**3. Mechanisms and techniques of synergy testing in complex biomedical settings**

An example, modified from Berenbaum (Berenbaum 1989) is that of a woodcutter, able to cut 10 trees in a day. He is joined by a second woodcutter, also able to cut down 10 trees in a day. Together, they manage to cut 15 trees in one day. How do we describe this situation?

One approach is that cutter A achieves 10 trees per day, our expectation value. Addition of cutter B results in 15 trees being cut, so there is synergy. Such an approach has been proposed e.g. by Gaddum, who only considered the effect of one agent and whether it was affected by another one being added (Gaddum 1940). This formalism is not used widely, as it obviously assigns synergism to the effects of several drugs too readily.

Conversely, one would say that with two cutters, each able to cut 10 trees per day, the expectation value is 20 trees/day. If only 15 are achieved, they are antagonising each other. This is the application of additivity, and clearly, the combined effect is sub-additive, 20 trees would be just additive, and more than 20 would mean synergy.

Mechanistically, one might argue that if cutter A works on a tree, then cutter B would not work on the same tree. Their action would be mutually exclusive, and the additive result would be expected. If, however, they are willing to work at the same tree together, they will be able to cut this tree in a much shorter time. In this case, they would be able to cut more than 20 trees in a day and their action would be mutually non-exclusive, leading to synergy.

As stated above, pure mechanistic analysis is not sufficient (and not possible) for most clinical cases, so a general, mechanism-free analysis of drug interaction is needed. Berenbaum (Berenbaum 1989) has pointed out the similarity to non-parametric statistical tests that do not require information about the meaning of the values, or the distribution of populations from where the values originate. The equivalent in dose-response analysis is a logistic equation, that just describes a dose-response curve without any requirement of a mechanism. In such a setting, one would just define the desired outcome (enzyme inhibition, cell death, reduction of virus titer, ...), and then measure the effect achieved by varying doses of each drug alone, and in combination.

The mechanisms shown above illustrate just the simplest mechanistic model. In real life, the situation is more complicated, as mechanisms of enzyme or receptor acitivity are more complex. Furthermore medical intervention is not only directed at single proteins, but at entire pathways or controlling structures, such as transcription factors, that initiate or control biochemical processes. Some therapies, such as cancer chemotherapy even aim at

Drug Synergy – Mechanisms and Methods of Analysis 157

*A UA*

*f d f M*

where fA and fUA are the fractions of affected and unaffected enzyme, respectively. The importance of the median effect equation is that it is composed of ratios of effects (Ed, (1-Ed), or fA and fUA) and of the dose ratio (actual dose d, median dose M). Although derived from mechanistic analysis, the median effect equation cancels out mechanism-specific constants, and just links dose and effect in dimensionless ratios. This makes it a very versatile tool for the analysis of complex systems. The median effect equation can be linearized by taking logarithms on either side, giving the Hill plot (see Berenbaum 1989) which is a straight line

log log log *<sup>A</sup>*

Thus the median effect equations can be seen as an extremely useful rearranged form of dose-response curves, linking ratios of drug doses to ratios of observed effects. The median equation will work with both, mechanism-based (eg Michaelis-Menten), and effect-based (eg logistic) equations, and provides a dimensionless measure for drug effects. The technique has been extensively tested and derived from mechanistic as well as purely mathematical considerations. The group of T.C. Chou have pioneered this field and developed software packages (CompuSyn ands CalcuSyn) that allow reliable testing of drug interaction parameters (Chou 2002; Chou 2006; Chou 2010). Well-founded in theory, the technique has found widespread use (Chou 2002; Chou 2006; Chou 2010; Bijnsdorp, Giovannetti et al. 2011), and the initital paper by Chou and Talalay (Chou and Talalay 1984)

The interaction of two or more drugs to produce a combined effect can be described by the

*D D <sup>I</sup> ID ID*

1 2 *X X* ,1 ,2

> 1 2 1 2

1 2 50,1 50,2

*D D <sup>I</sup> IC IC*

*d d <sup>I</sup> M M*

where, D1 , D2 d1 and d2 are concentrations of drug 1 and 2 that produce a certain effect if applied together; IDX,1 , IDX,2 , M1 and M2 are the concentrations that produce the same effect when given alone. For instance, if we want 50 % inhibition, then equation 34 would be:

(34)

(35)

(36)

*<sup>f</sup> nd M*

*UA*

*f* 

**3.2 Interaction index, isobole method and combination index** 

*n*

(32)

(33)

The equation can also be expressed in the form

for the plot of log(fA/fUA) vs. log d.

has been intensely cited and discussed.

interaction index I (Berenbaum 1977).

or written in terms of the median equations above

cell destruction, i.e. they interfere with a complete living organism. In most of these situations, mechanisms of action are not known, or are too complex to work with. The additional problem is that with increasing complexity of the biological system, one finds an increasing paucity of experimental data. Even a simple dose-response curve, traditionally recorded with seven sensibly spaced concentration points, carries a significant error. By the rule of parsimony, one has to choose the simplest possible mechanism to describe experimental data. Thus, research is confronted with the dilemma of either oversimplification, or overinterpretation of results – a working compromise between these two extremes is needed. The pertinent models and methods have been extensively analyzed and reviewed in two excellent papers by Berenbaum (Berenbaum 1989), and Greco et al. (Greco, Bravo et al. 1995).

