We have developed and implemented a novel mathematical model for simulating transients in surface pH (pHS) and intracellular pH (pHi) caused by the influx of carbon dioxide (CO2) into a Xenopus oocyte. These transients are important tools for studying gas channels. We assume that the oocyte is a sphere surrounded by a thin layer of unstirred fluid, the extracellular unconvected fluid (EUF), which is in turn surrounded by the well-stirred bulk extracellular fluid (BECF) that represents an infinite reservoir for all solutes. Here, we assume that the oocyte plasma membrane is permeable only to CO2. In both the EUF and intracellular space, solute concentrations can change because of diffusion and reactions. The reactions are the slow equilibration of the CO2 hydration-dehydration reactions and competing equilibria among carbonic acid (H2CO3)/bicarbonate ( HCO3-) and a multitude of non-CO2/HCO3- buffers. Mathematically, the model is described by a coupled system of reaction-diffusion equations that—assuming spherical radial symmetry—we solved using the method of lines with appropriate stiff solvers. In agreement with experimental data (Musa-Aziz et al, PNAS 2009, 106:5406–5411), the model predicts that exposing the cell to extracellular 1.5% CO2/10 mM HCO3- (pH 7.50) causes pHi to fall and pHS to rise rapidly to a peak and then decay. Moreover, the model provides insights into the competition between diffusion and reaction processes when we change the width of the EUF, membrane permeability to CO2, native extra-and intracellular carbonic anhydrase-like activities, the non-CO2/HCO3- (intrinsic) intracellular buffering power, or mobility of intrinsic intracellular buffers.

Musa-Aziz R, Occhipinti R, Boron WF. Evidence from simultaneous intracellular-and surface-pH transients that carbonic anhydrase II enhances CO2 fluxes across Xenopus oocyte plasma membranes.

ORCID IDs: 0000-0003-0538-6646 (H.H.); 0000-0001-6675-273X (M.B.).Elevated carbon dioxide (CO 2 ) in leaves closes stomatal apertures. Research has shown key functions of the b-carbonic anhydrases (bCA1 and bCA4) in rapid CO 2 -induced stomatal movements by catalytic transmission of the CO 2 signal in guard cells. However, the underlying mechanisms remain unclear, because initial studies indicate that these Arabidopsis (Arabidopsis thaliana) bCAs are targeted to distinct intracellular compartments upon expression in tobacco (Nicotiana benthamiana) cells. Which cellular location of these enzymes plays a key role in native guard cells in CO 2 -regulated stomatal movements remains unknown. Here, we express fluorescently tagged CAs in guard cells of ca1ca4 double-mutant plants and show that the specific locations of bCA4 at the plasma membrane and bCA1 in native guard cell chloroplasts each can mediate rapid CO 2 control of stomatal movements. Localization and complementation analyses using a mammalian aCAII-yellow fluorescent protein in guard cells further show that cytoplasmic localization is also sufficient to restore CO 2 regulation of stomatal conductance. Mathematical modeling of cellular CO 2 catalysis suggests that the dynamics of the intracellular HCO 3 2 concentration change in guard cells can be driven by plasma membrane and cytoplasmic localizations of CAs but not as clearly by chloroplast targeting. Moreover, modeling supports the notion that the intracellular HCO 3 2 concentration dynamics in guard cells are a key mechanism in mediating CO 2 -regulated stomatal movements but that an additional chloroplast role of CAs exists that has yet to be identified.

Exposing an oocyte to CO2/HCO3 (-) causes intracellular pH (pHi) to decline and extracellular-surface pH (pHS) to rise to a peak and decay. The two companion papers showed that oocytes injected with cytosolic carbonic anhydrase II (CA II) or expressing surface CA IV exhibit increased maximal rate of pHi change (dpHi/dt)max, increased maximal pHS changes (ΔpHS), and decreased time constants for pHi decline and pHS decay. Here we investigate these results using refinements of an earlier mathematical model of CO2 influx into a spherical cell. Refinements include 1) reduced cytosolic water content, 2) reduced cytosolic diffusion constants, 3) refined CA II activity, 4) layer of intracellular vesicles, 5) reduced membrane CO2 permeability, 6) microvilli, 7) refined CA IV activity, 8) a vitelline membrane, and 9) a new simulation protocol for delivering and removing the bulk extracellular CO2/HCO3 (-) solution. We show how these features affect the simulated pHi and pHS transients and use the refined model with the experimental data for 1.5% CO2/10 mM HCO3 (-) (pHo = 7.5) to find parameter values that approximate ΔpHS, the time to peak pHS, the time delay to the start of the pHi change, (dpHi/dt)max, and the change in steady-state pHi. We validate the revised model against data collected as we vary levels of CO2/HCO3 (-) or of extracellular HEPES buffer. The model confirms the hypothesis that CA II and CA IV enhance transmembrane CO2 fluxes by maximizing CO2 gradients across the plasma membrane, and it predicts that the pH effects of simultaneously implementing intracellular and extracellular-surface CA are supra-additive.

