How good are neuron models?

For several decades now, physicists, mathematicians, neurobiologists and other specialists have been joining efforts to build realistic mathematical models of neurons. A typical model consists on one or several differential equations that are able to predict the evolution of the membrane potential of a neuron for a given input. When introduced in a computer, these models may be used to have an idea about how real neurons would behave in realistic conditions, and this may help in the design of experiments or other protocols. It is, by no means, a barren field: Alan Lloyd Hodgkin and Andrew Huxley developed one of the very first realistic mathematical models of neurons in the early 50s to better understand the generation and propagation of action potentials, or spikes, on the squid giant axon. Not only the model helped them to gain understanding on this system, but they also ended up winning the Nobel Prize in Medicine or Physiology about ten years later for their work in this field ¹.

This so-called Hodgkin-Huxley neuron model is considered one of the main paradigms of neuron models in the field of computational neuroscience, but many other models have appeared since then. Some of them follow the spirit of this first model and consider the effect of different ionic contributions to the membrane dynamics in high levels of detail, for instance. Also, many of these models target to describe particular types of neurons, and they even model in detail the different branching parts of such neurons, reaching a prominent level of detail. Other researchers, however, focused on strategies to simplify these highly detailed models to arrive at some kind of simplified neuron model which could, under reasonable circumstances, mimic the behavior of more realistic models or even real neurons. The great advantage of such models is that their simplicity allows the researchers to understand better the effects of any slight modification in the model (it is usually easier to understand one equation that tens of them coupled), and even leading to analytical solutions of the model equations which are extremely useful for prediction purposes.

But having an enormous zoo of different models may be a little messy sometimes, as inexperienced researchers may have a hard time trying to decide for one. Even worse, we may decide to employ a model that, in the end, is not able to correctly predict the behavior of the real neuron, or it could be unable to give us meaningful information about it. So, considering a particular type of neuron in the brain, which model should we use to predict its behavior?

With this idea in mind, researchers from the EPFL in Lausanne, Switzerland, started and promoted an international competition that allowed a quantitative comparison between the performance of different models ². The competition was open for any researcher in the world, and has had several annual editions since its inception. The main goal of this competition was to find which model performs better at predicting the behavior of real neurons. To this end, the organizers arranged different categories for the competition, and for each one of them, they measured the response of a real neuron to a given irregular input. Each recording, consisting on the temporal evolution of the membrane potential of the neuron, was divided in two parts: a first part (for the model fitting) and a second part (for the prediction). In the fitting part, the participants had access to both the input and the response of the real neuron to this input, and this set of data was used to properly calibrate the model to the particular neuron measured. Once the model had been calibrated and the model parameters determined, the participants used it to predict the response of the neuron in the second part, while having only the input that was injected to the real neuron for this part (and, of course, ignoring how the real neuron behaved in this part). In particular, the goal was to predict, using the neuron model, each and every spike that the real neuron generated as a response for the input in the prediction part. A total of 33 submission were received for the 2009 competition.

For the first category, in which the input current was injected to the real neuron directly in the soma, the winning submission was able to predict the 81.6 % of the spikes emitted by the real neuron. Interestingly, such a submission did not use a very complicated neuron model: it used a leaky integrate-and-fire neuron model with a moving threshold, one of the simplest models available in the literature – the so-called threshold models. In another category, the experimental recording concerned the activity of a neuron responding to two simultaneous input currents, one in the soma and one in the apical dendrite of the real neuron. For this situation, a two-compartment version of a threshold model, similar to the one considered above, was the winning submission.

Even more striking is the fact that, in the final category, which considered in vivo recordings from a previously published study (with the input being a concrete visual stimulus to the retina), the winning model was able to correctly predict about 90.5 % of the spikes of the real neuron. The model used for this prediction: a simple threshold-type model.

The competition brought very interesting results to the discussion table. First, it was shown that very basic neuron models, belonging to the family of threshold models, where able to predict, grossly, between 80 and 90 % of the spikes emitted by the real neuron. And, surprisingly, this was true both for in vitro and in vivo conditions. On the other hand, the performance of highly detailed models of the Hodgkin-Huxley type is not known, since not a single prediction based on this type of models was submitted. This may have something to do with the difficulty of properly fitting the parameters of these models (some of them having several tens of different parameters). In the future, when more automated techniques to fit this type of models are developed, we would be able to use them as well. Until then, we will be waiting for the rematch.