BilayerAnalyzer analysis: halperin_nelson - Halperin and Nelson’s rotational invariant.

Description

Estimate the mean hexagonal packing orientation parameter.

This analysis implements Halperin and Nelson’s rotational invariant to estimate the hexagonal packing orientation parameter. The value for lipid l is given by phi_l = | (1/6) * sum_{j element nn(l)} exp(6i*theta_{lj}) |^2 , where i is complex and nn(l) are the 6 nearest neighbors of lipid l; theta_{lj} is the angle between the vector formed by beads representing lipid l and j and an arbitrary axis. The value is unity for perfect hexagonal packing, and it is zero to the extent that hexagonal packing is entirely absent. This protocol uses the ‘com_frame’ representation of the bilayer.

This protocol is identified by the analysis key: ‘halperin_nelson’

Initiated by instance of:

<class 'pybilt.bilayer_analyzer.analysis_protocols.HalperinNelsonProtocol'>

Syntax

halperin_nelson analysis-ID keyword value

  • halperin_nelson = analysis-Key - keyword/name for this analysis.

  • analysis-ID = The unique name/ID being assigned to this analysis.

  • keyword value = settings keyword value pairs

    • leaflet (str: ‘upper’, or ‘lower’): Specifies the bilayer leaflet to include in the estimate. Default: ‘upper’

Examples

Construct analyzer:

analyzer = BilayerAnalyzer(structure='name_of_structure_file',
                           trajectory='name_of_traj_file',
                           selection='resname POPC DOPC')

Add by string - use default settings:

analyzer.add_analysis('halperin_nelson halperin_nelson_1')

Add by string - adjust a setting:

analyzer.add_analysis('halperin_nelson halperin_nelson_1 leaflet upper')

Add by list:

analyzer.add_analysis(list(['halperin_nelson', 'halperin_nelson_1', dict({'leaflet':'upper'})]))

Add by dict:

analyzer.add_analysis(dict({'analysis_key': 'halperin_nelson', 'analysis_id': 'halperin_nelson_1','analysis_settings':dict({'leaflet':'upper'})}))

To remove from analyzer:

analyzer.remove_analysis('halperin_nelson_1')

Output Info:

Retrieve output after running analyses:

output = analyzer.get_analysis_data('halperin_nelson_1')

The output is type <type 'numpy.ndarray'>

References

  1. Shachi Katira, Kranthi K. Mandadapu, Suriyanarayanan Vaikuntanathan, Berend Smit, and David Chandler, The order-disorder transition in model lipid bilayers is a first-order hexatic to liquid phase transition, arXiv preprint [cond-mat.soft] 2015, arXiv:1506.04310. https://arxiv.org/pdf/1506.04310.pdf