Pharmacokinetics of isavuconazonium sulfate and its active metabolite isavuconazole in healthy dogs

Invasive fungal infections (IFIs) are growing in importance in veterinary and human medicine. IFIs such as aspergillosis, blastomycosis, coccidioidomycosis and histoplasmosis remain challenging to treat in dogs. Isavuconazole is a novel antifungal medication that, when compared to currently used azoles, has an expanded spectrum of antifungal activity Rudramurthy (2011), Pfaller (2013), Spec (2018), has more predictable pharmacokinetics in humans Desai (2016), Cojutti (2021) and may cause fewer side effects such as liver and renal toxicity Maertens (2016), DiPippo (2018). The pharmacokinetic profile and safety of isavuconazole in dogs has not yet been characterized. The purpose of this study was to evaluate the pharmacokinetics of isavuconazole in healthy dogs that received a single dose of the prodrug isavuconazonium sulfate. Using full crossover design, six healthy beagle dogs received isavuconazonium sulfate at a mean (+/- SD) dose of 20.6 (+/- 2.8) mg/kg orally and 21.8 (+/- 4.2) mg/kg intravenously. Plasma was collected for batched pharmacokinetic analysis of prodrug and metabolite, isavuconazole, by ultra-high-pressure liquid chromatography tandem mass spectrometry (UHPLC-MS/MS). The median (Q1-Q3) maximum isavuconazole peak plasma concentration was estimated at 3,876.5 (2,811.0-4,800.0) ng/mL following oral administration, with a median (Q1-Q3) peak level at 1.3 (1.0-2.0) hours. Following intravenous administration, the median (Q1-Q3) isavuconazole peak plasma concentration was estimated at 3,221.5 (2,241.5-3,609.0) ng/mL, with a median (Q1-Q3) peak level at 0.4 (0.3-0.6) hours. The median (Q1-Q3) half-life of isavuconazole was 9.4 (7.0-12.2) hours and 14.0 (8.1-21.7) hours for oral and intravenous routes, respectively. One dog received inadvertent subcutaneous drug administration without any apparent adverse effects. Another dog experienced an anaphylactic reaction following accidental rapid drug infusion. No other drug-related adverse events were observed. At dosages used in this study, healthy dogs achieved isavuconazole plasma levels comparable to human therapeutic targets, and when properly administered the drug was well-tolerated.

Non-regulated LC-MS/MS bioanalysis in support of early drug development - a Novartis perspective

Scientifically qualified LC-MS/MS methods are essential for the determination of small molecule drug candidates and/or their metabolite(s) in support of various non-regulated safety assessment and in vivo absorption, distribution, metabolism and excretion studies in preclinical development. This article outlines an effective method development workflow to fit for this purpose. The workflow features a 'universal' protein precipitation solvent for efficient sample extraction, a mobile phase additive for managing chromatographic resolution and addressing carryover and an internal standard cocktail to select the best analogue internal standard to track the analyte of interest in LC-MS/MS. In addition, good practices are recommended to prevent bioanalytical pitfalls due to instability, non-specific binding and dosing vehicle-induced matrix effect. Proper handling of non-liquid matrix is also discussed.

Simultaneous determination of ZL-01, a novel nucleotide prodrug, and its metabolites in rat plasma by LC-MS/MS: Application to pharmacokinetic study

ZL-01 is a novel dual-prodrug which shows promise to be an antiviral candidate for hepatitis C virus. Here we have established a liquid chromatography tandem mass spectrometry (LC-MS/MS) method for simultaneous determination of ZL-01 and its four metabolites (M1, M7, M8, and M9) in rat plasma with special consideration of ex vivo ZL-01, M1, and M7 stability. Several factors affecting the stability were investigated. EDTA and citric acid solution (1 M) were added to plasma to maintain the stability of analytes. The protein-precipitation method was selected with acetonitrile containing sofosbuvir as internal standard (IS). Adequate separation of ZL-01 and its metabolites was achieved on XSelect HSS T3 (3.5 µm, 4.6 × 150 mm) column by a gradient-elution with a mobile phase consisting of 0.1% formic acid and acetonitrile at a flow rate of 0.5 mL/min. The detection was performed on a triple quadrupole tandem mass spectrometer by multiple reaction monitoring (MRM) mode to monitor the precursor-to-product ion transitions of m/z 599.2→418.5 for ZL-01, m/z 529.7→398.2 for M1, m/z 330.5→182.0 for M7, m/z 260.3→112.1 for M8, m/z 261.3→113.2 for M9 and m/z 530.4→243.4 for IS. The calibration curves exhibited good linearity (r＞0.997) for all components. The lower limit of quantitation (LLOQ) was in the range of 1-2 ng/mL. The intra-day and inter-day precisions (RSD) at three different levels were both less than 10.2% and the accuracies (RE) ranged from -3.7-7.6%. The matrix effect and extraction recovery of them ranged from 84% to 110.3% and 88.3-106.3%. This LC-MS/MS method for the simultaneous quantitation of ZL-01 and its metabolites was developed successfully and applied in the pharmacokinetic studies of these in rats. Pharmacokinetic results indicated ZL-01 would be metabolized rapidly and M8 might be the main metabolites after oral absorption.

