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# Elucidation of the molecular mechanisms underlying adverse reactions associated with a kinase inhibitor using systems toxicology

• npj Systems Biology and Applications volume 1, Article number: 15005 (2015)
• doi:10.1038/npjsba.2015.5
Revised:
Accepted:
Published online:

## Abstract

### Background/Objectives:

Targeted kinase inhibitors are an important class of agents in anticancer therapeutics, but their limited tolerability hampers their clinical performance. Identification of the molecular mechanisms underlying the development of adverse reactions will be helpful in establishing a rational method for the management of clinically adverse reactions. Here, we selected sunitinib as a model and demonstrated that the molecular mechanisms underlying the adverse reactions associated with kinase inhibitors can efficiently be identified using a systems toxicological approach.

### Methods:

First, toxicological target candidates were short-listed by comparing the human kinase occupancy profiles of sunitinib and sorafenib, and the molecular mechanisms underlying adverse reactions were predicted by sequential simulations using publicly available mathematical models. Next, to evaluate the probability of these predictions, a clinical observation study was conducted in six patients treated with sunitinib. Finally, mouse experiments were performed for detailed confirmation of the hypothesized molecular mechanisms and to evaluate the efficacy of a proposed countermeasure against adverse reactions to sunitinib.

### Results:

In silico simulations indicated the possibility that sunitinib-mediated off-target inhibition of phosphorylase kinase leads to the generation of oxidative stress in various tissues. Clinical observations of patients and mouse experiments confirmed the validity of this prediction. The simulation further suggested that concomitant use of an antioxidant may prevent sunitinib-mediated adverse reactions, which was confirmed in mouse experiments.

### Conclusions:

A systems toxicological approach successfully predicted the molecular mechanisms underlying clinically adverse reactions associated with sunitinib and was used to plan a rational method for the management of these adverse reactions.

## Introduction

Targeted kinase inhibitors are an important class of therapeutics that are widely used to treat various types of cancer,1,2 and a large number of new compounds are under clinical development.3 Although these compounds show improved toxicity profiles compared with classical anticancer chemotherapeutics, the tolerability of kinase inhibitors is often limited, which can hamper their performance with respect to improving clinical outcomes.4,5 Although kinase inhibitors are designed and selected to inhibit specific kinases at the drug discovery stage, subsequent studies and clinical experience have revealed that kinase inhibitors also interact with various off-target molecules, i.e., those not intended as pharmacological targets, with off-target interactions leading to unanticipated adverse reactions.6,7 To maximize the clinical benefits of kinase inhibitors, it is desirable to develop a rational approach to improve their tolerability. Despite the development of novel technologies that enable comprehensive measurements of off-target interaction profiles,8 standard methods for elucidating the molecular mechanisms underlying development of adverse reactions in a clinical setting based on off-target data have not yet been established. Development of a method to identify means to mitigate adverse reactions based on the identification of toxicological targets and the molecular mechanisms is urgently required. In this study, we selected sunitinib as a model compound to demonstrate an efficient method to elucidate the molecular mechanisms underlying clinically adverse reactions associated with kinase inhibitors and to design a possible countermeasure for adverse effects.

Sunitinib is a multi-kinase inhibitor with antitumor and anti-angiogenic activities.9 It is indicated for the treatment of metastatic renal cell carcinoma (RCC), imatinib-resistant gastrointestinal stromal tumors, and metastatic pancreatic neuroendocrine tumors.10 Sunitinib targets multiple tyrosine kinases, including vascular endothelial growth factor receptors, platelet-derived growth factor receptors and stem cell factor receptors.11 However, despite its potent antitumor effects, sunitinib also causes numerous adverse reactions. These reactions are markedly more prevalent and severe in patients treated with sunitinib than in those treated with sorafenib, another multi-kinase inhibitor used in the treatment of RCC, even though their primary target profiles are similar.12 Among the adverse reactions associated with sunitinib, thrombocytopenia has an exceptionally high incidence and is generally recognized as a dose-limiting toxicity.5 Hyperthyrotropinemia is also more prevalent in patients treated with sunitinib than in those treated with sorafenib.13 Other associated adverse reactions include hepatic and cardiac dysfunction.13 In general, although sunitinib is currently recognized as the initial drug of choice for the treatment of advanced RCC, its toxicity is a matter of clinical concern.14

Understanding possible molecular mechanisms of such adverse reactions requires a systems toxicology approach where diverse data and knowledge are integrated to uncover dynamics of molecular interactions networks linked to physiological responses. It can be a power approach especially where the polypharmacological properties of a compound obscure the physiological mechanism of drug action.15,16 In addition, in silico simulation enables the examination of working hypotheses without time-consuming and costly experiments, thereby helping to develop plausible hypotheses that warrant experimental investigation. Although such approaches may ultimately contribute to the elucidation of the molecular mechanisms underlying physiological drug activities, few reports demonstrating concrete methodologies are available. In the present study, we used systems toxicology approach to efficiently elucidate the molecular mechanisms underlying the clinically adverse reactions associated with sunitinib and to identify a method to attenuate these adverse reactions based on an understanding of the molecular mechanisms.

## Materials and Methods

### Calculation of occupancy rates

The occupancy rates of sunitinib and sorafenib at various human kinases were calculated from a previous report that included the K d values of a number of kinase inhibitors obtained with high-throughput measurements.8 The full list of Kd values of sunitinib and sorafenib to human kinases is available as the Supplementary Information of this article.8 The steady state mean unbound plasma concentrations of these agents under clinical conditions (Cp,u,ss) were obtained from the information displayed on the Japanese package inserts. From a pharmacokinetic standpoint, the free drug concentration in cells is in equilibrium with the plasma-unbound concentration of the drug. Thus, the occupancy rates can be calculated using the Kd value for drug binding to the kinase and the mean plasma unbound concentration (Cp,u,ss) of the drug at steady state as $Cp,u,ssKd+Cp,u,ss$.

### Construction of a glycogen metabolism and related pathways map

Metabolic pathway maps were constructed utilizing previous reports17,18 and public databases, such as PANTHER19 and BioModels.20 Specifically, the glycogen metabolic pathway was retrieved from previous reports,17,18 and the glycolysis pathway, tricarboxylic acid cycle and pentose-phosphate pathway were retrieved from the PANTHER database (accession numbers P00024, P00051 and P02762, respectively). The glutathione metabolic pathway was retrieved from previous reports21,22 and from the BioModels database (ID: BIOMD0000000268). These pathways were then integrated to create a system-wide map using CellDesigner4.3.19,20,23

### Model simulations

Although there are no publicly available simulation models that include the entire relationship between PHKG1/2 and GSH, models for glycogen metabolism and glycolysis,24 the pentose–phosphate pathway,25 and the glutathione metabolism pathway26 are available. For glycogen metabolism and the glycolysis pathway, the inhibitory effects of sunitinib were added to the model by assuming competitive inhibition of phosphorylase kinase (PHK) with an inhibition constant of 5.5 μM, a reported value for the dissociation constant.8 This simulation model was published as a MATLAB script in the original paper.24 MATLAB 2012b was used to simulate the effects of varied sunitinib concentrations on PHK content, glycogen phosphorylase and glycogen synthase activity, and glycogen and G6P content, as measured at the end of the simulation. The kinetic behavior of the pentose–phosphate pathway was described by the kinetic laws published in a previous report25 and the SABIO-RK database.27 These kinetic data were implemented into a model formed using systems biology markup language (File S2). Simulations based on this model were performed using MATLAB 2012b. The glutathione metabolism model was taken from BioModels ID: BIOMD0000000268 in systems biology markup language format, and simulations were performed on COPASI.28 To simulate the effect of antioxidants, a node representing vitamin E was added to the glutathione model, which assumed direct quenching of H2O2 by vitamin E.

### Cell culture

293FT cells were cultured in Dulbecco’s modified Eagle’s medium (DMEM, Nacalai Tesque, Kyoto, Japan) supplemented with 10% fetal bovine serum (FBS, Biowest, Nuaillé, France), 2 mM L-glutamine (Nacalai Tesque), and 1% penicillin-streptomycin (PCSM, Life Technologies, Carlsbad, CA, USA). HEK 293 cells were cultured in DMEM supplemented with 10% FBS and 1% PCSM. Primary hepatocytes were isolated as described previously,29 seeded onto collagen-coated plates, and cultured in William E medium (Sigma-Aldrich, Carlsbad, CA, USA) supplemented with 10% FBS, 2 mM L-glutamine, and 1% PCSM.

### Preparation of recombinant PHKG1/2 kinase domains

Genes encoding human and mouse PHKG1 and PHKG2 were engineered to include a His-tag at the N-terminus and then subcloned into pcDNA3.3 vectors (Life Technologies), which were then transfected into 293FT cells using Lipofectamine 2000 (Life Technologies). At 48 h post-transfection, cells were lysed in lysis buffer containing phosphate-buffered saline (pH 8.0), 1% Nonidet P-40, and a protease inhibitor cocktail (Roche, Indianapolis, IN, USA). Recombinant proteins were purified using Profinity IMAC Ni-Charged Resin (Bio-Rad, Tokyo, Japan).

