Alexander D. Bird

Neuronal computation is constrained by the energetic cost of maintaining synaptic transmission, ionic gradients and action-potential generation. Prior work has shown that food restriction in mice shifts visual cortical neurons toward a different operating regime characterized by reduced excitatory synaptic drive, increased membrane resistance and a more depolarized resting membrane potential. This preserves neuronal firing rates, but comes at the cost of reduced coding precision. Deriving an improved estimate of neuronal energy consumption, we have recently shown that these adaptations reflect an optimal trade-off between neuronal information transmission and energy consumption. However, it remains unclear through which control strategies individual neurons adapt their biophysical parameters to maintain a favorable energy-information trade-off. Here we consider several candidate models implementing different control strategies. A „synapses-first” model, in which metabolic stress drives a downscaling of synaptic efficacies to save energy, while an intrinsic plasticity mechanism increases excitability to preserve the average firing rate, successfully reproduces key experimental observations. Alternative models in which energy shortages drive changes in intrinsic excitability or firing-rate variability can also reproduce the endpoint of neuronal adaptation, but predict different time courses and exhibit less energy-efficient and less stable dynamics. New experiments are needed to distinguish among these competing models. In brief: A dynamic energy-dependent integrate-and-fire model reproduces food-restriction-like parameter shifts when metabolic feedback first downscales synaptic efficacy and activity feedback subsequently increases intrinsic excitability. Reversing this control architecture, so that energy acts first on intrinsic excitability, produces suboptimal adaptation dynamics with transient hyperactivity, making it a less parsimonious explanation. Extending this control framework to large-scale recurrent network models could show how prolonged energy disruption destabilizes excitability and contributes to neurological disorders. Statement of significance: Neurons in the brain must function with a limited supply of energy. Recent work has shown that during energy scarcity neurons react by lowering their energy consumption at the expense of reduced information transmission. But through which mechanisms do they regulate their energy consumption and manage to remain as informative as possible? Here, we present a computational model that explains how neurons make coordinated adaptations of their synapses and cell membranes to regulate the trade-off between energy consumption and information transmission. Our work suggests that neurons are efficient energy savers that carefully regulate their energy consumption in response to current energy supply to transmit the maximum amount of information.

The dentate gyrus’ principal neuron, the granule cell (GC), plays a key role in pattern separation, transforming similar inputs into dissimilar outputs. We used a new measure based on information theory to evaluate this transformation in an experimentally derived in silico GC model with realistic ion channel distributions across its dendrites. We found that model performance aligned well with current-clamp recordings from mouse brain slices. However, it was also possible to find artificial parameter combinations in the model that functionally outperformed the recorded cells while matching their action potential shapes. Rather than maximising computational power, the biologically realistic GC model balanced energy efficiency against increased functionality in a Pareto optimal way: No possible parameter combination was found to improve one of the objectives without impairing the other. Interestingly, immature GCs adopted a different weighted trade-off with a stronger emphasis on energy efficiency than pattern separation, but they remained Pareto optimal over their putative developmental trajectory. Our results support the idea that evolution favours neurons that can satisfy functional and energetic demands simultaneously. Abstract Figure: In brief: We find that dentate gyrus granule cells are Pareto optimal for the simultaneous performance of pattern separation and energy economy, adopting a differently weighted trade-off depending on their developmental stage. Highlights: An experimentally constrained single granule cell (GC) model can perform temporal pattern separation in line with real data. Artificial channel configurations can improve pattern separation, but strictly at the cost of increased ATP consumption. GCs with realistic channel configurations appear Pareto optimal for the simultaneous performance of pattern separation and energy economy. Immature GCs remain on the Pareto front but prioritise low energy expenditure over pattern separation.

Among neurons of the same type, the different electrophysiological parameters vary drastically. It is presently unclear if there is any hidden structure in this diversity and how it relates to neuronal function. One potential source of structure is the evolutionary pressure that has sculpted brains to work in an energy-efficient manner. Here we show that neurons' parameters do not vary randomly, but that neurons populate a manifold within their parameter space permitting energy-efficient signaling. This manifold represents a Pareto front of degenerate solutions to the problem of energy-efficiency and explains the prevalence of low to intermediate firing rates (2 - 5 Hz) in neocortex. Furthermore, we show that neurons in different sensory brain areas populate different manifolds and that food restriction induces systematic shifts of neuronal parameters along this manifold. Our results suggest that the large diversity of neuronal properties is actually tightly regulated to ensure energy-efficient signaling in different contexts.

