Abstract
The visualization of multidimensional energy landscapes is important, providing insight into the kinetics and thermodynamics of a system, as well the range of structures a system can adopt. It is, however, highly nontrivial, with the number of dimensions required for a faithful reproduction of the landscape far higher than can be represented in two or three dimensions. Metric disconnectivity graphs provide a possible solution, incorporating the landscape connectivity information present in disconnectivity graphs with structural information in the form of a metric. In this study, we present a new software package, PyConnect, which is capable of producing both disconnectivity graphs and metric disconnectivity graphs in two or three dimensions. We present as a test case the analysis of the 69-bead BLN coarse-grained model protein and show that, by choosing appropriate order parameters, metric disconnectivity graphs can resolve correlations between structural features on the energy landscape with the landscapes energetic and kinetic properties.
Highlights
The potential energy surface, UðrÞ, of an N atom chemical system represents the potential energy as a function of 3N atomic coordinates
The topography of UðrÞ, or energy landscape, determines its structure, kinetics, and thermodynamics[1,2] and its analysis has proved useful in studying a range of physical systems and phenomena, including glasses,[3] biomolecules,[4,5,6] and clusters.[7,8,9]
Metric disconnectivity graph analysis was performed on a database of stationary points for a BLN model protein This database was generated with discrete path sampling[8,28] as implemented in PATHSAMPLE.[29]
Summary
The potential energy surface, UðrÞ, of an N atom chemical system represents the potential energy as a function of 3N atomic coordinates. The topography of UðrÞ, or energy landscape, determines its structure, kinetics, and thermodynamics[1,2] and its analysis has proved useful in studying a range of physical systems and phenomena, including glasses,[3] biomolecules,[4,5,6] and clusters.[7,8,9] For all but the simplest cases, UðrÞ has many more degrees of freedom than it is possible to visualize conventionally, making it impossible to assess the surface topography directly. One solution to the visualization problem is to partition the landscape into discrete regions, and hierarchically cluster these regions according to some similarity measure. This clustering can be represented as a tree-graph in either two or three dimensions (2D or 3D). There are a number of examples of hierarchical clustering methods in the literature, broadly based on either geometry, energetic barriers, or local ergodicity
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