In an article published in the journal PLOS Computational Biology, researchers applied metamodeling techniques to approximate the simulations of neuronal networks. They used two metamodeling techniques, deep Gaussian process regression (DGPR) and masked autoregressive flow (MAF), to estimate the power spectra of population spiking activities and local field potentials (LFPs) generated by a two-population network of point-neurons. Further, the metamodels helped infer posterior distributions over network parameters given observed simulation outputs and compare the information content of the two signals.
Study: Metamodeling Neuronal Networks: Power Spectra Estimation and Parameter Inference. Image credit: Kitsana1980/Shutterstock
Background
Neuronal network simulators are computational tools that can simulate the dynamics of networks of neurons based on biophysical principles. These simulators can produce various outputs, such as membrane potentials, spike times, firing rates, or extracellular potentials, depending on the level of detail and complexity of the models. However, running these simulators can be computationally demanding, especially for large-scale networks or high-dimensional parameter spaces.
Metamodels are statistical models that can approximate the outputs of the simulators given the inputs, such as model parameters or external stimuli. They can be trained on a set of inputs and outputs generated by the simulators and then used to make predictions or inferences on new inputs or outputs. They can also provide uncertainty estimates or distributions over the outputs, which can be useful for assessing the reliability or variability of the simulations. These models can provide faster and simpler predictions, interpretations, and parameter estimation compared to the original models.
Spiking network models are mechanistic models of neuronal systems that simulate the dynamics of individual neurons and their interactions through synapses. These models can produce rich and diverse behaviors, but they are also computationally expensive and have many parameters that need to be fitted to experimental data. LFP is a low-frequency signal that reflects the synaptic activity of neuronal populations and can be measured by extracellular electrodes.
About the Research
This paper aims to apply metamodels to a two-population recurrent spiking network model, known as the Brunel network, of point neurons. The authors use two different metamodeling techniques, DGPR and MAF, to determine the power spectra of two signals, the population spiking and the LFP. The population spiking activities are the sum of all spike trains in each population, and the LFP is the low-frequency part of the extracellular potentials, which reflects the synaptic inputs and dendritic processing of the neurons. The population spiking activities represent the outgoing signals of the network, while the LFPs represent the incoming signals processed by the network.
The authors train the metamodels on a set of simulations with randomly sampled parameters and then use the metamodels to make predictions on a test set of simulations. They also use the metamodels to determine the posterior probability distributions of parameters based on observed simulation outputs and compare the accuracy and efficiency of the metamodels.
Research Findings
The paper finds that the metamodels are capable of precisely modeling the power spectra in the asynchronous irregular regime, which is the regime where most of the simulations are. The DGPR metamodel gives a more precise estimation of the simulator compared to the MAF, both in terms of the forward predictions and the posterior distributions. Additionally, the DGPR metamodel produced narrower distributions over the simulator output compared to the MAF model, indicating that the DGPR metamodel captures the variability of the simulator better.
With the help of the model, the researchers measured the posterior probability distributions over given parameters and observed outputs of the simulator separately for both the population spiking activities and LFP. These distributions accurately recognized parameter combinations that give similar model outputs.
The present research can be applied to different types of neuronal network models, such as rate-based models, point-neurons with different synaptic models, or multi-compartment models with full morphology. It can be used to explore the behavioral repertoire of neuronal network models under different input conditions and to identify the regions of the parameter space that produce specific behaviors or match experimental data. Additionally, It can help investigate the effects of different network parameters on the power spectra of the signals, and how they can be inferred from the signals.
Conclusions
To sum up, the study findings show that metamodeling is a powerful technique for modeling and analyzing neuronal network simulations and that DGPR and MAF are two promising methods for this purpose. They also illustrate that the power spectra of the population spiking activities and LFPs carry different information about the network parameters. Moreover, observing both signals can provide more constraints on the parameter estimation.
The authors suggest that future work could extend the metamodeling approach to other types of network models and signals, and explore the effects of different input regimes and noise sources on the network dynamics and the metamodels.
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