Fit injected current

Fit injected current#

For our first example, we will look at a very simple dataset: patch-clamp recordings from a single neuron in layer 4 of mouse primary visual cortex. This data is from the Allen Brain Atlas, and experimenters injected current directly into the cell, while recording the neuron’s membrane potential and spiking behavior. The experiments varied the shape of the current across many sweeps, mapping the neuron’s behavior in response to a wide range of potential inputs.

For our purposes, we will examine only one of these sweeps, “Noise 1”, in which the experimentalists injected three pulses of current. The current is a square pulse multiplied by a sinusoid of a fixed frequency, with some random noise riding on top.

Allen Brain Atlas view of the data we will analyze.

In the figure above (from the Allen Brain Atlas website), we see the approximately 22 second sweep, with the input current plotted in the first row, the intracellular voltage in the second, and the recorded spikes in the third. (The grey lines and dots in the second and third rows comes from other sweeps with the same stimulus, which we’ll ignore in this exercise.) When fitting the Generalized Linear Model, we are attempting to model the spiking behavior, and we generally do not have access to the intracellular voltage, so for the rest of this notebook, we’ll use only the input current and the recorded spikes displayed in the first and third rows.

First, let us see how to load in the data and reproduce the above figure, which we’ll do using pynapple. This will largely be a review of what we went through yesterday. After we’ve explored the data some, we’ll introduce the Generalized Linear Model and how to fit it with NeMoS.

Learning objectives#

Learn how to explore spiking data and do basic analyses using pynapple
Learn how to structure data for NeMoS
Learn how to fit a basic Generalized Linear Model using NeMoS
Learn how to retrieve the parameters and predictions from a fit GLM for intrepetation.

# Import everything
import jax
import matplotlib.pyplot as plt
import numpy as np
import pynapple as nap

import nemos as nmo

# some helper plotting functions
from nemos import _documentation_utils as doc_plots

# configure plots some
plt.style.use(nmo.styles.plot_style)

WARNING:2025-01-07 21:05:21,231:jax._src.xla_bridge:969: An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.

Data Streaming#

While you can download the data directly from the Allen Brain Atlas and interact with it using their AllenSDK, we prefer the burgeoning Neurodata Without Borders (NWB) standard. We have converted this single dataset to NWB and uploaded it to the Open Science Framework. This allows us to easily load the data using pynapple, and it will immediately be in a format that pynapple understands!

Tip

Pynapple can stream any NWB-formatted dataset! See their documentation for more details, and see the DANDI Archive for a repository of compliant datasets.

The first time the following cell is run, it will take a little bit of time to download the data, and a progress bar will show the download’s progress. On subsequent runs, the cell gets skipped: we do not need to redownload the data.

path = nmo.fetch.fetch_data("allen_478498617.nwb")

Pynapple#

Data structures and preparation#

Now that we’ve downloaded the data, let’s open it with pynapple and examine its contents.

data = nap.load_file(path)
print(data)

/home/agent/workspace/rorse_ccn-software-jan-2025_main/lib/python3.11/site-packages/hdmf/spec/namespace.py:535: UserWarning: Ignoring cached namespace 'hdmf-common' version 1.7.0 because version 1.8.0 is already loaded.
  warn("Ignoring cached namespace '%s' version %s because version %s is already loaded."
/home/agent/workspace/rorse_ccn-software-jan-2025_main/lib/python3.11/site-packages/hdmf/spec/namespace.py:535: UserWarning: Ignoring cached namespace 'hdmf-experimental' version 0.4.0 because version 0.5.0 is already loaded.
  warn("Ignoring cached namespace '%s' version %s because version %s is already loaded."

allen_478498617
┍━━━━━━━━━━┯━━━━━━━━━━━━━┑
│ Keys     │ Type        │
┝━━━━━━━━━━┿━━━━━━━━━━━━━┥
│ units    │ TsGroup     │
│ epochs   │ IntervalSet │
│ stimulus │ Tsd         │
│ response │ Tsd         │
┕━━━━━━━━━━┷━━━━━━━━━━━━━┙

