Energy-Efficient Information Transfer by Visual Pathway Synapses

The type of inhibition provided by thalamic interneurons alters the input selectivity of thalamocortical neurons

A fundamental problem in neuroscience is how neurons select for their many inputs. A common assumption is that a neuron's selectivity is largely explained by differences in excitatory synaptic input weightings. Here we describe another solution to this important problem. We show that within the first order visual thalamus, the type of inhibition provided by thalamic interneurons has the potential to alter the input selectivity of thalamocortical neurons. To do this, we developed conductance injection protocols to compare how different types of synchronous and asynchronous GABA release influence thalamocortical excitability in response to realistic patterns of retinal ganglion cell input. We show that the asynchronous GABA release associated with tonic inhibition is particularly efficient at maintaining information content, ensuring that thalamocortical neurons can distinguish between their inputs. We propose a model where alterations in GABA release properties results in rapid changes in input selectivity without requiring structural changes in the network.

Plasticity in the Functional Properties of NMDA Receptors Improves Network Stability during Severe Energy Stress

Brain energy stress leads to neuronal hyperexcitability followed by a rapid loss of function and cell death. In contrast, the frog brainstem switches into a state of extreme metabolic resilience that allows them to maintain motor function during hypoxia as they emerge from hibernation. NMDA receptors (NMDARs) are Ca2+-permeable glutamate receptors that contribute to the loss of homeostasis during hypoxia. Therefore, we hypothesized that hibernation leads to plasticity that reduces the role of NMDARs within neural networks to improve function during hypoxia. To test this, we assessed a circuit with a large involvement of NMDAR synapses, the brainstem respiratory network of female bullfrogs, Lithobates catesbeianus Contrary to our expectations, hibernation did not alter the role of NMDARs in generating network output, nor did it affect the amplitude, kinetics, and hypoxia sensitivity of NMDAR currents. Instead, hibernation strongly reduced NMDAR Ca2+ permeability and enhanced desensitization during repetitive stimulation. Under severe hypoxia, the normal NMDAR profile caused network hyperexcitability within minutes, which was mitigated by blocking NMDARs. After hibernation, the modified complement of NMDARs protected against hyperexcitability, as disordered output did not occur for at least one hour in hypoxia. These findings uncover state-dependence in the plasticity of NMDARs, whereby multiple changes to receptor function improve neural performance during metabolic stress without interfering with their normal role during healthy conditions.

Robust and consistent measures of pattern separation based on information theory and demonstrated in the dentate gyrus

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.

A role for MCH neuron firing in modulating hippocampal plasticity threshold

It has been revealed that hypothalamic neurons containing the peptide, melanin-concentrating hormone (MCH) can influence learning [1] and memory formation [2], but the cellular mechanisms by which they perform this function are not well understood. Here, we examine the role of MCH neural input to the hippocampus, and show in vitro that optogenetically increasing MCH axon activity facilitates hippocampal plasticity by lowering the threshold for synaptic potentiation. These results align with increasing evidence that MCH neurons play a regulatory role in learning, and reveal that this could be achieved by modulating plasticity thresholds in the hippocampus.

An energy costly architecture of neuromodulators for human brain evolution and cognition

In comparison to other species, the human brain exhibits one of the highest energy demands relative to body metabolism. It remains unclear whether this heightened energy demand uniformly supports an enlarged brain or if specific signaling mechanisms necessitate greater energy. We hypothesized that the regional distribution of energy demands will reveal signaling strategies that have contributed to human cognitive development. We measured the energy distribution within the brain functional connectome using multimodal brain imaging and found that signaling pathways in evolutionarily expanded regions have up to 67% higher energetic costs than those in sensory-motor regions. Additionally, histology, transcriptomic data, and molecular imaging independently reveal an up-regulation of signaling at G-protein-coupled receptors in energy-demanding regions. Our findings indicate that neuromodulator activity is predominantly involved in cognitive functions, such as reading or memory processing. This study suggests that an up-regulation of neuromodulator activity, alongside increased brain size, is a crucial aspect of human brain evolution.

Mitochondrial fission drives neuronal metabolic burden to promote stress susceptibility in male mice

Neurons are particularly susceptible to energy fluctuations in response to stress. Mitochondrial fission is highly regulated to generate ATP via oxidative phosphorylation; however, the role of a regulator of mitochondrial fission in neuronal energy metabolism and synaptic efficacy under chronic stress remains elusive. Here, we show that chronic stress promotes mitochondrial fission in the medial prefrontal cortex via activating dynamin-related protein 1 (Drp1), resulting in mitochondrial dysfunction in male mice. Both pharmacological inhibition and genetic reduction of Drp1 ameliorates the deficit of excitatory synaptic transmission and stress-related depressive-like behavior. In addition, enhancing Drp1 fission promotes stress susceptibility, which is alleviated by coenzyme Q10, which potentiates mitochondrial ATP production. Together, our findings unmask the role of Drp1-dependent mitochondrial fission in the deficits of neuronal metabolic burden and depressive-like behavior and provides medication basis for metabolism-related emotional disorders.

