The impact of Hodgkin-Huxley models on dendritic research

A cortical field theory - dynamics and symmetries

We characterise cortical dynamics using partial differential equations (PDEs), analysing various connectivity patterns within the cortical sheet. This exploration yields diverse dynamics, encompassing wave equations and limit cycle activity. We presume balanced equations between excitatory and inhibitory neuronal units, reflecting the ubiquitous oscillatory patterns observed in electrophysiological measurements. Our derived dynamics comprise lowest-order wave equations (i.e., the Klein-Gordon model), limit cycle waves, higher-order PDE formulations, and transitions between limit cycles and near-zero states. Furthermore, we delve into the symmetries of the models using the Lagrangian formalism, distinguishing between continuous and discontinuous symmetries. These symmetries allow for mathematical expediency in the analysis of the model and could also be useful in studying the effect of symmetrical input from distributed cortical regions. Overall, our ability to derive multiple constraints on the fields - and predictions of the model - stems largely from the underlying assumption that the brain operates at a critical state. This assumption, in turn, drives the dynamics towards oscillatory or semi-conservative behaviour. Within this critical state, we can leverage results from the physics literature, which serve as analogues for neural fields, and implicit construct validity. Comparisons between our model predictions and electrophysiological findings from the literature - such as spectral power distribution across frequencies, wave propagation speed, epileptic seizure generation, and pattern formation over the cortical surface - demonstrate a close match. This study underscores the importance of utilizing symmetry preserving PDE formulations for further mechanistic insights into cortical activity.

DendroTweaks: An interactive approach for unraveling dendritic dynamics

Neurons rely on the interplay between dendritic morphology and ion channels to transform synaptic inputs into a sequence of somatic spikes. Detailed biophysical models with active dendrites have been instrumental in exploring this interaction. However, such models can be challenging to understand and validate due to the large number of parameters involved. In this work, we introduce DendroTweaks - a toolbox designed to illuminate how morpho-electric properties map to dendritic events and how these dendritic events shape neuronal output. DendroTweaks features a web-based graphical interface, where users can explore single-cell neuronal models and adjust their morphological and biophysical parameters with real-time visual feedback. In particular, DendroTweaks is tailored to interactive fine-tuning of subcellular properties, such as kinetics and distributions of ion channels, as well as the dynamics and allocation of synaptic inputs. It offers an automated approach for standardization and refinement of voltage-gated ion channel models to make them more comprehensible and reusable. The toolbox allows users to run various experimental protocols and record data from multiple dendritic and somatic locations, thereby enhancing model validation. Finally, it aims to deepen our understanding of which dendritic properties are essential for neuronal input-output transformation. Using this knowledge, one can simplify models through a built-in morphology reduction algorithm and export them for further use in faster, more interpretable networks. With DendroTweaks, users can gain better control and understanding of their models, advancing research on dendritic input-output transformations and their role in network computations.

Shaping dynamical neural computations using spatiotemporal constraints

Dynamics play a critical role in computation. The principled evolution of states over time enables both biological and artificial networks to represent and integrate information to make decisions. In the past few decades, significant multidisciplinary progress has been made in bridging the gap between how we understand biological versus artificial computation, including how insights gained from one can translate to the other. Research has revealed that neurobiology is a key determinant of brain network architecture, which gives rise to spatiotemporally constrained patterns of activity that underlie computation. Here, we discuss how neural systems use dynamics for computation, and claim that the biological constraints that shape brain networks may be leveraged to improve the implementation of artificial neural networks. To formalize this discussion, we consider a natural artificial analog of the brain that has been used extensively to model neural computation: the recurrent neural network (RNN). In both the brain and the RNN, we emphasize the common computational substrate atop which dynamics occur-the connectivity between neurons-and we explore the unique computational advantages offered by biophysical constraints such as resource efficiency, spatial embedding, and neurodevelopment.

A novel non-invasive brain stimulation technique: "Temporally interfering electrical stimulation"

For decades, neuromodulation technology has demonstrated tremendous potential in the treatment of neuropsychiatric disorders. However, challenges such as being less intrusive, more concentrated, using less energy, and better public acceptance, must be considered. Several novel and optimized methods are thus urgently desiderated to overcome these barriers. In specific, temporally interfering (TI) electrical stimulation was pioneered in 2017, which used a low-frequency envelope waveform, generated by the superposition of two high-frequency sinusoidal currents of slightly different frequency, to stimulate specific targets inside the brain. TI electrical stimulation holds the advantages of both spatial targeting and non-invasive character. The ability to activate deep pathogenic targets without surgery is intriguing, and it is expected to be employed to treat some neurological or psychiatric disorders. Recently, efforts have been undertaken to investigate the stimulation qualities and translation application of TI electrical stimulation via computational modeling and animal experiments. This review detailed the most recent scientific developments in the field of TI electrical stimulation, with the goal of serving as a reference for future research.