A volatile-based aroma complexity index for Nongxiangxing baijiu

Abstract

Aroma complexity is a comprehensive indicator for sensory evaluation of high-quality aromatic products, yet it traditionally relies on subjective assessment and remains difficult to estimate from objective chemical information. In this study, we developed a preliminary, chemistry-informed proxy framework to approximate aroma complexity in Nongxiangxing Baijiu by integrating odor-descriptor diversity, model-estimated odor persistence, and molecular structural complexity. The framework uses abundance-weighted chemical features to generate an interpretable volatile-based total aroma complexity index. Commercial Baijiu samples had calculated total aroma complexity index values of 438.69–513.57. The index values generally increased with manufacturer-declared product tier and revealed brand-dependent patterns. A small sensory evaluation subset showed a positive association between the index and expert-rated complexity, suggesting preliminary sensory relevance. This approach provides an interpretable way to summarize Nongxiangxing Baijiu volatile profiles from objective compositional information and may support exploratory comparative analysis within Baijiu systems, while requiring broader validation before industrial application.

Graphical abstract

Highlights

• •A volatile-based proxy index was developed for aroma complexity in Chinese Nongxiangxing Baijiu.
• •The index integrates predicted descriptors diversity, predicted persistence, and molecular complexity.
• •Brand-specific patterns varied across manufacturer-declared tiers.
• •A small-sample sensory comparisons suggested a preliminary positive association.

1. Introduction

Aroma perception in flavor products arises from mixtures of aroma molecules (Ma et al., 2025; Thomas-Danguin et al., 2014) and is often described by notes such as floral, fruity, roasted, or smoky (Doty, 2025). Beyond these specific descriptors, aroma evaluation has increasingly considered holistic attributes that describe the overall sensory profile of a product (Malfeito-Ferreira, 2023). Aroma complexity is one such attribute. Although it lacks a universal definition, it is widely used in evaluating premium products like wine, coffee, tea, and distilled spirits (Palczak et al., 2019; Q. J. Wang & Spence, 2018). In practice, it is often linked to the diversity and temporal development of aroma perception (Spence & Wang, 2018; Q. J. Wang et al., 2021). However, its assessment relies mainly on sensory scoring (Palczak et al., 2020; Pierguidi et al., 2019; Schlich et al., 2015), which is difficult to standardize due to the lack of reference anchors (Palczak et al., 2019). While chemical analysis offers a more objective basis, simple compound counts or concentrations are insufficient (Spence & Wang, 2018). An objective, reproducible, and interpretable chemistry-informed approach is therefore needed.

Recent advances in flavor chemistry and olfactory science have improved our understanding of aroma compounds and their sensory functions (Barabási et al., 2020). Molecular structure can be mapped onto perceptual odor space to predict odor descriptors from molecular graphs (Lee et al., 2023), and structurally more complex odorants tend to evoke a broader range of descriptors (Kermen et al., 2013). These findings suggest that molecular structure encodes information relevant to odor perception and can provide a basis for structure-derived aroma attributes. For aroma complexity, such information may capture odor-quality diversity, the expected persistence of odorants, and structural richness across a volatile profile. Information-theoretic metrics, such as Shannon entropy, can then provide an objective way to summarize diversity and balance in compositional or sensory-response distributions (Sturtewagen et al., 2025). We therefore hypothesized that aroma complexity can be approximated by integrating chemistry-derived, perception-relevant information from volatile compounds.

To test this hypothesis, Chinese Baijiu provides a suitable model system because its aroma is generated by a large and diverse set of volatile compounds formed during solid-state fermentation, distillation, and aging (Fang et al., 2018). Previous Baijiu flavor studies have mainly focused on compound identification, aroma-active screening, and compound–sensory attribution (Qia et al., 2023; L. Wang et al., 2024; Zhang et al., 2025), leaving aroma complexity rarely quantified and its link to compound-level interpretation undefined. In Baijiu evaluation, aroma complexity is a salient quality attribute, commonly expressed through sensory impressions of richness, layering, and persistence (China National Research Institute of Food and Fermentation Industries et al., 2016). Among Baijiu styles, Nongxiangxing Baijiu (strong-aroma-type Baijiu) has a particularly rich and representative aroma profile (Hong et al., 2023), making it an appropriate test bed for examining whether chemical information can be translated into an interpretable aroma-complexity index. Unlike cross-style comparisons, in which differences may largely reflect broad compositional and stylistic variation (Fang et al., 2018), within-style comparison examines products sharing a common aroma style and characteristic compounds but differing in perceived richness, layering, and persistence. This setting requires a profile-level index beyond the identification of key odorants.

In this study, we used Nongxiangxing Baijiu as a proof-of-concept system to evaluate a composition-based framework for characterizing aroma complexity from objective compositional data. Here, aroma complexity is operationally defined as the abundance-weighted integration of odor-descriptor diversity, model-estimated odor persistence, and molecular structural complexity across the volatile profile. This framework supports exploratory, comparative profiling of aroma-related chemical complexity in Baijiu under consistent analytical and computational conditions, and may inform future quantification of holistic aroma-related sensory concepts beyond individual-compound descriptions. It is not intended as an industrially-validated practical application. The novelty of this work lies in translating compound-level volatile information into a profile-level aroma complexity index that jointly accounts for odor-quality diversity, persistence, and molecular structural complexity.

2. Materials and methods

2.1. Chemicals and reagents

All analytical reagents and internal standards (ISs) were of GC grade and were supplied by Sigma-Aldrich Co., Ltd. (Shanghai, China) or Aladdin Co., Ltd. (Shanghai, China), as detailed in Supplementary Table 1. Sodium chloride (NaCl), anhydrous sodium sulfate (Na₂SO₄), as well as HPLC-grade ethanol, dichloromethane, methanol, pentane, ethyl acetate and acetone were purchased from China National Pharmaceutical Group Co., Ltd. (Shanghai, China). Ultrapure water was produced using a Milli-Q system (Millipore, Billerica, MA, USA).

2.2. Baijiu samples

A total of 21 commercial Nongxiangxing Baijiu samples (52% vol) were obtained from eight representative Chinese brands (NXX1–NXX8). Brands and products were selected based on market presence, coverage of major producing regions, and the availability of two or three 52% vol products spanning distinct within-brand commercial tiers. Thus, the sample set provided industry-relevant geographic and commercial coverage but was exploratory and was not intended to represent the entire Nongxiangxing Baijiu market. Products were denoted H, M (where available), and L according to the manufacturer-declared high, middle, and low market positioning, respectively. In the Chinese Baijiu industry, these tiers are commonly associated with sensory attributes such as aroma richness, layering, and persistence, but were not treated as direct indicators of aroma complexity or overall product quality.

For brands containing three tiers, changes were examined along the H–M–L sequence. For brands containing two tiers, only H–L contrasts were assessed. Because tier definitions varied among producers, H, M, and L represented brand-specific commercial positioning rather than standardized quality grades. Accordingly, analyses and interpretations focused on within-brand comparisons, whereas cross-brand tier comparisons were not emphasized.

To provide a preliminary sensory reference for aroma complexity, six samples from six different brands were selected from the 21 Baijiu samples and evaluated by professional tasters under controlled conditions. The subset covered multiple manufacturer-declared commercial tiers and a broad expected range of aroma complexity. Because the primary aim was framework development rather than large-scale sensory validation, these samples were used only to examine the directional consistency between the proposed index and expert-rated complexity; they were not intended to provide a representative sensory dataset or support category-wide conclusions.

