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

Size matters in metabolic scaling: Critical role of the thermodynamic efficiency of ATP synthesis and its dependence on mitochondrial H+ leak across mammalian species

In this last article of the trilogy, the unified biothermokinetic theory of ATP synthesis developed in the previous two papers is applied to a major problem in comparative physiology, biochemistry, and ecology-that of metabolic scaling as a function of body mass across species. A clear distinction is made between intraspecific and interspecific relationships in energy metabolism, clearing up confusion that had existed from the very beginning since Kleiber first proposed his mouse-to-elephant rule almost a century ago. It is shown that the overall mass exponent of basal/standard metabolic rate in the allometric relationship [Formula: see text] is composed of two parts, one emerging from the relative intraspecific constancy of the slope (b), and the other (b') arising from the interspecific variation of the mass coefficient, a(M) with body size. Quantitative analysis is shown to reveal the hidden underlying relationship followed by the interspecific mass coefficient, a(M)=P0M0.10, and a universal value of P0=3.23 watts, W is derived from empirical data on mammals from mouse to cattle. The above relationship is shown to be understood only within an evolutionary biological context, and provides a physiological explanation for Cope's rule. The analysis also helps in fundamentally understanding how variability and a diversity of scaling exponents arises in allometric relations in biology and ecology. Next, a molecular-level understanding of the scaling of metabolism across mammalian species is shown to be obtained by consideration of the thermodynamic efficiency of ATP synthesis η, taking mitochondrial proton leak as a major determinant of basal metabolic rate in biosystems. An iterative solution is obtained by solving the mathematical equations of the biothermokinetic ATP theory, and the key thermodynamic parameters, e.g. the degree of coupling q, the operative P/O ratio, and the metabolic efficiency of ATP synthesis η are quantitatively evaluated for mammals from rat to cattle. Increases in η (by ∼15%) over a 2000-fold body size range from rat to cattle, primarily arising from an ∼3-fold decrease in the mitochondrial H+ leak rate are quantified by the unified ATP theory. Biochemical and mechanistic consequences for the interpretation of basal metabolism, and the various molecular implications arising are discussed in detail. The results are extended to maximum metabolic rate, and interpreted mathematically as a limiting case of the general ATP theory. The limitations of the analysis are pointed out. In sum, a comprehensive quantitative analysis based on the unified biothermokinetic theory of ATP synthesis is shown to solve a central problem in biology, physiology, and ecology on the scaling of energy metabolism with body size.

Molecular Ratchets and Kinetic Asymmetry: Giving Chemistry Direction

Over the last two decades ratchet mechanisms have transformed the understanding and design of stochastic molecular systems-biological, chemical and physical-in a move away from the mechanical macroscopic analogies that dominated thinking regarding molecular dynamics in the 1990s and early 2000s (e.g. pistons, springs, etc), to the more scale-relevant concepts that underpin out-of-equilibrium research in the molecular sciences today. Ratcheting has established molecular nanotechnology as a research frontier for energy transduction and metabolism, and has enabled the reverse engineering of biomolecular machinery, delivering insights into how molecules 'walk' and track-based synthesisers operate, how the acceleration of chemical reactions enables energy to be transduced by catalysts (both motor proteins and synthetic catalysts), and how dynamic systems can be driven away from equilibrium through catalysis. The recognition of molecular ratchet mechanisms in biology, and their invention in synthetic systems, is proving significant in areas as diverse as supramolecular chemistry, systems chemistry, dynamic covalent chemistry, DNA nanotechnology, polymer and materials science, molecular biology, heterogeneous catalysis, endergonic synthesis, the origin of life, and many other branches of chemical science. Put simply, ratchet mechanisms give chemistry direction. Kinetic asymmetry, the key feature of ratcheting, is the dynamic counterpart of structural asymmetry (i.e. chirality). Given the ubiquity of ratchet mechanisms in endergonic chemical processes in biology, and their significance for behaviour and function from systems to synthesis, it is surely just as fundamentally important. This Review charts the recognition, invention and development of molecular ratchets, focussing particularly on the role for which they were originally envisaged in chemistry, as design elements for molecular machinery. Different kinetically asymmetric systems are compared, and the consequences of their dynamic behaviour discussed. These archetypal examples demonstrate how chemical systems can be driven inexorably away from equilibrium, rather than relax towards it.

Thermodynamic analysis of energy coupling by determination of the Onsager phenomenological coefficients for a 3×3 system of coupled chemical reactions and transport in ATP synthesis and its mechanistic implications

The nonequilibrium coupled processes of oxidation and ATP synthesis in the fundamental process of oxidative phosphorylation (OXPHOS) are of vital importance in biosystems. These coupled chemical reaction and transport bioenergetic processes using the OXPHOS pathway meet >90% of the ATP demand in aerobic systems. On the basis of experimentally determined thermodynamic OXPHOS flux-force relationships and biochemical data for the ternary system of oxidation, ion transport, and ATP synthesis, the Onsager phenomenological coefficients have been computed, including an estimate of error. A new biothermokinetic theory of energy coupling has been formulated and on its basis the thermodynamic parameters, such as the overall degree of coupling, q and the phenomenological stoichiometry, Z of the coupled system have been evaluated. The amount of ATP produced per oxygen consumed, i.e. the actual, operating P/O ratio in the biosystem, the thermodynamic efficiency of the coupled reactions, η, and the Gibbs free energy dissipation, Φ have been calculated and shown to be in agreement with experimental data. At the concentration gradients of ADP and ATP prevailing under state 3 physiological conditions of OXPHOS that yield Vmax rates of ATP synthesis, a maximum in Φ of ∼0.5J(hmgprotein)-1, corresponding to a thermodynamic efficiency of ∼60% for oxidation on succinate, has been obtained. Novel mechanistic insights arising from the above have been discussed. This is the first report of a 3 × 3 system of coupled chemical reactions with transport in a biological context in which the phenomenological coefficients have been evaluated from experimental data.

