Optimal Thinning of MCMC Output

The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to "burn in" and removed, whilst the remainder of the chain is "thinned" if compression is also required. In this paper we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path such that the approximation provided by their empirical distribution is close to optimal. A novel method is proposed, based on greedy minimisation of a kernel Stein discrepancy, that is suitable for problems where heavy compression is required. Theoretical results guarantee consistency of the method and its effectiveness is demonstrated in the challenging context of parameter inference for ordinary differential equations. Software is available in the Stein Thinning package in Python, R and MATLAB.Comment: To appear in the Journal of the Royal Statistical Society, Series B, 2021

Carbonic anhydrase IX promotes tumor growth and necrosis in vivo and inhibition enhances anti-VEGF therapy.

PURPOSE: Bevacizumab, an anti-VEGFA antibody, inhibits the developing vasculature of tumors, but resistance is common. Antiangiogenic therapy induces hypoxia and we observed increased expression of hypoxia-regulated genes, including carbonic anhydrase IX (CAIX), in response to bevacizumab treatment in xenografts. CAIX expression correlates with poor prognosis in most tumor types and with worse outcome in bevacizumab-treated patients with metastatic colorectal cancer, malignant astrocytoma, and recurrent malignant glioma. EXPERIMENTAL DESIGN: We knocked down CAIX expression by short hairpin RNA in a colon cancer (HT29) and a glioblastoma (U87) cell line which have high hypoxic induction of CAIX and overexpressed CAIX in HCT116 cells which has low CAIX. We investigated the effect on growth rate in three-dimensional (3D) culture and in vivo, and examined the effect of CAIX knockdown in combination with bevacizumab. RESULTS: CAIX expression was associated with increased growth rate in spheroids and in vivo. Surprisingly, CAIX expression was associated with increased necrosis and apoptosis in vivo and in vitro. We found that acidity inhibits CAIX activity over the pH range found in tumors (pK = 6.84), and this may be the mechanism whereby excess acid self-limits the build-up of extracellular acid. Expression of another hypoxia inducible CA isoform, CAXII, was upregulated in 3D but not two-dimensional culture in response to CAIX knockdown. CAIX knockdown enhanced the effect of bevacizumab treatment, reducing tumor growth rate in vivo. CONCLUSION: This work provides evidence that inhibition of the hypoxic adaptation to antiangiogenic therapy enhances bevacizumab treatment and highlights the value of developing small molecules or antibodies which inhibit CAIX for combination therapy

Off-target effects of SGLT2 blockers: empagliflozin does not inhibit Na+/H+ exchanger-1 or lower [Na+]i in the heart

Aims: Empagliflozin (EMPA) is a potent inhibitor of the renal sodium-glucose cotransporter 2 (SGLT2) and an effective treatment for type-2 diabetes. In patients with diabetes and heart failure, EMPA has cardioprotective effects independent of improved glycaemic control, despite SGLT2 not being expressed in the heart. A number of non-canonical mechanisms have been proposed to explain these cardiac effects, most notably an inhibitory action on cardiac Na+/H+ exchanger 1 (NHE1), causing a reduction in intracellular [Na+] ([Na+]i). However, at resting intracellular pH (pHi), NHE1 activity is very low and its pharmacological inhibition is not expected to meaningfully alter steady-state [Na+]i. We re-evaluate this putative EMPA target by measuring cardiac NHE1 activity. Methods and results: The effect of EMPA on NHE1 activity was tested in isolated rat ventricular cardiomyocytes from measurements of pHi recovery following an ammonium pre-pulse manoeuvre, using cSNARF1 fluorescence imaging. Whereas 10 µM cariporide produced near-complete inhibition, there was no evidence for NHE1 inhibition with EMPA treatment (1, 3, 10 or 30 µM). Intracellular acidification by acetate-superfusion evoked NHE1 activity and raised [Na+]i, reported by sodium binding benzofuran isophthalate (SBFI) fluorescence, but EMPA did not ablate this rise. EMPA (10 µM) also had no significant effect on the rate of cytoplasmic [Na+]i-rise upon superfusion of Na+-depleted cells with Na+-containing buffers. In Langendorff-perfused mouse, rat and guinea pig hearts, EMPA did not affect [Na+]i at baseline nor pHi recovery following acute acidosis, as measured by 23Na triple quantum filtered NMR and 31P NMR, respectively. Conclusions Our findings indicate that cardiac NHE1 activity is not inhibited by EMPA (or other SGLT2i’s) and EMPA has no effect on [Na+]i over a wide range of concentrations, including the therapeutic dose. Thus, the beneficial effects of SGLT2i’s in failing hearts should not be interpreted in terms of actions on myocardial NHE1 or intracellular [Na+]. Translational Perspective: Heart failure remains a huge clinical burden. Clinical trials of SGLT2 inhibitors in patients with diabetes and heart failure have reported highly significant cardiovascular benefit that appears independent of improved glycaemic control. As SGLT2 is not expressed in the heart, the mechanism by which SGLT2 inhibitors are cardioprotective remains unknown. Understanding this mechanism is clearly essential as the use of SGLT2 inhibitors in non-diabetics is increasing and a better understanding may allow refinement of therapeutic approaches in both HFpEF and HFrEF. One suggested mechanism that has received significant attention, inhibition of cardiac Na+/H+ exchanger, is investigated here