2.3. Quantitative analysis of aroma compounds

Candidate analytes were selected from quantitative and GC–O/GC–O–MS studies of Nongxiangxing Baijiu (Supplementary Table 1) based on clear chemical identity, authentic-standard availability, and analytical feasibility. Tentative or duplicate entries and compounds lacking reliable quantitative support were excluded.

Volatile aroma compounds were quantified using three complementary methods selected according to analyte abundance and physicochemical properties: direct-injection GC-FID for high-abundance compounds, HS-SPME–GC–MS for compounds requiring headspace enrichment, and DLLME–GC–MS or GC–MS/MS for compounds amenable to solvent extraction.

2.3.1. Sample preparation and extraction

Direct injection for GC-FID. Baijiu samples (1 mL) were spiked with 50 μL of a mixed internal-standard solution containing amyl acetate, tert-amyl alcohol, and 2-ethylbutanoic acid, and directly analyzed by GC-FID.

HS-SPME extraction for GC–MS. Headspace solid-phase microextraction (HS-SPME) was performed according to Feng et al. (2025). Baijiu samples were diluted with ultrapure water to an ethanol content of 10% vol. A 5 mL aliquot was placed in a 20 mL headspace vial containing 1.5 g NaCl and 20 μL mixed internal-standard solution (ethyl octanoate-d₁₅, phenethyl acetate-d₃, octanal-d₁₆, acetophenone-d₃, and isopropyl disulfide), and the vial was sealed with a PTFE/silicone septum. Extraction was performed using an MPS2 autosampler (Gerstel, Germany) with a DVB/CAR/PDMS fiber (2 cm, 50/30 μm; Supelco, USA). After equilibration at 50 °C for 5 min, extraction was performed at 50 °C and 400 r/min for 45 min, followed by desorption in the GC injector at 250 °C for 5 min.

Dispersive liquid-liquid microextraction for GC–MS and GC–MS/MS. Dispersive liquid–liquid microextraction was performed with reference to Feng et al. (2025). Baijiu sample (4 mL) was mixed with saline solution (16 mL, 300 g/L), ethyl acetate (2 mL), acetone (2 mL), and 20 μL mixed internal-standard solution (guaiacol-d₃, pivalic acid, α-terpineol-d₃, furfural-d₄, and 2-methylpyrazine-d₆). After stirring at 500 r/min for 10 min, the upper organic phase was collected and concentrated under nitrogen to 500 μL.

2.3.2. Instrumental analysis

GC-FID: High-abundance volatile compounds were quantified using an Agilent 7890 A GC-FID (Agilent Technologies, USA). Samples (1 μL) were injected at a split ratio of 20:1 onto a CP-WAX 57CB column (50 m × 0.25 mm i.d., 0.20 μm; Agilent, USA). Helium (≥99.999%) was used at 1.0 mL/min. The oven program was: 40 °C for 5 min; 40–65 °C at 2 °C/min; 65–75 °C at 3 °C/min; 75–140 °C at 8 °C/min; 140–200 °C at 15 °C/min; and 200 °C for 20 min. The injector and detector were maintained at 250 °C.

GC–MS: GC–MS analysis was performed using an Agilent 7890B GC coupled to an Agilent 5977B MSD (Agilent Technologies, USA) equipped with a DB-FFAP column (60 m × 0.32 mm i.d., 0.25 μm; Agilent, USA). Helium (≥99.999%) was used at 1.2 mL/min. Samples were injected in splitless mode at 250 °C. The oven program was: 45 °C for 2 min, 45–230 °C at 6 °C/min, and 230 °C for 25 min. For DLLME extracts, 1 μL was injected with an 8-min solvent delay. Mass spectra were acquired in EI full-scan mode (70 eV, m/z 35–350), with the ion source at 230 °C.

GC–MS/MS: GC–MS/MS determination was conducted using an Agilent 8890 gas chromatograph coupled to an Agilent 7000E triple quadrupole MS (Agilent Technologies, USA) with a DB-FFAP capillary column (60 m × 0.32 mm i.d., 0.25 μm film; Agilent, USA). Helium (≥99.999%) was used at 1.4 mL/min, and samples were injected in splitless mode at 250 °C. The oven temperature program was: 40 °C (2 min), ramp to 150 °C at 4 °C/min, then to 230 °C at 6 °C/min, followed by a final hold at 230 °C for 15 min. The EI source was operated at 70 eV, with source and quadrupole temperatures of 230 and 150 °C, respectively. Nitrogen collision gas and helium quench gas were used at 1.5 and 2.24 mL/min, respectively. Quantification was performed in MRM mode using compound-specific transitions and optimized collision energies; quantifier and qualifier ions are listed in Supplementary Table 2 and 3.

2.3.3. Compound identification, quantification, and method performance

GC-FID analytes were identified by retention-time matching with authentic standards. GC–MS identification was based on retention indices and mass spectra matched against authentic standards, whereas GC–MS/MS identification required agreement in retention time, MRM transitions, and ion ratios.

For all methods, calibration standards were prepared in 52% vol ethanol, spiked with the relevant internal standards, and subjected to the same sample-preparation procedures as the corresponding Baijiu samples. For HS-SPME, standards were diluted to 10% vol ethanol before extraction. Twelve calibration levels were prepared by serial two-fold dilution, and calibration curves were constructed from analyte-to-internal-standard peak-area ratios.

Method performance was evaluated by calibration linearity and spiked-sample recoveries. Limits of detection (LOD) and quantification (LOQ) were determined based on signal-to-noise ratios of 3 and 10, respectively, and are summarized in Supplementary Tables 2 and 3. Analyte-specific calibration ranges spanned 0.06–2.57 × 10⁶ μg/L; R² values ranged from 0.9131 to 1.0000, and recoveries ranged from 80.1% to 129.6%. Concentrations in the original Baijiu samples were calculated using internal-standard-corrected calibration curves because calibration standards underwent the same relevant preparation procedures. Compounds with concentrations below the LOD were assigned a value of zero for subsequent data processing.

2.4. Overview of the chemistry-informed aroma complexity characterization framework

This study developed a chemistry-informed framework to estimate aroma complexity in Nongxiangxing Baijiu based on quantified volatile composition, predicted odor descriptors, predicted odor persistence, and molecular structural features. These features were organized into three complementary and analytically accessible proxy dimensions: functional, temporal, and structural complexity.

The functional dimension describes the breadth and distribution of volatile compounds in predicted odor-descriptor space and was used as a proxy for qualitative aroma diversity. The temporal dimension quantifies the overall odor persistence contribution of all volatile compounds based on their predicted odor persistence values, serving as a proxy for the lingering sensory character inherent to complex aroma profiles. The structural dimension characterizes the molecular architectural richness of volatile compounds. Although structural complexity is not a sensory measure itself, it was included because molecular structure may constrain odor perceptual space.

As shown in Supplementary Fig. 1, volatile compounds were first identified and quantified by instrumental analysis. Compound-level features were then extracted, normalized, and converted into dimension-specific scores. These scores were aggregated at the sample level using log-transformed concentrations (original unit: μg/L) as weights, generating Total Functional Complexity Contribution (TFCC), Total Odor Persistence Contribution (TOPC), and Total Molecular Complexity Contribution (TMCC). The three indices were combined by equal-coefficient summation to generate the Total Aroma Complexity Index (TACI). An exploratory expert sensory comparison was subsequently used to assess the directional consistency between TACI and expert-rated aroma complexity.

Accordingly, TFCC, TOPC, TMCC, and TACI should be interpreted as chemistry-informed proxies for different aspects of aroma complexity rather than as direct measurements of perceived aroma complexity. Detailed calculations for the three dimensions are described in the following sections.

