RP-HPLC-grade methanol was purchased from Fisher Scientific, and trifluoroacetic acid (TFA) was purchased from Fluka (Buchs, Switzerland). All other reagents were from Kermel (Tianjin, China); these included citric acid, sodium citrate, disodium hydrogen phosphate, and sodium dihydrogen phosphate.

The pentapeptides (HGRFG and NPNPT) were isolated from Carapax Trionycis and showed high anti-fibrosis activity (Supplementary Figure S1). The C- or N-termini of the pentapeptides of HGRFG and NPNPT were replaced with the remaining 19 amino acids to obtain the sequences of the derived pentapeptides. Then, the derived pentapeptides were synthesized by solid-phase synthesis (SPPS) and purified by RPLC. In this study, the sequences of the 57 analyzed pentapeptides are as follows: NPNPA, NPNPC, NPNPD, NPNPE, NPNPG, NPNPH, NPNPI, NPNPK, NPNPM, NPNPN, NPNPP, NPNPQ, NPNPR, NPNPS, NPNPT, NPNPV, NPNPY, APNPT, CPNPT, DPNPT, EPNPT, GPNPT, HPNPT, IPNPT, KPNPT, LPNPT, MPNPT, PPNPT, QPNPT, RPNPT, SPNPT, TPNPT, VPNPT, YPNPT, HGRFA, HGRFD, HGRFE, HGRFG, HGRFH, HGRFK, HGRFN, HGRFQ, HGRFR, HGRFS, HGRFT, AGRFG, DGRFG, EGRFG, GGRFG, KGRFG, NGRFG, PGRFG, QGRFG, RGRFG, SGRFG, TGRFG, and VGRFG.

RP-HPLC was conducted via a Shimadzu Prominence LC-2030 Plus (Kyoto, Japan) instrument equipped with a SIL-20AC autosampler and two LC-20AD pumps. An SPD-20AV dual-wavelength detector at 215 nm and 254 nm was used to detect the pentapeptides. Instrument control, data acquisition, and processing were performed with LabSolutions software for RP-HPLC. A Shimadzu Shim-pack GIST C18 4.6 × 250 mm i. d., 5 μm particle size column was used as the stationary phase and was stable within the pH range of 1–10.

A PHS-25 pH meter purchased from INESA (Shanghai, China) was used to measure the pH values, combined with an E-201F-type composite electrode. Potassium hydrogen phthalate, mixed phosphate, and sodium tetraborate from INESA (Shanghai, China) were used for electrode calibration.

Mobile phases were prepared with water (A)–methanol (B) components, degassed, and mixed online. The pentapeptides were analyzed under isocratic elution of organic solvent B. The analysis procedures were, respectively, as follows: a: 8–14 v/v (increment 2 v/v) (NPNPA, NPNPD, NPNPE, NPNPG, NPNPH, NPNPK, NPNPN, NPNPQ, NPNPR, NPNPS, NPNPT, APNPT, DPNPT, EPNPT, GPNPT, HPNPT, KPNPT, PPNPT, RPNPT, SPNPT, and TPNPT); b: 20–26 v/v (increment 2 v/v) (HGRFA, HGRFD, HGRFE, HGRFG, HGRFH, HGRFK, HGRFN, HGRFQ, HGRFR, HGRFS, HGRFT, AGRFG, DGRFG, EGRFG, GGRFG, KGRFG, NGRFG, PGRFG, QGRFG, RGRFG, SGRFG, TGRFG, VGRFG, NPNPC, NPNPI, NPNPM, NPNPP, NPNPV, NPNPY, CPNPT, IPNPT, LPNPT, MPNPT, QPNPT, VPNPT, and YPNPT). The retention times were separately obtained at temperatures of 25°C, 35°C, and 45°C. The aqueous phase was prepared at 25°C by diluting stock solutions of buffer salt.

