Modelling of processes in nerve fibres at the interface of physiology and mathematics

Nerve Structure-Function: Unusual Structural Details and Unmasking of Sulfhydryl Groups by Electrical Stimulation or Asphyxia in Axon Membranes and Gap Junctions

This review describes and discusses unusual axonal structural details and evidence for unmasking sulfhydryl groups (-SH) in axoplasmic membranes resulting from electrical stimulation or asphyxia. Crayfish axons contain fenestrated septa (FS) that, in phase contrast, micrographs appear as repeated striations. In the electron microscope, each septum is made of two cross-sectioned membranes containing ~55 nm pores, each occupied by a microtubule. Thin filaments, which we believe are made of kinesin, bridge the microtubule to the edge of the pore. FS are believed to play a role in axoplasmic flow. The axons also display areas in which axon and sheath glial cell plasma membranes are sharply curved and project into the axoplasm. In freeze-fractures, the protoplasmic leaflet (P-face) of the projections appears as elongated indentations containing parallel chains of particles. The sheath glial cell plasma membrane also contains particles, but they are irregularly aggregated. The axons also display areas where axonal and glial plasma membranes fuse, creating intercellular pores. In axons fixed during electrical stimulation, the plasma membrane, the outer membrane of mitochondria, membranes of other cytoplasmic organelles, and gap junctions increase in electron opacity and thickness, resulting from unmasking of sulfhydryl groups (-SH). Similar changes occur in asphyxiated nerve cords.

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.

Membrane Charge Oscillations During Ultrasonic Neuromodulation by Intramembrane Cavitation

OBJECTIVE

To investigate the importance of membrane charge oscillations and redistribution in multi-compartmental ultrasonic neuromodulation (UNMOD) intramembrane cavitation models.

METHODS

The Neuronal Intramembrane Cavitation Excitation (NICE) model and multiScale Optimized model of Neuronal Intramembrane Cavitation (SONIC) of UNMOD are compared for a nanoscale multi-compartmental and point neuron approximation of the bilayer sonophore and surrounding proteins. The temporal dynamics of charge oscillations and their effect on the resulting voltage oscillations are investigated by fourier series analysis.

RESULTS

Comparison of excitation thresholds and neuronal response between nanoscale multi-compartmental and point models, implemented in the SONIC and NICE framework, demonstrates that the explicit modeling of fast spatial charge redistribution is critical for an accurate multi-compartmental UNMOD-model. Furthermore, the importance of modeling partial protein coverage is quantified by the excitability thresholds. Subsequently, we establish by fourier analysis that these charge oscillations are slowly changing in time.

CONCLUSION

Fast charge redistribution significantly alters neuronal excitability in a multi-compartmental nanoscale UNMOD-model. Also the mutual exclusivity between protein and sonophore coverage should be taken into account, when simulating the dependency of neuronal excitability on coverage fractions. Charge oscillations are periodic and their fourier components change on a slow timescale. Furthermore, the resulting voltage oscillations decrease in energy with overtone number, implying that an extension of the existing multiscale model (SONIC) to multi-compartmental neurons is possible by taking into account a limited number of fourier components.

SIGNIFICANCE

First steps are taken towards a morphologically realistic and computationally efficient UNMOD-model, improving our understanding of the underlying ultrasonic neuromodulation mechanisms.