Rossana Occhipinti

Astrocytes as the Glucose Shunt for Glutamatergic Neurons at High Activity: An In Silico Study

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.

Distinct Cellular Locations of Carbonic Anhydrases Mediate Carbon Dioxide Control of Stomatal Movements

Intracellular targeting of guard cell carbonic anhydrases is characterized and modeled in relation to their roles in CO2 control of stomatal movements. Elevated carbon dioxide (CO2) in leaves closes stomatal apertures. Research has shown key functions of the β-carbonic anhydrases (βCA1 and βCA4) in rapid CO2-induced stomatal movements by catalytic transmission of the CO2 signal in guard cells. However, the underlying mechanisms remain unclear, because initial studies indicate that these Arabidopsis (Arabidopsis thaliana) βCAs 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 CO2-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 βCA4 at the plasma membrane and βCA1 in native guard cell chloroplasts each can mediate rapid CO2 control of stomatal movements. Localization and complementation analyses using a mammalian αCAII-yellow fluorescent protein in guard cells further show that cytoplasmic localization is also sufficient to restore CO2 regulation of stomatal conductance. Mathematical modeling of cellular CO2 catalysis suggests that the dynamics of the intracellular HCO3− 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 HCO3− concentration dynamics in guard cells are a key mechanism in mediating CO2-regulated stomatal movements but that an additional chloroplast role of CAs exists that has yet to be identified.

Statistical analysis of metabolic pathways of brain metabolism at steady state.

The estimation of metabolic fluxes for brain metabolism is important, among other things, to test the validity of different hypotheses which have been proposed in the literature. The metabolic model that we propose considers, in addition to the blood compartment, the cytosol, and mitochondria of both astrocyte and neuron, including detailed metabolic pathways. In this work we use a recently developed methodology to perform a statistical Flux Balance Analysis (FBA) for this model. The methodology recasts the problem in the form of Bayesian statistical inference and therefore can take advantage of qualitative information about brain metabolism for the simultaneous estimation of all reaction fluxes and transport rates at steady state. By a Markov Chain Monte Carlo (MCMC) sampling method, we are able to provide for each reaction flux and transport rate a distribution of possible values. The analysis of the histograms of the reaction fluxes and transport rates provides a very useful tool for assessing the validity of different hypotheses about brain energetics proposed in the literature, and facilitates the design of the pathways network that is in accordance with what is understood of the functioning of the brain. In this work, we focus on the analysis of biochemical pathways within each cell type (astrocyte and neuron) at different levels of neural activity, and we demonstrate how statistical tools can help implement various bounds suggested by experimental data.

A reaction–diffusion model of CO2 influx into an oocyte

We have developed and implemented a novel mathematical model for simulating transients in surface pH (pH(S)) and intracellular pH (pH(i)) caused by the influx of carbon dioxide (CO(2)) 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 CO(2). In both the EUF and intracellular space, solute concentrations can change because of diffusion and reactions. The reactions are the slow equilibration of the CO(2) hydration-dehydration reactions and competing equilibria among carbonic acid (H(2)CO(3))/bicarbonate (HCO(3)(-)) and a multitude of non-CO(2)/HCO(3)(-) 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. 2009, PNAS 106 5406-5411], the model predicts that exposing the cell to extracellular 1.5% CO(2)/10 mM HCO(3)(-) (pH 7.50) causes pH(i) to fall and pH(S) 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 CO(2), native extra- and intracellular carbonic anhydrase-like activities, the non-CO(2)/HCO(3)(-) (intrinsic) intracellular buffering power, or mobility of intrinsic intracellular buffers.

Energetics of inhibition: insights with a computational model of the human GABAergic neuron-astrocyte cellular complex.

