Immunosuppressive Interactions among Calcium Channel Antagonists and Selected Corticosteroids and Macrolides Using Human whole Blood Lymphocytes

Summary

The immunosuppressive interactions of calcium channel antagonists [diltiazem (Dil), verapamil (Ver) and nifedipine (Nif)], with corticosteroids [methylprednisolone (Mpl), prednisolone (Prd)], and macrolides [tacrolimus (Tac) and sirolnnus (Sir)] were examined in human whole blood lymphocyte cultures. Gender-related differences in responses in the interactions between these drug classes were studied using blood from 6 males and 6 females. The nature and intensity of interactions were determined using an extended Loewe additivity model. All immunosuppressants exhibited higher potency than the calcium channel antagonists with mean IC₅₀ values of:

	Dil (mM)	Ver (mM)	Nif (mM)	Mpl (nM)	Prd (nM)	Tac (nM)	Sir (nM)
Male	135	41.9	213	12.1	18.6	150	327
Female	114	31.8	47.4	4.6	8.8	111	106

Gender-related differences in responses to Mpl and Prd were observed while the others were not significant. Additive interactions were found among calcium channel antagonists and corticosteroids. Significant synergistic interactions were observed between calcium channel antagonists and tacrolimus and sirolimus, although these are unlikely to be of clinical importance. These studies demonstrate diverse drug interactions in the examination of an important array of immunosuppressant drug combinations.

Introduction

Immunosuppressants have been widely used for prevention and treatment against organ rejection after transplantation procedures. These drugs often require close monitoring for efficacy and side effects. Among transplantation complications, hypertension is the most prevalent (40-60%) and controllable condition. Calcium channel antagonists (CA) are commonly used for this indication owing to their ease of use and few adverse effects. Both immunosuppressive therapy and hypertension treatment requires lifetime medication.

The major events in T cell activation involve plasma membrane receptor activation, increases in intracellular calcium concentrations, and phosphorylation of membrane and cytoplasmic proteins.¹⁾ Calcium, acting as a secondary messenger, is an important component in the calcium-dependent signaling pathway for lymphocyte activation. Calmodulin, a ubiquitous regulatory protein in lymphocyte, can activate several enzymes upon complexation with calcium. These lead to cytokine protein transcription and lymphocyte proliferation.²⁾ Figure 1 depicts the mechanisms of action of some of the major immunosuppressants: methylprednisolone, prednisolone, tacrolimus and sirolimus, as well as for CA in suppression of lymphocyte activation.

Fig. 1.

Scheme for T cell activation and mechanisms of drug action. CA, Calcium Channel Antagonists; Tac, Tacrolimus; Sir, Sirolimus; Mpi, Methylprednisolone; Prd, Prednisolone.

Methylprednisolone and prednisolone were first used in clinical transplantation to reverse acute rejection reactions in patients treated with maintenance doses of azathioprine. Corticosteroids exert their immunosuppressive effect by inhibiting the activities of transcription factors. One of the well-examined transcription factors is NF-κB. Corticosteroids increase the production of a NF-κB regulatory protein, I-κB. This protein stabilizes the cytoplasmic NF-κB and prevents NF-κB from entering the nucleus.³⁾ Hence, cytokine production is reduced.

Tacrolimus and sirolimus have a similar macrolide molecular structure and they both bind to the same class of immunophilin, FK binding protein (FKBP).⁴⁾ The tacrolimus-FKBP complex binds the calcium dependent calcineurin-camodulin complex and inhibits its phosphatase activity, thereby inhibiting cytokine transcription.⁵⁾ However, sirolimus-FKBP has no effect on calcineurin activity. The immunosuppressive activity of sirolimus appears to be a result of sirolimus-FKBP blocking the activation of protein kinases S6 CDK2 and CDK4, and the calcium-independent CD28/B7 costimulatory pathway.^4,5)

The immunosuppressive properties of CA have been illustrated in primary lymphocyte cell culture.^6,7) These drugs suppress the immune response of lymphocytes to foreign antigens. The CA block the influx of calcium into responsive lymphocytes, reducing production of cytokines and subduing lymphocyte proliferation. Although there is frequent use of combination therapy of immunosuppressants and CA in prevention of organ rejection and post-transplantation hypertension, the possible interactions in immunological response to antigen challenge have not been explored.