The dataset contains several different pynapple objects, which we will explore throughout this demo. The following illustrates how these fields relate to the data we visualized above:

Annotated view of the data we will analyze.

units: dictionary of neurons, holding each neuron’s spike timestamps.
epochs: start and end times of different intervals, defining the experimental structure, specifying when each stimulation protocol began and ended.
stimulus: injected current, in Amperes, sampled at 20k Hz.
response: the neuron’s intracellular voltage, sampled at 20k Hz. We will not use this info in this example

Now let’s go through the relevant variables in some more detail:

trial_interval_set = data["epochs"]

current = data["stimulus"]
spikes = data["units"]

First, let’s examine trial_interval_set:

trial_interval_set

index    start    end      tags
      0.0      34.02    ['Ramp']
      39.02    73.04    ['Ramp']
      78.04    112.06   ['Ramp']
      117.06   119.083  ['Short Square']
      124.083  126.106  ['Short Square']
      131.106  133.129  ['Short Square']
      138.129  140.152  ['Short Square']
...      ...      ...      ...
     0.0      34.02    ['Short Square - Triple']
     39.02    73.04    ['Short Square - Triple']
     78.04    112.06   ['Short Square - Triple']
     117.06   119.083  ['Short Square - Triple']
     124.083  126.106  ['Short Square - Triple']
     131.106  133.129  ['Short Square - Triple']
     138.129  140.152  ['Test']
shape: (67, 2), time unit: sec.

trial_interval_set is an IntervalSet, with a metadata columns (tags) defining the stimulus protocol.

noise_interval = trial_interval_set[trial_interval_set.tags == "Noise 1"]
noise_interval

  index    start      end  tags
      0  460.768  488.788  ['Noise 1']
      1  526.808  554.828  ['Noise 1']
      2  592.848  620.868  ['Noise 1']
shape: (3, 2), time unit: sec.

As described above, we will be examining “Noise 1”. We can see it contains three rows, each defining a separate sweep. We’ll just grab the first sweep (shown in blue in the pictures above) and ignore the other two (shown in gray).

noise_interval = noise_interval[0]
noise_interval

  index    start      end  tags
      0  460.768  488.788  Noise 1
shape: (1, 2), time unit: sec.

Now let’s examine current:

current

Time (s)
-------------  --
0             0
5e-05           0
0001          0
00015         0
0002          0
00025         0
0003          0
...
420649999   0
420699999   0
420749999   0
420799999   0
420849999   0
420899999   0
420949999   0
dtype: float64, shape: (11348420,)

current is a Tsd (TimeSeriesData) object with 2 columns. Like all Tsd objects, the first column contains the time index and the second column contains the data; in this case, the current in Ampere (A).

Currently, current contains the entire ~900 second experiment but, as discussed above, we only want one of the “Noise 1” sweeps. Fortunately, pynapple makes it easy to grab out the relevant time points by making use of the noise_interval we defined above:

current = current.restrict(noise_interval)
# convert current from Ampere to pico-amperes, to match the above visualization
# and move the values to a more reasonable range.
current = current * 1e12
current

Time (s)
-------------  --
768         0
76805       0
7681        0
76815       0
7682        0
76825       0
7683        0
...
787649993   0
787699993   0
787749993   0
787799993   0
787849993   0
787899993   0
787949993   0
dtype: float64, shape: (560400,)

Notice that the timestamps have changed and our shape is much smaller.

Finally, let’s examine the spike times. spikes is a TsGroup, a dictionary-like object that holds multiple Ts (timeseries) objects with potentially different time indices:

spikes

  Index     rate  location      group
-------  -------  ----------  -------
      0  0.87805  v1                0

Typically, this is used to hold onto the spike times for a population of neurons. In this experiment, we only have recordings from a single neuron, so there’s only one row.

