Mitochondrial morphology governs ATP production rate.

Life is based on energy conversion. In particular, in the nervous system, significant amounts of energy are needed to maintain synaptic transmission and homeostasis. To a large extent, neurons depend on oxidative phosphorylation in mitochondria to meet their high energy demand. For a comprehensive understanding of the metabolic demands in neuronal signaling, accurate models of ATP production in mitochondria are required. Here, we present a thermodynamically consistent model of ATP production in mitochondria based on previous work. The significant improvement of the model is that the reaction rate constants are set such that detailed balance is satisfied. Moreover, using thermodynamic considerations, the dependence of the reaction rate constants on membrane potential, pH, and substrate concentrations are explicitly provided. These constraints assure that the model is physically plausible. Furthermore, we explore different parameter regimes to understand in which conditions ATP production or its export are the limiting steps in making ATP available in the cytosol. The outcomes reveal that, under the conditions used in our simulations, ATP production is the limiting step and not its export. Finally, we performed spatial simulations with nine 3-D realistic mitochondrial reconstructions and linked the ATP production rate in the cytosol with morphological features of the organelles.

Morphological principles of neuronal mitochondria.

In the highly dynamic metabolic landscape of a neuron, mitochondrial membrane architectures can provide critical insight into the unique energy balance of the cell. Current theoretical calculations of functional outputs like adenosine triphosphate and heat often represent mitochondria as idealized geometries, and therefore, can miscalculate the metabolic fluxes. To analyze mitochondrial morphology in neurons of mouse cerebellum neuropil, 3D tracings of complete synaptic and axonal mitochondria were constructed using a database of serial transmission electron microscopy (TEM) tomography images and converted to watertight meshes with minimal distortion of the original microscopy volumes with a granularity of 1.64 nanometer isotropic voxels. The resulting in-silico representations were subsequently quantified by differential geometry methods in terms of the mean and Gaussian curvatures, surface areas, volumes, and membrane motifs, all of which can alter the metabolic output of the organelle. Finally, we identify structural motifs present across this population of mitochondria, which may contribute to future modeling studies of mitochondrial physiology and metabolism in neurons.

NMDAR-dependent long-term depression is associated with increased short term plasticity through autophagy mediated loss of PSD-95.

Long-term depression (LTD) of synaptic strength can take multiple forms and contribute to circuit remodeling, memory encoding or erasure. The generic term LTD encompasses various induction pathways, including activation of NMDA, mGlu or P2X receptors. However, the associated specific molecular mechanisms and effects on synaptic physiology are still unclear. We here compare how NMDAR- or P2XR-dependent LTD affect synaptic nanoscale organization and function in rodents. While both LTDs are associated with a loss and reorganization of synaptic AMPARs, only NMDAR-dependent LTD induction triggers a profound reorganization of PSD-95. This modification, which requires the autophagy machinery to remove the T19-phosphorylated form of PSD-95 from synapses, leads to an increase in AMPAR surface mobility. We demonstrate that these post-synaptic changes that occur specifically during NMDAR-dependent LTD result in an increased short-term plasticity improving neuronal responsiveness of depressed synapses. Our results establish that P2XR- and NMDAR-mediated LTD are associated to functionally distinct forms of LTD.

Differential Covariance: A New Method to Estimate Functional Connectivity in fMRI.

Measuring functional connectivity from fMRI recordings is important in understanding processing in cortical networks. However, because the brain's connection pattern is complex, currently used methods are prone to producing false functional connections. We introduce differential covariance analysis, a new method that uses derivatives of the signal for estimating functional connectivity. We generated neural activities from dynamical causal modeling and a neural network of Hodgkin-Huxley neurons and then converted them to hemodynamic signals using the forward balloon model. The simulated fMRI signals, together with the ground-truth connectivity pattern, were used to benchmark our method with other commonly used methods. Differential covariance achieved better results in complex network simulations. This new method opens an alternative way to estimate functional connectivity.

Mitochondrial morphology provides a mechanism for energy buffering at synapses.

