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Iñigo Marcos-Alcalde, Eduardo López-Viñas, Paulino Gómez-Puertas, MEPSAnd: minimum energy path surface analysis over n-dimensional surfaces, Bioinformatics, Volume 36, Issue 3, February 2020, Pages 956–958, https://doi.org/10.1093/bioinformatics/btz649
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Abstract
n-dimensional energy surfaces are becoming computationally accessible, yet interpreting their information is not straightforward. We present minimum energy path surface analysis over n-dimensional surfaces (MEPSAnd), an open source GUI-based program that natively calculates minimum energy paths across energy surfaces of any number of dimensions. Among other features, MEPSAnd can compute the path through lowest barriers and automatically provide a set of alternative paths. MEPSAnd offers distinct plotting solutions as well as direct python scripting.
MEPSAnd is freely available (under GPLv3 license) at: http://bioweb.cbm.uam.es/software/MEPSAnd/.
Supplementary data are available at Bioinformatics online.
1 Introduction
Multi-dimensional energy surfaces are broadly present in a range of biophysical research. In 2015, we published a computational tool (Marcos-Alcalde et al., 2015) able to analyze 3D surfaces (2 coordinates and energy), which has been widely used to study: enzyme reaction mechanisms (Fritz et al., 2018; Geronimo et al., 2018; Li et al., 2019; Marcos-Alcalde et al., 2017; Mendieta-Moreno et al., 2016), ligand binding (Banerjee et al., 2018; Duan et al., 2018; Yuan et al., 2018), protein folding and conformational sampling (Mondal and Reddy, 2019; Shao et al., 2019; Shao and Zhu, 2019a,b) as well as solvation in materials science (Kachmar et al., 2017; Kachmar and Goddard, 2018). It was also included into a catalog of molecular modeling tools (Pirhadi et al., 2016).
Now that n-dimensional surfaces are computationally accessible, a path-finding tool capable of working with this type of data without the need for dimensional reductions could dramatically facilitate their use. We are introducing minimum energy path surface analysis over n-dimensional surfaces (MEPSAnd), a GUI-based tool that natively handles n-dimensional energy surfaces and is capable of calculating (i) the path connecting two points through the lowest energy barrier/s, (ii) the region of the surface sampled to reach those barriers and (iii) a series of alternative sub-optimal paths. Also, a range of plotting and projection options is offered to facilitate the interpretation of the n-dimensional results. The main advantages of MEPSAnd over the previous program (Marcos-Alcalde et al., 2015) are the ability to work with surfaces with any number of dimensions, the handling of data without the need for predefined grids, the consideration of all equivalent trajectories at the same time, the automatic detection of multiple sub-optimal trajectories, the exhaustive sampling of minimum and barrier plateaus, providing a better description of topologically complex surfaces, the use of flexible graphic solutions for the interpretation of n-dimensional results, better calculation performance and scripting support.
2 Features
Network-based connectivity (grid independent): MEPSAnd abstracts surfaces using two networks (Fig. 1A): a Surface Connectivity Network (SCN) and a Global Network (GN). The SCN describes point-to-point connectivity using a list of neighbors per point that is not directly dependent on the number of dimensions. MEPSAnd can build the SCN from a given n-dimensional surface via cutoff-based connectivity inference. Alternatively, the user may provide any previously defined connectivity obtained by third party solutions. This approach allows MEPSAnd to natively handle surfaces with an arbitrary number of dimensions. GN is computed over the SCN, abstracting the surface as a network of minima connected by barriers. The GN computation consists on:
Minima detection: Minima in MEPSAnd can be single points or groups of points with the same energy value. All of them are called minimum clusters. A cluster is considered as a minimum cluster if none of its constituent points has a neighbor with lower energy.
Barrier detection: Every minimum cluster is extended to any higher energy point to which it is connected, until no more higher points can be reached (minima propagation). The overlapping regions between different minima propagations are used to define the barrier clusters.
GN building: Using the previously defined minimum and barrier clusters as vertices the GN is built in such way that minimum clusters are only connected to barrier clusters and vice versa.
GN -based path-finding: The new MEPSAnd algorithm searches for the minimum energy path in two sequential steps. First, once the GN path has been calculated, MEPSAnd computes paths over this network. This path returns a list of visited pairs of barrier and minimum clusters. Second, the paths connecting each of these pairs are computed over the SCN. Each of these real point paths is computed in the following manner: propagation to the lowest energy neighbors is performed from minimum to barrier annotating the loop step in which each point is occupied to later perform a steepest descent trace back from barrier to minimum minimizing the steps taken. Each of these paths is called a ‘path fragment’. MEPSAnd connects the ends of these fragments to build a ‘fragmentwise connectivity’ and path fragments are combined to reconstruct what is referred to as ‘fragmentwise path’, i.e. the complete minimum energy path. The algorithm in more extensively described in the Supplementary Material (user manual).
Automatic detection of alternative paths: MEPSAnd proposes alternative paths via iterative truncation of the GN (Fig. 1F). After a path is obtained, the edges connecting to the highest and latest barrier/s are removed, forcing to sample a different saddle-point. This process runs iteratively until the target cannot be reached anymore.
Data projections to facilitate the visualization of n-dimensional results: In order to provide interpretable representations of n-dimensional results, MEPSAnd offers three different plotting systems: (i) energy profile plots: representation of the energy evolution along a given path (Fig. 1D), (ii) coordinate projections: 2D and 3D projections of a path over sets of coordinates chosen by the user (Fig. 1C), (iii) network projections: customizable GN graphs over which results can be plotted (Fig. 1E). GraphML exportation is supported.
Other features: (i) Capacity of handling more than one million points in any average computer, (ii) varying degrees of path reduction including diagonal connectivity, (iii) periodic coordinates support (e.g. angles), (iv) session saving system and (vi) python scripting environment.
3 Implementation
MEPSAnd is written in Python 3 and depends on: numpy (Van der Walt et al., 2011), pandas (McKinney, 2010), matplotlib (Hunter, 2007), pycairo (https://www.cairographics.org), python-igraph (Csardi and Nepusz, 2006) and the python port (https://github.com/bhargavchippada/forceatlas2) of the Force Altas 2 (Jacomy et al., 2014) Gephi (Bastian et al., 2009) implementation, developed by Bhargav Chippada.
Acknowledgements
Grants from the Spanish State Research Agency—ERDF Funds (RTI2018-094434-B-I00 and RTC-2017-6494-1 with Repessa-Sistemas SA), and from the EC project ‘CONNECT—JPIAMR VRI’. Computational support of the ‘CCC-UAM’ is acknowledged.
Conflict of Interest: none declared.
References