We can index into the TsGroup to see the timestamps for this neuron’s spikes:

spikes[0]

Similar to current, this object originally contains data from the entire experiment. To get only the data we need, we again use restrict(noise_interval):

spikes = spikes.restrict(noise_interval)
print(spikes)
spikes[0]

  Index     rate  location      group
-------  -------  ----------  -------
      0  1.42755  v1                0

Now, let’s visualize the data from this trial, replicating rows 1 and 3 from the Allen Brain Atlas figure at the beginning of this notebook:

fig, ax = plt.subplots(1, 1, figsize=(8, 2))
ax.plot(current, "grey")
ax.plot(spikes.to_tsd([-5]), "|", color="k", ms = 10)
ax.set_ylabel("Current (pA)")
ax.set_xlabel("Time (s)")

Text(0.5, 0, 'Time (s)')

../../_images/2a498c7cec3d0eea4f07518fdc216da66c7e42735705478fa71470d369bb4400.png

Basic analyses#

Before using the Generalized Linear Model, or any model, it’s worth taking some time to examine our data and think about what features are interesting and worth capturing. As we discussed in the background, the GLM is a model of the neuronal firing rate. However, in our experiments, we do not observe the firing rate, only the spikes! Moreover, neural responses are typically noisy—even in this highly controlled experiment where the same current was injected over multiple trials, the spike times were slightly different from trial-to-trial. No model can perfectly predict spike times on an individual trial, so how do we tell if our model is doing a good job?

Our objective function is the log-likelihood of the observed spikes given the predicted firing rate. That is, we’re trying to find the firing rate, as a function of time, for which the observed spikes are likely. Intuitively, this makes sense: the firing rate should be high where there are many spikes, and vice versa. However, it can be difficult to figure out if your model is doing a good job by squinting at the observed spikes and the predicted firing rates plotted together.

One common way to visualize a rough estimate of firing rate is to smooth the spikes by convolving them with a Gaussian filter.

Note

This is a heuristic for getting the firing rate, and shouldn’t be taken as the literal truth (to see why, pass a firing rate through a Poisson process to generate spikes and then smooth the output to approximate the generating firing rate). A model should not be expected to match this approximate firing rate exactly, but visualizing the two firing rates together can help you reason about which phenomena in your data the model is able to adequately capture, and which it is missing.

For more information, see section 1.2 of Theoretical Neuroscience, by Dayan and Abbott.

Pynapple can easily compute this approximate firing rate, and plotting this information will help us pull out some phenomena that we think are interesting and would like a model to capture.

First, we must convert from our spike times to binned spikes:

# bin size in seconds
bin_size = 0.001
# Get spikes for neuron 0
count = spikes[0].count(bin_size)
count

Time (s)
----------  --
7685     0
7695     0
7705     0
7715     0
7725     0
7735     0
7745     0
...
7815     0
7825     0
7835     0
7845     0
7855     0
7865     0
7875     0
dtype: int64, shape: (28020,)

Now, let’s convert the binned spikes into the firing rate, by smoothing them with a gaussian kernel. Pynapple again provides a convenience function for this:

# the inputs to this function are the standard deviation of the gaussian in seconds and
# the full width of the window, in standard deviations. So std=.05 and size_factor=20
# gives a total filter size of 0.05 sec * 20 = 1 sec.
firing_rate = count.smooth(std=0.05, size_factor=20)
# convert from spikes per bin to spikes per second (Hz)
firing_rate = firing_rate / bin_size

Note that firing_rate is a Tsd!

print(type(firing_rate))

<class 'pynapple.core.time_series.Tsd'>

Now that we’ve done all this preparation, let’s make a plot to more easily visualize the data.

Note

We’re hiding the details of the plotting function for the purposes of this tutorial, but you can find it in the source code if you are interested.

doc_plots.current_injection_plot(current, spikes, firing_rate);

../../_images/950670a9e21fe1901875b13fbca210925be64e5283668968feba1f064c522d6a.png

So now that we can view the details of our experiment a little more clearly, what do we see?

We have three intervals of increasing current, and the firing rate increases as the current does.
While the neuron is receiving the input, it does not fire continuously or at a steady rate; there appears to be some periodicity in the response. The neuron fires for a while, stops, and then starts again. There’s periodicity in the input as well, so this pattern in the response might be reflecting that.
There’s some decay in firing rate as the input remains on: there are three or four “bumps” of neuronal firing in the second and third intervals and they decrease in amplitude, with the first being the largest.

