How Difficult Azide ion / Hydrazoic Acid Passes Biological Membranes: Experimental and Computational Study

doi:10.21203/rs.3.rs-2620851/v1

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How Difficult Azide ion / Hydrazoic Acid Passes Biological Membranes: Experimental and Computational Study

https://doi.org/10.21203/rs.3.rs-2620851/v1

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published 08 Jun, 2023

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Hydrazoic acid (HN₃) and its deprotonated form azide ion (N₃^ˉ) (AHA) are toxic since they inhibit cytochrome c oxidase complex IV (CoX IV) embedded in the inner mitochondrial membrane as part of the enzyme complexes of the respiratory chain. Especially critical for its toxicology is inhibition of CoX IV in the central nervous system and cardiovascular system. Hydrazoic acid is an ionizable species and its affinity toward membranes and therewith associated permeabilities depend on the pH values of aqueous media on both sides of the membranes. In article, we addressed permeability of AHA through the biological membrane. In order to understand affinity of the membrane for neutral and ionized form of azide we measured octanol-water partition coefficients at pH values of 2.0 and 8.0, which are 2.01 and 0.00034, respectively. By using Parallel Artificial Membrane Permeability Assay (PAMPA) experiment, we measured effective permeability through the membrane, which is logP_e -4.97 and -5.26 for pH values of 7.4 and pH 8.0, respectively. Experimental permeability was used to validate theoretical permeability, which was estimated by numerically solving a diffusion equation for AHA diffusion through the membrane. We demonstrated that the rate of permeation through the cell membrane of 8.46 ·10⁴s^-1 is much higher than the rate of chemical step of CoX IV inhibition by azide of 200 s^-1. The results of this study show that transport through the membranes does not represent the rate-limiting step and therefore does not control the rate of CoX IV inhibition in the mitochondria. Observed dynamics of azide poisoning is however controlled by circulation transport that takes place on a minute time scale.

azide ion

hydrazoic acid

octanol-water partition coefficient

effective permeability

PAMPA

diffusion

inhibition

cytochrome c oxidase complex IV

Sodium azide (NaN₃) is a white to colourless, crystalline solid that is highly water-soluble, odourless and tasteless [1]. It has a variety of uses; in agriculture, for production of pesticides, herbicides and for pest control, in biomedicine as chemical preservative in aqueous diagnostic reagents, in hospitals and laboratories as chemical preservative in biological fluids. Moreover, it is used for military purposes for production of detonators and other explosives [2, 3]. The most common use of sodium azide is as a propellant in air bags in vehicles. In this capacity, sodium azide is thermally unstable and it rapidly decomposes to nitrogen gas when it reaches a temperature of 300°C, causing rapid expansion of the air bag [4]. In pharmacy, NaN₃ is used as precursor in the synthesis of numerous compounds such as antiviral drugs, antibiotics [5] and a wide range of tetrazole derivatives, such as sartans. Sartan medicines (azilsartan medoxomil, azilsartan, candesartan cilexetil, candesartan, eprosartan, irbesartan, losartan, EXP3174, olmesartan medoxomil, olmesartan, telmisartan, valsartan [6]) are used as a long-term treatment for patients with arterial hypertension and those with certain heart or kidney diseases. Their use is well documented in a recent review concerning pharmacological treatment of arterial hypertension [7]. To smaller extent, sartans are used for the treatment of diabetes, anticoagulant therapy and cholesterol therapy [4]. Sartan medicines are known as antagonists of angiotensin II receptors and consequently, they block the action of angiotensin II, a hormone that constricts blood vessels and causes blood pressure to rise [8]. Active pharmaceutical ingredients of sartans and sartan medicines, contain residues of sodium azide in ppm levels as the result of synthetic processes.

Although genotoxic properties of sodium azide have been extensively studied, its in vivo genotoxic and mutagenic spectrum in mammalian cells is still controversial. European Chemical Agency (ECHA) reports sodium azide as non-carcinogenic and non-mutagen molecule [9] in mammalian cells due to 2-year rat study, conducted in 1991. OSHA has placed sodium azide in a group TLV-A4 as human non-carcinogen [10]. However, there are some studies reporting positive results to genotoxicity or mutagenicity of sodium azide in mammalian cells. Study on Drosophila melanogaster larvae conducted in 1996 reports induction of mitotic recombination in wing somatic cells of Drosophila melanogaster larvae after chronic exposure [11]. Raicu and Mixich reported in 1992 that sodium azide encapsulated in liposomes produced chromosomal aberrations when introduced into human heteroploid HFp-2 cells [12]. Jones et al. examining azide mutagenicity towards several rodent cell lines concluded that sodium azide is a mutagen for rodent cells [13]. Anyway, regulatory European Medicines Agency states a Threshold of Toxicological Concern (TTC) value of 1.5 µg day^-1 intake of a genotoxic or mutagenic impurity per person and is considered to be associated with an acceptable risk (excess cancer risk of < 1 in 100 000 over a lifetime of exposure) for most pharmaceuticals [14]. The United States Pharmacopoeia (USP) states the concentration NMT (not more than) of 10 ppm of azide in sartans [15].

