Energetic Constraints Produce Self-sustained Oscillatory Dynamics in Neuronal Networks

Burroni, Javier; Taylor, Patrick; Corey, Cassian; Vachnadze, Tengiz; Siegelmann, Hava T.

doi:10.3389/fnins.2017.00080

Cited by 14 publications

(20 citation statements)

References 89 publications

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“…For example, Gandolfo ( 2008 ) applied the predator-prey equations in economics to model resource interactions between industries. Neural network activity has been also modeled (Moreau et al, 1999 ; Burroni et al, 2017 ) by population ecology equations to describe the natural oscillations in neuronal networks. In this work, we investigate the feasibility of population ecology modeling for dendritic spine dynamics.…”

Section: Resultsmentioning

confidence: 99%

Population Dynamics and Long-Term Trajectory of Dendritic Spines

Özcan

Ozcan

2018

Front. Synaptic Neurosci.

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Structural plasticity, characterized by the formation and elimination of synapses, plays a big role in learning and long-term memory formation in the brain. The majority of the synapses in the neocortex occur between the axonal boutons and dendritic spines. Therefore, understanding the dynamics of the dendritic spine growth and elimination can provide key insights to the mechanisms of structural plasticity. In addition to learning and memory formation, the connectivity of neural networks affects cognition, perception, and behavior. Unsurprisingly, psychiatric and neurological disorders such as schizophrenia and autism are accompanied by pathological alterations in spine morphology and synapse numbers. Hence, it is vital to develop a model to understand the mechanisms governing dendritic spine dynamics throughout the lifetime. Here, we applied the density dependent Ricker population model to investigate the feasibility of ecological population concepts and mathematical foundations in spine dynamics. The model includes “immigration,” which is based on the filopodia type transient spines, and we show how this effect can potentially stabilize the spine population theoretically. For the long-term dynamics we employed a time dependent carrying capacity based on the brain's metabolic energy allocation. The results show that the mathematical model can explain the spine density fluctuations in the short-term and also account for the long term trends in the developing brain during synaptogenesis and pruning.

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Section: Resultsmentioning

confidence: 99%

Population Dynamics and Long-Term Trajectory of Dendritic Spines

Özcan

Ozcan

2018

Front. Synaptic Neurosci.

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“…The only other examples of models with an explicit variable representing energy levels we found were developed in [61] and in Model 2 from [26]. While the former is quite simple and not connected to any specific biological mechanism, the latter explicitly presents the second variable as a proxy for the ATP concentration in the neuron.…”

Section: Discussionmentioning

confidence: 99%

Simple models including energy and spike constraints reproduce complex activity patterns and metabolic disruptions

Fardet

Levina

2020

Preprint

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In this work, we introduce new phenomenological neuronal models (eLIF and mAdExp) that account for energy supply and demand in the cell as well as their interactions with spiking dynamics. Through energetic considerations, these new models reproduce a broad range of biologically-relevant behaviors that are identified to be crucial in many neurological disorders, but were not captured by commonly used phenomenological models. Because of their low dimensionality eLIF and mAdExp enable large-scale simulations that are necessary for more realistic studies of brain circuits involved in neuronal disorders. The new models enable both more accurate modeling and the possibility to study energy-associated disorders over the whole time-course of disease progression instead of only comparing the initially healthy status with the final diseased state. These models, therefore, provide new theoretical and computational methods to assess the opportunities of early diagnostics and the potential of energy-centered approaches to improve therapies.

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“…which has been used later in this section to derive a variant of a non-spiking GT neuron model. Rewriting (9) in terms of the objective function for the neuron model from (8), we get…”

Section: Growth Transform Non-spiking Neuron Modelmentioning

confidence: 99%

“…Recently, energy-based attractor networks have been used to design spiking neural networks 1 through phase-to-timing mappings in complex state space [8]. Energy has also been modeled as an external resource to constrain and control neural activity [9]. However, in all of these approaches, the energy functionals have been defined with respect to some statistical measure of neural activity, for example spike rates, instead of continuous-valued neuronal variables like the membrane potential.…”

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confidence: 99%

A Spiking Neuron and Population Model based on the Growth Transform Dynamical System

Gangopadhyay

Mehta

Chakrabartty

2019

Preprint

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AbstractIn neuromorphic engineering, neural populations are generally modeled in a bottom-up manner, where individual neuron models are connected through synapses to form large-scale spiking networks. Alternatively, a top-down approach treats the process of spike generation and neural representation of excitation in the context of minimizing some measure of network energy. However, these approaches usually define the energy functional in terms of some statistical measure of spiking activity (ex. firing rates), which does not allow independent control and optimization of neurodynamical parameters. In this paper, we introduce a new spiking neuron and population model where the dynamical and spiking responses of neurons can be derived directly from a network objective or energy functional of continuous-valued neural variables like the membrane potential. The key advantage of the model is that it allows for independent control over three neuro-dynamical properties: (a) control over the steady-state population dynamics that encodes the minimum of an exact network energy functional; (b) control over the shape of the action potentials generated by individual neurons in the network without affecting the network minimum; and (c) control over spiking statistics and transient population dynamics without affecting the network minimum or the shape of action potentials. At the core of the proposed model are different variants of Growth Transform dynamical systems that produce stable and interpretable population dynamics, irrespective of the network size and the type of neuronal connectivity (inhibitory or excitatory). In this paper, we present several examples where the proposed model has been configured to produce different types of single-neuron dynamics as well as population dynamics. In one such example, the network is shown to adapt such that it encodes the steady-state solution using a reduced number of spikes upon convergence to the optimal solution. In this paper we use this network to construct a spiking associative memory that uses fewer spikes compared to conventional architectures, while maintaining high recall accuracy at high memory loads.

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Energetic Constraints Produce Self-sustained Oscillatory Dynamics in Neuronal Networks

Cited by 14 publications

References 89 publications

Population Dynamics and Long-Term Trajectory of Dendritic Spines

Population Dynamics and Long-Term Trajectory of Dendritic Spines

Simple models including energy and spike constraints reproduce complex activity patterns and metabolic disruptions

A Spiking Neuron and Population Model based on the Growth Transform Dynamical System

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