Plasticity in the functional properties of NMDA receptors improves network stability during severe energy stress

Brain energy stress leads to neuronal hyperexcitability followed by a rapid loss of function and cell death. In contrast, the frog brainstem switches into a state of extreme metabolic resilience that allows them to maintain motor function during hypoxia as they emerge from hibernation. NMDA receptors (NMDARs) are Ca2+-permeable glutamate receptors that contribute to the loss of homeostasis during hypoxia. Therefore, we hypothesized that hibernation leads to plasticity that reduces the role of NMDARs within neural networks to improve function during energy stress. To test this, we assessed a circuit with a large involvement of NMDAR synapses, the brainstem respiratory network of female bullfrogs, Lithobates catesbeianus. Contrary to our expectations, hibernation did not alter the role of NMDARs in generating network output, nor did it affect the amplitude, kinetics, and hypoxia sensitivity of NMDAR currents. Instead, hibernation strongly reduced NMDAR Ca2+ permeability and enhanced desensitization during repetitive stimulation. Under severe hypoxia, the normal NMDAR profile caused network hyperexcitability within minutes, which was mitigated by blocking NMDARs. After hibernation, the modified complement of NMDARs protected against hyperexcitability, as disordered output did not occur for at least one hour in hypoxia. These findings uncover state-dependence in the plasticity of NMDARs, whereby multiple changes to receptor function improve neural performance during energy stress without interfering with its normal role during healthy activity.

A functional account of stimulation-based aerobic glycolysis and its role in interpreting BOLD signal intensity increases in neuroimaging experiments

In aerobic glycolysis, oxygen is abundant, and yet cells metabolize glucose without using it, decreasing their ATP per glucose yield by 15-fold. During task-based stimulation, aerobic glycolysis occurs in localized brain regions, presenting a puzzle: why produce ATP inefficiently when, all else being equal, evolution should favor the efficient use of metabolic resources? The answer is that all else is not equal. We propose that a tradeoff exists between efficient ATP production and the efficiency with which ATP is spent to transmit information. Aerobic glycolysis, despite yielding little ATP per glucose, may support neuronal signaling in thin (< 0.5 µm), information-efficient axons. We call this the efficiency tradeoff hypothesis. This tradeoff has potential implications for interpretations of task-related BOLD "activation" observed in fMRI. We hypothesize that BOLD "activation" may index local increases in aerobic glycolysis, which support signaling in thin axons carrying "bottom-up" information, or "prediction error"-i.e., the BIAPEM (BOLD increases approximate prediction error metabolism) hypothesis. Finally, we explore implications of our hypotheses for human brain evolution, social behavior, and mental disorders.

Synaptic modifications transform neural networks to function without oxygen

BACKGROUND

Neural circuit function is highly sensitive to energetic limitations. Much like mammals, brain activity in American bullfrogs quickly fails in hypoxia. However, after emergence from overwintering, circuits transform to function for approximately 30-fold longer without oxygen using only anaerobic glycolysis for fuel, a unique trait among vertebrates considering the high cost of network activity. Here, we assessed neuronal functions that normally limit network output and identified components that undergo energetic plasticity to increase robustness in hypoxia.

RESULTS

In control animals, oxygen deprivation depressed excitatory synaptic drive within native circuits, which decreased postsynaptic firing to cause network failure within minutes. Assessments of evoked and spontaneous synaptic transmission showed that hypoxia impairs synaptic communication at pre- and postsynaptic loci. However, control neurons maintained membrane potentials and a capacity for firing during hypoxia, indicating that those processes do not limit network activity. After overwintering, synaptic transmission persisted in hypoxia to sustain motor function for at least 2 h.

CONCLUSIONS

Alterations that allow anaerobic metabolism to fuel synapses are critical for transforming a circuit to function without oxygen. Data from many vertebrate species indicate that anaerobic glycolysis cannot fuel active synapses due to the low ATP yield of this pathway. Thus, our results point to a unique strategy whereby synapses switch from oxidative to exclusively anaerobic glycolytic metabolism to preserve circuit function during prolonged energy limitations.

Paying the brain's energy bill

How have animals managed to maintain metabolically expensive brains given the volatile and fleeting availability of calories in the natural world? Here we review studies in support of three strategies that involve: 1) a reallocation of energy from peripheral tissues and functions to cover the costs of the brain, 2) an implementation of energy-efficient neural coding, enabling the brain to operate at reduced energy costs, and 3) efficient use of costly neural resources during food scarcity. Collectively, these studies reveal a heterogeneous set of energy-saving mechanisms that make energy-costly brains fit for survival.

Astrocyte derived TSP2 contributes to synaptic alteration and visual dysfunction in retinal ischemia/reperfusion injury

BACKGROUND

Despite current intervention measures/therapies are able to ameliorate neuronal death following retinal injuries/diseases, the recovery of visual function remains unsatisfactory. Previous studies revealed that the retinal synapse and neurite changed during the early stage after retinopathy, which was considered to be detrimental to visual signal transmission. However, the specific profiles and the mechanisms underlying retinal neurite and synaptic alteration after retinal pathologies remain poorly understood.

METHODS

Here, we revealed the spatiotemporal pattern of neurite and synaptic alteration following retinal pathologies using a rat model of acute RI/R induced by high intraocular pressure (HIOP) with Western blotting, Immunofluorescence, and electron microscopy. We further explored the potential role of activated astrocytes and their derived thrombospondin 2 (TSP2) in RI/R induced retinal neurite and synaptic alteration and visual dysfunction through viral transduction and drug injection.

RESULTS

We found a defasciculation of RGC axons, a compensatory increase of presynaptic proteins (synaptophysin and synapsin 1) and synaptic vesicles between bipolar cells and ganglion cells in the inner plexiform layer (IPL), and the degenerated visual function preceded the neuronal death in rat retinae. These events were accompanied by the activation of astrocytes. Furthermore, we showed that suppressing the activation of astrocytes (intravitreal injection of fluorocitric acid, FC), TSP2 knockdown (TSP2 shRNA-AAV transduction), and competitively inhibiting the binding of TSP2 and α2δ1 (intraperitoneal injection of gabapentin, GBP) effectively alleviated the retinal synaptic and neurite alteration and the visual dysfunction following RI/R injury.