Human carbonic anhydrase IV (CA IV) is GPI-anchored to the outer membrane surface, catalyzing CO2/HCO3 (-) hydration-dehydration. We examined effects of heterologously expressed CA IV on intracellular-pH (pHi) and surface-pH (pHS) transients caused by exposing oocytes to CO2/HCO3 (-)/pH 7.50. CO2 influx causes a sustained pHi fall and a transient pHS rise; CO2 efflux does the opposite. Both during CO2 addition and removal, CA IV increases magnitudes of maximal rate of pHi change (dpHi/dt)max, and maximal pHS change (ΔpHS) and decreases time constants for pHi changes (τpHi ) and pHS relaxations (τpHS ). Decreases in time constants indicate that CA IV enhances CO2 fluxes. Extracellular acetazolamide blocks all CA IV effects, but not those of injected CA II. Injected acetazolamide partially reduces CA IV effects. Thus, extracellular CA is required for, and the equivalent of cytosol-accessible CA augments, the effects of CA IV. Increasing the concentration of the extracellular non-CO2/HCO3 (-) buffer (i.e., HEPES), in the presence of extracellular CA or at high [CO2], accelerates CO2 influx. Simultaneous measurements with two pHS electrodes, one on the oocyte meridian perpendicular to the axis of flow and one downstream from the direction of extracellular-solution flow, reveal that the downstream electrode has a larger (i.e., slower) τpHS , indicating [CO2] asymmetry over the oocyte surface. A reaction-diffusion mathematical model (third paper in series) accounts for the above general features, and supports the conclusion that extracellular CA, which replenishes entering CO2 or consumes exiting CO2 at the extracellular surface, enhances the gradient driving CO2 influx across the cell membrane.

The question of the preferred substrate of glutamatergic neurons at high neural activity has been vibrantly debated for over a decade since the classical hypothesis (CH) of the primacy of glucose has been challenged by the astrocyte-neuron lactate shuttle hypothesis (ANLSH), which replaces the primacy of glucose with astrocyte produced lactate. We perform Bayesian Flux Balance Analysis (BFBA) with a new mathematical model of cellular brain energetics, comprising detailed biochemical pathways in and between astrocytes and glutamatergic neurons and partitioning of each cell type into cytosol and mitochondria. Supported by the results of our in silico studies, which are in remarkable agreement with previously published results, we posit the Glucose Shunt Hypothesis (GSH) that during high activity, the inhibition of the phosphofructokinase (PFK) enzyme in neuron impairs neuronal glycolysis, enabling the process by which lactate effluxed by astrocytes is taken up by glutamatergic neurons, whereas at low activity, glucose remains the preferred substrate for neurons. We postulate that the ANLS is a shunt utilized by glutamatergic neurons to bypass their glycolysis impaired by the inhibition of PFK in connection with increased oxidative phosphorylation at high neuronal activity.

pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3− , NH4+) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cell–which to our knowledge is the first one capable of handling a multitude of buffer reaction–that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3− influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis.

We report a detailed study of a cohort of sporadic Creutzfeldt-Jakob disease (sCJD) VV1-2 type-mixed cases (valine homozygosity at codon 129 of the prion protein, PrP, gene harboring disease-related PrP, PrP D , types 1 and 2). Overall, sCJDVV1-2 subjects showed mixed clinical and histopathological features, which often correlated with the relative amounts of the corresponding PrP D type. However, type-specific phenotypic characteristics were only detected when the amount of the corresponding prp D type exceeded 20-25%. Overall, original features of types 1 (T1) and 2 (T2) in sCJDVV1 and-VV2, including rostrocaudal relative distribution and conformational indicators, were maintained in sCJDVV1-2 except for one of the two components of T1 identified by electrophoretic mobility as T1 21. The T1 21 conformational characteristics shifted in the presence of T2, inferring a conformational effect of prp D T2 on T1 21. The prevalence of sCJDVV1-2 was 23% or 57% of all sCJDVV cases, depending on whether standard or highly sensitive type-detecting procedures were adopted. This study, together with previous data from sCJDMM1-2 (methionine homozygosity at PrP gene codon 129) establishes the type-mixed sCJD variants as an important component of sCJD, which cannot be identified with current non-tissue based diagnostic tests of prion disease. The heterogeneity that characterizes sporadic Creutzfeldt-Jakob disease (sCJD), a group of diseases that accounts for 85-90% of all human prion diseases, is due to the existence of at least five clinically and pathologically distinct subtypes. According to a widely used molecular classification, each sCJD subtype is identified by the pairing of the patient's genotype-MM, MV or VV-at the methionine (M)/valine (V) polymorphic codon 129 of the prion protein (PrP), with the type, 1 or 2, of the abnormal, disease-related PrP (PrP D). The 1 and 2 typing identifies the two basic PrP D isoforms or strains associated with sCJD and most other prion diseases. The sCJD heterogeneity is further complicated by the frequent occurrence of type "mixed" cases where the disease phenotypes and PrP D type 1 (T1) and 2 (T2) associated with two subtypes coexist in variable ratios in the same patient. Therefore, besides the five "pure" subtypes (i.e.,-MM(MV)1,-VV1,-MM2,-MV2 and-VV2), sCJD includes the four mixed subtypes MM1-2, MV1-2 and VV1-2, as well as the MV2K-C (Table S1).