Scaling of Brain Metabolism with a Fixed Energy Budget per Neuron: Implications for Neuronal Activity, Plasticity and Evolution

It is usually considered that larger brains have larger neurons, which consume more energy individually, and are therefore accompanied by a larger number of glial cells per neuron. These notions, however, have never been tested. Based on glucose and oxygen metabolic rates in awake animals and their recently determined numbers of neurons, here I show that, contrary to the expected, the estimated glucose use per neuron is remarkably constant, varying only by 40% across the six species of rodents and primates (including humans). The estimated average glucose use per neuron does not correlate with neuronal density in any structure. This suggests that the energy budget of the whole brain per neuron is fixed across species and brain sizes, such that total glucose use by the brain as a whole, by the cerebral cortex and also by the cerebellum alone are linear functions of the number of neurons in the structures across the species (although the average glucose consumption per neuron is at least 10× higher in the cerebral cortex than in the cerebellum). These results indicate that the apparently remarkable use in humans of 20% of the whole body energy budget by a brain that represents only 2% of body mass is explained simply by its large number of neurons. Because synaptic activity is considered the major determinant of metabolic cost, a conserved energy budget per neuron has several profound implications for synaptic homeostasis and the regulation of firing rates, synaptic plasticity, brain imaging, pathologies, and for brain scaling in evolution

Co-evolution of cerebral and cerebellar expansion in cetaceans.

Cetaceans possess brains that rank among the largest to have ever evolved, either in terms of absolute mass or relative to body size. Cetaceans have evolved these huge brains under relatively unique environmental conditions, making them a fascinating case study to investigate the constraints and selection pressures that shape how brains evolve. Indeed, cetaceans have some unusual neuroanatomical features, including a thin but highly folded cerebrum with low cortical neuron density, as well as many structural adaptations associated with acoustic communication. Previous reports also suggest that at least some cetaceans have an expanded cerebellum, a brain structure with wide-ranging functions in adaptive filtering of sensory information, the control of motor actions, and cognition. Here, we report that, relative to the size of the rest of the brain, both the cerebrum and cerebellum are dramatically enlarged in cetaceans and show evidence of co-evolution, a pattern of brain evolution that is convergent with primates. However, we also highlight several branches where cortico-cerebellar co-evolution may be partially decoupled, suggesting these structures can respond to independent selection pressures. Across cetaceans, we find no evidence of a simple linear relationship between either cerebrum and cerebellum size and the complexity of social ecology or acoustic communication, but do find evidence that their expansion may be associated with dietary breadth. In addition, our results suggest that major increases in both cerebrum and cerebellum size occurred early in cetacean evolution, prior to the origin of the major extant clades, and predate the evolution of echolocation

Fuchs versus Painlev\'e

We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e VI. We then show that the polynomiality of the expressions of the correlation functions (and form factors) in terms of the complete elliptic integral of the first and second kind, $K$ and $E$, is a straight consequence of the fact that the differential operators corresponding to the entries of Toeplitz-like determinants, are equivalent to the second order operator $L_E$ which has $E$ as solution (or, for off-diagonal correlations to the direct sum of $L_E$ and $d/dt$). We show that this can be generalized, mutatis mutandis, to the anisotropic Ising model. The singled-out second order linear differential operator $L_E$ being replaced by an isomonodromic system of two third-order linear partial differential operators associated with $\Pi_1$, the Jacobi's form of the complete elliptic integral of the third kind (or equivalently two second order linear partial differential operators associated with Appell functions, where one of these operators can be seen as a deformation of $L_E$). We finally explore the generalizations, to the anisotropic Ising models, of the links we made, in two previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and elliptic curves. In particular the elliptic representation of Painlev\'e VI has to be generalized to an ``Appellian'' representation of Garnier systems.Comment: Dedicated to the : Special issue on Symmetries and Integrability of Difference Equations, SIDE VII meeting held in Melbourne during July 200

