Research Article

Model for Quantitative Estimation of Partition Coefficient of NAD+ and NADH in Nafion Membranes

Piyush Kar
Faculty of Engineering, University of Alberta, Edmonton, AB, T6E1Y2, Canada
*Corresponding author:

Piyush Kar, Faculty of Engineering, University of Alberta, Edmonton, AB, T6E1Y2, Canada, Email:


NAD+, NADH, Nafion, Partition coefficient model, Donan membrane equilibrium equation

Quantification of partition coefficient for nicotinamide adenine dinucleotide (NAD+) and NADH in Nafion membranes, of protonated and deprotonated types, reveal an order of magnitude increase of NAD+ partition coefficient, i.e. from 2.00 to 14.00 by decreasing concentration of NaNO3 from 0.8 M (molar) to zero in external solutions contacting with the Nafion membranes. Partition coefficient of approximately 2.00 is observed for NADH in protonated Nafion. Deprotonated Nafion membranes cause a much lower partitioning effect of 0.05 for NAD+ and zero for NADH. Further to experimental findings, this article also reports a validated modeling approach, using Donan membrane equilibrium equation and membrane charge balance to predict partition coefficients of NAD+ in protonated Nafion in contact with external solution of varying ionic strengths [20,21].

Partition coefficient (K) of a solute species is defined as the ratio of the concentration of the species in a semi-permeable membrane to that in an external solution when the membrane forms an interface with the solution. Nafion, a widely used semi-permeable material, consists of favorable microenvironment for enzyme immobilization in its matrix (schematic shown in Figure 1 (a)). Furthermore, Nafion is an ion transport membrane with perfluorinated sulfonate backbone [1] and has fixed charge sites consisting of negatively charged sulphonic acid (SO3-) groups that can potentially pre-concentrate NAD+, given the compatibility of size and charge of the molecule with porosity and fixed negative charge sites in the Nafion matrix. Given the fact that NAD+ and NADH (reduced form of NAD+) act as cofactors in majority of enzymatic reactions [2-6] concentrations of these species significantly affect enzymatic reaction kinetics and affect over performance of devices, such as biofuel cells [7, 8] Therefore, estimation of partition coefficients for NAD+ in Nafion membranes is critical to accurate performance analysis and designing of enzyme-based bio-engineered devices operating on heterogeneous enzyme catalysis within the membranes, e.g. biofuel cells and biosensors [7-17] To the best of the author’s knowledge there are no reports of NAD+ and NADH partitioning studies, and hence this is a first time report on quantification of partition coefficients of NAD+ in Nafion 117 membranes. Principal factors affecting K are temperature, external solution pH, dissolved ions, and time to equilibrate. Most of the enzyme-based devices perform at their peak at room temperature and thus room temperature was selected for our study. Na+ ions are often present in electrolytes used in enzyme-based electrochemical devices, and are obtained from dissolved salts, such as NaNO3 and Na2SO4, which impart adequate ionic strength that is a key requirement in good electrolytes. In this study, we analyze the effect of Na+ ions on partition coefficients of NAD+ in Nafion membranes by introducing varying amounts of NaNO3 in external solutions. Using a modeling approach based on Donnan membrane equilibrium equation and membrane charge neutrality, we also report effect of pH between 0.75 and 3.80 and that of Na+ content between 0 and 1 M, on partition coefficients of NAD+ in protonated Nafion.

NAD+, NADH and NaNO3, obtained from Sigma Aldrich (Saint Louis, MO, USA), were used in the study. External solution was made by dissolving desired amount of either NAD+ or NADH (strength, between 0.1 mM to 2 mM) and NaNO3 (strength, between 0 and 1 M) in a 10 mM phosphate buffer solution at neutral pH (≈ 7). Nafion 117 membranes were purchased from Ion Power Inc. (New Castle, DE, USA) and were used in as-received (i.e. protonated form) and also in deprotonated forms. De-protonation treatment, via incorporation of sodium, was performed by immersing the as-received membranes in a 1 M NaNO3 solution at 75 oC for 18 hours, and the step was followed by immersion of membranes in de-ionized water at 75 oC for 6 hours to yield the de-protonated form of Nafion. As-received membrane and de-protonated forms of the membrane samples of size 3 x 3 cm were used in the experiments for determining K for NAD+ and NADH. Contact of Nafion with external solutions, containing NAD+ or NADH species, was made by soaking the Nafion membrane samples in the solutions for at least 24 hours, a period of time, which is presumed to be adequate to allow electrochemical equilibrium between the solution inside the membrane and the external solution. Concentrations of NAD+ and NADH in the Nafion 117 membranes were determined by using UV-Vis (Varian Cary 50), by two approaches. One is by estimating the difference between initial and equilibrium NAD+ concentrations in external solution. The other approach is direct exposure of the Nafion membrane samples to UV-Vis spectra. All experiments were conducted at room temperature.