### In vitro kinase assay

To measure the kinase activity of PHKG1/2, 100 ng of the recombinant protein was incubated with 10 μg of κ-casein (Wako, Osaka, Japan), 2 μM ATP in kinase buffer (20 mM HEPES, 10 mM MgCl2, 3 mM MnCl2 and 0.1 mg/ml bovine serum albumin, pH 7.6) and 10 μM β-mercaptoethanol (Sigma-Aldrich) for 30 min at 37 °C. The concentration of the remaining ATP was determined using a Kinase-Glo Plus luminescent kinase assay (Promega, Madison, WI, USA). To determine the concentration for 50% inhibition (IC50), drugs were added to the reaction mixture at the indicated concentrations. ATP concentrations were fitted to the standard model, and IC50 values were determined according to Powell’s nonlinear least squares method with a uniform weighting factor. Analyses were performed using Scientist software (Micromath, St Louis, MO, USA).

### Clinical observations

Patients with advanced RCC scheduled for sunitinib treatment were recruited for the observational study. Written informed consent was obtained from each patient and blood samples were collected at the indicated times.

### Animal models and drug administration

Six-week-old male C57BL6/J mice were purchased from Japan SLC (Shizuoka, Japan) and fed an MF diet (Oriental Yeast, Tokyo, Japan) containing sunitinib (0.167 mg/g MF diet; estimated as 26.7 mg/kg/day) or sorafenib (0.129 mg/g MF diet; estimated as 20.6 mg/kg/day) for 14 days. The doses were adjusted to sustain plasma drug concentrations at levels comparable to those achieved in patients. To evaluate the effects of the concomitant use of an antioxidant, mice were fed a diet containing both α-tocopherol nicotinate (0.189 mg/g MF diet; estimated as 30 mg/kg/day) and sunitinib for 14 days. To examine the contribution of oxidative stress on sunitinib hepatotoxicity, buthionine sulfoximine was administered intraperitoneally (6 mmol/kg at −1 and 11 h) and sunitinib was administered orally (8 mg/kg at 0 h and 6 mg/kg at 6, 12 and 18 h). After 36 h, the mice were killed, and their organs and cells of interest were analyzed.

### Measurement of clinical test values and metabolites

Serum ALT levels were measured using an L-type Wako GPT J2 (Wako) kit and a Dimension Xpand analyzer (Siemens, Berlin, Germany) according to the manufacturers’ protocols. To measure tissue glycogen and G6P levels and the NADPH/NADP+ ratio, excised tissue samples were homogenized with the extraction buffers provided in the glycogen assay kit (BioVision, San Francisco, CA, USA), the glucose-6-phosphate assay kit (BioVision), or the NADP+/NADPH quantification kit (BioVision), and then centrifuged at 20,000g for 5 min at 4 °C. Supernatants were analyzed according to the manufacturers’ protocols. Tissue glutathione levels were measured in excised tissue samples homogenized with 6% metaphosphoric acid (Wako) and centrifuged at 20,000g for 5 min at 4 °C. Supernatants were divided into two aliquots, one of which was used to assay total glutathione, while 2-vinylpyridine (Nacalai Tesque) was added to the other sample to mask GSH. Total glutathione and GSSG were assayed at an absorbance of 405 nm in the presence of 25% triethanolamine (Nacalai Tesque), 6 mM 5,5’-dithiobis-(2-nitrobenzoic acid) (Nacalai Tesque), 0.3 mM NADPH (Wako), and 5 units/ml of glutathione reductase (Sigma-Aldrich). Troponin T measurements were conducted by SRL (Tokyo, Japan) using an electrochemiluminescence immunoassay. The N-terminal fragment of the prohormone B-type natriuretic peptide (NT-proBNP) was measured using an NT-proBNP ELISA kit (USCN Life Science, Wuhan, China) according to the manufacturer’s protocol. Platelet counts were performed by Mitsubishi Chemical Medience Corporation (Tokyo, Japan) using an electrical resistivity method. Thyroid-stimulating hormone levels were measured using a rodent thyroid-stimulating hormone assay kit (Endocrine Technologies, Newark, CA, USA) according to the manufacturer’s protocol. Total triiodothyronine (T3), total thyroxin (T4), free T3 (FT3) and free T4 (FT4) concentrations were measured using an ARCHITECT i1000SR analyzer (Abbott Japan, Katsuyama, Japan) with the corresponding kits.

### Quantification of drug concentrations

Plasma drug concentrations were measured using liquid chromatography coupled with tandem mass spectrometry (ACQUITY UPLC-Quattro Premier XE system, Waters, Milford, MA, USA) in a device equipped with an ACQUITY UPLC BEH shield (RP18, 1.7 μm) and a 2.1×100 mm column (Waters). All the data were acquired and processed using MassLynx software (version 4.1) with QuanLynx (Waters). Positive-ion electrospray tandem mass spectroscopy, operated under the multiple reaction monitoring mode, was used to detect mass transitions (parent to daughter ion), with m/z 399.48 to 283.1 for sunitinib, m/z 371.27 to 283.1 for N-desethylsunitinib, m/z 465.35 to 252.1 for sorafenib, and m/z 268.23 to 116.03 for metoprolol, which served as an internal standard. Plasma samples were deproteinized with 4 volumes of acetonitrile (Nacalai Tesque) and the supernatants were used for analysis.

### In vivo knockdown experiments

A small hairpin RNA (shRNA) sequence that inhibits murine PHKG2, specifically, 5′-GCCTTAAGCAGTCACCGTTTA-3′, was designed using BLOCK-iT RNAi Designer (Invitrogen, Carlsbad, CA, USA). The shRNA duplex contains a loop sequence (5´-TTCAAGAGA-3′) that was initially subcloned into an RNAi Ready pSIREN vector (Clontech Laboratories, Mountain View, CA, USA) and then into pAdeno-X (Clontech Laboratories), which was digested with PacI and transfected into HEK 293 cells to yield adenoviruses encoding shRNAs. Both virus production and amplification were performed according to the manufacturer’s protocols. A CsCl density gradient ultracentrifugation was used to purify crude adenoviral preparations. The viral titer was determined using an Adeno-X Rapid Titer Kit (Clontech Laboratories). Mice were intravenously injected with 1×109 infectious units of adenovirus. Seventy-two hours after adenovirus administration, the mice were killed, and the relevant tissues and cells were analyzed.

### Quantification of mRNA expression by real-time PCR

Total RNA was extracted from mouse liver using RNA isoplus reagent (TaKaRa, Shiga, Japan). Reverse transcription was performed using ReverTra Ace (Toyobo Engineering, Osaka, Japan) and mRNA expression levels were measured using real-time quantitative PCR with SYBR GreenER qPCR SuperMix Universal (Life Technologies), an Eco Real-Time PCR System (Illumina, San Diego, CA, USA) and the provided software. The following primers were used: 5′-GCACCAGAGATCCTTAAAT-3′ and 5′-TAGCATCAGGATTTGGCGC-3′ for mouse PHKG2, and 5′-CCGGAAGGAAAACTGACAGC-3′ and 5′-GTGGTGGTGAAGCTGTAGCC-3′ for β-actin.

### Statistical analyses

All the data are expressed as the mean±s.d. of at least five independent experiments. Statistical analysis was performed using Student’s t-test, analysis of variance followed by the Tukey–Kramer post hoc test, or analysis of covariance, where applicable.

### Study approval

Experiments using human samples were conducted according to a study protocol approved by the Institutional Review Board of the Graduate School of Medicine, The University of Tokyo. All animal procedures were approved by the Institutional Animal Care and Use Committee of the Graduate School of Medicine, The University of Tokyo.

## Results

### In silico simulations indicate that off-target inhibition of phosphorylase kinase gamma 1/2 by sunitinib decreases cellular glutathione levels