Handling unstable analytes: literature review and expert panel survey by Japan Bioanalysis Forum Discussion Group

Analyzing unstable small molecule drugs and metabolites in blood continues to be challenging for bioanalysis. Although scientific countermeasures such as immediate cooling, immediate freezing, addition of enzyme inhibitors, pH adjustment, dried blood spot or derivatization have been developed, selecting the best practices has become an issue in the pharmaceutical industry as the number of drugs with such problems is increasing, even for generic drugs. In this study, we conducted a comprehensive literature review and a questionnaire survey to determine a suitable practice for evaluating instability and implementing countermeasures. Three areas of focus, matrix selection, effect of hemolysis and selection of esterase inhibitors, are discussed.

Biostability study, quantitation method and preliminary pharmacokinetics of a new antifilovirus agent based on borneol and 3-(piperidin-1-yl)propanoic acid

The stability of the new antifiloviral agent AS-358, which is a derivative of borneol and 3-(piperidin-1-yl)propanoic acid, was studied in the blood and blood plasma of rats in vitro. It was found that both in the blood and in the plasma stabilized by EDTA or heparin, the compound is rapidly hydrolyzed at the ester bond. When sodium fluoride was added to the whole blood, the decomposition of the compound was significantly slowed down, which made it possible to develop and validate a method for the quantitative determination of the agent in this matrix. The method was validated in terms of selectivity, calibration dependence, LLOQ, accuracy and precision, stability in an autosampler, recovery, and carry-over. A 8:2 v/v mixture of methanol containing 2-adamantylamine hydrochloride (internal standard, IS) with 0.2 M aqueous zinc sulfate was used for blood sample treatment and protein precipitation. Analysis was performed by HPLC-MS/MS using reversed phase chromatography. MS/MS detection was performed on a triple quadrupole mass spectrometer 6500 QTRAP (SCIEX) in multiple reaction monitoring (MRM) mode. The transitions 294.5→158.2/98.1 and 152.2→107.2/93.1 were monitored for AS-358 and the IS, respectively. The calibration curve was built in the concentration range of 1-500 ng/mL, the intra-day and inter-day accuracy and precision, carry-over and recovery were within the acceptable limits. The developed method was used for a preliminary study of the pharmacokinetics of the agent AS-358 after its oral administration to rats. It was shown that when the substance was administered at a dose of 200 mg/kg, its concentration in the blood of animals reached 550 ng/mL after 1 h, despite its instability in blood.

Consideration of the Unbound Drug Concentration in Enzyme Kinetics

The study of enzyme kinetics in drug metabolism involves assessment of rates of metabolism and inhibitory potencies over a suitable concentration range. In all but the very simplest in vitro system, these drug concentrations can be influenced by a variety of nonspecific binding reservoirs that can reduce the available concentration to the enzyme system(s) under investigation. As a consequence, the apparent kinetic parameters, such as K_m or K_i, that are derived can deviate from the true values. There are a number of sources of these nonspecific binding depots or barriers, including membrane permeation and partitioning, plasma or serum protein binding, and incubational binding. In the latter case, this includes binding to the assay apparatus as well as biological depots, depending on the characteristics of the in vitro matrix being used. Given the wide array of subcellular, cellular, and recombinant enzyme systems utilized in drug metabolism, each of these has different components which can influence the free drug concentration. The physicochemical properties of the test compound are also paramount in determining the influential factors in any deviation between true and apparent kinetic behavior. This chapter describes the underlying mechanisms determining the free drug concentration in vitro and how these factors can be accounted for in drug metabolism studies, illustrated with case studies from the literature.

