Michelle Rudolph

Simulation of networks of spiking neurons: A review of tools and strategies

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin–Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.

SYNAPTIC BACKGROUND NOISE CONTROLS THE INPUT/OUTPUT CHARACTERISTICS OF SINGLE CELLS IN AN IN VITRO MODEL OF IN VIVO ACTIVITY

In vivo, in vitro and computational studies were used to investigate the impact of the synaptic background activity observed in neocortical neurons in vivo. We simulated background activity in vitro using two stochastic Ornstein-Uhlenbeck processes describing glutamatergic and GABAergic synaptic conductances, which were injected into a cell in real time using the dynamic clamp technique. With parameters chosen to mimic in vivo conditions, layer 5 rat prefrontal cortex cells recorded in vitro were depolarized by about 15 mV, their membrane fluctuated with a S.D. of about 4 mV, their input resistances decreased five-fold, their spontaneous firing had a high coefficient of variation and an average firing rate of about 5-10 Hz. Brief changes in the variance of the alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) synaptic conductance fluctuations induced time-locked spiking without significantly changing the average membrane potential of the cell. These transients mimicked increases in the correlation of excitatory inputs. Background activity was highly effective in modulating the firing-rate/current curve of the cell: the variance of the simulated gamma-aminobutyric acid (GABA) and AMPA conductances individually set the input/output gain, the mean excitatory and inhibitory conductances set the working point, and the mean inhibitory conductance controlled the input resistance. An average ratio of inhibitory to excitatory mean conductances close to 4 was optimal in generating membrane potential fluctuations with high coefficients of variation. We conclude that background synaptic activity can dynamically modulate the input/output properties of individual neocortical neurons in vivo.

Inhibition Determines Membrane Potential Dynamics and Controls Action Potential Generation in Awake and Sleeping Cat Cortex

Intracellular recordings of cortical neurons in awake cat and monkey show a depolarized state, sustained firing, and intense subthreshold synaptic activity. It is not known what conductance dynamics underlie such activity and how neurons process information in such highly stochastic states. Here, we combine intracellular recordings in awake and naturally sleeping cats with computational models to investigate subthreshold dynamics of conductances and how conductance dynamics determine spiking activity. We show that during both wakefulness and the “up-states” of natural slow-wave sleep, membrane-potential activity stems from a diversity of combinations of excitatory and inhibitory synaptic conductances, with dominant inhibition in most of the cases. Inhibition also provides the largest contribution to membrane potential fluctuations. Computational models predict that in such inhibition-dominant states, spikes are preferentially evoked by a drop of inhibitory conductance, and that its signature is a transient drop of membrane conductance before the spike. This pattern of conductance change is indeed observed in estimates of spike-triggered averages of synaptic conductances during wakefulness and slow-wave sleep up states. These results show that activated states are defined by diverse combinations of excitatory and inhibitory conductances with pronounced inhibition, and that the dynamics of inhibition is particularly effective on spiking, suggesting an important role for inhibitory processes in both conscious and unconscious cortical states.

Analytical Integrate-and-Fire Neuron Models with Conductance-Based Dynamics for Event-Driven Simulation Strategies

Event-driven simulation strategies were proposed recently to simulate integrate-and-fire (IF) type neuronal models. These strategies can lead to computationally efficient algorithms for simulating large-scale networks of neurons; most important, such approaches are more precise than traditional clock-driven numerical integration approaches because the timing of spikes is treated exactly. The drawback of such event-driven methods is that in order to be efficient, the membrane equations must be solvable analytically, or at least provide simple analytic approximations for the state variables describing the system. This requirement prevents, in general, the use of conductance-based synaptic interactions within the framework of event-driven simulations and, thus, the investigation of network paradigms where synaptic conductances are important. We propose here a number of extensions of the classical leaky IF neuron model involving approximations of the membrane equation with conductancebased synaptic current, which lead to simple analytic expressions for the membrane state, and therefore can be used in the event-driven framework. These conductance-based IF (gIF) models are compared to commonly used models, such as the leaky IF model or biophysical models in which conductances are explicitly integrated. All models are compared with respect to various spiking response properties in the presence of synaptic activity, such as the spontaneous discharge statistics, the temporal precision in resolving synaptic inputs, and gain modulation under in vivolike synaptic bombardment. Being based on the passive membrane equation with fixed-threshold spike generation, the proposed gIF models are situated in between leaky IF and biophysical models but are much closer to the latter with respect to their dynamic behavior and response characteristics, while still being nearly as computationally efficient as simple IF neuron models. gIF models should therefore provide a useful tool for efficient and precise simulation of large-scale neuronal networks with realistic, conductance-based synaptic interactions.

