An operating principle of the cerebral cortex, and a cellular mechanism for attentional trial-and-error pattern learning and useful classification extraction

A feature of the brains of intelligent animals is the ability to learn to respond to an ensemble of active neuronal inputs with a behaviorally appropriate ensemble of active neuronal outputs. Previously, a hypothesis was proposed on how this mechanism is implemented at the cellular level within the neocortical pyramidal neuron: the apical tuft or perisomatic inputs initiate "guess" neuron firings, while the basal dendrites identify input patterns based on excited synaptic clusters, with the cluster excitation strength adjusted based on reward feedback. This simple mechanism allows neurons to learn to classify their inputs in a surprisingly intelligent manner. Here, we revise and extend this hypothesis. We modify synaptic plasticity rules to align with behavioral time scale synaptic plasticity (BTSP) observed in hippocampal area CA1, making the framework more biophysically and behaviorally plausible. The neurons for the guess firings are selected in a voluntary manner via feedback connections to apical tufts in the neocortical layer 1, leading to dendritic Ca2+ spikes with burst firing, which are postulated to be neural correlates of attentional, aware processing. Once learned, the neuronal input classification is executed without voluntary or conscious control, enabling hierarchical incremental learning of classifications that is effective in our inherently classifiable world. In addition to voluntary, we propose that pyramidal neuron burst firing can be involuntary, also initiated via apical tuft inputs, drawing attention toward important cues such as novelty and noxious stimuli. We classify the excitations of neocortical pyramidal neurons into four categories based on their excitation pathway: attentional versus automatic and voluntary/acquired versus involuntary. Additionally, we hypothesize that dendrites within pyramidal neuron minicolumn bundles are coupled via depolarization cross-induction, enabling minicolumn functions such as the creation of powerful hierarchical "hyperneurons" and the internal representation of the external world. We suggest building blocks to extend the microcircuit theory to network-level processing, which, interestingly, yields variants resembling the artificial neural networks currently in use. On a more speculative note, we conjecture that principles of intelligence in universes governed by certain types of physical laws might resemble ours.

Sex Differences in Axonal Dynamic Responses Under Realistic Tension Using Finite Element Models

Existing axonal finite element models do not consider sex morphological differences or the fidelity in dynamic input. To facilitate a systematic investigation into the micromechanics of diffuse axonal injury, we develop a parameterized modeling approach for automatic and efficient generation of sex-specific axonal models according to specified geometrical parameters. Baseline female and male axonal models in the corpus callosum with random microtubule (MT) gap configurations are generated for model calibration and evaluation. They are then used to simulate a realistic tensile loading consisting of both a loading and a recovery phase (to return to an initial undeformed state) generated from dynamic corpus callosum fiber strain in a real-world head impact simulation. We find that MT gaps and the dynamic recovery phase are both critical to successfully reproduce MT undulation as observed experimentally, which has not been reported before. This strengthens confidence in model dynamic responses. A statistical approach is further employed to aggregate axonal responses from a large sample of random MT gap configurations for both female and male axonal models (n = 10,000 each). We find that peak strains in MTs and the Ranvier node and associated neurofilament failures in female axons are substantially higher than those in male axons because there are fewer MTs in the former and also because of the random nature of MT gap locations. Despite limitations in various model assumptions as a result of limited experimental data currently available, these findings highlight the need to systematically characterize MT gap configurations and to ensure a realistic model input for axonal dynamic simulations. Finally, this study may offer fresh and improved insight into the biomechanical basis of sex differences in brain injury, and sets the stage for more systematic investigations at the microscale in the future, both numerically and experimentally.