CONCLUSIONS

(1) At the early stage following RI/R injury, the rat retinae develop a degeneration of ganglion cell axons and the resulting compensatory synaptic remodeling between bipolar cells and ganglion cells in IPL. These changes occur earlier than the massive loss of neurons in the ganglion cell layer (GCL). (2) Activated astrocytes may secret TSP2, which bind to α2δ1, to mediate the degeneration of rat retinal ganglion cell axons, compensatory synaptic remodeling in IPL, and visual dysfunction following RI/R injury.

Multiscale simulation analysis of passive and active micro/nanoelectrodes for CMOS-based in vitro neural sensing devices

Neuron and neural network studies are remarkably fostered by novel stimulation and recording systems, which often make use of biochips fabricated with advanced electronic technologies and, notably, micro- and nanoscale complementary metal-oxide semiconductor (CMOS). Models of the transduction mechanisms involved in the sensor and recording of the neuron activity are useful to optimize the sensing device architecture and its coupling to the readout circuits, as well as to interpret the measured data. Starting with an overview of recently published integrated active and passive micro/nanoelectrode sensing devices for in vitro studies fabricated with modern (CMOS-based) micro-nano technology, this paper presents a mixed-mode device-circuit numerical-analytical multiscale and multiphysics simulation methodology to describe the neuron-sensor coupling, suitable to derive useful design guidelines. A few representative structures and coupling conditions are analysed in more detail in terms of the most relevant electrical figures of merit including signal-to-noise ratio. This article is part of the theme issue 'Advanced neurotechnologies: translating innovation for health and well-being'.

Pareto optimality, economy-effectiveness trade-offs and ion channel degeneracy: improving population modelling for single neurons

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.

Neuronal energy use and brain evolution

Consider how advantageous it might be to have eyes on our hands, rather than on our faces: depth perception would be improved by the greater distance between the eyes, and it would be easy to look into relatively inaccessible spaces by appropriate movement of the hands. The absence of mammals that use this visual strategy draws attention to constraints on how evolution is able to 'design' the nervous system. Energy use in particular, in this case the large amount of energy that would be needed to send visual information along the ∼10⁶ optic nerve axons over the length of the arms to the brain (instead of along the much shorter optic nerve), imposes significant design constraints on the nervous system.

Representing Stimulus Information in an Energy Metabolism Pathway

We explored a computational model of astrocytic energy metabolism and demonstrated the theoretical plausibility that this type of pathway might be capable of coding information about stimuli in addition to its known functions in cellular energy and carbon budgets. Simulation results indicate that glycogenolytic glycolysis triggered by activation of adrenergic receptors can capture the intensity and duration features of a neuromodulator waveform and can respond in a dose-dependent manner, including non-linear state changes that are analogous to action potentials. We show how this metabolic pathway can translate information about external stimuli to production profiles of energy-carrying molecules such as lactate with a precision beyond simple signal transduction or non-linear amplification. The results suggest the operation of a metabolic state-machine from the spatially discontiguous yet interdependent metabolite elements. Such metabolic pathways might be well-positioned to code an additional level of salient information about a cell's environmental demands to impact its function. Our hypothesis has implications for the computational power and energy efficiency of the brain.

Neocortex saves energy by reducing coding precision during food scarcity

Information processing is energetically expensive. In the mammalian brain, it is unclear how information coding and energy use are regulated during food scarcity. Using whole-cell recordings and two-photon imaging in layer 2/3 mouse visual cortex, we found that food restriction reduced AMPA receptor conductance, reducing synaptic ATP use by 29%. Neuronal excitability was nonetheless preserved by a compensatory increase in input resistance and a depolarized resting potential. Consequently, neurons spiked at similar rates as controls but spent less ATP on underlying excitatory currents. This energy-saving strategy had a cost because it amplified the variability of visually-evoked subthreshold responses, leading to a 32% broadening of orientation tuning and impaired fine visual discrimination. This reduction in coding precision was associated with reduced levels of the fat mass-regulated hormone leptin and was restored by exogenous leptin supplementation. Our findings reveal that metabolic state dynamically regulates the energy spent on coding precision in neocortex.

Neural optimization: Understanding trade-offs with Pareto theory

Nervous systems, like any organismal structure, have been shaped by evolutionary processes to increase fitness. The resulting neural 'bauplan' has to account for multiple objectives simultaneously, including computational function, as well as additional factors such as robustness to environmental changes and energetic limitations. Oftentimes these objectives compete, and quantification of the relative impact of individual optimization targets is non-trivial. Pareto optimality offers a theoretical framework to decipher objectives and trade-offs between them. We, therefore, highlight Pareto theory as a useful tool for the analysis of neurobiological systems from biophysically detailed cells to large-scale network structures and behavior. The Pareto approach can help to assess optimality, identify relevant objectives and their respective impact, and formulate testable hypotheses.

Presynaptic stochasticity improves energy efficiency and helps alleviate the stability-plasticity dilemma

When an action potential arrives at a synapse there is a large probability that no neurotransmitter is released. Surprisingly, simple computational models suggest that these synaptic failures enable information processing at lower metabolic costs. However, these models only consider information transmission at single synapses ignoring the remainder of the neural network as well as its overall computational goal. Here, we investigate how synaptic failures affect the energy efficiency of models of entire neural networks that solve a goal-driven task. We find that presynaptic stochasticity and plasticity improve energy efficiency and show that the network allocates most energy to a sparse subset of important synapses. We demonstrate that stabilising these synapses helps to alleviate the stability-plasticity dilemma, thus connecting a presynaptic notion of importance to a computational role in lifelong learning. Overall, our findings present a set of hypotheses for how presynaptic plasticity and stochasticity contribute to sparsity, energy efficiency and improved trade-offs in the stability-plasticity dilemma.

