Single-neuron criticality optimizes analog dendritic computation

Dendrites contribute to the gradient of intrinsic timescales encompassing cortical and subcortical brain networks

Introduction

Cytoarchitectonic studies have uncovered a correlation between higher levels of cortical hierarchy and reduced dendritic size. This hierarchical organization extends to the brain's timescales, revealing longer intrinsic timescales at higher hierarchical levels. However, estimating the contribution of single-neuron dendritic morphology to the hierarchy of timescales, which is typically characterized at a macroscopic level, remains challenging.

Method

Here we mapped the intrinsic timescales of six functional networks using functional magnetic resonance imaging (fMRI) data, and characterized the influence of neuronal dendritic size on intrinsic timescales of brain regions, utilizing a multicompartmental neuronal modeling approach based on digitally reconstructed neurons.

Results

The fMRI results revealed a hierarchy of intrinsic timescales encompassing both cortical and subcortical brain regions. The neuronal modeling indicated that neurons with larger dendritic structures exhibit shorter intrinsic timescales. Together these findings highlight the contribution of dendrites at the neuronal level to the hierarchy of intrinsic timescales at the whole-brain level.

Discussion

This study sheds light on the intricate relationship between neuronal structure, cytoarchitectonic maps, and the hierarchy of timescales in the brain.

Is the Papez circuit the location of the elusive episodic memory engram?

All of the brain structures and white matter that make up Papez' circuit, as well as the circuit as a whole, are implicated in the literature in episodic memory formation and recall. This paper shows that Papez' circuit has the detailed structure and connectivity that is evidently required to support the episodic memory engram, and that identifying Papez' circuit as the location of the engram answers a number of long-standing questions regarding the role of medial temporal lobe structures in episodic memory. The paper then shows that the process by which the episodic memory engram may be formed is a network-wide Hebbian potentiation termed "racetrack potentiation", whose frequency corresponds to that observed in vivo in humans for memory functions. Further, by considering the microcircuits observed in the medial temporal lobe structures forming Papez' circuit, the paper establishes the neural mechanisms behind the required functions of sensory information storage and recall, pattern completion, pattern separation, and memory consolidation. The paper shows that Papez' circuit has the necessary connectivity to gather the various elements of an episodic memory occurring within Pöppel's experienced time or "quantum of experience". Finally, the paper shows how the memory engram located in Papez' circuit might be central to the formation of a duplicate engram in the cortex enabling consolidation and long-term storage of episodic memories.

Excitation-Inhibition Balance, Neural Criticality, and Activities in Neuronal Circuits

Neural activities in local circuits exhibit complex and multilevel dynamic features. Individual neurons spike irregularly, which is believed to originate from receiving balanced amounts of excitatory and inhibitory inputs, known as the excitation-inhibition balance. The spatial-temporal cascades of clustered neuronal spikes occur in variable sizes and durations, manifested as neural avalanches with scale-free features. These may be explained by the neural criticality hypothesis, which posits that neural systems operate around the transition between distinct dynamic states. Here, we summarize the experimental evidence for and the underlying theory of excitation-inhibition balance and neural criticality. Furthermore, we review recent studies of excitatory-inhibitory networks with synaptic kinetics as a simple solution to reconcile these two apparently distinct theories in a single circuit model. This provides a more unified understanding of multilevel neural activities in local circuits, from spontaneous to stimulus-response dynamics.

Compressive sensing of functional connectivity maps from patterned optogenetic stimulation of neuronal ensembles

Mapping functional connectivity between neurons is an essential step toward probing the neural computations mediating behavior. Accurately determining synaptic connectivity maps in populations of neurons is challenging in terms of yield, accuracy, and experimental time. Here, we developed a compressive sensing approach to reconstruct synaptic connectivity maps based on random two-photon cell-targeted optogenetic stimulation and membrane voltage readout of many putative postsynaptic neurons. Using a biophysical network model of interconnected populations of excitatory and inhibitory neurons, we characterized mapping recall and precision as a function of network observability, sparsity, number of neurons stimulated, off-target stimulation, synaptic reliability, propagation latency, and network topology. We found that mapping can be achieved with far fewer measurements than the standard pairwise sequential approach, with network sparsity and synaptic reliability serving as primary determinants of the performance. Our results suggest a rapid and efficient method to reconstruct functional connectivity of sparsely connected neuronal networks.

