The discovery of antibiotics has been traditionally focused on natural products and semi-synthetic tailoring of these natural compounds chemically. Natural substances produced by microorganisms are the most important source of antibiotics. For example, gentamicin is an aminoglycoside antibiotic targeting bacterial ribosomes and is produced by fermentation using micromonospora. Many plant-derived materials, such as cinnamon oils and peppermint oils, are also natural antimicrobial agents [8], [9], [10]. In fact, the use of plants with antimicrobial activities for treating wound infections was described in Chinese medicine and other ancient cultures at least 2500 years ago [11]. After the intensive screening of natural antibiotics in the past 50 years, recent antibiotic research effort is migrating to newer sources of natural antimicrobials, such as cyanobacteria and antimicrobial peptides [12], [13]. Synthetic compounds can also provide new avenues in antimicrobials. As an example, sulfamethoxazole is a synthetic antimicrobial that inhibits the folate biosynthetic pathway. Novel libraries of synthetic compounds are being developed to provide improved architectural complexity approaching that of natural products to serve as structural scaffolds for creating new antibiotics [14].

Combination antimicrobial therapy using synergistic antibiotic cocktails, on the other hand, represents an appealing option for treating bacterial infections [7]. A finely tuned mixture of drugs, in many cases, is known to be more effective than monotherapy. A well-known success of drug cocktails in disease treatment is in the fight against human immunodeficiency virus, the virus that causes acquired immune deficiency syndrome [15]. Another example is the treatment of childhood acute lymphoblastic leukemia by the optimization of drug cocktails based on clinical empiricism and trial and error. Evidence for this is seen by the fact that the death rate for acute lymphoblastic leukemia has dropped 90% in the past 25 years [16]. A key advantage of combination therapy using synergistic, or even additive, cocktails is the reduction in drug concentration, which minimizes the toxicity and side effects of many antimicrobials to the host. For instance, high doses of gentamicin can cause renal failure, and permanent losses of equilibrioception and hearing [17], [18]. Combination antimicrobial therapy is, therefore, likely a fruitful option for the treatment of infectious diseases caused by bacterial pathogens. As a matter of fact, co-trimoxazole, a two-drug synergistic combination with trimethoprim and sulphamethoxazole at a 15 ratio, is one of the best selling antibiotics for the treatment of various bacterial infections [19]. Nevertheless, a first hurdle in implementing combination antimicrobial therapy is to identify potent cocktails out of a large number of possible drug combinations. It is difficult to predict synergistic activities between different antimicrobials by studying them individually. Furthermore, the optimal dose of a drug individually could often be different from the most effective dose in a potent cocktail. Identifying potent cocktails out of different concentrations of various antibiotics represent a classical combinatorial optimization problem and the possible combinations increases rapidly with the number of antimicrobials being considered [20], [21]. A systematic procedure for rapidly determining synergistic antimicrobial cocktails is, therefore, necessary to accelerate our progress in combination antimicrobial therapy. In addition, rapid determination of potent antimicrobial cocktails will also improve our ability to promptly response to multidrug resistant pathogens and biological warfare agents in emergency situations and high-risk areas such as temporary clinics established in response to natural and man-made disasters.

Optimization strategies in engineering and computer sciences are well-established approaches for controlling highly complex systems and will likely play an essential role in numerous biomedical sciences and clinical applications [20], [21], [22], [23], [24], [25]. For instance, search algorithms, which iteratively determine the optimal solutions (drug cocktails) in the parametric spaces (different drug combinations), can be applied for determining synergistic drug combinations. A closed-loop optimization strategy was demonstrated for rapid screening of antiviral drug cocktails and identifying cytokine combinations to regulate the NF-κB using signal transduction pathway using a stochastic search algorithm, Gur Game [26]. A Medicinal Algorithmic Combinatorial Screen based on the hill climbing algorithm was demonstrated for screening anti-cancer drug cocktails [27]. A parallel search scheme, Differential Evolution algorithm, was demonstrated for identifying antiviral cocktails for Kaposi's Sarcoma-associated Herpesvirus [28]. These search algorithms, which test drug cocktails sequentially, are especially effective for biological systems with smooth response surfaces in the parametric space. Due to the urgency of many infectious diseases, a metamodel antimicrobial cocktail optimization (MACO) scheme that combines fractional factorial design and stepwise regression is explored in this study. A potential advantage of MACO is that experiment trails are performed in parallel, which dramatically reduces the time required for determining a synergistic cocktail. In general, fractional factorial design is a statistical information-gathering strategy and has been widely applied in engineering research and industrial settings [21], [29]. Instead of brute-force or exhaustive search of all possible drug combinations, which are often impractical in many situations, fractional factorial design can dramatically reduce the number of experiments by defining trials that capture the individual and interactive effects on the response of a complex system. Based on the result, stepwise regression model building procedures can then be performed to extract the potential synergistic interactions between antibiotics.