Chang et al. [16] pointed out the hypotension as the most common symptom of poisoning with sodium azide. Acute poisonings can occur with ingestion of sodium azide or with inhalation of vapours of hydrazoic acid (HN₃) that is formed when sodium azide is dissolved in an acidic aqueous solution. At lower heart rate, the tissues are less well supplied with oxygen. Tissues that consume the largest amount of oxygen are muscles (20%), liver (20%), brain (20%), heart (10–12%) and kidney (7.2%) [17]. Particularly critical are neurons since in contrast to the most other cell types they do not easily regenerate and are not simply replaced after damage.

Sodium azide is primarily a mitochondrial toxin, which binds the electron transport chain (ETC), inhibiting oxidative phosphorylation [18]. Azide anion (N₃^ˉ) has greater affinity to hem complex than O₂ [19]. Instead of O₂, it covalently binds to fully reduced form of iron (Fe³⁺) in a binuclear complex of hem a₃${(\text{F}\text{e}}_{\text{h}\text{e}\text{m}\text{e} \text{a}3}^{3+}-{\text{C}\text{u}}_{\text{B}}^{2+})$ in cytochrome c oxidase complex IV (CoX IV), bound in the inner mitochondrial membrane [20]. In CoX IV, azide anion and trivalent iron form bridging structure of ${\text{F}\text{e}}_{\text{h}\text{e}\text{m}\text{e} \text{a}3}^{3+}-\text{N}=\text{N}=\text{N}-{\text{C}\text{u}}_{\text{B}}^{2+}$ [21]. The resulting reduction in adenosine triphosphate (ATP) production, even in the presence of oxygen, results in metabolic failure (See Fig. S1, Fig. S2 and Fig. S3 in Supplementary materials for schematic presentation of usual process of ETC in Complex IV and presentation of azide anion binding to complex CoX IV in ETC [22, 23] )

When sodium azide dissolves in water or in acidic medium it dissociates to sodium and azide ion. In acidic solution, azide ion takes over the proton and forms neutral, non-ionizable and volatile hydrazoic acid (HN₃). Chemical reaction takes place according to the following mechanism:

$$Na{N}_{3}+{H}_{2}O\to {Na}^{+}+{N}_{3}^{-}+{H}^{+}+{OH}^{-}$$

$${N}_{3}^{-}+{H}^{+}\to H{N}_{3}$$

HN₃ is a weak acid with pK_a value of 4.65 [18]. In acidic solution, neutral HN₃ distributes preferentially to the octanol phase rather than to water. In basic solution azide forms deprotonated form of azide anion, N₃^ˉ, that is distributed mainly in the aqueous phase when its octanol / water equilibrium is established.

In this study, we addressed permeability of AHA through the biological membrane. In order to understand affinity of the membrane for neutral and ionized form of azide we measured octanol-water partition coefficients at pH values of 2.0 and 8.0, respectively. By using PAMPA experiment, we measured effective permeability through the membrane. By numerically solving the diffusion equation, we demonstrated that the measured permeability is at least to some extent dependent on the diffusion through the unstirred water layer on each side of the membrane. Based on these experiments, we tried to clarify whether diffusion through the membrane is the limiting step in the inhibition of the complex.

2.1 Determination of octanol-water partition coefficients (K _ow ) of azide ion / hydrazoic acid for different pH values using a reversed-phase liquid chromatography and UV detection.

In our study we considered experimental n-octanol water partition coefficients for azidic acid and azide ion, respectively. In principle one can apply one of the developed constant pH simulation algorithms [24, 25], but it is worth to stress that HN₃ pK_a value at the interface is highly dependent on the coordinate and is computationally as demanding as pK_a values in protein interior [26, 27] and in contrast to proteins inaccessible to experiment [28].

Since hydrazoic acid is an ionizable species its octanol-water partition coefficient (K_ow) depends on pH. We have decided to measure K_ow for two pH values and apply extrapolation approach for all the pH values [29]. Determination of 1-octanol-water (octanol-water) partition coefficients (K_ow) of AHA was carried out using two different pH values of azide solutions (pH 2.0 and 8.0) and a reversed-phase liquid chromatography with UV detection. pH-dependent partition coefficients K_ow(pH) were calculated from the experimental data using equation:

$$\begin{array}{c}{K}_{ow}\left(pH\right)=\frac{{\left[A\right]}_{oct}}{{\left[A\right]}_{aq}}\#\left(1\right)\end{array}$$

where [A]_oct represents total azide concentration (sum of neutral HN₃ and deprotonated N₃⁻ species) in organic phase of 1-octanol and [A]_aq represents total azide concentration in aqueous phase.