Some of the main concepts are just briefly described:


#### **3.1 Median effect analysis**

Chou et al. derived the median effect equation which follows from a detailed derivation of MM enzyme mechanisms (Chou 1976; Chou and Talalay 1977; Chou and Talalay 1981; Chou 2006).

$$\frac{d}{dM} = \frac{E\_d}{1 - E\_d} \tag{29}$$

where d is the dose of a drug, Ed the effect caused by this amount of drug, M the median (dose causing 50 % effect, i.e. EC50 or IC50). Indeed, such an equation can be derived by rearrangement of the Michaelis-Menten equation (6):

$$\frac{\text{[S]}}{\text{K}\_M} = \frac{\frac{V\_0}{V\_{\text{max}}}}{\text{1} - \frac{V\_0}{V\_{\text{max}}}} \tag{30}$$

Here, [S] is the substrate concentration that gives the observed V0, KM is the Michaelis constant, and V0/Vmax is the effect caused by [S], expressed here as the fractional velocity. The median effect equation has been proposed as a central, unified equation from which the basic equation sets of Henderson-Hasselbalch, Scatchard, Hill, and Michaelis-Menten can be derived (Chou 2006; Chou 2010). The median effect equation has been derived from MM-type enzymes from mathematical analysis. It can be extended to multiple-site systems in the form (Chou 2006)

$$\frac{E\_d}{1 - E\_d} = \left(\frac{d}{\mathcal{M}}\right)^n \tag{31}$$

where n is the constant giving the slope of the dose-response curve. Note that n has often been equated with the number of binding sites, but this is an oversimplification that should be avoided since it is not valid in most cases. The value of n may be a measure of the degree of cooperativity between binding sites, but nothing more.

cell destruction, i.e. they interfere with a complete living organism. In most of these situations, mechanisms of action are not known, or are too complex to work with. The additional problem is that with increasing complexity of the biological system, one finds an increasing paucity of experimental data. Even a simple dose-response curve, traditionally recorded with seven sensibly spaced concentration points, carries a significant error. By the rule of parsimony, one has to choose the simplest possible mechanism to describe experimental data. Thus, research is confronted with the dilemma of either oversimplification, or overinterpretation of results – a working compromise between these two extremes is needed. The pertinent models and methods have been extensively analyzed and reviewed in two excellent papers by Berenbaum (Berenbaum 1989), and Greco et al.

Chou et al. derived the median effect equation which follows from a detailed derivation of MM enzyme mechanisms (Chou 1976; Chou and Talalay 1977; Chou and Talalay 1981; Chou

> 1 *d d*

where d is the dose of a drug, Ed the effect caused by this amount of drug, M the median (dose causing 50 % effect, i.e. EC50 or IC50). Indeed, such an equation can be derived by

[ ]

1

of cooperativity between binding sites, but nothing more.

*d d E d E M*

where n is the constant giving the slope of the dose-response curve. Note that n has often been equated with the number of binding sites, but this is an oversimplification that should be avoided since it is not valid in most cases. The value of n may be a measure of the degree

*<sup>M</sup>* 1

*S V K V*

 

0 max 0 max

*V*

*n*

Here, [S] is the substrate concentration that gives the observed V0, KM is the Michaelis constant, and V0/Vmax is the effect caused by [S], expressed here as the fractional velocity. The median effect equation has been proposed as a central, unified equation from which the basic equation sets of Henderson-Hasselbalch, Scatchard, Hill, and Michaelis-Menten can be derived (Chou 2006; Chou 2010). The median effect equation has been derived from MM-type enzymes from mathematical analysis. It can be extended to multiple-site systems in the form (Chou 2006)

*V*

*<sup>M</sup> <sup>E</sup>* (29)

(31)

(30)

*d E*

(Greco, Bravo et al. 1995).



**3.1 Median effect analysis** 

2006).

Some of the main concepts are just briefly described:

rearrangement of the Michaelis-Menten equation (6):


The equation can also be expressed in the form

$$\frac{f\_A}{f\_{UA}} = \left(\frac{d}{M}\right)^n\tag{32}$$

where fA and fUA are the fractions of affected and unaffected enzyme, respectively. The importance of the median effect equation is that it is composed of ratios of effects (Ed, (1-Ed), or fA and fUA) and of the dose ratio (actual dose d, median dose M). Although derived from mechanistic analysis, the median effect equation cancels out mechanism-specific constants, and just links dose and effect in dimensionless ratios. This makes it a very versatile tool for the analysis of complex systems. The median effect equation can be linearized by taking logarithms on either side, giving the Hill plot (see Berenbaum 1989) which is a straight line for the plot of log(fA/fUA) vs. log d.

$$\log\left[\frac{f\_A}{f\_{UA}}\right] = n\left(\log d - \log M\right) \tag{33}$$

Thus the median effect equations can be seen as an extremely useful rearranged form of dose-response curves, linking ratios of drug doses to ratios of observed effects. The median equation will work with both, mechanism-based (eg Michaelis-Menten), and effect-based (eg logistic) equations, and provides a dimensionless measure for drug effects. The technique has been extensively tested and derived from mechanistic as well as purely mathematical considerations. The group of T.C. Chou have pioneered this field and developed software packages (CompuSyn ands CalcuSyn) that allow reliable testing of drug interaction parameters (Chou 2002; Chou 2006; Chou 2010). Well-founded in theory, the technique has found widespread use (Chou 2002; Chou 2006; Chou 2010; Bijnsdorp, Giovannetti et al. 2011), and the initital paper by Chou and Talalay (Chou and Talalay 1984) has been intensely cited and discussed.

#### **3.2 Interaction index, isobole method and combination index**

The interaction of two or more drugs to produce a combined effect can be described by the interaction index I (Berenbaum 1977).

$$I = \frac{D\_1}{ID\_{X,1}} + \frac{D\_2}{ID\_{X,2}}\tag{34}$$

or written in terms of the median equations above

$$I = \frac{d\_1}{M\_1} + \frac{d\_2}{M\_2} \tag{35}$$

where, D1 , D2 d1 and d2 are concentrations of drug 1 and 2 that produce a certain effect if applied together; IDX,1 , IDX,2 , M1 and M2 are the concentrations that produce the same effect when given alone. For instance, if we want 50 % inhibition, then equation 34 would be:

$$I = \frac{D\_1}{IC\_{50,1}} + \frac{D\_2}{IC\_{50,2}}\tag{36}$$

Drug Synergy – Mechanisms and Methods of Analysis 159

Equations 34 – 36 define straight lines for two drugs that do not show any interaction (synergism or antagonism). Two drugs showing aditivity wold be expected to fall on the additivity line (Fig. 7). If the two drugs act synergistically, lower concentrations would be needed in the mixture to achieve the same effect. Their combination graph would be an

> 1 2 ,1 ,2

*X X D D ID ID*

> 1 2 ,1 ,2

*X X D D ID ID*

1 2 ,1 ,2

related to the median (IC50 in equation 36), to give the dose reduction index DRI.