These give us some good phenomena to try and predict! But there’s something that’s not quite obvious from the above plot: what is the relationship between the input and the firing rate? As described in the first bullet point above, it looks to be monotonically increasing: as the current increases, so does the firing rate. But is that exactly true? What form is that relationship?

Pynapple can compute a tuning curve to help us answer this question, by binning our spikes based on the instantaneous input current and computing the firing rate within those bins:

Tuning curve in pynapple

compute_1d_tuning_curves : compute the firing rate as a function of a 1-dimensional feature.

tuning_curve = nap.compute_1d_tuning_curves(spikes, current, nb_bins=15)
tuning_curve

	0
4.637500	0.000000
13.912500	0.000000
23.187501	0.000000
32.462501	0.000000
41.737501	0.000000
51.012501	0.000000
60.287501	3.960592
69.562502	1.755310
78.837502	4.294610
88.112502	10.993325
97.387502	12.501116
106.662502	10.275380
115.937503	33.476805
125.212503	61.585835
134.487503	24.067389

tuning_curve is a pandas DataFrame where each column is a neuron (one neuron in this case) and each row is a bin over the feature (here, the input current). We can easily plot the tuning curve of the neuron:

doc_plots.tuning_curve_plot(tuning_curve);

../../_images/8abe4c6d4e15ce47b105e56889c5b09035b8bd12a4aab1fa5489413dc2639e36.png

We can see that, while the firing rate mostly increases with the current, it’s definitely not a linear relationship, and it might start decreasing as the current gets too large.

So this gives us three interesting phenomena we’d like our model to help explain:

the tuning curve between the firing rate and the current.
the firing rate’s periodicity.
the gradual reduction in firing rate while the current remains on.

NeMoS#

Preparing data#

Now that we understand our data, we’re almost ready to put the model together. Before we construct it, however, we need to get the data into the right format.

NeMoS requires that the predictors and spike counts it operates on have the following properties:

predictors and spike counts must have the same number of time points.
predictors must be two-dimensional, with shape (n_time_bins, n_features). In this example, we have a single feature (the injected current).
spike counts must be one-dimensional, with shape (n_time_bins, ). As discussed above, n_time_bins must be the same for both the predictors and spike counts.
predictors and spike counts must be jax.numpy arrays, numpy arrays or pynapple TsdFrame/Tsd.

What is jax?

jax is a Google-supported python library for automatic differentiation. It has all sorts of neat features, but the most relevant of which for NeMoS is its GPU-compatibility and just-in-time compilation (both of which make code faster with little overhead!), as well as the collection of optimizers present in jaxopt.

First, we require that our predictors and our spike counts have the same number of time bins. We can achieve this by down-sampling our current to the spike counts to the proper resolution using the bin_average method from pynapple:

binned_current = current.bin_average(bin_size)

print(f"current shape: {binned_current.shape}")
# rate is in Hz, convert to KHz
print(f"current sampling rate: {binned_current.rate/1000.:.02f} KHz")

print(f"\ncount shape: {count.shape}")
print(f"count sampling rate: {count.rate/1000:.02f} KHz")

current shape: (28020,)
current sampling rate: 1.00 KHz

count shape: (28020,)
count sampling rate: 1.00 KHz

Secondly, we have to reshape our variables so that they are the proper shape:

predictors: (n_time_bins, n_features)
count: (n_time_bins, )

Because we only have a single predictor feature, we’ll use np.expand_dims to ensure it is a 2d array.

predictor = np.expand_dims(binned_current, 1)

# check that the dimensionality matches NeMoS expectation
print(f"predictor shape: {predictor.shape}")
print(f"count shape: {count.shape}")

predictor shape: (28020, 1)
count shape: (28020,)

What if I have more than one neuron?

In this example, we’re only fitting data for a single neuron, but you might wonder how the data should be shaped if you have more than one neuron.

We will discuss this in more detail in the following tutorial, but briefly: NeMoS has a separate PopulationGLM object for fitting a population of neurons. It operates very similarly to the GLM object we use here: it still expects a 2d input, with neurons concatenated along the second dimension. (NeMoS provides some helper functions for splitting the design matrix and model parameter arrays to make them more interpretable.)

