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Register a new userA Tridomain Model for Potassium Clearance in Optic Nerve of Necturus
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The accumulation of potassium in the narrow space outside nerve cells is a classical subject of biophysics that has received much attention recently. It may be involved in potassium accumulation textcolor{black}{including} spreading depression, perhaps migraine and some kinds of epilepsy, even (speculatively) learning. Quantitative analysis is likely to help evaluate the role of potassium clearance from the extracellular space after a train of action potentials. Clearance involves three structures that extend down the length of the nerve: glia, extracellular space, and axon and so need to be described as systems distributed in space in the tradition used for electrical potential in the `cable equations of nerve since the work of Hodgkin in 1937. A three-compartment model is proposed here for the optic nerve and is used to study the accumulation of potassium and its clearance. The model allows the convection, diffusion, and electrical migration of water and ions. We depend on the data of Orkand et al to ensure the relevance of our model and align its parameters with the anatomy and properties of membranes, channels, and transporters: our model fits their experimental data quite well. The aligned model shows that glia has an important role in buffering potassium, as expected. The model shows that potassium is cleared mostly by convective flow through the syncytia of glia driven by osmotic pressure differences. A simplified model might be possible, but it must involve flow down the length of the optic nerve. It is easy for compartment models to neglect this flow. Our model can be used for structures quite different from the optic nerve that might have different distributions of channels and transporters in its three compartments. It can be generalized to include a fourth (distributed) compartment representing blood vessels to deal with the glymphatic flow into the circulatory system.
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Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes [C. Nicholson, and S. Hrabv{e}tova, Biophysical Journal, 113(10), 2133(2017)]. However, the exact driving mechanisms are often not known. In this paper, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system (CNS). Different from traditional fluid dynamics problems, flows in biological tissues such as the CNS are coupled with ion transport. It is driven by osmosis created by concentration gradient of ionic solutions, which in term influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al [R.K. Orkand, J.G. Nicholls, S.W. Kuffler, Journal of Neurophysiology, 29(4), 788(1966)]. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.
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When DNA molecules are heated they denature. This occurs locally so that loops of molten single DNA strands form, connected by intact double-stranded DNA pieces. The properties of this melting transition have been intensively investigated. Recently there has been a surge of interest in this question, caused by experiments determining the properties of partially bound DNA confined to nanochannels. But how does such confinement affect the melting transition? To answer this question we introduce, and solve a model predicting how confinement affects the melting transition for a simple model system by first disregarding the effect of self-avoidance. We find that the transition is smoother for narrower channels. By means of Monte-Carlo simulations we then show that a model incorporating self-avoidance shows qualitatively the same behaviour and that the effect of confinement is stronger than in the ideal case.
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