*D D CI ID ID*

visualization of synergy or antagonism (Fig. 8, see (Chou 2006)).

Representing a form of median effect equationry, isoboles have become a useful tool to present complex modes of drug interaction. An excellent review by Greco et al (Greco, Bravo et al. 1995) derives isoboles as 2-D sections through three-dimensional plots of drug action data. Depending on the shapes of the dose-response curves of both drugs, isoboles do not need to be linear (Greco, Bravo et al. 1995). Also, drug combinations may be biphasic, showing concentration ranges of synergy and ranges of antagonism (Berenbaum 1989). Equations 34 and 35 apply to the case of Loewe additivity, where the two drugs do not show synergy or antagonism. For drugs showing any type of interaction, equation 34 was extended to define a combination index (CI), indicating type and amount of interaction between two (or more) drugs with respect to the experimantal parameter being studied

1 for synergy *X X*

1 2

Both, combination index CI and DRI can be used to plot drug combination data for

1 1 *CI DRI DRI*

The CI can take values between 1 and infinity for antagonism, and runs between 0 and 1 for synergy. Chou and Chou (1988) have introduced the dose reduction index DRI (Chou and Chou 1988), which is based on the interpretation of the Combination index equation (39). Assuming that two drugs show synergy, one expects that a lower dose of each is needed to achieve the same effect. This lower concentration (D1 and D2 in equations 34-39) can be

Conversely, two antagonistic drugs would require higher doses in combination to achieve the same effect, and the resulting isobole would be an upward convex line (red line in Fig.

1

1

 1 for antagonism 1 for additivity

(40)

(37)

(38)

(39)

would determine IC50 of one drug in the presence of a constant concentration of the other. IC50 would be found with the combination of 250 a.u. of A and 24 a.u. of B (point B2), or 110

a.u. of A and 50 a.u. of B (point B3).

7), of the general (un)equation

(Chou and Talalay 1983).

upward concave (gray line in Fig. 7), following the unequality

Here, IC50,1 and IC50,2 are the IC50 values of drug 1 and drug 2 alone. D1 and D2 are the doses of drug 1 and 2, respectively, that also produce 50 % inhibition when given together. The interaction index, proposed by Berenbaum (Berenbaum 1977), should be constant in case of zero interaction. The method has been extended by Berenbaum (Berenbaum 1985) and developed into a general method based on analysis of each drug alone and then simulating the combined action of both drugs based on Loewe additivity (see also Greco, Bravo et al. 1995). The interaction index underlies one of the most widely used graphical representations of drug synergism and antagonism, the isobologram. Isoboles were first used by Fraser in 1870 (Fraser 1870; Fraser 1872) as simple, intuitive illustration without mathematical derivation. Here, the doses of drugs A and B give abscissa and ordinate, respectively, and the effect of drug combinations is plotted as graph (Fig. 7). In the example (Fig. 7), the effect plotted is for 50 % inhibition of an enzyme. The effects of each drug alone (i.e. IC50) can be read from the axes. The isobologram shows an effect, such as IC50 (IC10 or IC80, whatever effect is of interest) and which drug concentration is needed to achieve this effect.

Fig. 7. Isobologram. Abscissa and ordinate units are the concentrations of drugs A and B. The solid black line connects concentrations that produce the same effect on the target protein, enzyme, or system. In this example, the IC50 line is given. In the simulation, drug A has an IC50 (concentration giving 50 % inhibition) of 500 a.u. (arbitrary units), IC50 of drug B is 100 a.u. From additivity (black line), the combination of 250 a.u. of A with 50 a.u. of B should also give 50 % inhibition (point A). If, 50 % inhibition are achieved at lower concentrations of the two drugs (e.g. 150 a.u. of A and 40 a.u. of B, point B1), the drugs would show synergism. If the observed inhibition by the combination was less than 50 %, drug A and B would interact in an antagonistic way (point C). Model lines of synergism (gray line) and antagonism (light gray line) are drawn. Note that in case of synergy between two drugs, the IC50 curve would not be a straight line but an upward concave (gray line), in case of antagonism a downward concave (light gray line). In practical application, one

Here, IC50,1 and IC50,2 are the IC50 values of drug 1 and drug 2 alone. D1 and D2 are the doses of drug 1 and 2, respectively, that also produce 50 % inhibition when given together. The interaction index, proposed by Berenbaum (Berenbaum 1977), should be constant in case of zero interaction. The method has been extended by Berenbaum (Berenbaum 1985) and developed into a general method based on analysis of each drug alone and then simulating the combined action of both drugs based on Loewe additivity (see also Greco, Bravo et al. 1995). The interaction index underlies one of the most widely used graphical representations of drug synergism and antagonism, the isobologram. Isoboles were first used by Fraser in 1870 (Fraser 1870; Fraser 1872) as simple, intuitive illustration without mathematical derivation. Here, the doses of drugs A and B give abscissa and ordinate, respectively, and the effect of drug combinations is plotted as graph (Fig. 7). In the example (Fig. 7), the effect plotted is for 50 % inhibition of an enzyme. The effects of each drug alone (i.e. IC50) can be read from the axes. The isobologram shows an effect, such as IC50 (IC10 or IC80, whatever effect is of

interest) and which drug concentration is needed to achieve this effect.

Fig. 7. Isobologram. Abscissa and ordinate units are the concentrations of drugs A and B. The solid black line connects concentrations that produce the same effect on the target protein, enzyme, or system. In this example, the IC50 line is given. In the simulation, drug A has an IC50 (concentration giving 50 % inhibition) of 500 a.u. (arbitrary units), IC50 of drug B is 100 a.u. From additivity (black line), the combination of 250 a.u. of A with 50 a.u. of B should also give 50 % inhibition (point A). If, 50 % inhibition are achieved at lower concentrations of the two drugs (e.g. 150 a.u. of A and 40 a.u. of B, point B1), the drugs would show synergism. If the observed inhibition by the combination was less than 50 %, drug A and B would interact in an antagonistic way (point C). Model lines of synergism (gray line) and antagonism (light gray line) are drawn. Note that in case of synergy between two drugs, the IC50 curve would not be a straight line but an upward concave (gray line), in case of antagonism a downward concave (light gray line). In practical application, one

would determine IC50 of one drug in the presence of a constant concentration of the other. IC50 would be found with the combination of 250 a.u. of A and 24 a.u. of B (point B2), or 110 a.u. of A and 50 a.u. of B (point B3).

Equations 34 – 36 define straight lines for two drugs that do not show any interaction (synergism or antagonism). Two drugs showing aditivity wold be expected to fall on the additivity line (Fig. 7). If the two drugs act synergistically, lower concentrations would be needed in the mixture to achieve the same effect. Their combination graph would be an upward concave (gray line in Fig. 7), following the unequality

$$\frac{D\_1}{ID\_{X,1}} + \frac{D\_2}{ID\_{X,2}} < 1\tag{37}$$

Conversely, two antagonistic drugs would require higher doses in combination to achieve the same effect, and the resulting isobole would be an upward convex line (red line in Fig. 7), of the general (un)equation

$$\frac{D\_1}{ID\_{X,1}} + \frac{D\_2}{ID\_{X,2}} > 1\tag{38}$$

Representing a form of median effect equationry, isoboles have become a useful tool to present complex modes of drug interaction. An excellent review by Greco et al (Greco, Bravo et al. 1995) derives isoboles as 2-D sections through three-dimensional plots of drug action data. Depending on the shapes of the dose-response curves of both drugs, isoboles do not need to be linear (Greco, Bravo et al. 1995). Also, drug combinations may be biphasic, showing concentration ranges of synergy and ranges of antagonism (Berenbaum 1989).

Equations 34 and 35 apply to the case of Loewe additivity, where the two drugs do not show synergy or antagonism. For drugs showing any type of interaction, equation 34 was extended to define a combination index (CI), indicating type and amount of interaction between two (or more) drugs with respect to the experimantal parameter being studied (Chou and Talalay 1983).

$$CI = \frac{D\_1}{ID\_{X,1}} + \frac{D\_2}{ID\_{X,2}} = \begin{array}{c} > & 1 \text{ for antagonism} \\ 1 & \text{for additivity} \\ & < & 1 \text{ for synergy} \end{array} \tag{39}$$

The CI can take values between 1 and infinity for antagonism, and runs between 0 and 1 for synergy. Chou and Chou (1988) have introduced the dose reduction index DRI (Chou and Chou 1988), which is based on the interpretation of the Combination index equation (39). Assuming that two drugs show synergy, one expects that a lower dose of each is needed to achieve the same effect. This lower concentration (D1 and D2 in equations 34-39) can be related to the median (IC50 in equation 36), to give the dose reduction index DRI.

$$CI = \frac{1}{\left(DRI\right)\_1} + \frac{1}{\left(DRI\right)\_2} \tag{40}$$

Both, combination index CI and DRI can be used to plot drug combination data for visualization of synergy or antagonism (Fig. 8, see (Chou 2006)).

Drug Synergy – Mechanisms and Methods of Analysis 161

Indeed all models refer to these two basic cases. Obviously, both have a different expecation of joint action of two drugs. Loewe additivity is best described by equation 34, and any deviation from this may be considered as synergy. In case of Bliss independencs, one would expect both drugs to act independently, and therefore the zero case already includes a more than additive effect of both drugs. The author sees two problems with this definition: (i) two purely additive drugs would have to be called antagonistic, including the sham combination of a drug with itself. (ii) If two mutually non-exclusive drugs already produce a superadditive effect, and we do not yet call this synergy, how do we define "true" synergy? In terms of isoboles, the baseline (no synergy, no antagonism) is already curved, in the ratio method (Fig. 6), the slope of the inhibition curve is increased already for the zero case, and one calculates a CI of less than one. Thus, to identify synergy, one has to select a gradual increase. It may be fairly easy to identify a deviation from a straight line (isobole), but for the CI a deviation from <1 to <<1 is expected. In the ration method, the steepness of th slope may be hard to compute, as the ratio SX/Scontrol is toe be calculated from small numerical

Thus the definition of Loewe additivity is preferred by this author as the definition of no synergy. As shown in Fig.s 2 and 3, it can clearly be defined in mechanistic term. Doseresponse analysis also follows the definition. Addtivity correctly describes the purest control experiment, sham mixtures of the same drug, and it follows the general definition of synergy, where a combination produces more thant the sum of the individual

It should be noted, however, that in many clinical applications, drug combinations are used that target two completely different target proteins, or pathways. In radiotherapy, the combination of radiation and drugs work together, and in combination lower doses of either are required compared to a single treatment. No baseline of Loewe additivity can be proposed for such a combination. Likewise, combinations of drugs that target completely different cellular pathways may work synergistically towards cell killing even though the two drugs are not mutually exclusive in their activity. Obviously, there is no single

An additional problem in interpreting drug combination data is the quality of the measured data. Biological systems invariably carry experimental error, and thus borderline cases are almost impossible to assign. For example, a combination index is calculated to be 0.9 – is this

Even with the best data, however, analysis of joint action of two drugs has another inherent problem. Two different drugs may have different dose-response characteristics. In this case, changes in effective concentrations may suggest synergy where there is none. A principal illustration of this problem is given in Fig. 9 (adapted from Chou (Chou 2006; Chou 2010)), showing that the same relative concentration change can produce quite different effects (Fig. 9 A,B). Even for a single compound, there is a marked difference whether one investigates concentrations below or around EC50, or near saturation. Addition of the same drug in the concentration range around EC50 (ie the steepest part of the dose-response curve) gives rise to a strong increase in signal which may be misinterpreted as synergy. The shapes of isobolograms for drugs with different dose-response characteristics, and the complications resulting from this fact have been extensively studied (Berenbaum 1989; Greco, Bravo et al.

methodology that is appropriate for all biomedical situations.

a real deviation from unity (and thus synergy), or is it experimental error?

values and thus carries a large error.

1995; Tallarida 2001; Chou 2006).

components.

Fig. 8. Visualization of drug interaction data. (A) CI-fA plot: The combination index CI is plotted versus fA, the fraction of affected enzyme or biological function. (B) DRI plot: the dose reduction index DRI is plotted against fA. See text for definitions of terms.