The objectives of this work were to examine the in vitro immunosuppressive nature of CA, and to assess gender-related differences of blood lymphocytes in response to CA and diverse immunosuppressants.

Materials and Methods

Subjects

Drug-free male (n=6) and female (n=6) healthy volunteers between 18 and 40 years of age were included in this study. Women receiving birth control pills were excluded. Blood was collected at 9 AM on the day of the experiment.

Materials

All chemicals were purchased from Sigma (St. Louis, MO) unless otherwise stated. Diltiazem and verapamil were dissolved at 50 mg/mL in RPMI 1640 as stock solutions and stored at 2°C before used. Nifedipine was dissolved at 15 mg/mL in ethanol, and stored at −4°C. Methylprednisolone, prednisolone and tacrolimus (gift from Fujisawa Pharmaceutical Co.) were dissolved in ethanol and stored at −20°C. Sirolimus (gift from Wyeth-Ayerst Research) was dissolved in ethanol and stored at −80°C.

Human whole blood lymphocyte proliferation

This procedure was adapted from Piekoszewski et al⁸⁾ with modification.⁹⁾ Blood samples (20 mL) were diluted 1:20 (v/v) with RPMI 1640 supplement with 100μg/mL streptomycin, lOOU/mL penicillin, 2mM L-glutamine, 20 mM HEPES, and 0.25 mM 2-mercaptoethanoI (Gibco, NY). Diluted blood was plated in 96-well plates at 165 μL/well with drug (20 μL) at various concentrations. Proliferation was induced by phytohemagglutinin (PHA) (15 μL) at an optimized concentration of 3 μg/mL/well. The drug concentration in each well was calculated based on the final volume of 200 μL/well. Cell cultures were incubated at 37°C in a 7.5% CO₂-humidified air incubator for 72 hr. Cultures were pulsed with 1 μCi of ³H-thymidine per well and incubated for 20 hr. The cells were then harvested into 96-well microplare filters. The filters were bleached with 3% hydrogen peroxide and dried with pure ethanol. Radioactivity in the filters was counted using a Top Count™ Microplate Scintillation Counter (Packard, CT) with 25 μL scintillation fluid. The counts per minute (CPM) values were recorded.

Single drug response

Diltiazem, verapamil, nifedipine, methylprednisolone, prednisolone, tacrolimus, and sirolimus were first studied separately. Background (no drug and no PHA), maximum (no drug) response, and 12 to 14 drug concentrations spanning over 3 log-units for each drug were studied in 4 replicates.

Interaction studies

Five concentrations producing between 25 to 75% of maximum proliferation (S_max) in the single drug response study were selected. Concentrations of two drugs were combined in five ratios: 1:1, 1:2, 2:1, 1:4 and 4:1 (v/v). Totals of 25 different combinations of concentrations were included in each interaction study. For each combination, four replicates were made by transferring the same volume of already mixed drug cocktails to four 96-well microplates. To avoid inter-day variations of blood samples, both single and interaction studies were done using the blood sample collected on the same day.

Data normalization

The background (CPM_back) and maximum (CPM_max) response values were used to normalize CPM of all drug responses (CPM_drug) as follows:

$$\%{\mathrm{S}}_{\max }=\frac{{\mathrm{CPM}}_{\mathrm{drug}}-{\mathrm{CPM}}_{\mathrm{back}}}{{\mathrm{CPM}}_{\max }-{\mathrm{CPM}}_{\mathrm{back}}}\cdot 100\%$$ (1)

where %S_max is the percent response from drug with respect to the maximum proliferation.