Mitochondria as the main energy suppliers of eukaryotic cells are highly dynamic organelles that fuse, divide and are transported along the cytoskeleton to ensure cellular energy homeostasis. While these processes are well established, substantial evidence indicates that the internal structure is also highly variable in dependence on metabolic conditions. However, a quantitative mechanistic understanding of how mitochondrial morphology affects energetic states is still elusive. To address this question, we here present an agent-based multiscale model that integrates three-dimensional morphologies from electron microscopy tomography with the molecular dynamics of the main ATP producing components. We apply our modeling approach to mitochondria at the synapse which is the largest energy consumer within the brain. Interestingly, comparing the spatiotemporal simulations with a corresponding space-independent approach, we find minor spatial effects when the system relaxes toward equilibrium but a qualitative difference in fluctuating environments. These results suggest that internal mitochondrial morphology is not only optimized for ATP production but also provides a mechanism for energy buffering and may represent a mechanism for cellular robustness.

Geometric principles of second messenger dynamics in dendritic spines.

Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14-19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity.

Epigenomic Signatures of Neuronal Diversity in the Mammalian Brain.

Neuronal diversity is essential for mammalian brain function but poses a challenge to molecular profiling. To address the need for tools that facilitate cell-type-specific epigenomic studies, we developed the first affinity purification approach to isolate nuclei from genetically defined cell types in a mammal. We combine this technique with next-generation sequencing to show that three subtypes of neocortical neurons have highly distinctive epigenomic landscapes. Over 200,000 regions differ in chromatin accessibility and DNA methylation signatures characteristic of gene regulatory regions. By footprinting and motif analyses, these regions are predicted to bind distinct cohorts of neuron subtype-specific transcription factors. Neuronal epigenomes reflect both past and present gene expression, with DNA hyper-methylation at developmentally critical genes appearing as a novel epigenomic signature in mature neurons. Taken together, our findings link the functional and transcriptional complexity of neurons to their underlying epigenomic diversity.

Top-down inputs enhance orientation selectivity in neurons of the primary visual cortex during perceptual learning.

Perceptual learning has been used to probe the mechanisms of cortical plasticity in the adult brain. Feedback projections are ubiquitous in the cortex, but little is known about their role in cortical plasticity. Here we explore the hypothesis that learning visual orientation discrimination involves learning-dependent plasticity of top-down feedback inputs from higher cortical areas, serving a different function from plasticity due to changes in recurrent connections within a cortical area. In a Hodgkin-Huxley-based spiking neural network model of visual cortex, we show that modulation of feedback inputs to V1 from higher cortical areas results in shunting inhibition in V1 neurons, which changes the response properties of V1 neurons. The orientation selectivity of V1 neurons is enhanced without changing orientation preference, preserving the topographic organizations in V1. These results provide new insights to the mechanisms of plasticity in the adult brain, reconciling apparently inconsistent experiments and providing a new hypothesis for a functional role of the feedback connections.

Learning where to look for a hidden target.

Survival depends on successfully foraging for food, for which evolution has selected diverse behaviors in different species. Humans forage not only for food, but also for information. We decide where to look over 170,000 times per day, approximately three times per wakeful second. The frequency of these saccadic eye movements belies the complexity underlying each individual choice. Experience factors into the choice of where to look and can be invoked to rapidly redirect gaze in a context and task-appropriate manner. However, remarkably little is known about how individuals learn to direct their gaze given the current context and task. We designed a task in which participants search a novel scene for a target whose location was drawn stochastically on each trial from a fixed prior distribution. The target was invisible on a blank screen, and the participants were rewarded when they fixated the hidden target location. In just a few trials, participants rapidly found the hidden targets by looking near previously rewarded locations and avoiding previously unrewarded locations. Learning trajectories were well characterized by a simple reinforcement-learning (RL) model that maintained and continually updated a reward map of locations. The RL model made further predictions concerning sensitivity to recent experience that were confirmed by the data. The asymptotic performance of both the participants and the RL model approached optimal performance characterized by an ideal-observer theory. These two complementary levels of explanation show how experience in a novel environment drives visual search in humans and may extend to other forms of search such as animal foraging.

Divide and conquer: functional segregation of synaptic inputs by astrocytic microdomains could alleviate paroxysmal activity following brain trauma.

Traumatic brain injury often leads to epileptic seizures. Among other factors, homeostatic synaptic plasticity (HSP) mediates posttraumatic epileptogenesis through unbalanced synaptic scaling, partially compensating for the trauma-incurred loss of neural excitability. HSP is mediated in part by tumor necrosis factor alpha (TNFα), which is released locally from reactive astrocytes early after trauma in response to chronic neuronal inactivity. During this early period, TNFα is likely to be constrained to its glial sources; however, the contribution of glia-mediated spatially localized HSP to post-traumatic epileptogenesis remains poorly understood. We used computational model to investigate the reorganization of collective neural activity early after trauma. Trauma and synaptic scaling transformed asynchronous spiking into paroxysmal discharges. The rate of paroxysms could be reduced by functional segregation of synaptic input into astrocytic microdomains. Thus, we propose that trauma-triggered reactive gliosis could exert both beneficial and deleterious effects on neural activity.