Whole blood stability in quantitative bioanalysis

Establishing stability at all stages of a sample’s lifespan is a critical part of performing regulated bioanalysis. For plasma assays, this includes the duration between when blood is drawn and when that blood is centrifuged to produce plasma. Here, we provide a discussion of current regulatory expectations around whole blood stability testing for LC–MS plasma assays, as well as the two primary experimental approaches utilized to assess whole blood stability. Next, we interrogated a large dataset of validated methods (1076 methods, the vast majority of which were for measurement of small molecules) to assess the correlation between whole blood and plasma stability profiles, finding them to be highly correlated. Finally, we summarize unique case studies; we have encountered during WB stability testing which offer lessons that may be broadly applicable.

The Impact of Carboxylesterases in Drug Metabolism and Pharmacokinetics

BACKGROUND

Carboxylesterases (CES) play a critical role in catalyzing hydrolysis of esters, amides, carbamates and thioesters, as well as bioconverting prodrugs and soft drugs. The unique tissue distribution of CES enzymes provides great opportunities to design prodrugs or soft drugs for tissue targeting. Marked species differences in CES tissue distribution and catalytic activity are particularly challenging in human translation.

METHODS

Review and summarization of CES fundamentals and applications in drug discovery and development.

RESULTS

Human CES1 is one of the most highly expressed drug metabolizing enzymes in the liver, while human intestine only expresses CES2. CES enzymes have moderate to high inter-individual variability and exhibit low to no expression in the fetus, but increase substantially during the first few months of life. The CES genes are highly polymorphic and some CES genetic variants show significant influence on metabolism and clinical outcome of certain drugs. Monkeys appear to be more predictive of human pharmacokinetics for CES substrates than other species. Low risk of clinical drug-drug interaction is anticipated for CES, although they should not be overlooked, particularly interaction with alcohols. CES enzymes are moderately inducible through a number of transcription factors and can be repressed by inflammatory cytokines.

CONCLUSION

Although significant advances have been made in our understanding of CESs, in vitro - in vivo extrapolation of clearance is still in its infancy and further exploration is needed. In vitro and in vivo tools are continuously being developed to characterize CES substrates and inhibitors.

Oral Bioavailability of Kinsenoside in Beagle Dogs Measured by LC-MS/MS: Improvement of Ex Vivo Stability of a Lactone-Containing Compound

Kinsenoside (KD), an active compound isolated from Anoectochilus roxburghii, has demonstrated multiple pharmacological activities including hepatoprotection, antihyperliposis, antihyperglycemia, and antiosteoporosis. To the best of our knowledge, there are no available data concerning its preclinical pharmacokinetics and bioavailability in beagle dogs. To support preclinical pharmacokinetic and bioavailability study, a reliable LC-MS/MS method was developed for KD concentration measurements in beagle dog plasma. The chromatographic separation was achieved on a Waters Atlantis^® Hilic Silica column with an optimum mobile phase consisting of 5 mM ammonium acetate in water (pH 3.0 adjusted with acetic acid) and acetonitrile at a flow rate of 0.2 mL/min. Mass spectrometric analyses were carried out by monitoring multiple reaction monitoring transitions at m/z 265.2→102.9 for KD and m/z 174.0→128.0 for l-phenyl-d₅-alanine-2,3,3-d₃ (IS). The stability of KD in beagle dog whole blood and plasma was systematically evaluated. Lowering the temperature played a more critical role in stabilizing KD than decreasing the pH and adding esterase inhibitors, indicating that the major reason for instability of KD was probably due to chemical hydrolysis rather than esterase-mediated degradation. The currently developed method was validated and applied to a pharmacokinetic and bioavailability study of KD in beagle dogs following oral administration at a dose of 3 mg/kg. The absolute oral bioavailability for KD was determined to be 27.6%. Compared with typical glycosides, KD has a better bioavailability and is suitable for developing an oral dosage form.

