BilayerAnalyzer analysis: `msd_multi` - Multiple time origin mean squared displacement.¶

Description¶

Estimate the mean squared displacement using multiple time origins.

This analysis computes the average mean squared displacement (MSD) of the centers of mass of the specified lipids using multiple time origins and thus multiple time blocks: MSD = <<(r(tau) - r_0)^2>_i>_tau where the inner angle brackets denote averaging over all lipids i and the outer brackets denote averaging over all time origins tau. The diffusion coefficient is estimated from the MSD using a simplified version Einstein’s relation: D_i ~ MSD_i/(4.0*tau)

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

Initiated by instance of:¶

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

Syntax¶

msd_multi analysis-ID keyword value

msd_multi = 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: ‘both’, ‘upper’, or ‘lower’): Specifies the bilayer leaflet to include in the estimate. Default: ‘both’
- resname (str): Specify the resname of the lipid type to include in this analysis. Default: ‘all’, averages over all lipid types.
- n_tau (int): Specify the time block size in number of frames. Default: 50 ( 1000 picoseconds for timestep of 2 fs and frame output ever 100 timesteps).
- n_sigma (int): Specify the time between origins in number of frames. Default: 50.

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('msd_multi msd_multi_1') 

Add by string - adjust a setting:

analyzer.add_analysis('msd_multi msd_multi_1 leaflet both')

Add by list:

analyzer.add_analysis(list(['msd_multi', 'msd_multi_1', dict({'leaflet':'both'})]))

Add by dict:

analyzer.add_analysis(dict({'analysis_key': 'msd_multi', 'analysis_id': 'msd_multi_1','analysis_settings':dict({'leaflet':'both'})}))

To remove from analyzer:

analyzer.remove_analysis('msd_multi_1')

Output Info:¶

Retrieve output after running analyses:

output = analyzer.get_analysis_data('msd_multi_1')

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

Note

According to results in Ref 3 the time blocks used to estimate the MSD should not be overlapping. Therefore, it is recommended to use n_sigma >= n_tau.

References¶

Christofer Hofsab, Erik Lindahl, and Olle Edholm, “Molecular Dynamics Simulations of Phospholipid Bilayers with Cholesterol”, Biophys J. 2003 Apr; 84(4): 2192-2206. doi: 10.1016/S0006-3495(03)75025-5
Orsi, Mario, Julien Michel, and Jonathan W. Essex. “Coarse-grain modelling of DMPC and DOPC lipid bilayers.” Journal of Physics: Condensed Matter 22.15 (2010): 155106. http://iopscience.iop.org/article/10.1088/0953-8984/22/15/155106/meta
Gaurav Pranami and Monica H. Lamm, Estimating Error in Diffusion Coefficients Derived from Molecular Dynamics Simulations, Journal of Chemical Theory and Computation 2015 11 (10), 4586-4592, DOI: 10.1021/acs.jctc.5b00574, http://pubs.acs.org/doi/full/10.1021/acs.jctc.5b00574

BilayerAnalyzer analysis: msd_multi - Multiple time origin mean squared displacement.¶