Distance to Criticality Undergoes Critical Transition Before Epileptic Seizure Attacks

Epilepsy is a common neurological disorder characterized by recurring seizures, but its underlying mechanisms remain poorly understood. Despite extensive research, there are still gaps in our knowledge about the relationship between brain dynamics and seizures. In this study, our aim is to address these gaps by proposing a novel approach to assess the role of brain network dynamics in the onset of seizures. Specifically, we investigate the relationship between brain dynamics and seizures by tracking the distance to criticality. Our hypothesis is that this distance plays a crucial role in brain state changes and that seizures may be related to critical transitions of this distance. To test this hypothesis, we develop a method to measure the evolution of the brain network's distance to the critical dynamic systems (i.e., the distance to the tipping point, DTP) using dynamic network biomarker theory and random matrix theory. The results show that the DTP of the brain decreases significantly immediately after onset of an epileptic seizure, suggesting that the brain loses its well-defined quasi-critical state during seizures. We refer to this phenomenon as the "criticality of the criticality" (COC). Furthermore, we observe that DTP exhibits a shape transition before and after the onset of the seizures. This phenomenon suggests the possibility of early warning signal (EWS) identification in the dynamic sequence of DTP, which could be utilized for seizure prediction. Our results show that the Hurst exponent, skewness, kurtosis, autocorrelation, and variance of the DTP sequence are potential EWS features. This study advances our understanding of the relationship between brain dynamics and seizures and highlights the potential for using criticality-based measures to predict and prevent seizures.

The quest for multiscale brain modeling

Addressing the multiscale organization of the brain, which is fundamental to the dynamic repertoire of the organ, remains challenging. In principle, it should be possible to model neurons and synapses in detail and then connect them into large neuronal assemblies to explain the relationship between microscopic phenomena, large-scale brain functions, and behavior. It is more difficult to infer neuronal functions from ensemble measurements such as those currently obtained with brain activity recordings. In this article we consider theories and strategies for combining bottom-up models, generated from principles of neuronal biophysics, with top-down models based on ensemble representations of network activity and on functional principles. These integrative approaches are hoped to provide effective multiscale simulations in virtual brains and neurorobots, and pave the way to future applications in medicine and information technologies.

Pacemaker translocations and power laws in 2D stem cell-derived cardiomyocyte cultures

Power laws are of interest to several scientific disciplines because they can provide important information about the underlying dynamics (e.g. scale invariance and self-similarity) of a given system. Because power laws are of increasing interest to the cardiac sciences as potential indicators of cardiac dysfunction, it is essential that rigorous, standardized analytical methods are employed in the evaluation of power laws. This study compares the methods currently used in the fields of condensed matter physics, geoscience, neuroscience, and cardiology in order to provide a robust analytical framework for evaluating power laws in stem cell-derived cardiomyocyte cultures. One potential power law-obeying phenomenon observed in these cultures is pacemaker translocations, or the spatial and temporal instability of the pacemaker region, in a 2D cell culture. Power law analysis of translocation data was performed using increasingly rigorous methods in order to illustrate how differences in analytical robustness can result in misleading power law interpretations. Non-robust methods concluded that pacemaker translocations adhere to a power law while robust methods convincingly demonstrated that they obey a doubly truncated power law. The results of this study highlight the importance of employing comprehensive methods during power law analysis of cardiomyocyte cultures.

Differential spatiotemporal development of Purkinje cell populations and cerebellum-dependent sensorimotor behaviors

Distinct populations of Purkinje cells (PCs) with unique molecular and connectivity features are at the core of the modular organization of the cerebellum. Previously, we showed that firing activity of PCs differs between ZebrinII-positive and ZebrinII-negative cerebellar modules (Zhou et al., 2014; Wu et al., 2019). Here, we investigate the timing and extent of PC differentiation during development in mice. We found that several features of PCs, including activity levels, dendritic arborization, axonal shape and climbing fiber input, develop differentially between nodular and anterior PC populations. Although all PCs show a particularly rapid development in the second postnatal week, anterior PCs typically have a prolonged physiological and dendritic maturation. In line herewith, younger mice exhibit attenuated anterior-dependent eyeblink conditioning, but faster nodular-dependent compensatory eye movement adaptation. Our results indicate that specific cerebellar regions have unique developmental timelines which match with their related, specific forms of cerebellum-dependent behaviors.