Single drug response analysis

A simple sigmoid equation (Eq. 2) was use to analyze lymphocyte proliferation data for single drug treatments.

$$\%{\mathrm{S}}_{\max }=100\left(1-\frac{{\mathrm{I}}_{\max }\cdot {\mathrm{C}}^{\gamma }}{{\mathrm{IC}}_{50}^{\gamma }+{\mathrm{C}}^{\gamma }}\right)$$ (2)

The 1C₅₀ is the drug concentration which inhibits 50% of the maximum lymphocyte proliferation, C is the molar concentration of drug, I_max is the fraction of drug activity eliciting full response (all were= 1.0), and γ is the Hill coefficient. Data from each single drug response profile was fitted for IC₅₀ and γ using the Adapt II release 4 software.¹⁰⁾ These two parameters were compared to explore drug- and gender-related differences.

Interaction data analysis

The classic additivity equation from Loewe¹¹⁾ assumes that the fractional effect contributed from each drug is additive to explain the full response from combinations.

$$\Lambda =\frac{{\mathrm{C}}_1}{{\mathrm{C}}_1^{\ast }}+\frac{{\mathrm{C}}_2}{{\mathrm{C}}_2^{\ast }}+\cdots \cdots +\frac{{\mathrm{C}}_{\mathrm{n}}}{{\mathrm{C}}_{\mathrm{n}}^{\ast }}$$ (3)

The general form of the Loewe additivity equation occurs when Λ = 1, C₁ are the concentrations of different drugs in combination, and ${\mathrm{C}}_{\mathrm{i}}^{\ast }$ are the concentrations of different drugs which would produce the same effect when used alone. This equation was used to describe drug combinations at one effect level (isoeffect) at a time. When the drug combination produces an additive condition, Λ = 1. When synergism is produced Λ < 1 while antagonism produces Λ < 1. Therefore, the Λ term can be utilized quantitatively to reflect the nature and intensity of drug interactions.

If ${\mathrm{C}}_{\mathrm{n}}^{\ast }$ is the concentration of drug n which alone produces the same effect, it can be obtained by rewrit-ing¹²⁾ equation 2 as follows:

$${\mathrm{C}}_{\mathrm{n}}^{\ast }={\left(\frac{{\mathrm{S}}_{\max }-\%{\mathrm{S}}_{\max }}{\%{\mathrm{S}}_{\max }}\right)}^{1∕\gamma \mathrm{n}}\cdot {\mathrm{IC}}_{{50}_{\mathrm{n}}}$$ (4)

For interaction of two drugs with sigmoid drug responses, the following equation can be obtained by inserting equation 4 into equation 3 for both drugs.

$$\Lambda =\frac{{\mathrm{C}}_1}{{\mathrm{IC}}_{{50}_1}}\cdot {\left(\frac{\%{\mathrm{S}}_{\max }}{{\mathrm{S}}_{\max }-\%{\mathrm{S}}_{\max }}\right)}^{1∕{\gamma }_1}+\frac{{\mathrm{C}}_2}{{\mathrm{IC}}_{{50}_2}}\times {\left(\frac{\%{\mathrm{S}}_{\max }}{{\mathrm{S}}_{\max }-\%{\mathrm{S}}_{\max }}\right)}^{1∕{\gamma }_2}$$ (5)

The IC_50i and γ_i values are obtained from the single drug responses and C₁ and C₂ are the two drug concentrations in combination. Here the %S_max is the percent of response to the drug combination. S_max is equal to 100% after all data have been normalized with equation 1. All data from each interaction study (%S_max) were fitted jointly with equation 5 for parameter Λ using Adapt II release 4 software. Since equation 5 is not in explicit form, iteration of this equation requires use of the bisection method, a standard Fortran subroutine.¹³⁾

The 95% confidence interval (CI) of the degree of interaction (Λ) was used as to assess the nature of interactions. When the 95% CI of Λ includes the value of 1, the interaction is assumed additive. When the 95% CI of Λ is smaller than and does not include the value of 1, the interaction is assumed synergistic. When the 95% CI of Λ is greater than and does not include the value of 1, the interaction is deemed antagonistic. A one-way ANOVA test was used to determine the degree of interaction differences among drugs and gender. Both linear and log-transformed IC₅₀ values were examined statistically.

