Bone resorption by osteoclasts occurs through the creation of a sealed extracellular compartment (ECC), or pit, adjacent to the bone that is subsequently acidified through a complex biological process. The low pH of the pit dissolves the bone mineral and activates acid proteases that further break down the bone matrix. There are many ion channels, transporters, and soluble proteins involved in osteoclast mediated resorption, and in the past few years, there has been an increased understanding of the identity and properties of some key proteins such as the ClC-7 Cl^-/H⁺ antiporter and the H_V1 proton channel. Here we present a detailed mathematical model of osteoclast acidification that includes the influence of many of the key regulatory proteins. The primary enzyme responsible for acidification is the vacuolar H⁺-ATPase (V-ATPase), which pumps protons from the cytoplasm into the pit. Unlike the acidification of small lysosomes, the pit is so large that protons become depleted from the cytoplasm. Hence, proton buffering and production in the cytoplasm by carbonic anhydrase II (CAII) is potentially important for proper acidification. We employ an ordinary differential equations (ODE)-based model that accounts for the changes in ionic species in the cytoplasm and the resorptive pit. Additionally, our model tracks ionic flow between the cytoplasm and the extracellular solution surrounding the cell. Whenever possible, the properties of individual channels and transporters are calibrated based on electrophysiological measurements, and physical properties of the cell, such as buffering capacity, surface areas, and volumes, are estimated based on available data. Our model reproduces many of the experimental findings regarding the role of key proteins in the acidification process, and it allows us to estimate, among other things, number of active pumps, protons moved, and the influence of particular mutations implicated in disease.

The lumenal pH of an organelle is one of its defining characteristics and central to its biological function. Experiments have elucidated many of the key pH regulatory elements and how they vary from compartment-to-compartment, and continuum mathematical models have played an important role in understanding how these elements (proton pumps, counter-ion fluxes, membrane potential, buffering capacity, etc.) work together to achieve specific pH setpoints. While continuum models have proven successful in describing ion regulation at the cellular length scale, it is unknown if they are valid at the subcellular level where volumes are small, ion numbers may fluctuate wildly, and biochemical heterogeneity is large. Here, we create a discrete, stochastic (DS) model of vesicular acidification to answer this question. We used this simplified model to analyze pH measurements of isolated vesicles containing single proton pumps and compared these results to solutions from a continuum, ordinary differential equations (ODE)-based model. Both models predict similar parameter estimates for the mean proton pumping rate, membrane permeability, etc., but, as expected, the ODE model fails to report on the fluctuations in the system. The stochastic model predicts that pH fluctuations decrease during acidification, but noise analysis of single-vesicle data confirms our finding that the experimental noise is dominated by the fluorescent dye, and it reveals no insight into the true noise in the proton fluctuations. Finally, we again use the reduced DS model explore the acidification of large, lysosome-like vesicles to determine how stochastic elements, such as variations in proton-pump copy number and cycling between on and off states, impact the pH setpoint and fluctuations around this setpoint.

Optimal lysosome function requires maintenance of an acidic pH maintained by proton pumps in combination with a counterion transporter such as the Cl-/H+ exchanger, CLCN7 (ClC-7), encoded by CLCN7. The role of ClC-7 in maintaining lysosomal pH has been controversial. In this paper, we performed clinical and genetic evaluations of two children of different ethnicities. Both children had delayed myelination and development, organomegaly, and hypopigmentation, but neither had osteopetrosis. Whole-exome and -genome sequencing revealed a de novo c.2144A>G variant in CLCN7 in both affected children. This p.Tyr715Cys variant, located in the C-terminal domain of ClC-7, resulted in increased outward currents when it was heterologously expressed in Xenopus oocytes. Fibroblasts from probands displayed a lysosomal pH approximately 0.2 units lower than that of control cells, and treatment with chloroquine normalized the pH. Primary fibroblasts from both probands also exhibited markedly enlarged intracellular vacuoles; this finding was recapitulated by the overexpression of human p.Tyr715Cys CLCN7 in control fibroblasts, reflecting the dominant, gain-of-function nature of the variant. A mouse harboring the knock-in Clcn7 variant exhibited hypopigmentation, hepatomegaly resulting from abnormal storage, and enlarged vacuoles in cultured fibroblasts. Our results show that p.Tyr715Cys is a gain-of-function CLCN7 variant associated with developmental delay, organomegaly, and hypopigmentation resulting from lysosomal hyperacidity, abnormal storage, and enlarged intracellular vacuoles. Our data supports the hypothesis that the ClC-7 antiporter plays a critical role in maintaining lysosomal pH.