Experimental Determination of Drug Diffusion Coefficients in Unstirred

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Experimental determination of drug diffusion coefficients in unstirred aqueous environments by temporally resolved concentration measurements Massimiliano Pio di Cagno, Fabrizio Clarelli, Jon Våbenø, Christina Lesley, Sokar Darsim Rahman, Jennifer Cauzzo, Erica Franceschinis, Nicola Realdon, and Paul C. Stein Mol. Pharmaceutics, Just Accepted Manuscript • DOI: 10.1021/acs.molpharmaceut.7b01053 • Publication Date (Web): 20 Feb 2018 Downloaded from http://pubs.acs.org on February 28, 2018

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Molecular Pharmaceutics

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Experimental determination of drug diffusion coefficients in unstirred aqueous

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environments by temporally resolved concentration measurements

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Massimiliano Pio di Cagnoa,*, Fabrizio Clarellib, Jon Våbenøc, Christina Lesleyd, Sokar

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Darsim Rahmand, Jennifer Cauzzoa,e, Erica Franceschinise, Nicola Realdone and Paul C.

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Steind

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a

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Arctic University of Norway, Tromsø, Norway

Drug Transport and Delivery Research Group, Department of Pharmacy, University of Tromsø, The

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b

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University of Norway, Tromsø, Norway

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c

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d

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Denmark

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e

Computational Pharmacology Group, Department of Pharmacy, University of Tromsø, The Arctic

Helgeland Hospital Trust, Sandnessjøen, Norway Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Odense,

Department of Pharmaceutical Sciences, University of Padova, Padova, Italy

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*Corresponding author: Massimiliano Pio di Cagno; Tel: +47 776 45301; e-mail:

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[email protected]

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1 ACS Paragon Plus Environment

Molecular Pharmaceutics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Table of contents graphics

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Abstract

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The diffusion coefficient (also known as diffusivity) of an active pharmaceutical ingredient

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(API) is a fundamental physicochemical parameter that affects passive diffusion through

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biological barriers and, as a consequence, bioavailability and biodistribution. However, this

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parameter is often neglected, and it is quite difficult to find diffusion coefficients of small

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molecules of pharmaceutical relevance in the literature. The available methods to measure

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diffusion coefficients of drugs all suffer from limitations that range from poor sensitivity to

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high selectivity of the measurements or the need for dedicated instrumentation. In this work, a

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simple but reliable method based on time resolved concentration measurements by UV-visible

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spectroscopy in an unstirred aqueous environment was developed. This method is based on

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spectroscopic measurement of the variation of the local concentration of a substance during

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spontaneous migration of molecules, followed by standard mathematical treatment of the data

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in order to solve Fick’s law of diffusion. This method is extremely sensitive and results in

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highly reproducible data. The technique was also employed to verify the influence of the

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environmental characteristics (i.e. ionic strength and presence of complexing agents) on the

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diffusivity. The method can be employed in any research laboratory equipped with a standard

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UV-visible spectrophotometer, and could become a useful and straightforward tool in order to

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characterize diffusion coefficients in physiological conditions and help to better understand

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the drug permeability process.

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Keywords: Diffusion coefficients, UV-visible spectroscopy, Fick’s laws of diffusion, data

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fitting, molecular modelling, ion strength

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1. Introduction

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Diffusion is the spontaneous migration of molecules of a substance from regions of higher

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chemical activity (high concentration) to regions of lower chemical activity (low

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concentration) through one or several isotropic environments. This process is of capital

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importance in pharmaceutics since passive transport of active pharmaceutical ingredients

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(APIs) remains a significant (and often primary) mechanism of biological membrane

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permeation (1) and therefore the diffusion process is crucial for reaching an appropriate

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bioavailability. According to Stokes-Einstein equation (Eq. 1), the diffusivity D (cm2/sec) is

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directly proportional to the absolute temperature T (K) and Boltzmann constant Kb

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(cm2*g/s2*K) but inversely proportional to the viscosity of the media η (g/cm*sec) and the

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hydrodynamic radius r (cm) of the molecules.