Global and regional brain metabolic scaling and its functional consequences

Background: Information processing in the brain requires large amounts of metabolic energy, the spatial distribution of which is highly heterogeneous reflecting complex activity patterns in the mammalian brain. Results: Here, it is found based on empirical data that, despite this heterogeneity, the volume-specific cerebral glucose metabolic rate of many different brain structures scales with brain volume with almost the same exponent around -0.15. The exception is white matter, the metabolism of which seems to scale with a standard specific exponent -1/4. The scaling exponents for the total oxygen and glucose consumptions in the brain in relation to its volume are identical and equal to $0.86\pm 0.03$, which is significantly larger than the exponents 3/4 and 2/3 suggested for whole body basal metabolism on body mass. Conclusions: These findings show explicitly that in mammals (i) volume-specific scaling exponents of the cerebral energy expenditure in different brain parts are approximately constant (except brain stem structures), and (ii) the total cerebral metabolic exponent against brain volume is greater than the much-cited Kleiber's 3/4 exponent. The neurophysiological factors that might account for the regional uniformity of the exponents and for the excessive scaling of the total brain metabolism are discussed, along with the relationship between brain metabolic scaling and computation.Comment: Brain metabolism scales with its mass well above 3/4 exponen

In vivo STED microscopy visualizes morphological changes of large PSD95 assemblies over several hours in the mouse visual cortex

Abstract The post-synaptic density (PSD) is an electron dense region consisting of ~1000 proteins, found at the postsynaptic membrane of excitatory synapses, which varies in size depending upon synaptic strength. PSD95 is an abundant scaffolding protein in the PSD and assembles a family of supercomplexes comprised of neurotransmitter receptors, ion channels, as well as signalling and structural proteins. We use superresolution STED (STimulated Emission Depletion) nanoscopy to determine the size and shape of PSD95 in the anaesthetised mouse visual cortex. Adult knock-in mice expressing eGFP fused to the endogenous PSD95 protein were imaged at time points from 1 min to 6 h. Superresolved large assemblies of PSD95 show different sub-structures; most large assemblies were ring-like, some horse-shoe or figure-8 shaped, and shapes were continuous or made up of nanoclusters. The sub-structure appeared stable during the shorter (minute) time points, but after 1 h, more than 50% of the large assemblies showed a change in sub-structure. Overall, these data showed a sub-morphology of large PSD95 assemblies which undergo changes within the 6 hours of observation in the anaesthetised mouse

Network Structure Implied by Initial Axon Outgrowth in Rodent Cortex: Empirical Measurement and Models

The developmental mechanisms by which the network organization of the adult cortex is established are incompletely understood. Here we report on empirical data on the development of connections in hamster isocortex and use these data to parameterize a network model of early cortical connectivity. Using anterograde tracers at a series of postnatal ages, we investigate the growth of connections in the early cortical sheet and systematically map initial axon extension from sites in anterior (motor), middle (somatosensory) and posterior (visual) cortex. As a general rule, developing axons extend from all sites to cover relatively large portions of the cortical field that include multiple cortical areas. From all sites, outgrowth is anisotropic, covering a greater distance along the medial/lateral axis than along the anterior/posterior axis. These observations are summarized as 2-dimensional probability distributions of axon terminal sites over the cortical sheet. Our network model consists of nodes, representing parcels of cortex, embedded in 2-dimensional space. Network nodes are connected via directed edges, representing axons, drawn according to the empirically derived anisotropic probability distribution. The networks generated are described by a number of graph theoretic measurements including graph efficiency, node betweenness centrality and average shortest path length. To determine if connectional anisotropy helps reduce the total volume occupied by axons, we define and measure a simple metric for the extra volume required by axons crossing. We investigate the impact of different levels of anisotropy on network structure and volume. The empirically observed level of anisotropy suggests a good trade-off between volume reduction and maintenance of both network efficiency and robustness. Future work will test the model's predictions for connectivity in larger cortices to gain insight into how the regulation of axonal outgrowth may have evolved to achieve efficient and economical connectivity in larger brains

What People Believe about How Memory Works: A Representative Survey of the U.S. Population

