Approximate invariance of metabolic energy per synapse during development in mammalian brains

Cooperativity, Information Gain, and Energy Cost During Early LTP in Dendritic Spines

We investigate a mutual relationship between information and energy during the early phase of LTP induction and maintenance in a large-scale system of mutually coupled dendritic spines, with discrete internal states and probabilistic dynamics, within the framework of nonequilibrium stochastic thermodynamics. In order to analyze this computationally intractable stochastic multidimensional system, we introduce a pair approximation, which allows us to reduce the spine dynamics into a lower-dimensional manageable system of closed equations. We found that the rates of information gain and energy attain their maximal values during an initial period of LTP (i.e., during stimulation), and after that, they recover to their baseline low values, as opposed to a memory trace that lasts much longer. This suggests that the learning phase is much more energy demanding than the memory phase. We show that positive correlations between neighboring spines increase both a duration of memory trace and energy cost during LTP, but the memory time per invested energy increases dramatically for very strong, positive synaptic cooperativity, suggesting a beneficial role of synaptic clustering on memory duration. In contrast, information gain after LTP is the largest for negative correlations, and energy efficiency of that information generally declines with increasing synaptic cooperativity. We also find that dendritic spines can use sparse representations for encoding long-term information, as both energetic and structural efficiencies of retained information and its lifetime exhibit maxima for low fractions of stimulated synapses during LTP. Moreover, we find that such efficiencies drop significantly with increasing the number of spines. In general, our stochastic thermodynamics approach provides a unifying framework for studying, from first principles, information encoding, and its energy cost during learning and memory in stochastic systems of interacting synapses.

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.

Information encoded in volumes and areas of dendritic spines is nearly maximal across mammalian brains

Many experiments suggest that long-term information associated with neuronal memory resides collectively in dendritic spines. However, spines can have a limited size due to metabolic and neuroanatomical constraints, which should effectively limit the amount of encoded information in excitatory synapses. This study investigates how much information can be stored in the population of sizes of dendritic spines, and whether it is optimal in any sense. It is shown here, using empirical data for several mammalian brains across different regions and physiological conditions, that dendritic spines nearly maximize entropy contained in their volumes and surface areas for a given mean size in cortical and hippocampal regions. Although both short- and heavy-tailed fitting distributions approach [Formula: see text] of maximal entropy in the majority of cases, the best maximization is obtained primarily for short-tailed gamma distribution. We find that most empirical ratios of standard deviation to mean for spine volumes and areas are in the range [Formula: see text], which is close to the theoretical optimal ratios coming from entropy maximization for gamma and lognormal distributions. On average, the highest entropy is contained in spine length ([Formula: see text] bits per spine), and the lowest in spine volume and area ([Formula: see text] bits), although the latter two are closer to optimality. In contrast, we find that entropy density (entropy per spine size) is always suboptimal. Our results suggest that spine sizes are almost as random as possible given the constraint on their size, and moreover the general principle of entropy maximization is applicable and potentially useful to information and memory storing in the population of cortical and hippocampal excitatory synapses, and to predicting their morphological properties.

Path-dependent dynamics induced by rewiring networks of inertial oscillators

In networks of coupled oscillators, it is of interest to understand how interaction topology affects synchronization. Many studies have gained key insights into this question by studying the classic Kuramoto oscillator model on static networks. However, new questions arise when the network structure is time varying or when the oscillator system is multistable, the latter of which can occur when an inertial term is added to the Kuramoto model. While the consequences of evolving topology and multistability on collective behavior have been examined separately, real-world systems such as gene regulatory networks and the brain may exhibit these properties simultaneously. It is thus relevant to ask how time-varying network connectivity impacts synchronization in systems that can exhibit multistability. To address this question, we study how the dynamics of coupled Kuramoto oscillators with inertia are affected when the topology of the underlying network changes in time. We show that hysteretic synchronization behavior in networks of coupled inertial oscillators can be driven by changes in connection topology alone. Moreover, we find that certain fixed-density rewiring schemes induce significant changes to the level of global synchrony that remain even after the network returns to its initial configuration, and we show that these changes are robust to a wide range of network perturbations. Our findings highlight that the specific progression of network topology over time, in addition to its initial or final static structure, can play a considerable role in modulating the collective behavior of systems evolving on complex networks.