=

6

Equation 1

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The relation between diffusion and flux of a drug substance in aqueous environment can be

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described by Fick’s first law as:

= −

Equation 2

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Where j represents the net flux (mol/cm2*sec) of drug substance through the media, dc/dx

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represents the concentration gradient and D is the diffusion coefficient. D is an essential

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parameter to understand pharmaceutically relevant processes such as mass transport through

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barriers (i.e. absorption) and bioavailability of APIs. However, pharmaceutical research has

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for years overlooked the importance of this parameter in favor of the measurement of the

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apparent permeability coefficient (Papp, 2-4). Since water is the primary component of the

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human body, a proper quantification of D values for APIs should be of crucial importance for

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a proper evaluation of the permeability process. Reliable D values, together with a proper

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evaluation of partition coefficients (LogP), could help to elucidate the role of unstirred water 4 ACS Paragon Plus Environment

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layers (UWL) (5) and interface transitions in passive transport through barriers (6). The

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scientific literature is significantly lacking in diffusivity values for APIs in aqueous

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environments, and methods to measure them in a simple but reliable manner. Currently,

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several techniques for measuring diffusion coefficients are available, including holographic

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laser interferometry (HLI (7)), electron speckle pattern interferometry (ESPI (8)), mass

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transfer through barrier studies (9), Taylor dispersion analysis (TDA (10,11)), nuclear

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magnetic resonance (NMR (12)), dual-focus fluorescence correlation spectroscopy (FCA

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(13)) and fluorescence recovery after photobleaching (FRAP (14)) just to mention the most

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employed ones. Just a few of these techniques (TDA, NMR and mass transfer studies) have

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been applied to estimate diffusivity of APIs, the reason being that all the techniques listed

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above show limitations when facing pharmaceutically relevant problems such as poor

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sensitivity (e.g. NMR), high specificity (e.g. FRAP) and the need for dedicated

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instrumentation (e.g. HLI, ESPI, FCA, TDA and NMR which are not standard

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instrumentations in most pharmaceutical research laboratories).

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Another approach to estimate diffusivities of small molecules in aqueous environment is to

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predict them from molecular properties such as molecular volume, molar volume or by

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molecular simulation (15). However, all these in silico approaches are prone to uncertainty

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and do not provide a complete interpretation of diffusion in the case of environmental changes

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such as ion strength or presence of complexing agents. In this work, a simple, versatile and

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easily implemented spectroscopic method (16, 17) for diffusion coefficient measurement is

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introduced. This versatile method is based on the measurement of variation of local

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concentration of a compound in aqueous media and subsequent temporal resolution of

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diffusion equation by means of analytical as well as numerical mathematical methods. By

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comparing different approaches to the solution of Fick’s diffusion equation we show that

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simple non-linear least-squares fitting is sufficient to extract the diffusion coefficient. The



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experiments are performed employing a regular quartz cuvette and a standard UV-visible

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spectrometer. This method is simple, reliable, reproducible and extremely sensitive.

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Moreover, it has the significant advantage that it could be employed in any research

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laboratory equipped with a standard UV-visible spectrophotometer and very small changes

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related to environmental alterations can be measured.

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2. Experimental section

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2.1 Materials

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Sodium-di-hydrogen-phosphate monohydrate (NaH2PO4·H2O), di-sodium hydrogen-

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phosphate dodeca-hydrate (Na2HPO4·12H2O), sodium chloride (NaCl), sodium hydroxide

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(NaOH), hydrochloric acid (HCl, ≥ 37%), caffeine, calcein, chloramphenicol, ketoprofen,

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nitrofurantoin, tetracycline hydrochloride, trimethoprim, vancomycin, and β-cyclodextrin

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(βCD) were all purchased from Sigma Aldrich Chemie GmbH (Steinheim, Germany).

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Paracetamol was purchased from Norsk Medisinaldepot AS (Oslo, Norway). Penicillin G

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employed was USP Reference Standard (Timbrook, USA). All chemicals were of analytical

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grade.

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2.2. UV–visible localized spectroscopy

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2.2.1 Preparation of the solutions

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Phosphate buffer saline (PBS) 73 mM was prepared mixing a solution of NaH2PO4·H2O

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(2.2% W/V) with a solution of Na2HPO4·12H2O (1.8 % W/V) in a ratio 1 to 5. The pH of the

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PBS was adjusted to 7.3-7.4 (pH meter Lab 744, Metrohm AG, Herisau, Switzerland) by the

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addition of NaOH solid pellets. Tonicity of the PBS solution was adjusted to 280-290 mOsm

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(Semi-Micro Osmometer K-7400, Knauer, Berlin, Germany) by the addition of NaCl. Each of

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the compounds was than adequately weighted and dissolved in the PBS in order to achieve a

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concentration of approximately 0.5-1.5 mM. The molecular weights of the compounds and the

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characteristics of the donor solutions (compound concentrations, buffer concentrations,


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solution densities, wavelengths of maximal absorption (λMAX) and specific absorptivities (ε))

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are reported in Table 1.