The parameters p H W W W and p H W W S of the RP-HPLC mobile phase were associated with the chromatographic retention of ionizable compounds through their thermodynamic acid-base constants in the methanol–water mixture. The p H W W W and p H W W S values were recorded before and after mixing water with the organic phase after the electrode was calibrated with the pH calibration solution at the working temperature, and the p H S S S values were calculated according to Eqs 2, 3. The p H W W S and p H S S S values at different temperatures and organic modifier compositions are shown in Table 1. All pH values are named according to IUPAC nomenclature.

The solutes were initially dissolved in pure water at a concentration lower than 1 mg/ml and then filtered through a 0.45 µm nylon mobile phase filter. The flow rate of the chromatographic system was maintained at 1.0 ml/min, and the injection volume was 10 μL.

Both non-linear regressions of the chromatographic retention factor k with pH or other parameters in the multiparameter equation and linear regression were performed using MATLAB R2019a (Version 9.6.0; MathWorks, Natick, MA, USA).

The theoretical sigmoidal function of pH and retention factor k derived from chromatographic theory has been widely used for ionizable compounds (Konçe et al., 2019). Previous studies have verified the wide applicability of ionizable compounds in chromatographic analysis (Yang et al., 2018; Soriano-Meseguer et al., 2019). Thus, according to Equation 1, the acid–base equilibrium determined by the acidity constant K a , i.e., the retention factor of the monoprotic acid solute, depends on the pH of the mobile phase. k = k H A + k A 10 p H − p K a 1 + 10 p H − p K a , (1) where k H A and k A represent the limiting retention factors of the protonated and dissociated forms of the analyte, respectively. The p K a is the acid-base equilibrium constant of the solute at a given mobile phase composition and temperature. Most important, the pH here is p H S S S because this has been widely studied and it has been found that the fitting ability of this equation can be ensured only when the pH and p K a correspond to the real values. p H S S S can be calculated using Equation 2, as follows (Alvarez-Segura et al., 2019; Soriano-Meseguer et al., 2019): p H S S S = p H W W S − δ , (2) where the empirical formula could be used to estimate δ from solvent composition as follows: δ = 0.09 φ M e O H − 0.11 φ M e O H 2 1 − 3.15 φ M e O H + 3.51 φ M e O H 2 − 1.35 φ M e O H 3 , (3) where φ M e O H is the volume fraction of methanol in the mixed mobile phase.

For a reversible process of chromatographic analysis, the dissociation of the analyte and buffer and the solute migration during retention, which could be affected by the column temperature change, are applicable to the Van’t Hoff equation (Faisal et al., 2018; Marchetti et al., 2019; Yuan et al., 2020) as follows: l o g k = − ∆ H 0 2.3 R T + ∆ S 0 2.3 R + log ⁡ Φ , (4) where ∆ H 0 and ∆ S 0 represent the D-values of enthalpy and entropy, respectively, when the solute is transferred from the mobile to the stationary phase; R is the gas constant; and Φ represents the phase ratio. Here, we assume that the enthalpy and entropy of this equilibrium process are definite constants in the studied temperature range and that the phase ratio Φ is free of the effect.

Similarly, for the reversible process H A ⇌ H + + A − , the acid dissociation constant p K a is the negative logarithm of the equilibrium constant K a ; thus, the correlation between p K a and temperature is described by the Van’t Hoff equation as follows: p K a = ∆ H a 0 2.3 R T − ∆ S a 0 2.3 R − log Φ , (5) where ∆ H a 0 and ∆ S a 0 are the changes in enthalpy and entropy caused by solute dissociation, respectively.