SGLT2 inhibitors and the cardiac Na⁺/H⁺ exchanger-1:the plot thickens

No abstract available

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable

Importance of Intracellular pH in Determining the Uptake and Efficacy of the Weakly Basic Chemotherapeutic Drug, Doxorubicin

Low extracellular pH (pHe), that is characteristic of many tumours, tends to reduce the uptake of weakly basic drugs, such as doxorubicin, thereby conferring a degree of physiological resistance to chemotherapy. It has been assumed, from pH-partition theory, that the effect of intracellular pH (pHi) is symmetrically opposite, although this has not been tested experimentally. Doxorubicin uptake into colon HCT116 cells was measured using the drug's intrinsic fluorescence under conditions that alter pHi and pHe or pHi alone. Acutely, doxorubicin influx across the cell-membrane correlates with the trans-membrane pH-gradient (facilitated at alkaline pHe and acidic pHi). However, the protonated molecule is not completely membrane-impermeant and, therefore, overall drug uptake is less pHe-sensitive than expected from pH-partitioning. Once inside cells, doxorubicin associates with slowly-releasing nuclear binding sites. The occupancy of these sites increases with pHi, such that steady-state drug uptake can be greater with alkaline cytoplasm, in contradiction to pH-partition theory. Measurements of cell proliferation demonstrate that doxorubicin efficacy is enhanced at alkaline pHi and that pH-partition theory is inadequate to account for this. The limitations in the predictive power of pH-partition theory arise because it only accounts for the pHi/pHe-sensitivity of drug entry into cells but not the drug's subsequent interactions that, independently, show pHi-dependence. In summary, doxorubicin uptake into cells is favoured by high pHe and high pHi. This modified formalism should be taken into account when designing manoeuvres aimed at increasing doxorubicin efficacy

Bicarbonate Recycling by HIF‐1–Dependent Carbonic Anhydrase Isoforms 9 and 12 Is Critical in Maintaining Intracellular pH and Viability of Nucleus Pulposus Cells

