Linking rate based and spiking models: A Quest towards biologically relevant neural systems

The brain is made of billions of neurons connected together to form networks. These networks give rise to various activities reflected in a range of behaviors. The branches of neuroscience have accomplished tremendous feats to explain these behaviors and shed light on how the brain works. However, up until now, neuroscience has been very descriptive. This is unfortunately not enough, and understanding the brain demands more. A multidisciplinary approach combining theoretical and experimental methodologies is used to understand the neurological and computational underpinnings of this wide variety of behaviors. Neural network dynamics is one such approach that deals with understanding how neural circuitry generates complex activity and accounts for most of the specific characteristics of the neuron and its responses. The dynamics of the brain are multiscale, ranging from ion channels and synapses at the molecular level to emergent behavior, like oscillations at the scale of the entire brain. The challenge, therefore, becomes how to create predictions regarding brain dynamics while simultaneously incorporating these various dimensions.
Theorists have proposed many models of neurons and their collective networks. Networks can be of many types depending on neurons, connectivity, external inputs, and synapses. Two main classes of neuron models and their networks are - rate-based and spiking neural networks. Due to the requirement to mimic the dynamics of individual spikes, they can be more computationally intensive, Spike-based neuron models, however, show promise for a wide range of applications where the temporal features of brain processing are crucial. Whereas for rate-based models, local instantaneous firing rates are monitored, individual neural spike dynamics are not. These rate-based methods are substantially less computationally intensive than equivalent research based on the direct computation of single-neuron dynamics. They are excellent for investigating large-scale phenomena and spanning scales. They do not, however, directly incorporate the spiking kinetics of individual neurons.

Neurons mainly communicate via the transfer of spikes. Thus we hypothesized that the brain follows a spiking-based model for information transfer. We aimed to determine under which conditions and parameters a spike-based model could potentially replace rate-based models. Present-day computational advancements allow us to model large networks with considerable detail in individual neurons. As much as rate-based networks are convenient and easily implemented, they lack biological relevance. Therefore we aim to find the parameters and conditions in which a spiking network can behave like a rate-based network and thus favorably replace them.
We have tried to make a comprehensive and general attempt to see if this is possible. To this end, we examined and compared two well-known networks the Brunel Network and the Continuous Attratcor Network.
The Brunel network, a spiking neuronal network, and the continuous attractor network, a rate-based neuronal network are carefully chosen as they have been reported multiple times and show a variety of essential behaviours. The Brunel network is a well-studied network of Leaky Integrated and Fire (LIF) neurons whose network behavior is very close to the theoretical behavior observed in real neurons. It shows a variety of states characterized by synchronous and asynchronous global activity and regular and irregular individual neuron activity which depends on the balance of excitatory and inhibitory connections and the magnitude of external inputs. Continuous attractor networks explain one of the high-level cognitive tasks: path integration for spatial navigation in grid cells. Using these models as a template, a simplistic model was created in which both networks with the same parameters could reproduce similar population activity.
After multiple simulations, it was evident that both rate-based and spiking neural networks explain many important experimentally observed behaviors, thus it is pertinent to ask which model is followed in the brain. Using the studied models as templates, we developed a simplistic model that allowed us to examine the link between spiking and rate-based models. A simplistic model, with minimum parameters, was simulated, and its population activity was observed. This was then scaled up to be able to incorporate the desired parameters. This could potentially pose

as the first step towards bridging the gap between rate-based and spiking neural networks. The next logical step would be to find out the necessary methods to extrapolate similar results for a network with known biological underpinnings.
Despite the fact that there is a lot to be done in the separate modeling of rate-based and spiking neural networks, the more significant question is how to bridge the gap between the two and understand what they tell us about the computations in the brain.
This will help us understand and replicate behavior better and will have a wide impact on neuroscientific research.