The Warburg Effect Reinterpreted 100 yr on: A First-Principles Stoichiometric Analysis and Interpretation from the Perspective of ATP Metabolism in Cancer Cells

The Warburg Effect is a longstanding enigma in cancer biology. Despite the passage of 100 yr since its discovery, and the accumulation of a vast body of research on the subject, no convincing biochemical explanation has been given for the original observations of aerobic glycolysis in cancer cell metabolism. Here, we have worked out a first-principles quantitative analysis of the problem from the principles of stoichiometry and available electron balance. The results have been interpreted using Nath's unified theory of energy coupling and adenosine triphosphate (ATP) synthesis, and the original data of Warburg and colleagues have been analyzed from this new perspective. Use of the biomass yield based on ATP per unit substrate consumed, [Formula: see text], or the Nath-Warburg number, NaWa has been shown to excellently model the original data on the Warburg Effect with very small standard deviation values, and without employing additional fitted or adjustable parameters. Based on the results of the quantitative analysis, a novel conservative mechanism of synthesis, utilization, and recycling of ATP and other key metabolites (eg, lactate) is proposed. The mechanism offers fresh insights into metabolic symbiosis and coupling within and/or among proliferating cells. The fundamental understanding gained using our approach should help in catalyzing the development of more efficient metabolism-targeting anticancer drugs.

Digital design of a spatial-pow-STDP learning block with high accuracy utilizing pow CORDIC for large-scale image classifier spatiotemporal SNN

The paramount concern of highly accurate energy-efficient computing in machines with significant cognitive capabilities aims to enhance the accuracy and efficiency of bio-inspired Spiking Neural Networks (SNNs). This paper addresses this main objective by introducing a novel spatial power spike-timing-dependent plasticity (Spatial-Pow-STDP) learning rule as a digital block with high accuracy in a bio-inspired SNN model. Motivated by the demand for precise and accelerated computation that reduces high-cost resources in neural network applications, this paper presents a methodology based on COordinate Rotation DIgital Computer (CORDIC) definitions. The proposed designs of CORDIC algorithms for exponential (Exp CORDIC), natural logarithm (Ln CORDIC), and arbitrary power function (Pow CORDIC) are meticulously detailed and evaluated to ensure optimal acceleration and accuracy, which respectively show average errors near 10-9, 10-6, and 10-5 with 4, 4, and 6 iterations. The engineered architectures for the Exp, Ln, and Pow CORDIC implementations are illustrated and assessed, showcasing the efficiency achieved through high frequency, leading to the introduction of a Spatial-Pow-STDP learning block design based on Pow CORDIC that facilitates efficient and accurate hardware computation with 6.93 × 10-3 average error with 9 iterations. The proposed learning mechanism integrates this structure into a large-scale spatiotemporal SNN consisting of three layers with reduced hyper-parameters, enabling unsupervised training in an event-based paradigm using excitatory and inhibitory synapses. As a result, the application of the developed methodology and equations in the computational SNN model for image classification reveals superior accuracy and convergence speed compared to existing spiking networks by achieving up to 97.5%, 97.6%, 93.4%, and 93% accuracy, respectively, when trained on the MNIST, EMNIST digits, EMNIST letters, and CIFAR10 datasets with 6, 2, 2, and 6 training epochs.

Coupling and biological free-energy transduction processes as a bridge between physics and life: Molecular-level instantiation of Ervin Bauer's pioneering concepts in biological thermodynamics

The nonequilibrium coupled processes of oxidation and ATP synthesis in the biological process of oxidative phosphorylation (OXPHOS) are fundamental to all life on our planet. These steady-state energy transduction processes ‒ coupled by proton and anion/counter-cation concentration gradients in the OXPHOS pathway ‒ generate ∼95 % of the ATP requirement of aerobic systems for cellular function. The rapid energy cycling and homeostasis of metabolites involved in this coupling are shown to be responsible for maintenance and regulation of stable nonequilibrium states, the latter first postulated in pioneering biothermodynamics work by Ervin Bauer between 1920 and 1935. How exactly does this occur? This is shown to be answered by molecular considerations arising from Nath's torsional mechanism of ATP synthesis and two-ion theory of energy coupling developed in 25 years of research work on the subject. A fresh analysis of the biological thermodynamics of coupling that goes beyond the previous work of Stucki and others and shows how the system functions at the molecular level has been carried out. Thermodynamic parameters, such as the overall degree of coupling, q of the coupled system are evaluated for the state 4 to state 3 transition in animal mitochondria with succinate as substrate. The actual or operative P to O ratio, the efficiency of the coupled reactions, η, and the Gibbs energy dissipation, Φ have been calculated and shown to be in good agreement with experimental data. Novel mechanistic insights arising from the above have been discussed. A fourth law/principle of thermodynamics is formulated for a sub-class of physical and biological systems. The critical importance of constraints and time-varying boundary conditions for function and regulation is discussed in detail. Dynamic internal structural changes essential for torsional energy storage within the γ-subunit in a single molecule of the FOF1-ATP synthase and its transduction have been highlighted. These results provide a molecular-level instantiation of Ervin Bauer's pioneering concepts in biological thermodynamics.

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.

The hardware is the software

Human brains and bodies are not hardware running software: the hardware is the software. We reason that because the physics of artificial intelligence hardware and of human biological "hardware" is distinct, neuromorphic engineers need to be selective in the inspiration we take from neuroscience.

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.

