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

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

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

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

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

Carbonic anhydrase IX is a pH-stat that sets an acidic tumour extracellular pH in vivo

Background Tumour Carbonic Anhydrase IX (CAIX), a hypoxia-inducible tumour-associated cell surface enzyme, is thought to acidify the tumour microenvironment by hydrating CO2 to form protons and bicarbonate, but there is no definitive evidence for this in solid tumours in vivo. Methods We used 1H magnetic resonance spectroscopic imaging (MRSI) of the extracellular pH probe imidazolyl succinic acid (ISUCA) to measure and spatially map extracellular pH in HCT116 tumours transfected to express CAIX and empty vector controls in SCID mice. We also measured intracellular pH in situ with 31P MRS and measured lactate in freeze-clamped tumours. Results CAIX expressing tumours had 0.15 pH-unit lower median extracellular pH than control tumours (pH 6.71 tumour vs pH 6.86 control, P = 0.01). Importantly, CAIX expression imposed an upper limit for tumour extracellular pH at 6.93. Despite the increased lactate concentration in CAIX-expressing tumours, 31P MRS showed no difference in intracellular pH, suggesting that CAIX acidifies only the tumour extracellular space. Conclusions CAIX acidifies the tumour microenvironment, and also provides an extracellular pH control mechanism. We propose that CAIX thus acts as an extracellular pH-stat, maintaining an acidic tumour extracellular pH that is tolerated by cancer cells and favours invasion and metastasis.We are grateful for the support of CRUK [grant number C14303/A17197], the Breast Cancer Research Foundation, the Royal Society, Worldwide Cancer Research and the European Research Council [SURVIVE: 723397]. JP-T and SC received support from the Spanish Ministry of Economy and Competitiveness SAF2014-23622

What is pH regulation, and why do cancer cells need it?

Metabolism is a continuous source of acids. To keep up with a desired metabolic rate, tumors must establish an adequate means of clearing their acidic end-products. This homeostatic priority is achieved by various buffers, enzymes, and transporters connected through the common denominator of H+ ions. Whilst this complexity is proportionate to the importance of adequate pH control, it is problematic for developing an intuition for tracking the route taken by acids, assessing the relative importance of various acid-handling proteins, and predicting the outcomes of pharmacological inhibition or genetic alteration. Here, with the help of a simplified mathematical framework, the genesis of cancer pH regulation is explained in terms of the obstacles to efficient acid venting and how these are overcome by specific molecules, often associated with cancer. Ultimately, the pH regulatory apparatus in tumors must (i) provide adequate lactic acid permeability through membranes, (ii) facilitate CO2/HCO3−/H+ diffusivity across the interstitium, (iii) invest in a form of active transport that strikes a favorable balance between intracellular pH and intracellular lactate retention under the energetic constraints of a cell, and (iv) enable the necessary feedback to complete the homeostatic loop. A more informed and quantitative approach to understanding acid-handling in cancer is mandatory for identifying vulnerabilities, which could be exploited as therapeutic targets

A Barter Economy in Tumors: Exchanging Metabolites through Gap Junctions

To produce physiological functions, many tissues require their cells to be connected by gap junctions. Such diffusive coupling is important in establishing a cytoplasmic syncytium through which cells can exchange signals, substrates and metabolites. Often the benefits of connectivity become apparent solely at the multicellular level, leading to the notion that cells work for a common good rather than exclusively in their self-interest. In some tumors, gap junctional connectivity between cancer cells is reduced or absent, but there are notable cases where it persists or re-emerges in late-stage disease. Diffusive coupling will blur certain phenotypic differences between cells, which may seem to go against the establishment of population heterogeneity, a central pillar of cancer that stems from genetic instability. Here, building on our previous measurements of gap junctional coupling between cancer cells, we use a computational model to simulate the role of connexin-assembled channels in exchanging lactate and bicarbonate ions down their diffusion gradients. Based on the results of these simulations, we propose that an overriding benefit of gap junctional connectivity may relate to lactate/bicarbonate exchange, which would support an elevated metabolic rate in hypoxic tumors. In this example of barter, hypoxic cancer cells provide normoxic neighbors with lactate for mitochondrial oxidation; in exchange, bicarbonate ions, which are more plentiful in normoxic cells, are supplied to hypoxic neighbors to neutralize the H+ ions co-produced glycolytically. Both cells benefit, and so does the tumor