Axonal Computations

Beyond a Transmission Cable-New Technologies to Reveal the Richness in Axonal Electrophysiology

The axon is a neuronal structure capable of processing, encoding, and transmitting information. This assessment contrasts with a limiting, but deeply rooted, perspective where the axon functions solely as a transmission cable of somatodendritic activity, sending signals in the form of stereotypical action potentials. This perspective arose, at least partially, because of the technical difficulties in probing axons: their extreme length-to-diameter ratio and intricate growth paths preclude the study of their dynamics through traditional techniques. Recent findings are challenging this view and revealing a much larger repertoire of axonal computations. Axons display complex signaling processes and structure-function relationships, which can be modulated via diverse activity-dependent mechanisms. Additionally, axons can exhibit patterns of activity that are dramatically different from those of their corresponding soma. Not surprisingly, many of these recent discoveries have been driven by novel technology developments, which allow for in vitro axon electrophysiology with unprecedented spatiotemporal resolution and signal-to-noise ratio. In this review, we outline the state-of-the-art in vitro toolset for axonal electrophysiology and summarize the recent discoveries in axon function it has enabled. We also review the increasing repertoire of microtechnologies for controlling axon guidance which, in combination with the available cutting-edge electrophysiology and imaging approaches, have the potential for more controlled and high-throughput in vitro studies. We anticipate that a larger adoption of these new technologies by the neuroscience community will drive a new era of experimental opportunities in the study of axon physiology and consequently, neuronal function.

How far neuroscience is from understanding brains

The cellular biology of brains is relatively well-understood, but neuroscientists have not yet generated a theory explaining how brains work. Explanations of how neurons collectively operate to produce what brains can do are tentative and incomplete. Without prior assumptions about the brain mechanisms, I attempt here to identify major obstacles to progress in neuroscientific understanding of brains and central nervous systems. Most of the obstacles to our understanding are conceptual. Neuroscience lacks concepts and models rooted in experimental results explaining how neurons interact at all scales. The cerebral cortex is thought to control awake activities, which contrasts with recent experimental results. There is ambiguity distinguishing task-related brain activities from spontaneous activities and organized intrinsic activities. Brains are regarded as driven by external and internal stimuli in contrast to their considerable autonomy. Experimental results are explained by sensory inputs, behavior, and psychological concepts. Time and space are regarded as mutually independent variables for spiking, post-synaptic events, and other measured variables, in contrast to experimental results. Dynamical systems theory and models describing evolution of variables with time as the independent variable are insufficient to account for central nervous system activities. Spatial dynamics may be a practical solution. The general hypothesis that measurements of changes in fundamental brain variables, action potentials, transmitter releases, post-synaptic transmembrane currents, etc., propagating in central nervous systems reveal how they work, carries no additional assumptions. Combinations of current techniques could reveal many aspects of spatial dynamics of spiking, post-synaptic processing, and plasticity in insects and rodents to start with. But problems defining baseline and reference conditions hinder interpretations of the results. Furthermore, the facts that pooling and averaging of data destroy their underlying dynamics imply that single-trial designs and statistics are necessary.

Functional imaging of conduction dynamics in cortical and spinal axons

Mammalian axons are specialized for transmitting action potentials to targets within the central and peripheral nervous system. A growing body of evidence suggests that, besides signal conduction, axons play essential roles in neural information processing, and their malfunctions are common hallmarks of neurodegenerative diseases. The technologies available to study axonal function and structure integrally limit the comprehension of axon neurobiology. High-density microelectrode arrays (HD-MEAs) allow for accessing axonal action potentials at high spatiotemporal resolution, but provide no insights on axonal morphology. Here, we demonstrate a method for electrical visualization of axonal morphologies based on extracellular action potentials recorded from cortical and motor neurons using HD-MEAs. The method enabled us to reconstruct up to 5-cm-long axonal arbors and directly monitor axonal conduction across thousands of recording sites. We reconstructed 1.86 m of cortical and spinal axons in total and found specific features in their structure and function.

