Water usability as a descriptive parameter of thermodynamic properties and water mobility in food solids

The study addresses why microbes can still grow in low-moisture solid foods and whether conventional indicators like water activity (a_w) and glass transition temperature (T_g) adequately explain or predict microbial behavior. While a_w has long been used to predict microbial growth potential, it may be insufficient in non-equilibrium, heterogeneous solid matrices where glass transitions and compositional effects alter molecular mobility. Prior observations show microbes can grow even below matrix T_g, suggesting that water mobility, rather than a_w or viscosity proxies alone, governs nutrient and metabolite diffusion needed for growth. The purpose is to quantify water mobility in glucose/whey protein isolate (WPI) solid matrices, relate it to thermodynamic properties, and link it to growth of Debaryomyces hansenii at 30 °C. The authors introduce a new descriptor, water usability (U_w), derived from the mobility difference between system-involved water and liquid water, to better describe and potentially control microbial growth in low-moisture foods.

The introduction synthesizes work showing: (1) a_w correlates with microbial growth but can misrepresent systems with glassy/crystallizable components and time-dependent properties; (2) T_g serves as a physicochemical boundary affecting viscosity and stability but does not universally inhibit xerophilic microbes; (3) NMR-based measures of water translational mobility correlate with microbial lag and germination, indicating the importance of water dynamics; (4) dynamic mechanical analyses (DMA) and relaxation times (e.g., T_2, translational relaxation) have been used as indicators of system mobility; (5) the Strength parameter (S) was previously defined to capture allowable temperature increases above T_g that reflect structural relaxation and mobility. Collectively, literature suggests water mobility is central to diffusion-limited processes governing microbial activity, motivating a descriptor that integrates thermodynamics and mobility.

Model systems: α-D-glucose and whey protein isolate (WPI) were prepared as 20% (w/w) aqueous solutions and mixed to mass ratios of glucose:WPI = 7:3, 1:1, 3:7, and 0:1 (pure WPI). Amorphous samples were obtained by freezing and lyophilizing (pressure <2 bar); amorphous glucose was additionally prepared by a quench-cooling method (melt at 160 °C, quench to −30 °C). Samples were stored over P2O5 to prevent sorption at 30 °C.

Water sorption: Samples were equilibrated over saturated salt solutions at 30 °C to achieve a_w = 0.11, 0.20, 0.31, 0.43, 0.53, 0.65, and 0.75. Mass was recorded at 24 h intervals up to 120 h. Sorption data were fitted with the GAB model to obtain monolayer moisture m0. Additivity of sorption in phase-separated sugar/protein matrices was applied to estimate non-crystalline glucose sorption.

Thermal analysis: Differential scanning calorimetry (DSC) determined onset-T_g from second heating scans (−20 °C to above T_g; 5 °C/min heating, 10 °C/min cooling). The Gordon–Taylor (GT) equation related T_g to water content; K_GT reflects interaction strength.

Dynamic-mechanical analysis (DMA): Loss modulus E'' was measured across −20 to >T_g at frequencies 0.5–10 Hz using single cantilever mode. T_α (E'' peak) provided α-relaxation temperatures. WLF equation was used to model relaxation times τ as a function of T − T_g, yielding constants C1 and C2.

Molecular mobility and Strength (S): Using WLF constants and a Deborah-number-based criterion, S (allowable temperature rise above T_g related to flow/relaxation) was calculated. Composition dependence of S vs water content was modeled with an empirical partition relation S_p = (w1 S_d1 + k_sp w2 S_d2) / (w1 + k_sp w2), where k_sp represents mobility partitioning. Classical thermodynamic analysis (Couchman–Karasz framework) was used to interpret k_sp and its relation to K_GT via heat capacity changes at T_g.

Water usability (U_w): Defined as U_w = S_1 / S_2, where S_1 is molecular mobility of liquid pure water (from literature) and S_2 is extrapolated S for water within the solid matrix (estimated via GT-informed fit). U_w ranges 0–1, with higher values indicating more freely mobile water within the solid matrix.

Microbial experiments: Debaryomyces hansenii (ACCC 20010) was activated in YM agar broth at 30 °C. Approximately 0.2 µL yeast suspension was streaked on the lyophilized matrices (1:0, 7:3, 1:1, 3:7, 0:1), then rehumidified over NaCl, KCl, and K2SO4 to achieve a_w ≈ 0.75, 0.83, and 0.92 at 30 °C. Controls were non-inoculated. Growth was monitored every 3 h up to 36 h using an ATP fluorescence detector to construct growth curves. Specific growth rate (µ) and doubling time (g) were calculated: µ = (ln N_t − ln N_0)/t; g = ln(2)/µ. Morphology and colonization were observed by SEM (10 kV; Au/Pd coated; ×8000). Statistical analysis used triplicates, means ± SD, and two-sided t-tests at 95% confidence.

