A tridomain model for potassium clearance in optic nerve of Necturus

Cellular communication among smooth muscle cells: The role of membrane potential via connexins

Communication via action potentials among neurons has been extensively studied. However, effective communication without action potentials is ubiquitous in biological systems, yet it has received much less attention in comparison. Multi-cellular communication among smooth muscles is crucial for regulating blood flow, for example. Understanding the mechanism of this non-action potential communication is critical in many cases, like synchronization of cellular activity, under normal and pathological conditions. In this paper, we employ a multi-scale asymptotic method to derive a macroscopic homogenized bidomain model from the microscopic electro-neutral (EN) model. This is achieved by considering different diffusion coefficients and incorporating nonlinear interface conditions. Subsequently, the homogenized macroscopic model is used to investigate communication in multi-cellular tissues. Our computational simulations reveal that the membrane potential of syncytia, formed by interconnected cells via connexins, plays a crucial role in propagating oscillations from one region to another, providing an effective means for fast cellular communication. Statement of Significance: In this study, we investigated cellular communication and ion transport in vascular smooth muscle cells, shedding light on their mechanisms under normal and abnormal conditions. Our research highlights the potential of mathematical models in understanding complex biological systems. We developed effective macroscale electro-neutral bi-domain ion transport models and examined their behavior in response to different stimuli. Our findings revealed the crucial role of connexinmediated membrane potential changes and demonstrated the effectiveness of cellular communication through syncytium membranes. Despite some limitations, our study provides valuable insights into these processes and emphasizes the importance of mathematical modeling in unraveling the complexities of cellular communication and ion transport.

Setting Boundaries for Statistical Mechanics

Statistical mechanics has grown without bounds in space. Statistical mechanics of noninteracting point particles in an unbounded perfect gas is widely used to describe liquids like concentrated salt solutions of life and electrochemical technology, including batteries. Liquids are filled with interacting molecules. A perfect gas is a poor model of a liquid. Statistical mechanics without spatial bounds is impossible as well as imperfect, if molecules interact as charged particles, as nearly all atoms do. The behavior of charged particles is not defined until boundary structures and values are defined because charges are governed by Maxwell's partial differential equations. Partial differential equations require boundary structures and conditions. Boundary conditions cannot be defined uniquely 'at infinity' because the limiting process that defines 'infinity' includes such a wide variety of structures and behaviors, from elongated ellipses to circles, from light waves that never decay, to dipolar fields that decay steeply, to Coulomb fields that hardly decay at all. Boundaries and boundary conditions needed to describe matter are not prominent in classical statistical mechanics. Statistical mechanics of bounded systems is described in the EnVarA system of variational mechanics developed by Chun Liu, more than anyone else. EnVarA treatment does not yet include Maxwell equations.

An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain

Within the computational neuroscience community, there has been a focus on simulating the electrical activity of neurons, while other components of brain tissue, such as glia cells and the extracellular space, are often neglected. Standard models of extracellular potentials are based on a combination of multicompartmental models describing neural electrodynamics and volume conductor theory. Such models cannot be used to simulate the slow components of extracellular potentials, which depend on ion concentration dynamics, and the effect that this has on extracellular diffusion potentials and glial buffering currents. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine compartmental neuron modeling with an electrodiffusive framework for intra- and extracellular ion concentration dynamics in a local piece of neuro-glial brain tissue. The edNEG model (i) keeps track of all intraneuronal, intraglial, and extracellular ion concentrations and electrical potentials, (ii) accounts for action potentials and dendritic calcium spikes in neurons, (iii) contains a neuronal and glial homeostatic machinery that gives physiologically realistic ion concentration dynamics, (iv) accounts for electrodiffusive transmembrane, intracellular, and extracellular ionic movements, and (v) accounts for glial and neuronal swelling caused by osmotic transmembrane pressure gradients. The edNEG model accounts for the concentration-dependent effects on ECS potentials that the standard models neglect. Using the edNEG model, we analyze these effects by splitting the extracellular potential into three components: one due to neural sink/source configurations, one due to glial sink/source configurations, and one due to extracellular diffusive currents. Through a series of simulations, we analyze the roles played by the various components and how they interact in generating the total slow potential. We conclude that the three components are of comparable magnitude and that the stimulus conditions determine which of the components that dominate.