How Nox2-containing NADPH oxidase affects cortical circuits in the NMDA receptor antagonist model of schizophrenia.

SIGNIFICANCE: Schizophrenia is a complex neuropsychiatric disorder affecting around 1% of the population worldwide. Its mode of inheritance suggests a multigenic neurodevelopmental disorder with symptoms appearing during late adolescence/early adulthood, with its onset strongly influenced by environmental stimuli. Many neurotransmitter systems, including dopamine, glutamate, and gamma-aminobutyric acid, show alterations in affected individuals, and the behavioral and physiological characteristics of the disease can be mimicked by drugs that produce blockade of N-methyl-d-aspartate glutamate receptors (NMDARs). RECENT ADVANCES: Mounting evidence suggests that drugs that block NMDARs specifically impair the inhibitory capacity of parvalbumin-expressing (PV+) fast-spiking neurons in adult and developing rodents, and alterations in these inhibitory neurons is one of the most consistent findings in the schizophrenic postmortem brain. Disruption of the inhibitory capacity of PV+ inhibitory neurons will alter the functional balance between excitation and inhibition in prefrontal cortical circuits producing impairment of working memory processes such as those observed in schizophrenia. CRITICAL ISSUES: Mechanistically, the effect of NMDAR antagonists can be attributed to the activation of the Nox2-dependent reduced form of nicotinamide adenine dinucleotide phosphate oxidase pathway in cortical neurons, which is consistent with the emerging role of oxidative stress in the pathogenesis of mental disorders, specifically schizophrenia. Here we review the mechanisms by which NMDAR antagonists produce lasting impairment of the cortical PV+ neuronal system and the roles played by Nox2-dependent oxidative stress mechanisms. FUTURE DIRECTIONS: The discovery of the pathways by which oxidative stress leads to unbalanced excitation and inhibition in cortical neural circuits opens a new perspective toward understanding the biological underpinnings of schizophrenia.

The Hodgkin-Huxley heritage: from channels to circuits.

The Hodgkin-Huxley studies of the action potential, published 60 years ago, are a central pillar of modern neuroscience research, ranging from molecular investigations of the structural basis of ion channel function to the computational implications at circuit level. In this Symposium Review, we aim to demonstrate the ongoing impact of Hodgkin's and Huxley's ideas. The Hodgkin-Huxley model established a framework in which to describe the structural and functional properties of ion channels, including the mechanisms of ion permeation, selectivity, and gating. At a cellular level, the model is used to understand the conditions that control both the rate and timing of action potentials, essential for neural encoding of information. Finally, the Hodgkin-Huxley formalism is central to computational neuroscience to understand both neuronal integration and circuit level information processing, and how these mechanisms might have evolved to minimize energy cost.

Thalamic burst firing propensity: a comparison of the dorsal lateral geniculate and pulvinar nuclei in the tree shrew.

Relay neurons in dorsal thalamic nuclei can fire high-frequency bursts of action potentials that ride the crest of voltage-dependent transient (T-type) calcium currents [low-threshold spike (LTS)]. To explore potential nucleus-specific burst features, we compared the membrane properties of dorsal lateral geniculate nucleus (dLGN) and pulvinar nucleus relay neurons using in vitro whole-cell recording in juvenile and adult tree shrew (Tupaia) tissue slices. We injected current ramps of variable slope into neurons that were sufficiently hyperpolarized to de-inactivate T-type calcium channels. In a small percentage of juvenile pulvinar and dLGN neurons, an LTS could not be evoked. In the remaining juvenile neurons and in all adult dLGN neurons, a single LTS could be evoked by current ramps. However, in the adult pulvinar, current ramps evoked multiple LTSs in >70% of recorded neurons. Using immunohistochemistry, Western blot techniques, unbiased stereology, and confocal and electron microscopy, we found that pulvinar neurons expressed more T-type calcium channels (Ca(v) 3.2) and more small conductance potassium channels (SK2) than dLGN neurons and that the pulvinar nucleus contained a higher glia-to-neuron ratio than the dLGN. Hodgkin-Huxley-type compartmental models revealed that the distinct firing modes could be replicated by manipulating T-type calcium and SK2 channel density, distribution, and kinetics. The intrinsic properties of pulvinar neurons that promote burst firing in the adult may be relevant to the treatment of conditions that involve the adult onset of aberrant thalamocortical interactions.