Energy optimisation predicts the capacity of ion buffering in the brain

Neurons store energy in the ionic concentration gradients they build across their cell membrane. The amount of energy stored, and hence the work the ions can do by mixing, can be enhanced by the presence of ion buffers in extra- and intracellular space. Buffers act as sources and sinks of ions, however, and unless the buffering capacities for different ion species obey certain relationships, a complete mixing of the ions may be impeded by the physical conditions of charge neutrality and isotonicity. From these conditions, buffering capacities were calculated that enabled each ion species to mix completely. In all valid buffer distributions, the [Formula: see text] ions were buffered most, with a capacity exceeding that of [Formula: see text] and [Formula: see text] buffering by at least an order of magnitude. The similar magnitude of the (oppositely directed) [Formula: see text] and [Formula: see text] gradients made extracellular space behave as a [Formula: see text]-[Formula: see text] exchanger. Anions such as [Formula: see text] were buffered least. The great capacity of the extra- and intracellular [Formula: see text] buffers caused a large influx of [Formula: see text] ions as is typically observed during energy deprivation. These results explain many characteristics of the physiological buffer distributions but raise the question how the brain controls the capacity of its ion buffers. It is suggested that neurons and glial cells, by their great sensitivity to gradients of charge and osmolarity, respectively, sense deviations from electro-neutral and isotonic mixing, and use these signals to tune the chemical composition, and buffering capacity, of the extra- and intracellular matrices.

Dendrites and efficiency: Optimizing performance and resource utilization

The brain is a highly efficient system that has evolved to optimize performance under limited resources. In this review, we highlight recent theoretical and experimental studies that support the view that dendrites make information processing and storage in the brain more efficient. This is achieved through the dynamic modulation of integration versus segregation of inputs and activity within a neuron. We argue that under conditions of limited energy and space, dendrites help biological networks to implement complex functions such as processing natural stimuli on behavioral timescales, performing the inference process on those stimuli in a context-specific manner, and storing the information in overlapping populations of neurons. A global picture starts to emerge, in which dendrites help the brain achieve efficiency through a combination of optimization strategies that balance the tradeoff between performance and resource utilization.

Phosphorus Chemistry at the Roots of Bioenergetics: Ligand Permutation as the Molecular Basis of the Mechanism of ATP Synthesis/Hydrolysis by FOF1-ATP Synthase

The integration of phosphorus chemistry with the mechanism of ATP synthesis/hydrolysis requires dynamical information during ATP turnover and catalysis. Oxygen exchange reactions occurring at β-catalytic sites of the FOF1-ATP synthase/F1-ATPase imprint a unique record of molecular events during the catalytic cycle of ATP synthesis/hydrolysis. They have been shown to provide valuable time-resolved information on enzyme catalysis during ATP synthesis and ATP hydrolysis. The present work conducts new experiments on oxygen exchange catalyzed by submitochondrial particles designed to (i) measure the relative rates of Pi-ATP, Pi-HOH, and ATP-HOH isotope exchanges; (ii) probe the effect of ADP removal on the extent of inhibition of the exchanges, and (iii) test their uncoupler sensitivity/resistance. The objectives have been realized based on new experiments on submitochondrial particles, which show that both the Pi-HOH and ATP-HOH exchanges occur at a considerably higher rate relative to the Pi-ATP exchange, an observation that cannot be explained by previous mechanisms. A unifying explanation of the kinetic data that rationalizes these observations is given. The experimental results in (ii) show that ADP removal does not inhibit the intermediate Pi-HOH exchange when ATP and submitochondrial particles are incubated, and that the nucleotide requirement of the intermediate Pi-HOH exchange is adequately met by ATP, but not by ADP. These results contradicts the central postulate in Boyer's binding change mechanism of reversible catalysis at a F1 catalytic site with Keq~1 that predicts an absolute requirement of ADP for the occurrence of the Pi-HOH exchange. The prominent intermediate Pi-HOH exchange occurring under hydrolytic conditions is shown to be best explained by Nath's torsional mechanism of energy transduction and ATP synthesis/hydrolysis, which postulates an essentially irreversible cleavage of ATP by mitochondria/particles, independent from a reversible formation of ATP from ADP and Pi. The explanation within the torsional mechanism is also shown to rationalize the relative insensitivity of the intermediate Pi-HOH exchange to uncouplers observed in the experiments in (iii) compared to the Pi-ATP and ATP-HOH exchanges. This is shown to lead to new concepts and perspectives based on ligand displacement/substitution and ligand permutation for the elucidation of the oxygen exchange reactions within the framework of fundamental phosphorus chemistry. Fast mechanisms that realize the rotation/twist, tilt, permutation and switch of ligands, as well as inversion at the γ-phosphorus synchronously and simultaneously and in a concerted manner, have been proposed, and their stereochemical consequences have been analyzed. These considerations take us beyond the binding change mechanism of ATP synthesis/hydrolysis in bioenergetics.

Elucidating Events within the Black Box of Enzyme Catalysis in Energy Metabolism: Insights into the Molecular Mechanism of ATP Hydrolysis by F1-ATPase

