Diffusion Coefficient Fitting

Python class library to determine the diffusion coefficient of a time series using a Generalized Least Squares (GLS) minimization procedure, which accounts for the correlation of MSD data.

Please read and cite the reference: J. Bullerjahn, S. v. Bülow, G. Hummer, Optimal estimates of diffusion coeffcients from molecular dynamics simulations, Journal of Chemical Physics 153, 024116 (2020).

The input trajectory is analyzed as a whole and split into segments. For each segment, a quality factor Q is computed, indicating how well the trajectory fits a model of random diffusion with noise. The analysis is done for different time steps $\mathrm{\Delta }{t}_n$ of the trajectory. Given the quality factor analysis, the user decides on a time step/diffusion coefficient pair to use.

Basic Example

import Dfit
res = Dfit.Dcov(m=20,fz='mytrajectory.dat',tmin=1,tmax=100,nseg=150)
res.run_Dfit()
res.analysis(tc=10)
res.finite_size_correction()

Input for Dfit.Dcov()

Required:

• fz (str): Filename of input trajectory. Format: Center-of-mass position x [y z ...] in nm. Each row corresponds to a timestep indicated in the optional argument dt. The number of columns determines the number of dimensions. Use no header. Separate columns by whitespace, no comma.

(NOTE: Alternatively, you can provide a list of input trajectories. The code will then treat these lists as copies of the same molecule in the same simulation [e.g. several water molecules, or several copies of the same protein in a dense protein solution, or several DOPC lipids...]. The individual trajectories will then not be segmented; instead, each individual trajectory will be treated as one segment of a long simulation. The resulting diffusion coefficient is then the mean across all segments.)

Optional:

• dt (float): Timestep [in ps] (default: 1.0).
• m (int): Number of MSD values to consider (default: 20).
• tmin (int): Minimum timestep (default: 1).
• tmax (int): Maximum timestep (default: 100).
• d2max (float): Convergence criterion for GLS iteration (default: 1e-10).
• nitmax (int): Maximum number of iterations in GLS procedure (default: 100).
• nseg (int): Number of segments (default: N / (100*tmax)).
• fout (str): Name for output files w/o extension (default 'D_analysis').
• imgfmt (str): Output format for plot. Choose 'pdf' or 'png' (default: 'pdf').

Run res.run_Dfit() without additional arguments (everything is stored in self).

Output

Files:

• D_analysis.dat: Summary of output, including diffusion coefficient and Q-factor analysis.
• D_analysis.pdf: (or .png) Output plots. Use this to assess which diffusion coefficient to select. Refer to Figs. 2 and 4 in the paper.

Stored values in the Dfit class instance:

• res.D: Optimal diffusion coefficient estimates per timestep
• res.Dstd: Estimated standard deviation of res.D per timestep
• res.Dempstd: Empirical standard deviation of res.D per timestep (should be close to res.Dstd if the diffusive model is appropriate)
• res.q_m: Mean quality factor per timestep
• res.q_std: Standard deviation of quality factor per timestep

Additional input for method analysis():

• tc (int/float): 'Timestep chosen' [in ps] for the diffusion coefficient. Must be a multiple of dt.

The analysis can be repeated with different values of tc. A red vertical line indicates the chosen timestep in the plot. Repeat until you are content with the chosen timestep

Additional input for finite_size_correction():

• tc (int/float): Use tc determined in the previous analysis step
• eta (float): Viscosity in units of Pa*s
• L (float): Edge length of cubic (!) simulation box in nm
• T (float): Temperature in Kelvin
• boxtype (str): Only 'cubic' currently allowed.