Since HPLC method does not distinguish between neutral and ionizable species of hydrazoic acid and azide anion, partition coefficient K_ow(pH) below can be expressed as distribution coefficient Q(pH). Azide exists in its neutral or protonated form both in aqueous solution and in 1-octanol. The ratio of concentrations of azide in 1-octanol (organic phase) and in water regardless of its protonation state at a certain pH value of the environment is described by distribution coefficient Q. Q(pH) is an equilibrium constant and a measure of free energy. We define Q(pH) as:

$$\begin{array}{c}Q\left(pH\right)=\frac{{\left[{A}^{0}\right]}_{org} + {\left[{A}^{-}\right]}_{org} }{{\left[{A}^{0}\right]}_{aq}+ {\left[{A}^{-}\right]}_{aq}}\#\left(2\right)\end{array}$$

where [A⁰]_org stands for concentration of neutral form of azide (HN₃, hydrazoic acid) in the organic phase (1-octanol), [A⁰]_aq for the concentration in the aqueous solution, [A^¯]_org for concentration of deprotonated form of azide (N₃^¯) in the organic phase and [A^¯]_aq for the concentration of azide in the aqueous solution.

By expanding the numerator and denominator of the right-hand side of the Eq. (2) by factor 1/[A⁻]_aq one obtains

$$\begin{array}{c}Q=\frac{{\left[{A}^{0}\right]}_{org}/{\left[{A}^{-}\right]}_{aq}+ {\left[{A}^{-}\right]}_{org}/{\left[{A}^{-}\right]}_{aq} }{{\left[{A}^{0}\right]}_{aq}/{\left[{A}^{-}\right]}_{aq} + 1}\#\left(3\right)\end{array}$$

If a new variable P⁰ is introduced as the partition coefficient of neutral species; P⁰ = [A⁰]_org/[A⁰]_aq, and P^¯ as the partition coefficient of deprotonated species P^¯ = [A^¯]_org/[A^¯]_aq, equation simplifies to a more compact form:

$$\begin{array}{c}Q=\frac{{P}^{0}{\left[{A}^{0}\right]}_{aq}/{\left[{A}^{-}\right]}_{aq} + {P}^{-} }{ {\left[{A}^{0}\right]}_{aq}/{\left[{A}^{-}\right]}_{aq}+ 1}\#\left(4\right)\end{array}$$

[A⁰]_aq/[A⁻]_aq is the equilibrium constant of neutral and deprotonated species in organic and in aqueous solution that depends both on pK_a value of azide and the aqueous phase pH value.

Free energy for azide deprotonation (ΔG) with a certain value of pK_a in the solution with certain pH value reads:

$$\begin{array}{c}\varDelta G={ln}10\bullet {k}_{b}T\bullet \left(pH-{pK}_{a}\right)\#\left(5\right)\end{array}$$

where k_B is Boltzmann's constant and equals 1.987 kcal (mol K)⁻¹ and T is the absolute temperature in Kelvins (310 K at physiological conditions). Eq. 5 implies that ionizable group with a certain pK_a value is in contact and equilibrium with the aqueous solution with a certain pH value. There is one to one correspondence between the equilibrium constant and free energy [30] and is expressed as

$$\begin{array}{c}\varDelta G=-{k}_{b}T\bullet {ln}\left(\frac{{\left[{A}^{0}\right]}_{aq}}{{\left[{A}^{-}\right]}_{aq}}\right)\#\left(6\right)\end{array}$$

By combining Equations 5 and 6 and by considering the identity $\text{ln}x=\text{ln}10\bullet \text{log}x$, and introducing the relation $\text{log}\beta =pH-{pK}_{a}$ or $\beta ={10}^{{\text{p}\text{K}}_{\text{a}}-\text{p}\text{H}}$, it is possible to write an equation for azide distribution coefficient as a function of pH and pK_a.

$$\begin{array}{c}Q=\frac{{P}^{0} + \beta {P}^{-} }{1+ \beta }=\frac{{P}^{0}{10}^{{pK}_{a}-pH} + {P}^{-} }{1+ {10}^{{pK}_{a}-pH}}\#\left(7\right)\end{array}$$