Optimal Organization of Functional Connectivity Networks for Segregation and Integration With Large-Scale Critical Dynamics in Human Brains

The optimal organization for functional segregation and integration in brain is made evident by the “small-world” feature of functional connectivity (FC) networks and is further supported by the loss of this feature that has been described in many types of brain disease. However, it remains unknown how such optimally organized FC networks arise from the brain's structural constrains. On the other hand, an emerging literature suggests that brain function may be supported by critical neural dynamics, which is believed to facilitate information processing in brain. Though previous investigations have shown that the critical dynamics plays an important role in understanding the relation between whole brain structural connectivity and functional connectivity, it is not clear if the critical dynamics could be responsible for the optimal FC network configuration in human brains. Here, we show that the long-range temporal correlations (LRTCs) in the resting state fMRI blood-oxygen-level-dependent (BOLD) signals are significantly correlated with the topological matrices of the FC brain network. Using structure-dynamics-function modeling approach that incorporates diffusion tensor imaging (DTI) data and simple cellular automata dynamics, we showed that the critical dynamics could optimize the whole brain FC network organization by, e.g., maximizing the clustering coefficient while minimizing the characteristic path length. We also demonstrated with a more detailed excitation-inhibition neuronal network model that loss of local excitation-inhibition (E/I) balance causes failure of critical dynamics, therefore disrupting the optimal FC network organization. The results highlighted the crucial role of the critical dynamics in forming an optimal organization of FC networks in the brain and have potential application to the understanding and modeling of abnormal FC configurations in neuropsychiatric disorders.

Single-neuron dynamical effects of dendritic pruning implicated in aging and neurodegeneration: towards a measure of neuronal reserve

Aging is a main risk factor for neurodegenerative disorders including Alzheimer's disease. It is often accompanied by reduced cognitive functions, gray-matter volume, and dendritic integrity. Although age-related brain structural changes have been observed across multiple scales, their functional implications remain largely unknown. Here we simulate the aging effects on neuronal morphology as dendritic pruning and characterize its dynamical implications. Utilizing a detailed computational modeling approach, we simulate the dynamics of digitally reconstructed neurons obtained from Neuromorpho.org. We show that dendritic pruning affects neuronal integrity: firing rate is reduced, causing a reduction in energy consumption, energy efficiency, and dynamic range. Pruned neurons require less energy but their function is often impaired, which can explain the diminished ability to distinguish between similar experiences (pattern separation) in older people. Our measures indicate that the resilience of neuronal dynamics is neuron-specific, heterogeneous, and strongly affected by dendritic topology and the position of the soma. Based on the emergent neuronal dynamics, we propose to classify the effects of dendritic deterioration, and put forward a topological measure of “neuronal reserve” that quantifies the resilience of neuronal dynamics to dendritic pruning. Moreover, our findings suggest that increasing dendritic excitability could partially mitigate the dynamical effects of aging.

Information processing in tree networks of excitable elements

We study the collective response of small random tree networks of diffusively coupled excitable elements to stimuli applied to leaf nodes. Such networks model the morphology of certain sensory neurons that possess branched myelinated dendrites with excitable nodes of Ranvier at every branch point and at leaf nodes. Leaf nodes receive random inputs along with a stimulus and initiate action potentials that propagate through the tree. We quantify the collective response registered at the central node using mutual information. We show that in the strong-coupling limit, the statistics of the number of nodes and leaves determines the mutual information. At the same time, the collective response is insensitive to particular node connectivity and distribution of stimulus over leaf nodes. However, for intermediate coupling, the mutual information may strongly depend on the stimulus distribution among leaf nodes. We identify a mechanism behind the competition of leaf nodes that leads to nonmonotonous dependence of mutual information on coupling strength. We show that a localized stimulus given to a tree branch can be occluded by the background firing of unstimulated branches, thus suppressing mutual information. Nonetheless, the mutual information can be enhanced by a proper stimulus localization and tuning of coupling strength.

Spatially resolved dendritic integration: towards a functional classification of neurons

The vast tree-like dendritic structure of neurons allows them to receive and integrate input from many neurons. A wide variety of neuronal morphologies exist, however, their role in dendritic integration, and how it shapes the response of the neuron, is not yet fully understood. Here, we study the evolution and interactions of dendritic spikes in excitable neurons with complex real branch structures. We focus on dozens of digitally reconstructed illustrative neurons from the online repository NeuroMorpho.org, which contains over 130,000 neurons. Yet, our methods can be promptly extended to any other neuron. This approach allows us to estimate and map specific and heterogeneous patterns of activity observed across extensive dendritic trees with thousands of compartments. We propose a classification of neurons based on the location of the soma (centrality) and the number of branches connected to the soma. These are key topological factors in determining the neuron's energy consumption, firing rate, and the dynamic range, which quantifies the range in synaptic input rate that can be reliably encoded by the neuron's firing rate. Moreover, we find that bifurcations, the structural building blocks of complex dendrites, play a major role in increasing the dynamic range of neurons. Our results provide a better understanding of the effects of neuronal morphology in the diversity of neuronal dynamics and function.