Oxygen exchange reactions occurring at β-catalytic sites of the FOF1-ATP synthase/F1-ATPase imprint a unique record of molecular events during the catalytic cycle of ATP synthesis/hydrolysis. This work presents a new theory of oxygen exchange and tests it on oxygen exchange data recorded on ATP hydrolysis by mitochondrial F1-ATPase (MF1). The apparent rate constant of oxygen exchange governing the intermediate Pi-HOH exchange accompanying ATP hydrolysis is determined by kinetic analysis over a ~50,000-fold range of substrate ATP concentration (0.1-5000 μM) and a corresponding ~200-fold range of reaction velocity (3.5-650 [moles of Pi/{moles of F1-ATPase}-1 s-1]). Isotopomer distributions of [18O]Pi species containing 0, 1, 2, and 3 labeled oxygen atoms predicted by the theory have been quantified and shown to be in perfect agreement with the experimental distributions over the entire range of medium ATP concentrations without employing adjustable parameters. A novel molecular mechanism of steady-state multisite ATP hydrolysis by the F1-ATPase has been proposed. Our results show that steady-state ATP hydrolysis by F1-ATPase occurs with all three sites occupied by Mg-nucleotide. The various implications arising from models of energy coupling in ATP synthesis/hydrolysis by the ATP synthase/F1-ATPase have been discussed. Current models of ATP hydrolysis by F1-ATPase, including those postulated from single-molecule data, are shown to be effectively bisite models that contradict the data. The trisite catalysis formulated by Nath's torsional mechanism of energy transduction and ATP synthesis/hydrolysis since its first appearance 25 years ago is shown to be in better accord with the experimental record. The total biochemical information on ATP hydrolysis is integrated into a consistent model by the torsional mechanism of ATP synthesis/hydrolysis and shown to elucidate the elementary chemical and mechanical events within the black box of enzyme catalysis in energy metabolism by F1-ATPase.

Learning heterogeneous delays in a layer of spiking neurons for fast motion detection

The precise timing of spikes emitted by neurons plays a crucial role in shaping the response of efferent biological neurons. This temporal dimension of neural activity holds significant importance in understanding information processing in neurobiology, especially for the performance of neuromorphic hardware, such as event-based cameras. Nonetheless, many artificial neural models disregard this critical temporal dimension of neural activity. In this study, we present a model designed to efficiently detect temporal spiking motifs using a layer of spiking neurons equipped with heterogeneous synaptic delays. Our model capitalizes on the diverse synaptic delays present on the dendritic tree, enabling specific arrangements of temporally precise synaptic inputs to synchronize upon reaching the basal dendritic tree. We formalize this process as a time-invariant logistic regression, which can be trained using labeled data. To demonstrate its practical efficacy, we apply the model to naturalistic videos transformed into event streams, simulating the output of the biological retina or event-based cameras. To evaluate the robustness of the model in detecting visual motion, we conduct experiments by selectively pruning weights and demonstrate that the model remains efficient even under significantly reduced workloads. In conclusion, by providing a comprehensive, event-driven computational building block, the incorporation of heterogeneous delays has the potential to greatly improve the performance of future spiking neural network algorithms, particularly in the context of neuromorphic chips.

Beyond ℓ1 sparse coding in V1

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the ℓ1 norm as a penalty due to its convexity, which makes it amenable to fast and simple algorithmic solvers. In this work, we use biological vision as a test-bed and show that the soft thresholding operation associated to the use of the ℓ1 norm is highly suboptimal compared to other functions suited to approximating ℓp with 0 ≤ p < 1 (including recently proposed continuous exact relaxations), in terms of performance. We show that ℓ1 sparsity employs a pool with more neurons, i.e. has a higher degree of overcompleteness, in order to maintain the same reconstruction error as the other methods considered. More specifically, at the same sparsity level, the thresholding algorithm using the ℓ1 norm as a penalty requires a dictionary of ten times more units compared to the proposed approach, where a non-convex continuous relaxation of the ℓ0 pseudo-norm is used, to reconstruct the external stimulus equally well. At a fixed sparsity level, both ℓ0- and ℓ1-based regularization develop units with receptive field (RF) shapes similar to biological neurons in V1 (and a subset of neurons in V2), but ℓ0-based regularization shows approximately five times better reconstruction of the stimulus. Our results in conjunction with recent metabolic findings indicate that for V1 to operate efficiently it should follow a coding regime which uses a regularization that is closer to the ℓ0 pseudo-norm rather than the ℓ1 one, and suggests a similar mode of operation for the sensory cortex in general.

A proposal for leaky integrate-and-fire neurons by domain walls in antiferromagnetic insulators

Brain-inspired neuromorphic computing is a promising path towards next generation analogue computers that are fundamentally different compared to the conventional von Neumann architecture. One model for neuromorphic computing that can mimic the human brain behavior are spiking neural networks (SNNs), of which one of the most successful is the leaky integrate-and-fire (LIF) model. Since conventional complementary metal-oxide-semiconductor (CMOS) devices are not meant for modelling neural networks and are energy inefficient in network applications, recently the focus shifted towards spintronic-based neural networks. In this work, using the advantage of antiferromagnetic insulators, we propose a non-volatile magnonic neuron that could be the building block of a LIF spiking neuronal network. In our proposal, an antiferromagnetic domain wall in the presence of a magnetic anisotropy gradient mimics a biological neuron with leaky, integrating, and firing properties. This single neuron is controlled by polarized antiferromagnetic magnons, activated by either a magnetic field pulse or a spin transfer torque mechanism, and has properties similar to biological neurons, namely latency, refraction, bursting and inhibition. We argue that this proposed single neuron, based on antiferromagnetic domain walls, is faster and has more functionalities compared to previously proposed neurons based on ferromagnetic systems.

Physical Constraints in Intracellular Signaling: The Cost of Sending a Bit

Many biological processes require timely communication between molecular components. Cells employ diverse physical channels to this end, transmitting information through diffusion, electrical depolarization, and mechanical waves among other strategies. Here we bound the energetic cost of transmitting information through these physical channels, in k_{B}T/bit, as a function of the size of the sender and receiver, their spatial separation, and the communication latency. These calculations provide an estimate for the energy costs associated with information processing arising from the physical constraints of the cellular environment, which we find to be many orders of magnitude larger than unity in natural units. From these calculations, we construct a phase diagram indicating where each strategy is most efficient. Our results suggest that intracellular information transfer may constitute a substantial energetic cost. This provides a new tool for understanding tradeoffs in cellular network function.