Optimising the energetic cost of the glutamatergic synapse

As for electronic computation, neural information processing is energetically expensive. This is because information is coded in the brain as membrane voltage changes, which are generated largely by passive ion movements down electrochemical gradients, and these ion movements later need to be reversed by active ATP-dependent ion pumping. This article will review how much of the energetic cost of the brain reflects the activity of glutamatergic synapses, consider the relative amount of energy used pre- and postsynaptically, outline how evolution has energetically optimised synapse function by adjusting the presynaptic release probability and the postsynaptic number of glutamate receptors, and speculate on how energy use by synapses may be sensed and adjusted.

Artificial neurovascular network (ANVN) to study the accuracy vs. efficiency trade-off in an energy dependent neural network

Artificial feedforward neural networks perform a wide variety of classification and function approximation tasks with high accuracy. Unlike their artificial counterparts, biological neural networks require a supply of adequate energy delivered to single neurons by a network of cerebral microvessels. Since energy is a limited resource, a natural question is whether the cerebrovascular network is capable of ensuring maximum performance of the neural network while consuming minimum energy? Should the cerebrovascular network also be trained, along with the neural network, to achieve such an optimum? In order to answer the above questions in a simplified modeling setting, we constructed an Artificial Neurovascular Network (ANVN) comprising a multilayered perceptron (MLP) connected to a vascular tree structure. The root node of the vascular tree structure is connected to an energy source, and the terminal nodes of the vascular tree supply energy to the hidden neurons of the MLP. The energy delivered by the terminal vascular nodes to the hidden neurons determines the biases of the hidden neurons. The "weights" on the branches of the vascular tree depict the energy distribution from the parent node to the child nodes. The vascular weights are updated by a kind of "backpropagation" of the energy demand error generated by the hidden neurons. We observed that higher performance was achieved at lower energy levels when the vascular network was also trained along with the neural network. This indicates that the vascular network needs to be trained to ensure efficient neural performance. We observed that below a certain network size, the energetic dynamics of the network in the per capita energy consumption vs. classification accuracy space approaches a fixed-point attractor for various initial conditions. Once the number of hidden neurons increases beyond a threshold, the fixed point appears to vanish, giving place to a line of attractors. The model also showed that when there is a limited resource, the energy consumption of neurons is strongly correlated to their individual contribution to the network's performance.

Frequency-Dependent Energy Demand of Dendritic Responses to Deep Brain Stimulation in Thalamic Neurons: A Model-Based Study

Thalamic deep brain stimulation (DBS) generates excitatory postsynaptic currents and action potentials (APs) by triggering large numbers of synaptic inputs to local cells, which also activates axonal spikes to antidromically invade the soma and dendrites. To maintain signaling, the evoked dendritic responses require metabolic energy to restore ion gradients in each dendrite. The objective of this study is to estimate the energy demand associated with dendritic responses to thalamic DBS. We use a morphologically realistic computational model to simulate dendritic activity in thalamocortical (TC) relay neurons with axonal intracellular stimulation or DBS-like extracellular stimulation. We determine the metabolic cost by calculating the number of adenosine triphosphate (ATP) expended to pump Na⁺ and Ca²⁺ ions out of each dendrite. The ATP demand of dendritic activity exhibits frequency dependence, which is determined by the number of spikes in the dendrites. Each backpropagating AP from the soma activates a spike in the dendrites, and the dendritic firing is dominated by antidromic activation of the soma. High stimulus frequencies decrease dendritic ATP cost by reducing the fidelity of antidromic activation. Synaptic inputs and stimulus-induced polarization govern the ATP cost of dendritic responses by facilitating/suppressing antidromic activation, which also influences the ATP cost by depolarizing/hyperpolarizing each dendrite. These findings are important for understanding the synaptic signaling energy in TC relay neurons and metabolism-dependent functional imaging data of thalamic DBS.

A Low-Power Spiking Neural Network Chip Based on a Compact LIF Neuron and Binary Exponential Charge Injector Synapse Circuits

To realize a large-scale Spiking Neural Network (SNN) on hardware for mobile applications, area and power optimized electronic circuit design is critical. In this work, an area and power optimized hardware implementation of a large-scale SNN for real time IoT applications is presented. The analog Complementary Metal Oxide Semiconductor (CMOS) implementation incorporates neuron and synaptic circuits optimized for area and power consumption. The asynchronous neuronal circuits implemented benefit from higher energy efficiency and higher sensitivity. The proposed synapse circuit based on Binary Exponential Charge Injector (BECI) saves area and power consumption, and provides design scalability for higher resolutions. The SNN model implemented is optimized for 9 × 9 pixel input image and minimum bit-width weights that can satisfy target accuracy, occupies less area and power consumption. Moreover, the spiking neural network is replicated in full digital implementation for area and power comparisons. The SNN chip integrated from neuron and synapse circuits is capable of pattern recognition. The proposed SNN chip is fabricated using 180 nm CMOS process, which occupies a 3.6 mm² chip core area, and achieves a classification accuracy of 94.66% for the MNIST dataset. The proposed SNN chip consumes an average power of 1.06 mW—20 times lower than the digital implementation.