2.5. Computational odor descriptor analysis and calculation of the descriptor-based Total functional complexity contribution (TFCC)

Odor descriptor profile of each compound was predicted using the principal odor map model of Lee et al. (2023), implemented in the OpenPOM framework. Molecular structures were supplied as SMILES strings, the pretrained MPNN-POM model generated sigmoid probability outputs for 138 odor descriptors.

As a database-consistency check, the ten highest-probability predictions for each compound were compared with standardized odor annotations retrieved from the Good Scents database (Supplementary Table 4). The compound-level match rate was defined as the proportion of compounds for which at least one database annotation occurred among the ten highest-ranked predictions. Descriptor recovery was defined as the mean within-compound proportion of database annotations recovered among these predictions. The corresponding values were 99.29% and 66.93%, respectively. This comparison was used only as a descriptive consistency check and did not constitute independent sensory validation of OpenPOM. OpenPOM was used as a pretrained black-box model; thus, its outputs may not fully translate to odor perception in complex Baijiu matrices.

For descriptor-based Total Functional Complexity Contribution (TFCC) calculation, the 138 predicted odor descriptors were aggregated into 12 broader semantic aroma categories: fruity, floral, vegetal, woody, sweet/milky, baked, alcoholic, chemical, animal, spicy, herbal, and overall sensory. Aggregation reduced redundancy among semantically similar descriptors, thereby avoiding their treatment as fully independent dimensions when calculating distributional complexity. Each descriptor was assigned to one primary category to avoid repeated assignment during TFCC calculation. The grouping was guided by semantic similarity and aroma interpretability, consistent with higher-order organization of complex aroma lexicons in sensory research (Lawrence et al., 2013; Souza Gonzaga et al., 2020). The complete descriptor-to-category mapping is provided in Supplementary Table 5. Accordingly, TFCC is a heuristic, study-specific index whose values depend on this operational 12-category taxonomy, rather than an established universal criterion of aroma complexity.

Let $y_{\mathit{kj}}$denote the OpenPOM-predicted sigmoid probability of odor descriptor k for compound j (k = 1, 2, …, 138). For each aroma category i, the category-level descriptor activation of compound j was calculated according to Eq. (1):

$$p_{\mathit{ij}}=\sum _{k\in D_i}{y}_{\mathit{kj}}\#\left(1\right)$$

Here, $D_i$ denotes the set of descriptors assigned to category i, where i = 1, 2, …, 12. The relative distribution of predicted odor information across the 12 aroma categories was then normalized within each compound according to Eq. (2):

$$\begin{array}{c}{r}_{\mathit{ij}}=\frac{p_{\mathit{ij}}}{{\sum }_{i=1}^{12}{p}_{\mathit{ij}}}\#\left(2\right)\end{array}$$

The descriptor distribution entropy of compound j was calculated according to Eq. (3):

$$\begin{array}{c}{H}_j^{\mathit{dist}}=-\sum _{i=1}^{12}{r}_{\mathit{ij}}{\mathit{log}}_2\left(r_{\mathit{ij}}\right)\#\left(3\right)\end{array}$$

Terms with $r_{\mathit{ij}}$= 0 were set to zero. This entropy represents the evenness of the predicted descriptor distribution across the 12 semantic categories.

The mean predicted probability across the 138 descriptors, $S_j$ was calculated according to Eq. (4):

$$\begin{array}{c}{S}_j=\frac{{\sum }_{k=1}^{138}{y}_{\mathit{kj}}}{138}\#\left(4\right)\end{array}$$

The binary entropy of the mean descriptor probability was then calculated according to Eq. (5):

$$\begin{array}{c}{H}_j^{\mathit{cov}}=-\left[S_j{\mathit{log}}_2{S}_j+\left(1-S_j\right){\mathit{log}}_2\left(1-S_j\right)\right]\#\left(5\right)\end{array}$$

Terms with $S_j$ = 0 or $S_j$ = 1 were defined as zero. Thus, $H_j^{\mathit{dist}}$ and $H_j^{\mathit{cov}}$ represented complementary aspects of predicted odor-descriptor complexity, namely distributional evenness and the global mean descriptor-probability level, respectively.

For comparable scaling, both entropy terms were min–max normalized across the target volatile compounds and rescaled to 0–0.5 according to Eqs. (6) and (7):

$$\begin{array}{c}{H}_j^{\mathit{dist}\ast }=\frac{H_j^{\mathit{dist}}-\mathit{min}\left(H^{\mathit{dist}}\right)}{\mathit{max}\left(H^{\mathit{dist}}\right)-\mathit{min}\left(H^{\mathit{dist}}\right)}\times 0.5\#\left(6\right)\end{array}$$

$$\begin{array}{c}{H}_j^{\mathit{cov}\ast }=\frac{H_j^{\mathit{cov}}-\mathit{min}\left(H^{\mathit{cov}}\right)}{\mathit{max}\left(H^{\mathit{cov}}\right)-\mathit{min}\left(H^{\mathit{cov}}\right)}\times 0.5\#\left(7\right)\end{array}$$

The compound-level functional complexity score was then defined as in Eq. (8):

$$\begin{array}{c}{\mathit{FC}}_j=H_j^{\mathit{dist}\ast }+H_j^{\mathit{cov}\ast }\#\left(8\right)\end{array}$$

For each Baijiu sample, TFCC was calculated by concentration-weighted aggregation according to Eq. (9):

$$\begin{array}{c}\mathit{TFCC}=\sum _{j=1}^n\left[{\mathit{log}}_{10}\left(C_j+1\right)·{\mathit{FC}}_j\right]\#\left(9\right)\end{array}$$

Here, n is the number of quantified aroma compounds in the sample, $C_j$ is the measured concentration of compound j in μg/L, and ${\mathit{FC}}_j$ is its functional complexity score. Non-detected compounds were handled according to the data-processing procedure described above. The logarithmic transformation reduced the influence of highly abundant compounds while retaining their contribution to sample-level descriptor complexity.

2.6. Calculation of the predicted Total odor persistence contribution (TOPC)

To characterize the persistence-related temporal dimension of Baijiu aroma, a predicted Total Odor Persistence Contribution (TOPC) was calculated for each sample. Here, odor persistence denotes the relative odor-longevity potential of an individual volatile compound. TOPC therefore represents a concentration-weighted proxy for predicted odor-persistence potential.

Persistence values were predicted using a machine-learning model trained on a curated public fragrance dataset compiled primarily from Perfumery Techniques, 2nd ed. (Lin, 2008), which adopted the historical 1–100 relative-persistence scale of Poucher (1959). In this study, these values are treated as empirical relative odor-longevity indices from fragrance references, independent of odor-threshold measurements.

Molecular structures were standardized from SMILES using RDKit and represented by six physicochemical descriptors—molecular weight, logP, topological polar surface area, hydrogen-bond donor and acceptor counts, and rotatable-bond count—together with a 2048-bit Morgan fingerprint (radius 3) and graph-based atom and bond features.

A hybrid PyTorch/DGL model combined a two-layer graph attention network with a multilayer perceptron for descriptor-based features. The concatenated representations were used for regression after log(1 + x) transformation of the target values. Model optimization was performed using AdamW for 300 epochs with a batch size of 32, and a sample-weighted L1 loss was used to improve sensitivity to compounds with extreme persistence values. Five-fold random cross-validation yielded an average MAE of 5.43 and an R² of 0.93 on the source dataset. Because random-split validation may provide optimistic estimates relative to scaffold-based validation or external validation, these results should be interpreted as internal validation performance.