Free energy and inference in living systems

Organisms are non-equilibrium, stationary systems self-organized via spontaneous symmetry breaking and undergoing metabolic cycles with broken detailed balance in the environment. The thermodynamic free-energy (FE) principle describes an organism's homeostasis as the regulation of biochemical work constrained by the physical FE cost. By contrast, recent research in neuroscience and theoretical biology explains a higher organism's homeostasis and allostasis as Bayesian inference facilitated by the informational FE. As an integrated approach to living systems, this study presents an FE minimization theory overarching the essential features of both the thermodynamic and neuroscientific FE principles. Our results reveal that the perception and action of animals result from active inference entailed by FE minimization in the brain, and the brain operates as a Schrödinger's machine conducting the neural mechanics of minimizing sensory uncertainty. A parsimonious model suggests that the Bayesian brain develops the optimal trajectories in neural manifolds and induces a dynamic bifurcation between neural attractors in the process of active inference.

Beyond binding change: the molecular mechanism of ATP hydrolysis by F1-ATPase and its biochemical consequences

F1-ATPase is a universal multisubunit enzyme and the smallest-known motor that, fueled by the process of ATP hydrolysis, rotates in 120o steps. A central question is how the elementary chemical steps occurring in the three catalytic sites are coupled to the mechanical rotation. Here, we performed cold chase promotion experiments and measured the rates and extents of hydrolysis of preloaded bound ATP and promoter ATP bound in the catalytic sites. We found that rotation was caused by the electrostatic free energy change associated with the ATP cleavage reaction followed by Pi release. The combination of these two processes occurs sequentially in two different catalytic sites on the enzyme, thereby driving the two rotational sub-steps of the 120o rotation. The mechanistic implications of this finding are discussed based on the overall energy balance of the system. General principles of free energy transduction are formulated, and their important physical and biochemical consequences are analyzed. In particular, how exactly ATP performs useful external work in biomolecular systems is discussed. A molecular mechanism of steady-state, trisite ATP hydrolysis by F1-ATPase, consistent with physical laws and principles and the consolidated body of available biochemical information, is developed. Taken together with previous results, this mechanism essentially completes the coupling scheme. Discrete snapshots seen in high-resolution X-ray structures are assigned to specific intermediate stages in the 120o hydrolysis cycle, and reasons for the necessity of these conformations are readily understood. The major roles played by the "minor" subunits of ATP synthase in enabling physiological energy coupling and catalysis, first predicted by Nath's torsional mechanism of energy transduction and ATP synthesis 25 years ago, are now revealed with great clarity. The working of nine-stepped (bMF1, hMF1), six-stepped (TF1, EF1), and three-stepped (PdF1) F1 motors and of the α3β3γ subcomplex of F1 is explained by the same unified mechanism without invoking additional assumptions or postulating different mechanochemical coupling schemes. Some novel predictions of the unified theory on the mode of action of F1 inhibitors, such as sodium azide, of great pharmaceutical importance, and on more exotic artificial or hybrid/chimera F1 motors have been made and analyzed mathematically. The detailed ATP hydrolysis cycle for the enzyme as a whole is shown to provide a biochemical basis for a theory of "unisite" and steady-state multisite catalysis by F1-ATPase that had remained elusive for a very long time. The theory is supported by a probability-based calculation of enzyme species distributions and analysis of catalytic site occupancies by Mg-nucleotides and the activity of F1-ATPase. A new concept of energy coupling in ATP synthesis/hydrolysis based on fundamental ligand substitution chemistry has been advanced, which offers a deeper understanding, elucidates enzyme activation and catalysis in a better way, and provides a unified molecular explanation of elementary chemical events occurring at enzyme catalytic sites. As such, these developments take us beyond binding change mechanisms of ATP synthesis/hydrolysis proposed for oxidative phosphorylation and photophosphorylation in bioenergetics.

Revisiting neural information, computing and linking capacity

Neural information theory represents a fundamental method to model dynamic relations in biological systems. However, the notion of information, its representation, its content and how it is processed are the subject of fierce debates. Since the limiting capacity of neuronal links strongly depends on how neurons are hypothesized to work, their operating modes are revisited by analyzing the differences between the results of the communication models published during the past seven decades and those of the recently developed generalization of the classical information theory. It is pointed out that the operating mode of neurons is in resemblance with an appropriate combination of the formerly hypothesized analog and digital working modes; furthermore that not only the notion of neural information and its processing must be reinterpreted. Given that the transmission channel is passive in Shannon's model, the active role of the transfer channels (the axons) may introduce further transmission limits in addition to the limits concluded from the information theory. The time-aware operating model enables us to explain why (depending on the researcher's point of view) the operation can be considered either purely analog or purely digital.

Growing dendrites enhance a neuron's computational power and memory capacity

Neocortical pyramidal neurons have many dendrites, and such dendrites are capable of, in isolation of one-another, generating a neuronal spike. It is also now understood that there is a large amount of dendritic growth during the first years of a humans life, arguably a period of prodigious learning. These observations inspire the construction of a local, stochastic algorithm based on an earlier stochastic, homeostatic, Hebbian developmental theory. Here we investigate the neurocomputational advantages and limits on this novel algorithm that combines dendritogenesis with supervised adaptive synaptogenesis. Neurons created with this algorithm have enhanced memory capacity, can avoid catastrophic interference (forgetting), and have the ability to unmix mixture distributions. In particular, individual dendrites develop within each class, in an unsupervised manner, to become feature-clusters that correspond to the mixing elements of class-conditional mixture distribution. Error-free classification is demonstrated with input perturbations up to 40%. Although discriminative problems are used to understand the capabilities of the stochastic algorithm and the neuronal connectivity it produces, the algorithm is in the generative class, it thus seems ideal for decisions that require generalization, i.e., extrapolation beyond previous learning.

