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

Predicting spike timing of neocortical pyramidal neurons by simple threshold models

Neurons generate spikes reliably with millisecond precision if driven by a fluctuating current—is it then possible to predict the spike timing knowing the input? We determined parameters of an adapting threshold model using data recorded in vitro from 24 layer 5 pyramidal neurons from rat somatosensory cortex, stimulated intracellularly by a fluctuating current simulating synaptic bombardment in vivo. The model generates output spikes whenever the membrane voltage (a filtered version of the input current) reaches a dynamic threshold. We find that for input currents with large fluctuation amplitude, up to 75% of the spike times can be predicted with a precision of ±2ms. Some of the intrinsic neuronal unreliability can be accounted for by a noisy threshold mechanism. Our results suggest that, under random current injection into the soma, (i) neuronal behavior in the subthreshold regime can be well approximated by a simple linear filter; and (ii) most of the nonlinearities are captured by a simple threshold proces

Deciphering Neuron-Glia Compartmentalization in Cortical Energy Metabolism

Energy demand is an important constraint on neural signaling. Several methods have been proposed to assess the energy budget of the brain based on a bottom-up approach in which the energy demand of individual biophysical processes are first estimated independently and then summed up to compute the brain's total energy budget. Here, we address this question using a novel approach that makes use of published datasets that reported average cerebral glucose and oxygen utilization in humans and rodents during different activation states. Our approach allows us (1) to decipher neuron-glia compartmentalization in energy metabolism and (2) to compute a precise state-dependent energy budget for the brain. Under the assumption that the fraction of energy used for signaling is proportional to the cycling of neurotransmitters, we find that in the activated state, most of the energy (∼80%) is oxidatively produced and consumed by neurons to support neuron-to-neuron signaling. Glial cells, while only contributing for a small fraction to energy production (∼6%), actually take up a significant fraction of glucose (50% or more) from the blood and provide neurons with glucose-derived energy substrates. Our results suggest that glycolysis occurs for a significant part in astrocytes whereas most of the oxygen is utilized in neurons. As a consequence, a transfer of glucose-derived metabolites from glial cells to neurons has to take place. Furthermore, we find that the amplitude of this transfer is correlated to (1) the activity level of the brain; the larger the activity, the more metabolites are shuttled from glia to neurons and (2) the oxidative activity in astrocytes; with higher glial pyruvate metabolism, less metabolites are shuttled from glia to neurons. While some of the details of a bottom-up biophysical approach have to be simplified, our method allows for a straightforward assessment of the brain's energy budget from macroscopic measurements with minimal underlying assumptions

The quantitative single-neuron modeling competition

As large-scale, detailed network modeling projects are flourishing in the field of computational neuroscience, it is more and more important to design single neuron models that not only capture qualitative features of real neurons but are quantitatively accurate in silico representations of those. Recent years have seen substantial effort being put in the development of algorithms for the systematic evaluation and optimization of neuron models with respect to electrophysiological data. It is however difficult to compare these methods because of the lack of appropriate benchmark tests. Here, we describe one such effort of providing the community with a standardized set of tests to quantify the performances of single neuron models. Our effort takes the form of a yearly challenge similar to the ones which have been present in the machine learning community for some time. This paper gives an account of the first two challenges which took place in 2007 and 2008 and discusses future directions. The results of the competition suggest that best performance on data obtained from single or double electrode current or conductance injection is achieved by models that combine features of standard leaky integrate-and-fire models with a second variable reflecting adaptation, refractoriness, or a dynamic threshol

Non-signalling energy use in the developing rat brain

Energy use in the brain constrains its information processing power, but only about half the brain's energy consumption is directly related to information processing. Evidence for which non-signalling processes consume the rest of the brain's energy has been scarce. For the first time, we investigated the energy use of the brain's main non-signalling tasks with a single method. After blocking each non-signalling process, we measured oxygen level changes in juvenile rat brain slices with an oxygen-sensing microelectrode and calculated changes in oxygen consumption throughout the slice using a modified diffusion equation. We found that the turnover of the actin and microtubule cytoskeleton, followed by lipid synthesis, are significant energy drains, contributing 25%, 22% and 18%, respectively, to the rate of oxygen consumption. In contrast, protein synthesis is energetically inexpensive. We assess how these estimates of energy expenditure relate to brain energy use in vivo, and how they might differ in the mature brain

Predicting neuronal activity with simple models of the threshold type: Adaptive Exponential Integrate-and-Fire model with two compartments

An adaptive Exponential Integrate-and-Fire (aEIF) model was used to predict the activity of layer-V-pyramidal neurons of rat neocortex under random current injection. A new protocol has been developed to extract the parameters of the aEIF model using an optimal filtering technique combined with a black-box numerical optimization. We found that the aEIF model is able to accurately predict both subthreshold fluctuations and the exact timing of spikes, reasonably close to the limits imposed by the intrinsic reliability of pyramidal neurons

Two-photon microscopy with double-circle trajectories for in vivo cerebral blood flow measurements

Scanning microscopes normally use trajectories which produce full-frame images of an object at a low frame rate. Time-resolved measurements are possible if scans along a single line are repeated at a high rate. In conjunction with fluorescence labeling techniques, in vivo recording of blood flow in single capillaries is possible. The present work investigates scanning with double-circle trajectories to measure blood flow simultaneously in several vessels of a capillary network. With the trajectory centered near a bifurcation, a double circle crosses each vessel twice, creating a sensing gate for passing dark red blood cells in fluorescently labeled plasma. From the stack of scans repeated at 1,300Hz, the time-resolved velocity is retrieved using an image correlation approach. Single bifurcation events can be identified from a few fluorescently labeled red blood cells. The applicability of the method for in vivo measurements is illustrated on the basis of two-photon laser scanning microscopy of the cerebral capillary network of mice. Its performance is assessed with synthetic data generated from a two-phase model for the perfusion in a capillary network. The calculation of velocities is found to be sufficiently robust for a wide range of conditions. The achievable limits depend significantly on the experimental conditions and are estimated to be in the 1μm/s (velocity) and 0.1s (time resolution) ranges, respectively. Some manual fine-tuning is required for optimal performance in terms of accuracy and time resolution. Further work may lead to improved reliability with which bifurcation events are identified in the algorithm and to include red blood cell flux and hematocrit measurements. With the capability for time-resolved measurements in all vessels of a bifurcation, double-circle scanning trajectories allow a detailed study of the dynamics in vascular network