Energy constraints on brain network formation

Energy constraints are a fundamental limitation of the brain, which is physically embedded in a restricted space. The collective dynamics of neurons through connections enable the brain to achieve rich functionality, but building connections and maintaining activity come at a high cost. The effects of reducing these costs can be found in the characteristic structures of the brain network. Nevertheless, the mechanism by which energy constraints affect the organization and formation of the neuronal network in the brain is unclear. Here, it is shown that a simple model based on cost minimization can reproduce structures characteristic of the brain network. With reference to the behavior of neurons in real brains, the cost function was introduced in an activity-dependent form correlating the activity cost and the wiring cost as a simple ratio. Cost reduction of this ratio resulted in strengthening connections, especially at highly activated nodes, and induced the formation of large clusters. Regarding these network features, statistical similarity was confirmed by comparison to connectome datasets from various real brains. The findings indicate that these networks share an efficient structure maintained with low costs, both for activity and for wiring. These results imply the crucial role of energy constraints in regulating the network activity and structure of the brain.

Communication consumes 35 times more energy than computation in the human cortex, but both costs are needed to predict synapse number

Darwinian evolution tends to produce energy-efficient outcomes. On the other hand, energy limits computation, be it neural and probabilistic or digital and logical. Taking a particular energy-efficient viewpoint, we define neural computation and make use of an energy-constrained computational function. This function can be optimized over a variable that is proportional to the number of synapses per neuron. This function also implies a specific distinction between adenosine triphosphate (ATP)-consuming processes, especially computation per se vs. the communication processes of action potentials and transmitter release. Thus, to apply this mathematical function requires an energy audit with a particular partitioning of energy consumption that differs from earlier work. The audit points out that, rather than the oft-quoted 20 W of glucose available to the human brain, the fraction partitioned to cortical computation is only 0.1 W of ATP [L. Sokoloff, Handb. Physiol. Sect. I Neurophysiol. 3, 1843-1864 (1960)] and [J. Sawada, D. S. Modha, "Synapse: Scalable energy-efficient neurosynaptic computing" in Application of Concurrency to System Design (ACSD) (2013), pp. 14-15]. On the other hand, long-distance communication costs are 35-fold greater, 3.5 W. Other findings include 1) a [Formula: see text]-fold discrepancy between biological and lowest possible values of a neuron's computational efficiency and 2) two predictions of N, the number of synaptic transmissions needed to fire a neuron (2,500 vs. 2,000).

Spatio-chromatic information available from different neural layers via Gaussianization

How much visual information about the retinal images can be extracted from the different layers of the visual pathway? This question depends on the complexity of the visual input, the set of transforms applied to this multivariate input, and the noise of the sensors in the considered layer. Separate subsystems (e.g. opponent channels, spatial filters, nonlinearities of the texture sensors) have been suggested to be organized for optimal information transmission. However, the efficiency of these different layers has not been measured when they operate together on colorimetrically calibrated natural images and using multivariate information-theoretic units over the joint spatio-chromatic array of responses.In this work, we present a statistical tool to address this question in an appropriate (multivariate) way. Specifically, we propose an empirical estimate of the information transmitted by the system based on a recent Gaussianization technique. The total correlation measured using the proposed estimator is consistent with predictions based on the analytical Jacobian of a standard spatio-chromatic model of the retina-cortex pathway. If the noise at certain representation is proportional to the dynamic range of the response, and one assumes sensors of equivalent noise level, then transmitted information shows the following trends: (1) progressively deeper representations are better in terms of the amount of captured information, (2) the transmitted information up to the cortical representation follows the probability of natural scenes over the chromatic and achromatic dimensions of the stimulus space, (3) the contribution of spatial transforms to capture visual information is substantially greater than the contribution of chromatic transforms, and (4) nonlinearities of the responses contribute substantially to the transmitted information but less than the linear transforms.

Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach

We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge–Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray’s law in this context.

Local Design Principles at Hippocampal Synapses Revealed by an Energy-Information Trade-Off

Synapses across different brain regions display distinct structure-function relationships. We investigated the interplay of fundamental design constraints that shape the transmission properties of the excitatory CA3-CA1 pyramidal cell connection, a prototypic synapse for studying the mechanisms of learning in the mammalian hippocampus. This small synapse is characterized by probabilistic release of transmitter, which is markedly facilitated in response to naturally occurring trains of action potentials. Based on a physiologically motivated computational model of the rat CA3 presynaptic terminal, we show how unreliability and short-term dynamics of vesicular release work together to regulate the trade-off of information transfer versus energy use. We propose that individual CA3-CA1 synapses are designed to operate near the maximum possible capacity of information transmission in an efficient manner. Experimental measurements reveal a wide range of vesicular release probabilities at hippocampal synapses, which may be a necessary consequence of long-term plasticity and homeostatic mechanisms that manifest as presynaptic modifications of the release probability. We show that the timescales and magnitude of short-term plasticity (STP) render synaptic information transfer nearly independent of differences in release probability. Thus, individual synapses transmit optimally while maintaining a heterogeneous distribution of presynaptic strengths indicative of synaptically-encoded memory representations. Our results support the view that organizing principles that are evident on higher scales of neural organization percolate down to the design of an individual synapse.