Motor cortex analogue neurons in songbirds utilize Kv3 channels to generate ultranarrow spikes

Complex motor skills in vertebrates require specialized upper motor neurons with precise action potential (AP) firing. To examine how diverse populations of upper motor neurons subserve distinct functions and the specific repertoire of ion channels involved, we conducted a thorough study of the excitability of upper motor neurons controlling somatic motor function in the zebra finch. We found that robustus arcopallialis projection neurons (RAPNs), key command neurons for song production, exhibit ultranarrow spikes and higher firing rates compared to neurons controlling non-vocal somatic motor functions (dorsal intermediate arcopallium [AId] neurons). Pharmacological and molecular data indicate that this striking difference is associated with the higher expression in RAPNs of high threshold, fast-activating voltage-gated Kv3 channels, that likely contain Kv3.1 (KCNC1) subunits. The spike waveform and Kv3.1 expression in RAPNs mirror properties of Betz cells, specialized upper motor neurons involved in fine digit control in humans and other primates but absent in rodents. Our study thus provides evidence that songbirds and primates have convergently evolved the use of Kv3.1 to ensure precise, rapid AP firing in upper motor neurons controlling fast and complex motor skills.

Systems of axon-like circuits for self-assembled and self-controlled growth of bioelectric networks

By guiding cell and chemical migration and coupling with genetic mechanisms, bioelectric networks of potentials influence biological pattern formation and are known to have profound effects on growth processes. An abstract model that is amenable to exact analysis has been proposed in the circuit tile assembly model (cTAM) to understand self-assembled and self-controlled growth as an emergent phenomenon that is capable of complex behaviors, like self-replication. In the cTAM, a voltage source represents a finite supply of energy that drives growth until it is unable to overcome randomizing factors in the environment, represented by a threshold. Here, the cTAM is extended to the axon or alternating cTAM model (acTAM) to include a circuit similar to signal propagation in axons, exhibiting time-varying electric signals and a dependence on frequency of the input voltage. The acTAM produces systems of circuits whose electrical properties are coupled to their length as growth proceeds through self-assembly. The exact response is derived for increasingly complex circuit systems as the assembly proceeds. The model exhibits complicated behaviors that elucidate the interactive role of energy, environment, and noise with electric signals in axon-like circuits during biological growth of complex patterns and function.

Modular Organization of Signal Transmission in Primate Somatosensory Cortex

Axonal patches are known as the major sites of synaptic connections in the cerebral cortex of higher order mammals. However, the functional role of these patches is highly debated. Patches are formed by populations of nearby neurons in a topographic manner and are recognized as the termination fields of long-distance lateral connections within and between cortical areas. In addition, axons form numerous boutons that lie outside the patches, whose function is also unknown. To better understand the functional roles of these two distinct populations of boutons, we compared individual and collective morphological features of axons within and outside the patches of intra-areal, feedforward, and feedback pathways by way of tract tracing in the somatosensory cortex of New World monkeys. We found that, with the exception of tortuosity, which is an invariant property, bouton spacing and axonal convergence properties differ significantly between axons within patch and no-patch domains. Principal component analyses corroborated the clustering of axons according to patch formation without any additional effect by the type of pathway or laminar distribution. Stepwise logistic regression identified convergence and bouton density as the best predictors of patch formation. These findings support that patches are specific sites of axonal convergence that promote the synchronous activity of neuronal populations. On the other hand, no-patch domains could form a neuroanatomical substrate to diversify the responses of cortical neurons.

Long-Term Changes in Axon Calibers after Injury: Observations on the Mouse Corticospinal Tract

White matter pathology is common across a wide spectrum of neurological diseases. Characterizing this pathology is important for both a mechanistic understanding of neurological diseases as well as for the development of neuroimaging biomarkers. Although axonal calibers can vary by orders of magnitude, they are tightly regulated and related to neuronal function, and changes in axon calibers have been reported in several diseases and their models. In this study, we utilize the impact acceleration model of traumatic brain injury (IA-TBI) to assess early and late changes in the axon diameter distribution (ADD) of the mouse corticospinal tract using Airyscan and electron microscopy. We find that axon calibers follow a lognormal distribution whose parameters significantly change after injury. While IA-TBI leads to 30% loss of corticospinal axons by day 7 with a bias for larger axons, at 21 days after injury we find a significant redistribution of axon frequencies that is driven by a reduction in large-caliber axons in the absence of detectable degeneration. We postulate that changes in ADD features may reflect a functional adaptation of injured neural systems. Moreover, we find that ADD features offer an accurate way to discriminate between injured and non-injured mice. Exploring injury-related ADD signatures by histology or new emerging neuroimaging modalities may offer a more nuanced and comprehensive way to characterize white matter pathology and may also have the potential to generate novel biomarkers of injury.