Modelling brain-wide neuronal morphology via rooted Cayley trees

Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent features of brain-wide neuronal morphology. We observe that axonal trees are self-affine while dendritic trees are self-similar. We also show that tree size appear to be random, independent of the number of dendrites within single neurons. Moreover, we consider inhomogeneous branching model which stochastically generates rooted 3-Cayley trees for the brain-wide neuron topology. Based on estimated order-dependent branching probability from actual axonal and dendritic trees, our inhomogeneous model quantitatively captures a number of topological features including size and shape of both axons and dendrites. This sheds lights on a universal mechanism behind the topological formation of brain-wide axonal and dendritic trees.

Dynamic range maximization in excitable networks

We study the strategy to optimally maximize the dynamic range of excitable networks by removing the minimal number of links. A network of excitable elements can distinguish a broad range of stimulus intensities and has its dynamic range maximized at criticality. In this study, we formulate the activation propagation in excitable networks as a message passing process in which a critical state is reached when the largest eigenvalue of the weighted non-backtracking matrix is close to one. By considering the impact of single link removal on the largest eigenvalue, we develop an efficient algorithm that aims to identify the optimal set of links whose removal will drive the system to the critical state. Comparisons with other competing heuristics on both synthetic and real-world networks indicate that the proposed method can maximize the dynamic range by removing the smallest number of links, and at the same time maintaining the largest size of the giant connected component.

Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding

The vicinity of phase transitions selectively amplifies weak stimuli, yielding optimal sensitivity to distinguish external input. Along with this enhanced sensitivity, enhanced levels of fluctuations at criticality reduce the specificity of the response. Given that the specificity of the response is largely compromised when the sensitivity is maximal, the overall benefit of criticality for signal processing remains questionable. Here, it is shown that this impasse can be solved by heterogeneous systems incorporating functional diversity, in which critical and subcritical components coexist. The subnetwork of critical elements has optimal sensitivity, and the subnetwork of subcritical elements has enhanced specificity. Combining segregated features extracted from the different subgroups, the resulting collective response can maximize the trade-off between sensitivity and specificity measured by the dynamic-range-to-noise ratio. Although numerous benefits can be observed when the entire system is critical, our results highlight that optimal performance is obtained when only a small subset of the system is at criticality.

Emergent stochastic oscillations and signal detection in tree networks of excitable elements

We study the stochastic dynamics of strongly-coupled excitable elements on a tree network. The peripheral nodes receive independent random inputs which may induce large spiking events propagating through the branches of the tree and leading to global coherent oscillations in the network. This scenario may be relevant to action potential generation in certain sensory neurons, which possess myelinated distal dendritic tree-like arbors with excitable nodes of Ranvier at peripheral and branching nodes and exhibit noisy periodic sequences of action potentials. We focus on the spiking statistics of the central node, which fires in response to a noisy input at peripheral nodes. We show that, in the strong coupling regime, relevant to myelinated dendritic trees, the spike train statistics can be predicted from an isolated excitable element with rescaled parameters according to the network topology. Furthermore, we show that by varying the network topology the spike train statistics of the central node can be tuned to have a certain firing rate and variability, or to allow for an optimal discrimination of inputs applied at the peripheral nodes.