Astrocyte strategies in the energy-efficient brain

Astrocytes generate ATP through glycolysis and mitochondrion respiration, using glucose, lactate, fatty acids, amino acids, and ketone bodies as metabolic fuels. Astrocytic mitochondria also participate in neuronal redox homeostasis and neurotransmitter recycling. In this essay, we aim to integrate the multifaceted evidence about astrocyte bioenergetics at the cellular and systems levels, with a focus on mitochondrial oxidation. At the cellular level, the use of fatty acid β-oxidation and the existence of molecular switches for the selection of metabolic mode and fuels are examined. At the systems level, we discuss energy audits of astrocytes and how astrocytic Ca2+ signaling might contribute to the higher performance and lower energy consumption of the brain as compared to engineered circuits. We finish by examining the neural-circuit dysregulation and behavior impairment associated with alterations of astrocytic mitochondria. We conclude that astrocytes may contribute to brain energy efficiency by coupling energy, redox, and computational homeostasis in neural circuits.

Electro-optical synaptic characteristics of ferroelectric liquid crystals for artificial intelligence

We propose electro-optical synaptic devices using surface-stabilized ferroelectric liquid crystals. Typical synaptic characteristics were observed for varying pulse time intervals, numbers of pulses, and signal voltages. Plasticity only occurred when pulses were applied at intervals shorter than the response time of the ferroelectric liquid crystal. Moreover, the plasticity increased with a higher pulse voltage and number of pulses. This demonstrates the importance of repeated learning. The synaptic weights required to make connections through learning in an artificial neural network can be determined by tuning the pulse signal. We discuss the high-speed computational potential of optical neuromorphic devices using liquid crystals.

Nine insights from internet engineering that help us understand brain network communication

Philosophers have long recognized the value of metaphor as a tool that opens new avenues of investigation. By seeing brains as having the goal of representation, the computer metaphor in its various guises has helped systems neuroscience approach a wide array of neuronal behaviors at small and large scales. Here I advocate a complementary metaphor, the internet. Adopting this metaphor shifts our focus from computing to communication, and from seeing neuronal signals as localized representational elements to seeing neuronal signals as traveling messages. In doing so, we can take advantage of a comparison with the internet's robust and efficient routing strategies to understand how the brain might meet the challenges of network communication. I lay out nine engineering strategies that help the internet solve routing challenges similar to those faced by brain networks. The internet metaphor helps us by reframing neuronal activity across the brain as, in part, a manifestation of routing, which may, in different parts of the system, resemble the internet more, less, or not at all. I describe suggestive evidence consistent with the brain's use of internet-like routing strategies and conclude that, even if empirical data do not directly implicate internet-like routing, the metaphor is valuable as a reference point for those investigating the difficult problem of network communication in the brain and in particular the problem of routing.

DNA Damage Response-Associated Cell Cycle Re-Entry and Neuronal Senescence in Brain Aging and Alzheimer's Disease

Chronological aging is by far the strongest risk factor for age-related dementia and Alzheimer's disease. Senescent cells accumulated in the aging and Alzheimer's disease brains are now recognized as the keys to describing such an association. Cellular senescence is a classic phenomenon characterized by stable cell arrest, which is thought to be applicable only to dividing cells. Emerging evidence indicates that fully differentiated post-mitotic neurons are also capable of becoming senescent, with roles in contributing to both brain aging and disease pathogenesis. The key question that arises is the identity of the upstream triggers and the molecular mechanisms that underly such changes. Here, we highlight the potential role of persistent DNA damage response as the major driver of senescent phenotypes and discuss the current evidence and molecular mechanisms that connect DNA repair infidelity, cell cycle re-entry and terminal fate decision in committing neuronal cell senescence.

Efficient processing of natural scenes in visual cortex

Neural circuits in the periphery of the visual, auditory, and olfactory systems are believed to use limited resources efficiently to represent sensory information by adapting to the statistical structure of the natural environment. This "efficient coding" principle has been used to explain many aspects of early visual circuits including the distribution of photoreceptors, the mosaic geometry and center-surround structure of retinal receptive fields, the excess OFF pathways relative to ON pathways, saccade statistics, and the structure of simple cell receptive fields in V1. We know less about the extent to which such adaptations may occur in deeper areas of cortex beyond V1. We thus review recent developments showing that the perception of visual textures, which depends on processing in V2 and beyond in mammals, is adapted in rats and humans to the multi-point statistics of luminance in natural scenes. These results suggest that central circuits in the visual brain are adapted for seeing key aspects of natural scenes. We conclude by discussing how adaptation to natural temporal statistics may aid in learning and representing visual objects, and propose two challenges for the future: (1) explaining the distribution of shape sensitivity in the ventral visual stream from the statistics of object shape in natural images, and (2) explaining cell types of the vertebrate retina in terms of feature detectors that are adapted to the spatio-temporal structures of natural stimuli. We also discuss how new methods based on machine learning may complement the normative, principles-based approach to theoretical neuroscience.