The effect of inhibition on rate code efficiency indicators

In this paper we investigate the rate coding capabilities of neurons whose input signal are alterations of the base state of balanced inhibitory and excitatory synaptic currents. We consider different regimes of excitation-inhibition relationship and an established conductance-based leaky integrator model with adaptive threshold and parameter sets recreating biologically relevant spiking regimes. We find that given mean post-synaptic firing rate, counter-intuitively, increased ratio of inhibition to excitation generally leads to higher signal to noise ratio (SNR). On the other hand, the inhibitory input significantly reduces the dynamic coding range of the neuron. We quantify the joint effect of SNR and dynamic coding range by computing the metabolic efficiency-the maximal amount of information per one ATP molecule expended (in bits/ATP). Moreover, by calculating the metabolic efficiency we are able to predict the shapes of the post-synaptic firing rate histograms that may be tested on experimental data. Likewise, optimal stimulus input distributions are predicted, however, we show that the optimum can essentially be reached with a broad range of input distributions. Finally, we examine which parameters of the used neuronal model are the most important for the metabolically efficient information transfer.

Energy-efficient information transfer at thalamocortical synapses

We have previously shown that the physiological size of postsynaptic currents maximises energy efficiency rather than information transfer across the retinothalamic relay synapse. Here, we investigate information transmission and postsynaptic energy use at the next synapse along the visual pathway: from relay neurons in the thalamus to spiny stellate cells in layer 4 of the primary visual cortex (L4SS). Using both multicompartment Hodgkin-Huxley-type simulations and electrophysiological recordings in rodent brain slices, we find that increasing or decreasing the postsynaptic conductance of the set of thalamocortical inputs to one L4SS cell decreases the energy efficiency of information transmission from a single thalamocortical input. This result is obtained in the presence of random background input to the L4SS cell from excitatory and inhibitory corticocortical connections, which were simulated (both excitatory and inhibitory) or injected experimentally using dynamic-clamp (excitatory only). Thus, energy efficiency is not a unique property of strong relay synapses: even at the relatively weak thalamocortical synapse, each of which contributes minimally to the output firing of the L4SS cell, evolutionarily-selected postsynaptic properties appear to maximise the information transmitted per energy used.

Compared to other organs, the brain consumes a vast amount of energy for its size. Most of this energy is used to power the electrical and chemical processes that support neural computation. As the energy supply to the brain is limited, it follows that this computation should be energetically efficient. Previously, we showed that this is indeed the case for transmission of information between cells at synapses. Synapses transferring information from the retina to the brain do not maximise information transmission—some information is lost and does not reach the visual cortex. Instead, these synapses maximise the information transmitted per energy used. Here, we demonstrate that this principle of energetic efficiency also holds at the next synapse in the visual pathway, the thalamocortical synapse. This synapse is weaker and competes with hundreds of other inputs to influence the output firing of the next cell. Using detailed simulations of cortical neurons, and electrophysiological recordings in rodent brain slices, we found that this relatively weak synapse also does not maximise information transmission. Instead, it maximises the amount of information transmitted per energy used. This suggests that energy efficiency at synapses could be a common design principle in the brain.

Information processing in the LGN: a comparison of neural codes and cell types

To understand how anatomy and physiology allow an organism to perform its function, it is important to know how information that is transmitted by spikes in the brain is received and encoded. A natural question is whether the spike rate alone encodes the information about a stimulus (rate code), or additional information is contained in the temporal pattern of the spikes (temporal code). Here we address this question using data from the cat Lateral Geniculate Nucleus (LGN), which is the visual portion of the thalamus, through which visual information from the retina is communicated to the visual cortex. We analyzed the responses of LGN neurons to spatially homogeneous spots of various sizes with temporally random luminance modulation. We compared the Firing Rate with the Shannon Information Transmission Rate , which quantifies the information contained in the temporal relationships between spikes. We found that the behavior of these two rates can differ quantitatively. This suggests that the energy used for spiking does not translate directly into the information to be transmitted. We also compared Firing Rates with Information Rates for X-ON and X-OFF cells. We found that, for X-ON cells the Firing Rate and Information Rate often behave in a completely different way, while for X-OFF cells these rates are much more highly correlated. Our results suggest that for X-ON cells a more efficient "temporal code" is employed, while for X-OFF cells a straightforward "rate code" is used, which is more reliable and is correlated with energy consumption.

Short-term synaptic depression can increase the rate of information transfer at a release site

The release of neurotransmitters from synapses obeys complex and stochastic dynamics. Depending on the recent history of synaptic activation, many synapses depress the probability of releasing more neurotransmitter, which is known as synaptic depression. Our understanding of how synaptic depression affects the information efficacy, however, is limited. Here we propose a mathematically tractable model of both synchronous spike-evoked release and asynchronous release that permits us to quantify the information conveyed by a synapse. The model transits between discrete states of a communication channel, with the present state depending on many past time steps, emulating the gradual depression and exponential recovery of the synapse. Asynchronous and spontaneous releases play a critical role in shaping the information efficacy of the synapse. We prove that depression can enhance both the information rate and the information rate per unit energy expended, provided that synchronous spike-evoked release depresses less (or recovers faster) than asynchronous release. Furthermore, we explore the theoretical implications of short-term synaptic depression adapting on longer time scales, as part of the phenomenon of metaplasticity. In particular, we show that a synapse can adjust its energy expenditure by changing the dynamics of short-term synaptic depression without affecting the net information conveyed by each successful release. Moreover, the optimal input spike rate is independent of the amplitude or time constant of synaptic depression. We analyze the information efficacy of three types of synapses for which the short-term dynamics of both synchronous and asynchronous release have been experimentally measured. In hippocampal autaptic synapses, the persistence of asynchronous release during depression cannot compensate for the reduction of synchronous release, so that the rate of information transmission declines with synaptic depression. In the calyx of Held, the information rate per release remains constant despite large variations in the measured asynchronous release rate. Lastly, we show that dopamine, by controlling asynchronous release in corticostriatal synapses, increases the synaptic information efficacy in nucleus accumbens.