Introducing Eqs 4, and 5 into Eq. 1 produces the following equation: k = 10 a + b T + 10 c + d T 10 p H − e − f T 1 + 10 p H − e − f T , (6) where the fitting parameter includes the thermodynamic quantities related to the dissociation and transformation of the analyzed compound, i.e., the function composed of these quantities: a = △ S H A 0 2.3 R + log ⁡ Φ , b = − △ H H A 0 2.3 R , c = △ S A 0 2.3 R + log ⁡ Φ , d = − △ H A 0 2.3 R , e = △ S a 0 2.3 R + log ⁡ Φ , f = − △ H a 0 2.3 R , and the subscripts HA and A apart represent the protonation and deprotonation forms of acid–base solutes.

The composition of the mobile phase is the main variable used to optimize retention and selectivity in RP-HPLC. The Soczewiński–Wachtmeister equation is commonly used to describe the relationship between k and the change in mobile phase (Flieger et al., 2020; Lin et al., 2022). l o g k = − S φ + log k W , (7) where log k W is the intercept and represents the retention coefficient of solute in pure water, S is the slope of the equation and represents the sensitivity of solute molecules to solvent strength, and φ is the volume fraction of organic modifier in the mobile phase.

Considering the influence of the polarity of the solute, stationary phase, and mobile phase on k, another linear model was proposed to accurately describe k, which represents the linear relationship between the retention rate and the polarity of the eluent (Gisbert-Alonso et al., 2021; Zhu et al., 2022); the relationship is as follows: l o g k = l o g k 0 − p P m N − P s N , (8) where p is the parameter describing the polarity of the solute, P m N and P s N are the standard polarity parameters of the mobile and stationary phases, and l o g k 0 is the retention factor when the polarity of the mobile phase is the same as that of the stationary phase. Numerous experimental studies have shown that for a specific column and water-methanol mobile phase, the parameters of Eq. 8 can be obtained by measuring the retention rate l o g k of a group of solutes, where l o g k 0 and P s N are the system constants. In addition, the l o g k value in the model is linear with respect to P m N over the entire range of water-methanol mobile phase compositions (0–100%) and intersects at a common extrapolation point in the majority of cases.

For the water–methanol system, the relationship between P m N and φ is as follows (Zhu et al., 2022): P m N = 1.00 − 1.33 φ 1 + 0.47 φ . (9)

To eliminate the limit of all l o g k and P m N lines that must cross at the same point, a deformation of Eq. 8 is proposed to represent the solute in the model by two descriptors (q and p) (den Uijl et al., 2021) and shown as follows: l o g k = q + p P m N , (10) where fitting parameters concerning the solute are twice those before, which improves the accuracy of model prediction.

The mobile phase composition affects not only the retention rate but also the ionization degree of the acid–base solute, and the addition of an organic solvent to the aqueous solution containing ionizable compounds changes the value of p K a . For a specific solute, the solute parameters are constant, and p K a only depends on the solvent properties or temperature, whereas when using mixed solvents (such as the mobile phase), the solvent properties and p K a change monotonically with the mobile phase composition. Therefore, the relationship between the p K a value and the solvent volume fraction can usually be expressed as follows: p K a = E + F φ . (11)

Similarly, the relationship between p K a and mobile phase polarity parameters can be expressed as follows: p K a = E + F P m N . (12)

Based on the aforementioned analysis, combined with the model of pH and different mobile phase compositions, the six-parameter model is obtained as follows: k = 10 A + B X + 10 C + D X 10 p H − E − F X 1 + 10 p H − E − F X , (13) and log k H A = A + B X , (14) log k A = C + D X , (15) p K a = E + F X , (16) where X is the variable describing the change in the mobile phase, representing φ or P m N in the two-parameter solvent model. Parameters A, B, C, D, E, and F of the model have a simple chemical interpretation. If X is the volume fraction φ of the organic modifier in the mobile phase, then A, C, and E are the extrapolation of the logarithm of k in acidic and alkaline forms and the p K a of the compound in pure water, respectively, while B, D, and F are the changes in these parameters from pure water to pure organic solvent. Similarly, if the polarity parameter P m N is fitted as the X variable, then A, C, and E are the reserves in a non-polar medium, and the p K a , and B, D, and F are the changes from the medium to pure water (defined as P m N =1).

