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The presence of impermeant molecules within a cell can lead to an increase in cell volume through the influx of water driven by osmosis. This phenomenon is known as the Donnan (or Gibbs–Donnan) effect. Animal cells actively transport ions to counteract the Donnan effect and regulate their volume, actively pumping Na+ out and K+ into their cytosol using the Na+/K+ ATPase (NKA) pump. The pump-leak equations (PLEs) are a system of algebraic-differential equations to model the membrane potential, ion (Na+, K+, and Cl−), and water flux across the cell membrane, which provide insight into how the combination of passive ions fluxes and active transport contribute to stabilizing cell volume. Our broad objective is to provide analytical insight into the PLEs through three lines of investigation: (1) we show that the provision of impermeant extracellular molecules can stabilize the volume of a passive cell; (2) we demonstrate that the mathematical form of the NKA pump is not as important as the stoichiometry for cell stabilization; and (3) we investigate the interaction between the NKA pump and cation–chloride co-transporters (CCCs) on cell stabilization, showing that NCC can destabilize a cell while NKCC and KCC can stabilize it. We incorporate extracellular impermeant molecules, NKA pump, and CCCs into the PLEs and derive the exact formula for the steady states in terms of all the parameters. This analytical expression enables us to easily explore the effect of each of the system parameters on the existence and stability of the steady states. 

ABSTRACT Hemolymph is driven through the antennae of Drosophila melanogaster by the rhythmic contraction of muscle 16 (m16), which runs through the brain. Contraction of m16 results in the expansion of an elastic ampulla, opening ostia and filling the ampulla. Relaxation of the ampullary membrane forces hemolymph through vessels into the antennae. We show that m16 is an auto-active rhythmic somatic muscle. The activity of m16 leads to the rapid perfusion of the antenna by hemolymph. In addition, it leads to the rhythmic agitation of the brain, which could be important for clearing the interstitial space. 

Potassium ion (K + ) plays a critical role as an essential electrolyte in all biological systems. Genetically-encoded fluorescent K + biosensors are promising tools to further improve our understanding of K + -dependent processes under normal and pathological conditions. Here, we report the crystal structure of a previously reported genetically-encoded fluorescent K + biosensor, GINKO1, in the K + -bound state. Using structure-guided optimization and directed evolution, we have engineered an improved K + biosensor, designated GINKO2, with higher sensitivity and specificity. We have demonstrated the utility of GINKO2 for in vivo detection and imaging of K + dynamics in multiple model organisms, including bacteria, plants, and mice.