becomes more severe for molecules with a very rough en- ergy surface. The conformational sampling is generally done by dif- ferent simulation techniques such as molecular dynamics (MD), Monte Carlo (MC) or Langevin dynamics [2–6], although other methods such as systematic search, energy smoothing have also been used [7,8]. Experimental techniques such as fluorescence spectroscopy, NMR can give idea of the ruggedness of the land- scape and the different time scales associated with it [9,10]. Standard MD or MC simulations can get trapped in one of the large number of minima present in the landscape. It is often neces- sary to use enhanced simulation techniques such as steered molec- ular dynamics, umbrella sampling, replica exchange etc. to sample the rugged energy landscapes [11]. Stochastic methods are one of the most widely used methods to sample rough energy landscapes [12–16]. The use of MC methods in stochastic techniques requires special mention. One class of important technique in this context is the use of memory of the simulation [12,16] for better sampling. In Energy Landscape Paving (ELP) method, one memory based MC simulation technique, the history of the simulation trajectory is used to increase the probability of visiting states less visited before and vice versa. This is achieved by modifying the Boltzmann weight factor dynamically during the simulation. This method has been used successfully for small peptides and water clusters [2,12,17]. In the related Basin Paving (BP) method, the barriers be- tween minima are effectively eliminated by combining ELP method with the Basin Hopping method [18]. It is to be noted that there have been previous works, such as conformational flooding (CF) [19] and stochastic tunneling (ST) [20,21], which work in spirits similar to ELP and BP. In the CF method, free energy barrier involv- ing a subset of coordinates is lowered by adding a potential energy term obtained from the conformation density of the system for this subset of coordinates. The main difference between BP (and ELP) and CF is that there is no explicit energy term added to the poten- tial energy in BP and ELP, rather the Boltzmann factor is modified by the history of the trajectory, which can also be thought of mod- ifying the energy function with fixed Boltzmann factor. In the ST method, a non-linear transformation is given to the potential en- ergy to map the whole energy surface between values 0 and 1 reducing the actual barrier. Comparison of ST and ELP has been dis- cussed in reference 17. Memory based simulation has also been used in MD simulation [22,23]. Till now ELP and BP method have not been applied to RNA systems. In the present work, the effi- ciency and applicability of ELP and BP methods in exploring the conformational landscape of RNA hairpin is investigated. RNA can fold into specific three dimensional structures like pro- teins. However, it is known to have a dynamic ensemble of struc- tures due to the diversity of its secondary structure. Although RNA is usually single stranded, it can fold back to itself to form dif- ferent secondary structural elements. There are several structural motifs in RNA which recur in the three dimensional structures. One of the most prevalent structural motifs is RNA hairpin, which can start as a nucleation site for the three dimensional structure of RNA. The hairpin loops also play important role in RNA–protein recognition and gene regulation by RNA such as riboswitches and 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.12.019 ⇑ Corresponding author. Fax: +91 11 26741586. E-mail address: praban07@gmail.com (P. Bandyopadhyay). 1 Formerly known as School of Information Technology. Chemical Physics Letters 502 (2011) 130–135 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett