Recently it has been demonstrated that synergy follows physicochemical mass-action law, which briefly states that the ratio between the concentration of reactants and products is constant for a chemical reaction mixture that is in equilibrium. From mass-action law, a simplified mathematic equation for the combination index (CI) was further developed for the quantitative determination of synergy in multiple agents acting on the same target/receptor (Chou, 2010). Synergism occurs when the CI value is < 1 (the more the CI value approaches 0, the stronger the synergistic effect); additive effect occurs when the CI value is equals to 1, and antagonism happens when the CI value is >1.

The CI is a practical model used for the analysis of synergy of a multi-component combination in a fixed ratio. To calculate the CI, the dose-response curves (inhibitory effect, stimulatory effect, etc.) of individual components A and B and their combination in a fixed ratio are determined using the same assay. The doses of each individual component that achieves a specified effect (e.g. 50%, ED₅₀) are determined. Further, the doses of A and B required in the combination to produce the same level of effect can be calculated. Then, based on the doses, the synergism/addition/antagonism is calculated according to Equation (1) below for two agents and Equation (2) for multiple agents.

In addition, computer software including “CalcuSyn” and its third-generation “CompuSyn” have been developed, which greatly facilitates the CI analysis (Patrick Reynolds and Maurer, 2005; Chou, 2006). By inputting the dose-effect data of agents 1 and 2 and their combination, the software can generate a Fa (effect level)–CI curve, which demonstrates a complete dataset of CI values (represent antagonistic/additive/synergistic interactions) at all tested doses. Also, a CI-Fa (effect levels) can be generated (an example is shown in Figure 1). This model can also be applied for the determination of interactions among multiple agents in a mixture. The calculation is based on Equation (2), which demonstrates n-drug combination at x% inhibition. Examples using CI model for the determination of synergistic interaction in CHM are discussed in Section Synergistic Interactions within Single Herb Analyzed by CI or Isobologram Method. (1)CI =D1d1+D2d2    (1) (2)(CI)nx=∑j = 1n(D)j(d)j    (2) ⁿ(CI)x = combination index for n drugs at x% inhibition

D1 and D2 = doses of individual constituent alone, required to produce a chosen effect level (usually ED₅₀)

d1 to d2 = the doses of individual constituent in the combination required to produce the same effect, respectively.

It is worth mentioning that many studies also reported a synergistic effect when certain pharmacological effects can be observed with a drug combination, but not with one or more of its individual components. This effect is classified as potentiation or augmentation rather than synergism based on Chou's theory (Chou, 2010). If an individual component does not generate an effect when used alone, the D1 value is equals to 0, thus the synergy cannot be determined in the CI equations. This potentiation or augmentation effect can be considered as a form of complementary interactions.

Isobologram, was first introduced by Fraser in 1870 based on Loewe additivity (Fraser, 1872). This method has been widely accepted as one of the most practical models in terms of experimental design and effectiveness to illustrate the synergistic/additive/antagonistic interactions. Similar to the CI model, the isobole method requires the determination of dose-response relationship of the combination and its individual components independently to assess if synergism exists. This is expressed as a dose response curve on an isobole graph as shown in Figure 2. The isobole is an “iso-effect” curve, in which a combination of components (A or B) at different dose levels is represented on the graph, the axes of which are the dose-axes of the individual constituent (A and B). The dashed line joining the points (i.e. ED₅₀ of A and B) which represent the same dosage required from the combination as the sum of the individual component to reach the same effect. If the dots of the combination falls on this dashed line, it represents an additive effect, i.e., no interactions between components A and B. If synergy occurs the curve becomes “concave.” The opposite applies for antagonism representing by a “convex” isobole (Figure 2). It is also possible to have synergy at one dose combination and antagonism at another, with the same substances and this would give a complicated isobole with a wave-like or even elliptical appearance.

In theory, isobologram and Fa-CI plot are both based on the same CI equation and therefore should yield an identical conclusion. However, isobologram explains synergy from a dose-oriented perspective (reaching the same therapeutic activity but with a lower dose level required), while Fa-CI plot from an effect-oriented perspective (resulting in a higher therapeutic activity at the same dosage level). Additionally, Fa-CI plot can be used to determine multi-component interactions, whereas isobologram is only feasible for a two drug combination as it is not possible to construct multidimensional isobologram curves.

Both CI and isobologram models are designed for evaluating the synergistic/antagonistic interaction between two or more single-entity agents acting on the same target/receptor. Even though these models have been recently used for analyzing possible synergistic interactions in simple herbal formula (herb-pair), they are by and large less adequate for evaluation of the complex interactions among multiple bioactive components of CHM formulations (Gu and Chen, 2014) (for more detailed discussions see Section Current Status of Synergy Research in Chinese Herbal Medicine).

The CI and isobologram methods both require combination-by-combination evaluations of individual components in a mixture specifically acting on the same target/receptor. However, for a complex combinational therapy especially TCM multi-herb formulations, which often contain hundreds of potentially bioactive components that may act on a network targets, it is technically impossible to use these two models to evaluate all combinations of bioactive components on each of the target one by one.

A systematic analysis (or S2S) approach integrating literature, experimental data, and computational sciences has been recently developed to address the multi-target synergistic actions. To conduct this analysis, the three-dimensional structures of individual compounds in the combination are obtained from relevant database, handbooks or literature, and the known crystal structures of all the key genes/proteins associated with targeted disease are retrieved from relevant data banks or databases. The network constructions between agents and targeted protein/genes are then constructed via a molecular docking approach. Molecular docking is usually applied for computer-assisted drug design, which predicts the predominant binding mode(s) of a ligand with a protein of known structure. Here, it is used to analyse binding modes between the potential active compounds and their corresponding target proteins based on their structure binding modes, in order to generate a drug-target network. The predicted interaction between bioactive and targeted receptors from the generated network can either be confirmed by literature or validated through experimental studies (Wang X. et al., 2012; Leung et al., 2013). This model investigates the multi-target mechanisms of action of multi-constituents mixtures and identifies the key active components, which can bind to most of the corresponding targets. In addition, this method can be used in drug development through selecting and combining the most active components that act on the maximum amount of the protein or gene targets. This minimal effective composition with definite constituents and controllable quality can optimize the composition of the mixture while maintaining their curative effects (Li et al., 2012; Liang et al., 2012).

The S2S approach has gained popularity as a promising and valuable tool to evaluate synergy of complex herbal formulations (Lee, 2015). However, due to the poor understanding of the chemical and pharmacological properties of bioactive constituents of many TCM herbs, the application of this method in studying synergistic effects of TCM herbs to gain insight of the holistic approach of CHM remains a challenge (Wang X. et al., 2012).

In microbiology, several bioassays and mathematics models have been developed and applied to the investigations of the synergistic anti-bacterial effects of individual bioactive components of Chinese herbs and antibiotic agents including diffusion assay, checkerboard array, and time-kill assay.

Chemical fingerprint studies utilizing high-performance liquid chromatography chromatography, gas chromatography, liquid chromatography–mass spectrometry and chemometric resolution methods have been conducted to detect changes in the amount of pharmacologically active compounds in individual herbs when given in combination (Han et al., 2007; Wang et al., 2011; Kaliappan et al., 2014). During the decocting preparation, the chemical composition is often altered due to solvent's polarity, heating effects or changed pH environment (Li, 2014). These changes in chemical composition could account for the increased therapeutic effects and/or reduced side effects of the individual herbs. Li et al. (2006) demonstrated that the amount of main volatile chemical components present in Rhizoma Ligustici Chuanxiong (Chuanxiong) and Radix Paeoniae Rubra (Chishao), which are commonly used to promote blood circulation and remove stasis, were markedly altered when given together due to the formation of non-volatile, water soluble salts during the decoction process (Li et al., 2006). In addition, the amount of aconitine, a toxic component of Aconitum carmichaeli Debx. (Fuzi) is significantly reduced due to its chemical reaction with tannine under high temperature.

Chemical fingerprint studies have also shown that new compounds are formed when herbs are given in combination during the preparation. For instance, Wang Y. L. et al. (2012) identified four new compounds in a Radix Polygalae (Yuanzhi) and Acorus Tatarinowii Rhizoma (Shichangpu) combination that were not detected in the individual extracts (Wang Y. L. et al., 2012). Although, the biological effects of these new compounds were not evaluated in this study, it provides possible explanations for the changes in pharmacological properties when herbs are used in combination.

Individual herbal extracts consist of a complex mixture of bioactive compounds, concomitant agents and other minor substances among which interactions can occur leading to synergistic effects. For example, Ginkgo biloba extract has been shown to possess an anti-platelet aggregation property (Dutta Roy et al., 1999), which could contribute to its therapeutic effects for vascular cognitive impairment through enhancing cerebral blood flow (Zhang and Xue, 2012). Synergistic interaction between ginkgolides A and B, two bioactive components of Ginkgo biloba, has been demonstrated in a platelet aggregation test using the isobole method (Williamson, 2001).

In a study conducted by Lin et al. (2007), the anti-cancer property of four H₂O sub-fraction phytocompounds (indole-3-caroxyaldehyde, wedelolactone, luteolin, and apigenin) from Wedlia chinensis were evaluated using three different androgen receptor (AR)-dependent cancer cell lines (human PCa22 Rv1, 103E, and LNCaP cells) (Lin et al., 2007). Interestingly, as revealed by the CI analysis using CalcuSyn software, a significantly stronger anti-cancer effect was observed when the four compounds were combined at the same ratio as in the original herb extract when compared with that of each individual compound highlighting the synergistic property of these compounds present in Wedlia chinensis. It is worth mentioning that the anti-cancer activity was significantly reduced when any one of these bioactive compounds was removed from the combination, indicating the significance of the four bioactive compounds acting as a whole.

Kan et al. (2008) demonstrated the anti-cancer activities of the three major phthalides mixture [butylidenephthalide (BLP), senkyunolide A (SKA), and z-ligustilide (LGT)] from Angelica sinensis with the same ratio as they were in the extract on colon cancer HT-29 cell line. Although three phthalides mixture demonstrated synergistic cytoxic effects, it was shown that the anti-proliferative effects of the whole A. sinensis extract was still significantly higher than of the corresponding phthalide mixture. Therefore, it suggested positive interactions of active components and other co-existing components within the herb (Kan et al., 2008).

Due to the rapid expansion of the concurrent use of pharmaceutical medicines and Chinse herbal medicine, research into their interactions and the underlying mechanisms is urgently needed. Some of these interactions may be therapeutically beneficial via synergism to enhance therapeutic effects or via antagonism to reduce side effects. Most of the synergistic studies available relate to anti-cancer therapies. For example, anti-cancer properties of Polyphyllin I (PPI–active component from Rhizoma of Paris polyphyllin) and Evodiamine (EVO–active component from Evodia rutaecarpa) are well-documented (Lee et al., 2005; Adams et al., 2007; Chan et al., 2009; Kong et al., 2010), but their efficacy is generally weaker than that of chemotherapeutic agents such as platinum (Pt), 5-Fluorouracil (5-Fu), and irinotecan (CPT-11). However, when PPI or EVO were combined with Pt or 5-Fu, it produced a significantly stronger inhibition rate than Pt or 5-Fu alone on freshly-removed gastric cancer tissues from patients. The CI values were found to be <1 in all combinations at fraction affected (Fa) = 80%, indicating a synergistic anti-cancer effect (Yue et al., 2013).