In vivo synaptic density relates to glucose metabolism at rest in healthy subjects, but is strongly modulated by regional differences

Preclinical and postmortem studies have suggested that regional synaptic density and glucose consumption (CMRGlc) are strongly related. However, the relation between synaptic density and cerebral glucose metabolism in the human brain has not directly been assessed in vivo. Using [¹¹C]UCB-J binding to synaptic vesicle glycoprotein 2 A (SV2A) as indicator for synaptic density and [¹⁸F]FDG for measuring cerebral glucose consumption, we studied twenty healthy female subjects (age 29.6 ± 9.9 yrs) who underwent a single-day dual-tracer protocol (GE Signa PET-MR). Global measures of absolute and relative CMRGlc and specific binding of [¹¹C]UCB-J were indeed highly significantly correlated (r > 0.47, p < 0.001). However, regional differences in relative [¹⁸F]FDG and [¹¹C]UCB-J uptake were observed, with up to 19% higher [¹¹C]UCB-J uptake in the medial temporal lobe (MTL) and up to 17% higher glucose metabolism in frontal and motor-related areas and thalamus. This pattern has a considerable overlap with the brain regions showing different levels of aerobic glycolysis. Regionally varying energy demands of inhibitory and excitatory synapses at rest may also contribute to this difference. Being unaffected by astroglial and/or microglial energy demands, changes in synaptic density in the MTL may therefore be more sensitive to early detection of pathological conditions compared to changes in glucose metabolism.

Energetics of stochastic BCM type synaptic plasticity and storing of accurate information

Excitatory synaptic signaling in cortical circuits is thought to be metabolically expensive. Two fundamental brain functions, learning and memory, are associated with long-term synaptic plasticity, but we know very little about energetics of these slow biophysical processes. This study investigates the energy requirement of information storing in plastic synapses for an extended version of BCM plasticity with a decay term, stochastic noise, and nonlinear dependence of neuron’s firing rate on synaptic current (adaptation). It is shown that synaptic weights in this model exhibit bistability. In order to analyze the system analytically, it is reduced to a simple dynamic mean-field for a population averaged plastic synaptic current. Next, using the concepts of nonequilibrium thermodynamics, we derive the energy rate (entropy production rate) for plastic synapses and a corresponding Fisher information for coding presynaptic input. That energy, which is of chemical origin, is primarily used for battling fluctuations in the synaptic weights and presynaptic firing rates, and it increases steeply with synaptic weights, and more uniformly though nonlinearly with presynaptic firing. At the onset of synaptic bistability, Fisher information and memory lifetime both increase sharply, by a few orders of magnitude, but the plasticity energy rate changes only mildly. This implies that a huge gain in the precision of stored information does not have to cost large amounts of metabolic energy, which suggests that synaptic information is not directly limited by energy consumption. Interestingly, for very weak synaptic noise, such a limit on synaptic coding accuracy is imposed instead by a derivative of the plasticity energy rate with respect to the mean presynaptic firing, and this relationship has a general character that is independent of the plasticity type. An estimate for primate neocortex reveals that a relative metabolic cost of BCM type synaptic plasticity, as a fraction of neuronal cost related to fast synaptic transmission and spiking, can vary from negligible to substantial, depending on the synaptic noise level and presynaptic firing.

Invariant Synapse Density and Neuronal Connectivity Scaling in Primate Neocortical Evolution

Synapses are involved in the communication of information from one neuron to another. However, a systematic analysis of synapse density in the neocortex from a diversity of species is lacking, limiting what can be understood about the evolution of this fundamental aspect of brain structure. To address this, we quantified synapse density in supragranular layers II-III and infragranular layers V-VI from primary visual cortex and inferior temporal cortex in a sample of 25 species of primates, including humans. We found that synapse densities were relatively constant across these levels of the cortical visual processing hierarchy and did not significantly differ with brain mass, varying by only 1.9-fold across species. We also found that neuron densities decreased in relation to brain enlargement. Consequently, these data show that the number of synapses per neuron significantly rises as a function of brain expansion in these neocortical areas of primates. Humans displayed the highest number of synapses per neuron, but these values were generally within expectations based on brain size. The metabolic and biophysical constraints that regulate uniformity of synapse density, therefore, likely underlie a key principle of neuronal connectivity scaling in primate neocortical evolution.

