Transition-state theory-based analysis of diffusion of water in yeast cells

Saccharomyces cerevisiae, water, membrane transport, diffusion, transition state theory, yeast

MAIN TEXT

In a recent article, the authors employed a technique of nuclear magnetic resonance (NMR) spectroscopy to investigate water transport through the plasma membrane of several yeast species (Šoltésová et al. 2019). The authors also examined water transport at various temperatures to derive kinetic information of the process. By applying the Arrhenius approach, the authors identified activation energy of water transport across the membrane to be 29 kJ/mol, which is comparable to the values obtained by using other techniques. For example, Madeira et al. found that the activation energy for water transport in yeast cells was 5.9 kcal/mol (or 24.7 kJ/mol) by using stopped flow spectroscopy (Madeira et al. 2010). In addition to the rate constant of water transport, the authors also reported diffusion constants of water at various temperatures. Specifically, the authors found that diffusion constant of intracellular water molecules was two-orders smaller than that of extracellular water. The article, however, fell-short of providing an in-depth discussion of the feature. We thought thermodynamic explanations for the phenomenon would be useful for the understanding of the diffusion of cytoplasmic water. The purpose of this letter, therefore, is to derive a thermodynamic basis for the feature to gain additional insight to the phenomenon of water diffusion.

The authors reported diffusion constants (D) of intracellular and extracellular water molecules of Saccharomyces cerevisiae at various temperatures (Šoltésová et al. 2019). From this data, we calculated the Gibbs free energy of activation of the diffusion (⁠|$\Delta G_{\rm{a}}^{\circ}$|⁠) for each temperature (T) using a modified version of the Eyring equation (Bergethon 1998; Eq. (1)):

$$\begin{eqnarray*} \Delta G_a^{\circ} = - RT\ln \frac{{Dh}}{{{\lambda ^2}{k_B}T}} \end{eqnarray*}$$

(1)

where R is the gas constant (8.314 J/mol/K), h is Planck's constant (6.626 × 10⁻³⁴ J s), and k_B is the Boltzmann constant (1.381 × 10⁻²³ J/K). The value of λ, the mean jump distance of diffusing water molecules, was obtained from Wang's paper to be 3.7 × 10⁻¹⁰ m (Wang, Robinson and Edelman 1953). Multiple diffusion constants for the same temperature (15°C, 25°C and 40°C) in the data (Šoltésová et al. 2019) were averaged in the calculation of |$\Delta G_{\rm{a}}^{\circ}$|⁠. The resulting |$\Delta G_{\rm{a}}^{\circ}$| values for intracellular and extracellular water molecules at seven different temperatures are shown in the associated online material (Figure S1, Supporting Information).

Two features in the plot (Figure S1, Supporting Information) are evident. First, |$\Delta G_{\rm{a}}^{\circ}$| of intracellular water molecules is larger than that of extracellular water molecules by ∼10 kJ/mol. Second, the origin of the difference in |$\Delta G_{\rm{a}}^{\circ}$| between intracellular and extracellular water molecules can be examined in terms of thermodynamics (Chang 2000) using Eq. (2):

$$\begin{eqnarray*} \Delta G_a^{\circ} = \Delta H_a^{\circ} - T\Delta S_a^{\circ} \end{eqnarray*}$$

(2)

where |$\Delta H_{\rm{a}}^{\circ}$| and |$\Delta S_{\rm{a}}^{\circ}$| are standard molar enthalpy and entropy of activation in the diffusion of water molecules, respectively. Linear regression allows us to obtain both |$\Delta H_{\rm{a}}^{\circ}$| and |$\Delta S_{\rm{a}}^{\circ}$| for each case (Figure S1, Supporting Information). |$\Delta H_{\rm{a}}^{\circ}$| and |$\Delta S_{\rm{a}}^{\circ}$| obtained from our analysis are − 0.3 kJ/mol and −0.09 kJ/mol/K for intracellular water and 17.3 kJ/mol and 0.005 kJ/mol/K for extracellular water, respectively. This indicates that intracellular water diffusion is limited by entropy, while extracellular water diffusion is limited by enthalpy. This suggests that the physical state of intracellular water molecules is highly different from that of extracellular water molecules.

While our analysis explains the difference of water diffusion between intracellular and extracellular medium, the R² value, obtained from the linear fitting of the relation between |$\Delta G_{\rm{a}}^{\circ}$| and temperature, was very small for extracellular water (0.0563) whereas it was high for intracellular water (0.9931; Figure S1, Supporting Information). Therefore, we included diffusion of water from another study (Wang 1965), which measured coefficients of diffusion using a capillary method, in our analysis. Linear fitting of the data (Wang 1965) resulted in a significant correlation (R² = 0.9580) with |$\Delta H_{\rm{a}}^{\circ}$| and |$\Delta S_{\rm{a}}^{\circ}$| being 17.9 kJ/mol and 0.012 kJ/mol/K, respectively. These values of |$\Delta H_{\rm{a}}^{\circ}$| and |$\Delta S_{\rm{a}}^{\circ}$| are comparable to those obtained from the NMR-based measurements (Šoltésová et al. 2019). Therefore, the NMR-based method is comparable to other methods for the determination of D of extracellular water. However, it is more suitable for the determination of D of intracellular water because of its large value of R².

Water is the most abundant molecule in cells (Milo and Phillips 2016). It plays a critical role in numerous biochemical and cellular processes (Clegg 1984; Watterson 1987; Dellerue and Bellisent-Funel 2000; Chaplin 2006; Shepherd 2006; Ball 2008, 2017). A recent study using molecular dynamics indicated that water molecules play a crucial role in insulin dimerization (Banerjee and Bagchi 2020). Collective movements of water molecules were found to transmit chemical energy over very long distances along proteins as well (Phillips 2020). On the other hand, the physical and chemical state of cells (Luby-Phelps 2000, 2013) may affect the diffusion constant of cellular water through the Stokes–Einstein relation (Milo and Phillips 2016). Therefore, the NMR-based measurement of the D of cellular water (Šoltésová et al. 2019) can be useful for the quantitative characterization of cells in conjunction of the transition-state theory-based analysis shown in this paper.

FUNDING

This work was supported by Valdosta State University [CoSM Research Scholar funding to J.K.].

Conflicts of Interest

None declared.