Microdosing Cocktail Assay Development for Drug-Drug Interaction Studies

Methodology for analysis of a microdosing drug cocktail designed to evaluate the contribution of drug transporters and drug metabolizing enzymes to disposition was developed using liquid chromatography-mass spectrometry-based detection. Fast and sensitive methods were developed and qualified for the quantification of statins (pitavastatin, pitavastain lactone, rosuvastatin, atorvastatin, 2-hydroxy, and 4-hydroxy atorvastatin), midazolam, and dabigatran in human plasma. Chromatographic separation was accomplished using reversed-phase liquid chromatography or hydrophilic interaction liquid chromatography with gradient elution and detection by tandem mass spectrometry in the positive ionization mode using electrospray ionization. The lower limit of quantitation (LLOQ) for the statins assay was 1 pg/mL for the 6 analytes with a linear range from 1 to 1000 pg/mL processing 250 μL plasma sample. The midazolam assay LLOQ was 0.5 pg/mL with a linear range of 0.5 to 1000 pg/mL. For the dabigatran assay, the LLOQ was 10 pg/mL with a linear range of 10 to 5000 pg/mL processing 100 μL plasma sample. The intraday and interday precision and accuracy of the assays were within acceptable ranges, and the assays were successfully applied to support a study where a microdose cocktail was dosed to healthy human subjects for simultaneous assessment of clinical drug-drug interactions mediated by major drug transporters and CYP3A.

Enhancement of Curcumin Bioavailability Via the Prodrug Approach: Challenges and Prospects

Curcumin is a natural product with many interesting pharmacological properties. However, these are offset by the particularly poor biopharmaceutical properties. The oral bioavailability of curcumin in humans is very low, mainly due to low solubility, poor stability, and extensive metabolism. This has led to multiple approaches to improve bioavailability, including administration of curcumin with metabolism inhibitors, formulation into nanoparticles, modification of the curcumin structure, and development of curcumin prodrugs. In this paper, we focus on the pharmacokinetic outcomes of these approaches. Pharmacokinetic parameters of curcumin after release from prodrugs are dependent on the linker between curcumin and the promoiety, and the release itself may depend on the physiological and enzymatic environment at the site of cleavage. This is an area in which more data are required for rational design of improved linkers. Cytotoxicity of curcumin prodrugs seems to correlate well with cellular uptake in vitro, but the in vivo relevance is uncertain. We conclude that improved experimental and theoretical models of absorption of curcumin prodrugs, development of accurate analytical methods for simultaneous measurement of plasma levels of prodrug and released curcumin, and acquisition of more pharmacokinetic data in animal models for dose prediction in humans are required to facilitate movement of curcumin prodrugs into clinical trials.

Simultaneous determination of curcumin diethyl disuccinate and its active metabolite curcumin in rat plasma by LC-MS/MS: Application of esterase inhibitors in the stabilization of an ester-containing prodrug

Four esterase inhibitors, ethylenediamine tetraacetic acid disodium (Na2EDTA), sodium fluoride (NaF), bis(4-nitrophenyl) phosphate (BNPP) and phenylmethanesulfonyl fluoride (PMSF), were evaluated for their inhibitory effects on enzymatic hydrolysis of labile phenolate esters in curcumin diethyl disuccinate (CDD), a prodrug of curcumin (CUR), in rat plasma. BNPP and PMSF at 10mM exhibited stabilization by preventing degradation of CDD. BNPP at a final concentration of 10mM was subsequently selected to prevent ex vivo metabolism of CDD throughout LC-MS/MS analysis of CDD and CUR in rat plasma. A simple protein precipitation technique using acetonitrile as a precipitating agent was used to extract CDD, CUR and dimethylcurcumin (DMC), an internal standard, from rat plasma. Chromatographic separation was performed on a Halo C8 column (4.6×50mm, 2.7μm) using an isocratic mobile phase containing acetonitrile-0.2% formic acid in water (73:27v/v) with a flow rate of 0.4mLmin(-1). An AB SCIEX QTRAP(®) 6500 mass spectrometer was operated using a positive ion electrospray mode for ionization and detection of analytes and internal standard. Calibration curves for CDD and CUR were established using 50μL of rat plasma over the concentration range of 1-500ngmL(-1). The developed method was fully validated according to US Food and Drug Administration (FDA) guidelines for selectivity, sensitivity, linearity, accuracy, precision, dilution integrity, recovery, matrix effect, and stability. The validated method was applied to evaluate the pharmacokinetics of CDD and CUR in rats after a single intravenous dose of 40mgkg(-1). The method using BNPP as an esterase inhibitor was successful in determining the remaining CDD in rat plasma. The pharmacokinetic results indicate that CDD in rats is converted instantaneously to CUR after intravenous administration and a higher CUR plasma concentration at 5min is achieved in comparison with direct intravenous injection of CUR.