Metabolic constraints on synaptic learning and memory

Dendritic spines, the carriers of long-term memory, occupy a small fraction of cortical space, and yet they are the major consumers of brain metabolic energy. What fraction of this energy goes for synaptic plasticity, correlated with learning and memory? It is estimated here based on neurophysiological and proteomic data for rat brain that, depending on the level of protein phosphorylation, the energy cost of synaptic plasticity constitutes a small fraction of the energy used for fast excitatory synaptic transmission, typically 4.0-11.2%. Next, this study analyzes a metabolic cost of new learning and its memory trace in relation to the cost of prior memories, using a class of cascade models of synaptic plasticity. It is argued that these models must contain bidirectional cyclic motifs, related to protein phosphorylation, to be compatible with basic thermodynamic principles. For most investigated parameters longer memories generally require proportionally more energy to store. The exceptions are the parameters controlling the speed of molecular transitions (e.g., ATP-driven phosphorylation rate), for which memory lifetime per invested energy can increase progressively for longer memories. Furthermore, in general, a memory trace decouples dynamically from a corresponding synaptic metabolic rate such that the energy expended on new learning and its memory trace constitutes in most cases only a small fraction of the baseline energy associated with prior memories. Taken together, these empirical and theoretical results suggest a metabolic efficiency of synaptically stored information.NEW & NOTEWORTHY Learning and memory involve a sequence of molecular events in dendritic spines called synaptic plasticity. These events are physical in nature and require energy, which has to be supplied by ATP molecules. However, our knowledge of the energetics of these processes is very poor. This study estimates the empirical energy cost of synaptic plasticity and considers theoretically a metabolic rate of learning and its memory trace in a class of cascade models of synaptic plasticity.

Highly Heterogeneous Excitatory Connections Require Less Amount of Noise to Sustain Firing Activities in Cortical Networks

Cortical networks both in vivo and in vitro sustain asynchronous irregular firings with extremely low frequency. To realize such self-sustained activity in neural network models, balance between excitatory and inhibitory activities is known to be one of the keys. In addition, recent theoretical studies have revealed that another feature commonly observed in cortical networks, i.e., sparse but strong connections and dense weak connections, plays an essential role. The previous studies, however, have not thoroughly considered the cooperative dynamics between a network of such heterogeneous synaptic connections and intrinsic noise. The noise stimuli, representing inherent nature of the neuronal activities, e.g., variability of presynaptic discharges, should be also of significant importance for sustaining the irregular firings in cortical networks. Here, we numerically demonstrate that highly heterogeneous distribution, typically a lognormal type, of excitatory-to-excitatory connections, reduces the amount of noise required to sustain the network firing activities. In the sense that noise consumes an energy resource, the heterogeneous network receiving less amount of noise stimuli is considered to realize an efficient dynamics in cortex. A noise-driven network of bi-modally distributed synapses further shows that many weak and a few very strong synapses are the key feature of the synaptic heterogeneity, supporting the network firing activity.

Evaluating the gray and white matter energy budgets of human brain function

The insatiable appetite for energy to support human brain function is mainly supplied by glucose oxidation (CMR_glc(ox)). But how much energy is consumed for signaling and nonsignaling processes in gray/white matter is highly debated. We examined this issue by combining metabolic measurements of gray/white matter and a theoretical calculation of bottom-up energy budget using biophysical properties of neuronal/glial cells in conjunction with species-exclusive electrophysiological and morphological data. We calculated a CMR_glc(ox)-derived budget and confirmed it with experimental results measured by PET, autoradiography, ¹³C-MRS, and electrophysiology. Several conserved principles were observed regarding the energy costs for brain's signaling and nonsignaling components in both human and rat. The awake resting cortical signaling processes and mass-dependent nonsignaling processes, respectively, demand ∼70% and ∼30% of CMR_glc(ox). Inhibitory neurons and glia need 15-20% of CMR_glc(ox), with the rest demanded by excitatory neurons. Nonsignaling demands dominate in white matter, in near opposite contrast to gray matter demands. Comparison between ¹³C-MRS data and calculations suggests ∼1.2 Hz glutamatergic signaling rate in the awake human cortex, which is ∼4 times lower than signaling in the rat cortex. Top-down validated bottom-up budgets could allow computation of anatomy-based CMR_glc(ox) maps and accurate cellular level interpretation of brain metabolic imaging.

Energy-efficient neural information processing in individual neurons and neuronal networks

Brains are composed of networks of an enormous number of neurons interconnected with synapses. Neural information is carried by the electrical signals within neurons and the chemical signals among neurons. Generating these electrical and chemical signals is metabolically expensive. The fundamental issue raised here is whether brains have evolved efficient ways of developing an energy-efficient neural code from the molecular level to the circuit level. Here, we summarize the factors and biophysical mechanisms that could contribute to the energy-efficient neural code for processing input signals. The factors range from ion channel kinetics, body temperature, axonal propagation of action potentials, low-probability release of synaptic neurotransmitters, optimal input and noise, the size of neurons and neuronal clusters, excitation/inhibition balance, coding strategy, cortical wiring, and the organization of functional connectivity. Both experimental and computational evidence suggests that neural systems may use these factors to maximize the efficiency of energy consumption in processing neural signals. Studies indicate that efficient energy utilization may be universal in neuronal systems as an evolutionary consequence of the pressure of limited energy. As a result, neuronal connections may be wired in a highly economical manner to lower energy costs and space. Individual neurons within a network may encode independent stimulus components to allow a minimal number of neurons to represent whole stimulus characteristics efficiently. This basic principle may fundamentally change our view of how billions of neurons organize themselves into complex circuits to operate and generate the most powerful intelligent cognition in nature. © 2017 Wiley Periodicals, Inc.