Candidate kinases potentially responsible for the adverse reactions associated with sunitinib were identified by comparing two compounds that share primary target kinases, sunitinib and sorafenib, on the basis of the assumption that differences in the prevalence and severity of the adverse reactions induced by these drugs are related to preferential inhibition of off-target kinases by sunitinib. Kinase occupancy profiles for the two drugs were calculated from their mean unbound plasma concentrations30,31 and reported dissociation constant (Kd) values8 (Figure 1a). A comparison of the two profiles identified four candidate kinases: serine/threonine kinase 17a (STK17A), phosphorylase kinase gamma 1 (PHKG1), PHKG2 and BMP2 inducible kinase (BMP2K). Only a limited number of reports are available on the physiological roles of STK17A and BMP2K. STK17A was first identified as a proapoptotic human kinase,32 and rodents were shown to lack a homologous gene.33 Some reports indicated that STK17A induction in cancer cells enhances cell sensitivity to anticancer agents.34 BMP2K was first isolated from prechondroblastic cells treated with BMP-2 and was shown to negatively regulate osteoblast differentiation.35 On the basis of these data, it seems unlikely that development of the prevalent adverse reactions associated with sunitinib can be explained by STK17A or BMP2K inhibition. In contrast, PHKG1 and PHKG2 were reported to act as catalytic subunits for distinct isoforms of phosphorylase kinase, a kinase that regulates the activation of glycogen phosphorylase, a rate-limiting enzyme in glycogen catabolism.17,36 Phosphorylase kinase is ubiquitously expressed,37 although the distribution of the catalytic subunit, either PHKG1 or PHKG2, is tissue-specific, with the former expressed in skeletal muscle, heart and thyroid, and the latter in liver and testis.36 Sunitinib inhibits both isoforms, thereby disrupting glucose metabolism, which is essential for the normal physiological function of all tissues, particularly those associated with adverse reactions to sunitinib. Thus, the influence of sunitinib-mediated PHKG1/2 inhibition on physiological homeostasis was selected for investigation. First, we used in vitro kinase assays to confirm that sunitinib inhibited the kinase activity of human and mouse PHKG1/2 at levels comparable with those calculated from reported Kd values (Supplementary Figure S1). Next, a metabolic map was created by integrating information on glycogen metabolism and associated regulatory systems from public databases19,20 and previous reports17 (Supplementary Figure S2). This comprehensive map indicated that glycogen metabolism is linked to glycolysis via glucose-6-phosphate (G6P),17 which is also located at the gateway to the pentose–phosphate pathway (Figure 1b). The pentose–phosphate pathway is the only pathway in mammalian cells that produces the reduced form of nicotinamide adenine dinucleotide phosphate (NADPH),38 which regulates the glutathione redox balance. The reduced form of glutathione (GSH) is a typical radical scavenger involved in eliminating the reactive oxygen species produced by numerous physiological processes.39 However, it remains unclear whether GSH redox balance is affected by phosphorylase kinase inhibition or the influence of phosphorylase kinase inhibition is diminished before affecting GSH redox balance owing to the buffering or feedback effects of metabolic pathways. Therefore, in silico simulations were used to examine whether sunitinib-mediated inhibition of PHKG1/2 affects GSH levels. Although models of glycogen metabolism and glycolysis,24 the pentose–phosphate pathway,25 and glutathione metabolism26 are available, to the best of our knowledge, there is currently no single available model that includes the entire relationship between PHKG1/2 and GSH. Therefore, we performed sequential simulations using all these models (Supplementary Figure S3). To simulate the effects of sunitinib, sunitinib-mediated inhibition of PHKG1/2 was added to the model of glycogen metabolism.24 The activities of related kinases or the levels of various metabolites were plotted against the sunitinib concentration (Figures 1c–f). The simulation indicated that sunitinib induced glycogen accumulation and G6P reduction by altering the activity of the relevant enzymes. Next, we simulated the effect of reduced G6P levels on the pentose–phosphate pathway.25 The results indicated that a decrease in the initial content of G6P decreased the ratio of NADPH to NADP+ (the oxidized form of NADPH; Figure 1g). Finally, we performed simulations of the glutathione metabolic pathway26 and found that the lower NADPH content decreased GSH levels (Figure 1h). Collectively, the sequential simulations suggest that sunitinib-mediated inhibition of PHKG1/2 lowers GSH levels, likely causing oxidative stress in various organs and tissues.

### Clinical observations confirm that glycogen accumulation and oxidative stress are associated with sunitinib administration

A clinical observational study was conducted to validate the above in silico simulation results. To determine whether glycogen accumulation and oxidative stress occur in patients treated with sunitinib (as predicted by the in silico simulations), six patients receiving sunitinib as a therapy for advanced or relapsing RCC were enrolled in the study (Supplementary Table S1). Blood samples were collected before sunitinib treatment, once per week during the first course of treatment, and once every 2 weeks during the second and third courses. Changes in blood glycogen and serum thiobarbituric acid reactive substance (TBARS) levels, which reflect lipid peroxide levels, were analyzed. Sunitinib therapy increased both blood glycogen (Figure 2a) and serum TBARS levels (Figure 2b) in all the six patients, indicating the development of oxidative stress. These results demonstrate that sunitinib induces glycogen accumulation and oxidative stress in clinical patients and suggest that the in silico simulations successfully predicted the unfavorable drug actions associated with sunitinib-mediated off-target kinase inhibition.

### Experimental confirmation that sunitinib-mediated inhibition of PHKG2 induces oxidative stress in the liver

To further validate the in silico predictions, we used an animal model to examine the metabolite content of those tissues adversely affected by sunitinib. Six-week-old male C57BL/6 mice were treated with sunitinib or sorafenib for 14 days; the amount of sunitinib or sorafenib in the chow was adjusted to achieve plasma concentrations within the respective clinical concentration ranges of the two drugs (Supplementary Figure S4a). Sunitinib treatment increased blood glycogen and serum TBARS levels, whereas sorafenib had no significant effect on these two parameters (Figures 3a and b). We next examined the mice for signs of hepatotoxicity, which develops in response to sunitinib but not sorafenib. Both sunitinib and sorafenib increased the amount of the liver enzyme alanine aminotransferase (ALT) in the serum, although ALT levels were lower in the sorafenib-treated than in the sunitinib-treated animals (Figure 3c). In addition, sunitinib but not sorafenib increased hepatic glycogen content (Figure 3d), which is consistent with the results of the in silico simulation. The changes observed for other metabolites were also consistent with the simulation results. Specifically, in the livers of sunitinib-treated mice, hepatic G6P content was 50% lower (Figure 3e), the NADPH/NADP+ ratio was significantly lower (Figure 3f), and the ratio of GSH to the oxidized form (GSSG) was 90% lower than those in the livers of untreated control mice (Figure 3g), whereas no significant changes in these metabolites were observed in sorafenib-treated mice. In addition, the development of oxidative stress in the livers of sunitinib-treated mice was confirmed by measuring hepatic TBARS levels (Figure 3h). These results indicated that the in silico simulations successfully predicted the sunitinib-mediated disruption of metabolic homeostasis in the liver. To confirm that the sunitinib-induced disruption of hepatic redox balance was mediated by PHKG2 inhibition, in vivo gene silencing experiments were performed using an adenovirus encoding an shRNA targeting PHKG2 (shPHKG2) because intravenously administered adenoviruses preferentially infect and accumulate in the liver.40 Indeed, hepatic PHKG2 mRNA (Supplementary Figure S4b) and PHKG2 protein expression levels (Figure 3i) were significantly lower in shPHKG2-treated mice than in mice treated with a negative control shRNA adenovirus. As expected, shPHKG2-treated mice showed significantly higher levels of hepatic glycogen and significantly lower levels of hepatic G6P (Figures 3j and k), with significantly lower NADPH/NADP+ and GSH/GSSG ratios than control mice (Figures 3l and m). In addition, the effects of sunitinib administration and shPHKG2 treatment were not additive (Figures 3n and o). Overall, these results confirm that sunitinib-induced hepatic oxidative stress is mediated by the inhibition of PHKG2.

### Experimental validation that sunitinib induces oxidative stress in heart, platelets and thyroid

Sunitinib treatment is associated with cardiac disorders, reduced platelet counts and thyroid dysfunction.41 Therefore, we examined the influence of sunitinib administration on glycogen-related metabolic pathways and oxidative stress generation in the mouse heart, platelets and thyroid. Mice were administered sunitinib or sorafenib for 14 days as described above, and clinical tests were performed to confirm the development of adverse reactions. Notably, serum concentrations of troponin T, a marker indicative of cardiocyte damage, were significantly higher in the sunitinib-treated group than those in the control or sorafenib-treated groups (Figure 4a). In addition, peripheral blood platelet counts were significantly lower and serum concentrations of thyroid-stimulating hormone were significantly higher in the sunitinib group than those in the control or sorafenib groups (Figures 4b and c). Next, the metabolite content of these tissues was measured. Similar to the results shown above for the liver, sunitinib increased the glycogen content and decreased the NADPH/NADP+ and GSH/GSSG ratios in the heart, thyroid and platelets compared with control and sorafenib groups (Figures 4d–f). In the sunitinib-treated group, elevation of the NADP+ level was higher in thyroid tissue than in other tissues. This might be partly because, in thyroid tissue, NADPH is consumed to produce thyroid hormone as well as to reduce GSSG.42 These results again confirm that the in silico simulations accurately predict the sunitinib-induced disruption of metabolic homeostasis and generation of oxidative stress in these tissues and cells.

### Vitamin E alleviates adverse reactions associated with sunitinib

As a result of these simulations and experiments, we formulated a hypothesis: if oxidative stress mediates the various adverse reactions associated with sunitinib, then concomitant use of antioxidants, such as vitamin E, could alleviate those adverse effects. To verify this hypothesis, a series of in silico studies and animal experiments were carried out. First, we performed a simulation of the glutathione metabolism model that included vitamin E administration; a node representing vitamin E, which assumed that vitamin E directly traps hydrogen peroxide (H2O2), was added to the original model (Figure 5a). GSH levels under conditions of low NADPH, which reflects the influence of the sunitinib administration, were calculated and plotted against the initial loading concentration of vitamin E. The results showed that vitamin E loading restores GSH levels (Figure 5b). Next, we validated this in silico prediction by examining the in vivo effects of a vitamin E preparation consisting of α-tocopherol nicotinate (α-TN) in sunitinib-treated mice. Mice were administered sunitinib with or without α-TN, and the metabolite content of the tissues was measured. In all four tissues examined, co-administration of α-TN prevented sunitinib-induced decreases in the GSH/GSSG ratio, which was maintained at levels similar to those observed in the tissues of control mice (Figures 5c–f). In addition, clinical test values (for serum ALT, troponin T, thyroid-stimulating hormone and platelet counts) obtained for the co-treated animals were comparable to those obtained for the control group (Figures 5g–j), suggesting that the sunitinib-mediated oxidative stress was ameliorated by antioxidant administration. We also determined the mechanisms underlying several sunitinib-induced adverse reactions (hepatotoxicity, cardiotoxicity, thrombocytopenia and thyroid dysfunction) mediated by oxidative stress (Supplementary Figures S5–S8).