Graphical presentation

The classic isobolograph explores the degree and nature of interactions at one effect level. When isobolographs are stacked up at different levels of effects, their interaction curves produce a three-dimensional surface.^14,15) When %S_max is plotted against log drug concentration, the fiat surface becomes a concave surface. Therefore, an antagonistic interaction will increase the concavity of the surface, and a synergistic interaction will decrease the concavity of the surface. The vertical distance between the observed data to the interaction surface is minimized during nonlinear regression with equation 5.

Results

Single drug response

All whole blood lymphocyte proliferation (WBLP) studies showed sigmoidal inhibition responses in relation to increased drug concentrations. Typical data profiles of all drugs are shown in Fig. 2. The mean parameter estimates of the single response to each drug are summarized in Table 1. The IC₅₀ values of CA ranged from 0.04 to 0.2 mM. Verapamil (41 μM) was 3-5 times more potent than diltia-zem (135 μM) and nifedipine (213 μM). The Hill coefficients (γ) of diltiazem (3.2) and verapamil (2.2) were similar, but the γ of nifedipine was much smaller (0.9). Nifedipine had a more gradual change of response as concentrations increased (Fig. 2).

Fig. 2.

Typical WBLP responses versus concentration for the indicated single drugs. Symbols are the observed data and lines are fitted with equation 2.

Table 1.

Summary of parameters from whole blood proliferation

Parameters	Diltiazem	Verapamil	Nifedipine
Male
IC50 (μM)	135 (26)	41.9 (15.3)	213 (196)
γ	3.2 (0.8)	2.2 (0.2)	0.9 (0.3)
Female
IC50 (μM)	113 (11)	31.8 (6.8)	47.4 (40.2)
γ	3.0 (0.8)	2.8 (0.5)	0.8 (0.4)

Parameters	Methyl prednisolone	Prednisolone	Tacrolimus	Sirolimus
Male
IC50 (nM)	a12.1 (7.8)	b18.6 (4.4)	150 (86)	327 (588)
γ	1.9 (0.3)	1.6 (0.8 )	0.7 (0.1)	0.8 (0.4)
Female
IC50 (nM)	a4.6 (1.5)	b8.8 (5.7)	110 (45)	106 (71)
γ	2.1 (1.1)	1.5 (0.5)	0.8 (0.2)	0.8 (0.1)

Values are presented as Mean (SD)

^ap<0.05

^bp<0.01

The immunosuppressants were 1000 times more potent than CA. Their IC₅₀ values ranged from 4.6 to 327 nM. The two corticosteroids, methylprednisolone and prednisolone, showed the strongest inhibition potency with IC₅₀ values of 12 and 19 nM in males. The two macrolides, tacrolimus and sirolimus, had IC₅₀ values of 150 and 327 nM. The Hill coefficients were similar within the same class of drugs. The two corticosteroids had higher γ values (1.9 and 1.6) than those of the macrolides (0.7 and 0.8). The change of response as tacrolimus and sirolimus concentrations increased was more gradual than those of corticosteroids (Fig. 2).

Gender-related differences were not observed for CA. Although the mean IC₅₀ of nifedipine in males (213 fxM) showed lower potency than in females (47.4^M), the variability was too great to yield any statistical difference. Similar results were found (M vs. F) with sirolimus (327 vs 106nM) and tacrolimus (150 vs ISO nM). More definite gender-related differences were observed with prednisolone (p<0.01) and methylprednisolone (p<0.05). As shown in Fig. 3, the IC;0 values for methylprednisolone (12.1 vs 4.6 nM) and prednisolone (18.6 vs 8.8 nM) were higher in males. Similar statistical findings were obtained when the IC₅₀ values were log transformed (results not shown).