Fold-specific models were used to predict persistence for Baijiu volatile compounds, and the predictions were averaged across models. Values were constrained to 1–100 and normalized to 0–1, denoted as $F_j^{\ast }$. For each Baijiu sample, the TOPC was calculated according to Eq. (10):

$$\begin{array}{c}\mathit{TOPC}=\sum _{j=1}^n\left[{\mathit{log}}_{10}\left(C_j+1\right)·F_j^{\ast }\right]\#\left(10\right)\end{array}$$

Here, n is the number of target volatile compounds, $C_j$ is the concentration of compound j in the Baijiu sample (μg/L), and $F_j^{\ast }$ is its normalized predicted persistence value. TOPC thus integrates compound abundance and predicted odor-longevity potential as a concentration-weighted proxy for the persistence-related temporal dimension of aroma complexity.

Because the predictions were generated by a fragrance-domain model rather than measured under Baijiu-specific sensory conditions, TOPC was interpreted as a theoretical model-derived descriptor, not a direct measure of Baijiu aroma persistence.

2.7. Calculation of the composite Total molecular complexity contribution (TMCC)

To characterize the structural dimension of aroma complexity, an integrated molecular complexity score was calculated for the volatile compounds quantified in Baijiu. Molecular complexity here refers to structural features such as atom connectivity, branching, ring systems, heteroatom composition, topological arrangement, and three-dimensional structural richness. The compound-level scores were subsequently used to estimate the Total Molecular Complexity Contribution (TMCC) of each sample.

Four established molecular complexity metrics were jointly used: SCScore (Coley et al., 2018), CM and Cse (Proudfoot, 2017), and Spacial-Score (nSPS) (Krzyzanowski et al., 2023). Scores were computed from SMILES using RDKit: SCScore was obtained using the pretrained 1024-bit binary Morgan-fingerprint model (radius 2), whereas CM/Cse and nSPS were calculated using the published atom-environment and atom-level algorithms, respectively. SCScore primarily reflects synthetic or architectural elaboration learned from chemical reaction data, CM and Cse describe constitution- and topology-related complexity features, and nSPS emphasizes three-dimensional and stereochemical richness. These metrics were combined to obtain a broader structure-based representation of molecular complexity than would be provided by any single descriptor.

For each compound, the raw values of SCScore, CM, Cse, and nSPS were separately normalized across all quantified compounds using min-max scaling. Because no validated basis is currently available for assigning differential importance to these complementary structural dimensions in Baijiu, equal weighting was used as a transparent baseline. Each normalized metric was therefore rescaled to 0–0.25, giving all four metrics an identical maximum contribution, preventing dominance due to numerical scale, and constraining their summed score to 0–1 for comparability with the functional and temporal component scores, as shown in Eq. (11):

$$\begin{array}{c}{X}_j^{\ast }=\frac{X_j-\mathit{min}\left(X\right)}{\mathit{max}\left(X\right)-\mathit{min}\left(X\right)}\times 0.25\#\left(11\right)\end{array}$$

Here, $X_j$ is the raw value of a given molecular complexity metric for compound j, and min(X) and max(X) are its minimum and maximum values across all quantified compounds.

The normalized metrics were summed to obtain the integrated molecular complexity score according to Eq. (12):

$$\begin{array}{c}{M}_j^{\ast }={\mathit{SC}}_j^{\ast }+{\mathit{CM}}_j^{\ast }+{\mathit{Cse}}_j^{\ast }+{\mathit{nSPS}}_j^{\ast }\#\left(12\right)\end{array}$$

In Eq. (12), ${\mathit{SC}}_j^{\ast }$, ${\mathit{CM}}_j^{\ast }$, ${\mathit{Cse}}_j^{\ast }$, and ${\mathit{nSPS}}_j^{\ast }$ are the normalized SCScore, CM, Cse, and Spacial-Score values, respectively. This equal-weight integration is an operational choice rather than a claim that the four metrics are intrinsically equally important; alternative weighting schemes require future validation.

For each Baijiu sample, TMCC was estimated according to Eq. (13):

$$\begin{array}{c}\mathit{TMCC}=\sum _{j=1}^n\left[{\mathit{log}}_{10}\left(C_j+1\right)·M_j^{\ast }\right]\#\left(13\right)\end{array}$$

Here, $n$ is the number of aroma compounds in the sample, $C_j$ is the concentration of compound j (μg/L), and $M_j^{\ast }$ is its integrated structural complexity score. Consistent with TFCC and TOPC, concentration was log-transformed to reduce the disproportionate influence of highly abundant compounds. TMCC should thus be interpreted as a structure-derived proxy for the molecular dimension of aroma complexity rather than a direct measure of perceived complexity.

2.8. Derivation of the chemistry-informed Total aroma complexity index (TACI)

To obtain a sample-level chemistry-informed aroma complexity index, the three complementary dimensions defined in this study were integrated into a single composite index. Specifically, the functional, temporal, and structural dimensions were represented by the Total Functional Complexity Contribution (TFCC), Total Odor Persistence Contribution (TOPC), and Total Molecular Complexity Contribution (TMCC), respectively.

For each Baijiu sample, the Total Aroma Complexity Index (TACI) was calculated by equal-weight additive integration according to Eq. (14):

$$\begin{array}{c}\mathit{TACI}=\mathit{TFCC}+\mathit{TOPC}+\mathit{TMCC}\#\left(14\right)\end{array}$$

In this framework, TFCC reflects the diversity and balance of predicted odor-descriptor information, TOPC reflects the predicted temporal persistence of odor cues, and TMCC reflects the integrated structural richness of the volatile compounds present. Their additive integration was supported by a common log-transformed concentration-weighting scheme and normalization of the three compound-level scores to comparable ranges before sample-level aggregation.

TACI was developed as a provisional, chemistry-informed composite index intended to summarize these three dimensions, rather than as a validated predictive model of perceived aroma complexity. Equal unit coefficients (1:1:1) were used as a transparent, non-fitted baseline, rather than estimating dimension-specific coefficients from the limited sensory dataset. This equal-coefficient integration does not imply that the three dimensions make equal contributions to human aroma perception. At the compound level, all three component scores were calculated using log-transformed concentration weighting, thereby retaining concentration information while limiting the dominance of highly abundant compounds.

OAV weighting was not applied because matrix-matched odor-threshold data were not consistently available for the volatile compounds identified in Nongxiangxing Baijiu. Moreover, OAV-based weighting may overemphasize a small number of high-OAV compounds, thereby favoring odor intensity or key-odorant dominance over whole-profile complexity, while underrepresenting potentially relevant low-abundance or subthreshold compounds. Concentration-based weighting was therefore used as a practical and reproducible alternative. Although concentration-based weighting may still overrepresent abundant compounds with relatively weak odor potency, it was used as a practical and reproducible alternative in the absence of reliable matrix-matched threshold data.

Accordingly, TACI should be interpreted as an exploratory chemical proxy for relative comparison among samples analyzed under identical experimental, analytical, and computational conditions, rather than as a direct sensory measure of aroma complexity. Its absolute values should not be compared across studies employing different compound-identification procedures, concentration units, normalization methods, or predictive models. Future studies with larger independent sensory datasets should evaluate its sensory relevance and test alternative scaling, weighting, and non-additive integration strategies.

2.9. Expert sensory reference for aroma complexity

A panel of nine professional Baijiu tasters participated in the sensory assessment, including five males and four females aged 30–55 years. Each panelist had more than 8 years of experience in the sensory evaluation and grading of Nongxiangxing Baijiu. All panelists had received formal professional training and were routinely involved in commercial Baijiu quality evaluation.

Six representative Baijiu samples were selected from the 21 commercial Nongxiangxing Baijiu samples analyzed in this study for expert sensory comparison. The selected subset included one sample from each of six different brands. The samples were selected to span a broad range of calculated Total Aroma Complexity Index (TACI) values while maintaining a balanced representation of brand and commercial-level variation.

