Understanding the interaction of taste sensations is crucial for advancing food sensory science and its applications in the food and beverage industries. Taste perception is a complex process involving the interplay of multiple taste qualities, such as sweet, sour, bitter, salty, and umami. These interactions are driven by synergistic and antagonistic effects, significantly influencing our overall sensory experience and enjoyment of food. Previous research has explored the interactions between different taste pairs, revealing that certain combinations can enhance or suppress the perceived intensity of individual tastes. For instance, studies have shown that umami can enhance sweet and salty tastes at moderate concentrations but suppress sour and bitter tastes. Similarly, the interaction between sweet and bitter tastes is often characterized by mutual suppression, while sweet and salty interactions demonstrate a concentration-dependent effect, with low concentrations of salt enhancing sweetness and high concentrations suppressing it. While these studies highlight the trends in taste interactions, a comprehensive quantitative model describing the strength variations in these interactions has remained elusive. Psychophysical studies commonly use the Weber-Fechner law and Stevens' power law to describe the relationship between stimulus concentration and perceived sensory intensity. However, these models primarily focus on single taste qualities, and a model accounting for the interaction effects between different tastes is lacking. This study aims to develop a quantitative model to explain the interaction of sweet and sour tastes, using sucrose and citric acid as model compounds. Building upon previous work establishing an optimized human sensory method for sweetness and sourness using a "close type" question based on triangle and paired comparison tests, this research sought to create a detailed quantitative equation describing the variation in sweet and sour taste strength when both stimuli are present. This would provide a valuable tool for food scientists and others.

Numerous studies have explored the synergistic and antagonistic effects of different taste combinations. Woskow's work demonstrated the impact of umami on other taste qualities. Kemp et al. investigated the influence of monosodium glutamate on taste perception. Breslin, Calvino, Curtis, Prescott and Schiffman's research highlighted the concentration-dependent effects of sweetness on other tastes. Stevens and Keast's studies detailed the interactions between salty and other tastes. Tian et al. compared the interactions of basic tastes using electronic and human tongues. However, most studies focused on qualitative descriptions of synergistic and antagonistic effects, lacking a detailed quantitative model to explain the variations in perceived intensity. This gap has motivated the current research to develop a comprehensive quantitative model.

The study employed sucrose and citric acid as model compounds representing sweet and sour tastes, respectively. Test samples were prepared using ultrapure water, with concentrations carefully controlled and listed in Supplementary Table 1 and 2. A sensory panel of 32 trained assessors (16 males, 16 females, aged 20–35) participated in the sensory evaluation. Assessors underwent two weeks of training to ensure consistent and reliable evaluations. The training covered sensory evaluation terminology (absolute and difference thresholds), basic taste distinction, triangle test and paired comparison methods, and taste intensity evaluation. **Absolute Threshold Sensory Analysis:** The absolute threshold was determined using the triangle test method, adapted from previous work by Mao et al. The absolute threshold of sucrose was assessed under different citric acid concentrations, and vice-versa for citric acid under varying sucrose concentrations. **Difference Threshold Sensory Analysis:** The difference threshold was determined using the paired comparison method, also adapted from previous work by Mao et al. Difference thresholds of sucrose were evaluated under various citric acid backgrounds, and vice-versa for citric acid under varying sucrose backgrounds. **Sweet-Sour Taste Sensory Strength Variation Models (SSTVM) Establishment:** Sensory difference strength curves were plotted using absolute and difference thresholds as the x-axis and sensory difference strength as the y-axis. Equations were derived to describe the variation in absolute thresholds and Weber fractions under different background concentrations. The Weber-Fechner law was used to establish the SSTVM for both sucrose (sweetness) and citric acid (sourness). **SSTVM Verification:** The model's accuracy was validated using additional sucrose and citric acid concentrations not used in model establishment. Human sensory evaluations were compared with model predictions using relative error and root mean squared error analyses.

The study found that citric acid significantly affected sucrose's perceived sweetness. Citric acid increased sucrose's absolute threshold, indicating a reduced ability to detect initial sweetness, and increased its Weber fraction, showing diminished sensitivity to changes in sucrose concentration. Conversely, sucrose influenced citric acid's perceived sourness. Sucrose increased citric acid's absolute threshold, reducing the detection of initial sourness, but it decreased citric acid's Weber fraction, enhancing sensitivity to changes in citric acid concentration. The researchers established two mathematical models: one for the sweetness of sucrose under varying citric acid concentrations and another for the sourness of citric acid under varying sucrose concentrations. These models, collectively termed SSTVM, accurately predicted human sensory perceptions of sweetness and sourness in sucrose-citric acid mixtures, demonstrating a high degree of accuracy (average relative error of 0.47% for sucrose and 1.56% for citric acid). The SSTVM provides quantitative relationships for the interaction of sweet and sour tastes, revealing how each compound modifies the perception of the other. The models confirm that the Weber-Fechner law applies to mixtures of sucrose and citric acid. The high correlation between model predictions and actual sensory evaluation data validated the applicability of the SSTVM.

The findings provide a quantitative description of sweet-sour taste interactions, filling a gap in current understanding. The SSTVM addresses the limitation of previous research that focused on qualitative trends instead of quantitative relationships. The results suggest that the interplay of sweet and sour taste receptors within taste buds, mediated by neurotransmitters, might underlie the observed interactive effects. The accurate prediction of sensory responses by the SSTVM demonstrates its potential as a valuable tool for food scientists and product developers. The SSTVM allows for precise calculations of perceived sweetness and sourness based on ingredient concentrations, providing guidance in formulating food and beverage products with desired sensory characteristics. This has significant implications for applications such as creating healthier food products (reducing sugar and acid levels while maintaining flavor), optimizing beverage formulations, and understanding the impact of diet on health outcomes.

This study successfully developed a quantitative model, the SSTVM, to describe the interactive effects of sweetness and sourness in sucrose-citric acid mixtures. The high accuracy of the model underscores its potential for applications in food science and technology, including optimizing food and beverage formulations and developing healthier products. Future research could explore the interactions of other taste combinations and investigate the underlying physiological mechanisms responsible for these interactions.

The study focused solely on the interaction of sucrose and citric acid. The generalizability of the SSTVM to other sweet and sour compounds requires further investigation. The sensory panel was composed of a specific demographic group, and cultural differences in taste perception might influence the results. Further research using larger and more diverse sensory panels is warranted to broaden the generalizability of the findings.