Imbalance of ionic conductances contributes to diverse symptoms of demyelination.

Fast axonal conduction of action potentials in mammals relies on myelin insulation. Demyelination can cause slowed, blocked, desynchronized, or paradoxically excessive spiking that underlies the symptoms observed in demyelination diseases. The diversity and timing of such symptoms are poorly understood, often intermittent, and uncorrelated with disease progress. We modeled the effects of demyelination (and secondary remodeling) on intrinsic axonal excitability using Hodgkin-Huxley and reduced Morris-Lecar models. Simulations and analysis suggested a simple explanation for the breadth of symptoms and revealed that the ratio of sodium to leak conductance, g(Na)/g(L), acted as a four-way switch controlling excitability patterns that included spike failure, single spike transmission, afterdischarge, and spontaneous spiking. Failure occurred when this ratio fell below a threshold value. Afterdischarge occurred at g(Na)/g(L) just below the threshold for spontaneous spiking and required a slow inward current that allowed for two stable attractor states, one corresponding to quiescence and the other to repetitive spiking. A neuron prone to afterdischarge could function normally unless it was switched to its "pathological" attractor state; thus, although the underlying pathology may develop slowly by continuous changes in membrane conductances, a discontinuous change in axonal excitability can occur and lead to paroxysmal symptoms. We conclude that tonic and paroxysmal positive symptoms as well as negative symptoms may be a consequence of varying degrees of imbalance between g(Na) and g(L) after demyelination. The KCNK family of g(L) potassium channels may be an important target for new drugs to treat the symptoms of demyelination.

Metabolic cost as a unifying principle governing neuronal biophysics.

The brain contains an astonishing diversity of neurons, each expressing only one set of ion channels out of the billions of potential channel combinations. Simple organizing principles are required for us to make sense of this abundance of possibilities and wealth of related data. We suggest that energy minimization subject to functional constraints may be one such unifying principle. We compared the energy needed to produce action potentials singly and in trains for a wide range of channel densities and kinetic parameters and examined which combinations of parameters maximized spiking function while minimizing energetic cost. We confirmed these results for sodium channels using a dynamic current clamp in neocortical fast spiking interneurons. We find further evidence supporting this hypothesis in a wide range of other neurons from several species and conclude that the ion channels in these neurons minimize energy expenditure in their normal range of spiking.

Does schizophrenia arise from oxidative dysregulation of parvalbumin-interneurons in the developing cortex?

An imbalance in the redox-state of the brain may be part of the underlying pathophysiology in schizophrenia. Inflammatory mediators, such as IL-6, which can tip the redox balance into a pro-oxidant state, have been consistently found to be altered in schizophrenia patients. However, the relationship of altered redox-state to altered brain functions observed in the disease has been unclear. Recent data from a pharmacological model of schizophrenia suggest that redox and inflammatory imbalances may be directly linked to the pathophysiology of the disease by alterations in fast-spiking interneurons. Repetitive adult exposure to the NMDA-R antagonist ketamine increases the levels of the proinflammatory cytokine interleukin-6 in brain which, through activation of the superoxide-producing enzyme NADPH oxidase (Nox2), leads to the loss of the GABAergic phenotype of PV-interneurons and to decreased inhibitory activity in prefrontal cortex. This effect is not observed after a single exposure to ketamine, suggesting that the first exposure to the NMDA-R antagonist primes the brain such that deleterious effects on PV-interneurons appear upon repetitive exposures. The effects of activation of the IL-6/Nox2 pathway on the PV-interneuronal system are reversible in the adult brain, but permanent in the developing cortex. The slow development of PV-interneurons, although essential for shaping of neuronal circuits during postnatal brain development, increases their vulnerability to deleterious insults that can permanently affect their maturational process. Thus, in individuals with genetic predisposition, the persistent activation of the IL-6/Nox2 pathway may be an environmental factor that tips the redox balance leading to schizophrenia symptoms in late adolescence and early adulthood.

Biophysical basis for three distinct dynamical mechanisms of action potential initiation.