Reducing the number of animals required for a given experiment is part of the 3Rs strategies for animal welfare. Sample size estimation is a critical step in efficient and ethical experimental design. It is generally believed that pilot studies can be used to estimate sample sizes, which could lead to an overall reduction in the number of animals used. As part of the standard approach to ensuring that a planned animal experiment has sufficient statistical power, estimates of effect size and population variance are required. Here we derive the distribution of the sample size estimator when both effect size and variance are unknown. We show that, in this case, it is not feasible to conduct a preliminary pilot study to estimate the required sample size. Our analysis indicates that the sample size of a useful pilot study will often be much larger than that of the main study itself when the effect size is unknown. Therefore, we conclude that performing pilot studies with the aim of estimating sample size will not help to minimize the overall number of animal experiments in basic or pre-clinical research. A practical example is given, and alternative approaches are proposed and discussed. Plain language summaryWhen conducting an experiment, researchers attempt to achieve a high probability of getting conclusive data regarding a treatment effect, i.e., to have high statistical power. This power depends on, among other things, the unknown true effect size of a treatment, the unknown population variability, and the sample size. In animal experiments, ethics require using the smallest sample size necessary to produce adequate power. Estimating this sample size requires assumptions about the unknown true effect size and the population variability. We show mathematically that these assumptions are poorly constrained by data from preliminary pilot studies. We conclude that additional pilot studies should not be conducted as part of the estimation process as the data they provide cannot lead to a reduction in the total number of animal test subjects.

Pattern separation is a valuable computational function performed by neuronal circuits, such as the dentate gyrus, where dissimilarity between inputs is increased, reducing noise and increasing the storage capacity of downstream networks. Pattern separation is studied from both in vivo experimental and computational perspectives and, a number of different measures (such as orthogonalisation, decorrelation, or spike train distance) have been applied to quantify the process of pattern separation. However, these are known to give conclusions that can differ qualitatively depending on the choice of measure and the parameters used to calculate it. We here demonstrate that arbitrarily increasing sparsity, a noticeable feature of dentate granule cell firing and one that is believed to be key to pattern separation, typically leads to improved classical measures for pattern separation even, inappropriately, up to the point where almost all information about the inputs is lost. Standard measures therefore both cannot differentiate between pattern separation and pattern destruction, and give results that may depend on arbitrary parameter choices. We propose that techniques from information theory, in particular mutual information, transfer entropy, and redundancy, should be applied to penalise the potential for lost information (often due to increased sparsity) that is neglected by existing measures. We compare five commonly-used measures of pattern separation with three novel techniques based on information theory, showing that the latter can be applied in a principled way and provide a robust and reliable measure for comparing the pattern separation performance of different neurons and networks. We demonstrate our new measures on detailed compartmental models of individual dentate granule cells and a dentate microcircuit, and show how structural changes associated with epilepsy affect pattern separation performance. We also demonstrate how our measures of pattern separation can predict pattern completion accuracy. Overall, our measures solve a widely acknowledged problem in assessing the pattern separation of neural circuits such as the dentate gyrus, as well as the cerebellum and mushroom body. Finally we provide a publicly available toolbox allowing for easy analysis of pattern separation in spike train ensembles.

Dendritic spines are crucial for excitatory synaptic transmission as the size of a spine head correlates with the strength of its synapse. The distribution of spine head sizes follows a lognormal-like distribution with more small spines than large ones. We analysed the impact of synaptic activity and plasticity on the spine size distribution in adult-born hippocampal granule cells from rats with induced homo- and heterosynaptic long-term plasticity in vivo and CA1 pyramidal cells from Munc13–1/Munc13–2 knockout mice with completely blocked synaptic transmission. Neither the induction of extrinsic synaptic plasticity nor the blockage of presynaptic activity degrades the lognormal-like distribution but changes its mean, variance and skewness. The skewed distribution develops early in the life of the neuron. Our findings and their computational modelling support the idea that intrinsic synaptic plasticity is sufficient for the generation, while a combination of intrinsic and extrinsic synaptic plasticity maintains lognormal-like distribution of spines.