The Need for Consistency with Physical Laws and Logic in Choosing Between Competing Molecular Mechanisms in Biological Processes: A Case Study in Modeling ATP Synthesis

Traditionally, proposed molecular mechanisms of fundamental biological processes have been tested against experiment. However, owing to a plethora of reasons-difficulty in designing, carrying out, and interpreting key experiments, use of different experimental models and systems, conduct of studies under widely varying experimental conditions, fineness in distinctions between competing mechanisms, complexity of the scientific issues, and the resistance of some scientists to discoveries that are contrary to popularly held beliefs-this has not solved the problem despite decades of work in the field/s. The author would like to prescribe an alternative way: that of testing competing models/mechanisms for their adherence to scientific laws and principles, and checking for errors in logic. Such tests are fairly commonly carried out in the mathematics, physics, and engineering literature. Further, reported experimental measurements should not be smaller than minimum detectable values for the measurement technique employed and should truly reflect function of the actual system without inapplicable extrapolation. Progress in the biological fields would be greatly accelerated, and considerable scientific acrimony avoided by adopting this approach. Some examples from the fundamental field of ATP synthesis in oxidative phosphorylation (OXPHOS) have been reviewed that also serve to illustrate the approach. The approach has never let the author down in his 35-yr-long experience on biological mechanisms. This change in thinking should lead to a considerable saving of both time and resources, help channel research efforts toward solution of the right problems, and hopefully provide new vistas to a younger generation of open-minded biological scientists.

Volitional Generation of Reproducible, Efficient Temporal Patterns

One of the extraordinary characteristics of the biological brain is the low energy expense it requires to implement a variety of biological functions and intelligence as compared to the modern artificial intelligence (AI). Spike-based energy-efficient temporal codes have long been suggested as a contributor for the brain to run on low energy expense. Despite this code having been largely reported in the sensory cortex, whether this code can be implemented in other brain areas to serve broader functions and how it evolves throughout learning have remained unaddressed. In this study, we designed a novel brain-machine interface (BMI) paradigm. Two macaques could volitionally generate reproducible energy-efficient temporal patterns in the primary motor cortex (M1) by learning the BMI paradigm. Moreover, most neurons that were not directly assigned to control the BMI did not boost their excitability, and they demonstrated an overall energy-efficient manner in performing the task. Over the course of learning, we found that the firing rates and temporal precision of selected neurons co-evolved to generate the energy-efficient temporal patterns, suggesting that a cohesive rather than dissociable processing underlies the refinement of energy-efficient temporal patterns.

Enhancing spiking neural networks with hybrid top-down attention

As the representatives of brain-inspired models at the neuronal level, spiking neural networks (SNNs) have shown great promise in processing spatiotemporal information with intrinsic temporal dynamics. SNNs are expected to further improve their robustness and computing efficiency by introducing top-down attention at the architectural level, which is crucial for the human brain to support advanced intelligence. However, this attempt encounters difficulties in optimizing the attention in SNNs largely due to the lack of annotations. Here, we develop a hybrid network model with a top-down attention mechanism (HTDA) by incorporating an artificial neural network (ANN) to generate attention maps based on the features extracted by a feedforward SNN. The attention map is then used to modulate the encoding layer of the SNN so that it focuses on the most informative sensory input. To facilitate direct learning of attention maps and avoid labor-intensive annotations, we propose a general principle and a corresponding weakly-supervised objective, which promotes the HTDA model to utilize an integral and small subset of the input to give accurate predictions. On this basis, the ANN and the SNN can be jointly optimized by surrogate gradient descent in an end-to-end manner. We comprehensively evaluated the HTDA model on object recognition tasks, which demonstrates strong robustness to adversarial noise, high computing efficiency, and good interpretability. On the widely-adopted CIFAR-10, CIFAR-100, and MNIST benchmarks, the HTDA model reduces firing rates by up to 50% and improves adversarial robustness by up to 10% with comparable or better accuracy compared with the state-of-the-art SNNs. The HTDA model is also verified on dynamic neuromorphic datasets and achieves consistent improvements. This study provides a new way to boost the performance of SNNs by employing a hybrid top-down attention mechanism.

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.

Neuromorphic object localization using resistive memories and ultrasonic transducers

Real-world sensory-processing applications require compact, low-latency, and low-power computing systems. Enabled by their in-memory event-driven computing abilities, hybrid memristive-Complementary Metal-Oxide Semiconductor neuromorphic architectures provide an ideal hardware substrate for such tasks. To demonstrate the full potential of such systems, we propose and experimentally demonstrate an end-to-end sensory processing solution for a real-world object localization application. Drawing inspiration from the barn owl’s neuroanatomy, we developed a bio-inspired, event-driven object localization system that couples state-of-the-art piezoelectric micromachined ultrasound transducer sensors to a neuromorphic resistive memories-based computational map. We present measurement results from the fabricated system comprising resistive memories-based coincidence detectors, delay line circuits, and a full-custom ultrasound sensor. We use these experimental results to calibrate our system-level simulations. These simulations are then used to estimate the angular resolution and energy efficiency of the object localization model. The results reveal the potential of our approach, evaluated in orders of magnitude greater energy efficiency than a microcontroller performing the same task.

The real-world object localization application needs a low-latency and power efficient computing system. Here, Moro et al. demonstrate a neuromorphic in-memory event driven system, inspired by the barn owl’s neuroanatomy, which is orders of magnitude more energy efficient than microcontrollers.

Supercomplex supercomplexes: Raison d’etre and functional significance of supramolecular organization in oxidative phosphorylation