#### **3.3 Response surface analysis**

Response surfaces can be calculated and are a way to represent effects of drug combinations as a contour plot where drug concentrations are plotted as a horizontal x-y- plane, and the effect is plotted on the z axis. Isoboles can be seen as 2D sections through response surfaces, and the method allows graphical analysis of drug interaction data, albeit at requirement of quite some mathematical and computational effort. From the dose-response data of each drug alone, the expected response surface based on the zero interaction reference of choice, is plotted. Then actual drug combination data are entered into the plot, and similar to isobole analysis, deviations from the reference surface indicate synergism or antagonism. The technique has been applied to synergism studies (Tallarida, Stone et al. 1999), and its general use reviewed and commented in great detail (Berenbaum 1989; Greco, Bravo et al. 1995; Tallarida 2001).

#### **3.4 Practical limitations**

There is a need for a definition of synergy, antagonism, and the zero case (neither one nor the other). Sometimes, specific problems are discussed and authors feel compelled to use a unique treatment of the data. Pharmacologists, stasticians, clinicians, and representatives from other fields have different views and concepts. In various major reviews, 13 models to treat drug combination data have been proposed. The author would not encourage decisions as to right or wrong. Each model may be appropriate for a given situation, and not applicable to others. However, all models discussing synergy can be traced back to only two types of the "zero" (no interaction) case as discussed before


Both drugs exert an effect but are mutually exclusive, either one or the other can be active at a given time. This corresponds to a common site of interaction in the simplest mechanistic case (Fig. 2).


Both drugs are mutually non-exclusive, both can be active at the same time. In the simplest case, each drug has a specific, independent interaction site (Fig. 3).

**B** 

0

1

Synergy

Antagonism

2

DRI

3

4

0,0 0,2 0,4 0,6 0,8 1,0

f A Additivity

Fig. 8. Visualization of drug interaction data. (A) CI-fA plot: The combination index CI is plotted versus fA, the fraction of affected enzyme or biological function. (B) DRI plot: the

Response surfaces can be calculated and are a way to represent effects of drug combinations as a contour plot where drug concentrations are plotted as a horizontal x-y- plane, and the effect is plotted on the z axis. Isoboles can be seen as 2D sections through response surfaces, and the method allows graphical analysis of drug interaction data, albeit at requirement of quite some mathematical and computational effort. From the dose-response data of each drug alone, the expected response surface based on the zero interaction reference of choice, is plotted. Then actual drug combination data are entered into the plot, and similar to isobole analysis, deviations from the reference surface indicate synergism or antagonism. The technique has been applied to synergism studies (Tallarida, Stone et al. 1999), and its general use reviewed and commented in great detail (Berenbaum 1989; Greco, Bravo et al.

There is a need for a definition of synergy, antagonism, and the zero case (neither one nor the other). Sometimes, specific problems are discussed and authors feel compelled to use a unique treatment of the data. Pharmacologists, stasticians, clinicians, and representatives from other fields have different views and concepts. In various major reviews, 13 models to treat drug combination data have been proposed. The author would not encourage decisions as to right or wrong. Each model may be appropriate for a given situation, and not applicable to others. However, all models discussing synergy can be traced back to only two

Both drugs exert an effect but are mutually exclusive, either one or the other can be active at a given time. This corresponds to a common site of interaction in the simplest

Both drugs are mutually non-exclusive, both can be active at the same time. In the

simplest case, each drug has a specific, independent interaction site (Fig. 3).

types of the "zero" (no interaction) case as discussed before

dose reduction index DRI is plotted against fA. See text for definitions of terms.

Synergy

Antagonism

**3.3 Response surface analysis** 

0,0 0,2 0,4 0,6 0,8 1,0

f A Additivity

**A** 

CI

0,0

0,5

1,0

1,5

2,0

1995; Tallarida 2001).

**3.4 Practical limitations** 



mechanistic case (Fig. 2).

Indeed all models refer to these two basic cases. Obviously, both have a different expecation of joint action of two drugs. Loewe additivity is best described by equation 34, and any deviation from this may be considered as synergy. In case of Bliss independencs, one would expect both drugs to act independently, and therefore the zero case already includes a more than additive effect of both drugs. The author sees two problems with this definition: (i) two purely additive drugs would have to be called antagonistic, including the sham combination of a drug with itself. (ii) If two mutually non-exclusive drugs already produce a superadditive effect, and we do not yet call this synergy, how do we define "true" synergy? In terms of isoboles, the baseline (no synergy, no antagonism) is already curved, in the ratio method (Fig. 6), the slope of the inhibition curve is increased already for the zero case, and one calculates a CI of less than one. Thus, to identify synergy, one has to select a gradual increase. It may be fairly easy to identify a deviation from a straight line (isobole), but for the CI a deviation from <1 to <<1 is expected. In the ration method, the steepness of th slope may be hard to compute, as the ratio SX/Scontrol is toe be calculated from small numerical values and thus carries a large error.

Thus the definition of Loewe additivity is preferred by this author as the definition of no synergy. As shown in Fig.s 2 and 3, it can clearly be defined in mechanistic term. Doseresponse analysis also follows the definition. Addtivity correctly describes the purest control experiment, sham mixtures of the same drug, and it follows the general definition of synergy, where a combination produces more thant the sum of the individual components.

It should be noted, however, that in many clinical applications, drug combinations are used that target two completely different target proteins, or pathways. In radiotherapy, the combination of radiation and drugs work together, and in combination lower doses of either are required compared to a single treatment. No baseline of Loewe additivity can be proposed for such a combination. Likewise, combinations of drugs that target completely different cellular pathways may work synergistically towards cell killing even though the two drugs are not mutually exclusive in their activity. Obviously, there is no single methodology that is appropriate for all biomedical situations.

An additional problem in interpreting drug combination data is the quality of the measured data. Biological systems invariably carry experimental error, and thus borderline cases are almost impossible to assign. For example, a combination index is calculated to be 0.9 – is this a real deviation from unity (and thus synergy), or is it experimental error?

Even with the best data, however, analysis of joint action of two drugs has another inherent problem. Two different drugs may have different dose-response characteristics. In this case, changes in effective concentrations may suggest synergy where there is none. A principal illustration of this problem is given in Fig. 9 (adapted from Chou (Chou 2006; Chou 2010)), showing that the same relative concentration change can produce quite different effects (Fig. 9 A,B). Even for a single compound, there is a marked difference whether one investigates concentrations below or around EC50, or near saturation. Addition of the same drug in the concentration range around EC50 (ie the steepest part of the dose-response curve) gives rise to a strong increase in signal which may be misinterpreted as synergy. The shapes of isobolograms for drugs with different dose-response characteristics, and the complications resulting from this fact have been extensively studied (Berenbaum 1989; Greco, Bravo et al. 1995; Tallarida 2001; Chou 2006).

Drug Synergy – Mechanisms and Methods of Analysis 163

Synergy, Synergism Synergism

Antagonism Antagonism

Table 1. The terminology of the combined action of drugs (after Greco, Bravo et al. 1995)

Another effect leading to apparent synergy or antagonism is the effect some drug may have on uptake, metabolism and clearance of other drugs. Depending on the route of administration, metabolism by first liver pass must be considered, including one of the most critical steps of drug biotransformation, namely oxygenation (thus hydrophilization) by cytochrome P450, an oxygenase that catalyzes oxygenations of substrates using NADPH and oxygen (O2). This oxygenation R–H R–OH is a crucial step in metabolism and eventual clearance of drugs and pharmaceuticals from the body. To date, 56 subtypes of cytochrome P450 are found in humans, some of which are critical in metabolism of endogenous substances such as medical drugs. Substances interfering with cytochrome P450 may, therefore, have an impact on drug clearance and thus on the actual concentration of a certain drug in the body (Flockhart 1995; Flockhart and Oesterheld 2000; Shin, Park et al.

**Only one drug is** 

**None of the two drugs has an effect individually** 

Coalism

Tool to query compounds that interact with a given drug

Tool to report on interactions

List of drugs metabolized by cyt P450 isoforms (Flockhart 2007)

Short list of drugs that interact with

Website discussing case individual

studies of interfering drugs

between two drugs

dietary citrus fruits

**effective individually** 

(potentiation)

Inertism Inertism

**Both drugs have same effect individually** 

Additiviy / Independence

**Resource Internet address Comment** 

\_interactions.html

npharm/ddis/

health/food-andnutrition/AN00413

Private resources http://www.environmentaldi

Table 2. Internet tools for drug interactions in clinical settings

http://www.drugs.com/drug

http://reference.medscape.co m/drug-interactionchecker

http://medicine.iupui.edu/cli

http://www.mayoclinic.com/

There are numerous internet tools that list known drug interactions. A brief list of some such resources is given in table 2. Thus, some practical aspects have been covered, although synergisms and other interactions of drugs are not yet given enough weight in approval or recommendations of drug use. This is particularly relevant for the less well-defined field of herbal remedies. Their interaction with anticancer agents has been studied (Sparreboom,

seases.com/article-druginteractions.html

Cox et al. 2004), but our knowledge in this area is still far from comprehensive.

**Effect of drug combination** 

Greater than zero

Smaller than zero

2002; Takada, Arefayene et al. 2004).

Drug interactions

Medscape drug interaction checker

Cytochrome P450 drug interaction table

Grapefruit juice/citrus fruit juice interactions

checker

reference

reference

Equal to zero reference

Fig. 9. Dose-effect curves of different shape. Both curves were simulated using the Hill equation and the parameters Emax = 100 % , EC50 = 20 au (arbitrary units). (A) Curve simulated for n =1 (hyperbolic curve). (B) Simulated for n = 3 (sigmoidal curve). Note the difference in curve shape, and the different effect of a change of concentration of agonist A from 5 to 30 au. In the hyperbolic case, the effect increases 3-fold, in the sigmoidal case, the increase is 28.3-fold. Effects of changes in agonist concentration are different depending on the response range where they happen. Sigmoidal dose-response curves are steepest around the median (panel B). In the example, a 6-fold raise in concentration (from 5 to 30 au) will cause a 28.3-fold increase in the observed effect. Raising the concentration from 15 to 90 au, the effect only increases 3.2-fold. Thus, if presence of a second drug B increases cooperativity of drug A, or if drug B shifts the relevant dose-response range of A towards the median by purely additive (non-synergistic) means, one would observe a higher increase in effect than expected from addition and wrongly interpret this as synergy.

#### **4. Borderlines of synergism – Potentiation, coalism, inertism, metabolic interference**

From the simplest models presented here to advanced discussions, the situations of synergy could be traced back to the simple principles of additivity vs. independence. In all those cases, both drugs were having the same effect alone or in combination. The only difference was the magnitude of the effects. Synergism can also occur with combinations of drugs or methods that have completely different modes of action. In cancer therapy a combination of radiation and cytotostatica is often used. Combination of substances and environmental conditions (heat, pH, radiation) have indeed been analyzed for synergy (Johnson, Eyring et al. 1945). There are cases of one drug having no activity, but augmenting the activity of another, as observed for antinociception by acetaminophen in combination with phentolamine (Raffa, Stone et al. 2001). The extreme case would be the combination of two drugs that have no effect alone, but are effective in combination. On the othe hand, selfsynergy of paracetamol has been described by Tallarida et al., who showed that the drug binds to targets in different locations and thus facilitates its own activity (Raffa, Stone et al. 2000). An interesting approach is an attempt to predict drug synergism from gene microarray data (Jin, Zhao et al. 2011).

**B** 

Fig. 9. Dose-effect curves of different shape. Both curves were simulated using the Hill equation and the parameters Emax = 100 % , EC50 = 20 au (arbitrary units). (A) Curve simulated for n =1 (hyperbolic curve). (B) Simulated for n = 3 (sigmoidal curve). Note the difference in curve shape, and the different effect of a change of concentration of agonist A from 5 to 30 au. In the hyperbolic case, the effect increases 3-fold, in the sigmoidal case, the increase is 28.3-fold. Effects of changes in agonist concentration are different depending on the response range where they happen. Sigmoidal dose-response curves are steepest around the median (panel B). In the example, a 6-fold raise in concentration (from 5 to 30 au) will cause a 28.3-fold increase in the observed effect. Raising the concentration from 15 to 90 au,

Effect (% of maximum)

Hill equation E = Emax \* Emax = 100 EC50 = 20 au n = 3

0 10 20 30 40 50 60 70 80 90 100

Drug A (a.u.)

Drug: 5 au --> 30 au Effect: 3 % --> 85 % 28.3-fold increase

1 + (EC50/[A])n 1

> Drug: 15 au --> 90 au Effect: 30 % --> 95 % 3.2-fold increase

0 10 20 30 40 50 60 70 80 90 100

Drug A (a.u.)

1 + (EC50/[A])n 1

Drug: 5 au --> 30 au Effect: 20 % --> 60 % 3-fold increase

Hill equation E = Emax \* Emax = 100 EC50 = 20 au n = 1

the effect only increases 3.2-fold. Thus, if presence of a second drug B increases

in effect than expected from addition and wrongly interpret this as synergy.

**interference** 

Effect (% of maximum)

**A** 

microarray data (Jin, Zhao et al. 2011).

cooperativity of drug A, or if drug B shifts the relevant dose-response range of A towards the median by purely additive (non-synergistic) means, one would observe a higher increase

**4. Borderlines of synergism – Potentiation, coalism, inertism, metabolic** 

From the simplest models presented here to advanced discussions, the situations of synergy could be traced back to the simple principles of additivity vs. independence. In all those cases, both drugs were having the same effect alone or in combination. The only difference was the magnitude of the effects. Synergism can also occur with combinations of drugs or methods that have completely different modes of action. In cancer therapy a combination of radiation and cytotostatica is often used. Combination of substances and environmental conditions (heat, pH, radiation) have indeed been analyzed for synergy (Johnson, Eyring et al. 1945). There are cases of one drug having no activity, but augmenting the activity of another, as observed for antinociception by acetaminophen in combination with phentolamine (Raffa, Stone et al. 2001). The extreme case would be the combination of two drugs that have no effect alone, but are effective in combination. On the othe hand, selfsynergy of paracetamol has been described by Tallarida et al., who showed that the drug binds to targets in different locations and thus facilitates its own activity (Raffa, Stone et al. 2000). An interesting approach is an attempt to predict drug synergism from gene


Table 1. The terminology of the combined action of drugs (after Greco, Bravo et al. 1995)

Another effect leading to apparent synergy or antagonism is the effect some drug may have on uptake, metabolism and clearance of other drugs. Depending on the route of administration, metabolism by first liver pass must be considered, including one of the most critical steps of drug biotransformation, namely oxygenation (thus hydrophilization) by cytochrome P450, an oxygenase that catalyzes oxygenations of substrates using NADPH and oxygen (O2). This oxygenation R–H R–OH is a crucial step in metabolism and eventual clearance of drugs and pharmaceuticals from the body. To date, 56 subtypes of cytochrome P450 are found in humans, some of which are critical in metabolism of endogenous substances such as medical drugs. Substances interfering with cytochrome P450 may, therefore, have an impact on drug clearance and thus on the actual concentration of a certain drug in the body (Flockhart 1995; Flockhart and Oesterheld 2000; Shin, Park et al. 2002; Takada, Arefayene et al. 2004).


Table 2. Internet tools for drug interactions in clinical settings

There are numerous internet tools that list known drug interactions. A brief list of some such resources is given in table 2. Thus, some practical aspects have been covered, although synergisms and other interactions of drugs are not yet given enough weight in approval or recommendations of drug use. This is particularly relevant for the less well-defined field of herbal remedies. Their interaction with anticancer agents has been studied (Sparreboom, Cox et al. 2004), but our knowledge in this area is still far from comprehensive.

Drug Synergy – Mechanisms and Methods of Analysis 165

Chou, T. C. & P. Talalay (1981). Generalized equations for the analysis of inhibitions of

Chou, T. C. & P. Talalay (1984). Quantitative analysis of dose-effect relationships: the

Colquhoun, D. (1998). Binding, gating, affinity and efficacy: the interpretation of structure-

Finney, D. J. (1942). The analysis of toxicity tests on mixtures of poisons. *Ann. App!. Biol.* Vol.

Flockhart, D. A. (1995). Drug interactions and the cytochrome P450 system. The role of cytochrome P450 2C19. *Clin Pharmacokinet* Vol. 29 Suppl 1, No., pp. 45-52. Flockhart, D. A. (2007). Drug Interactions: Cytochrome P450 Drug Interaction Table. *Indiana University School of Medicine* . http://medicine.iupui.edu/clinpharm/ddis/ Flockhart, D. A. & J. R. Oesterheld (2000). Cytochrome P450-mediated drug interactions.

Fraser, T. R. (1870). An experimental research on the antagonism between the actions of physostigma and atropia. *Proc. Roy. Soc. Edin.* Vol. 7, No., pp. 506-511. Fraser, T. R. (1872). The antagonism between the actions of active substances. *Br. Med. J.* Vol.

Gessner, P. K. (1974). *The isobolographic method applied to drug interactions*. In: Drug

Greco, W. R., G. Bravo & J. C. Parsons (1995). The search for synergy: a critical review from a response surface perspective. *Pharmacol Rev* Vol. 47, No. 2, pp. 331-385. Hess, G. P. (1993). Determination of the chemical mechanism of neurotransmitter receptor-

Jin, G., H. Zhao, X. Zhou & S. T. Wong (2011). An enhanced Petri-net model to predict

Johnson, F. H., H. Eyring, R. Steblay, H. Chaplin, C. Huber & G. Gherardi (1945). The Nature

Karpen, J. W., H. Aoshima, L. G. Abood & G. P. Hess (1982). Cocaine and phencyclidine

Karpen, J. W. & G. P. Hess (1986). Cocaine, phencyclidine, and procaine inhibition of the

Interactions. P. L. Morselli, S. Garattini & S. N. Cohen (Eds), pp. 349-362, Raven

mediated reactions by rapid chemical kinetic techniques. *Biochemistry* Vol. 32, No.

synergistic effects of pairwise drug combinations from gene microarray data.

and Control of Reactions in Bioluminescence : With Special Reference to the Mechanism of Reversible and Irreversible Inhibitions by Hydrogen and Hydroxyl Ions, Temperature, Pressure, Alcohol, Urethane, and Sulfanilamide in Bacteria. *J* 

inhibition of the acetylcholine receptor: analysis of the mechanisms of action based on measurements of ion flux in the millisecond-to-minute time region. *Proc Natl* 

acetylcholine receptor: characterization of the binding site by stopped-flow

problem. *Trends Pharmacol Sci* Vol. 4, No., pp. 450–454.