The pH of the mobile phase is one of the critical factors affecting the retention of compounds in chromatography due to its interference with the ionization efficiency and change in the protonation of analytes (Fan et al., 2022; Guo et al., 2023). Because the increased or decreased degree of chromatographic retention for compounds was different with the change in pH, adjusting the pH of the mobile phase was capable of separating the compounds with similar structures or confirming the absence of unrelated impurities (Fan et al., 2022; Tengattini et al., 2022). MATLAB R2019a was used to fit the S-curve of different pH values and the experimental retention factors (k) under the same temperature and the same mobile phase composition. From Eq. 1, we obtained the parameters k H A , k A , and p K a , as shown in Table 2 Table 3 Table 4. With the analysis of k and their corresponding pH values, the p K a determination by the inflection point in the curve was the most established method for its calculation for a compound (Numviyimana et al., 2019). However, the retention times in RP-HPLC were generally short owing to the high polarity of solutes, leading to unsatisfactory fitting outcomes of the S-curve and predictions for inflection point p K a . Only the p K a -values of the acid and basic compounds from fitting were close to the software calculation results (Figure 1), consistent with the study by Rook et al. (2021) on particular sidechains.

In addition, the k-values calculated by the parameters k H A , k A , p K a , and different pH values as described in Eq. 1 were fitted with 1 / T , φ, and P m N to examine the consistency of the parameter results in the S-curve according to Eqs 4, 5, and Eq. 7 (Supplementary Tables S1, S2). For the independent variable 1 / T , we obtained 1,596 correlation coefficients (R²), and 73.1% of the R² values were greater than 0.9. For the independent variable of φ or P m N , 1197 R² values were obtained, and 95.4% of the R² values were greater than 0.9 for the independent variable. The results suggested that the parameters conformed to the relationship described in Eqs 4, 5, and Eq. 7 and further indicated the applicability of Eq. 1.

The temperature of the column could alter the density of the mobile phase, solute diffusion coefficients, and solute–stationary phase interactions and then affect the chromatographic retention (Nagase et al., 2021). The retention of solutes generally decreased as the column temperature was increased due to the accelerated molecular movement in RP-HPLC (Caltabiano et al., 2018; Idroes et al., 2020). Moreover, the k H A , k A , and p K a of solutes were theoretically correlated with the Van’t Hoff equation since they similarly represented an equilibrium state of ionization. Therefore, the relationships between log k H A , log k A , and p K a with respect to 1 / T of each compound under different mobile phase compositions were characterized, 684 R² values (Supplementary Table S3), and 60-line charts of each parameter with respect to 1 / T were obtained, and some representative graphs are shown in Figure 2. In this study, the plots of log k H A , log k A , and p K a with respect to 1 / T showed linear relationships consistent with Eqs 4 and 5 for most pentapeptides, indicating that the effect of the temperature on ∆ H 0 , ∆ S 0 , and log ⁡ Φ could be commonly disregarded. The linear correlations of acid pentapeptides for the plots of log k H A vs. 1 / T were the most evident, with each R² greater than 0.92 under different mobile phase compositions. The neutral pentapeptides displayed the most apparent linear correlation between log k A and 1 / T , with 63% of the R² > 0.9 and 97.5% of the R² > 0.75. The linear correlations of all pentapeptides between log k H A , log k A with respect to 1 / T (43.1% of the R² > 0.9 and 56.1% of the R² > 0.9) were better than p K a vs. 1 / T (18.4% of the R² > 0.9), especially for the basic pentapeptides. Furthermore, the correlations from the same group of compounds in different methanol concentrations were quite different due to the influence of the mobile phase compositions on the retention of the pentapeptides, and the linear correlations of the acid pentapeptides were slightly better than those of the neutral and basic pentapeptides.