Incorrect beliefs about the properties of memory have broad implications: The media conflate normal forgetting and inadvertent memory distortion with intentional deceit, juries issue verdicts based on flawed intuitions about the accuracy and confidence of testimony, and students misunderstand the role of memory in learning. We conducted a large representative telephone survey of the U.S. population to assess common beliefs about the properties of memory. Substantial numbers of respondents agreed with propositions that conflict with expert consensus: Amnesia results in the inability to remember one's own identity (83% of respondents agreed), unexpected objects generally grab attention (78%), memory works like a video camera (63%), memory can be enhanced through hypnosis (55%), memory is permanent (48%), and the testimony of a single confident eyewitness should be enough to convict a criminal defendant (37%). This discrepancy between popular belief and scientific consensus has implications from the classroom to the courtroom

Neuropathological Similarities and Differences between Schizophrenia and Bipolar Disorder: A Flow Cytometric Postmortem Brain Study

Recent studies suggest that schizophrenia (SCH) and bipolar disorder (BPD) may share a similar etiopathology. However, their precise neuropathological natures have rarely been characterized in a comprehensive and quantitative fashion. We have recently developed a rapid, quantitative cell-counting method for frozen unfixed postmortem brains using a flow cytometer. In the present study, we not only counted stained nuclei, but also measured their sizes in the gray matter of frontopolar cortices (FPCs) and inferior temporal cortices (ITCs) from patients with SCH or BPD, as well as in that from normal controls. In terms of NeuN(+) neuronal nuclei size, particularly in the reduced densities of small NeuN(+) nuclei, we found abnormal distributions present in the ITC gray matter of both patient groups. These same abnormalities were also found in the FPCs of SCH patients, whereas in the FPCs of BPD patients, a reduction in oligodendrocyte lineage (olig2(+)) cells was much more common. Surprisingly, in the SCH FPC, normal left-greater-than-right asymmetry in neural nuclei densities was almost completely reversed. In the BPD FPC, this asymmetry, though not obvious, differed significantly from that in the SCH FPC. These findings indicate that while similar neuropathological abnormalities are shared by patients with SCH or BPD, differences also exist, mainly in the FPC, which may at least partially explain the differences observed in many aspects in these disorders

Neural representations of the sense of self

The brain constructs representations of what is sensed and thought about in the form of nerve impulses that propagate in circuits and network assemblies (Circuit Impulse Patterns, CIPs). CIP representations of which humans are consciously aware occur in the context of a sense of self. Thus, research on mechanisms of consciousness might benefit from a focus on how a conscious sense of self is represented in brain. Like all senses, the sense of self must be contained in patterns of nerve impulses. Unlike the traditional senses that are registered by impulse flow in relatively simple, pauci-synaptic projection pathways, the sense of self is a system- level phenomenon that may be generated by impulse patterns in widely distributed complex and interacting circuits. The problem for researchers then is to identify the CIPs that are unique to conscious experience. Also likely to be of great relevance to constructing the representation of self are the coherence shifts in activity timing relations among the circuits. Consider that an embodied sense of self is generated and contained as unique combinatorial temporal patterns across multiple neurons in each circuit that contributes to constructing the sense of self. As with other kinds of CIPs, those representing the sense of self can be learned from experience, stored in memory, modified by subsequent experiences, and expressed in the form of decisions, choices, and commands. These CIPs are proposed here to be the actual physical basis for conscious thought and the sense of self. When active in wakefulness or dream states, the CIP representations of self act as an agent of the brain, metaphorically as an avatar. Because the selfhood CIP patterns may only have to represent the self and not directly represent the inner and outer worlds of embodied brain, the self representation should have more degrees of freedom than subconscious mind and may therefore have some capacity for a free-will mind of its own. S everal lines of evidence for this theory are reviewed. Suggested new research includes identifying distinct combinatorially coded impulse patterns and their temporal coherence shifts in defined circuitry, such as neocortical microcolumns. This task might be facilitated by identifying the micro-topography of field-potential oscillatory coherences among various regions and between different frequencies associated with specific conscious mentation. Other approaches can include identifying the changes in discrete conscious operations produced by focal trans-cranial magnetic stimulation