Bidirectional flow of action potentials in axons drives activity dynamics in neuronal cultures

Objective. Recent technological advances are revealing the complex physiology of the axon and challenging long-standing assumptions. Namely, while most action potential (AP) initiation occurs at the axon initial segment in central nervous system neurons, initiation in distal parts of the axon has been reported to occur in both physiological and pathological conditions. The functional role of these ectopic APs, if exists, is still not clear, nor its impact on network activity dynamics.Approach. Using an electrophysiology platform specifically designed for assessing axonal conduction we show here for the first time regular and effective bidirectional axonal conduction in hippocampal and dorsal root ganglia cultures. We investigate and characterize this bidirectional propagation both in physiological conditions and after distal axotomy.Main results.A significant fraction of APs are not coming from the canonical synapse-dendrite-soma signal flow, but instead from signals originating at the distal axon. Importantly, antidromic APs may carry information and can have a functional impact on the neuron, as they consistently depolarize the soma. Thus, plasticity or gene transduction mechanisms triggered by soma depolarization can also be affected by these antidromic APs. Conduction velocity is asymmetrical, with antidromic conduction being slower than orthodromic.Significance.Altogether these findings have important implications for the study of neuronal functionin vitro, reshaping our understanding on how information flows in neuronal cultures.

Myelin: A gatekeeper of activity-dependent circuit plasticity?

[Figure: see text].

Periods of synchronized myelin changes shape brain function and plasticity

Myelin, a lipid membrane that wraps axons, enabling fast neurotransmission and metabolic support to axons, is conventionally thought of as a static structure that is set early in development. However, recent evidence indicates that in the central nervous system (CNS), myelination is a protracted and plastic process, ongoing throughout adulthood. Importantly, myelin is emerging as a potential modulator of neuronal networks, and evidence from human studies has highlighted myelin as a major player in shaping human behavior and learning. Here we review how myelin changes throughout life and with learning. We discuss potential mechanisms of myelination at different life stages, explore whether myelin plasticity provides the regenerative potential of the CNS white matter, and question whether changes in myelin may underlie neurological disorders.

Prolegomena to an Operator Theory of Computation

Defining computation as information processing (information dynamics) with information as a relational property of data structures (the difference in one system that makes a difference in another system) makes it very suitable to use operator formulation, with similarities to category theory. The concept of the operator is exceedingly important in many knowledge areas as a tool of theoretical studies and practical applications. Here we introduce the operator theory of computing, opening new opportunities for the exploration of computing devices, processes, and their networks.

Axonal Tree Morphology and Signal Propagation Dynamics Improve Interneuron Classification

Neurons are diverse and can be differentiated by their morphological, electrophysiological, and molecular properties. Current morphology-based classification approaches largely rely on the dendritic tree structure or on the overall axonal projection layout. Here, we use data from public databases of neuronal reconstructions and membrane properties to study the characteristics of the axonal and dendritic trees for interneuron classification. We show that combining signal propagation patterns observed by biophysical simulations of the activity along ramified axonal trees with morphological parameters of the axonal and dendritic trees, significantly improve classification results compared to previous approaches. The classification schemes introduced here can be utilized for robust neuronal classification. Our work paves the way for understanding and utilizing form-function principles in realistic neuronal reconstructions.

Myelination Increases the Spatial Extent of Analog-Digital Modulation of Synaptic Transmission: A Modeling Study

Analog-digital facilitations (ADFs) have been described in local excitatory brain circuits and correspond to a class of phenomena describing how subthreshold variations of the presynaptic membrane potential influence spike-evoked synaptic transmission. In many brain circuits, ADFs rely on the propagation of somatic membrane potential fluctuations to the presynaptic bouton where they modulate ion channels availability, inducing modifications of the presynaptic spike waveform, the spike-evoked Ca²⁺ entry, and the transmitter release. Therefore, one major requirement for ADFs to occur is the propagation of subthreshold membrane potential variations from the soma to the presynaptic bouton. To date, reported ADFs space constants are relatively short (250–500 μm) which limits their action to proximal synapses. However, ADFs have been studied either in unmyelinated axons or in juvenile animals in which myelination is incomplete. We examined here the potential gain of ADFs spatial extent caused by myelination using a realistic model of L5 pyramidal cell. Myelination of the axon was found to induce a 3-fold increase in the axonal length constant. As a result, the different forms of ADF were found to display a much longer spatial extent (up to 3,000 μm). In addition, while the internodal length displayed a mild effect, the number of myelin wraps ensheathing the internodes was found to play a critical role in the ADFs spatial extents. We conclude that axonal myelination induces an increase in ADFs spatial extent in our model, thus making ADFs plausible in long-distance connections.