A learning rule balancing energy consumption and information maximization in a feed-forward neuronal network

Information measures are often used to assess the efficacy of neural networks, and learning rules can be derived through optimization procedures on such measures. In biological neural networks, computation is restricted by the amount of available resources. Considering energy restrictions, it is thus reasonable to balance information processing efficacy with energy consumption. Here, we studied networks of non-linear Hawkes neurons and assessed the information flow through these networks using mutual information. We then applied gradient descent for a combination of mutual information and energetic costs to obtain a learning rule. Through this procedure, we obtained a rule containing a sliding threshold, similar to the Bienenstock-Cooper-Munro rule. The rule contains terms local in time and in space plus one global variable common to the whole network. The rule thus belongs to so-called three-factor rules and the global variable could be related to a number of biological processes. In neural networks using this learning rule, frequent inputs get mapped onto low energy orbits of the network while rare inputs aren't learned

Editorial: Advances in Computational Neuroscience

© 2022 Nowotny, van Albada, Fellous, Haas, Jolivet, Metzner and Sharpee. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). https://creativecommons.org/licenses/by/4.0/Peer reviewedFinal Published versio

On the role of theory and modeling in neuroscience

In recent years, the field of neuroscience has gone through rapid experimental advances and extensive use of quantitative and computational methods. This accelerating growth has created a need for methodological analysis of the role of theory and the modeling approaches currently used in this field. Toward that end, we start from the general view that the primary role of science is to solve empirical problems, and that it does so by developing theories that can account for phenomena within their domain of application. We propose a commonly-used set of terms - descriptive, mechanistic, and normative - as methodological designations that refer to the kind of problem a theory is intended to solve. Further, we find that models of each kind play distinct roles in defining and bridging the multiple levels of abstraction necessary to account for any neuroscientific phenomenon. We then discuss how models play an important role to connect theory and experiment, and note the importance of well-defined translation functions between them. Furthermore, we describe how models themselves can be used as a form of experiment to test and develop theories. This report is the summary of a discussion initiated at the conference Present and Future Theoretical Frameworks in Neuroscience, which we hope will contribute to a much-needed discussion in the neuroscientific community

Amyloid plaques and normal ageing have differential effects on microglial Ca2+ activity in the mouse brain

In microglia, changes in intracellular calcium concentration ([Ca2+]i) may regulate process motility, inflammasome activation, and phagocytosis. However, while neurons and astrocytes exhibit frequent spontaneous Ca2+ activity, microglial Ca2+ signals are much rarer and poorly understood. Here, we studied [Ca2+]i changes of microglia in acute brain slices using Fluo-4–loaded cells and mice expressing GCaMP5g in microglia. Spontaneous Ca2+ transients occurred ~ 5 times more frequently in individual microglial processes than in their somata. We assessed whether microglial Ca2+ responses change in Alzheimer's disease (AD) using AppNL−G−F knock-in mice. Proximity to Aβ plaques strongly affected microglial Ca2+ activity. Although spontaneous Ca2+ transients were unaffected in microglial processes, they were fivefold more frequent in microglial somata near Aβ plaques than in wild-type microglia. Microglia away from Aβ plaques in AD mice showed intermediate properties for morphology and Ca2+ responses, partly resembling those of wild-type microglia. By contrast, somatic Ca2+ responses evoked by tissue damage were less intense in microglia near Aβ plaques than in wild-type microglia, suggesting different mechanisms underlying spontaneous vs. damage-evoked Ca2+ signals. Finally, as similar processes occur in neurodegeneration and old age, we studied whether ageing affected microglial [Ca2+]i. Somatic damage-evoked Ca2+ responses were greatly reduced in microglia from old mice, as in the AD mice. In contrast to AD, however, old age did not alter the occurrence of spontaneous Ca2+ signals in microglial somata but reduced the rate of events in processes. Thus, we demonstrate distinct compartmentalised Ca2+ activity in microglia from healthy, aged and AD-like brains

Comparative performance of mutual information and transfer entropy for analyzing the balance of information flow and energy consumption at synapses

Information theory has become an essential tool of modern neuroscience. It can however be difficult to apply in experimental contexts when acquisition of very large datasets is prohibitive. Here, we compare the relative performance of two information theoretic measures, mutual information and transfer entropy, for the analysis of information flow and energetic consumption at synapses. We show that transfer entropy outperforms mutual information in terms of reliability of estimates for small datasets. However, we also show that a detailed understanding of the underlying neuronal biophysics is essential for properly interpreting the results obtained with transfer entropy. We conclude that when time and experimental conditions permit, mutual information might provide an easier to interpret alternative. Finally, we apply both measures to the study of energetic optimality of information flow at thalamic relay synapses in the visual pathway. We show that both measures recapitulate the experimental finding that these synapses are tuned to optimally balance information flowing through them with the energetic consumption associated with that synaptic and neuronal activity. Our results highlight the importance of conducting systematic computational studies prior to applying information theoretic tools to experimental data

A learning rule balancing energy consumption and information maximization in a feed-forward neuronal network

Information measures are often used to assess the efficacy of neural networks, and learning rules can be derived through optimization procedures on such measures. In biological neural networks, computation is restricted by the amount of available resources. Considering energy restrictions, it is thus reasonable to balance information processing efficacy with energy consumption. Here, we studied networks of non-linear Hawkes neurons and assessed the information flow through these networks using mutual information. We then applied gradient descent for a combination of mutual information and energetic costs to obtain a learning rule. Through this procedure, we obtained a rule containing a sliding threshold, similar to the Bienenstock-Cooper-Munro rule. The rule contains terms local in time and in space plus one global variable common to the whole network. The rule thus belongs to so-called three-factor rules and the global variable could be related to a number of biological processes. In neural networks using this learning rule, frequent inputs get mapped onto low energy orbits of the network while rare inputs aren't learned

Spike-frequency adaptation is modulated by interacting currents in an Hodgkin-Huxley-type model: Role of the Na,K-ATPase

Spike-frequency adaptation is a prominent feature of spiking neurons. Using a Hodgkin-Huxley-type model, we studied adaptation originating from the Na,K-ATPase electrogenic pump and its evolution in presence of a medium-duration calcium-dependent potassium channel. We found that the Na,K-ATPase induces spike-frequency adaptation with a time constant of up to a few seconds and interacts with the calcium-dependent potassium current through the output frequency, yielding a very typical pattern of instantaneous frequencies. Because channels responsible for spike-frequency adaptation can interact with each other, our results suggest that their meaningful time courses and parameters can be difficult to measure experimentally. To circumvent this problem, we developed a simple phenomenological model that captures the interaction between currents and allows the direct evaluation of the underlying biophysical parameters directly from the frequency vs. current curves. Finally, we found that for weak stimulations, the pump induces phasic spiking and linearly converts the stimulus amplitude in a finite number of spikes acting like an inhibitory spike-counter. Our results point to the importance of considering interacting currents involved in spike-frequency adaptation collectively rather than as isolated elements and underscore the importance of sodium as a messenger for long-term signal integration in neurons. Within this context, we propose that the Na,K-ATPase plays an important role and show how to recover relevant biological parameters from adapting channels using simple electrophysiological measurements. ### Competing Interest Statement The authors have declared no competing interest

Acknowledgements

benchmark test for a quantitative assessment of simple neuron model