Aroma complexity was evaluated using a 9-point scale, where 1 indicated “extremely simple” and 9 indicated “extremely complex”. Before scoring, panelists were instructed to evaluate complexity as an overall perceptual attribute reflecting aromatic diversity, layering, harmony, and persistence rather than aroma intensity alone. Samples were presented under blind conditions using randomized three-digit codes. Each sample (15 mL) was served in standard Chinese Baijiu tasting glasses at 25 °C. The presentation order was randomized, and all panelists evaluated the samples independently in a controlled sensory environment, with each panelist assessing every sample in duplicate.

For each sample, an individual panelist's score was first averaged over the two replicate assessments. The final sensory complexity score for a sample was then calculated as the mean of these averaged scores across the nine panelists. These sample-level mean sensory scores were used as the expert sensory reference for comparison with the chemistry-informed TACI values.

The sensory evaluation protocol was reviewed and approved by the Institutional Review Board of Jiangnan University (JNU202409RB0032). Written informed consent was obtained from all panelists prior to participation.

2.10. Data analysis

Data were processed and visualized using Python (pandas, matplotlib), Origin 2020b, and R 4.4.0. Results are expressed as mean ± standard deviation from three parallel determinations. For each brand, commercial-tier differences were evaluated primarily within the brand using DPS 9.01. One-way analysis of variance (ANOVA) was performed with commercial tier as the grouping factor, followed by Duncan's new multiple range test for post-hoc comparisons. Tier comparisons were conducted within brands because commercial-tier labels were not standardized across brands and some brands included only two products. Statistical significance was defined as p < 0.05. Using Python's scipy.stats module, Spearman's rank correlation was used to evaluate pairwise associations among TFCC, TOPC, TMCC, and TACI. For the six sensory samples, Pearson's correlation and linear regression were used to examine the relationship between calculated TACI values and expert sensory complexity scores; Pearson correlation coefficients and corresponding p-values were calculated using scipy.stats.pearsonr. Given the small sample size (n = 6), these analyses were interpreted as exploratory associations rather than confirmatory evidence of predictive validity.

3. Results and discussion

3.1. Selection and quantification of aroma compounds

Following the literature-based and analytical eligibility criteria described in Section 2.3, 140 volatile compounds with potential aroma relevance were retained for quantitative analysis. It covered esters, alcohols, acids, aldehydes, terpenes, and other relevant classes. This targeted panel provided a representative and analytically accessible basis for aroma-complexity characterization, rather than an exhaustive inventory of all volatile or odor-active compounds in Nongxiangxing Baijiu.

GC-FID, GC–MS, and GC–MS/MS quantification revealed substantial concentration variation across the eight brands (Table 1). Esters and alcohols were generally the most abundant classes, whereas pyrazines, lactones, and sulfur-containing compounds generally occurred at lower concentrations. This compositional pattern is broadly consistent with previous quantitative characterizations of Nongxiangxing Baijiu (Feng et al., 2025; Huang et al., 2026). Nevertheless, the inclusion of lower-abundance volatiles broadened the functional and structural coverage required for profile-level complexity analysis.

Table 1.

Concentration ranges (minimum-maximum, μg/L) of 140 aroma compounds in eight brands of Nongxiangxing Baijiu. For each brand, the values represent the range observed across different quality grades of samples.

These data were subsequently used to calculate TFCC (Section 3.2), TOPC (Section 3.3), TMCC (Section 3.4), and the composite TACI (Section 3.5).

3.2. Total functional complexity contribution of Nongxiangxing baijiu samples

The model described in Section 2.5 generated 138-descriptors prediction profiles for the quantitatively identified volatile compounds in Nongxiangxing Baijiu. TFCC was derived by integrating these model-predicted semantic attributes with experimentally measured concentrations through concentration weighting. PCA was performed on the 140 compounds using their 138-dimensional predicted descriptor profiles to visualize their relative positions and overall relationships in the predicted odor-descriptor space (Fig. 1). PC1 and PC2 explained 24.4% and 19.2% of the variance, respectively, whereas the first six components cumulatively explained 76.17%, indicating that the the heterogeneous predicted profiles could not be adequately represented in two dimensions.

Fig. 1.

Exploratory PCA biplot of OpenPOM-predicted odor descriptor profiles for volatile compounds in Nongxiangxing Baijiu. Grey triangles represent volatile compounds, and colored descriptor labels represent predicted odor descriptors grouped into 12 semantic aroma categories. Colors indicate the assigned aroma groups of the descriptors. PC1 and PC2 explain 24.4% and 19.2% of the total variance, respectively, together accounting for 43.6%. The biplot is therefore intended as an exploratory two-dimensional visualization of the predicted descriptor space, rather than a complete representation of descriptor variation.

The 138 descriptors were further aggregated into 12 semantic categories, and compound-level functional complexity scores were calculated by integrating the distribution characteristics and overall predicted levels of odor descriptors, following the procedure described in Section 2.5. These scores were then weighted by log-transformed concentrations and summed to obtain the total functional complexity contribution (TFCC) of each sample (Fig. 2, Fig. 3).

Fig. 2.

Concentration-weighted distribution of OpenPOM-predicted odor descriptor probabilities across 12 broad aroma categories in Nongxiangxing Baijiu samples. The 138 OpenPOM-predicted odor descriptors were aggregated into 12 semantic aroma categories: fruity, floral, vegetal, woody, sweet/milky, baked, alcoholic, chemical, animal, spicy, herbal, and overall sensory. Bubble size represents the relative proportion (%) of concentration-weighted predicted descriptor probability assigned to each aroma category within each sample. Panels and colors distinguish sample series. In the sample codes, NXX denotes Nongxiangxing Baijiu, the number indicates the sample series or brand, and H, M, and L indicate high-, medium-, and low-grade products, respectively.

Fig. 3.

Total functional complexity contribution (TFCC) at the sample level in Nongxiangxing Baijiu. TFCC represents the concentration-weighted diversity and distribution of predicted odor activity across 12 semantic aroma categories. TFCC values are shown for different Nongxiangxing Baijiu samples and are expressed as mean ± standard deviation from three parallel determinations. Within each brand, bars not sharing a common letter differ significantly according to one-way ANOVA followed by Duncan's new multiple range test (p < 0.05); letters are not comparable between brands. The broken y-axis is used to facilitate visualization of differences among samples. In the sample codes, NXX denotes Nongxiangxing Baijiu, the number denotes the brand, and H, M, and L denote manufacturer-declared high-, medium-, and low-tier products, respectively.

Across the 21 commercial samples, TFCC values ranged from approximately 199 to 232, with the highest values observed in NXX1-H (231.69) and the lowest in NXX6-L (198.99), indicating substantial between-sample variation in concentration-weighted descriptor complexity. At the category level, most samples were dominated by Sweet/Milky, Alcoholic, and Fruity dimensions. However, higher TFCC was also associated with elevated concentration-weighted contributions from predicted Woody, Floral, Vegetal, and Herbal descriptors. For example, in NXX1, the increase in TFCC from L to M to H was accompanied by coordinated increases in Woody (0.05, 0.07, and 0.09), Floral (0.09, 0.11, and 0.12), Herbal (0.34, 0.37, and 0.39), and Fruity (0.54, 0.58, and 0.60). By contrast, the NXX6 series, which showed the lowest TFCC values, also exhibited markedly compressed category-level contributions, particularly for Woody and Floral dimensions.