Note that fitting each neuron separately is equivalent to fitting the entire population at once. Fitting them separately can make your life easier by e.g., allowing you to parallelize more easily.

Fitting the model#

Now we’re ready to fit our model!

First, we need to define our GLM model object. We intend for users to interact with our models like scikit-learn estimators. In a nutshell, a model instance is initialized with hyperparameters that specify optimization and model details, and then the user calls the .fit() function to fit the model to data. We will walk you through the process below by example, but if you are interested in reading more details see the Getting Started with scikit-learn webpage.

To initialize our model, we need to specify the solver, the regularizer, and the observation model. All of these are optional.

solver_name: this string specifies the solver algorithm. The default behavior depends on the regularizer, as each regularization scheme is only compatible with a subset of possible solvers. View the GLM docstring for more details.

Warning

With a convex problem like the GLM, in theory it does not matter which solver algorithm you use. In practice, due to numerical issues, it generally does. Thus, it’s worth trying a couple to see how their solutions compare.

regularizer: this string or object specifies the regularization scheme. Regularization modifies the objective function to reflect your prior beliefs about the parameters, such as sparsity. Regularization becomes more important as the number of input features, and thus model parameters, grows. NeMoS’s solvers can be found within the nemos.regularizer module. If you pass a string matching the name of one of our solvers, we initialize the solver with the default arguments. If you need more control, you will need to initialize and pass the object yourself.
observation_model: this object links the firing rate and the observed data (in this case spikes), describing the distribution of neural activity (and thus changing the log-likelihood). For spiking data, we use the Poisson observation model, but we discuss other options for continuous data in our documentation.

For this example, we’ll use an un-regularized LBFGS solver. We’ll discuss regularization in a later tutorial.

Why LBFGS?

LBFGS is a quasi-Netwon method, that is, it uses the first derivative (the gradient) and approximates the second derivative (the Hessian) in order to solve the problem. This means that LBFGS tends to find a solution faster and is often less sensitive to step-size. Try other solvers to see how they behave!

# Initialize the model, specifying the solver. Since unregularized is the 
# default choice, we don't need to specify it.
model = nmo.glm.GLM(solver_name="LBFGS")

Now that we’ve initialized our model with the optimization parameters, we can fit our data! In the previous section, we prepared our model matrix (predictor) and target data (count), so to fit the model we just need to pass them to the model:

model.fit(predictor, count)

<nemos.glm.GLM at 0x7f6d68715f10>

Now that we’ve fit our data, we can retrieve the resulting parameters. Similar to scikit-learn, these are stored as the coef_ and intercept_ attributes:

print(f"firing_rate(t) = exp({model.coef_} * current(t) + {model.intercept_})")

firing_rate(t) = exp([0.05331734] * current(t) + [-9.762487])

Note that model.coef_ has shape (n_features, ), while model.intercept_ has shape (n_neurons) (for the GLM object, this will always be 1, but it will differ for the PopulationGLM object!):

print(f"coef_ shape: {model.coef_.shape}")
print(f"intercept_ shape: {model.intercept_.shape}")

coef_ shape: (1,)
intercept_ shape: (1,)

It’s nice to get the parameters above, but we can’t tell how well our model is doing by looking at them. So how should we evaluate our model?

First, we can use the model to predict the firing rates and compare that to the smoothed spike train. By calling predict() we can get the model’s predicted firing rate for this data. Note that this is just the output of the model’s linear-nonlinear step, as described earlier!

predicted_fr = model.predict(predictor)
# convert units from spikes/bin to spikes/sec
predicted_fr = predicted_fr / bin_size


# and let's smooth the firing rate the same way that we smoothed the firing rate
smooth_predicted_fr = predicted_fr.smooth(0.05, size_factor=20)

# and plot!
fig = doc_plots.current_injection_plot(current, spikes, firing_rate,
                                 # plot the predicted firing rate that has
                                 # been smoothed the same way as the
                                 # smoothed spike train
                                 predicted_firing_rate=smooth_predicted_fr)

/home/agent/workspace/rorse_ccn-software-jan-2025_main/lib/python3.11/site-packages/pynapple/core/utils.py:196: UserWarning: Converting 'd' to numpy.array. The provided array was of type 'ArrayImpl'.
  warnings.warn(

../../_images/05adc68dd819bc9a4cca672be33e38b5f05de1d3be454fec54975e36f94734f9.png

What do we see above? Note that the y-axes in the final row are different for each subplot!