Fatigue is an intrinsic property of living systems and synapses are no exception. Synaptic depression reduces the ability of synapses to release vesicles in response to an incoming action potential. Whether synaptic depression simply reflects the exhaustion of neuronal resources or whether it serves some additional function is still an open question. We ask how synaptic depression modulates the information transfer between neurons by keeping the synapse in an appropriate operating range. Using a tractable mathematical model for synaptic depression of both synchronous spike-evoked and asynchronous release of neurotransmitter, we derive a closed-form expression for the mutual information rate. Depression, it turns out, can both enhance or impair information transfer, depending on the relative level of depression for synchronous spike-evoked and asynchronous releases. We also study the compromise a synapse makes between its energy consumption and the rate of information transmission. Interestingly, we show that synaptic depression can regulate energy use without affecting the information (measured in bits) per synaptic release. By applying our mathematical framework to experimentally measured synapses, we show that some synapses can compensate for intrinsic variability in asynchronous release rates; moreover, we show how neuromodulators such as dopamine act to improve the information transmission rate.

Function and energy consumption constrain neuronal biophysics in a canonical computation: Coincidence detection

Neural morphology and membrane properties vary greatly between cell types in the nervous system. The computations and local circuit connectivity that neurons support are thought to be the key factors constraining the cells' biophysical properties. Nevertheless, additional constraints can be expected to further shape neuronal design. Here, we focus on a particularly energy-intense system (as indicated by metabolic markers): principal neurons in the medial superior olive (MSO) nucleus of the auditory brainstem. Based on a modeling approach, we show that a trade-off between the level of performance of a functionally relevant computation and energy consumption predicts optimal ranges for cell morphology and membrane properties. The biophysical parameters appear most strongly constrained by functional needs, while energy use is minimized as long as function can be maintained. The key factors that determine model performance and energy consumption are 1) the saturation of the synaptic conductance input and 2) the temporal resolution of the postsynaptic signals as they reach the soma, which is largely determined by active membrane properties. MSO cells seem to operate close to pareto optimality, i.e., the trade-off boundary between performance and energy consumption that is formed by the set of optimal models. Good performance for drastically lower costs could in theory be achieved by small neurons without dendrites, as seen in the avian auditory system, pointing to additional constraints for mammalian MSO cells, including their circuit connectivity.

A Process for Digitizing and Simulating Biologically Realistic Oligocellular Networks Demonstrated for the Neuro-Glio-Vascular Ensemble

One will not understand the brain without an integrated exploration of structure and function, these attributes being two sides of the same coin: together they form the currency of biological computation. Accordingly, biologically realistic models require the re-creation of the architecture of the cellular components in which biochemical reactions are contained. We describe here a process of reconstructing a functional oligocellular assembly that is responsible for energy supply management in the brain and creating a computational model of the associated biochemical and biophysical processes. The reactions that underwrite thought are both constrained by and take advantage of brain morphologies pertaining to neurons, astrocytes and the blood vessels that deliver oxygen, glucose and other nutrients. Each component of this neuro-glio-vasculature ensemble (NGV) carries-out delegated tasks, as the dynamics of this system provide for each cell-type its own energy requirements while including mechanisms that allow cooperative energy transfers. Our process for recreating the ultrastructure of cellular components and modeling the reactions that describe energy flow uses an amalgam of state-of the-art techniques, including digital reconstructions of electron micrographs, advanced data analysis tools, computational simulations and in silico visualization software. While we demonstrate this process with the NGV, it is equally well adapted to any cellular system for integrating multimodal cellular data in a coherent framework.

Responsive Neural Activities in the Primary Visual Cortex of Retina-Degenerated Rats

To study the responsive neural activities in the primary visual cortex (V1) of retinal degeneration (RD) models, experiments involving the wild-type (WT) and RD rats were conducted. The neural responses in the V1 were recorded extracellularly, while a visual stimulus with varied light intensity was given to the subjects. First, the firing rate and its relationship with light intensity were compared between the WT and RD groups. Second, the mutual information (MI) between the visual stimulus and neural response was determined for every isolated unit to quantify the amount and efficiency of information transmission in the V1 for both the control and experimental groups. Third, the local field potential (LFP) signal was characterized and its power used to compute the MI and further evaluate the function change in the RD model regarding information transmission. Analysis of spiking activity showed that the RD group exhibited a relatively decreased firing rate, information amount and efficiency compared with the control group. However, the information transmission performance of the RD model was similar to that of the WT group in the context of LFP activity. Therefore, for the RD rats, the early stage of the visual system was impaired, while the later stage of the visual system, V1, was able to capture the information about the visual stimulus, especially at the population level. Thus, this pathway could be used to restore visual ability, such as by visual prostheses.

Sum Rate of MISO Neuro-Spike Communication Channel With Constant Spiking Threshold

Communication among neurons, known as neuro-spike communication, is the most promising technique for realization of a bio-inspired nanoscale communication paradigm to achieve biocompatible nanonetworks. In neuro-spike communication, the information, encoded into spike trains, is communicated to various brain regions through neuronal network. An output neuron needs to receive signal from multiple input neurons to generate a spike. Hence, in this paper, we aim to quantify the information transmitted through the multiple-input single-output (MISO) neuro-spike communication channel by considering models for axonal propagation, synaptic transmission, and spike generation. Moreover, the spike generation and propagation in each neuron requires opening and closing of numerous ionic channels on the cell membrane, which consumes considerable amount of ATP molecules called metabolic energy. Thus, we evaluate how applying a constraint on available metabolic energy affects the maximum achievable mutual information of this system. To this aim, we derive a closed form equation for the sum rate of the MISO neuro-spike communication channel and analyze it under the metabolic cost constraints. Finally, we discuss the impacts of changes in number of pre-synaptic neurons on the achievable rate and quantify the tradeoff between maximum achievable sum rate and the consumed metabolic energy.