On mathematical modeling of the propagation of a wave ensemble within an individual axon

The long history of studying the propagation of an action potential has revealed that an electrical signal is accompanied by mechanical and thermal effects. All these effects together generate an ensemble of waves. The consistent models of such a complex phenomenon can be derived by using properly the fundamental physical principles. In this paper, attention is paid to the analysis of concepts of continuum physics that constitute a basis for deriving the mathematical models which describe the emergence and propagation of a wave ensemble in an axon. Such studies are interdisciplinary and based on biology, physics, mathematics, and chemistry. The governing equations for the action potential together with mechanical and thermal effects are derived starting from basics: Maxwell equations, conservation of momentum, Fourier's law, etc., but modified following experimental studies in electrophysiology. Several ideas from continuum physics like external forces and internal variables can also be used in deriving the corresponding models. Some mathematical concepts used in modeling are also briefly described. A brief overview of several mathematical models is presented that allows us to analyze the present ideas of modeling. Most mathematical models deal with the propagation of signals in a healthy axon. Further analysis is needed for better modeling the pathological situations and the explanation of the influence of the structural details like the myelin sheath or the cytoskeleton in the axoplasm. The future possible trends in improving the models are envisaged.

Flow-driven control of pulse width in excitable media

Models of pulse formation in nerve conduction have provided manifold insight not only into neuronal dynamics but also the nonlinear dynamics of pulse formation in general. Recent observation of neuronal electrochemical pulses also driving mechanical deformation of the tubular neuronal wall, and thereby generating ensuing cytoplasmic flow, now question the impact of flow on the electrochemical dynamics of pulse formation. Here, we theoretically investigate the classical Fitzhugh-Nagumo model, now accounting for advective coupling between the pulse propagator typically describing membrane potential and triggering mechanical deformations, and thus governing flow magnitude, and the pulse controller, a chemical species advected with the ensuing fluid flow. Employing analytical calculations and numerical simulations, we find that advective coupling allows for a linear control of pulse width while leaving pulse velocity unchanged. We therefore uncover an independent control of pulse width by fluid flow coupling.

Neuromechanical modulation of transmembrane voltage in a model of a nerve

Despite substantial evidence that mechanical variables play a crucial role in transmembrane voltage regulation, most research efforts focus mostly on the nerve cell's biochemical or electrophysiological activities. We propose an electromechanical model of a nerve in order to advance our understanding of how mechanical forces and thermodynamics also regulate neural electrical activities. We explore the spatiotemporal dynamics of the transmembrane potential using the proposed nonlinear model with a sinusoid as the initial transmembrane potential and periodic boundary conditions. The localized wave from our numerical simulation and transmembrane potentials in nerves are solitary and show the three stages of action potential (depolarization, repolarization, and hyperpolarization), as well as threshold and saturation effects. We show that the mechanical properties of membranes affect the localization of the transmembrane potential. According to simulation data, mechanical pulses of sufficient magnitude can modulate a transmembrane voltage. The current model could be used to describe the dynamics of a transmembrane potential modulated by sound. Mechanical perturbations that modulate an electrical signal have a lot of clinical potential for treating pain and other neurological diseases.

Improved alpha-beta power reduction via combined electrical and ultrasonic stimulation in a parkinsonian cortex-basal ganglia-thalamus computational model

