Simulation of time traces

class fret_tester.TwoStateExpTruth(lifetimes, efficiencies)

Simulate ground truth smFRET time traces (two states, exp. lifetimes)

Lifetimes are exponentially distributed.

Parameters:

• life_times (array_like, shape=(2,)) – Mean (of the exponentially distributed) life times of the states
• efficiencies (array_like, shape=(2,)) – FRET efficiencies for the states

generate(duration)

Create a time trace that of at least duration length

Parameters:duration (float) – Minimum duration of the time trace. In practice, it will be longer. Returns:

• time (numpy.ndarray) – Time points of state changes. These are bi-exponentially distributed.
• eff (numpy.ndarray) – Corresponding FRET efficiencies. The i-th entry lasts from time[i-1] (or 0 for i=0) to time[i].

__call__(*args, **kwargs)

Synonym for generate()

fret_tester.sample(time, eff, exposure_time, data_points=inf, frame_time=0.0)

Sample the true smFRET time trace with finite exposure time

This means that there will be integration over all transitions that happen during a single exposure.

Parameters:

• time (array_like, shape=(n,)) – Sequence of transition times as returned by two_state_truth()
• eff (array_like, shape=(n,)) – Sequence of FRET efficiencies as returned by two_state_truth()
• exposure_time (float) – Exposure time for sampling. All transition during a exposure will be integrated.
• data_points (scalar, optional) – Number of data points to return. If the FRET time trace is too short, the maximum number of data points the trace allows is returned. Defaults to infinity.
• frame_time (float, optional) – Total time for one frame, i.e. minimum time between two data points. If this is less than exposure_time, use exposure_time. Defaults to 0, i.e. use exposure_time.

Returns:

• sample_time (numpy.ndarray) – Time points of sampling. They are evenly spaced with exposure_time difference.
• sample_eff (numpy.ndarray) – Corresponding sampled FRET efficiencies

fret_tester.experiment(eff, photons, donor_brightness, acceptor_brightness)

From sampled smFRET time traces, simulate (noisy) experiment results

This adds noise coming from the rather broad brightness distributions of fluorophores to the time traces, resulting in a trace as one would get out of an experiment.

The acceptor signal is generated by acceptor_brightness(eff * photons), the donor signal is generated by donor_brightness((1 - eff) * photons).

Parameters:

• eff (array_like) – Sampled FRET efficiencies
• photons (float) – Mean summed number of photons emitted by donor and acceptor per exposure.
• donor_brightness, acceptor_brightness (callable) – Takes one argument, an array of mean brightness values. For each entry m it returns a random value drawn from the brightness distribution with mean m.

Returns:

donor_noisy, acceptor_noisy – Donor and acceptor fluorescence including noise

Return type:

numpy.ndarray

class fret_tester.DataSet

Named tuple containing a full data set of a simulation run

true_time, true_eff

array_like – True state trajectory as produced by two_state_truth()

samp_time, samp_eff

array_like – Sampled state trajectory as produced by sample()

exp_don, exp_acc

array_like – (Noisy) donor and acceptor intensities as produced by experiment()

exp_eff

array_like – Experiment FRET efficiency, i.e. exp_acc / (exp_acc + exp_don)

Create new instance of DataSet(true_time, true_eff, samp_time, samp_eff, exp_don, exp_acc, exp_eff)

fret_tester.simulate_dataset(truth, exposure_time, data_points, photons, donor_brightness, acceptor_brightness, frame_time=0.0)

Simulate a whole data set

Consecutively run two_state_truth(), sample(), and experiment().

Parameters:

• truth (callable or tuple of numpy.ndarray, shape=(n,)) – Ground truth smFRET time trace. If this is an array, truth[0] should be the sequence of time points where state transitions occur and truth[1] the FRET efficiency between the (i-1)-th time point (or 0 for i = 0) and the i-th time point. If this is callable, it should return a ground truth smFRET time trace as described above. It should take one float parameter, which is the minimum duration of the generated trace.
• exposure_time (float) – Exposure time for sampling. All transition during a exposure will be integrated.
• data_points (scalar, optional) – Number of data points to return. If the FRET time trace is too short, the maximum number of data points the trace allows is returned. Defaults to infinity.
• photons (float) – Mean summed number of photons emitted by donor and acceptor per exposure.
• donor_brightness, acceptor_brightness (callable) – Takes one argument, an array of mean brightness values. For each entry m it returns a random value drawn from the brightness distribution.
• frame_time (float, optional) – Total time for one frame, i.e. minimum time between two data points. If this is less than exposure_time, use exposure_time. Defaults to 0, i.e. use exposure_time.

Returns:

Collected simulated data

Return type:

DataSet