For more than a century, the neuron doctrine has provided the bedrock of neuroscience, proclaiming that the neuron is the fundamental unit of the nervous system, both in structure and function (Yuste, 2015). This viewpoint emerged during an era when single-neuron techniques prevailed, emphasizing the significance of individual cells. However, the advent of advanced brain imaging methods capable of capturing the simultaneous activity from multiple neurons at the macro-scale has revealed a broader understanding. It is now apparent that ensembles of neurons, connected over long distances, rather than individual, isolated cells, form neurophysiological units and exhibit emergent functional properties and states (Hutchison et al., 2013; Martin et al., 2021). But rather than the former replacing the latter, we see the further continuation of a narrative where the architecture of individual neurons governs electrical signal characteristics which, in turn, effects broad levels of network connectivity, and is evident in patterns of cortical activity. Perhaps now is the time to consider forming a more general quantitative model of brain networks not governed by statistical measures of association between spatial signals but upon the underlying physical properties of neural tissues from which those signals emerge.

An impressive article by Pang et al. (2023) has reiterated, utilizing brain imaging, that “the close link between geometry and function is explained by a dominant role for wave-like activity” in the brain. That the dynamics of functional connectivity of the meso-scale brain are governed by geometrical and physical constraints is not unexpected. Indeed, the fundamental equation explored by these authors is a version of Heaviside’s (1876) noted Telegrapher’s Equation - derived from Maxwell’s Equations - to model the electrical signal transmission properties of Trans-Atlantic telegraph cables. Hodgkin and Huxley (1952) considered the giant squid axon as a representative special instance of this equation in the famous Cable Equation. Rushton (1951) observed that the wave propagation velocity of action potentials is nominally predicated on the ratio of axonal to myelinated diameters, which also describes the spacing of Nodes of Ranvier along the axon. Producing traveling waves along their axonal and dendritic lengths, with distance-attenuated signal magnitudes, dynamic systems of neural connectivity are parameterized by the physical structure of the cellular membrane, relative extent of myelination, electromagnetic characteristics, connection densities, and neurovascular coupling. Importantly, the brain’s temporal signals are not spatially restricted but, by their nature, travel, conveying sensory and cognitive information between distal neuroanatomic loci via a dense network of medullated fiber pathways. These connections are evolutionarily and developmentally optimized toward the maximal rate and fidelity of neural signal transduction.

How individual neurons transmit information via action potentials over distance is only part of the story. There is also an increasing awareness that information storage and processing depend on spatially distributed, dynamic groupings of neurons. Beyond synaptic-levels of connectivity, the activity of nearby electrical fields is thought to shape the structure of and influence the functional responses of neurons through ephaptic coupling (Cunha et al., 2022). Ephapses are sites where neighboring nerve cells establish anatomical or electrical connections, resulting from the modulation of the extracellular space. As a consequence of their close proximity, ephaptic transmission occurs, enabling the transmission of electrical fields generated by one nerve cell to affect neighboring neurons. This phenomenon has been observed to drive the electrical inhibition of cerebellar Purkinje cells in rats and in the Mauthner cell system in various Teleostei (Faber et al., 2018). Specifically, ephaptic coupling is believed to influence the synchronization and timing of action potential firing in neurons (Schmidt et al., 2021). Pinotsis and Miller (2023) have recently argued that, so-called, ‘engram complexes’ in the human brain are formed through ephaptic processes which “sculpt and guide the neural activity and tie together participating brain areas”. While myelination is thought to inhibit ephaptic interactions, the concept has important implications for understanding healthy brain connectomics but suggest a putative role in the observable effects of epilepsy and in demyelinating diseases. The presence of ephaptic processes, also obtained using Kirchoff’s electrical current laws (Anastassiou et al., 2011), suggest that both long-range as well as local influences on neural activity exist which may generate interesting observable dynamics.

For instance, in another study, Xu et al. (2023) observed moment-to-moment fluctuations of human cortical functional magnetic resonance imaging (fMRI) signals revealed widespread presence of spiral-like, rotational wave patterns during both resting and cognitive task states. These ‘brain spirals’ propagate across the cortex while revolving around phase singularity centers, producing spatiotemporal activity dynamics characterized by non-stationary features. Likely resulting from a dynamic process not-too-dissimilar to the Belousov-Zhabotinsky Reaction in chemistry and electrical field theory (Amrutha et al., 2023), the pattern of neuronal activity in the cortex likely is influenced by the trade-off between neuronal states. Notably, the rotational directions and locations of brain spirals appear relevant to specific cognitive tasks and can be utilized in their classification. Furthermore, multiple interacting brain spirals may play a role in coordinating the synchronized activations and deactivations of distributed functional regions. Such a mechanism allows for the flexible reconfiguration of task-driven activity flow between bottom-up and top-down directions during cognitive processing.

In each of these instances, the physical characteristics of neurons likely govern how such signals propagate throughout the system. For instance, as the firing state of neurons changes, the propagation of spiral waves over the cortex may, with each passing wave front, influence patterns of signal propagation along white matter fiber pathways to more distal regions. Furthermore, the degree of myelin insulation may affect the synchronization and coordination of neural activity dynamics, influencing cell morphology, and modulating time-dependent functional connections via ephaptic processes.

The intricate relationship between the physical properties of neurons and their firing rates and electrical signal properties is undeniable. These diminutive neurobiological structures possess a remarkable complexity, and their firing behavior is tightly regulated by various factors such as ion channel dynamics, membrane capacitance, myelination, synaptic connectivity, and other factors. Their physical attributes collectively determine how neurons process and transmit information, enabling the brain to perform astonishing computational feats. Understanding the interplay between the physical structure of neurons and their functional outcomes is crucial for unraveling neural networks and advancing our comprehension of the brain’s workings. Putative brain network models derived from neuroimaging data, with their focus on what is statistically correlated with what, are very likely incomplete and poor representations of how the larger nervous system is physically wired.

By integrating insights from traditional single-neuron methods, new models applied using multimodal neuroimaging data types hold great potential in unraveling how emergent functional states underlie behavior, cognition, and mental disorders (Koch, 1993). Quantitative models of brain networks from neuroimaging would do well to incorporate such properties, where any statistical correlation between brain regions is a consequence rather than the determinant of connectivity. Indeed, the Pang et al., Pinotsis and Miller, and Xu et al. articles are reminders that, as the traversal of a flame down the wick of a candle is controlled by the composition of the paraffin, the spatiotemporal dynamics of functional connectivity are, not unexpectedly, a direct function of the brain’s most elemental physical characteristics. We suggest that now is the time for a foundational theory of brain connectivity - based on these characteristics, modern technological methods to measure them, with a formal mathematical formulation - which helps to explain more completely the why and how of observable functional networks in the brain.