Distribution coefficient Q is the equilibrium constant for azide distribution between the organic phase and the aqueous phase regardless of the azide protonation state. The corresponding free energy ΔG, associated with azide transfer from aqueous solution with certain pH value to the membrane is:

$$\begin{array}{c}\varDelta G=-{k}_{b}T\bullet {ln}Q=-{k}_{b}T\bullet {ln}\frac{{P}^{0} + \beta {P}^{-} }{1+ \beta }=-{k}_{b}T\bullet {ln}\left(\frac{{P}^{0} {10}^{{pK}_{a}-pH}+ {P}^{-} }{1+ {10}^{{pK}_{a}-pH}}\right)\#\left(8\right)\end{array}$$

Since extracellular fluid (ECF) and cytoplasm (CYT) have different pH values of 7.4 and 7.2, free energy for transfer of AHA is not zero. AHA tends to concentrate in the compartment with more favourable solvation free energy. To calculate relative population of AHA in the cell membrane, the appropriate Q for given pH value is used:

$$\begin{array}{c}{\left[A\right]}_{ memb\left({pH}_{1}\right)}={Q}_{\left({pH}_{1}\right)}\bullet {\left[A\right]}_{ ECF\left({pH}_{1}\right)}={Q}_{\left({pH}_{1}\right)}\#\left(9\right)\end{array}$$

The same relation can be used for equilibrium between the cytoplasm and the membrane. By combining these two relative populations of AHA in the cytoplasm and ECF can be found.

$$\begin{array}{c}{\left[A\right]}_{ CYT\left({pH}_{2}\right)}=\frac{1}{{Q}_{\left({pH}_{2}\right)}}\bullet {\left[A\right]}_{ memb\left({pH}_{1}\right)}=\frac{{Q}_{\left({pH}_{1}\right)}}{{Q}_{\left({pH}_{2}\right)}}\#\left(10\right)\end{array}$$

The relative AHA population in cytoplasm is therefore simply the ration of both Q.

By inserting Eq. 7, we can derive a simplified formula:

$$\begin{array}{c}{\left[A\right]}_{ CYT\left({pH}_{2}\right)}=\frac{{Q}_{\left({pH}_{1}\right)}}{{Q}_{\left({pH}_{2}\right)} }=\frac{{10}^{{pH}_{1}-{pK}_{a}} }{{10}^{{pH}_{2}-{pK}_{a}}}={10}^{{pH}_{1}-{pH}_{2}}\#\left(11\right)\end{array}$$

As seen in Eq. 11, the overall AHA concentration in the cytoplasm is pK_a independent and depends only on the pH value difference of the cytoplasm and ECF.

2.2. Determination of effective permeability, P_e (pH) using the method PAMPA

Simulation of azide partition between extracellular fluid and biological membrane was performed using the method PAMPA (Parallel Artificial Membrane Permeability Assay), the schematics of which is seen in Fig. 1. PAMPA is an in vitro tool for high-throughput prediction of in vivo drug permeability and is also useful for the assessment of passive transport mechanisms [31]. Our experiments were performed using Corning BioCoat Pre-Coated PAMPA Plate System with 96-well insert system with 0.45 µm PVDF (polyvinyliden fluoride) filter plate which has been pre-coated with structured layers of phospholipids and a matched receiver microplate. The thickness d of phospholipid membrane was 125 µm = 1 250 000 Å.

PAMPA experimental conditions are described in Table S3 in Supplementary materials. Prior to use, the pre-coated PAMPA plate system was warmed to room temperature for 60 minutes. The compound solutions of NaN₃ with concentrations of 0.241 and 0.120 mg mL^− 1 were prepared by dilution of stock solutions (1.2 mg mL^− 1) into a PBS buffer adjusted to two pH values of 7.4 and 8.0 with 1M NaOH. 300 µL of solvent per well was pipetted into acceptor plate and 200 µL of sample per well was pipetted into upper donor plate. Upper donor plate with sample was sealed with the Sealing Tape for 96-Well Plates to prevent hydrazoic acid to evaporate and contaminate other wells. We placed the filter plate on the receiver plate and incubated the assembly at room temperature for 5 hours, without stirring. After that we separated plates and determined the compound concentrations in both plates using HPLC with UV detection; chromatographic conditions are listed in Table S4 in Supplementary materials.