Intervertebral disc degeneration is a ubiquitous condition closely linked to chronic low‐back pain. The health of the avascular nucleus pulposus (NP) plays a crucial role in the development of this pathology. We tested the hypothesis that a network comprising HIF‐1α, carbonic anhydrase (CA) 9 and 12 isoforms, and sodium‐coupled bicarbonate cotransporters (NBCs) buffer intracellular pH through coordinated bicarbonate recycling. Contrary to the current understanding of NP cell metabolism, analysis of metabolic‐flux data from Seahorse XF analyzer showed that CO2 hydration contributes a significant source of extracellular proton production in NP cells, with a smaller input from glycolysis. Because enzymatic hydration of CO2 is catalyzed by plasma membrane‐associated CAs we measured their expression and function in NP tissue. NP cells robustly expressed isoforms CA9/12, which were hypoxia‐inducible. In addition to increased mRNA stability under hypoxia, we observed binding of HIF‐1α to select hypoxia‐responsive elements on CA9/12 promoters using genomic chromatin immunoprecipitation. Importantly, in vitro loss of function studies and analysis of discs from NP‐specific HIF‐1α null mice confirmed the dependency of CA9/12 expression on HIF‐1α. As expected, inhibition of CA activity decreased extracellular acidification rate independent of changes in HIF activity or lactate/H+ efflux. Surprisingly, CA inhibition resulted in a concomitant decrease in intracellular pH that was mirrored by inhibition of sodium‐bicarbonate importers. These results suggested that extracellular bicarbonate generated by CA9/12 is recycled to buffer cytosolic pH fluctuations. Importantly, long‐term intracellular acidification from CA inhibition lead to compromised cell viability, suggesting that plasma‐membrane proton extrusion pathways alone are not sufficient to maintain homeostatic pH in NP cells. Taken together, our studies show for the first time that bicarbonate buffering through the HIF‐1α–CA axis is critical for NP cell survival in the hypoxic niche of the intervertebral disc. © 2017 American Society for Bone and Mineral Research.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142506/1/jbmr3293.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142506/2/jbmr3293-sup-0001-SuppData-S1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142506/3/jbmr3293_am.pd

Disrupting Hypoxia-Induced Bicarbonate Transport Acidifies Tumor Cells and Suppresses Tumor Growth

Tumor hypoxia is associated clinically with therapeutic resistance and poor patient outcomes. One feature of tumor hypoxia is activated expression of carbonic anhydrase IX (CA9), a regulator of pH and tumor growth. In this study, we investigated the hypothesis that impeding the reuptake of bicarbonate produced extracellularly by CA9 could exacerbate the intracellular acidity produced by hypoxic conditions, perhaps compromising cell growth and viability as a result. In 8 of 10 cancer cell lines, we found that hypoxia induced the expression of at least one bicarbonate transporter. The most robust and frequent inductions were of the sodium-driven bicarbonate transporters SLC4A4 and SLC4A9, which rely upon both HIF1α and HIF2α activity for their expression. In cancer cell spheroids, SLC4A4 or SLC4A9 disruption by either genetic or pharmaceutical approaches acidified intracellular pH and reduced cell growth. Furthermore, treatment of spheroids with S0859, a small-molecule inhibitor of sodium-driven bicarbonate transporters, increased apoptosis in the cell lines tested. Finally, RNAi-mediated attenuation of SLC4A9 increased apoptosis in MDA-MB-231 breast cancer spheroids and dramatically reduced growth of MDA-MB-231 breast tumors or U87 gliomas in murine xenografts. Our findings suggest that disrupting pH homeostasis by blocking bicarbonate import might broadly relieve the common resistance of hypoxic tumors to anticancer therapy

Measuring intracellular pH in the heart using hyperpolarized carbon dioxide and bicarbonate: a 13C and 31P magnetic resonance spectroscopy study

