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Protein folding occurs in a high dimensional phase space, and the representation of the associated energy landscape is non-trivial. A widely applied approach to studying folding landscapes is to describe the dynamics along a small number of reaction coordinates. However, other strategies involve more elaborate analysis of the complex phase space. There have been many attempts to obtain a more detailed representation of all available conformations for a given system. In this work, we address this problem using a metric based on internal distances between amino acids to describe the differences between any two conformations. Using an effective projection method, we are able to go beyond the usual one-dimensional representation and thus visualize landscapes in two dimensions. We refer to this method as Energy Landscape Visualization Method (ELViM). We have applied this methodology using Cα structure-based model (SBM) to study the folding of two well-known proteins: SH3 domain and Protein-A. Our visualization method yields a detailed description of the folding process, making possible the identification of transition state regions, and establishing the paths that lead to the native state. For SH3, we have analyzed structural differences in the distribution of folding routes. The competition between the native and mirror structures in protein A is discussed. Finally the method is applied to discuss the conformational changes of the Elongation Factor Thermally unstable (EF-Tu) and its transition states. Distinct features of the ELViM are that it does not require or assume an existence of a reaction coordinate, and it does not require kinetic information regarding the investigated system.
ABOJr was supported by CAPES - Brazil. VBPL was supported by the CNPq and FAPESP Grant 2018/18668-1, 2016/19766-1 and 2014/50739-5. PCW was supported by a NSF CAREER Award (grant No. MCB-1350312). This work was partially supported byt he Center for Theoretical Biological Physics sponsored by the NSF Grant PHY-1427654