Fig. 3.

WBLP responses to methylprednisolone and prednisolone for a typical male (●) and female (○) subject. Curves were fitted using equation 2.

Drug interactions

Table 2 summarizes of the degree of interaction (Λ) for all 12 interactions according to gender. There were no gender-related differences in these interactions. Therefore, these data were combined and the degree of interaction (Λ) was reanalyzed. Figure 4 shows the mean and 95% CI for Λ from Table 2 for all interaction studies. In general, the interaction among CA and the two corticosteroids was additive. All of these interactions have Λ with the 95% CI overlapping the additivity line (Λ = 1), except for the interaction between diltiazem and prednisolone where the lower limit of the 95% CI (1.08) was close to the additivity line (Λ = 1). The nature of interaction among CA and the two macrolides can be classified as synergistic. All the means and 95% CI of Λ were smaller than 1.0 and were well away from the additivity line. Among them, verapamil with tacrolimus (Λ =0.32) and nifedipine with tacrolimus (Λ = 0.33) showed the strongest synergistic interactions. Despite the inter-subject variation in the single drug responses of nifedipine and sirolimus, Ihe interaction between these drugs showed definite synergism.

Table 2.

Quantitative parameter (Λ) for interactions among calcium channel antagonists and immunosuppressants

	Methylprednisolone		Prednisolone		Tacrolimus		Sirolimus
vs Diltiazem
Male
Mean (SD)	1.01 (0.33)	Z	1.20 (0.39)	Z	0.58 (0.18)	S	0.70 (0.19)	S
95% CI	0.66 - 1.36		0.79 - 3.60		0.39 - 0.77		0.50 - 0.89
Female
Mean (SD)	1.27 (0.20)	A	1.56 (0.62)	Z	0.58 (0.13)	S	0.68 (0.27)	S
95% CI	1.05 - 1.48		0.91 - 2.21		0.44 - 0.71		0.40 - 0.97
All Subjects
Mean (SD)	1.14 (0.30)	Z	1.38 (0.53)	A	0.58 (0.15)a	S	0.69 (0.22)	S
95 % CI	0.97 - 1.31		1.08 - 1.68		0.49 - 0.66		0.56 - 0.82
vs Verapamil
Male
Mean (SD)	0.79 (0.34)	Z	0.91 (0.38)	Z	0.34 (0.19)	S	0.48 (0.24)	S
95% CI	0.44 - 1.14		0.51 - 1.32		0.14 - 0.53		0.23 - 0.72
Female
Mean (SD)	0.89 (0.26)	Z	0.91 (0.33)	Z	0.31 (0.14)	S	0.62 (0.51)	Z
95% CI	0.62 - 1.17		0.57 - 1.26		0.16 - 0.45		0.09 - 1.50
All Subjects
Mean (SD)	0.84 (0.29)	Z	0.91 (0.34)	Z	0.32 (0.16)a	S	0.55 (0.38)	S
95% CI	0.68 - 1.01		0.72 - 1.11		0.23 - 0.41		0.33 - 0.77
vs Nifedipine
Male
Mean (SD)	0.95 (0.64)	Z	1.27 (0.98)	Z	0.33 (0.30)	S	0.58 (0.60)	Z
95% CI	0.28 - 1.63		0.25 - 2.30		0.009 - 0.65		–0.05 - 1.2
Female
Mean (SD)	1.08 (0.27)	Z	1.41 (0.45)	Z	0.33 (0.20)	S	0.59 (0.34)	S
95% CI	0.80 - 1.36		0.94 - 3.88		0.13 - 0.54		0.24 - 0.95
All Subjects
Mean (SD)	1.02 (0.47)	Z	1.34 (0.73)	Z	0.33 (0.24)a	S	0.59 (0.46)	S
95% CI	0.75 - 1.29		0.93 - 1.75		0.19 - 0.47		0.33 - 0.85

^ap<0.01

Notation for Λ:

^ZZero interaction (Additivity): Λ = 1 or 95%> CI includes 1.0

^AAntagonism: Λ >1 and 95% CI does not include 1.0

^SSynergy: Λ < 1 and 95% CI does not include 1.