Predicted firing rate increases as injected current goes up — Success! 🎉
The amplitude of the predicted firing rate only matches the observed amplitude in the third interval: it’s too high in the first and too low in the second — Failure! ❌
Our predicted firing rate has the periodicity we see in the smoothed spike train — Success! 🎉
The predicted firing rate does not decay as the input remains on: the amplitudes are identical for each of the bumps within a given interval — Failure! ❌

The failure described in the second point may seem particularly confusing — approximate amplitude feels like it should be very easy to capture, so what’s going on?

To get a better sense, let’s look at the mean firing rate over the whole period:

# compare observed mean firing rate with the model predicted one
print(f"Observed mean firing rate: {np.mean(count) / bin_size} Hz")
print(f"Predicted mean firing rate: {np.mean(predicted_fr)} Hz")

Observed mean firing rate: 1.4275517487508922 Hz
Predicted mean firing rate: 1.4306069612503052 Hz

We matched the average pretty well! So we’ve matched the average and the range of inputs from the third interval reasonably well, but overshot at low inputs and undershot in the middle.

We can see this more directly by computing the tuning curve for our predicted firing rate and comparing that against our smoothed spike train from the beginning of this notebook. Pynapple can help us again with this:

# pynapple expects the input to this function to be 2d,
# so let's add a singleton dimension
tuning_curve_model = nap.compute_1d_tuning_curves_continuous(predicted_fr[:, np.newaxis], current, 15)
fig = doc_plots.tuning_curve_plot(tuning_curve)
fig.axes[0].plot(tuning_curve_model, color="tomato", label="glm")
fig.axes[0].legend()

<matplotlib.legend.Legend at 0x7f6d6046c590>

../../_images/f73ddd2f027ab9cd8b16c825b0d0533f6d1731c61a1766a9077841a113dea005.png

In addition to making that mismatch discussed earlier a little more obvious, this tuning curve comparison also highlights that this model thinks the firing rate will continue to grow as the injected current increases, which is not reflected in the data (or in our knowledge of how neurons work!).

Viewing this plot also makes it clear that the model’s tuning curve is approximately exponential. We already knew that! That’s what it means to be a LNP model of a single input. But it’s nice to see it made explicit.

Finishing up#

There are a handful of other operations you might like to do with the GLM. First, you might be wondering how to simulate spikes — the GLM is a LNP model, but the firing rate is just the output of LN, its first two steps. The firing rate is just the mean of a Poisson process, so we can pass it to jax.random.poisson:

spikes = jax.random.poisson(jax.random.PRNGKey(123), predicted_fr.values)

Note that this is not actually that informative and, in general, it is recommended that you focus on firing rates when interpreting your model.

Also, while including spike history is often helpful, it can sometimes make simulating spikes like this unstable: if your GLM includes auto-regressive inputs (e.g., neurons are connected to themselves or each other), simulations can sometimes can behave poorly because of runaway excitation \(^{[1, 2]}\).

Finally, you may want a number with which to evaluate your model’s performance. As discussed earlier, the model optimizes log-likelihood to find the best-fitting weights, and we can calculate this number using its score method:

log_likelihood = model.score(predictor, count, score_type="log-likelihood")
print(f"log-likelihood: {log_likelihood}")

log-likelihood: -0.007939910516142845

This log-likelihood is un-normalized and thus doesn’t mean that much by itself, other than “higher=better”. When comparing alternative GLMs fit on the same dataset, whether that’s models using different regularizers and solvers or those using different predictors, comparing log-likelihoods is a reasonable thing to do.

Note

Under the hood, NeMoS is minimizing the negative log-likelihood, as is typical in many optimization contexts. score returns the real log-likelihood, however, and thus higher is better.