Determination of effective permeability, P_e(pH) for azide (cm s^− 1) at pH values of 7.4 and 8.0 was calculated using as follows:

$$\begin{array}{c}{P}_{e}=\frac{-ln\left[1-{C}_{A}\left(t\right)/{C}_{equilibrium}\right]}{S*\left(\frac{1}{{V}_{D}}+\frac{1}{{V}_{A}}\right)*t}\#\left(12\right)\end{array}$$

We calculated Mass Retention (%) using Eq. 13:

$$\begin{array}{c}1-\frac{\left[{C}_{D}\left(t\right)\bullet {V}_{D}+{C}_{A}\left(t\right)\bullet {V}_{A}\right]}{{C}_{0}\bullet {V}_{0}}\#\left(13\right)\end{array}$$

where C₀ is initial azide concentration in donor well (mM), C_D(t) is azide concentration in donor well at time t (mM), C_A(t) is azide concentration in acceptor well at time t (mM), V_D is donor well volume of 0.2 mL (including compound in buffer), V_A is acceptor well volume of 0.3 mL (including buffer), S is filter area of 0.3 cm² and t is incubation time (5 h = 18000 s). Equilibrium concentration, C_equilibrium (µM), was calculated as

$$\begin{array}{c}{C}_{equilibrium}\frac{\left[{C}_{D}\left(t\right)\bullet {V}_{D}+{C}_{A}\left(t\right)\bullet {V}_{A}\right]}{{V}_{D}+{V}_{A}}\#\left(14\right)\end{array}$$

2.3. Theoretical prediction of permeability (P_t)

Herman J.C. Berendsen was among the first who performed molecular simulation of membranes to address their structure, stability, and transport properties [32–37], followed by his disciples that included simulation of membrane embedded transporters [38–42]

Diffusion is a passive process of the net movement of a substance down driven by a concentration gradient. Diffusion is described by diffusion equation in n-dimensions:

$$\begin{array}{c}\frac{\partial u}{\partial t}=D{\nabla }^{2}u\#\left(15\right)\end{array}$$

where u is the coordinate and time-dependent concentration, D stands for diffusion coefficient and ${\nabla }^{2}$ is Laplace operator. It must be noted, that in our calculation D is coordinate and time independent. Furthermore, in complex environments, such as in a nerve cell, the concentration difference is not the only force driving diffusion. Therefore, we include the coordinate-dependent chemical potential ($\mu$) to the Eq. 15, which alters the time dependent concentration profiles. This is a special case of a more general Fokker-Planck equation, called the Smoluchowski equation [43], which reads:

$$\begin{array}{c}\frac{\partial u}{\partial t}=\nabla \left[D\left(\nabla u+\frac{1}{{k}_{b}T}\left(u\bullet \nabla \mu \right)\right)\right]\#\left(16\right)\end{array}$$

where $\mu$ is the coordinate-dependent chemical potential, k_b is Boltzmann constant, T is absolute temperature and $\nabla$ is gradient of a function.

Since the diffusion equation with coordinate-dependant chemical potential described above does not allow for analytical solution, we proceeded with numerical solving on a grid. Algorithms for numerical solving of such diffusion equation appeared only recently [44]. Especially illustrative is a carefully performed computational study of oxygen diffusion through the membranes by Ghysels et al. [45]. We have used finite differences numerical method. Two numerical simulations were made, once with dimensions of a realistic cell membrane with thickness of 50 Å and one with real PAMPA membrane thickness of 125 µm according to the manufacturer. First experiment used grid spacing of 1 Å and time step of 0.1 ns, while second experiment used grid spacing of 1 µm and time step of 1 µs. In both simulations the diffusion coefficient D from Huang and co-workers of 820 µm² s^− 1 [46] was used. Moreover, both simulations used the free energy profiles of the transition to and from the membrane, which were experimentally determined earlier in this study.

Secondly, the permeability across a membrane is described by the following equation:

$$\begin{array}{c}j=-P\varDelta c\#\left(17\right)\end{array}$$

where j is the flux, P is the membrane permeability and $\varDelta c$ is the difference of concentration of both sides of the membrane. Flux was calculated numerically from diffusion equation with coordinate-dependent chemical potential, while concentration difference was initially 1.

2.4. Preparation of solutions

Solvents of sample solution were prepared by mixing acetonitrile and water in ratio 1:10 (V/V). Solvents were adjusted to pH 2.0 with 20% H₃PO₄ and to pH 8.0 with 0.01 M NaOH before filling to the calibration mark.

First, calibration curves were prepared at 5 concentration levels; for pH value of 2.0 from 0.12 to 1.5 mg mL^− 1 of NaN₃ (that corresponds 0.08 to 1.0 mg mL^− 1 of HN₃) and 0.0019 to 0.12 mg mL^− 1 of NaN₃ (that corresponds 0.0013 to 0.08 mg mL^− 1 of HN₃) for pH value 8.0.