Fig. 4.

Degree of interaction in WBLP among calcium channel antagonists and immunosuppressants where Λ = 1 for additivity. The mean (●) and 95% CI (horizontal line) of each interaction for the twelve subjects are shown.

Typical fitted interaction surfaces among CA and corticosteroids and among CA and macrolides are shown in Fig. 5. These interaction surfaces were generated via simulation using equation 5 and the parameters from both the single and interaction fittings to the observed data. All data from these studies were well described by the surfaces. Of all synergistic interactions observed, verapamil/tacrolimus, and nifedipine/ tacrolimus were the strongest with Λ of 0.32.

Fig. 5.

Fitted interaction surfaces for diltiazem/methylprednisolone and diltiazem/tacrolimus. Symbols are observed data. The surfaces are simulated with the fitted parameters for the data including the indicated Λ values.

Discussion

The use of whole blood lymphocyte proliferation (WBLP) was reported in 1989¹⁶⁾ and utilized further by us in 1994.⁸⁾ Ferron and Jusko⁹⁾ then carried this method into the 96-weIl micr opiate format that fully optimized its advantages. With minute amounts of blood (8.25 μL /well) and culture medium (~ 200 μ/well), the technique allows rich data collection (over 2000 data points) from a single 20 mL blood sample. In contrast, use of isolated lymphocytes yields about 70 data points from 20 mL of blood.⁸⁾

The subtype of mononuclocytes grown in WBLP is also specific. A flow cytometry study following the growth of mononucleocyte subtypes, granulocytes, monocytes and lymphocytes was done in WBLP culture over 5 days.¹⁷⁾ Both granulocyte and monocyte cell morphology deteriorated over the first 3 days of culture. Only the shape and density of lymphocytes remained the same over time. With the stimulation by PHA, lym-phoblasts developed by day 3 and remained through day 5. These findings support our standard culture conditions indicating that 72 hr incubation with PHA was sufficient to produce lymphoblasts.

One complication in assessing in vitro immunosuppressive activity is the in vitro stability of the drugs over 3 days. While the corticosteroids are stable in aqueous media, the immunosuppressants, particularly Sir, are not. The CA are probably stable, but this is uncertain. However, stability is greater for Sir in the presence of RBC as presently used. Nevertheless all reported values using cell culture techniques may over-estimate the IC₅₀ of some of these drugs.

This may be the first time that CA have been studied in WBLP. The IC₅₀ values of CA in this study are similar to values reported by Birx et al.⁷⁾ using separated lymphocytes (~10−⁵ M). This IC₅₀ value is about 30-fold higher than therapeutic concentrations found during treatment of hypertension (eg. 120 mg/day diltiazem produces concentrations of 150μg/L or 333 nM¹⁸)). Unfortunately, such low therapeutic exposures would produce very little direct immunosuppressive activity (Fig. 2) and realize practically no synergistic benefit in joint use of CA and macrolides. The IC₅₀ values of CA are also 1000 times larger than the two corticosteroids and the exposures too low to augment therapy with these drugs as well. These effete interactions are in contrast to the marked synergy and exposures produced during joint administration of prednisolone and sirolimus.⁹⁾

Gender-related differences in response to corticosteroids have been reported. Lew et al.¹⁹⁾ studied in vivo act ivity of methylprednisolone in suppressing Cortisol secretion and T-lymphocyte trafficking in normal male and i'emaie volunteers. They found that suppression of these biomarkers is more sensitive in females. Our WBLP culture system also produces lower IC₅₀ values for females for both steroids.