Because it’s un-normalized, however, the log-likelihood should not be compared across datasets (because e.g., it won’t account for difference in noise levels). We provide the ability to compute the pseudo-\(R^2\) for this purpose:

model.score(predictor, count, score_type='pseudo-r2-Cohen')

Array(0.30376726, dtype=float32)

Further Exercises#

Despite the simplicity of this dataset, there is still more that we can do here. The following sections provide some possible exercises to try yourself!

Other stimulation protocols#

We’ve only fit the model to a single stimulation protocol, but our dataset contains many more! How does the model perform on “Ramp”? On “Noise 2”? Based on the example code above, write new code that fits the model on some other stimulation protocol and evaluate its performance. Which stimulation does it perform best on? Which is the worst?

Train and test sets#

In this example, we’ve used been fitting and evaluating our model on the same data set. That’s generally a bad idea! Try splitting the data in to train and test sets, fitting the model to one portion of the data and evaluating on another portion. You could split this stimulation protocol into train and test sets or use different protocols to train and test on.

Model extensions#

Even our extended model did not do a good job capturing the onset transience seen in the data, and we could probably improve the match between the amplitudes of the predicted firing rate and smoothed spike train. How would we do that?

We could try adding the following inputs to the model, alone or together:

Spiking history: we know neurons have a refactory period (they are unable to spike a second time immediately after spiking), so maybe making the model aware of whether the neuron spiked recently could help better capture the onset transience.
Current history: the model’s input here is the current at the same moment as the spike, but that information is probably integrated over time. Maybe we can add additional time points.
More complicated tuning curve: as we saw with the tuning curve plots, this model model implicitly assumes that the relationship between current and firing rate is exponential, which is close but not quite right. Maybe we can improve that.

The proper way to add these in nemos makes use of Basis objects, which we’ll explore more in later tutorials. You can try the adding the spiking or current history inputs without them (though the model won’t do as well), or return to this example after you’ve learned about Basis objects and how to use them.

Citation#

The data used in this tutorial is from the Allen Brain Map, with the following citation:

Contributors: Agata Budzillo, Bosiljka Tasic, Brian R. Lee, Fahimeh Baftizadeh, Gabe Murphy, Hongkui Zeng, Jim Berg, Nathan Gouwens, Rachel Dalley, Staci A. Sorensen, Tim Jarsky, Uygar Sümbül Zizhen Yao

Dataset: Allen Institute for Brain Science (2020). Allen Cell Types Database – Mouse Patch-seq [dataset]. Available from brain-map.org/explore/classes/multimodal-characterization.

Primary publication: Gouwens, N.W., Sorensen, S.A., et al. (2020). Integrated morphoelectric and transcriptomic classification of cortical GABAergic cells. Cell, 183(4), 935-953.E19. https://doi.org/10.1016/j.cell.2020.09.057

Patch-seq protocol: Lee, B. R., Budzillo, A., et al. (2021). Scaled, high fidelity electrophysiological, morphological, and transcriptomic cell characterization. eLife, 2021;10:e65482. https://doi.org/10.7554/eLife.65482

Mouse VISp L2/3 glutamatergic neurons: Berg, J., Sorensen, S. A., Miller, J., Ting, J., et al. (2021) Human neocortical expansion involves glutamatergic neuron diversification. Nature, 598(7879):151-158. doi: 10.1038/s41586-021-03813-8

References#

[1] Arribas, Diego, Yuan Zhao, and Il Memming Park. “Rescuing neural spike train models from bad MLE.” Advances in Neural Information Processing Systems 33 (2020): 2293-2303.

[2] Hocker, David, and Memming Park. “Multistep inference for generalized linear spiking models curbs runaway excitation.” International IEEE/EMBS Conference on Neural Engineering, May 2017.

Fit injected current

Contents

Fit injected current#

Learning objectives#

Data Streaming#

Pynapple#

Data structures and preparation#

Basic analyses#

NeMoS#

Preparing data#

Fitting the model#

Finishing up#

Further Exercises#

Other stimulation protocols#

Train and test sets#

Model extensions#

Citation#

References#