Aqueous sample solutions of NaN₃ with pH values of 2.0 and 8.0 were prepared also; concentration of sample solution with pH value of 2.0 was 1.5 mg mL^− 1 of NaN₃ (equal to 1.0 mg mL^− 1 of HN₃) and sample solutions with pH value of 8.0 was 12 mg mL^− 1 (equal to 8.0 mg mL^− 1 of HN₃). Then, equal volumes, 15 mL of solution of NaN₃ and 15 mL of 1-octanol, was pipetted into a 50 mL separatory funnel and mixed well every 10 minutes in 1 hour to equilibrate. Finally, upper organic and lower aqueous phase was sampled. Aqueous phase with pH value of 8.0 was diluted to factor 0.0008. All solutions for calibration curves and final solutions of organic and aqueous phases were injected into a HPLC system.

3.1. Determination of octanol-water partition coefficients (K_ow)

Octanol-water partition coefficient is defined as the ratio of equilibrium concentrations of a given species between 1-octanol and water. For ionizable species as azide the ratio depends on the pH value of aqueous solution.

Octanol-water partition coefficients (K_ow) were calculated from experimentally determined concentrations of AHA in both phases; organic phase of 1-octanol and water phase of 10% solution of acetonitrile. K_ow was 2.01 for pH value of 2.0 and 0.00034 for pH value of 8.0. R² of calibration curves with solutions of sodium azide were 0.974 (pH 2.00) and 1.0 for pH value of pH 8.0. We used Eq. 7 to interpolate and extrapolate experimental data and to calculate K_ow(pH) = Q(pH).

Experimental results show that in acid environment (pH 2.0) in which azide mostly forms its neutral form (HN₃), 67% of azide is in octanol phase. In basic environment by pH above pK_a value of 4.65, azide mostly exists in its ionic form of N₃^ˉ, so lower partition coefficient and concentration in octanol is expected; experimentally determined value is 0.00034 (pH of 8.0) of azide in 1-octanol. Experimental values of corresponding calculated free Gibbs energies of activation ΔG^‡(pH) for transition of AHA from aqueous to organic phase are − 0.413 kcal mol^− 1 (pH 2.0) and 3.29 kcal mol^− 1 (pH 8.0) and were calculated using equation ΔG^‡ = ∆G_ow = -k_BT ∙ ln K_ow. Utilizing extrapolation of experimental results, distribution coefficients Q and free energies ΔG for transfer AHA were calculated and are listed in Table 1.

Table 1

Partition coefficients, K_ow(pH), and free energies, ΔG, for transfer of AHA from water to octanol.
pH	Q = K_ow	logQ	ΔG [kcal mol^− 1]
1	2.00955	0.303	-0.414
2	2.00551	0.302	-0.413
3	1.96599	0.294	-0.401
4	1.64239	0.215	-0.294
4.65	1.00517	0.002	-0.003
6	0.08627	-1.064	1.453
6.8	0.01447	-1.840	2.512
7.1	0.00745	-2.128	2.906
7.2	0.00599	-2.223	3.035
7.4	0.00391	-2.408	3.288
8	0.00124	-2.908	3.970
9	0.00043	-3.367	4.597
10	0.00035	-3.457	4.721

To aid with the understanding of the local environment around the cell membrane, please see Fig. 2.

3.2. Experimental determination of effective permeability, P_e (pH)

Results of effective permeability of artificial membrane for AHA were obtained using following approaches; experimentally by using method PAMPA and theoretically by numerical solving diffusion equation.

Experimentally, we obtained value of P_e of 11.2 · 10^− 6 cm s^− 1 at pH value of 7.4 and 5.5 · 10^− 6 cm s^− 1 at pH value of 8.0 (see Table 2). Near 11% of azide crossed the membrane into acceptor solution with pH value of 7.4 and 9% into acceptor solution with pH value of 8.0. Mass retention, calculated on donor and acceptor side was on average − 0.15% and − 0.03% for pH 7.4 and 8.0, respectively, which indicates a minor analytical error.

Table 2

Experimental results of effective permeability (P_e) for AHA for two pH values using method PAMPA.
Input Data				Calculation Results
pH	Acceptor concentration (µM)	Donor concentration (µM)	Initial concentration (µM)	Equilibrium concentration (µM)	Mass retention (%)	Permeability P_e (cm s^− 1)	Permeability logP_e
7.4	675.5	3247.7	3700.9	1704.4	-0.15	11.2 · 10^− 6	-4.97
8.0	329.9	3296.8	3696.3	1516.6	-0.03	5.5 · 10^− 6	-5.26

3.3. Computational prediction of permeability (P_t)

By numerical solving of diffusion equation, we obtained two permeability values P_t (logP_t) for AHA transition from ECF to CYT (Fig. 2) of 4.23 ·10^− 2 cm s^− 1 (-1.73) and 22.3 ·10^− 6 cm s^− 1 (-4.65), for 50 Å and 125 µm membrane, respectively.