Several reports in post-transplantation patients regarding the imeraction of diliiazem and cyclosporine, a drug with a similar mechanism of action as tacrolimus, have concluded that diltiazem decreased the clearance of cyclosporine,²⁰⁾ increased renal blood flow, and decreased the frequency of cyclosporine-induced renal toxicity.²¹⁾ One retrospective study in transplant patients medicated with both tacrolimus and nifedipine²²⁾ reported decreased tacrolimus doses after 90 days of nifedipine treatment. Most in vivo findings point towards pharmacokinetic interactions among CA and macroJidc immunosuppressants. These drugs are metabolized by the same cytochrome P450 CYP3A4 system in liver.²³⁾ Some CA metabolites such as N-inonodemetbylated diltiazem are potent cytochrome P450 inhibitors and may contribute to other activities as well.²⁴⁾ Therefore, through competition and partial inhibition of this metabolic pathway, long-term treatment wiih CA may decrease the clearance of some macrolides and steroids. Such an interaction was reported by Imani et al²⁵⁾ Doses of 15 mg of prednisolone and 180 mg of diltiazem were given to healthy volunteers for 3 days. The prednisolone AUC increased 21% after coadministration of diliiazem. However, there were no changes in suppression of T lymphocyte trafficking in blood albeit sampling was very limited. These drugs may also interact in their absorption in the GI tract and distribution in tissues. The multidrug transporters, P-glycoprotein (Pgp), cause drug efflux from many sites.²⁶⁾ These transporters are expressed in high levels in many organs and cells including liver, small intestine and T lymphocytes. ²⁷⁾ The CA and many immunosuppressants are both substrates and inhibitors of these transporters.^28-30) Therefore, via metabolic inhibition and/or competition for Pgp, the CA and immunosuppressants may interact during absorption and uptake into liver and lymphocytes . With these complications, possible pharmacodynamic interactions are difficult to assess in vivo. The WBLP culture allows screening for possible immunological interactions among these drugs.

Three-dimensional graphs have been proposed as a means to determine the nature of two drug interactions. ^14,15) By counting the number of data points above or below the additive interaction surface, these graphs provide qualitative analysis of the nature of the interaction. However, the variation of the data and the number of data points from the in vitro study affect the conclusions from this type of analysis. Such graphs are best viewed using computer rotation.

The current model (Eq. 5) has the same general assumption as the Loewe additivity equation, that the fractional effect contributed by the drugs is additive. However, with the use of the iterative bisection method and computer fitting we removed the restraint that an isoeffect has to be achieved for data analysis. This allows us to replace the left-hand side of the Loewe equation with a summary parameter (Λ). By fitting the observed interaction data with this model, we can obtain a single parameter to reflect the nature and degree of interaction. Since statistical information is available at the end of iteration, Λ can be used as a comparative index as well as for determination of the nature of interaction. The concavity of the surfaces also reflects the nature and degree of interactions among different drugs. The meaningfulness of Λ relies on spreading of data over the interaction surface, especially the area that determines the concavity and the shape of the surface (Fig. 5). A method that produces large amounts of data with numerous combinations of interacting concentrations (i.e. WBLP) is most appropriate for this type of analysis.

In conclusion, this report presents a lymphocyte cell culture study using human whole blood samples without the requirement of lymphocyte separation. An extension of the Loewe additivity equation quantitatively described the degree of interactions. We found that CA and the two corticosteroids, methylprednisolone and prednisolone, interact additively with a mild antagonistic response between diltiazem and prednisolone. The interactions among CA and the two macrolides, tacrolimus and sirolimus, are clearly synergistic with the strongest synergy found for nifedipine with tacrolimus and verapamil with tacrolimus. However, therapeutic exposures are likely to be too low for CA to meaningfully augment immunosuppressive effects of these other drugs.