The linear relationship between k H A , k A , and p K a with respect to 1 / T depended on the ∆ H 0 , ∆ S 0 , and Φ under different chromatographic conditions. However, the contributions of enthalpy and entropy to the retention process varied with the change in temperature. Enthalpy-driven effects substituted entropy-driven effects at a higher column temperature and affected the linearity of the Van’t Hoff equation (Tanase et al., 2019). Moreover, the Φ value was affected by mobile phase composition and continuously increased with an increase in temperature in the range of 5–50°C (Flieger et al., 2019). A previous study reported the linear dependence of acid compounds and the non-linear behavior of basic compounds with the Van’t Hoff equation (Galaon and David, 2011; Yılmaz Ortak and Cubuk Demiralay, 2019). Except for the compounds with unique structures, other compounds potentially participated in multiple interactions with the stationary phase, likely causing the deviations from the Van’t Hoff equation. In summary, the log k H A and log k A of acidic and neutral pentapeptides followed the description of Van’t Hoff equation and had apparent linear relationships with 1 / T . Therefore, in this study, only a limited prediction capacity of p K a was observed with a minimal deviation contribution to the overall retention due to the assumption of linearity.

An appropriate composition of the mobile phase is beneficial for chromatographic separation and improving the chromatographic peak profile and efficiencies (Guo et al., 2018; Attwa et al., 2023). Adjusting the proportion of organic modifiers in the mobile phase is the most frequently used approach to achieve the separation of a series of compounds (Hong et al., 2020; Oney-Montalvo et al., 2022). Furthermore, the methanol volume fraction φ and polarity parameter P m N are commonly used to characterize the composition of the mobile phase. Hence, in this study, the two factors were considered simultaneously. We examined the influence of the composition of the mobile phase on log k H A , log k A , and p K a at a constant temperature. 90-line charts of five groups and 1026 R² values (Supplementary Table S4) were obtained, and some representative charts were selected as shown in Figure 3. Identical R² values were acquired depending on the descriptor (φ or P m N ) of the composition of the mobile phase at the same temperature; these results indicated that the relationship between φ and P m N could be regarded as linear in a narrow range of mobile phase compositions. Moreover, all plots of log k H A , log k A , and p K a with respect to X exhibited linear correlations for the five groups of pentapeptides, which was consistent with Eq. 7; Eq. 10; Eqs 11, 12. More importantly, the linear model was highly suitable for describing the relationship of acid pentapeptides between log k H A and log k A with respect to X , with each R² greater than 0.98 or 0.9. For neutral or basic pentapeptides, the linear fitting results of log k A and X (90% of the R² > 0.9 and 79.7% of the R² > 0.9, respectively) surpassed those of log k H A and p K a . Due to the influence of temperature on chromatographic retention, there were differences in the correlations of the same group of compounds at different temperatures, and the R² values were generally lower with increasing temperature. These results indicated that the two functional relationships of Eqs 11, 12 were appropriate for studying the change in the chromatographic retention of the 57 pentapeptides in the range of mobile phase compositions, and it was very difficult to compare the superiority of the independent variables of φ and P m N based on the current results. Specifically, log k H A , log k A , and p K a had evident linear relationships with φ or P m N , and there was basically no difference regardless of whether φ or P m N was used as the descriptor of the composition of the mobile phase.

The coefficient log k W of the Soczewiński–Wachtmeister equation is related to not only the length of the alkyl chain in the molecule but also the latitude of the mobile phase composition (Żesławska et al., 2022). Generally, a wider range of methanol concentrations correlates with more accurate coefficients. A previous study reported the linear relationship of k and φ at 60%–80% methanol (Elmansi et al., 2019). However, in our study, the pentapeptides analyzed generally had short carbon chains with high polarity and showed low retention in RP-HPLC. No retention occurred at a high proportion of methanol, and a broad chromatographic peak with long tailing was observed at a low proportion of methanol. Hence, we used a narrow range of methanol concentrations to produce symmetrical and sharp peaks, which was crucial for accurately recording the retention time. Furthermore, we classified the pentapeptides into two groups to investigate their linear dependence at different ranges of methanol concentrations. The linear relationships need to be verified at a wider range of methanol concentrations in future studies.