Relationship in Pacemaker Neurons Between the Long-Term Correlations of Membrane Voltage Fluctuations and the Corresponding Duration of the Inter-Spike Interval

Several studies of the behavior in the voltage and frequency fluctuations of the neural electrical activity have been performed. Here, we explored the particular association between behavior of the voltage fluctuations in the inter-spike segment (VFIS) and the inter-spike intervals (ISI) of F1 pacemaker neurons from H. aspersa, by disturbing the intracellular calcium handling with cadmium and caffeine. The scaling exponent α of the VFIS, as provided by detrended fluctuations analysis, in conjunction with the corresponding duration of ISI to estimate the determination coefficient R ² (48-50 intervals per neuron, N = 5) were all evaluated. The time-varying scaling exponent α(t) of VFIS was also studied (20 segments per neuron, N = 11). The R ² obtained in control conditions was 0.683 ([0.647 0.776] lower and upper quartiles), 0.405 [0.381 0.495] by using cadmium, and 0.151 [0.118 0.222] with caffeine (P < 0.05). A non-uniform scaling exponent α(t) showing a profile throughout the duration of the VFIS was further identified. A significant reduction of long-term correlations by cadmium was confirmed in the first part of this profile (P = 0.0001), but no significant reductions were detected by using caffeine. Our findings endorse that the behavior of the VFIS appears associated to the activation of different populations of ionic channels, which establish the neural membrane potential and are mediated by the intracellular calcium handling. Thus, we provide evidence to consider that the behavior of the VFIS, as determined by the scaling exponent α, conveys insights into mechanisms regulating the excitability of pacemaker neurons.

Diversity improves performance in excitable networks

As few real systems comprise indistinguishable units, diversity is a hallmark of nature. Diversity among interacting units shapes properties of collective behavior such as synchronization and information transmission. However, the benefits of diversity on information processing at the edge of a phase transition, ordinarily assumed to emerge from identical elements, remain largely unexplored. Analyzing a general model of excitable systems with heterogeneous excitability, we find that diversity can greatly enhance optimal performance (by two orders of magnitude) when distinguishing incoming inputs. Heterogeneous systems possess a subset of specialized elements whose capability greatly exceeds that of the nonspecialized elements. We also find that diversity can yield multiple percolation, with performance optimized at tricriticality. Our results are robust in specific and more realistic neuronal systems comprising a combination of excitatory and inhibitory units, and indicate that diversity-induced amplification can be harnessed by neuronal systems for evaluating stimulus intensities.

Cortical burst dynamics predict clinical outcome early in extremely preterm infants

Intermittent bursts of electrical activity are a ubiquitous signature of very early brain activity. Previous studies have largely focused on assessing the amplitudes of these transient cortical bursts or the intervals between them. Recent advances in basic neuroscience have identified the presence of scale-free 'avalanche' processes in bursting patterns of cortical activity in other clinical contexts. Here, we hypothesize that cortical bursts in human preterm infants also exhibit scale-free properties, providing new insights into the nature, temporal evolution, and prognostic value of spontaneous brain activity in the days immediately following preterm birth. We examined electroencephalographic recordings from 43 extremely preterm infants (gestational age 22-28 weeks) and demonstrated that their cortical bursts exhibit scale-free properties as early as 12 h after birth. The scaling relationships of cortical bursts correlate significantly with later mental development-particularly within the first 12 h of life. These findings show that early preterm brain activity is characterized by scale-free dynamics which carry developmental significance, hence offering novel means for rapid and early clinical prediction of neurodevelopmental outcomes.

Quasicritical brain dynamics on a nonequilibrium Widom line

Is the brain really operating at a critical point? We study the nonequilibrium properties of a neural network which models the dynamics of the neocortex and argue for optimal quasicritical dynamics on the Widom line where the correlation length and information transmission are optimized. We simulate the network and introduce an analytical mean-field approximation, characterize the nonequilibrium phase transitions, and present a nonequilibrium phase diagram, which shows that in addition to an ordered and disordered phase, the system exhibits a "quasiperiodic" phase corresponding to synchronous activity in simulations, which may be related to the pathological synchronization associated with epilepsy.

Fractal-like correlations of the fluctuating inter-spike membrane potential of a Helix aspersa pacemaker neuron

We analyzed the voltage fluctuations of the membrane potential manifested along the inter-spike segment of a pacemaker neuron. Time series of intracellular inter-spike voltage fluctuations were obtained in the current-clamp configuration from the F1 neuron of 12 Helix aspersa specimens. To assess the dynamic or stochastic nature of the voltage fluctuations these series were analyzed by Detrended Fluctuation Analysis (DFA), providing the scaling exponent α. The median α result obtained for the inter-spike segments was 0.971 ([0.963, 0.995] lower and upper quartiles). Our results indicate a critical-like dynamic behavior in the inter-spike membrane potential that, far from being random, shows long-term correlations probably linked to the dynamics of the mechanisms involved in the regulation of the membrane potential, thereby endorsing the occurrence of critical-like phenomena at a single-neuron level.