High-level languages (Matlab, Python) are popular in neuroscience because they are flexible and accelerate development. However, for simulating spiking neural networks, the cost of interpretation is a bottleneck. We describe a set of algorithms to simulate large spiking neural networks efficiently with high-level languages using vector-based operations. These algorithms constitute the core of Brian, a spiking neural network simulator written in the Python language. Vectorized simulation makes it possible to combine the flexibility of high-level languages with the computational efficiency usually associated with compiled languages.

Neuronal spike trains display correlations at diverse timescales throughout the nervous system. The functional significance of these correlations is largely unknown, and computational investigations can help us understand their role. In order to generate correlated spike trains with given statistics, several case-specific methods have been described in the litterature. This letter presents two general methods to generate sets of spike trains with given firing rates and pairwise correlation functions, along with efficient simulation algorithms.

Neural networks can be simulated exactly using event-driven strategies, in which the algorithm advances directly from one spike to the next spike. It applies to neuron models for which we have (1) an explicit expression for the evolution of the state variables between spikes and (2) an explicit test on the state variables that predicts whether and when a spike will be emitted. In a previous work, we proposed a method that allows exact simulation of an integrate-and-fire model with exponential conductances, with the constraint of a single synaptic time constant. In this note, we propose a method, based on polynomial root finding, that applies to integrate-and-fire models with exponential currents, with possibly many different synaptic time constants. Models can include biexponential synaptic currents and spike-triggered adaptation currents.

Computational neuroscience relies heavily on the simulation of large networks of neuron models. There are essentially two simulation strategies: (1) using an approximation method (e.g., Runge-Kutta) with spike times binned to the time step and (2) calculating spike times exactly in an event-driven fashion. In large networks, the computation time of the best algorithm for either strategy scales linearly with the number of synapses, but each strategy has its own assets and constraints: approximation methods can be applied to any model but are inexact; exact simulation avoids numerical artifacts but is limited to simple models. Previous work has focused on improving the accuracy of approximation methods. In this article, we extend the range of models that can be simulated exactly to a more realistic model: an integrate-and-fire model with exponential synaptic conductances.

The responses of neurons to time-varying injected currents are reproducible on a trial-by-trial basis in vitro, but when a constant current is injected, small variances in interspike intervals across trials add up, eventually leading to a high variance in spike timing. It is unclear whether this difference is due to the nature of the input currents or the intrinsic properties of the neurons. Neuron responses can fail to be reproducible in two ways: dynamical noise can accumulate over time and lead to a desynchronization over trials, or several stable responses can exist, depending on the initial condition. Here we show, through simulations and theoretical considerations, that for a general class of spiking neuron models, which includes, in particular, the leaky integrate-and-fire model as well as nonlinear spiking models, aperiodic currents, contrary to periodic currents, induce reproducible responses, which are stable under noise, change in initial conditions and deterministic perturbations of the input. We provide a theoretical explanation for aperiodic currents that cross the threshold.