Equilibria of biological aggregations with nonlocal repulsive-attractive interactions

We consider the aggregation equation $\rho_{t}-\nabla\cdot(\rho\nabla K\ast\rho) =0$ in $\mathbb{R}^{n}$, where the interaction potential $K$ incorporates short-range Newtonian repulsion and long-range power-law attraction. We study the global well-posedness of solutions and investigate analytically and numerically the equilibrium solutions. We show that there exist unique equilibria supported on a ball of $\mathbb{R}^n$. By using the method of moving planes we prove that such equilibria are radially symmetric and monotone in the radial coordinate. We perform asymptotic studies for the limiting cases when the exponent of the power-law attraction approaches infinity and a Newtonian singularity, respectively. Numerical simulations suggest that equilibria studied here are global attractors for the dynamics of the aggregation model

Evaluation of a SPLUNC1-derived peptide for the treatment of cystic fibrosis lung disease

In cystic fibrosis (CF) lungs, epithelial Na+ channel (ENaC) hyperactivity causes a reduction in airway surface liquid volume, leading to decreased mucocilliary clearance, chronic bacterial infection, and lung damage. Inhibition of ENaC is an attractive therapeutic option. However, ENaC antagonists have failed clinically because of off-target effects in the kidney. The S18 peptide is a naturally occurring short palate lung and nasal epithelial clone 1 (SPLUNC1)-derived ENaC antagonist that restores airway surface liquid height for up to 24 h in CF human bronchial epithelial cultures. However, its efficacy and safety in vivo are unknown. To interrogate the potential clinical efficacy of S18, we assessed its safety and efficacy using human airway cultures and animal models. S18-mucus interactions were tested using superresolution microscopy, quartz crystal microbalance with dissipation, and confocal microscopy. Human and murine airway cultures were used to measure airway surface liquid height. Off-target effects were assessed in conscious mice and anesthetized rats. Morbidity and mortality were assessed in the β-ENaC-transgenic (Tg) mouse model. Restoration of normal mucus clearance was measured in cystic fibrosis transmembrane conductance regulator inhibitor 172 [CFTR(inh)-172]-challenged sheep. We found that S18 does not interact with mucus and rapidly penetrated dehydrated CF mucus. Compared with amiloride, an early generation ENaC antagonist, S18 displayed a superior ability to slow airway surface liquid absorption, reverse CFTR(inh)-172-induced reduction of mucus transport, and reduce morbidity and mortality in the β-ENaC-Tg mouse, all without inducing any detectable signs of renal toxicity. These data suggest that S18 is the first naturally occurring ENaC antagonist to show improved preclinical efficacy in animal models of CF with no signs of renal toxicity