### Vitamin E has no effect on the pharmacology of sunitinib

Considering the clinical applications of sunitinib and vitamin E combination therapy, we investigated whether vitamin E negatively impacts the therapeutic efficacy of sunitinib by examining the effect of vitamin E co-administration on the anticancer efficacy of sunitinib in an animal model. Mice subcutaneously inoculated with Lewis lung carcinoma cells were administered sunitinib with or without α-TN for 14 days, after which the therapeutic effects of sunitinib on tumor growth were analyzed. Sunitinib treatment significantly reduced tumor weight (at the site of inoculation) and lung weight, which reflects the metastasis of Lewis lung carcinoma cells (Figures 6a and b). These effects were not impaired by concomitant use of α-TN (Figures 6a and b). Sunitinib primarily acts by inhibiting tumor neoangiogenesis;43 therefore, we also examined tumor tissue hemoglobin content, which indicates the extent of the blood supply to tumor tissues (Figure 6c). As expected, sunitinib administration decreased tumor hemoglobin content and, again, this effect was not impaired by co-administration of α-TN. These results suggest that vitamin E co-administration has little or no effect on the pharmacology of sunitinib.

## Discussion

Various targeted kinase inhibitors are available for clinical use, and these drugs have contributed to the drastic improvement in treatment outcomes for anti-cancer therapies.1,2 Although these agents are less toxic than classical anticancer chemotherapeutics, the spectra of adverse reactions associated with kinase inhibitors are often different from those of anticancer chemotherapies, causing an emerging problem in clinics.4,5 Clinical management methods for frequent adverse reactions associated with anticancer chemotherapies, such as diarrhea, nausea and myelosuppression, have been established on the basis of empirical evaluations.44,45,46 However, clinical management methods have not been well established for adverse reactions that are rarely observed by clinicians.47 Fast-paced launches of new kinase inhibitors might also make it more difficult to establish clinical management methods for adverse reactions in a timely manner. To overcome this problem, development of a system-oriented framework is critical so that countermeasures for adverse reactions can be designed on the basis of an understanding of the molecular mechanisms and system dynamics underlying adverse reactions. Various in silico tools have been developed to predict the toxicological properties of new chemical entities, including quantitative structure–activity relationship-based approaches and rule-based expert systems. However, most of these tools presupposed their utility during the drug designing steps, aiming to predict properties of a compound related to general toxicity such as genotoxicity, carcinogenicity and irritancy based on its chemical structure.48,49,50 These tools are useful for reducing the risk of discontinuation due to serious safety issues at the later stages of drug development; however, they are not intended to provide information on the detailed molecular mechanisms underlying clinically adverse reactions. Accordingly, we examined the usefulness of a systems toxicological approach in the present study and demonstrated a method to predict the reactions that may be triggered by a compound at the molecular level based on the experimental measurement of its kinase interaction profile.

The present analysis was guided by the off-target interaction profile associated with sunitinib. Off-target candidates that are affected at clinically relevant concentrations can be identified using the calculations shown in Figure 1a. It is then necessary to determine whether the effects on candidate molecules are related to the development of adverse physiological effects, i.e., to explore the associations between off-target molecules and molecules that have direct physiological effects. In cases of adverse drug reactions, the physiological responses requiring examination include broad phenomena such as apoptosis, inflammation and oxidative stress generation. Once the inputs and outputs have been determined, we can perform in silico simulations to examine whether a change in an input actually affects the output. The challenges in implementing this approach lie in the preparation and use of mathematical models. Obtaining quantitatively accurate predictions requires simulations using an integrated model that encompasses the entire processes of interest. However, it is not always practical to develop a large-scale integrated model and therefore, the use of multiple models that represent a subset of the entire interaction network may be necessary. A simple merger of independently derived models often results in inconsistency in the kinetic parameter values and therefore, these values have to be re-tuned after model integration. The constraint here is that fine-tuning the kinetic parameters in an integrated model may not work owing to different levels of abstraction among models. Even if the level of abstraction and methods of model description have been made consistent, it is a computationally intensive and time-consuming task that often requires additional experimental data for accurate estimates of kinetic parameter values.

In this study, we applied an alternative approach that involves a tandem use of multiple models, each of which is validated to be consistent with the experiments. In general, computational models of biological networks are developed focusing on a subset of networks such as the MAPK and insulin receptor pathways and a model of the entire network is not created. Nevertheless, many of these models achieve a practically sufficient accuracy that can be used for further scientific studies and drug discovery.51 This degree of accuracy may be attributable to the modularity and robustness of the biological network. If the entire network is so tightly connected, perturbation of any part of the network affects the behaviors of all other parts. This results in an extremely unstable system, leading to an evolutionary dead-end.52 Thus, in practice, we can define a subset of the interaction network and consider the rest to be a ‘black box’ from which effects can be implicitly represented within a specific parameter setting of the model (Figure 7a). The success of this approach largely depends on appropriately defining the boundary of a focused network, so that strong interactions with a black box do not affect the dynamical behaviors of the model beyond the level adjustable by parameter settings. In this study, we used three models each representing a distinct functional pathway in the metabolic network, and they were validated experimentally (Figure 7b). Furthermore, the models were interfaced by the dose change of specific molecules. The output of the first model (glycogen metabolism and glycolysis) is a dose change of glucose and G6P that in turn became inputs for the second model (pentose–phosphate pathway). The interface between the second model and the third model (glutathione metabolism) is NADP+ and NADPH. Fortunately, no obvious feedback loop exists between the models that could seriously alter the behaviors of an upstream model depending on the outcome of the downstream models. It is noteworthy that the purpose of the simulation was to understand the qualitative propensity of this part of the metabolic network following sunitinib administration, rather than computing the exact dynamics with quantitative precision. The results of this tandem simulation correctly predicted physiological responses to the administration of sunitinib. Further studies may reveal conditions for this tandem approach to be practically applicable, which would lay the foundation for scaling-up computational studies efficiently for larger networks. It should be noted that we used the model to understand how sunitinib administration may qualitatively influence the metabolic system, rather than to obtain precise numerical results. To this end, the models were only required to deliver the proper degree of change in output and therefore, could have different baseline variables. In other words, the dose of the interface molecule could be 100 units in one model, and the dose level of the same molecule could be represented as 1,000 units in the other model. This is because the only information required is the degree of change and not the absolute number in each model. In such cases, a combination of simulations using separate models is expected to provide reasonable predictions.

The results reported herein demonstrate that in silico prediction (with appropriately designed experimental validation) is an effective strategy to examine toxicological issues associated with kinase inhibitors. Results of this study have major implications for the use of sunitinib in clinical practice, as it is essential to overcome adverse reactions associated with sunitinib tolerability.13 Suppression of sunitinib-mediated thyroid dysfunction may improve patients’ quality of life by ameliorating subjective symptoms, such as fatigue. More importantly, since the sunitinib-mediated reduction in platelet counts is a dose-limiting toxicity, an improvement in thrombocytopenia will allow the continued use of higher doses, which is desirable in treating the primary disease. Indeed, the therapeutic efficacy of sunitinib in RCC correlates positively with the area under the plasma concentration curve for the drug.53 The experiments conducted in the present study strongly indicate that the multi-organ toxicity suffered by patients receiving sunitinib may be alleviated by the concomitant administration of α-TN.

In conclusion, we demonstrated that a systems toxicological approach could be successfully utilized to elucidate molecular mechanisms underlying adverse reactions associated with kinase inhibitors. This approach may be applicable to other kinase inhibitors to maximize their clinical benefits.

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, , , , , et al. 2010 update of EORTC guidelines for the use of granulocyte-colony stimulating factor to reduce the incidence of chemotherapy-induced febrile neutropenia in adult patients with lymphoproliferative disorders and solid tumours. Eur J Cancer 2011; 47: 8–32.

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, , , , , . Relationship between exposure to sunitinib and efficacy and tolerability endpoints in patients with cancer: results of a pharmacokinetic/pharmacodynamic meta-analysis. Cancer Chemother Pharmacol 2010; 66: 357–371.

## Acknowledgements

This work was supported in part by a Grant-in-Aid for Scientific Research (B) 21390041 and a Grant-in-Aid for Scientific Research (A) 24249034 from the Japan Society for the Promotion of Science, and a Grant-in-Aid for Challenging Exploratory Research 26670265 and a Grant-in-Aid for Scientific Research on Innovative Areas ‘HD-physiology’ 22136015 from the Ministry of Education, Culture, Sports, Science and Technology. A part of this research was carried out under Memorandum of Understanding (MOU Number 225-12-8000) between The United States Food and Drug Administration (FDA) and the Systems Biology Institute.

## Author notes

• Takahiro Amemiya
• , Masashi Honma
•  & Yoshiaki Kariya

These authors contributed equally to this work.