Discovery of 2-Pyridinone Aminals: A Prodrug Strategy to Advance a Second Generation of HIV-1 Integrase Strand Transfer Inhibitors

The search for new molecular constructs that resemble the critical two-metal binding pharmacophore required for HIV integrase strand transfer inhibition represents a vibrant area of research within drug discovery. Here we present the discovery of a new class of HIV integrase strand transfer inhibitors based on the 2-pyridinone core of MK-0536. These efforts led to the identification of two lead compounds with excellent antiviral activity and preclinical pharmacokinetic profiles to support a once-daily human dose prediction. Dose escalating PK studies in dog revealed significant issues with limited oral absorption and required an innovative prodrug strategy to enhance the high-dose plasma exposures of the parent molecules.

Screening of stabilizers for LC–MS/MS analysis of clevidipine and its primary metabolite in dog whole blood

Background: Clevidipine is an ester-containing antihypertensive agent that undergoes rapid hydrolysis in blood. A reliable stabilizer cocktail containing citric acid and ascorbic acid was established and the LC–MS/MS method was validated for simultaneous determination of clevidipine and its major metabolite in beagle dog whole blood. Results: The stabilizer could nearly completely inhibit the esterase activity. Both analytes were extracted from whole blood by toluene and detected by MS/MS in positive ESI mode. The linearity range was 0.1–100.0 ng/ml for clevidipine and 1.0–1000.0 ng/ml for the primary metabolite. Conclusion: The stabilizer cocktail was able to effectively suppress the activity of esterase in blood. The method was successfully applied to a PK study of clevidipine in beagle dogs.

Simultaneous determination of carboprost methylate and its active metabolite carboprost in dog plasma by liquid chromatography-tandem mass spectrometry with positive/negative ion-switching electrospray ionization and its application to a pharmacokinetic study

A liquid chromatography-tandem mass spectrometric (LC-MS/MS) method using positive/negative electrospray ionization (ESI) switching for the simultaneous quantitation of carboprost methylate and carboprost in dog plasma has been developed and validated. After screening, the esterase inhibitor, dichlorvos was added to the whole blood at a ratio of 1:99 (v/v) to stabilize carboprost methylate during blood collection, sample storage and LLE. Indomethacin was added to plasma to inhibit prostaglandins synthesis after sampling. After liquid-liquid extraction of 500μL plasma with ethyl ether-dichloromethane (75:25, v/v), analytes and internal standard (IS), alprostadil-d4, were chromatographed on a CAPCELL PAK Phenyl column (150×2.0mm, 5μm) using acetonitrile-5mM ammonium acetate as mobile phase. Carboprost methylate was detected by positive ion electrospray ionization followed by multiple reaction monitoring (MRM) of the transition at m/z 400.5→329.3; the carboprost and IS were detected by negative ion electrospray ionization followed by MRM of the transitions at m/z 367.2→323.2, and 357.1→321.2, respectively. The method was linear for both analytes in the concentration range 0.05-30ng/mL with intra- and inter-day precisions (as relative standard deviation) of ≤6.75% and accuracy (as relative error) of ≤7.21% and limit of detection (LOD) values were 10 and 20pg/mL, respectively. The method was successfully applied to a pharmacokinetic study of the analytes in beagle dogs after intravaginal administration of a suppository containing 0.5mg carboprost methylate.