Objective. To investigate computationally the interaction of combined electrical and ultrasonic modulation of isolated neurons and of the parkinsonian cortex-basal ganglia-thalamus loop.Approach. Continuous-wave or pulsed electrical and ultrasonic neuromodulation is applied to isolated Otsuka plateau-potential generating subthalamic nucleus (STN) and Pospischil regular, fast and low-threshold spiking cortical cells in a temporally alternating or simultaneous manner. Similar combinations of electrical/ultrasonic waveforms are applied to a parkinsonian biophysical cortex-basal ganglia-thalamus neuronal network. Ultrasound-neuron interaction is modelled respectively for isolated neurons and the neuronal network with the NICE and SONIC implementations of the bilayer sonophore underlying mechanism. Reduction inα-βspectral energy is used as a proxy to express improvement in Parkinson's disease by insonication and electrostimulation.Main results. Simultaneous electro-acoustic stimulation achieves a given level of neuronal activity at lower intensities compared to the separate stimulation modalities. Conversely, temporally alternating stimulation with50 Hzelectrical and ultrasound pulses is capable of eliciting100 HzSTN firing rates. Furthermore, combination of ultrasound with hyperpolarizing currents can alter cortical cell relative spiking regimes. In the parkinsonian neuronal network, continuous-wave and pulsed ultrasound reduce pathological oscillations by different mechanisms. High-frequency pulsed separated electrical and ultrasonic deep brain stimulation (DBS) reduce pathologicalα-βpower by entraining STN-neurons. In contrast, continuous-wave ultrasound reduces pathological oscillations by silencing the STN. Compared to the separated stimulation modalities, temporally simultaneous or alternating electro-acoustic stimulation can achieve higher reductions inα-βpower for the same safety contraints on electrical/ultrasonic intensity.Significance. Focused ultrasound has the potential of becoming a non-invasive alternative of conventional DBS for the treatment of Parkinson's disease. Here, we elaborate on proposed benefits of combined electro-acoustic stimulation in terms of improved dynamic range, efficiency, spatial resolution, and neuronal selectivity.

Critical analysis of explanations for cellular homeostasis and electrophysiology from murburn perspective

Pursuits in modern cellular electrophysiology are fraught with disagreements at a fundamental level. While the membrane theory of homeostasis deems the cell membrane and proteins embedded therein as the chief players, the association-induction (or sorption/bulk-phase) hypothesis considers the aqueous phase of dissolved proteins (cytoplasm/protoplasm) as the key determinant of cellular composition and ionic fluxes. In the first school of thought, trans-membrane potential (TMP) and selective ion pumps/channels are deemed as key operative principles. In the latter theory, sorption-desorption dynamics and rearrangements of bulk phase determine the outcomes. In both these schools of thought, theorists believe that the macroscopic phase electroneutrality holds, TMP (whether in resting or in activated state) results solely due to ionic concentration differentials across the membrane, and the concerned proteins undergo major conformation changes to affect/effect the noted outcomes. The new entry into the field, murburn concept, builds starting from molecular considerations to macroscopic observations. It moots "effective charge separation" and intricate "molecule-ion-radical" electron transfer equilibriums as a rationale for ionic concentration differentials and TMP variation. After making an unbiased appraisal of the two classical schools of thought, the review makes a point-wise analysis of some hitherto unresolved observations/considerations and suggests the need to rethink the mechanistic perspectives.

A Physical Perspective to the Inductive Function of Myelin-A Missing Piece of Neuroscience

Starting from the inductance in neurons, two physical origins are discussed, which are the coil inductance of myelin and the piezoelectric effect of the cell membrane. The direct evidence of the coil inductance of myelin is the opposite spiraling phenomenon between adjacent myelin sheaths confirmed by previous studies. As for the piezoelectric effect of the cell membrane, which has been well-known in physics, the direct evidence is the mechanical wave accompany with action potential. Therefore, a more complete physical nature of neural signals is provided. In conventional neuroscience, the neural signal is a pure electrical signal. In our new theory, the neural signal is an energy pulse containing electrical, magnetic, and mechanical components. Such a physical understanding of the neural signal and neural systems significantly improve the knowledge of the neurons. On the one hand, we achieve a corrected neural circuit of an inductor-capacitor-capacitor (LCC) form, whose frequency response and electrical characteristics have been validated by previous studies and the modeling fitting of artifacts in our experiments. On the other hand, a number of phenomena observed in neural experiments are explained. In particular, they are the mechanism of magnetic nerve stimulations and ultrasound nerve stimulations, the MRI image contrast issue and Anode Break Excitation. At last, the biological function of myelin is summarized. It is to provide inductance in the process of neural signal, which can enhance the signal speed in peripheral nervous systems and provide frequency modulation function in central nervous systems.