*Child Adolesc Psychiatr Clin N Am* Vol. 9, No. 1, pp. 43-76.

Gaddum, J. H. (1940). *Pharmacology*. Oxford University Press, London.

*Bioinformatics* Vol. 27, No. 13, pp. i310-316.

*Gen Physiol* Vol. 28, No. 5, pp. 463-537.

*Acad Sci U S A* Vol. 79, No. 8, pp. 2509-2513.

*Pharmacol* Vol. 125, No. 5, pp. 924-947.

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29, No., pp. 82-94.

2, No., pp. 485-487.

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4, pp. 989-1000.

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combined effects of multiple drugs or enzyme inhibitors. *Adv Enzyme Regul* Vol. 22,

activity relationships for agonists and of the effects of mutating receptors. *Br J* 

To date, the study of drug interaction in the biomedical field is widespread and must include the following aspects:


Going down this list it becomes clear that pure mechanistic studies – although essential – are not sufficient to cover all aspects of drug interaction. Clinical observation is the – equally essential – other end of the spectrum and the gap between these two positions is indeed narrowing.

#### **5. References**


To date, the study of drug interaction in the biomedical field is widespread and must


Going down this list it becomes clear that pure mechanistic studies – although essential – are not sufficient to cover all aspects of drug interaction. Clinical observation is the – equally essential – other end of the spectrum and the gap between these two positions is indeed

Asante-Appiah, E. & W. W. Chan (1996). Analysis of the interactions between an enzyme

Berenbaum, M. C. (1977). Synergy, additivism and antagonism in immunosuppression. A

Berenbaum, M. C. (1978). A method for testing for synergy with any number of agents. *J* 

Berenbaum, M. C. (1980). Correlations between methods for measurement of synergy. *J* 

Berenbaum, M. C. (1985). The expected effect of a combination of agents: the general

Bijnsdorp, I. V., E. Giovannetti & G. J. Peters (2011). Analysis of drug interactions. *Methods* 

Bliss, C. I. (1939). The toxicity of poisons applied jointly. *Ann Appl Biol* Vol. 26, pp. 585-615. Breitinger, H.-G., N. Geetha & G. P. Hess (2001). Inhibition of the serotonin 5-HT3 receptor

Chou, T. C. (1976). Derivation and properties of Michaelis-Menten type and Hill type equations for reference ligands. *J Theor Biol* Vol. 59, No. 2, pp. 253-276. Chou, T. C. (2002). Synergy determination issues. *J Virol* Vol. 76, No. 20, pp. 10577; author

Chou, T. C. (2006). Theoretical basis, experimental design, and computerized simulation of

Chou, T. C. (2010). Drug combination studies and their synergy quantification using the

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Berenbaum, M. C. (1989). What is synergy? *Pharmacol Rev* Vol. 41, No. 2, pp. 93-141.

and multiple inhibitors using combination plots. *Biochem J* Vol. 320 ( Pt 1), pp. 17-


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solution. *J Theor Biol* Vol. 114, No. 3, pp. 413-431.

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include the following aspects:

narrowing.

**5. References** 

26.

reply 10578

3, pp. 621-681.

6438-6442.




**8** 

Anoka A. Njan

*Nigeria* 

**Herbal Medicine in the Treatment of Malaria:** 

**An Overview of Evidence and Pharmacology** 

*Department of Pharmacology and Toxicology, Faculty of Pharmaceutical Scinces,* 

Traditional medicines occupy a central place among rural communities of developing countries for the provision of health care in the absence of an efficient public health care

The use of traditional remedies is common in sub-Saharan Africa, and visits to traditional healers remain a mainstay of care for many people because of preference, affordability, and

It is an important part of medical care in Uganda and throughout Africa, representing first line therapy for 70% of the population, (Homsy et al., 2004). For many, traditional herbal medicines may be the only source of treatment available. The main reasons to explain this are: traditional medicines are often more accessible compared with licensed drugs; there are no records attesting the resistance to whole-plant extracts possibly due to the synergistic action of their constituents; phytotherapy, possibly produces fewer adverse effect than

In Africa more than 2,000 plants have been identified and use as herbal medicines. However, very few of these plants have been screened for safety in resource-constrained countries including Uganda. It is time to ask in a systematic and scientific manner how these local treatments work, what are the best means to establish their safety and can they be used as traditionally prepared? The source of antimalarial drugs such as artemisinin derivatives and quinolines currently in use today were isolated from medicinal plants. Renewed interest in traditional pharmacopoeias has meant that researchers are concerned not only with determining the scientific rationale for plants usage, but also with the discovering of novel

Herbals are as old as human civilization and they have provided a complete storehouse of remedies to cure acute and chronic diseases. Numerous nutraceuticals are present in medicinal herbs as key components. Scientific evaluation of herbal products has been limited, yet herbal products are the most commonly consumed health care products. Because of known pharmacological effects and potential interaction of many of these compounds with therapeutic drugs, a history of herbal intake should be considered as part of routine medical history and should be evaluated before any change in prescription drugs

limited access to hospitals and modern health practitioners (Homsy et al., 1999).

**1. Introduction** 

system (WHO, 2003).

chemotherapy (Willcox and Bodeker, 2000).

compounds of pharmaceutical value for the treatment of malaria.

and before medical procedures (Schwartz et al 2000)

*Vernonia amygdalina***:** 

*Usmanu Danfodiyo University, Sokoto,* 

measurements of receptor-controlled ion flux in membrane vesicles. *Biochemistry* Vol. 25, No. 7, pp. 1777-1785.

