New paper on the arXiv. Theoretical neuroscience complements experimental and clinical neuroscience. We provide a theoretical analysis of a second-generation Hodgkin-Huxley (HH) formalism, that has been used before in models for muscle cells (myocytes) and pancreatic beta-cells, but not in models of brain cells (neurons) to better understand pathological stress conditions in migraine and stroke.
The HH formulation of action potentials is certainly one of the most successful models in mathematical biology. It describes an essential part of cell-to-cell communication in the brain and other organs. The original HH model was in various ways extended to also describe when the brain’s normal performance fails, such as in migraine hallucinations and acute stroke. However, the fundamental mechanism of these extensions remained poorly understood. We study the structure of biophysical neuron models that starve from their ‚free‘ energy, that is, the energy that can directly be converted to do work. Neurons still have access to the chemical energy stored in the bonds of molecules. But chemical energy needs first to be converted by the metabolism to obtain free energy. We found, quite surprisingly, that even in the presence of chemical energy and normal metabolism, the free energy-starvation of neurons can be more stable then expected. This probably explains pathological conditions that have been observed in migraine and stroke.
We shed a new light on ion dynamics in the brain under these pathological stress conditions. In a recent article in Nature Review Neurology this phenomenon was reviewed: a nearly complete release of Gibbs free energy stored in the transmembrane gradients and potential of neurons. With our paper, we now describe the fundamental mechanistic structure of free energy-starvation. Furthermore, our model provides the missing link between HH formalsim and a large body of generic macroscopic models for migraine with aura, that was identified as one of the open problem in this review article.
Some more details on what we did and what others did before: In the neuroscience literature, models with time-dependent ion concentration suffer from a structural problem, a problem that has also been dominated the myocytes and pancreatic beta-cells literature before it was resolved for both type of cell models. We cite this relevant literature that was partly developed independently and build on it. Our analysis of the next generation neuron model goes, however, beyond what is known today in either of these other models of muscle and pancreatic cells. We hope that our theoretical analysis contribute some insights, which help to better interpret data and guide our principal understanding of the nervous systems in both health and disease.
Below is the arXiv abstract. Here the link to arxiv, where you can get the full pdf.
Bistable dynamics of ion homeostasis in ion-based neuron models
When neurons fire action potentials, dissipation of free energy is usually not directly considered, because the change in free energy is often negligible compared to the immense reservoir stored in neural transmembrane ion gradients and the long-term energy requirements are met through chemical energy, i.e., metabolism. However, these gradients can temporarily nearly vanish in neurological diseases, such as migraine and stroke, and in traumatic brain injury from concussions to severe injuries. We study biophysical neuron models based on the Hodgkin-Huxley (HH) formalism extended to include time-dependent ion concentrations inside and outside the cell and metabolic energy-driven pumps. For the first time, a minimal model is developed, which resolves a structural instability inherent in this HH extension. We reveal the basic mechanism of a state of free energy-starvation (FES) with bifurcation analyses showing that ion dynamics are bistable for a large range of pump rates. This is interpreted as a threshold reduction of a new fundamental mechanism of ionic excitability that causes a long-lasting but transient FES as observed in pathological states. We can in particular conclude that a coupling of extracellular ion concentrations to a large glial-vascular bath can take a role as an inhibitory mechanism crucial in ion homeostasis, while the Na+/K+ pumps alone are insufficient to recover from FES. Our results provide the missing link between the HH formalism and activator-inhibitor models that have been successfully used for modeling migraine phenotypes, and therefore will allow us to validate the hypothesis that migraine symptoms are explained by disturbed function in ion channel subunits, Na+/K+ pumps, and other proteins that regulate ion homeostasis.