From a brand-level perspective, TFCC was broadly consistent with the manufacturer-declared commercial tier. Among the eight brands investigated, six showed an increasing trend in TFCC with increasing product tier, and five of these exhibited a clear monotonic increase from lower- to higher-tier products (NXX1, NXX2, NXX3, NXX6, and NXX8). NXX4 generally followed the same trend, although the difference between the middle- and low-tier samples was minimal. In contrast, NXX5 did not show a monotonic pattern, and NXX7 showed an inverse trend, with the low-tier sample exhibiting the highest TFCC within the brand.

The above results describe TFCC patterns calculated from measured volatile concentrations and predicted odor descriptors; they do not constitute direct sensory measurements of perceived aroma complexity. The dominance of Sweet/Milky, Alcoholic, and Fruity categories in the TFCC profiles is consistent with the typical sensory profile of Nongxiangxing Baijiu reported previously (Hong et al., 2023; Xiangli et al., 2024). Within the present framework, the higher TFCC values observed in some samples indicate that their measured volatile profiles were distributed across a broader or more balanced set of predicted odor-semantic categories. This pattern was not limited to the major Sweet/Milky, Alcoholic, and Fruity dimensions, but also involved secondary categories such as Woody, Floral, Vegetal, and Herbal.

This interpretation is consistent with previous studies on aroma complexity in alcoholic beverages. Premium wines have been reported to exhibit multidimensional aroma structures involving secondary notes such as spicy and toasted characteristics rather than simple dominance of a single aroma family (Picard et al., 2015; Q. J. Wang & Spence, 2019). Similarly, enhanced expression of compounds related to woody or herbal aroma characteristics has been observed during Baijiu aging in Jiuhai containers (Feng et al., 2025). Together, these findings support the view that increased aroma complexity is associated with diversification of secondary aroma dimensions within the volatile-composition-derived odor-semantic profile. Importantly, however, the tier-associated TFCC patterns observed for several brands should not be interpreted as evidence of an inherent or universally higher aroma complexity of higher-tier products, as they may also reflect brand-specific production and positioning strategies that influence volatile composition.

Previous profile-level approaches have addressed either compositional balance or sensory descriptor differentiation in Baijiu. The composition evenness index reflects the relative abundance distribution of volatile compounds (Liu et al., 2023) but does not consider their odor-semantic functions. In contrast, RATA-based sensory evaluation captures actual descriptor patterns perceived by assessors and has shown that Nongxiangxing Baijiu samples can be differentiated within the same aroma style (Xiangli et al., 2024). TFCC is distinct from both approaches because it integrates compound concentrations with the distribution and overall level of model-predicted odor descriptors. Accordingly, higher TFCC values indicate greater concentration-weighted descriptor complexity, reflecting more even semantic-category distributions and/or higher overall predicted descriptor probabilities within the volatile profile. TFCC should therefore be interpreted as a concentration-weighted, descriptor-based representation of volatile-profile complexity.

3.3. Total odor persistence contribution of Nongxiangxing baijiu samples

Following the procedure in Section 2.6, model-predicted odor-persistence values were used to characterize the temporal properties of the quantitatively identified volatile compounds in Nongxiangxing Baijiu. These fragrance-domain-derived predictions provide relative, rather than absolute, persistence estimates and were used as compound-level attributes in the concentration-weighted TOPC calculation. Taking sample NXX1-H as an example (Fig.4-A), compounds spanning multiple chemical classes distribute across a broad concentration-persistence space; higher model-predicted persistence values do not correspond to the highest measured concentrations. Concentration-weighted sample-level contributions were then summarized as total odor persistence contribution (TOPC) (Fig.4-B).

Fig. 4.

Predicted odor persistence and total odor persistence contribution (TOPC) at the compound and sample levels in Nongxiangxing Baijiu. TOPC represents the concentration-weighted contribution of predicted odor persistence. (A) Relationship between predicted odor persistence and normalized compound content in sample NXX1-H. Each point represents one volatile compound, and its color and symbol indicate the corresponding chemical class. The colored vertical lines below the scatter plot indicate the predicted persistence values of individual compounds, whereas the colored horizontal lines to the left indicate their normalized contents in NXX1-H. Compounds toward the upper-right region have both relatively high predicted persistence and high normalized content. (B) TOPC values of different Nongxiangxing Baijiu samples. Values are expressed as mean ± standard deviation from three parallel determinations. Within each brand, bars not sharing a common letter differ significantly according to one-way ANOVA followed by Duncan's new multiple range test (p < 0.05); letters should not be compared across brands. The broken y-axis is used to facilitate visualization of differences among samples. In the sample codes, NXX denotes Nongxiangxing Baijiu, the number denotes the brand, and H, M, and L denote manufacturer-declared high-, medium-, and low-tier products, respectively.

Compounds with high predicted persistence, represented by normalized odor-persistence scores ≥0.50, were mainly distributed among medium-chain fatty acids and their esters, lactones, aromatic aldehydes and related acetals, phenolic compounds, terpenoid alcohols, and selected ketones (Supplementary Table 6). Representative compounds included octanoic acid, decanoic acid, ethyl pelargonate, ethyl caprylate, ethyl caprate, isopentyl octanoate, β-damascenone, oaklactone, γ-decalactone, γ-nonalactone, vanillin, 4-methylguaiacol, cedrol, and others. These compounds were associated with fruity, creamy, woody, sweet, roasted, and floral odor qualities, showing that compounds assigned relatively high predicted persistence values covered multiple chemical classes and odor categories.

At the sample level, TOPC showed partial correspondence with manufacturer-declared commercial tier, although the relationship was not universal. Across NXX1–NXX5, the high-tier product had the highest TOPC within each brand, with a monotonic increase across tiers observed in several brands. In contrast, this trend was weak in NXX6 and NXX8, and absent in NXX7, where the middle-tier product showed the highest TOPC. Thus, the observed relationship between TOPC and commercial tier differed among brands.

Within the fragrance-derived relative-persistence framework, compounds with lower persistence values are associated mainly with early aroma impressions, whereas those with higher values may have greater potential to contribute to lingering perceptions (Lin, 2008). This temporal distinction is conceptually relevant to empty-cup aroma in Baijiu, which is closely associated with fragrance persistence and is generally more persistent in aged Baijiu (Liu et al., 2026). The high-persistence predictions partly agreed with previous Baijiu empty-cup aroma studies: octanoic acid, decanoic acid, benzeneacetic acid, γ-nonalactone, and ethyl hydrocinnamate were predicted as relatively persistent here and have also been reported in persistent empty-cup aroma (Liu et al., 2026; Qin et al., 2024; Qin et al., 2026). Because these compounds represent medium-chain fatty acids, aromatic acids/esters, and lactones, this overlap suggests that the predicted high-persistence compounds are consistent with the major compound types reported in empty-cup aroma studies. Nevertheless, this overlap should be regarded as supporting consistency rather than sensory validation, because odorant persistence in Baijiu may also be affected by matrix effects, such as lactic-acid-mediated modulation of volatile release (Liu et al., 2026).

Sample-level results show that higher-tier products from several brands exhibit larger concentration-weighted contributions from compounds with high model-predicted persistence values. However, non-monotonic patterns among NXX6–NXX8 demonstrate that this association does not hold across all brands. Importantly, TOPC should therefore be interpreted as a persistence-oriented compositional index based on measured volatile concentrations and model-predicted relative persistence, not as a direct measure of sensory persistence or overall aroma quality.

3.4. Structural complexity based on molecular complexity indices

To characterize the concentration-weighted structural complexity of the identified volatile composition, integrated molecular complexity scores were calculated for the identified volatile compounds following the procedure described in Section 2.7. These structure-derived scores served as compound-level attributes for TMCC calculation, providing a structural perspective on volatile-profile complexity rather than a sensory-complexity measurement. As illustrated in Fig. 5-A, using NXX1-H as an example, higher molecular complexity values were concentrated in a limited subset of compounds, particularly terpenes, lactones, phenolic compounds, and related aromatic compounds, rather than in the numerically dominant ester fraction. The concentration-weighted contributions were subsequently summarized at the sample level as TMCC (Fig. 5-B). TMCC ranged from 134.88 to 159.52, with the highest value observed in NXX4-H and the lowest in NXX6-L, indicating substantial between-sample variation in the concentration-weighted structural complexity of volatile composition.