AIMS: Technological limitations have restricted in vivo assessment of intracellular pH (pH(i)) in the myocardium. The aim of this study was to evaluate the potential of hyperpolarized [1-(13)C]pyruvate, coupled with (13)C magnetic resonance spectroscopy (MRS), to measure pH(i) in the healthy and diseased heart. METHODS AND RESULTS: Hyperpolarized [1-(13)C]pyruvate was infused into isolated rat hearts before and immediately after ischaemia, and the formation of (13)CO(2) and H(13)CO(3)(-) was monitored using (13)C MRS. The HCO(3)(-)/CO(2) ratio was used in the Henderson-Hasselbalch equation to estimate pH(i). We tested the validity of this approach by comparing (13)C-based pH(i) measurements with (31)P MRS measurements of pH(i). There was good agreement between the pH(i) measured using (13)C and (31)P MRS in control hearts, being 7.12 +/- 0.10 and 7.07 +/- 0.02, respectively. In reperfused hearts, (13)C and (31)P measurements of pH(i) also agreed, although (13)C equilibration limited observation of myocardial recovery from acidosis. In hearts pre-treated with the carbonic anhydrase (CA) inhibitor, 6-ethoxyzolamide, the (13)C measurement underestimated the (31)P-measured pH(i) by 0.80 pH units. Mathematical modelling predicted that the validity of measuring pH(i) from the H(13)CO(3)(-)/(13)CO(2) ratio depended on CA activity, and may give an incorrect measure of pH(i) under conditions in which CA was inhibited, such as in acidosis. Hyperpolarized [1-(13)C]pyruvate was also infused into healthy living rats, where in vivo pH(i) from the H(13)CO(3)(-)/(13)CO(2) ratio was measured to be 7.20 +/- 0.03. CONCLUSION: Metabolically generated (13)CO(2) and H(13)CO(3)(-) can be used as a marker of cardiac pH(i) in vivo, provided that CA activity is at normal levels

Acidic environments trigger intracellular H+-sensing FAK proteins to re-balance sarcolemmal acid-base transporters and auto-regulate cardiomyocyte pH

AIMS: In cardiomyocytes, acute disturbances to intracellular pH (pHi) are promptly corrected by a system of finely-balanced sarcolemmal acid-base transporters. However, these fluxes become thermodynamically re-balanced in acidic environments, which inadvertently causes their set-point pHi to fall outside the physiological range. It is unclear whether an adaptive mechanism exists to correct this thermodynamic challenge and return pHi to normal. METHODS AND RESULTS: Following left-ventricle cryo-damage, a diffuse pattern of low extracellular pH (pHe) was detected by acid-sensing pHLIP. Despite this, pHi measured in the beating heart (13C NMR) was normal. Myocytes had adapted to their acidic environment by reducing Cl–/HCO3- exchange (CBE)-dependent acid-loading and increasing Na+/H+ exchange (NHE1)-dependent acid-extrusion, as measured by fluorescence (cSNARF1). The outcome of this adaptation on pHi is revealed as a cytoplasmic alkalinisation when cells are superfused at physiological pHe. Conversely, mice given oral bicarbonate to improve systemic buffering had reduced myocardial NHE1 expression, consistent with a needs-dependent expression of pHi-regulatory transporters. The response to sustained acidity could be replicated in vitro using neonatal ventricular myocytes (NRVMs) incubated at low pHe for 48 h. The adaptive increase in NHE1 and decrease in CBE activities was linked to Slc9a1 (NHE1) upregulation and Slc4a2 (AE2) downregulation. This response was triggered by intracellular H+ ions because it persisted in the absence of CO2/HCO3- and became ablated when acidic incubation media had low chloride concentration, a manoeuvre that reduces the extent of pHi decrease. Pharmacological inhibition of FAK-family non-receptor kinases, previously characterised as pH-sensors, ablated pHi autoregulation. In support of a pHi-sensing role, FAK protein Pyk2 (auto)phosphorylation was reduced within minutes of exposure to acidity, ahead of adaptive changes to pHi control. CONCLUSIONS: Cardiomyocytes fine-tune the expression of pHi-regulators so that pHi is at least 7.0. This autoregulatory feedback mechanism defines physiological pHi and protects it during pHe vulnerabilities. TRANSLATIONAL PERSPECTIVE: As a consequence of the inherent thermodynamic coupling between intra- and extracellular pH (pHi/pHe), sustained changes to perfusion, such as those in coronary disease or development, would have deleterious effects on the internal acid-base milieu of myocytes and hence cardiac function, unless offset by a corrective process. Using in-vivo and in-vitro models of acidification, we characterise this adaptive process functionally, and describe how it is engaged to auto-regulate pHi. This additional layer of homeostatic oversight enables the myocardium to operate within its optimal pHi-range, even at times when vascular perfusion is failing to maintain chemical constancy of the interstitial fluid