• Water sorption and crystallization: Pure amorphous glucose crystallized during storage at all studied a_w at 30 °C, evidenced by rapid decreases in sorbed water after ~12 h. In glucose/WPI matrices, water loss due to partial glucose crystallization was minimal below a_w 0.44 and increased at higher a_w (notably 7:3 and 1:1), mitigated by WPI’s physical-blocking and water-binding effects. Pure WPI showed no crystallization across the a_w range. GAB monolayer moisture (m0) exhibited composition dependence, supporting phase separation and additive sorption behavior in sugar/protein matrices.
• Thermodynamics: T_g decreased with increasing a_w and increased with higher WPI content, reflecting reduced water mobility via protein binding. GT fits showed K_GT increased with WPI fraction, indicating stronger interactions and reduced water mobility.
• Molecular mobility and S: DMA showed E'' peak temperature increased with WPI content and decreased with a_w. WLF constants often negative (downward concavity), consistent with plasticization: τ drops rapidly above T_g as a_w increases. The Strength parameter S decreased with a_w and increased with WPI fraction (e.g., pure glucose S ≈ 16.9 °C dry; progressively lower at higher a_w; mixtures showed larger S than pure glucose at comparable conditions). Empirical S vs water content was well described by the partition model; k_sp values were similar to K_GT, aligning with thermodynamic interpretation via heat capacity increments at T_g.
• Water usability (U_w): Extrapolations using K_GT to estimate S for matrix-involved water yielded higher S than literature S for liquid water, consistent with reduced translational mobility of water when constrained by matrix interactions. U_w = S_1/S_2 provided a normalized measure of water mobility within solids (0–1), integrating thermodynamic and dynamic information.
• Microbial growth: D. hansenii did not survive on pure glucose at high a_w due to extreme osmotic stress; it grew on WPI and glucose/WPI matrices, with more vigorous growth at higher protein content. Structural collapse at high a_w (0.75–0.92) was observed in all composites and pure WPI after 36 h.
• Quantitative growth metrics (means ± SD): At a_w ≈ 0.92, µ increased with protein content, reaching 0.0697 ± 0.0216 h−1 in pure WPI (0:1), with corresponding g = 14.35 ± 0.27 h; at a_w ≈ 0.81, µ ≈ 0.0577 ± 0.0125 h−1 (WPI) with g ≈ 17.31 ± 0.27 h; at a_w ≈ 0.75, µ ≈ 0.0531 ± 0.0521 h−1 (WPI) with g ≈ 18.82 ± 0.03 h. Across matrices, µ rose and g fell as a_w and WPI increased.
• Correlation with U_w: Specific growth rate µ increased with U_w, while doubling time g decreased with U_w across all compositions and a_w conditions. Both a_w and U_w correlated with growth parameters, but U_w was argued to better capture water mobility effects governing microbial response.

Findings support that microbial growth in low-moisture solid foods is governed more by water mobility than by a_w or T_g alone. WPI reduces water mobility (higher K_GT, higher S), altering the matrix’s relaxation dynamics and diffusion properties. The classical thermodynamic connection between mobility partitioning (k_sp) and GT interaction parameter (K_GT) rationalizes the compositional dependence of S and the similarity of these constants. Introducing U_w as a ratio of liquid-water mobility to matrix-confined water mobility provides a practical, normalized descriptor reflecting the availability and usability of water for microbial processes. The positive association between U_w and D. hansenii growth rate (and inverse for doubling time) indicates that U_w captures essential diffusion-limiting processes such as nutrient and metabolite transport. While a_w remains correlated with growth, it lacks specificity regarding dynamic water behavior in heterogeneous, partially glassy matrices; U_w refines this by embedding mobility and thermodynamic context. These insights suggest strategies for food preservation that target water mobility (via composition, structure, and interactions) rather than relying solely on lowering a_w or remaining below T_g.

The study introduces water usability (U_w) as a dynamic descriptor of water mobility in solid food matrices, derived from the mobility difference between matrix-involved water and liquid pure water. Through measurements of sorption isotherms, thermal properties (DSC/GT), mechanical relaxations (DMA/WLF), and derived Strength (S) in glucose/WPI systems, the authors show that microbial growth of D. hansenii at 30 °C correlates strongly with water mobility. U_w increases aligned with higher specific growth rates and shorter doubling times, outperforming a_w as a sole descriptor in these solid systems. The work bridges thermodynamics (K_GT, heat capacities) and relaxation dynamics (k_sp, S) to rationalize mobility changes with composition. Practically, U_w can guide formulation and storage strategies to modulate microbial growth in low-moisture foods. Future work should examine effects of U_w on additional growth parameters (e.g., lag phase) and on a broader set of microorganisms and pharmaceutical solids.

• At higher a_w (≥0.54), crystallization hindered reliable T_g measurement in several samples, and T_g was not observed for pure WPI due to weak vitrification signals.
• Microbial experiments focused on a single yeast species (D. hansenii) and a specific temperature (30 °C) in model glucose/WPI matrices, which may limit generalizability to other organisms and food systems.
• Experimental conditions were not conducive for substantial glycerol production by D. hansenii, potentially minimizing organism-driven plasticization effects.
• U_w was inferred via extrapolation combining GT and mobility models and compared against literature S for liquid water; direct spectroscopic quantification of water translational mobility (e.g., 17O-NMR) within the same samples was discussed conceptually but not performed here.
• The study did not quantify certain growth parameters (e.g., lag phase) for correlation with U_w, which is noted for future work.