Coordinate invariance as a fundamental constraint on the form of stimulus-specific information measures

The value of Shannon's mutual information is commonly used to describe the total amount of information that the neural code transfers between the ensemble of stimuli and the ensemble of neural responses. In addition, it is often desirable to know which features of the stimulus or response are most informative. The literature offers several different decompositions of the mutual information into its stimulus or response-specific components, such as the specific surprise or the uncertainty reduction, but the number of mutually distinct measures is in fact infinite. We resolve this ambiguity by requiring the specific information measures to be invariant under invertible coordinate transformations of the stimulus and the response ensembles. We prove that the Kullback-Leibler divergence is then the only suitable measure of the specific information. On a more general level, we discuss the necessity and the fundamental aspects of the coordinate invariance as a selection principle. We believe that our results will encourage further research into invariant statistical methods for the analysis of neural coding.

The Energy Landscape of Neurophysiological Activity Implicit in Brain Network Structure

A critical mystery in neuroscience lies in determining how anatomical structure impacts the complex functional dynamics of the brain. How does large-scale brain circuitry constrain states of neuronal activity and transitions between those states? We address these questions using a maximum entropy model of brain dynamics informed by white matter tractography. We demonstrate that the most probable brain states - characterized by minimal energy - display common activation profiles across brain areas: local spatially-contiguous sets of brain regions reminiscent of cognitive systems are co-activated frequently. The predicted activation rate of these systems is highly correlated with the observed activation rate measured in a separate resting state fMRI data set, validating the utility of the maximum entropy model in describing neurophysiological dynamics. This approach also offers a formal notion of the energy of activity within a system, and the energy of activity shared between systems. We observe that within- and between-system energies cleanly separate cognitive systems into distinct categories, optimized for differential contributions to integrated versus segregated function. These results support the notion that energetic and structural constraints circumscribe brain dynamics, offering insights into the roles that cognitive systems play in driving whole-brain activation patterns.

Information transmission in the primary visual cortex of retinal degenerated rats

To study the information transmission in the primary visual cortex (V1) of retinal degenerated (RD) models, wild type (WT) and RD rats were used in the experiments. The neural response in V1 was recorded extracellularly while the flicker with varied intensity levels was given as the visual stimulus. The mutual information (MI) and normalized mutual information (NMI) were determined for every isolated neuron, in order to quantify the amount and efficiency of information transmission in V1 of both control and experimental groups. The results showed that, on one hand, the RD group manifested relatively decreased information transmission amount and efficiency, comparing to the control group; On the other hand, it also implied that even for the RD rat, whose early stage of visual system was impaired, the later parts of visual system, especially the primary visual cortex, were still able to capture the information on visual stimulation, thus they can be utilized for restoring the visual ability, for example, via the visual prosthesis. In addition, it certainly requires more experiments for testifying and extending those results and implications.

Macroglia-derived thrombospondin 2 regulates alterations of presynaptic proteins of retinal neurons following elevated hydrostatic pressure

Many studies on retinal injury and repair following elevated intraocular pressure suggest that the survival ratio of retinal neurons has been improved by various measures. However, the visual function recovery is far lower than expected. The homeostasis of retinal synapses in the visual signal pathway is the key structural basis for the delivery of visual signals. Our previous studies found that complicated changes in the synaptic structure between retinal neurons occurred much earlier than obvious degeneration of retinal ganglion cells in rat retinae. The lack of consideration of these earlier retinal synaptic changes in the rescue strategy may be partly responsible for the limited visual function recovery with the types of protective methods for retinal neurons used following elevated intraocular pressure. Thus, research on the modulatory mechanisms of the synaptic changes after elevated intraocular pressure injury may give new light to visual function rescue. In this study, we found that thrombospondin 2, an important regulator of synaptogenesis in central nervous system development, was distributed in retinal macroglia cells, and its receptor α2δ-1 was in retinal neurons. Cell cultures including mixed retinal macroglia cells/neuron cultures and retinal neuron cultures were exposed to elevated hydrostatic pressure for 2 h. The expression levels of glial fibrillary acidic protein (the marker of activated macroglia cells), thrombospondin 2, α2δ-1 and presynaptic proteins were increased following elevated hydrostatic pressure in mixed cultures, but the expression levels of postsynaptic proteins were not changed. SiRNA targeting thrombospondin 2 could decrease the upregulation of presynaptic proteins induced by the elevated hydrostatic pressure. However, in retinal neuron cultures, elevated hydrostatic pressure did not affect the expression of presynaptic or postsynaptic proteins. Rather, the retinal neuron cultures with added recombinant thrombospondin 2 protein upregulated the level of presynaptic proteins. Finally, gabapentin decreased the expression of presynaptic proteins in mixed cultures by blocking the interaction of thrombospondin 2 and α2δ-1. Taken together, these results indicate that activated macroglia cells may participate in alterations of presynaptic proteins of retinal neurons following elevated hydrostatic pressure, and macroglia-derived thrombospondin 2 may modulate these changes via binding to its neuronal receptor α2δ-1.