Following structural determination by recent advances in electron cryomicroscopy, it is now well established that the respiratory Complexes I–IV in oxidative phosphorylation (OXPHOS) are organized into supercomplexes in the respirasome. Nonetheless, the reason for the existence of the OXPHOS supercomplexes and their functional role remains an enigma. Several hypotheses have been proposed for the existence of these supercomplex supercomplexes. A commonly-held view asserts that they enhance catalysis by substrate channeling. However, this – and other views – has been challenged based on structural and biophysical information. Hence, new ideas, concepts, and frameworks are needed. Here, a new model of energy transfer in OXPHOS is developed on the basis of biochemical data on the pure competitive inhibition of anionic substrates like succinate by the classical anionic uncouplers of OXPHOS (2,4-dinitrophenol, carbonyl cyanide 4-(trifluoromethoxy)phenylhydrazone, and dicoumarol), and pharmacological data on the unique site-selective, energy-linked inhibition of energy conservation pathways in mitochondria induced by the guanidine derivatives. It is further found that uncouplers themselves are site-specific and exhibit differential selectivity and efficacy in reversing the inhibition caused by the Site 1/Complex I or Site 2/Complexes II–III-selective guanidine derivatives. These results lead to new vistas and sufficient complexity in the network of energy conservation pathways in the mitochondrial respiratory chain that necessitate discrete points of interaction with two classes of guanidine derivatives and uncoupling agents and thereby separate and distinct energy transfer pathways between Site 1 and Site 2 and the intermediate that energizes adenosine triphosphate (ATP) synthesis by Complex V. Interpretation based on Mitchell’s single-ion chemiosmotic theory that postulates only a single energy pool is inadequate to rationalize the data and account for the required complexity. The above results and available information are shown to be explained by Nath’s two-ion theory of energy coupling and ATP synthesis, involving coupled movement of succinate anions and protons, along with the requirement postulated by the theory for maintenance of homeostasis and ion translocation across the energy-transducing membrane of both succinate monoanions and succinate dianions by Complexes I–V in the OXPHOS supercomplexes. The new model of energy transfer in mitochondria is mapped onto the solved structures of the supercomplexes and integrated into a consistent model with the three-dimensional electron microscope computer tomography visualization of the internal structure of the cristae membranes in mammalian mitochondria. The model also offers valuable insights into diseased states induced in type 2 diabetes and especially in Alzheimer’s and other neurodegenerative diseases that involve mitochondrial dysfunction.

Does Machine Understanding Require Consciousness?

This article addresses the question of whether machine understanding requires consciousness. Some researchers in the field of machine understanding have argued that it is not necessary for computers to be conscious as long as they can match or exceed human performance in certain tasks. But despite the remarkable recent success of machine learning systems in areas such as natural language processing and image classification, important questions remain about their limited performance and about whether their cognitive abilities entail genuine understanding or are the product of spurious correlations. Here I draw a distinction between natural, artificial, and machine understanding. I analyse some concrete examples of natural understanding and show that although it shares properties with the artificial understanding implemented in current machine learning systems it also has some essential differences, the main one being that natural understanding in humans entails consciousness. Moreover, evidence from psychology and neurobiology suggests that it is this capacity for consciousness that, in part at least, explains for the superior performance of humans in some cognitive tasks and may also account for the authenticity of semantic processing that seems to be the hallmark of natural understanding. I propose a hypothesis that might help to explain why consciousness is important to understanding. In closing, I suggest that progress toward implementing human-like understanding in machines—machine understanding—may benefit from a naturalistic approach in which natural processes are modelled as closely as possible in mechanical substrates.

What kind of network is the brain?

The different areas of the cerebral cortex are linked by a network of white matter, comprising the myelinated axons of pyramidal cells. Is this network a neural net, in the sense that representations of the world are embodied in the structure of the net, its pattern of nodes, and connections? Or is it a communications network, where the same physical substrate carries different information from moment to moment? This question is part of the larger question of whether the brain is better modeled by connectionism or by symbolic artificial intelligence (AI), but we review it in the specific context of the psychophysics of stimulus comparison and the format and protocol of information transmission over the long-range tracts of the brain.

Information and the single cell

Understanding the evolution of cognition requires an understanding of the costs and benefits of neural computation. This requires analysis of neuronal circuitry in terms of information-processing efficiency, ultimately cashed out in terms of ATP expenditures relative to adaptive problem-solving abilities. Despite a preoccupation in neuroscience with the synapse as the source of stored neural information, it is clear that, along with synaptic weights and electrochemical dynamics, neurons have multiple mechanisms which store and process information, including 'wetware' (protein phosphorylation, gene transcription, and so on) and cell morphology (dendritic form). Insights into non-synaptic information-processing can be gained by examining the surprisingly complex abilities of single-celled organisms ('cellular cognition') because neurons share many of the same abilities. Cells provide the fundamental level at which information processing interfaces with gene expression, and cell-internal information-processing mechanisms are both powerful and energetically efficient. Understanding cellular computation should be a central goal of research on cognitive evolution.

Energy landscapes and dynamics of ion translocation through membrane transporters: a meeting ground for physics, chemistry, and biology

The dynamics of ion translocation through membrane transporters is visualized from a comprehensive point of view by a Gibbs energy landscape approach. The ΔG calculations have been performed with the Kirkwood-Tanford-Warshel (KTW) electrostatic theory that properly takes into account the self-energies of the ions. The Gibbs energy landscapes for translocation of a single charge and an ion pair are calculated, compared, and contrasted as a function of the order parameter, and the characteristics of the frustrated system with bistability for the ion pair are described and quantified in considerable detail. These calculations have been compared with experimental data on the ΔG of ion pairs in proteins. It is shown that, under suitable conditions, the adverse Gibbs energy barrier can be almost completely compensated by the sum of the electrostatic energy of the charge-charge interactions and the solvation energy of the ion pair. The maxima in ΔG_KTW with interionic distance in the bound H⁺ - A^- charge pair on the enzyme is interpreted in thermodynamic and molecular mechanistic terms, and biological implications for molecular mechanisms of ATP synthesis are discussed. The timescale at which the order parameter moves between two stable states has been estimated by solving the dynamical equations of motion, and a wealth of novel insights into energy transduction during ATP synthesis by the membrane-bound F_OF₁-ATP synthase transporter is offered. In summary, a unifying analytical framework that integrates physics, chemistry, and biology has been developed for ion translocation by membrane transporters for the first time by means of a Gibbs energy landscape approach.