Experimental (-4.97) and theoretical values (-4.65) of permeability at physiological pH of 7.4 for 125 µm PAMPA membrane differ only slightly. However, the realistic 50 Å membrane has a much higher permeability (10⁴ times). Similarly, we can calculate the theoretical rate constant of permeation through the membrane, which is 8.46 · 10⁴ s^− 1 and 1.55 · 10^− 3 s^− 1 for 50 Å and 125 µm membrane, respectively.

Current opinion is that azide enters the cell through the plasma membrane rather than via any of the transporters. In this respect it is very likely that it enters in its neutral form of HN₃, since its deprotonated form (N₃^ˉ) has too favourable free energy of hydration, consequently the free energy cost for entering the membrane would be too high. Free energy for protonation of ionized species with certain pK_a value in aqueous medium with certain pH value reads: $\varDelta G=-{ln}\left(10\right){k}_{B}T\left(pH-p{K}_{a}\right)$, where $\varDelta G$ is free energy, ${k}_{B}$ is Boltzmann constant, T is absolute temperature (310 K for human body) and pK_a value for hydrazoic acid is 4.65. Hence, free energy for its protonation at pH of 7.4 is $-2.303\bullet 0.593 \text{k}\text{c}\text{a}\text{l} {\text{m}\text{o}\text{l}}^{-1}\bullet (7.4-4.65)=-3.75 \text{k}\text{c}\text{a}\text{l} {\text{m}\text{o}\text{l}}^{-1}$. On the other hand, the energy cost for HN₃ deprotonation in media with the pH value of 2.0 is 3.62 kcal mol^− 1. Since deprotonated ionic species (N₃^ˉ) have more favourable hydration energy in more basic media, equilibrium populations of HN₃ are higher in cytoplasm (CYT, with pH value of 7.2) than in the extracellular fluid (ECF, with pH value of 7.4) or in the mitochondrion (with pH value of 8) and equilibrium populations of N₃^ˉ are highest in the mitochondrion.

At lower pH, azide mostly exists in the protonated form of hydrazoic acid (HN₃) that is to some extent hydrophobic and preferably distributes to the gas phase or lipid membrane from the aqueous solution. Hydrazoic acid has a relatively small dipole moment of 0.847 ± 0.005 Debye [47]. Observing the measured octanol-water partition coefficient supports this reasoning. At pH 2, there is more AHA in nonpolar solvent (2:1), while at pH 8 there is significantly more AHA in the water phase (1:2940). Consequently, at physiological pH range azide is always hydrophilic and predominantly in ionized form (N₃⁻). According to Overton rule [48] more hydrophilic substances are less membrane permeable [49, 50]. Consequently, one could predict, that AHA will not permeate easily through the cell membrane. However, its small molecular size and the spread charge in its ionized form yield a moderately low free energy barrier of 3.29 kcal mol^− 1 for entry into the membrane. For comparison a popular drug that crosses blood brain barrier MMB4 has a free energy barrier of 28 kcal mol^− 1 [51], morphine has a free energy barrier of 7 kcal mol^− 1 [52] and carbon dioxide has a free energy barrier of around 1 kcal mol^− 1 [53]. AHA diffuses from region of higher pH value (ECF) to the region with lower pH value. In cytoplasm with pH value of 7.2 more azide molecules are in protonated form (HN₃) than in ECF at higher pH value of 7.4, consequently the total free energy cost for permeation from ECF to cytoplasm is 0.25 kcal mol^− 1, which is solely due to the difference in pH. Local acidosis or alkalosis would change this. More interesting is that the equilibrium concentration ratio between the cytoplasm and the ECF changes depending on the pH difference. In case of physiological pH values, less AHA is in cells than in ECF (0.238), while in case of local acidosis, additional AHA would accumulate in cells. For example, poisoning with azide disturbs the aerobic metabolism of the cell, shifting it to anaerobic, which produces acidic lactic acid, lowering the ECF pH and starting a positive feedback loop or a death spiral.

Our experimental data for permeability of AHA using PAMPA method gave a permeability value (logP_e) of -4.97, which is still considered fast, according to Bennion et al. who estimate that compounds with logP_e < -5.5 have low permeability [51]. Bodor et al. studied the correlation of octanol-water partition ratio (Q) and blood brain barrier permeability [54]. AHA with Q of 0.00391 would have a low blood brain barrier permeability, similar to urea. It should be noted that PAMPA is specifically designed to study intestinal absorption of drugs, but we study permeation through the cell membrane, which is about 25000 times thinner. Therefore, we have conducted two simulations. For a membrane of 125 µm results of numerical solutions of the diffusion equation predict the experimental permeability reasonably well. In fact, a surprisingly good agreement between experimental and calculated value was found. It is worth to stress that currently there are no reliable experimental methods that would provide permeability of a cell membrane with the thickness of approximately 50 Å. Since the computational predictions proved to be valid for a 125 µm thick membrane we firmly believe that prediction of permeability for a 50 Å membrane are equal reliable.

