Exploring the energy landscapes of flexible molecular loops using higher‐dimensional continuation

Abstract

The conformational space of a flexible molecular loop includes the set of conformations fulfilling the geometric loop-closure constraints and its energy landscape can be seen as a scalar field defined on this implicit set. Higher-dimensional continuation tools, recently developed in Dynamical Systems and also applied to Robotics, provide efficient algorithms to trace out implicitly defined sets. This paper describes these tools and applies them to obtain full descriptions of the energy landscapes of short molecular loops that, otherwise, can only be partially explored, mainly via sampling. Moreover, to deal with larger loops, this paper exploits the higher-dimensional continuation tools to find local minima and minimum energy transition paths between them, without deviating from the loop-closure constraints. The proposed techniques are applied to previously studied molecules revealing the intricate structure of their energy landscapes. This paper introduces the use of higher-dimensional continuation tools to explore the energy landscapes of the implicitly-defined conformational spaces of flexible molecular loops. These tools produce an atlas composed by coordinated charts that parametrize the conformational space. The atlas captures the structure of this space, which determines the motion of the loop and the transition paths between conformations, something that is hard to obtain using existing approaches.

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