Fig. 5.

Integrated structural complexity and total molecular complexity contribution (TMCC) at the compound and sample levels in Nongxiangxing Baijiu. TMCC represents the concentration-weighted contribution of integrated molecular structural complexity. (A) Relationship between integrated structural complexity scores ($M_j^{\ast }$) and normalized compound content in sample NXX1-H. Each point represents one volatile compound, and its color and symbol indicate the corresponding chemical class. The colored vertical lines below the scatter plot indicate the integrated structural complexity scores of individual compounds, whereas the colored horizontal lines to the left indicate their normalized contents in NXX1-H. Compounds toward the upper-right region have both relatively high integrated structural complexity scores and high normalized content. (B) TMCC values of different Nongxiangxing Baijiu samples. Values are expressed as mean ± standard deviation from three parallel determinations. Within each brand, bars not sharing a common letter differ significantly according to one-way ANOVA followed by Duncan's new multiple range test (p < 0.05); letters should not be compared across brands. The broken y-axis is used to facilitate visualization of differences among samples. In the sample codes, NXX denotes Nongxiangxing Baijiu, the number denotes the brand, and H, M, and L denote manufacturer-declared high-, medium-, and low-tier products, respectively.

Compound-level scores were relatively high for terpenes, terpenoid alcohols, lactones, phenolic compounds, and selected aromatic compounds (Supplementary Table 6). These compounds generally contain ring systems, branching patterns, multiple functional groups, or stereochemical features, and therefore contribute disproportionately to the structural richness of the volatile matrix. In the present dataset, this group included cedrol, 3,7,11-trimethyl-1,6,10-dodecatrien-3-ol, oaklactone, γ-decalactone, γ-undecalactone, γ-dodecalactone, vanillin, 4-ethylguaiacol, and related compounds. Thus, the higher end of the calculated molecular complexity distribution was represented by several chemical classes rather than by a single dominant class.

At the sample level, TMCC was broadly consistent with manufacturer-declared commercial tier, although the relationship was not universal. In NXX1, NXX2, and NXX5, TMCC increased monotonically from the low- to the high-tier product. In NXX3 and NXX4, the high-tier product also had the highest TMCC, although the values did not increase monotonically across all three tiers. In contrast, tier-related differences were less pronounced in NXX6 and NXX8, while the middle-tier product had the highest TMCC in NXX7. Therefore, the association between TMCC and commercial tier varied among brands, despite the higher TMCC values observed for the high-tier products in NXX1–NXX5.

The distribution of molecular complexity scores reflects the structural features captured by the scoring method. A previous study of monomolecular odorants reported that structurally more complex molecules tended to evoke a greater number of olfactory notes, although this relationship showed saturation at higher complexity levels (Kermen et al., 2013). Thus, molecular complexity may be associated with the breadth of odor descriptions. Notably, several high-scoring compound classes identified here have also been associated with Baijiu aging-related compositional changes. For example, terpenes were more abundant in Jiuhai-aged than in young Baijiu in a recent comparative study (Feng et al., 2025), while lactones and furanones showed broadly positive associations with Baijiu aging time across different aroma types (Huang et al., 2026). As terpenoids and lactones were among the compound classes with relatively high molecular complexity scores in the present dataset, their accumulation or enrichment during aging may contribute to changes in the concentration-weighted structural complexity of the volatile composition.

Comparison with TFCC and TOPC revealed broadly similar tier-related tendencies across several brands, although detailed sample patterns differed. This overall correspondence was confirmed by Spearman correlation analysis for the 21 samples (Supplementary Table 7): TFCC strongly correlated with TOPC (ρ = 0.9643, p < 0.001) and TMCC (ρ = 0.9762, p < 0.001), while TOPC and TMCC showed comparable correlation (ρ = 0.9714, p < 0.001). These strong correlations partly stem from the shared measured-concentration matrix, whereas local differences in sample ranking arise from dimension-specific compound scores used in each index.

3.5. Assessment of total aroma complexity index

To integrate the three related components of aroma complexity, the Total Aroma Complexity Index (TACI) was calculated as the sum of TFCC, TOPC, and TMCC. Across the 21 commercial Nongxiangxing Baijiu samples, TACI ranged from 438.69 to 513.57 (Fig. 6), with the highest value observed in NXX4-H and the lowest in NXX6-L. Correlation analysis showed that TACI was strongly associated with TFCC, TOPC, and TMCC (ρ = 0.9810–0.9909, all p < 0.001).

Fig. 6.

Total aroma complexity index (TACI) at the sample level in Nongxiangxing Baijiu. TACI was calculated as the equal-coefficient sum of TFCC, TOPC, and TMCC. Each annular sector represents one brand, and the bars within each sector represent the corresponding high-, medium-, and low-tier products. The radial axes indicate TACI values, and the radial lengths of the bars represent the corresponding TACI values. Bars are colored according to product grade, with H, M, and L denoting manufacturer-declared high-, medium-, and low-tier products, respectively. Values are expressed as mean ± standard deviation from three parallel determinations. Within each brand, bars not sharing a common letter differ significantly according to one-way ANOVA followed by Duncan's new multiple range test (p < 0.05); letters should not be compared across brands. In the sample codes, NXX denotes Nongxiangxing Baijiu, and the number denotes the brand.

At the brand level, TACI generally followed the manufacturer-declared commercial tier, although this pattern was not universal. Six of the eight brands showed a monotonic increase in TACI with increasing commercial tier, including NXX1, NXX2, NXX3, NXX4, NXX5, and NXX8. No significant difference was detected between NXX6-H and NXX6-L (p > 0.05), although NXX6-H was slightly higher across TACI and all three component indices. NXX7 showed a non-monotonic pattern: NXX7-M ranked highest for TACI and each component index, while NXX7-L was slightly higher than NXX7-H.

The strong correlations between TACI and its component indices were expected, as TACI was constructed from their sum and all three components shared the same concentration matrix. TACI should therefore be interpreted as a composite summary of shared sample-level variation, whereas TFCC, TOPC, and TMCC retain distinct interpretive roles related to odor descriptors, predicted persistence, and molecular structure, respectively. The monotonic trends observed for most brands indicate that their higher-tier products generally had volatile profiles with higher abundance-weighted complexity scores across these attributes.

The patterns for NXX6 and NXX7 further illustrate that commercial tier and calculated aroma complexity are not always aligned. For NXX6, weak tier separation resulted from closely matched values across all three component indices, indicating broadly similar measured volatile-complexity profiles. For NXX7, the intermediate-tier product ranked highest in every component, showing that its elevated TACI reflected a broad profile-level pattern rather than variation within a single index. Commercial grades may represent products designed for different sensory styles or market positions (Dwivedi et al., 2018) rather than successive levels of chemical complexity. Differences in raw materials, fermentation, distillation, aging, and blending may alter volatile composition non-linearly among products. Aging and blending, for example, may modify the abundance and balance of volatile compounds without necessarily increasing TACI. Manufacturer-declared tier should therefore be treated as contextual product information rather than an independent benchmark for aroma complexity.