## Affiliations

1. ### Department of Pharmacy, The University of Tokyo Hospital, Faculty of Medicine, The University of Tokyo, Tokyo, Japan

• Takahiro Amemiya
• , Masashi Honma
• , Yoshiaki Kariya
•  & Hiroshi Suzuki
2. ### Laboratory of Pharmacology and Pharmacokinetics, The University of Tokyo Hospital, Faculty of Medicine, The University of Tokyo, Tokyo, Japan

• Masashi Honma
3. ### The Systems Biology Institute, Tokyo, Japan

• Samik Ghosh
•  & Hiroaki Kitano
4. ### Integrated Open Systems Unit, Okinawa Institute of Science and Technology, Okinawa, Japan

• Hiroaki Kitano
5. ### Sony Computer Science Laboratories, Inc., Tokyo, Japan

• Hiroaki Kitano
6. ### Laboratory for Disease Systems Modeling, RIKEN Center for Integrative Medical Sciences, Kanagawa, Japan

• Hiroaki Kitano
7. ### Department of Pharmacology, Graduate School of Medicine, Osaka University, Osaka, Japan

• Yoshihisa Kurachi
8. ### Institute of Molecular Oncology, Showa University, Tokyo, Japan

• Ken-ichi Fujita
•  & Yasutsuna Sasaki
9. ### Division of Medical Oncology, Department of Medicine, Showa University School of Medicine, Tokyo, Japan

• Yasutsuna Sasaki
10. ### Department of Urology, The University of Tokyo Hospital, Faculty of Medicine, The University of Tokyo, Tokyo, Japan

• Yukio Homma
•  & Haruki Kume
11. ### Office of Clinical Pharmacology, Office of Translational Sciences, US Food and Drug Administration, Silver Spring, MD, USA

• Darrel R Abernethy

## Authors

### Competing interests

The University of Tokyo has filed a patent application about concomitant use of sunitinib and anti-oxidants (PCT/JP2013/081210, inventors: Masashi Honma, Hiroshi Suzuki, Takahiro Amemiya and Haruki Kume).

## Corresponding author

Correspondence to Masashi Honma.

1. 1.


text:
5:06 AM

5:23 AM
@Scrooble welcome to hell

5:51 AM
@quartata do you have suggestion on how to do spam classification for Axtell besides training a crap RNN

6 hours later…
11:44 AM
0

Be there, for the square Sometimes when you're lying in bed and reading a message, your phone screen will pop into landscape mode right in the middle of a sentence. Only being able to read left to right, you find yourself incapacitated, unable to process the text in front of you. To ensure that...

12:42 PM
I have a stupid question y'all. My prof just breezed through an argument and I'm lost af
We're working in Haskell, and he said the code (1::Integer)+2*(3::Double) causes a type error, which can be revealed through trivial analysis of (+) or (*).
I don't get this

@RushabhMehta You can't add Integer and Double.

that part I got
but what is the second way
like what analysis of (*) tells you there's a type error
@user202729

(*) alone doesnt cause issues

Exactly what I thought!
But clearly my prof thinks otherwise

@RushabhMehta maybe he meant "both"?
because you have to analyze the "*" to figure out the return type

12:48 PM
Here's the exact wording
Consider the expression (1 :: Integer) + 2 * (3 :: Double). This will cause a type error, because the two different type constraints are inconsistent. One bit of trickiness is that the inconsistency could be revealed either in the analysis of (+) or (*). Provide both analyses.

Huh.

I suppose the "analysis" here is by hand.

oh, I think he's saying "It could be in the (+) or it could be in the (*). Analyze both to identify which one it is"?
"either" could mean "xor" or it could mean "or"

Huh. That would be a really longwinded way of saying something a lot more simple

12:50 PM
yeah, possibly? That's the only way to make the question make sense

I suppose it's like this
1. Consider the (+). --> (1::Integer) must have the same type as (2*(3::Double)) --> 2*(3::Double) has the type Integer. (etc)
2. Consider the (*). --> (2*(3::Double)) must have the same type as (3::Double) --> 2*(3::Double) has the type Double. (etc)
Either way, I think it's simple, don't overthink it.

@user202729 @NathanMerrill I've literally been stuck for 3 hours on this stupid shit
but thank you!

1:34 PM
Unpopular Topic Time -- Is PPCG dying? 19th Byte seems to have intermittent chat rather than the near-constant stream it used to have. We're getting maybe one or two challenges per day rather than the 5/day we used to have. Prominent figures are leaving or have left without a word. Even the Sandbox seems to be more sluggish than usual.
21

The chat sure have seemed a lot more dead than usual recently. Answers to challenges seem to more in line with what it's usually been. Challenge frequence seem to have gone down some yeah, but in fairness, the more challenges we have the harder it is to come up new unique ones
I am a contributor to all 3 of these issues as well

From what I've seen, the nature of the challenges have changed greatly over the past few years. It seems like people want to post harder and harder challenges, and that people avoid posting to avoid having questions marked as duplicates.

As a user who only started recently actually using this site - it seems fairly active to me, in everything except maybe new questions posted, which can be attributed to reasons above. But answers are plentiful

Also, the more challenges are posted, the bigger the chance for dupes, I guess?

Also regarding the chat: I had been visiting this site for over 6 months before I even heard about this chat. I'd say that it needs some advertising to attract new visitors, and maybe some examples of things that are on-topic for the chat?

1:45 PM
So people just think "oh this is a good challenge" and bam, dupe.

I don't feel as if the difficulty of challenges have increased in any meaingful way. There is still a healthy mix there I feel, with a bias towards easier challenges since those are easier to write and tend to get more answers

@J.Sallé Of course, but you can always put a twist on it to make it unique enough. I posted this challenge, which was almost a duplicate of this one before I put a twist on it

I tend to agree with Emigna -- I don't think the difficulty ratio of hard to easy challenges has changed, I just think there are fewer challenges overall.

Writing a good challenge isn't easy. And making one that isn't a duplicate or close to one is not trivial with the amount of challenges we have in total
At least that's my impression. I know there are people here who make it seem easy

^ agreed.

1:53 PM
Another thing could be that people end up here because they like coding and golfing, not because they like creating challenges. I agree that it's much more work to create a challenge compared to coming up with a solution (especially since you can get inspiration from other answers). But it's up to all of us to post challenges, and to leave feedback in the sandbox.
I try to have one challenge in progress most of the time, but the sandbox doesn't get the attention that it needs most of the time.

Personally, I think we could start "reviving" select challenges (in a language-of-the-month fashion or some such thing). People could suggest old(er) challenges they find interesting with a low number of answers and bump them (maybe after some editing so the challenge is up to current standards).

@J.Sallé something like this?
(up to 1 answer, at least 60 days old, no accepted answer, open, unlocked)

@EriktheOutgolfer sounds good. I think I might make a meta post asking for opinions on that

@J.Sallé and another approach could be answers:..4 created:..60d closed:0 locked:0 (ignoring whether an answer has been accepted, as well as upping the bar to 4)

2:09 PM
Yep, I'll make a meta-post on that so everyone can chip in on what would be the best parameters

that can't really be done with just a meta post...
nobody wants to dig through the comments just to get an average

Well, I meant presenting the idea properly to the community to see if people would, first of all, be on board with it
the parameters and such could be decided after that

@J.Sallé I guess a CW-locked question would be fit
and the answer having a bunch of code snippets
those snippets will contain numbers, and each user should be able to add one number to every one, if they want to
(and not delete other numbers)
after enough are added for each, the average is taken (the question then is: to floor or to ceil?)

I'm making a meta-post presenting the idea. If people think it's a good idea, we could make that in another post?

also, you might want to consider the Community bumping factor

2:24 PM
What is that?

the Community bot bumps questions from time to time, although not all of them are what this is about, and not all such posts are ever bumped

Ah, I see. I'll mention that as well

I'm really sorry for being super help vampirey this morning, but I've been so frustrated. I'm getting an indentation error in ghci (haskell) on the line allp ::...
module Divisibility where
-- | This module is filled with functions aimed at finding divisble numbers.

-- | Return a sublist comprised of the elements of a list that satisfies a predicate.

filter :: (a -> Bool) -> [a] -> [a]
filter p [] = []
filter p (x:xs)
| p x = x : filter p xs
| otherwise = filter p xs

-- | divisibleBy checks that one number evenly divides the other through mods.

divisibleBy :: Num a => a->a->Bool
let divisibleBy d n = (n mod d == 0)

allp :: [Bool] -> Bool
let allp [] = True

@J.Sallé I like this idea. +1 from me once we figure out the parameters.

@Downgoat Use SmokeDetector's blacklist. It's not as SE-centric as you might think.
In fact, Medium used it successfully.
I think a system where users could see domains used in recently-deleted posts and then vote to blacklist could help to expand any blacklist also.

2:32 PM
Trivia question of the moment: What was Gumby's horse's name?

Pokey?

ding ding ding
have a star

I see what you did there

0

ASCII Schedule / Calendar (title suggestions welcome) code-golf date ascii-art Given a list of activities and their start time/date, output an ASCII-art calendar showing the activities on the appropriate days. All activities are guaranteed to be in the same month, no two activities will be on ...

ha

2:55 PM
@RushabhMehta let can't be used on the top level like that

@J.Sallé I've tried to do this
perhaps there was too much process with my method, but it failed pretty pooly
17

We've got some pretty great challenges here. However, after a month or so, challenges get little to no activity. Since we aren't a Q&A site, we rarely get traffic via searches. I would love it if we could introduce users to high quality questions that they may not have found on their own. I b...

(I didn't end up getting enough challenges posted/voted on)
The reason I chose the one-time "Tour" method vs a "challenge of a month" or something is due to the duration required. We've had so many programs here on PPCG to promote making challenges/answers, and none of them have lasted a long time
but since my method involved editing the questions themselves, it would naturally lead to discovery as people came across these questions
Anyways, I'm not saying all of this to dissuade you, but rather to take into consideration how your method should work

3:18 PM
Turn ppcg into something like Project Euler where we have lists of known-good challenges
/me shrugs

Right, that sounds great: The process is the problem here
how do we create that list?

