LangevinFunctions module

Created on Mon Sep 4 10:00:36 2023

@author: jbeckwith

class LangevinFunctions.LF

Bases: object

BrownianRot(DR, TStep, NSteps)
BrownianRot function

generates random rotational motion using DR and TStep

Parameters:

  • DR (float) – rotational diffusion coefficient

  • TStep (float) – time step relative to DT

  • NSteps (int) – number of steps to simulate

Returns:

sph_coords (np.3Darray) – are theta, phi over time

BrownianTrans_Ideal(DT, n_d, deltaT, N)
BrownianTrans_Ideal function

generates random translational motion of N coordinates using DT and TStep assumes no localisation error, or effects from imaging

Parameters:

  • DT (float) – translational diffusion coefficient

  • NAxes (int) – mumber of dimensions of diffusion

  • TStep (float) – time step relative to DT

  • NSteps (int) – number of steps to simulate

Returns:

coordinates (np.ndarray) – coordinates over time

BrownianTrans_Realistic(DT, N, n_d, deltaT, tE, sigma0, s0, R=0.16666666666666666)

BrownianTrans_Realistic function Generates displacements Delta from equations 2–5 of Michalet, X.; Berglund, A. J. Phys. Rev. E 2012, 85 (6), 061916. https://doi.org/10.1103/PhysRevE.85.061916. More realistic Brownian motion assuming tracked with a camera

Parameters:

  • DT (float) – translational diffusion coefficient

  • N (int) – number of steps to simulate

  • n_d (int) – mumber of dimensions of diffusion

  • deltaT (flaot) – time step between data points

  • tE (float) – camera exposure duration (can be same as deltaT)

  • sigma0 (float) – static localisation error

  • s0 (float) – standard deviation of the PSF

  • R (float) – motion blur coefficient (see Equation 5 of paper)

Returns:

coordinates (np.ndarray) – coordinates over time

MultiBrownianTrans_Par(DT, N, n_d, deltaT, tE, sigma0, s0, n_molecules=10, volume=array([8, 8, 8]), R=0.16666666666666666, min_track_length=3)

MultiBrownianTrans_Volume function Generates displacements Delta from equations 2–5 of Michalet, X.; Berglund, A. J. Phys. Rev. E 2012, 85 (6), 061916. https://doi.org/10.1103/PhysRevE.85.061916. More realistic Brownian motion assuming tracked with a camera Simulates a specific volume Will split tracks that reach sigma0 from each other

Parameters:

  • DT (float) – translational diffusion coefficient

  • N (int) – number of steps to simulate

  • n_d (int) – mumber of dimensions of diffusion

  • deltaT (flaot) – time step between data points

  • tE (float) – camera exposure duration (can be same as deltaT)

  • sigma0 (float) – static localisation error

  • s0 (float) – standard deviation of the PSF

  • n_molecules (int) – number of molecules simualted in the volume

  • volume (np.1darray) – dimensions of volume simulated, in same units as DT (same number of dimensions as n_d)

  • R (float) – motion blur coefficient (see Equation 5 of paper)

Returns:

coordinates (dict) – coordinates of n_molecules over time

MultiBrownianTrans_Volume(DT, N, n_d, deltaT, tE, sigma0, s0, n_molecules=10, volume=array([8, 8, 8]), bleach_probability=0.0, R=0.16666666666666666, min_track_length=10)

MultiBrownianTrans_Volume function Generates displacements Delta from equations 2–5 of Michalet, X.; Berglund, A. J. Phys. Rev. E 2012, 85 (6), 061916. https://doi.org/10.1103/PhysRevE.85.061916. More realistic Brownian motion assuming tracked with a camera Simulates a specific volume Will split tracks that reach sigma0 from each other

Parameters:

  • DT (float) – translational diffusion coefficient

  • N (int) – number of steps to simulate

  • n_d (int) – mumber of dimensions of diffusion

  • deltaT (flaot) – time step between data points

  • tE (float) – camera exposure duration (can be same as deltaT)

  • sigma0 (float) – static localisation error

  • s0 (float) – standard deviation of the PSF

  • n_molecules (int) – number of molecules simualted in the volume

  • volume (np.1darray) – dimensions of volume simulated, in same units as DT (same number of dimensions as n_d)

  • bleach_probability (float) – if above 0, assigns a random proportion of frames to “off” and replaces them with interpolation.

  • R (float) – motion blur coefficient (see Equation 5 of paper)

Returns:

coordinates (dict) – coordinates of n_molecules over time