Lin et al. (2014) demonstrated that the combination of aqueous extract of the leaves and fruit of Camptotheca acuminate (AE-CA) and cisplatin (platinum analogs) exerted synergistic cytotoxicity effects in HEC-1A and HEC-1B human endometrial carcinoma cells. This study also demonstrated that the cytotoxic effect of the mixed AE-CA extracts was significantly stronger than that of camptothecin (CPT), a chemotherapeutic drug isolated from C. acuminate. However, the AE-CA extracts produced similar effects on cell-cycle regulation and the accumulation of cyclin-A2 and -B1 as CPT. Therefore, the existence of synergistic effects among the individual components in C. acuminate extracts remains unclear (Lin et al., 2014).

Similarly, the synergistic effects of bioactive dichloromethane (DCM) subfraction of Strobilanthes crispus leaves (SCS) and tamoxifen (antiestrogen drug) were investigated using estrogen receptor-responsive and non-responsive breast cancer cells (MCF-7 and MDA-MB-231 cell lines). SCS extracts alone induced around 50% cell death after 24 h treatment. When combined with low doses of tamoxifen (which did exert any significant cytotoxic effect on its own), SCS extracts produced 80% cell death after 24 h treatment, which was proved to be a synergistic effect based on the method of CI using Calcusyn software (Yaacob et al., 2014).

A study by Seo et al. (2014) has shown that a mixture of curcumin, a main bioactive component of Curcuma longa and NVP-BEZ 235 (a potent dual inhibitor of PI3K and mTOR) can synergistically induce apoptosis in human renal carcinoma caki cells (Seo et al., 2014). The mixture of 2 μM NVP-BEZ235 and 30 μM curcumin significantly provoked cell shrinkage, membrane blebbing, chromatin damage in the nuclei and DNA fragmentation; none of these effects were as significant when curcumin and NVP-BEZ235 were used alone. Isobologram analyses demonstrated that there were synergistic activities between curcumin and NVP-BEZ 235.

Synergistic effects between antibiotics and herbal medicine have also been extensively studied. Agar diffusion assay is often used for screening the anti-bacterial activity of individual agent, and used as qualitative guide for positive/negative interaction guide for agents' mixture. For example, four active constituents (pseudolaric acid B, gentiopicrin, rhein and alion) extracted from CHMs (herbal source was not stated in the paper) were tested on agar diffusion assay, and only pseudolaric acid B showed significant fungicidal activity with growth inhibition zones ranging from 8 to 25 mm against C. albicans, C. glabrata, C. krusei, C. tropicalis, C. dubliniensis and C. parapsilosis. Furthermore, a positive interaction was observed between pseudolaric acid B and fluconazole in the agar diffusion assay on the same disc, where there was no microcolony growth in the cross-sectional area of pseudolaric acid B and fluconazole observed (Jiang et al., 2010). In addition, checkerboard array and time-kill assay are commonly used methods to quantitively determine the synergism/addition/antagonism interactions. Jang et al. (2014) explored the synergistic antibacterial activities of baicalein, a flavonoid originally isolated from the root of S. baicalensis Georgi, with ampicillin and/or gentamicin against a range of oral bacteria strains. Their results showed that both baicalein-ampicillin and baicalein-gentamicin combinations demonstrated synergistic bactericidal effects evidenced by FICI ≤ 0.5 determined by checkerboard array (Jang et al., 2014). In addition, time-kill array results confirmed the positive interaction between baicalen–ampicillin and baicalen–gentamicin, respectively, which showed substantially stronger bactericidal effect in combination compared with individual effect from 0 to 24 h (Jang et al., 2014). Similarly, Hwang et al. (2013) also utilized checker-board array to analyse the synergistic effect between amentoflavone (biflavonoid class of flavonoids, isolated from Selaginella tamariscina) and antibiotics such as ampicillin, cefotaxime and chloramphenicol. Their results showed that amentoflavone had a considerable antibacterial effect and exerted synergistic interactions with antibiotics against all bacterial strains tested (FICI ≤ 0.5) except for Streptococcus mutans. This synergistic effect was suggested to be largely mediated by the formation of hydroxyl radical by nicotinamide adenine dinucleotide phosphate (NADH) depletion (Hwang et al., 2013).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.