We combined the two variables of temperature and pH into a six-parameter model (as shown in Eq. 6) to explore the combined effect of temperature and pH on chromatographic retention. The fitting parameters a, b, c, d, e, and f (Table 5) of the 57 pentapeptides under the four mobile phase compositions were calculated by an established six-parameter model with pH and T as independent variables and k as the dependent variable to predict the k-value according to different pH and T values. All fitting parameters varied with the change in the mobile phase composition except pH and T. Moreover, a higher proportion of methanol in the mobile phase correlated to a smaller parameter of the acid pentapeptides. Only parameter c displayed an inversely proportional relationship with the proportion of methanol for neutral and basic pentapeptides, and there were no clear trends for other parameters in most cases.

According to the results of the six-parameter model, linear fitting of the experimental k-value and predicted k-value was conducted to assess the prediction capability of chromatographic retention. The R² calculated by linear fitting was used as an evaluation criterion. A random error was present for all data, but the residuals were symmetrically distributed around the axis of y = 0 (Supplementary Figure S3). We then fitted the data from five groups of pentapeptides, and the R₁ ² value was just 0.6055, showing the unsatisfactory capacity to predict the chromatographic retention of the studied pentapeptides (Figure 4A). Further classifying the data according to their acid–base properties and fittings, the R₂ ² value was 0.8603 for the acid pentapeptides (Figure 4B), while both the R₃ ² and R₄ ² values were lower than 0.7 for the basic and neutral pentapeptides (Figures 4C, D). The results indicated that the six-parameter model had a certain prediction capability for the chromatographic retentions for the acid pentapeptides but was unable to characterize the chromatographic retentions for the basic or neutral pentapeptides. In addition, the R² values fitted by the experimental k-value and predicted k-value under different chromatographic conditions in the six-parameter model of T and pH are shown in Supplementary Table S5. The R² decreased with the increase in column temperature or the methanol volume fraction, indicating that this model was suitable for compounds with higher chromatographic retention.

Internal validation is a commonly used method for evaluating models free of experimental and environmental conditions’ limitations (Luo et al., 2020; Vasconcelos et al., 2023). In this study, we used 10-fold cross validation to conduct internal validation. The root mean squared error (RMSE) obtained from 10-fold cross validation was used to evaluate the prediction capability of the models in this study. The average RMSE from the 10 test sets was used to minimize the biased prediction results. The residuals of all pentapeptides and acid pentapeptides were randomly distributed around the y = 0 axis (Supplementary Figure S5). Moreover, the average RMSE of all pentapeptides and acid pentapeptides was 0.48 and 0.20 in the 10 tests (Supplementary Table S7), respectively, indicating that the six-parameter model had both random error and certain prediction capability.

We considered the combined influence of the mobile phase composition and pH on chromatographic retention by substituting pH and X into Eq. 13 and obtained the fitting parameters A, B, C, D, E, and F of the 57 pentapeptides at three temperatures (Tables 6, 7). X represented φ or P m N in the solvent model and was used as the variable to describe the change in the mobile phase. Hence, a six-parameter model was constructed with pH and X as the independent variables and k as the dependent variable, and this model was applied for the prediction of the k-value based on different pH and X values. All fitting parameters varied with the change in temperature expect pH and φ or P m N . More importantly, parameter A of acid pentapeptides and parameter C of neutral pentapeptides increased with a decrease in column temperature when φ was the descriptor for the mobile phase composition, while there was no distinct tendency from the other parameters. The six parameters of the 57 pentapeptides deviated from a positive or negative correlation when P m N was the descriptor for the mobile phase composition.