3:59 PM
0

Supreme Sum String Given an input string, return the word with the highest sum of each of its unicode characters. Rules The input should be seperated by whitespace The value of each word is based on the sum of each character in the word's UTF-16 code The output should be the first word with ...

4:10 PM
0

Length of a UTF-8 byte sequence Determine the length of a UTF-8 byte sequence given its first byte. The following table shows which ranges map to each possible length: Range Length --------- ------ 0x00-0x7F 1 0xC2-0xDF 2 0xE0-0xEF 3 0xF0-0xF4 4 Notes: 0x80-0xBF are continua...

0

Related. Earlier today, AdmBorkBork posted this question on TNB, asking whether or not PPCG was dying. In the following discussion, I have suggested we, as a community, could start "reviving" (for lack of a better term) select challenges, based on suggestions given by us. The reasoning behind i...

^ Sniping New Meta Posts because I don't remember if that still exists.

yes, it does exist

4:28 PM
3

Related. Earlier today, AdmBorkBork posted this question on TNB, asking whether or not PPCG was dying. In the following discussion, I have suggested we, as a community, could start "reviving" (for lack of a better term) select challenges, based on suggestions given by us. The reasoning behind i...

1 hour later…
5:31 PM
52

Trust the community and add a standard loophole I think the community can handle the add-a-builtin problem (I may be very wrong). I think that if someone adds a feature to their language that is clearly meant to only solve one particular challenge, the community will probably downvote that answe...

0

Welcome to the Winter Pools challenge! Game In this challenge, you have to write a Python script in which you compete with your opponent to drain pools. There are three pools- yours, your opponent, and a neutral one. You take it in turns with your opponent to drain water from one pool and put ...

@dzaima I tried searching for like 15 keywords and none of them are in the title D: thanks

5:51 PM
@AdmBorkBork I think previously a lot of the 'constant stream' used to be noise and as we cleaned up on that it's just that now we're seeing more signal over noise
quality over quantity kinda thing
@quartata looking at the code for spam detection (findspam.py) it seems to be pretty hardcoded for SE if I'm not mistaken?

@Downgoat blacklisted_websites.txt. It's a list of regexes.

@Downgoat That's a fair point, and likely a contributor as well. Thanks for bringing that up.

what should happen in case of spam? Should it just be rejected from being posted?
not sure how SE handles it

6:07 PM
I thought they just let it all get posted and then let charcoal take care of things

yeah, that's what charcoal does but not sure if for Axtell we should automate any part of it

7:02 PM
So both Charcoals are in one place now...

1

Inspired by this Stack Overflow question. The challenge Input An array of square matrices containing non-negative integers. Output A square matrix built from the input matrices as follows. Let \$N \times N\$ be the size of each input matrix, and \$P\$ the number of input matrices. For clar...

7:30 PM
How long is your MATL solution for this? — Giuseppe 5 mins ago
ah, when you start associating users with languages...

@AdmBorkBork Maybe. It's hard to tell.
I've done a couple of queries
Our monthly post count is going down
However, the average number of views those posts are getting is about the same

@NathanMerrill Oh, that's an interesting metric I hadn't considered.

@AdmBorkBork I was originally going for traffic count, but stackexchange only shows you the current numbers, not the history
This is a cheap substitute, as it doesn't include traffic on old (before the current month) questions, and doesn't include traffic not on questions
it also overestimates older questions, as they accumulate view count over time

8:00 PM
Quick question: Are "other" python libraries(such as numpy) allowed in codegolf as long as we import them, or no?

yep

8:22 PM
@Quintec yes, since you count the import, and they define a "Python + numpy" language, for example

Got it

One weird rule about libraries is that (at least so far right now) vim libraries plugins carry no byte penalty.

I mean, what if I created a new language named PyNumPy

I think so far with our rules, you totally could. But it would be really cheap and not very popular

8:26 PM
Interpreter: exec(“from numpy import *;” +input())

(^^ number of messages per week, thanks to tnbde)

@Quintec we encourage intra-language competition, that is, competition among answers in the same "language", as defined by PPCG's rules; "cheating" with an external (non-built-in) library isn't going to work there
(and, well, it isn't really that fun)
also, your "reference interpreter" won't really work :-D

from numpy import*\n then :P

8:46 PM
...almost
the thing is, you shouldn't be altering the file itself

Bah
I’m going way too far for a joke now
Nah too lazy to write out dir(numpy) etc
lol

0

Intro A friend posed this question today in a slightly different way - "Can a single [Python] command determine the largest of some integers AND that they aren't equal?". While we didn't find a way to do this within reasonable definitions of "a single command", I thought it might be a fun probl...

9:12 PM
@NewMainPosts 32 bytes lambda l:sorted(set(l))[1:][-1:] if IO was more lenient

yeah, outputting singletons is allowed by default...

Yeah but it breaks several rules of the challenge even though effectively doing the task

@DJMcMayhem Golfable in Py3

Ooooh duh {*l}?

Sure

9:17 PM
Or even [*{*l}][1:][-1:]

Yeah I was looking for the set[1:] thing but realizing it’s hard to type brackets and asterisks and whatnot on a phone. :P

Psssh, I write V and jelly from my phone all the time :P

Bah, I was going to write apl, then I realied I couldn’t
Need a AltGrrrrrrr key
@DJMcMayhem thanks

Don't you mean max(eval(x))`? :P

Grrr
I'm just deleting this mess

9:53 PM
@DJMcMayhem No. SpamRam blocks most of all the spam, actually.
just by simple IP blocking

10:14 PM
@quartata what is a SpamRam

Anonymous
10:50 PM
@Downgoat Like a goat but angrier

Anonymous
SpamRam is SE's first line of defense against spam. The exact details of how it blocks spam aren't public knowledge, but IP blocking is a factor. Just by blocking IPs that have posted spam that got red-flagged, a lot of spam never makes it onto SE.

format: plain


text:
# Remove formalin from food using chemical found in kitchen

In some parts of the world food is stored with formalin so it looks fresh forever! This is astonishing, but true (See refs here). As formalin is very bad for health and damages kidneys and liver very quickly, I am looking for a way to remove it.

When I buy fish, I know it has formalin in it. Every fruit I bought has formalin. I remember I bought 2 kilgrams of apples once. And it lasted for 1 month, looking fresh whole time. Then I threw it away.

My question is: how can you remove formalin from food? (Especially fish and fruit). It's best if we can use a chemical found in the kitchen. If not, I'd think one that is found at a chemical store.

• This is astonishing but true. Do you have a reference for that information? – jonsca Jul 14 '12 at 20:14
• Firstly, this formalin business sounds a lot like one of those hoax chain emails (though I can't find anything to support that). Secondly, are you sure that it is formalin? There are hundreds of other preservatives which can keep stuff fresh for a long time if added in sufficient quantity. Thirdly, I think that any chemical method of removing formalin will involve adding more harmful chemicals to the object, so that won't work either. :\ – ManishEarth Jul 15 '12 at 2:48
• @Manishearth - Consult this WP page and references therein. Outrageous, but then people put melamine in milk to fool protein tests. :( – Richard Terrett Jul 15 '12 at 9:08
• @richard Oh, there is a lot of this where I live (fortunately, it's avoidable). Thanks for the WP ref--note that this doesn't ensure that the observed preservative is indeed formalin. But that's irrelevant to the question – ManishEarth Jul 15 '12 at 12:25
• @shiplu Remember, Googling stuff may not give reputable sources. I've seen hoaxes that get backed up by a quick Google Search. In this case, though, the refs on the WO article are good enough. Note that it's not just Bangladesh--Indonesia, Vietnam, and probably some other countries as well. – ManishEarth Jul 15 '12 at 12:27

While the idea of filtering formaldehyde from food might sound naive, the motivation is understandable and the problem apparently real.

I've found at least one publication on the topic:

T Yeasmin, *M S Reza, M N A Khan, F H Shikha and M Kamal

PRESENT STATUS OF MARKETING OF FORMALIN TREATED FISHES IN DOMESTIC MARKETS AT MYMENSINGH DISTRICT IN BANGLADESH

Int. J. BioRes. 2010, 1, 21-24

From the abstract:

[...]Study showed that formalin was not detected in any fish produced locally, but was detected in the imported ones of catla and rohu ranging from 0.5% to 1% which was sold in different markets of Mymensingh with comparatively lower price than those produced locally. The shelf life of the locally produced fish was much longer than those of imported fish which may be related to the loss of shelf life during its transport from importing countries. [...]

Concerning the initial question: I'm afraid but i don't see any chance to remove formaldehyde from food without turning it to another toxic cocktail.

But since formaldehyde was mostly used to increase the shelf time of imported fish, buying from markets predominantly selling local products might be a way--if available and affordable.

• ""ranging from 0.5% to 1% which was sold"" did You ever handle/smell formaldehyde? .5 % would render a fish unsellable due to the pungent smell. – Georg Jul 16 '12 at 14:33
• I do prefer the smell of geranial too ;) Seriously, whenever possible, i rather used paraformaldehyde in synthesis, e.g. for m-meconine on the route to fluorescent phthalimides. Even then, the synthesis isn't particular nice and thus best left to undergraduates :D – Klaus-Dieter Warzecha Jul 16 '12 at 17:35
• Sorry, but formaline is often used to kill parasites in shellfishes and other farmed animals, so the whole conclusion "But since formaldehyde was mostly used to increase the shelf time of imported fish, buying from markets predominantly selling local products might be a way--if available and affordable." is pretty questionable. – Greg Jul 23 '14 at 0:13


text:
# Talk:Determinacy

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Field: Foundations, logic, and set theory

## Rationale for this page

I can easily imagine someone stumbling across this page and thinking it's an unnecessary duplication of Axiom of determinacy, an article of long standing, and ask why I don't simply try to improve that page.

