Efficiently refining a transition path using clustering.

In this study, Wang et al. (1xEnergetic and structural details of the trigger loop closing transition in RNA polymerase II. Wang, B., Predeus, A.V...., and Feig, M. Biophys. J. 2013; 105: 767–775Abstract | Full Text | Full Text PDF | PubMed | Scopus (9)See all References1) use molecular simulations and free energy calculations to characterize the transition pathway between open and closed states in RNA polymerase II. This important enzyme is responsible for the majority of mRNA production in eukaryotes. Wang et al. (1xEnergetic and structural details of the trigger loop closing transition in RNA polymerase II. Wang, B., Predeus, A.V...., and Feig, M. Biophys. J. 2013; 105: 767–775Abstract | Full Text | Full Text PDF | PubMed | Scopus (9)See all References1) studied conformational changes of a regulatory element in the enzyme known as the trigger loop (TL). In response to nucleotide triphosphate binding, the TL undergoes structural changes thought to regulate the conversion between open and closed conformational states of the enzyme. Information from conventional all-atom molecular dynamics trajectories, Hamiltonian replica exchange simulations, and targeted molecular dynamics were combined to assemble a connectivity map of the conformational transition (Fig. 1Fig. 1).Figure 1Schematic illustration of the use of clustering to refine a transition pathway. (Topographical map) Hypothetical free energy landscape. (Upper panel) Initial path (dashed line) drawn from the minimum in the upper left to the basin in the upper right. Crosses represent structural data present in snapshots taken from molecular simulations performed on this free energy landscape. The density of crosses is greatest at the location of the free energy minima, which tend to give rise to a larger number of structures that are similar to each other. The increased density of structurally similar conformations at these locations can be identified by clustering the data. This information can then be used to refine the route between the two states (lower panel) to more accurately describe a low free energy transition pathway between them.View Large Image | View Hi-Res Image | Download PowerPoint SlideThe authors find that with a cognate nucleotide triphosphate present, the closed TL conformation is energetically favored by ∼2 kcal/mol over the open conformation. This observation indicates that the closing of TL should be a spontaneous process under these conditions. The authors also identify key structural features of states along the transition pathway. The potential of mean force along the pathway features a stable intermediate between two transition states with significant free energy barriers. The presence of the stable intermediate raises the possibility that partial rather than complete opening may be sufficient to allow completion of the transcription cycle during processive elongation. In this case, it would only be necessary to overcome one of the two barriers observed for elongation to proceed. This would suggest that the open state is only attained during relatively rare events, such as pausing or backtracking of the polymerase. However, the authors note that conclusively answering this question will require additional studies.One of the notable features of the article is that the authors employ clustering of the protein coordinates in an innovative way to identify intermediates along the transition pathway. In this way, conformational minima (which are by definition low free energy states) are selected as locations to help define the path rather than a path being imposed based on an arbitrary reaction coordinate. Determining relevant transition pathways for biophysical processes is an important component of understanding how these processes occur (2xAtomistic view of the conformational activation of Src kinase using the string method with swarms-of-trajectories. Gan, W.X., Yang, S.C., and Roux, B. Biophys. J. 2009; 97: L8–L10Abstract | Full Text | Full Text PDF | PubMed | Scopus (46)See all References, 3xFree energy of translocating an arginine-rich cell-penetrating peptide across a lipid bilayer suggests pore formation. Huang, K. and Garcia, A.E. Biophys. J. 2013; 104: 412–420Abstract | Full Text | Full Text PDF | PubMed | Scopus (33)See all References). However, such efforts can be challenging and methods to define transition paths continue to be a highly active research area (4xMaximum flux transition paths of conformational change. Zhao, R.J., Shen, J.F., and Skeel, R.D. J. Chem. Theory Comput. 2010; 6: 2411–2423Crossref | PubMed | Scopus (18)See all References, 5xUnrestrained computation of free energy along a path. Dickson, B.M., Huang, H., and Post, C.B. J. Phys. Chem. B. 2012; 116: 11046–11055Crossref | PubMed | Scopus (9)See all References). In many cases, pathway-finding algorithms can be computationally demanding (6xRate constant and reaction coordinate of Trp-cage folding in explicit water. Juraszek, J. and Bolhuis, P.G. Biophys. J. 2008; 95: 4246–4257Abstract | Full Text | Full Text PDF | PubMed | Scopus (86)See all References, 7xFree energy of conformational transition paths in biomolecules: the string method and its application to myosin VI. Ovchinnikov, V., Karplus, M., and Vanden-Eijnden, E. J. Chem. Phys. 2011; 134: 085103Crossref | Scopus (44)See all References).A benefit of the approach employed by Wang et al. (1xEnergetic and structural details of the trigger loop closing transition in RNA polymerase II. Wang, B., Predeus, A.V...., and Feig, M. Biophys. J. 2013; 105: 767–775Abstract | Full Text | Full Text PDF | PubMed | Scopus (9)See all References1) is that it should have modest computational cost because clustering methods have undergone significant algorithmic development in recent years and employ sophisticated techniques to reduce their computational expense (8xFast large-scale clustering of protein structures using Gauss integrals. Harder, T., Borg, M...., and Hamelryck, T. Bioinformatics. 2012; 28: 510–515Crossref | PubMed | Scopus (12)See all References, 9xA fast parallel clustering algorithm for molecular simulation trajectories. Zhao, Y., Sheong, F.K...., and Huang, X. J. Comput. Chem. 2013; 34: 95–104Crossref | PubMed | Scopus (12)See all References, 10xPrincipal component and clustering analysis on molecular dynamics data of the ribosomal L11·23S subdomain. Wolf, A. and Kirschner, K.N. J. Mol. Model. 2013; 19: 539–549Crossref | PubMed | Scopus (4)See all References). The authors’ general approach could be employed in a wide variety of contexts and would be particularly useful in complex systems where precisely defining a reaction coordinate can be difficult.