Acoustic Waves in Axonal Membrane and Caveolins are the New Targets for Pain Treatment with High Frequency Ultrasound

Reciprocal interaction between electrical and mechanical waves observed in axonal membrane during its excitation leads to a paradigm shift in pain research making the uncoupling of electro-mechanical signals an interesting target in pain treatment. This uncoupling can be realized either through direct disturbance of the mechanical surface waves in axonal membrane or through shifting of the thermodynamic state of this membrane far from its phase transition point. Both effects can be effectively realized through application of the very high frequency ultrasound waves. Additional target for application of ultrasound in pain treatment is the caveolin-1, which is abundantly present in Schwann cells as well as in the non-axonal tissues. Both targets demonstrate frequency-dependent reactions, thus making a very high frequency ultrasound a promising treatment modality in pain treatment.

Action Potential: A Vortex Phenomena; Driving Membrane Oscillations

Hodgkin-Huxley (HH) model has been one of the most successful electrical interpretation of nerve membrane which led to revolutions in the field of computational neuroscience. On the contrary, experimental observations indicate that, an Action Potential (AP) is accompanied with certain physiological changes in the nerve membrane such as, production and absorption of heat; variation of axon diameter, pressure and length. Although, in the early 1900's a Pressure Wave Theory was proposed by E. Wilke, but, due to lack of sophisticated experimental techniques it was left uncharted. Until recently, when Heimburg-Jackson, Hady-Machta and Rvachev, independently proposed Soliton Theory (thermodynamic interpretation of nerve membrane), Mechanical Surface Waves theory (electro-mechanical interpretation) and Rvachev Model (mechano-electrical activation of voltage gated sodium ion channels) respectively; encouraging a deviation from the traditional HH interpretation with justification for the physical changes in the nerve membrane observed experimentally. But, these theories lead to a “hit and miss” scenario because, they do explain certain features (increase/decrease in axon diameter) but miss to explain, correlation between the strength of stimuli and spike rate of AP. Bio-physical models of nerve membrane are thus important for enhancing our understanding regarding the governing dynamics of neural activities encompassing the experimental observations. A novel theory is proposed here which, unravels vortex ring formation due to ion currents in the intracellular and extracellular region leading to variation of pressure causing the increment/decrement in axon diameter. These formations manifest as membrane oscillations which are used to establish a correlation between the strength of stimuli and spike rate of AP. The theory proposed in this paper, brings a paradigm shift in our understanding of neural dynamics from a thorough bio-physical and physiological perspective with promising applications.

Nerve impulse propagation: Mechanical wave model and HH model

The Hodgkin-Huxley model (HH model) of nerve propagation from the middle of the 20th century has not remained untouched by criticism. Complementary as well as ambivalent views of this model have been published. A real breakthrough of another model does not exist yet. Many similarities as well as contradictions between the HH model and the alternative mechanical impulse model are shown.

The mechanosensitive ion channel TRAAK is localized to the mammalian node of Ranvier

TRAAK is a membrane tension-activated K⁺ channel that has been associated through behavioral studies to mechanical nociception. We used specific monoclonal antibodies in mice to show that TRAAK is localized exclusively to nodes of Ranvier, the action potential propagating elements of myelinated nerve fibers. Approximately 80 percent of myelinated nerve fibers throughout the central and peripheral nervous system contain TRAAK in what is likely an all-nodes or no-nodes per axon fashion. TRAAK is not observed at the axon initial segment where action potentials are first generated. We used polyclonal antibodies, the TRAAK inhibitor RU2 and node clamp amplifiers to demonstrate the presence and functional properties of TRAAK in rat nerve fibers. TRAAK contributes to the ‘leak’ K⁺ current in mammalian nerve fiber conduction by hyperpolarizing the resting membrane potential, thereby increasing Na⁺ channel availability for action potential propagation. We speculate on why nodes of Ranvier contain a mechanosensitive K⁺ channel.

