FastLZeroSpikeInference Python Tutorial

Python tutorial

In this tutorial, we demonstrate how the FastLZeroSpikeInference package can be used to deconvolve calcium imaging data from a single neuron. All demos require the FastLZeroSpikeInference package; installation instructions are provided here.

from FastLZeroSpikeInference import fast
import numpy as np
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt

To illustratre the software, we use the following toy dataset.

gam = 0.98
y = np.power(gam, np.concatenate([np.arange(100), np.arange(100)]))
plt.plot(y)

png

The estimate_spikes function estimates spikes based on the calcium trace, exponential decay parameter $\gamma$, and a tuning parameter $\lambda$. This function solves

$\underset{c_1,\ldots,c_T, z_2,\ldots,z_T}{\mathrm{minimize}} \frac{1}{2} \sum_{t=1}^T \left( y_t - c_t \right)^2 + \lambda \sum_{t=2}^T 1_{\left( z_t \neq 0 \right) }$

if the constraint parameter is set to false (default), and

$\underset{c_1,\ldots,c_T, z_2,\ldots,z_T}{\mathrm{minimize}} \frac{1}{2} \sum_{t=1}^T \left( y_t - c_t \right)^2 + \lambda \sum_{t=2}^T 1_{\left( z_t \neq 0 \right) } \mbox{ subject to } z_t = c_t - \gamma c_{t-1} \geq 0,$

if the constraint parameter is set to true. Here’s an example of the function applied to the toy data.

fit = fast.estimate_spikes(y, gam, 1, False)

By default, and to save computation time, the calcium concentration is not automatically estimated. However, the estimate_calcium function can be used to estimate the calcium concentration based on a prior fit.

# Determine calcium concentration from fit
fit = fast.estimate_calcium(fit)
plt.plot(fit['estimated_calcium'])

png

With estimated spike(s)

fit['spikes'][0]
101

Alternatively, both spikes and calcium concentrations can be computed with the estimate_spikes function with estimate_calcium parameter set to true.

fit = fast.estimate_spikes(y, gam, 1, False, True)

To solve the constrained problem

we set the constraint parameter to true in the estimate_spikes function. Consider the following example.

fit = fast.estimate_spikes(y, gam, 1, True, True)