To further examine the sensory relevance of the proposed framework, an exploratory comparison was performed between TACI and expert-rated sensory complexity scores for six selected Baijiu samples selected from the 21-sample dataset (Fig. 7). As described in Section 2.9, these six samples covered different brands, manufacturer-declared commercial tiers, and a wide range of calculated TACI values. Each data point in Fig. 7 represents one evaluated Baijiu sample; the sensory-complexity score denotes the sample-level mean from nine professional panelists, not individual assessor scores. A positive descriptive relationship was observed between TACI and expert-rated sensory complexity for the six samples (Pearson's r = 0.84, R² = 0.70, n = 6). Samples with higher TACI generally received higher sensory complexity scores. Thus, the calculated index and expert assessments exhibited a consistent positive trend across these six samples.

Fig. 7.

Exploratory relationship between calculated Total Aroma Complexity Index (TACI) values and expert-rated sensory complexity scores for six selected Nongxiangxing Baijiu samples. TACI was calculated as the equal-coefficient sum of TFCC, TOPC, and TMCC. Each point in the scatter plot represents one of the six selected Baijiu samples, which were chosen from the 21-sample dataset for expert sensory comparison. Sensory complexity scores are sample-level mean values: each panelist scored every sample in duplicate, individual replicate scores were first averaged per panelist, followed by averaging across nine professional Baijiu panelists using a 9-point scale. The fitted linear regression line, Pearson's correlation coefficient (r), and coefficient of determination (R²) are shown for descriptive purposes. Given the limited sample size (n = 6), the association should be interpreted as exploratory rather than as confirmatory evidence of predictive validity. In the sample codes, NXX denotes Nongxiangxing Baijiu, the number denotes the brand, and H, M, and L denote manufacturer-declared high-, medium-, and low-tier products, respectively.

This relationship provides preliminary evidence that chemical variation captured by TACI may relate to perceived aroma complexity. However, the analysis relied on only six sample-level observations, rendering the estimated relationship sensitive to individual samples and inadequate for confirmatory validation. Because TFCC and TOPC incorporate model-predicted attributes and TMCC is derived from molecular structure, TACI should be regarded as a chemical index of aroma-related complexity rather than a direct measure of sensory perception.

Studies of Baijiu flavor have traditionally been compound-centered, using OAV-based screening and molecular sensory techniques to identify key odorants and verify their contributions to characteristic aroma attributes (Qiao et al., 2023; L. Wang et al., 2024). This framework has recently been extended toward temporal perception through the integration of dynamic sensory analysis and high-resolution metabolomics (Zhang et al., 2025), and toward quality classification through flavoromics and machine learning (Li et al., 2025). TACI addresses a different but complementary question by characterizing aroma-related chemical complexity at the whole-sample level. Rather than assigning causal sensory roles or predictive importance to individual compounds, it integrates abundance-weighted odor-descriptor diversity, predicted persistence, and molecular structural complexity to summarize variation across measured volatile profiles.

Existing aroma-complexity research has mainly approached complexity from the sensory side, asking how tasters define, describe, and evaluate it in wine and other foods. These studies suggest that perceived complexity is a multidimensional attribute involving sensory diversity, harmony, balance, persistence, and temporal development, rather than a simple count of flavours or compounds (Palczak et al., 2019; Spence et al., 2018). Wine studies further show that complexity ratings are shaped by quality, liking, expertise, and fermentation- or aging-related descriptors, highlighting both the sensory relevance of complexity and the difficulty of standardizing its evaluation across contexts (Q. J. Wang et al., 2018, 2019). Dynamic sensory methods such as TDS have helped capture the temporal aspect of complexity, but they still depend on panel-based perception and product-specific vocabularies (Palczak et al., 2019; Watanabe et al., 2023).

In contrast, this study examines whether measured volatile profiles can provide a composition-based characterization of aroma-related chemical complexity that may be relevant to sensory complexity. TACI therefore does not rely on compound counts or total concentrations alone; it integrates abundance-weighted odor-descriptor diversity, model-estimated odor persistence, and molecular structural complexity to reflect chemical features plausibly linked to perceived richness, layering, and lastingness. It is therefore proposed as a composition-based, preliminary descriptor for comparative profiling of Baijiu aroma-related chemical complexity, complementary to sensory evaluation and requiring further sensory validation.

Within this context, the tier-related trends observed in several brands and the positive exploratory association with expert-rated sensory complexity suggest that the framework captures chemically meaningful variation among the examined Nongxiangxing Baijiu samples. TACI can therefore serve as an integrated metric for comparative sample profiling, while its component indices retain their distinct interpretive roles.

Several limitations define the current scope of this proof-of-concept framework. The dataset comprised 21 products from eight Nongxiangxing Baijiu brands with an unbalanced tier structure, and the sensory comparison included only six samples. Moreover, manufacturer-declared tiers provided contextual references for within-brand comparisons but are not standardized analytical or sensory benchmarks. Consequently, the observed tier patterns and sensory association require confirmation in larger, independent datasets. Methodologically, TFCC is a heuristic, study-specific measure based on model-predicted descriptors, an author-defined taxonomy, and entropy-based scoring; OpenPOM is a pretrained black-box model, and its descriptor outputs may not fully reflect perception in complex Baijiu matrices. TOPC relies on relative persistence information derived from fragrance data, whereas TMCC reflects molecular architecture rather than odor-specific perceptual effects. Although their integration provides complementary views of aroma complexity, cumulative uncertainty propagation was not quantified. Concentration-based weighting and equal-coefficient integration were transparent baseline choices; effects of OAV weighting, alternative descriptor groupings, and component weights remain to be evaluated. TACI should therefore currently be used primarily for comparative analysis of samples examined under consistent analytical and computational conditions. Future validation in broader Baijiu collections using matrix-relevant temporal measurements and independent sensory datasets is needed to assess robustness and transferability.

4. Conclusions

This study proposes an abundance-weighted, chemistry-informed framework to characterize the aroma-related chemical complexity of Nongxiangxing Baijiu. To our knowledge, it is among the first computational approaches to Baijiu aroma complexity that combines functional (odor-descriptor diversity), temporal (predicted persistence), and structural (molecular complexity) proxy dimensions. Across the commercial samples, the integrated Total Aroma Complexity Index (TACI) ranged from 438.69 to 513.57, showing brand-dependent variation but no universal association with manufacturer-declared product tier. Higher-tier products in several brands displayed broader contributions beyond the sweet–alcoholic–fruity core and stronger contributions from odorants with greater predicted persistence and higher molecular complexity. Although the component indices were strongly correlated, partly because they shared the same concentration matrix, they retained complementary interpretive roles related to predicted odor-descriptor diversity, model-estimated persistence, and molecular structure. An exploratory sensory comparison showed a positive relationship with expert-rated complexity, but confirmatory validation is precluded by the limited dataset. This proof-of-concept approach offers a transparent and scalable basis for comparative profiling of aroma-related chemical complexity under consistent analytical and computational conditions. Future work should expand independent sensory validation, test robustness to descriptor grouping and normalization, and component weighting, consider odor thresholds, OAV-based weighting, and matrix effects in weighting, and examine applicability across other Baijiu styles and aroma-rich fermented beverages.

CRediT authorship contribution statement

Huijing Lan: Writing – original draft, Visualization, Methodology. Jia Zheng: Validation, Investigation, Formal analysis. Dong Zhao: Software, Resources, Formal analysis. Jian Su: Investigation, Formal analysis. Yanping Lu: Resources. Shuang Chen: Writing – review & editing, Project administration, Conceptualization. Yan Xu: Supervision, Funding acquisition.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Shuang Chen reports financial support was provided by National Natural Science Foundation of China. Huijing Lan reports financial support was provided by Postgraduate Research & Practice Innovation Program of Jiangsu Province. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary material

Data availability

Data will be made available on request.