The MACO scheme was then performed for screening antimicrobial cocktails from a larger number of antibiotics. In addition to TMP, AMP, and GEN, sulfamethoxazole (SMX), cinnamon oil (CIN), and peppermint oil (PEP) were considered in the tests. Similar to the 3-drug experiment, 3 concentrations were assigned for each antibiotic. The highest concentrations of CIN and PEP were chosen to be both 0.02% (Figure 3a and Figure 4a), which was 4-fold smaller than their MIC. EC132 is known to be resistant to SMX and the highest concentration was chosen based on the 119 ratio of the synergistic TMP-SMX combination, which is recommend by the Clinical and Laboratory Standards Institute [30]. The fractional factorial designs for 6 antibiotics required 18 trials out of 729 (3⁶) combinations (Figure 3b and Figure 4b). The bacterial growths under these conditions are shown in Figure 3c and Figure 4c. The results of the regression analyses using the fractional regression and quadratic response surface models are shown in Figure 3d and Figure 4d. In agreement with the 3-drug experiment, TMP and GEN were identified to have the most potent interaction in the 5-drug and 6-durg experiments using both regression models.

In the 5-drug experiment, trials 8 and 16, which had the highest concentrations for both TMP and GEN, were indeed highly effective in inhibiting the growth of the bacteria. The results of the 6-drug experiment were not as intuitive as the other experiments. In the 6-drug experiment, multiple cocktails, trials 5, 8, 9, 11, 14, and 16, were able to effectively inhibit the growth of the pathogens. Based on these data, one could suggest SMX-CIN, TMP-GEN-PEP, CIN-PEP, and TMP-GEN-CIN may processes synergistic activities. A close inspection of the data revealed TMP is critical for inhibiting the bacterial growth based on trials 1, 2, 3 and 10 and TMP-GEN was likely to have the strongest activity based on trials 8 and 16. It should also be note that co-trimoxazole, the combination of TMP and SMX, is also a well-known synergistic cocktail. Interestingly, the regression analyses selected TMP-GEN instead of TMP-SMX as the most potent cocktail for the E. coli clinical isolate using both models. It could be a result of the low concentration of TMP in the experiment and the SMX resistant property of EC132. In fact, the concentration of SMX as a synergist was 20-fold higher than the concentration of GEN in the experiment. This suggests TMP may have a stronger interaction with GEN than with SMX.

The MACO scheme suggested TMP and GEN interacted synergistically for inhibiting the bacterial growth. A sensitivity analysis was thus performed to evaluate the activity between TMP and GEN (Figure 5a). In the range of 0 to 0.5 µg/ml, TMP showed only a weak-to-moderate effect on the bacterial growth without GEN. It is consistent with the fact that the MIC of TMP for EC132 (i.e., 4 µg/ml) is much higher than the concentration range tested in this experiment (0 to 0.5 µg/ml). When a small amount of GEN is added, TMP displayed dose dependent inhibitions on the bacterial growth. The effect of TMP was significantly enhanced by GEN in a dose dependent manner. For instance, the MIC of GEN could reduce to 0.1 µg/ml with 0.5 µg/ml of TMP and MIC of TMP could reduce to 0.1 µg/ml, a 40-fold reduction, with 0.25 µg/ml of GEN. This supports that TMP and GEN work synergistically and can significantly reduce the MIC of the antibiotics. The synergistic activity of the cocktail was then tested for several strains of uropathogenic E. coli clinical isolates (Figure 5b). TMP alone only slightly reduced the bacterial growth for all three strains of E. coli. Similarly, GEN alone at 0.25 µg/ml showed a negligible effect on the growth. It should be noted that EC136 and EC137 are sensitivity to GEN at a higher concentration. With the combination of TMP and GEN at the same concentration, total inhibition of the bacteria growth was observed for all three strains of uropathogenic E. coli. These results indicate that TMP and GEN exhibit a strong synergistic interaction and that this interaction is applicable to various strains of E. coli.

Optimizing a drug cocktail based on trial and error or clinical empiricism is a challenging task, as evidenced by the time required for developing combination therapies for various diseases. Since the number of possible drug combinations is practically unlimited, a systematic approach for rapidly identifying the most promising cocktails and prioritizing their evaluation is critical. This study demonstrated that potent antimicrobial cocktails could be systematically determined using the MACO scheme. Our result showed the robustness of the procedures of MACO, which consistently identified the synergistic cocktails from different drug combinations. An important advantage of the MACO scheme is the simplicity of the approach that allows the dramatic reduction in the number of experiment trails. The MACO scheme can be easily accessible to researchers with standard microbiology equipments and commercial statistic software. In this study, rapid identification of a potent antimicrobial cocktail was demonstrated from over seven hundred possible combinations in the antimicrobial search space. If the number of antibiotics increases to 13, a full factorial design will require 1,594,323 (3¹³) trials while the fractional factorial design can reduce the number of trial to 27 only.