Well, that was my thought originally, but I was running into all sorts of difficulties figuring out where things should go. Axiom of determinacy didn't have a good definition of "game", "strategy", or "winning strategy", and it wasn't clear where to put them. There's a winning strategy article, but it wants to be useful to game theorists as well, which was too much of a constraint.

Moreover, lots of times one wants to talk about determinacy but is not, in context, particularly interested in the axiom of determinacy. In particular, several pages had links that looked like [[Axiom of determinacy|determinacy]], when AD was perhaps not the main point of interest.

So it occurred to me that there should be a central article about determinacy in general. This is it, or rather the start of it. My vision is that this article will give the basic notions and say something about how they stand in relation to each other. Then there will be links out to more detailed articles on particular topics, such as axiom of determinacy, axiom of real determinacy, projective determinacy, long games, Blackwell games, axiom of quasideterminacy.

This article should be the central reference point for the new Category:Determinacy. If a major aspect of determinacy theory has been left out, then ideally in addition to writing an article on that particular topic, a new section or subsection should be added to this article, describing the topic briefly and saying how it relates to the other determinacy topics. --Trovatore 05:46, 2 September 2005 (UTC)

## Too technical

This page needs some help to make it more accessible. I have a semi-math background (CS + statistics) and I have no idea what is going on. This needs a bit of a gentler intro (like the one for NP vs. P article which is very good ) novacatz 13:17, 13 January 2006 (UTC)

Well, that's what I had in mind for the Determinacy#Basic notions section. That strikes me as being of roughly the same level of technicality as the lead section of Complexity classes P and NP. Would you look over the "Basic notions" section again and see if you agree, and if not, let me know where it is you get lost? (As for the rest of the article, I wouldn't really expect it to be accessible to anyone without a set theory background; it's an inherently technical subject.) Thanks, Trovatore 00:13, 14 January 2006 (UTC)
Currently, the basic notions section reads like a math textbook (cf. 'firstly we shall consider...' and 'More formally, ... , recall that the latter consists of...'). If you look at the gentle introduction of NP vs. P article intro, you will see they spend a lot of time explaining what is the problem using layman English (cf. the 'time space tradeoff' has an explanation what 'time' mean and what 'space' means. You can see that the page has a lot of somewhat loose descriptions that are useful on helping people grasp why the area is interesting (eg. 'NP Complete problems can be loosely described as...'). For determinacy - the intro is a bit weak on why the field is important (some examples might help) and starts getting into the results without explaning why they are significant (eg. determinacy from ZFC). Someone with some elementary set theory knowledge (me) can appeciate this result a lot more if some explaination is provided on interepetations of the result. novacatz 04:58, 14 January 2006 (UTC)

## Query

What does this phrase mean? (for example, if we say that Black wins draws at chess) Stephen B Streater 07:54, 1 April 2006 (UTC)

It means, if we modify the rules of chess, keeping everything the same except that if the play ends in a draw according to traditional chess, we'll say that Black has won. It hadn't occurred to me that this wasn't clear. Can you think of better, but still hopefully concise, language? --Trovatore 15:28, 1 April 2006 (UTC)
I misread "draws" as a verb like "wins". It makes sense as a noun. How about "wins all draws"? Stephen B Streater 16:37, 1 April 2006 (UTC)
Or "wins all drawn positions". Stephen B Streater 16:37, 1 April 2006 (UTC)
Go for it. You might also mention that Black should win if play continues forever (that's optional because it doesn't really matter; in any play that continues forever there are opportunities for Black to claim a draw, and therefore a win). --Trovatore 16:40, 1 April 2006 (UTC)
I've made the first change. Is your second point about play continuing for ever referring only to the modified chess (ie repeated positions leading to a draw)? Presumably there are games which can go on for ever without leading to a draw eg two sides take turns to write down numbers and the one with the biggest number written down wins. I'll have to think this game through to see if it counts as a game in this article, as the game may never finish but it never be obvious this is going to happen so never be a draw either. Stephen B Streater 18:37, 1 April 2006 (UTC)
Oh yes, that point was specific to chess. In most of the interesting cases studied, play can go on forever without any finite part of the play determining the winner. (However I don't really follow your "biggest number" example; why should the set of numbers written down have a greatest element?) --Trovatore 18:40, 1 April 2006 (UTC)
Thanks - I'll put something in, though the chess example is getting quite long, particularly as we can't necessarily assume that everyone understands the draw-by-repetition rule - I might put all the chess bits together and not in brackets. The game I described may not have a biggest element, but it may do. But if it did have a biggest element, I was thinking you wouldn't know in finite time, so couldn't end the game. But then perhaps you could find the maximum element in an infinite set. Stephen B Streater 19:20, 1 April 2006 (UTC)
An infinite set of naturals cannot have a maximal element. However, you could make rules like:
• If there is a greatest number played, then the player who played it, wins. If both players have played that number, then the first one to play it wins.
• If there is no greatest number played, then the second player wins.
This game is trivially a win for the second player, who can guarantee that no greatest number is played, just by playing ever-bigger numbers on subsequent plays. But it is an example of a game whose winning condition is not determined by any finite part of the play (after any finitely many moves, it is still possible for either player to win; while the second player can always force a win if he wants to, there's no guarantee that he will). --Trovatore 19:26, 1 April 2006 (UTC)

## chess example

So I agree that the wording is now clearer, but I see a couple of problems:

• You assert that "Black can eventually force a win", which assumes that unmodified chess is not an outright win for White. Surely this is still unknown?
• Yes - it is unknown whether white can force a win in chess. I assumed that if play continued long enough then repetition would have occurred, so Black could claim a draw/win. Stephen B Streater 21:47, 1 April 2006 (UTC)
I think your wording makes this clear. Stephen B Streater 21:49, 1 April 2006 (UTC)
• You've lost the point about the connection with clopen sets. --Trovatore 19:39, 1 April 2006 (UTC)
Fixed the first point. I await your input on the second (your help here could be very useful in making this section accessible). --Trovatore 21:33, 1 April 2006 (UTC)
I didn't change the mention of clopen sets - it is now in the first paragraph general description. Would you prefer it to be referred to again in the particular example of modified chess? Stephen B Streater 21:47, 1 April 2006 (UTC)
Sorry, you're right; I looked at the diff too fast. --Trovatore 23:03, 1 April 2006 (UTC)

## Discussion from the AC page

Aleph4 pointed out at Talk:Axiom of choice that determinacy for games on arbitary sets implies the axiom of choice, and also implies that a countable union of countable sets is countable. The second result can be modified to show in AD that a countable union of countable sets of reals is countable. These facts are very interesting to me and ought to appear here. Also, Martin's later paper on Borel Determinacy would be good to reference; it is much easier to read than his first one from the Annals. I will get to this sometime, so you can view this message as a reminder to myself as much as a prod to everyone else. CMummert 12:09, 6 October 2006 (UTC)

## Split out Gale-Stewart games?

I want to suggest making an article on Gale-Stewart games, which would be an expansion of the Games section here. Then this article could just have a summary of the topic with a link to the main article. The topics for the Gale-Stewart games article would be:

• The definition of a Gale-Stewart game on $X^\omega$ where X is any set (as in Martin's paper on Borel determinacy). The specific cases for Cantor and Baire space.
• The definition of a winning strategy.
• A statement of the theorem that closed games are determined.
• A link to Determinacy.

I am willing to do the writing; I want to see if there are objections before I do it. CMummert 17:37, 15 November 2006 (UTC)

Well, I guess my concern is, what exactly is a Gale–Stewart game? One with a clopen payoff set? Is this really standard terminology? Gale's and Stewart's result is key, of course, but I really don't recall coming across this nomenclature for the games. --Trovatore 19:48, 15 November 2006 (UTC)
A Gale-Stewart game is just a two-player game of perfect information of length ω. This is standard terminology in some parts of the world; a google search turned up quite a few papers such as [1] [2] that use the term without further citation. From JStor, I found that Jockusch uses the term (The Journal of Symbolic Logic Vol. 38, No. 2 (Jun., 1973), pp. 293-294) and so does Becker (The Journal of Symbolic Logic Vol. 50, No. 1 (Mar., 1985), pp. 110-122). So I think it is standard. CMummert 20:35, 15 November 2006 (UTC)
Hm, still not too excited about giving the concept a name I'd never really heard for it. This is the content I'd intended to treat in the "games played on trees" section of the article. --Trovatore 21:36, 15 November 2006 (UTC)
The idea I had in mind is to separate the material on games (which don't require strong axioms to define and are of interest in ZFC) from the material on determinacy beyond ZFC, which is more esoteric. Since Gale-Stewart game is a standard term describing these games, that was the title I suggested, but any other title is OK with me. The present article, if all the sections were filled in, would be quite long and intimidating. CMummert 22:02, 15 November 2006 (UTC)
The article might be a good idea. I think it would be unfortunate, though, if it presented ZFC as some sort of natural dividing line. I really don't think it is. --Trovatore 07:07, 9 December 2006 (UTC)

## Angle brackets

I think the angle brackets should be written as "\langle" and "\rangle" instead of "<" and ">". --Trigamma 18:15, 8 December 2006 (UTC)

I don't like \langle and \rangle; never have. They are too tall, and the angle is too obtuse. It would be nice to have something a little bit in between. --Trovatore 18:46, 8 December 2006 (UTC)
My problem is that < and > are typeset the wrong way: they are not treated as delimiters but as binary relations. You can see that in the first formula, where the closing > is next to the \in. But by the way: Why do you use angle brackets at all and not round parentheses? --Trigamma 19:54, 8 December 2006 (UTC)
Um. In my experience, angle brackets are just more usual, in set theory, as a way to indicate tuples, than are round brackets. I don't really know why this should be so. Maybe they have fewer other meanings (for example, (αβ) could be the pair <α,β> or the open interval from α to β). --Trovatore 21:09, 8 December 2006 (UTC)

## Determinacy from ZFC

Quote from the article:

"Martin's proof uses the powerset axiom in an essential way. There is a level-by-level result detailing what fragment of the powerset axiom is necessary to guarantee determinacy through what level of the Borel hierarchy."