Branching of dendrites and axons allows neurons to make synaptic contacts with large numbers of other neurons, facilitating the high connectivity of the nervous system. Neurons have geometric properties, such as the lengths and diameters of their branches, that change systematically throughout the arbor in ways that are thought to minimize construction costs and to optimize the transmission of electrical signals and the intracellular transport of materials. In this work, we investigated whether neuronal arbors also have topological properties that reflect the growth and/or functional properties of their dendritic arbors. In our efforts to uncover possible topological rules, we discovered a function that depends only on the topology of bifurcating trees such as dendritic arbors: the tip-support distribution , which is the average number of branches that support n dendrite tips. We found that for many, but not all, neurons from a wide range of invertebrate and vertebrate species, the tip-support distribution follows a power law with slopes ranging from -1.4 and -1.8 on a log-log plot. The slope is invariant under iterative trimming of terminal branches and under random ablation of internal branches. We found that power laws with similar slopes emerge from a variety of iterative growth processes including the Galton-Watson (GW) process, where the power-law behavior occurs after the percolation threshold. Through simulation, we show the slope of the power-law increases with the branching probability of a GW process, which corresponds to a more regular tree. Furthermore, the inclusion of postsynaptic spines and other terminal processes on branches causes a characteristic deviation of the tip-support distribution from a power law. Therefore, the tip-support function is a topological property that reflects the underlying branching morphogenesis of dendritic trees.

Pattern separation is a valuable computational function performed by neuronal circuits, such as the dentate gyrus, where dissimilarity between inputs is increased, reducing noise and increasing the storage capacity of downstream networks. Pattern separation is studied from both in vivo experimental and computational perspectives and, a number of different measures (such as orthogonalisation, decorrelation, or spike train distance) have been applied to quantify the process of pattern separation. However, these are known to give conclusions that can differ qualitatively depending on the choice of measure and the parameters used to calculate it. We here demonstrate that arbitrarily increasing sparsity, a noticeable feature of dentate granule cell firing and one that is believed to be key to pattern separation, typically leads to improved classical measures for pattern separation even, inappropriately, up to the point where almost all information about the inputs is lost. Standard measures therefore both cannot differentiate between pattern separation and pattern destruction, and give results that may depend on arbitrary parameter choices. We propose that techniques from information theory, in particular mutual information, transfer entropy, and redundancy, should be applied to penalise the potential for lost information (often due to increased sparsity) that is neglected by existing measures. We compare five commonly-used measures of pattern separation with three novel techniques based on information theory, showing that the latter can be applied in a principled way and provide a robust and reliable measure for comparing the pattern separation performance of different neurons and networks. We demonstrate our new measures on detailed compartmental models of individual dentate granule cells and a dentate microcircuit, and show how structural changes associated with epilepsy affect pattern separation performance. We also demonstrate how our measures of pattern separation can predict pattern completion accuracy. Overall, our measures solve a widely acknowledged problem in assessing the pattern separation of neural circuits such as the dentate gyrus, as well as the cerebellum and mushroom body. Finally we provide a publicly available toolbox allowing for easy analysis of pattern separation in spike train ensembles. Author summary: The hippocampus is a region of the brain strongly associated with spatial navigation and encoding of episodic memories. To perform these functions effectively it makes use of circuits that perform pattern separation , where redundant structure is removed from neural representations leaving only the most salient information. Pattern separation allows downstream pattern completion networks to better distinguish between similar situations. Pathological changes, caused by Alzheimer’s, schizophrenia, or epilepsy, to the circuits that perform pattern separation are associated with reduced discriminative ability in both animal models and humans. Traditionally, pattern separation has been described alongside the complementary process of pattern completion, but more recent studies have focussed on the detailed neuronal and circuit features that contribute to pattern separation alone. We here show that traditional measures of pattern separation are inappropriate in this case, as they do not give consistent conclusions when parameters are changed and can confound pattern separation with the loss of important information. We show that directly accounting for the information throughput of a pattern separation circuit can provide new measures of pattern separation that are robust and consistent, and allow for nuanced analysis of the structure-function relationship of such circuits and how this may be perturbed by pathology.

Editorial: Unveiling the structure and function of brain microcircuits: Experiments, algorithms and simulations

Neurons encounter unavoidable evolutionary trade-offs between multiple tasks. They must consume as little energy as possible while effectively fulfilling their functions. Cells displaying the best performance for such multi-task trade-offs are said to be Pareto optimal, with their ion channel configurations underpinning their functionality. Ion channel degeneracy, however, implies that multiple ion channel configurations can lead to functionally similar behaviour. Therefore, instead of a single model, neuroscientists often use populations of models with distinct combinations of ionic conductances. This approach is called population (database or ensemble) modelling. It remains unclear, which ion channel parameters in the vast population of functional models are more likely to be found in the brain. Here we argue that Pareto optimality can serve as a guiding principle for addressing this issue by helping to identify the subpopulations of conductance-based models that perform best for the trade-off between economy and functionality. In this way, the high-dimensional parameter space of neuronal models might be reduced to geometrically simple low-dimensional manifolds, potentially explaining experimentally observed ion channel correlations. Conversely, Pareto inference might also help deduce neuronal functions from high-dimensional Patch-seq data. In summary, Pareto optimality is a promising framework for improving population modelling of neurons and their circuits.