Cortical Composition Hierarchy Driven by Spine Proportion Economical Maximization or Wire Volume Minimization

The structure and quantitative composition of the cerebral cortex are interrelated with its computational capacity. Empirical data analyzed here indicate a certain hierarchy in local cortical composition. Specifically, neural wire, i.e., axons and dendrites take each about 1/3 of cortical space, spines and glia/astrocytes occupy each about (1/3)², and capillaries around (1/3)⁴. Moreover, data analysis across species reveals that these fractions are roughly brain size independent, which suggests that they could be in some sense optimal and thus important for brain function. Is there any principle that sets them in this invariant way? This study first builds a model of local circuit in which neural wire, spines, astrocytes, and capillaries are mutually coupled elements and are treated within a single mathematical framework. Next, various forms of wire minimization rule (wire length, surface area, volume, or conduction delays) are analyzed, of which, only minimization of wire volume provides realistic results that are very close to the empirical cortical fractions. As an alternative, a new principle called “spine economy maximization” is proposed and investigated, which is associated with maximization of spine proportion in the cortex per spine size that yields equally good but more robust results. Additionally, a combination of wire cost and spine economy notions is considered as a meta-principle, and it is found that this proposition gives only marginally better results than either pure wire volume minimization or pure spine economy maximization, but only if spine economy component dominates. However, such a combined meta-principle yields much better results than the constraints related solely to minimization of wire length, wire surface area, and conduction delays. Interestingly, the type of spine size distribution also plays a role, and better agreement with the data is achieved for distributions with long tails. In sum, these results suggest that for the efficiency of local circuits wire volume may be more primary variable than wire length or temporal delays, and moreover, the new spine economy principle may be important for brain evolutionary design in a broader context.

Cerebral cortex is an outer layer of the brain in mammals, and it plays a critical part in various cognitive processes such as learning, memory, attention, language, and consciousness. The cerebral cortex contains a number of neuroanatomical parameters whose values are essentially conserved across species and brain sizes, which suggests that these particular parameters are somehow important for brain efficient functioning. This study shows that the fractional volumes of five major cortical components both neuronal and non-neuronal (axons, dendrites, spines, glia/astrocytes, capillaries) are also approximately conserved across mammals, and neural wire (axons and dendrites) occupies the most of cortical space. Moreover, the fractional volumes form a special hierarchy of dependencies, being approximately equal to integer powers of 1/3. Is there any evolutionary principle of cortical organization that would explain these properties? This study finds that there are two different theoretical principles that can provide answers: one standard related to minimization of neural wire fractional volume, and a new proposition associated with economical maximization of spine content. However, the latter principle produces more robust results, which suggests that spine economical maximization is potentially an alternative to the more common “wire minimization” in explaining the cortical layout. Therefore, the current study can become an important contribution to our understanding (or debating) of the main factors influencing the evolution of local cortical circuits in the brain.

Constancy and trade-offs in the neuroanatomical and metabolic design of the cerebral cortex

Mammalian brains span about four orders of magnitude in cortical volume and have to operate in different environments that require diverse behavioral skills. Despite these geometric and behavioral diversities, the examination of cerebral cortex across species reveals that it contains a substantial number of conserved characteristics that are associated with neuroanatomy and metabolism, i.e., with neuronal connectivity and function. Some of these cortical constants or invariants have been known for a long time but not sufficiently appreciated, and others were only recently discovered. The focus of this review is to present the cortical invariants and discuss their role in the efficient information processing. Global conservation in neuroanatomy and metabolism, as well as their correlated regional and developmental variability suggest that these two parallel systems are mutually coupled. It is argued that energetic constraint on cortical organization can be strong if cerebral blood supplied is either below or above a certain level, and it is rather soft otherwise. Moreover, because maximization or minimization of parameters associated with cortical connectivity, function and cost often leads to conflicts in design, it is argued that the architecture of the cerebral cortex is a result of structural and functional compromises.