We investigate metabolic interactions between astrocytes and GABAergic neurons at steady states corresponding to different activity levels using a six-compartment model and a new methodology based on Bayesian statistics. Many questions about the energetics of inhibition are still waiting for definite answers, including the role of glutamine and lactate effluxed by astrocytes as precursors for γ-aminobutyric acid (GABA), and whether metabolic coupling applies to the inhibitory neurotransmitter GABA. Our identification and quantification of metabolic pathways describing the interaction between GABAergic neurons and astrocytes in connection with the release of GABA makes a contribution to this important problem. Lactate released by astrocytes and its neuronal uptake is found to be coupled with neuronal activity, unlike glucose consumption, suggesting that in astrocytes, the metabolism of GABA does not require increased glycolytic activity. Negligible glutamine trafficking between the two cell types at steady state questions glutamine as a precursor of GABA, not excluding glutamine cycling as a transient dynamic phenomenon, or a prominent role of GABA reuptake. Redox balance is proposed as an explanation for elevated oxidative phosphorylation and adenosine triphosphate hydrolysis in astrocytes, decoupled from energy requirements.

Evidence from simultaneous intracellular- and surface-pH transients that carbonic anhydrase IV enhances CO2 fluxes across Xenopus oocyte plasma membranes

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.

Mathematical modeling of acid-base physiology.

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(-), [Formula: see text] ) 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 cells-which to our knowledge is the first one capable of handling a multitude of buffer reactions-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.

Evidence from mathematical modeling that carbonic anhydrase II and IV enhance CO2 fluxes across Xenopus oocyte plasma membranes.

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.

Na+/HCO3– Cotransporter NBCn2 Mediates HCO3− Reclamation in the Apical Membrane of Renal Proximal Tubules

The kidney maintains systemic acid-base balance by reclaiming from the renal tubule lumen virtually all HCO3- filtered in glomeruli and by secreting additional H+ to titrate luminal buffers. For proximal tubules, which are responsible for about 80% of this activity, it is believed that HCO3- reclamation depends solely on H+ secretion, mediated by the apical Na+/H+ exchanger NHE3 and the vacuolar proton pump. However, NHE3 and the proton pump cannot account for all HCO3- reclamation. Here, we investigated the potential contribution of two variants of the electroneutral Na+/HCO3- cotransporter NBCn2, the amino termini of which start with the amino acids MCDL (MCDL-NBCn2) and MEIK (MEIK-NBCn2). Western blot analysis and immunocytochemistry revealed that MEIK-NBCn2 predominantly localizes at the basolateral membrane of medullary thick ascending limbs in the rat kidney, whereas MCDL-NBCn2 localizes at the apical membrane of proximal tubules. Notably, NH4Cl-induced systemic metabolic acidosis or hypokalemic alkalosis downregulated the abundance of MCDL-NBCn2 and reciprocally upregulated NHE3 Conversely, NaHCO3-induced metabolic alkalosis upregulated MCDL-NBCn2 and reciprocally downregulated NHE3 We propose that the apical membrane of the proximal tubules has two distinct strategies for HCO3- reclamation: the conventional indirect pathway, in which NHE3 and the proton pump secrete H+ to titrate luminal HCO3-, and the novel direct pathway, in which NBCn2 removes HCO3- from the lumen. The reciprocal regulation of NBCn2 and NHE3 under different physiologic conditions is consistent with our mathematical simulations, which suggest that HCO3- uptake and H+ secretion have reciprocal efficiencies for HCO3- reclamation versus titration of luminal buffers.

CrossTalk proposal: Physiological CO2 exchange can depend on membrane channels

Since the discovery that CO2 passes through aquaporin-1 (AQP1; Nakhoul et al. 1998; Cooper & Boron, 1998), the importance of channelvs. lipid-mediated gas transport has often been portrayed as an either/or issue. However, depending upon physiological context, the role of channels may be insignificant or dominant. In a landmark study, Mitchell (1830) examined gas permeation across barriers of natural rubber or animal tissue, rank-ordered the ‘relative facility of transmission’ of several gases, and recognized that these move independently of one another in a mechanism dependent upon ‘infiltration’ (i.e. solubility) in the organic molecular barrier – the first statement of ‘solubility theory’. Later, Graham showed that permeation across rubber membranes depends on not only solubility but also diffusion through the barrier (Graham, 1866) – the first statement of ‘solubility–diffusion theory’. Meanwhile, Fick proposed his law of mass diffusion, which Wroblewski combined with Henry’s