Resistance to antibacterial agents is a major public health threat affecting humans worldwide mainly due to the uncontrolled use of such bioactive compounds, particularly in countries without standard treatment guidelines. Among those antibacterial agents, fluoroquinolones, a fluoro substituent series derived from nalidixic acid, showed escalating rate of resistance after domination over the therapeutic practice for a time particularly against gram-negative pathogens [1–3]. Such class of active compounds needs to be monitored carefully regarding their use and their abundance in the environment. Hence, from the analytical view, the urgent detection and analysis of these drugs become essential considering finding fast, simple, economical and accurate methods for their analysis.
The literature survey revealed that quinolones could be determined thoroughly via high performance liquid chromatography in different matrices viz., biological fluids and tissues [4–10], milk and food of animal origin [11–16], marine products , honey , waste water [19–21] and in many pharmaceutical formulations [22–27]. Moreover, the relationship between the retention factors and lipophilicity of quinolones using RP-TLC has been assessed . In addition, Wu et al  investigated the retention factors-activity relationship of some quinolones using micellar chromatography.
On the other hand, sulfonamides are other synthetic antimicrobial agents, unfortunately with widespread resistance which made them infrequently utilized for medical interventions. However, the application of sulfonamides has been extended from their old capabilities as antimicrobial agents to another medical roles viz., anticancer, antiglaucoma, cyclooxygenase-2 and lipoxygenase inhibitors, anticonvulsant and hypoglycemic activities . Regarding the analytical tools used in their detection, literature survey revealed that the determination of this class was also dominated by reversed phase liquid chromatography [31–34]. In context of their retention mechanisms, Cazenave-Gassiot et al discussed the correlation between sulfonamides retention factors and the proportion of modifier in the mobile phase using supercritical fluid chromatography . However, like quinolones, the separation behavior of this class on reversed phase liquid chromatography needs to be scrutinized.
Among different models and theories applied to draw an image about the retention manners in reversed phase liquid chromatography, quantitative structure–retention relationship (QSRR) offers some useful insights not only to elucidate how different chemical drugs perform their retention upon analysis, but also to expect their retention chromatographic systems relatively well . Such relationship provides a powerful alternative to the conventional trial-and-error approach with marked improvement in time and cost of experiments.
In these mathematical models, a link between compounds’ chemical structures represented by their descriptors and the retention data in different chromatographic systems is built. The number of molecular descriptors that could be obtained for one analyte is enormous where some software could calculate up to 5000 descriptors per analyte . Such massive increase in the dimensionality of the descriptors along with the possible incorporation of some nonempirical features could affect the performance of various QSRR models. Therefore, methods for feature selection are necessary to untangle this problem and decide which descriptors are important regarding the retention of compounds of interest. These methods ranged from classical type as forward and backward elimination to advanced nature inspired ones for example particle swarm optimization (PSO), genetic algorithm (GA) and its descendants (firefly, flower pollination and ant colony algorithms) [38–43].
Furthermore, different chemometric and artificial intelligence methods viz., partial least square (PLS), multiple linear regression (MLR), artificial neural networks (ANN) and support vector regression (SVR) proved to be effective in building reliable QSRR models owing to their ability in extracting maximal chemical information in addition to enhancing the speed and quality of analysis. The application of QSRR models have been reported to different chemical families on reversed-phase liquid chromatography such as non-steroidal anti-inflammatory drugs , azole antifungal agents  and some pain killers drugs .
Support vector machine (SVM), a machine learning algorithm, was firstly published by Vapnik, Chervonenkis and co-workers . The algorithm is based on finding a linear function that explains most of the variation of the response and at the same time links the nonlinear relationship between input and the target data . Compared to conventional regression and neural network methods, SVM displays some advantages, including good generalization ability, global optimization and dimensional independence . Thanks to its capability to model possible nonlinear relations between molecular descriptors and retention time, it has been incorporated in building powerful QSRR models [51, 52].
Previously our group developed two QSRR models aimed to provide some essence of the retention behavior for some β-lactams using multiple linear regression models combined with forward or firefly variable selection algorithms . Our scope in this report is to continue our work regarding QSRR modeling of other antibacterial agents (quinolones and sulfonamides), hopefully to highlight their reversed phase chromatographic retention mechanisms with respect to different ionization states and various percentage of organic modifiers for quinolones and sulfonamides, respectively. Owing to the complexity of the generated data, the use of advanced variable selection technique coupled to a machine learning approach seems imperative. Hence, firefly algorithm coupled to SVR has been employed to develop the QSRR models. Moreover, the obtained models have been assessed regarding their predictive ability with strict validation criteria, thus could be further employed to predict retention of potential degradation products and even metabolites of these compounds.