Utilizing Internal Standard Responses to Assess Risk on Reporting Bioanalytical Results from Hemolyzed Samples

Bioanalytical analysis of toxicokinetic and pharmacokinetic samples is an integral part of small molecule drugs development and liquid chromatography-tandem mass spectrometry (LC-MS/MS) has been the technique of choice. One important consideration is the matrix effect, in which ionization of the analytes of interest is affected by the presence of co-eluting interfering components present in the sample matrix. Hemolysis, which results in additional endogenous components being released from the lysed red blood cells, may cause additional matrix interferences. The effects of the degree of hemolysis on the accuracy and precision of the method and the reported sample concentrations from hemolyzed study samples have drawn increasing attention in recent years, especially in cases where the sample concentrations are critical for pharmacokinetic calculation. Currently, there is no established procedure to objectively assess the risk of reporting potentially inaccurate bioanalytical results from hemolyzed study samples. In this work, we evaluated the effect of different degrees of hemolysis on the internal standard peak area, accuracy, and precision of the analyses of BMS-906024 and its metabolite, BMS-911557, in human plasma by LC-MS/MS. In addition, we proposed the strategy of using the peak area of the stable isotope-labeled internal standard (SIL-IS) from the LC-MS/MS measurement as the surrogate marker for risk assessment. Samples with peak areas outside of the pre-defined acceptance criteria, e.g., less than 50% or more than 150% of the average IS response in study samples, plasma standards, and QC samples when SIL-IS is used, are flagged out for further investigation.

Stabilization of clinical samples collected for quantitative bioanalysis – a reflection from the European Bioanalysis Forum

In bioanalysis of small molecules, the analyte concentration in the measured samples should reflect the concentration during sample collection. Precautions may be needed to prevent over- or under-estimation of the obtained result. This might require the addition of stabilizers to prevent degradation or nonspecific binding. For unstable drugs, it is essential to know how analytes can be stabilized before the start of the clinical study. Although the stabilization methods are well documented, the impact of the stabilization on the clinical workflow is not properly addressed. Already during method development, the clinical implications in terms of personnel safety, ease of use, training possibilities and staff capacity should be taken into account, and validation of the bioanalytical method should reflect collection procedures.

Current advances and strategies towards fully automated sample preparation for regulated LC–MS/MS bioanalysis

Robotic liquid handlers (RLHs) have been widely used in automated sample preparation for liquid chromatography–tandem mass spectrometry (LC–MS/MS) bioanalysis. Automated sample preparation for regulated bioanalysis offers significantly higher assay efficiency, better data quality and potential bioanalytical cost-savings. For RLHs that are used for regulated bioanalysis, there are additional requirements, including 21 CFR Part 11 compliance, software validation, system qualification, calibration verification and proper maintenance. This article reviews recent advances in automated sample preparation for regulated bioanalysis in the last 5 years. Specifically, it covers the following aspects: regulated bioanalysis requirements, recent advances in automation hardware and software development, sample extraction workflow simplification, strategies towards fully automated sample extraction, and best practices in automated sample preparation for regulated bioanalysis.

Consideration of the unbound drug concentration in enzyme kinetics

The study of enzyme kinetics in drug metabolism involves assessment of rates of metabolism and inhibitory potencies over a suitable concentration range. In all but the very simplest in vitro system, these drug concentrations can be influenced by a variety of nonspecific binding reservoirs that can reduce the available concentration to the enzyme system under investigation. As a consequence, the apparent kinetic parameters that are derived, such as K m or K i, can deviate from the true values. There are a number of sources of these nonspecific binding depots or barriers, including membrane permeation and partitioning, plasma or serum protein binding, and incubational binding. In the latter case, this includes binding to the assay apparatus, as well as biological depots, depending on the characteristics of the in vitro matrix being used. Given the wide array of subcellular, cellular, and recombinant enzyme systems utilized in drug metabolism, each of these has different components that can influence the free drug concentration. The physicochemical properties of the test compound are also paramount in determining the influential factors in any deviation between true and apparent kinetic behavior. This chapter describes the underlying mechanisms determining the free drug concentration in vitro and how these factors can be accounted for in drug metabolism studies, illustrated with case studies from the literature.

The bioanalytical challenge of determining unbound concentration and protein binding for drugs

Knowledge regarding unbound concentrations is of vital importance when exploring the PK and PD of a drug. The accurate and reproducible determination of plasma protein binding and unbound concentrations for a compound/drug is a serious challenge for the bioanalytical laboratory. When the drug is in equilibrium with the binding protein(s), this equilibrium will shift when physiological conditions are not met. Furthermore, the true unbound fraction/concentration is unknown, and there are numerous publications in the scientific literature reporting and discussing data that have been produced without sufficient control of the parameters influencing the equilibrium. In this Review, different parameters affecting the equilibrium and analysis are discussed, together with suggestions on how to control these parameters in order to produce as trustworthy results for unbound concentrations/fractions as possible.