Supplementary information "Anomalous diffusion and asymmetric tempering memory in neutrophil chemotaxis"

This supplement contains the python software that was used to perform Bayesian data analysis of migrating neutrophils. Results and experimental data as well as details of the approach are contained in "Anomalous diffusion and asymmetric tempering memory in neutrophil chemotaxis" by Dieterich, Lindemann, Moskopp, Tauzin, Huttenlocher, Klages, Chechkin, Schwab (2022). 

The given python3 programs requires the installation of the python interface to the nested sampling algorithm PyMultiNest of Johannes Bucher (see http://johannesbuchner.github.io/PyMultiNest/install.html). In addition, numpy, scipy and pandas libraries are used. 

1. myCov.py contains the covariance matrices of positions < x(t) x(t') > of fractional Brownian motion (fBm), power-law and exponentially tempered fBm and the Ornstein-Uhlenbeck process.
2. A_CovSimData.py allows the simulation of paths for stochastic processes based on the covariances that are defined in myCov.py. Simulated paths are saved in an excel file simulatedPaths_data.xlsx.
3. B_BayesianAnalysis.py performs parameter estimation (fit) of the corresponding stochastic model. It reads simulated or experimental data from the excel file simulatedPaths_data.xlsx. Further details on the usage are given as comments with the source code.

An example is also given for the simulation of fBm with H = 0.75, DH = 50, vd = 8, dt = 1, L = 200, Ntra = 100.

     # python3 -u A_CovSimData.py

The resulting simulated data are contained in simulatedPaths_data.xlsx. Taking these data for B_BayesianAnalysis.py

     # python3 -u B_BayesianAnalysis.py fBm 100 200 bayesian

performs the Bayesian analysis for the fBm model with Ntra = 100 paths, each with L = 200 points. This generates the results in the directory chains-bayesian. Parameter estimates and evidences are found in 1-stats.dat.  

   _{Nested Sampling Global Log-Evidence           :   -0.693084281285445904E+05  +/-    0.243291143601513438E+00
    ...
   Dim No.       Mean        Sigma}

   _{1    0.751769979578737702E+00    0.455083467192393416E-02
   2    0.498035123200753063E+02    0.942398486544506864E+00
   3    0.769194950342420203E+01    0.221286113968375997E+00}

The estimated parameters [H, DH, vd] and their uncertainties are given in lines starting with 1, 2, 3. They are in good agreement with the parameters used for simulations H = 0.75, DH = 50 and vd = 8. in addition, the logarithmic evidence is given that can be used to calculate model probabilities.

Further details on the information contained in the other result files can be found here: http://johannesbuchner.github.io/PyMultiNest/