The schematic of the NAD+ partitioning process is shown in Figure 1a and 1b. The Ion Exchange Capacityfor Nafion 117 membrane, I, is 1 milli-mole per gram (m.mole/g), a value obtained from literature provided by the manufacturer DuPont Inc. A wet density of 1.77 gram per mill-liter (g/ml) is taken from literature [1,18,19]. Applying the value of density for Nafion, the ion exchange capacity, value of I, was determined to be 1.77 M. In order to apply Donan membrane equilibrium equation and to calculate partition coefficient, we express the electrochemical potential of the chemical species in the external solution and those in the Nafion membrane byEquations (1a) and (1b), respectively.

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In Equations (1a) and (1b), e i, ext μ and e i, Naf μ are the electrochemical potentials of the species, and, i, ext μ and i, Naf μ are the standard potentials of the species, in the external solution and membrane, respectively. R and T are the universal gas constant and temperature, respectively. ai, ext and ai, Naf are the activities of the ionic species in the external solution and membrane, respectively. zi is the charge on the species, i, ext φ and i, Naf φ are the electrostatic potentials of the species in the external solution and membrane, respectively. At equilibrium, the electrochemical potential of each ionic species in the membrane can be equated to that in the external solution. Expanding the electrochemical potential terms, and equating out the standard potential terms in Equations (1a) and (1b) and re-arranging, we obtain Equation (2).

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The constant term on the right hand side of the Equation (2) is the partition coefficient, and is expressed in terms of Donan potential, which is the difference between the electrostatic potential of the species in the external solution from that in the membrane. The Donan membrane equilibrium equation can thus expressed by Equation (3), which states that the ratio of activities (expressed here as concentrations for simplicity) of ionic species raised to the power of inverse of the charge on the species is a constant. Applying Donan membrane equilibrium equation [20,21] to cationic species, K can be expressed as:

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NAD+cations are denoted by CNAD+, Naf and CNAD+, ext for concentrations in Nafion 117 membrane and external solutions, respectively. NAD+ is assumed to have net charge of +1, below pH 3.80 [21]. Therefore, the calculation used in this manuscript is valid for pH ≤3.8. Concentrations of Na+ are denoted by CNa+, Naf and CNa+, ext, in Nafion 117 membrane and external solution, respectively. Concentrations of H+ are denoted by CH+, Naf and CH+, ext in Nafion 117 membrane and external solutions, respectively. Similarly, applying Donan membrane equilibrium to anions, the corresponding K is expressed as:

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NO-3cations, are denoted by and for concentrations in Nafion 117 membrane and external solutions, respectively. H2PO4-cations are denoted by and for concentrations in Nafion 117 membrane and external solutions, respectively. HPO4- cations are denoted by and for concentrations in Nafion 117 membrane and external solutions, respectively. Concentration of cations, denoted by and for concentrations in Nafion 117 membrane and external solutions, respectively. Therefore, we can write:
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Partition coefficient, K, can be obtained by solving (6), obtained by applying membrane charge balance for ions within the solution in Nafion 117 membrane, at equilibrium:

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The solution to Equation (6) was obtained using non-linear regression analysis using the MATLAB software.

Concentrations of NAD+ and NADH in Nafion membranes were evaluated for various concentrations of the species in external solution. Time to reach equilibration was estimated to be 22 hours. Experimental K values were obtained from the slopes of the linear fits between the membrane and external solution concentration data. Partitioning phenomena of the NAD+ in protonated Nafion was affected by adding NaNO3 in the external solution. K of approximately 14.00 was observed with protonated Nafion when NaNO3 concentration in external solution was zero. K decreased to 2.00 when concentration of NaNO3 was 0.8 M in external solution. Higher density of unbalanced fixed charge, i.e. sulphonic acid sites, in protonated Nafion is the likely cause of higher partition coefficient values. Figure 2 [A] shows the linear fit K plots of the protonated Nafion membrane with external solutions having different NaNO3 concentrations. It is evident from the data that NAD+ favorably partitions into protonated (or acidic) Nafion membranes and unfavorably partitions into de-protonated (or neutral) Nafion membranes.