Considering the rate constant of permeation through the cell membrane for AHA is 8.46 ·10⁴ s^− 1 and the rate constant for association of AHA with the of Cytochrome c oxidase Complex IV which is 200 s^− 1 measured by Antalis et al. [55] for association with myoglobin, gives evidence that the diffusion through the membrane is not a rate limiting step and does not control the rate CoX IV inhibition by AHA. Chemical step, that is in our case reaction of the heme group when AHA forms Michaelis complex with CoX IV, controls the overall rate of inhibition. Myoglobin association rate is similar to CoX IV, because they both have heme groups, which are targeted by azide ion. It was anticipated that the rate limiting step is the association with heme, since AHA is a small molecule that can easily permeate the membrane regardless of its hydrophilic nature. It is worth to stress that for most of the enzymatic reactions in aqueous solution diffusion is rarely a rate-limiting step. The “average enzyme” is far from kinetic perfection as it exhibits a k_cat of ∼10 s^− 1 [56]. We are aware that observed dynamics of azide poisoning is however controlled by circulation transport that takes place on a minute time scale and to some extent depends on the route of administration (IV, Inhale, IM).

By measuring octanol-water partition coefficients for azide ion / hydrazoic acid (AHA) we have demonstrated that at physiological pH values of extracellular fluid AHA prefers extracellular fluid over cytoplasm, while membrane and other lipophilic compartments have the lowest relative populations.

The experimental values of effective permeability obtained using method PAMPA were critically compared with the results of the numerical solving diffusion equation through the membrane. For 50 Å thick membrane we estimated permeability of AHA of 8.46 · 10⁴ s^− 1 while the rate constant for association of AHA with the heme group is 200 s^− 1 as measured by Antalis et al. [55]. One can conclude that complex IV inhibition by azide ion is controlled by chemical step rather than by diffusion through the membrane. It is worth to emphasize that this study was focused on the events that follow complete embedding of the cell to the azide ion / hydrazoic acid solution. Observed dynamics of azide poisoning is however controlled by circulation transport that takes place on a minute time scale.

Acknowledgments: /

Funding: Slovenian Research Agency Grant P1-0012 (JM)

Author contributions:

Conceptualization: SLH, SZ, VS, MSD, JM

Methodology: SLH, SZ, VS

Investigation: SLH, SZ, VS

Visualization: SLH, VS

Funding acquisition: JM

Project administration: MSD, VS, JM

Supervision: SZ, VS, MSD, JM

Writing – original draft: SLH, VS, JM

Writing – review & editing: SLH, SZ, VS, MSD, JM

Competing interests: Authors declare that they have no competing interests.

Data and materials availability: All data and code can be obtained from the authors upon request.

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How Difficult Azide ion / Hydrazoic Acid Passes Biological Membranes: Experimental and Computational Study

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Materials And Methods

2.1 Determination of octanol-water partition coefficients (K _ow ) of azide ion / hydrazoic acid for different pH values using a reversed-phase liquid chromatography and UV detection.

2.2. Determination of effective permeability, P_e (pH) using the method PAMPA

2.3. Theoretical prediction of permeability (P_t)

2.4. Preparation of solutions

3. Results

3.1. Determination of octanol-water partition coefficients (K_ow)

3.2. Experimental determination of effective permeability, P_e (pH)

3.3. Computational prediction of permeability (P_t)

4. Discussion

5. Conclusions

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1

How Difficult Azide ion / Hydrazoic Acid Passes Biological Membranes: Experimental and Computational Study

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Materials And Methods

2.1 Determination of octanol-water partition coefficients (K ow ) of azide ion / hydrazoic acid for different pH values using a reversed-phase liquid chromatography and UV detection.

2.2. Determination of effective permeability, Pe (pH) using the method PAMPA

2.3. Theoretical prediction of permeability (Pt)

2.4. Preparation of solutions

3. Results

3.1. Determination of octanol-water partition coefficients (Kow)

3.2. Experimental determination of effective permeability, Pe (pH)

3.3. Computational prediction of permeability (Pt)

4. Discussion

5. Conclusions

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1

2.1 Determination of octanol-water partition coefficients (K _ow ) of azide ion / hydrazoic acid for different pH values using a reversed-phase liquid chromatography and UV detection.

2.2. Determination of effective permeability, P_e (pH) using the method PAMPA

2.3. Theoretical prediction of permeability (P_t)

3.1. Determination of octanol-water partition coefficients (K_ow)

3.2. Experimental determination of effective permeability, P_e (pH)

3.3. Computational prediction of permeability (P_t)