Frequency-selectivity of a thalamocortical relay neuron during parkinson's disease and deep brain stimulation: A computational study

In this computational study, we investigated (i) the functional importance of correlated basal ganglia (BG) activity associated with Parkinson’s disease (PD) motor symptoms by analysing the effects of globus pallidus internum (GPi) bursting frequency and synchrony on a thalamocortical (TC) relay neuron, which received GABAergic projections from this nucleus; (ii) the effects of subthalamic nucleus (STN) deep brain stimulation (DBS) on the response of the TC relay neuron to synchronized GPi oscillations; and (iii) the functional basis of the inverse relationship that has been reported between DBS frequency and stimulus amplitude, required to alleviate PD motor symptoms [A. L. Benabid et al. (1991)Lancet, 337, 403–406]. The TC relay neuron selectively responded to and relayed synchronized GPi inputs bursting at a frequency located in the range 2–25 Hz. Input selectivity of the TC relay neuron is dictated by low‐threshold calcium current dynamics and passive membrane properties of the neuron. STN‐DBS prevented the TC relay neuron from relaying synchronized GPi oscillations to cortex. Our model indicates that DBS alters BG output and input selectivity of the TC relay neuron, providing an explanation for the clinically observed inverse relationship between DBS frequency and stimulus amplitude.

How much can we trust neural simulation strategies

Despite a steady improvement of computational hardware, results of numerical simulation are still tightly bound to the simulation tool and strategy used, and may substantially vary across available simulation tools or for different settings within the same simulator. Clock-driven simulation strategies proved efficient for large and highly active networks but are outperformed with respect to precision by the recently introduced event-driven strategies. Focusing on most commonly used clock-driven and event-driven approaches, in this paper we evaluate to which extent the temporal precision of spiking events impacts on neuronal dynamics of single as well as small networks of IF neurons with plastic synapses. We find that the used strategy can severely alter simulated neural dynamics and, therefore, turns out to be crucial for the interpretation of the result of numerical simulations. Drastic differences were observed in models with spike timing dependent plasticity, arguing that the speed of neuronal simulations should not be the sole criteria for evaluation of the efficiency of simulation tools, but must complement an evaluation of their exactness, possibly in disfavour of their speed.

A non-parametric electrode model for intracellular recording

We present a new way to model the response of an electrode to an injected current. The electrode is represented by an unknown complex linear circuit, characterized by a kernel which we determine by injecting a noisy current. We show both in simulations and experiments that, when applied to a full recording setup (including acquisition board and amplifier), the method captures not only the characteristics of the electrode, but also those of all the devices between the computer and the tip of the electrode, including filters and the capacitance neutralization circuit on the amplifier. Simulations show that the method allows correct predictions of the response of complex electrode models. Finally, we successfully apply the technique to challenging intracellular recording situations in which the voltage across the electrode during injection needs to be subtracted from the recording, in particular conductance injection with the dynamic clamp protocol. We show in numerical simulations and confirm with experiments that the method performs well in cases when both bridge recording and recording in discontinuous mode (DCC) exhibit artefacts. (This work was supported by: CNRS, INRIA, European Commission (FACETS, FP6-2004-IST-FET), Action Concertee Incitative (NIC0005).)

On the use of analytical expressions for the voltage distribution to analyze intracellular recordings

Different analytical expressions for the membrane potential distribution of membranes subject to synaptic noise have been proposed and can be very helpful in analyzing experimental data. However, all of these expressions are either approximations or limit cases, and it is not clear how they compare and which expression should be used in a given situation. In this note, we provide a comparison of the different approximations available, with an aim of delineating which expression is most suitable for analyzing experimental data.

Event-based simulation strategy for conductance-based synaptic interactions and plasticity

The immense computational and adaptive power of the cerebral cortex emerges from the collective dynamics of large populations of interacting neurons. Thus, for theoretical investigations, optimal strategies for modeling biophysically faithful neuronal dynamics are required. Here, we propose an extension of the classical leaky integrate-and-fire neuronal model, the gIF model. It incorporates various aspects of high-conductance state dynamics typically seen in cortical neurons in vivo, as well as activity-dependent modulation of synaptic weights. The analytic description of the resulting neuronal models allows their use together with the event-driven simulation strategy. The latter provides an efficient tool for exact simulations of large-scale neuronal networks. orks.

Convergence in an Adaptive Neural Network: The Influence of Noise Inputs Correlation

This paper presents a study of convergence modalities in a small adaptive network of conductance-based neurons, receiving input patterns with different degrees correlation . The models for the neurons, synapses and plasticity rules (STDP) have a common biophysics basis. The neural network is simulated using a mixed analog-digital platform, which performs real-time simulations. We describe the study context, and the models for the neurons and for the adaptation functions. Then we present the simulation platform, including analog integrated circuits to simulate the neurons and a real-time software to simulate the plasticity. We also detail the analysis tools used to evaluate the final state of the network by the way of its post-adaptation synaptic weights. Finally, we present experimental results, with a systematic exploration of the network convergence when varying the input correlation, the initial weights and the distribution of hardware neurons to simulate the biological variability.