Apart from distribution density of fixed charge sites, other factors affecting partition coefficients of NAD+ are ionic mobility, temperature and presence of secondary, tertiary or other ions. Ionic mobility depends on species charge number, membrane pore size, temperature and ionic radius, and will be lower in Nafion membranes (of both, protonated and de-protonated, types) as compared to that in the case Tetrabutyl Ammonium Bromide (TBAB) modified Nafion membranes [15] with enlarged pores. This study does not attempt to relate ionic mobility to K, except that it must be remarked that faster ionic mobility may allow shorter time to reach equilibrium conditions. Experimental and calculated plots for K in protonated Nafion versus NaNO3 concentration in external solution are shown Figure 2 [B], and indicate that the calculated and experimental partition coefficient values of NAD+ match closely. Thus it is reasonable to claim that the Donan membrane equilibrium and membrane charge balance model, as applied in this study, is a robust method to calculate partition coefficients of NAD+ in Nafion membranes.  

Although calculations were reliable in determination of partition coefficients, consideration of unit activity limits applicability of the method, as ionic mobility and temperature effects cannot be incorporated. Plot of calculated partition coefficients (Figure 2 [B]) for NAD+ shows that a partition coefficient of 100 is attainable at pH 3.8, with protonated Nafion immersed in solutions that are free of NaNO3. Furthermore, the model also predicts that partition coefficient values tend towards unity for more than when NaNO3 concentration in external solution exceeds 0.8 M. Table 1 summarizes the experimentally determined partition coefficient values of NAD+ and NADH for both deprotonated and protonated forms of Nafion. The equilibration process takes at least 22 hours. An equilibrium pH of 2.25 is observed for the external solution in case of protonated Nafion, which is indicative of an ion-exchange process that facilitates selective adsorption and hence partitioning of positively charged NAD+ cations. The external solution, while in the equilibration process, gets protonated by the protonated Nafion and pH decreases making conditions favorable for ionization of NAD+ at pH < 4, where NAD+ exists with a net positive charge [20]. Increase in sodium content in external solution, however, diminishes the extent of NAD+ partitioning because of the higher mobility or diffusivity of smaller sized Na+, as compared to NAD+. In case of deprotonated Nafion membranes, external solution pH remains unchanged, and so a physio-sorption process may be attributed to the mechanism of the partitioning phenomenon. From device (biosensors and biofuel cells) design stand-point, wherein it is necessary to balance solution ionic strengths by dissolving calculated amount of salts (such as NaNO3 or Na2SO4) with desired partitioning effects, the model serves as a viable methodology to estimate partition coefficient values of co-factors such as NAD+ and NADH in protonated Nafion membranes [20,21].

NAD+ partition coefficient is approximately 0.05 in deprotonated Nafion, and is approximately 14.00 in protonated Nafion, Partition coefficient of NAD+ decreases with increasing NaNO3 in external solution, indicative of the partitioning processes getting affected by presence of secondary cations in external solution. NADH partition coefficient was approximately 2.00 in protonated Nafion and is negligibly small in deprotonated Nafion, confirming similarity of the partitioning mechanism to that of NAD+. A NAD+ partition coefficient model developed using Donan membrane equilibrium equation and membrane charge balance predicted that partition coefficient values tend towards unity as NaNO3 concentrations approach 1 M. The reliability of the model makes it a viable method for quantification of co-factors such as NAD+ and NADH in nano-porous membranes for enzyme immobilized devices, which from an engineering standpoint, is essential to bring about designs for improved performance.

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Figure 1. (a) Immobilized enzymes in Nafion matrix; (b) Schematic illustration of NAD+ pre-concentration (or partitioning) process in the Nafion 117 membrane, when exposed to external solution, containing NAD+; and (c) Schematic representation of Nafion membrane and external solution denoting the various electrochemical potentials of the ionic species in external solution.

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Figure 2. [A] Plots of the NAD+ equilibrium concentration in Nafion 117 membrane versus the same in external solution, at various NaNO3 concentrations. Linear relationship between the two concentrations is established by the linear fit. Nafion 117 was used as-received (i.e. protonated form). [B] Plots of experimental (taken from [A]) and calculated partition coefficients of NAD+ versus NaNO3 concentration in the external solution. Curves represent calculated partition coefficients and were obtained at pH values, as indicated.

Equilibrium pH

Nafion 117 type

[NaNO3] / M




As-received (protonated form)





As-received (protonated form)





De-protonated with sodium





Table 1. Summary of the partition coefficients of the NAD+ and NADH in Nafion membranes.

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Published: 19 May 2017


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