Approximating Nonlinear Functions With Latent Boundaries in Low-Rank Excitatory-Inhibitory Spiking Networks.

Deep feedforward and recurrent neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation.

Training deep neural density estimators to identify mechanistic models of neural dynamics.

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-trained using model simulations-to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics.

Computational neuroscientists use mathematical models built on observational data to investigate what's happening in the brain. Models can simulate brain activity from the behavior of a single neuron right through to the patterns of collective activity in whole neural networks. Collecting the experimental data is the first step, then the challenge becomes deciding which computer models best represent the data and can explain the underlying causes of how the brain behaves. Researchers usually find the right model for their data through trial and error. This involves tweaking a model's parameters until the model can reproduce the data of interest. But this process is laborious and not systematic. Moreover, with the ever-increasing complexity of both data and computer models in neuroscience, the old-school approach of building models is starting to show its limitations. Now, Gonçalves, Lueckmann, Deistler et al. have designed an algorithm that makes it easier for researchers to fit mathematical models to experimental data. First, the algorithm trains an artificial neural network to predict which models are compatible with simulated data. After initial training, the method can rapidly be applied to either raw experimental data or selected data features. The algorithm then returns the models that generate the best match. This newly developed machine learning tool was able to automatically identify models which can replicate the observed data from a diverse set of neuroscience problems. Importantly, further experiments showed that this new approach can be scaled up to complex mechanisms, such as how a neural network in crabs maintains its rhythm of activity. This tool could be applied to a wide range of computational investigations in neuroscience and other fields of biology, which may help bridge the gap between 'data-driven' and 'theory-driven' approaches.

Mapping the function of neuronal ion channels in model and experiment.

Ion channel models are the building blocks of computational neuron models. Their biological fidelity is therefore crucial for the interpretation of simulations. However, the number of published models, and the lack of standardization, make the comparison of ion channel models with one another and with experimental data difficult. Here, we present a framework for the automated large-scale classification of ion channel models. Using annotated metadata and responses to a set of voltage-clamp protocols, we assigned 2378 models of voltage- and calcium-gated ion channels coded in NEURON to 211 clusters. The IonChannelGenealogy (ICGenealogy) web interface provides an interactive resource for the categorization of new and existing models and experimental recordings. It enables quantitative comparisons of simulated and/or measured ion channel kinetics, and facilitates field-wide standardization of experimentally-constrained modeling.