Thinking About the Nerve Impulse: The Prospects for the Development of a Comprehensive Account of Nerve Impulse Propagation

Currently, a scientific debate is ongoing about modeling nerve impulse propagation. One of the models discussed is the celebrated Hodgkin-Huxley model of the action potential, which is central to the electricity-centered conception of the nerve impulse that dominates contemporary neuroscience. However, this model cannot represent the nerve impulse completely, since it does not take into account non-electrical manifestations of the nerve impulse for which there is ample experimental evidence. As a result, alternative models of nerve impulse propagation have been proposed in contemporary (neuro)scientific literature. One of these models is the Heimburg-Jackson model, according to which the nerve impulse is an electromechanical density pulse in the neural membrane. This model is usually contrasted with the Hodgkin-Huxley model and is supposed to potentially be able to replace the latter. However, instead of contrasting these models of nerve impulse propagation, another approach integrates these models in a general unifying model. This general unifying model, the Engelbrecht model, is developed to unify all relevant manifestations of the nerve impulse and their interaction(s). Here, we want to contribute to the debate about modeling nerve impulse propagation by conceptually analyzing the Engelbrecht model. Combining the results of this conceptual analysis with insights from philosophy of science, we make recommendations for the study of nerve impulse propagation. The first conclusion of this analysis is that attempts to develop models that represent the nerve impulse accurately and completely appear unfeasible. Instead, models are and should be used as tools to study nerve impulse propagation for varying purposes, representing the nerve impulse accurately and completely enough to achieve the specified goals. The second conclusion is that integrating distinct models into a general unifying model that provides a consistent picture of nerve impulse propagation is impossible due to the distinct purposes for which they are developed and the conflicting assumptions these purposes often require. Instead of explaining nerve impulse propagation with a single general unifying model, it appears advisable to explain this complex phenomenon using a ‘mosaic’ framework of models in which each model provides a partial explanation of nerve impulse propagation.

Breathing pulses in the damped-soliton model for nerves

Unlike the Hodgkin-Huxley picture in which the nerve impulse results from ion exchanges across the cell membrane through ion-gate channels, in the so-called soliton model the impulse is seen as an electromechanical process related to thermodynamical phenomena accompanying the generation of the action potential. In this work, account is taken of the effects of damping on the nerve impulse propagation, within the framework of the soliton model. Applying the reductive perturbation expansion on the resulting KdV-Burgers equation, a damped nonlinear Schrödinger equation is derived and shown to admit breathing-type solitary wave solutions. Under specific constraints, these breathing pulse solitons become self-trapped structures in which the damping is balanced by nonlinearity such that the pulse amplitude remains unchanged even in the presence of damping.

Nodal versus Total Axonal Strain and the Role of Cholesterol in Traumatic Brain Injury

Traumatic brain injury (TBI) is a health threat that affects every year millions of people involved in motor vehicle and sporting accidents, and thousands of soldiers in battlefields. Diffuse axonal injury (DAI) is one of the most frequent types of TBI leading to death. In DAI, the initial traumatic event is followed by a cascade of biochemical changes that take time to develop in full, so that symptoms may not become apparent until days or weeks after the original injury. Hence, DAI is a dynamic process, and the opportunity exists to prevent its progression provided the initial trauma can be predicted at the molecular level. Here, we present preliminary evidence from micro-finite element (FE) simulations that the mechanical response of central nervous system myelinated fibers is dependent on the axonal diameter, the ratio between axon diameter and fiber diameter (g-ratio), the microtubules density, and the cholesterol concentration in the axolemma and myelin. A key outcome of the simulations is that there is a significant difference between the overall level of strain in a given axonal segment and the level of local strain in the Ranvier nodes contained in that segment, with the nodal strain being much larger than the total strain. We suggest that the acquisition of this geometric and biochemical information by means of already available high resolution magnetic resonance imaging techniques, and its incorporation in current FE models of the brain will enhance the models capacity to predict the site and magnitude of primary axonal damage upon TBI.