I am curious about what "fragment of the powerset axiom" means more precisely. Does it mean that in this and that model, built not using the full power set operation but something that is possibly weaker (like when L is built compared to when V is built), then determinacy is guaranteed through a lower degree inte the model? YohanN7 (talk) 14:47, 14 September 2009 (UTC)

It means: how many iterations of the powerset axiom are required in order to guarantee the desired amount of determinacy. In other words, there is result giving the minimum necessary α for Vα to be a model of the desired amount of determinacy. Now the powerset axiom itself says nothing about iteration; it is really the axiom of replacement that is used to ensure that the ordinals in the model are long enough. — Carl (CBM · talk) 15:18, 14 September 2009 (UTC)
Ah, that explains it. Would you mind if I attempt a rewording of that passage in the article? YohanN7 (talk) 16:37, 14 September 2009 (UTC)
It appears to be done already. Things happen quickly here;) YohanN7 (talk) 16:49, 14 September 2009 (UTC)

## Blackwell Games

Didn't Donald Martin prove that determinacy for a set implies Blackwell determinacy for that set? I don't think that's mentioned on the page (and I don't have access to the paper).Chimpionspeak (talk) 17:33, 12 March 2011 (UTC)

I don't believe he ever proved that, no, though I wouldn't swear to it. I think that's still open. Generally what has been proved is consistent with that (e.g. I think that the large cardinals you need to prove Π11-determinacy are the same as you need to prove Π11-Blackwell determinacy) but as far as I know the proof has not been uniformized. I could be completely wrong though. Get in touch with Benedikt Löwe if you really want to know. --Trovatore (talk) 21:21, 12 March 2011 (UTC)
Hi, I checked this, and it is as I remembered. Have made the necessary changes. Chimpionspeak (talk) 16:30, 14 March 2011 (UTC)
I just took a ten-second look at the paper, and I don't actually see that result. Could you point me to it? What it says in the opening is that if all (length-ω on the naturals) perfect-information games are determined, then so are all Blackwell games, which is not the same thing as saying that if an individual game is determined then it's determined as a Blackwell game. --Trovatore (talk) 18:23, 14 March 2011 (UTC)
I found Martin's 1998 paper. What he says is
[W]e associate with each Blackwell game a family of perfect information games, and we show that the (mixed strategy) determinacy of the former follows from the (pure strategy) determinacy of the latter. The complexity of the payoff function for the Blackwell game is approximately the same as the complexity of the payoff sets for the perfect information games. In particular, this means that the determinacy of Blackwell games with Borel measurable payoff function follows from the known determinacy of perfect information games with Borel payoff sets.
So this is close to the idea you were trying to get across, but does not appear to justify the precise text you added. --Trovatore (talk) 19:00, 14 March 2011 (UTC)
I think I have the outline of a refutation of the game-by-game claim. First, consider the trivial "matching game": The players play zeroes and ones and, at the end, II wins if his every move exactly matches I's immediately previous move. Clearly II has a winning strategy for this game, as a perfect-information game. On the other hand, as a Blackwell game, I simply plays each value with probability 0.5, and then any strategy for II has value 0 for II.
That by itself doesn't refute the claim — the game is determined in both senses; it just has a different winner.
But now take some non-Blackwell-determined game G (with a 0-1 payoff function). Now I and II play the matching game on even pairs of moves, and G on odd pairs of moves. For I to win, he has to win both games.
As a perfect-information game, this is a win for II. He just plays his winning strategy on the even pairs of moves, and doesn't care what happens on the odd.
But as a Blackwell game, presumably I plays his winning strategy on the even pairs, and then the game (more or less) reduces to G on the odd pairs, which is not determined.
There's some work to be done in the "(more or less)" part. You have to make sure that the even moves don't in some tricky way help one of the players win on the odd moves. But I'm confident it can be done (might require a careful choice of G). --Trovatore (talk) 20:28, 14 March 2011 (UTC)
Right, there is some subtlety that I had missed out on, sorry. I searched a little more, and theorems 7 and 12 here say that for boldface pointclasses, determinacy for omega-games in the pointclass implies Blackwell-determinacy for the same pointclass. Have made the necessary changes. Chimpionspeak (talk) 20:37, 14 March 2011 (UTC)
We were editing at the same time. I think your argument should work (again, modulo the "more or less"). I am a little embarrassed to admit that I do not know much about Blackwell games! But your argument does make sense. Chimpionspeak (talk) 20:48, 14 March 2011 (UTC)

## Does an infinite game ever end?

Yes it does. At least in the sense that if both players actually have strategies as described in the article, then the recursion theorem guarantees that there is a sequence f:ω->ω whose values can be matched against the lookup table. This escaped me when I first read the article (quite some time ago). Perhaps the article could point out that (and why) the infinite games end? YohanN7 (talk) 19:57, 5 April 2011 (UTC)

## Payoff sets

Hi!

Q: Does the payoff set (A in the article) by definition include finite sequences too?

If not, the subsection "Winning Strategies" need to be clarified. I.e. there is a sequence in A beginning with the old moves plus our new one.

/Johan — Preceding unsigned comment added by 90.225.13.43 (talk) 09:52, 5 April 2012 (UTC)

I'm not entirely clear what you're saying here. The sequence
$\langle\sigma(\langle\rangle),a_1,\sigma(\langle\sigma(\langle\rangle),a_1\rangle),a_3,\ldots\rangle$
is infinite (that's what the dot dot dot means), so I don't see any issue raised by the fact that A consists of infinite sequences. Did you have some other piece of text in mind? --Trovatore (talk) 21:59, 5 April 2012 (UTC)


text:
The open source CFD toolbox
Go to the documentation of this file.
1/*---------------------------------------------------------------------------*\
2 ========= |
3 \\ / F ield | OpenFOAM: The Open Source CFD Toolbox
4 \\ / O peration |
5 \\ / A nd | www.openfoam.com
6 \\/ M anipulation |
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25 along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
26
27Class
29
30Description
31 Handles the specification for grading within a section of a block
32
33 The grading specification is handled is controlled by three parameters:
34
35 - blockFraction: the fraction of the block the section occupies
36
37 - nDivFraction: the fraction of the divisions of the block allocated to
38 the section
39
40 - expansionRatio:
41 the expansion ratio for the grading with the section of
42 block defined as the ratio of end-size / start-size for the section.
43 A negative value is trapped and treated as its inverse.
44
45SourceFiles
47
48\*---------------------------------------------------------------------------*/
49
52
53#include "scalar.H"
54
55// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
56
57namespace Foam
58{
59
60// Forward Declarations
61class Istream;
62class Ostream;
65
68
69/*---------------------------------------------------------------------------*\
71\*---------------------------------------------------------------------------*/
74{
75 // Private Data
76
77 scalar blockFraction_;
78 scalar nDivFraction_;
79 scalar expansionRatio_;
80
81
82public:
83
86
87
88 // Constructors
89
90 //- Default construct (1, 1, 1)
92
93 //- Construct from components
95 (
96 const scalar blockFraction,
97 const scalar nDivFraction,
98 const scalar expansionRatio
99 );
100
101 //- Construct from expansionRatio
103
104 //- Construct from Istream
106
107
108 //- Destructor
110
111
112 // Member Functions
114 scalar blockFraction() const
115 {
116 return blockFraction_;
117 }
119 scalar nDivFraction() const
120 {
121 return nDivFraction_;
122 }
124 scalar expansionRatio() const
125 {
126 return expansionRatio_;
127 }
128
130 // Trap negative value and treat as its inverse.
131 void correct();
132
133 //- Return the inverse gradingDescriptor with 1/expansionRatio
135
136
137 // Member Operators
138
141
142
143 // IOstream Operators
147};
148
149
150// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
151
152} // End namespace Foam
153
154// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
155
156#endif
157
158// ************************************************************************* //
An Istream is an abstract base class for all input systems (streams, files, token lists etc)....
Definition: Istream.H:64
An Ostream is an abstract base class for all output systems (streams, files, token lists,...
Definition: Ostream.H:62
Handles the specification for grading within a section of a block.
void correct()
Destructor.
friend Istream & operator>>(Istream &, gradingDescriptor &)