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Table 1. General characteristics and composition of the aqueous solutions used as donor

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environments. The diffusional medium was composed of plain distilled water (DW, density of

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1.0015 g/mL). Each of the compounds was detected at its maximum wavelength of absorption

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(λMAX) and the local concentration was calculated using its specific absorptivity (ε). Nominal conc. (mM)

Buffer conc. (mM)

Density*

λMAX

ε

name

Molecular Weight (g/mol)

(g/mL)

(nm)

(cm2/µmol)

DW

Caffeine

194.2

1.23

72.8

1.0086

269

11.3

DW

Calcein

622.6

1.23

72.8

1.0083

294

11.3

DW

Chloramphenicol

323.2

1.20

72.8

1.0095

277

10.0

DW

Ketoprofen

254.3

1.17

72.8

1.0064

257

18.4

DW

Nitrofurantoin

238.2

0.77

72.8

1.0113

274

13.7

DW

Paracetamol

151.2

1.42

72.8

1.0079

236

13.2

DW

Penicillin G

334.4

0.60

72.8

1.0071

207

19.9

DW

Tetracycline

444.4

0.83

72.8

1.0197

361

14.8

DW

Trimethoprim

290.3

1.19

72.8

1.0085

278

5.6

DW Vancomycin 1449.3 1.20 72.8 *Data are reported as mean of three measurements. SD below 0.5%

1.0011

280

6.7

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Solutions of βCD (used in the diffusion experiments to investigate complexation effects) were

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prepared by adding solid powder of the dextrin derivative (3.4-4 mg) directly into 2 mL of

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ketoprofen neutral and acidic solution (pH 1.0, obtained by mixing 1.9 mL of neutral

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ketoprofen solution plus 0.1 mL of HCl) in order to achieve a molar ratio drug:βCD of

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approximately 1:1.

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2.2.2 Experimental procedure

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For the spectrophotometric measurements, a double array VWR (VWR International, Radnor,

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USA) UV-visible spectrophotometer (model UV-6300 PC) equipped with a Hellma®

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Suprasil® (Sigma-Aldrich) quartz absorption cuvettes (chamber volume of 700 µL and path

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length of 10 mm) was employed. The experimental setup is schematized in Fig. 1.

Diffusional medium

Compound



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Figure 1. Schematic representation of localized UV-visible spectroscopy experimental setup.

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Both reference and sample cuvette were filled with 675 µl of distilled water and placed in the

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respective compartment of the spectrophotometer. At time (t) = 0 sec (starting of the

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experiment), 25 µL of drug solution was gently injected in the bottom of the sample cuvette

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by a needle syringe. The reference and sample cuvette were both sealed with parafilm in order

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to avoid evaporation of the solvent. Absorbance readings were recorded at fixed wavelength

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(Table 1) at regular time intervals (120 sec) for 24 hours at room temperature (23-24°C).

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Absorbance was recorded at a specific position (x1) corresponding to 0.51 cm from the bottom

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of the cuvette (Figure 2). This was obtained by keeping the sample cuvette lifted 0.60 cm

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(Hard Head calliper, Jula Norge AS, Lørenskog, Norway) from the bottom of the cuvette

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holder.


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Figure 2. Adaptation of the mono-dimensional diffusional model used to the cuvette

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geometry and related relevant spatial points (initial point x0, measurement points x1 and x2

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and total length of the diffusion chamber L).

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For each of the API studied, two independent experiments were conducted (n=2) and the final

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diffusional profile (employed for the mathematical data treatment and diffusivity calculations)

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was obtained by averaging the respective absorbances at each time point. The average

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variance (in percentage, %) between the absorbance registered at each time point between the

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two parallel experiments was used to estimate the experimental error (≤ 5 %).

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2.2.3 Mathematical model and UV-visible spectroscopy data interpretation

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The mathematical approach used in this work to fit the experimental data obtained by UV-

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visible spectroscopy to calculate the diffusion coefficients was based on the standard diffusion

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equation (Eq. 3) and well-known classical physical models (9, 18). Due to the geometry of the

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experimental setup (Figure 2), the diffusion process was approximated with a one-

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dimensional model. The diffusion equation (Eq. 3) describes the concentration of a solute

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over time and space in a homogenous medium (assuming constant diffusivity) as:



, , =

Page 10 of 25

Equation 3

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Where c represents the concentration of the substance, t the time, x the position and D the

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diffusivity. In theory, any x between 0.51 cm and 1.11 cm can be selected (Fig. 2) by lifting

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the cuvette from its standard recording position. In this work, the recording point was

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primarily set to 0.51 cm (see experimental procedure section).

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The first mathematical approach used to find numerical solution of D was analytical. This

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approach is based on the assumption that for times t, t

Experimental Determination of Drug Diffusion Coefficients in Unstirred

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