Transduction of graded synaptic input into trains of all-or-none action potentials (spikes) is a crucial step in neural coding. Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties. Despite widespread use of this classification scheme, a generalizable explanation of its biophysical basis has not been described. We recorded from spinal sensory neurons representing each class and reproduced their transduction properties in a minimal model. With phase plane and bifurcation analysis, each class of excitability was shown to derive from distinct spike initiating dynamics. Excitability could be converted between all three classes by varying single parameters; moreover, several parameters, when varied one at a time, had functionally equivalent effects on excitability. From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin's classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents. Class 1 excitability occurs through a saddle node on invariant circle bifurcation when net current at perithreshold potentials is inward (depolarizing) at steady state. Class 2 excitability occurs through a Hopf bifurcation when, despite net current being outward (hyperpolarizing) at steady state, spike initiation occurs because inward current activates faster than outward current. Class 3 excitability occurs through a quasi-separatrix crossing when fast-activating inward current overpowers slow-activating outward current during a stimulus transient, although slow-activating outward current dominates during constant stimulation. Experiments confirmed that different classes of spinal lamina I neurons express the subthreshold currents predicted by our simulations and, further, that those currents are necessary for the excitability in each cell class. Thus, our results demonstrate that all three classes of excitability arise from a continuum in the direction and magnitude of subthreshold currents. Through detailed analysis of the spike-initiating process, we have explained a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input.

Pyramidal neurons switch from integrators in vitro to resonators under in vivo-like conditions.

During wakefulness, pyramidal neurons in the intact brain are bombarded by synaptic input that causes tonic depolarization, increased membrane conductance (i.e., shunting), and noisy fluctuations in membrane potential; by comparison, pyramidal neurons in acute slices typically experience little background input. Such differences in operating conditions can compromise extrapolation of in vitro data to explain neuronal operation in vivo. For instance, pyramidal neurons have been identified as integrators (i.e., class 1 neurons according to Hodgkin's classification of intrinsic excitability) based on in vitro experiments but that classification is inconsistent with the ability of hippocampal pyramidal neurons to oscillate/resonate at theta frequency since intrinsic oscillatory behavior is limited to class 2 neurons. Using long depolarizing stimuli and dynamic clamp to reproduce in vivo-like conditions in slice experiments, we show that CA1 hippocampal pyramidal cells switch from integrators to resonators, i.e., from class 1 to class 2 excitability. The switch is explained by increased outward current contributed by the M-type potassium current I(M), which shifts the balance of inward and outward currents active at perithreshold potentials and thereby converts the spike-initiating mechanism as predicted by dynamical analysis of our computational model. Perithreshold activation of I(M) is enhanced by the depolarizing shift in spike threshold caused by shunting and/or sodium channel inactivation secondary to tonic depolarization. Our conclusions were validated by multiple comparisons between simulation and experimental data. Thus even so-called "intrinsic" properties may differ qualitatively between in vitro and in vivo conditions.

Model of traveling waves in a coral nerve network.

Coral polyps contract when electrically stimulated and a wave of contraction travels from the site of stimulation at a constant speed. Models of coral nerve networks were optimized to match one of three different experimentally observed behaviors. To search for model parameters that reproduce the experimental observations, we applied genetic algorithms to increasingly more complex models of a coral nerve net. In a first stage of optimization, individual neurons responded with spikes to multiple, but not single pulses of activation. In a second stage, we used these neurons as the starting point for the optimization of a two-dimensional nerve net. This strategy yielded a network with parameters that reproduced the experimentally observed spread of excitation.

Division accuracy in a stochastic model of Min oscillations in Escherichia coli.

Accurate cell division in Escherichia coli requires the Min proteins MinC, MinD, and MinE as well as the presence of nucleoids. MinD and MinE exhibit spatial oscillations, moving from pole to pole of the bacterium, resulting in an average MinD concentration that is low at the center of the cell and high at the poles. This concentration minimum is thought to signal the site of cell division. Deterministic models of the Min oscillations reproduce many observed features of the system, including the concentration minimum of MinD. However, there are only a few thousand Min proteins in a bacterium, so stochastic effects are likely to play an important role. Here, we show that Monte Carlo simulations with a large number of proteins agree well with the results from a deterministic treatment of the equations. The location of minimum local MinD concentration is too variable to account for cell division accuracy in wild-type, but is consistent with the accuracy of cell division in cells without nucleoids. This finding confirms the need to include additional mechanisms, such as reciprocal interactions with the cell division ring or positioning of the nucleoids, to explain wild-type accuracy.