Data and calculus on isobolographic analysis to determine the antinociceptive interaction between calcium channel blocker and a TRPV1 blocker in acute pain model in mice.

Determining antinociceptive interaction between Phα1β toxin (a voltage gated calcium channel blocker) and SB366791 (selective TRPV1 antagonist) may have both clinical and mechanistic implications for the pain management. This data in brief article is associated to the research paper "Synergistic antinociceptive effect of a calcium channel blocker and a TRPV1 blocker in an acute pain model in mice". This material supports the isobolographic analysis performed with the above drugs and shows: data of the dose response curves of the agents given as single drug or combination regimens. Mathematics and statistical processing of dose response curves, proportion of drugs dosage to be used in the combination, calculus of theoretical additive DE20 dose as well as experimentally obtained DE20 are provided. It is also presented details of statistical comparison between theoretical and experimentally obtained DE20.

Specifications Table

Value of the data

Data tables and calculus from this article may serves as a practical guide on isobolographic analysis for testing other drug regimens of even using different pain models.

Determining the interaction index by isobolographic analysis provides a measure of the in vivo degree of interaction of two drugs for a specified effect.

Data analysis presented in this article can be systematically compared to other data from probit analysis with analgesic drugs given in combination.

Data

Summary of linear regression analyses for the agents administered alone

Intraplantar SB366791

See Table 1.

Table 1

Dose-effect data of SB366791 (i.p.) on capsaicin-induced nociception.

Dose	xi	yi	xi.yi	(xi-X®)2
0.10	-1.00	8.86	-8.86	0.74
0.10	-1.00	-14.77	14.77	0.74
0.10	-1.00	-41.77	41.77	0.74
0.10	-1.00	38.29	-38.29	0.74
0.10	-1.00	37.43	-37.43	0.74
0.10	-1.00	-22.57	22.57	0.74
0.10	-1.00	-23.58	23.58	0.74
0.10	-1.00	0.81	-0.81	0.74
0.10	-1.00	-10.76	10.76	0.74
0.10	-1.00	-0.63	0.63	0.74
0.10	-1.00	-13.83	13.83	0.74
0.10	1.00	64.31	-64.31	0.74
0.10	-1.00	48.42	-48.42	0.74
0.10	-1.00	18.18	-18.18	0.74
0.40	-0.40	-13.08	5.23	0.07
0.40	-0.40	-23.21	9.28	0.07
0.40	-0.40	4.64	-1.86	0.07
0.40	-0.40	9.14	-3.66	0.07
0.40	-0.40	36.57	-14.63	0.07
0.40	-0.40	27.14	-10.86	0.07
0.40	-0.40	45.80	-18.32	0.07
0.40	-0.40	33.33	-13.33	0.07
0.40	-0.40	0.27	-0.11	0.07
0.40	-0.40	12.03	-4.81	0.07
0.40	-0.40	59.49	-23.80	0.07
1.00	0.00	-25.75	0.00	0.02
1.00	0.00	18.16	0.00	0.02
1.00	0.00	12.20	0.00	0.02
1.00	0.00	-1.90	0.00	0.02
1.00	0.00	17.72	0.00	0.02
1.00	0.00	25.32	0.00	0.02
1.00	0.00	2.53	0.00	0.02
1.00	0.00	5.06	0.00	0.02
1.00	0.00	-19.61	0.00	0.02
1.00	0.00	6.43	0.00	0.02
1.00	0.00	-12.06	0.00	0.02
1.00	0.00	50.79	0.00	0.02
1.00	0.00	29.37	0.00	0.02
1.00	0.00	15.08	0.00	0.02
1.00	0.00	44.44	0.00	0.02
1.00	0.00	31.75	0.00	0.02
2.00	0.30	26.58	7.97	0.19
2.00	0.30	70.46	21.14	0.19
2.00	0.30	53.59	16.08	0.19
2.00	0.30	22.86	6.86	0.19
2.00	0.30	40.86	12.26	0.19
2.00	0.30	13.43	4.03	0.19
2.00	0.30	13.28	3.98	0.19
2.00	0.30	22.49	6.75	0.19
2.00	0.30	52.85	15.85	0.19
2.00	0.30	-10.13	-3.04	0.19
6.00	0.78	30.62	23.89	0.85
6.00	0.78	65.31	50.94	0.85
6.00	0.78	17.07	13.32	0.85
6.00	0.78	84.28	65.74	0.85
6.00	0.78	25.95	20.24	0.85
6.00	0.78	23.42	18.27	0.85
6.00	0.78	18.99	14.81	0.85
6.00	0.78	6.33	4.94	0.85
6.00	0.78	60.13	46.90	0.85

Legend: Dose (nmol/site); xi: Log of dose (nmol/site); yi: (% of MEP); xiyi: product xi.yi; (xi-)2: (xi – xi average)2.

-Linear regression summary:

= -8.38; = 1118.42; N= 60; = -0.1397; =18.64; 2 = 22.13;

= 185.67; N.x.y = -156.20; 2= 0.0195

b= ;

a = - b. thus b = 16.3 (slope) and a = 20.9 (intercept)

-Slope variance = . wherein s2 = Q/(N-2) and Q =

V(b) = 31.3

- Assessment if slope differs from 0:

t = b/{V(b)}1/2; t = 2.91 which exceeds t-tabulated, thus slope differs from zero.

t (N-2 degrees of freedom; P=0.05; from t-distribution) = 1.96

- DE20 calculation: DE20 = (20 – a)/b (in log scale); DE20 = −0.056 or 0.88 nmol/site

- Variance of DE20 (VDE20); = s2 / b2 [ 1/N + (x1−x¨)2/ Sxx]; VDE20 = 0.042 (in log scale)

Table 6

Dose-effect data of Phα1β (i.p.) combined with SB366791 (i.p.) on capsaicin-induced nociception.

Dose	xi	yi	xiyi	(xi−X̅)2
0.013	-1.92	34.00	-64.79	1.57
0.013	-1.92	24.85	-47.71	1.57
0.013	-1.92	3.93	-7.54	1.57
0.013	-1.92	27.50	-52.81	1.57
0.013	-1.92	-19.89	38.19	1.57
0.013	-1.92	-2.37	4.55	1.57
0.013	-1.92	32.66	-62.72	1.57
0.013	-1.92	-63.64	122.18	1.57
0.013	-1.92	25.00	-48.00	1.57
0.013	-1.92	29.09	-55.85	1.57
0.013	-1.92	-20.00	38.40	1.57
0.013	-1.92	25.68	-49.31	1.57
0.038	-1.42	36.81	-52.27	0.57
0.038	-1.42	43.56	-61.85	0.57
0.038	-1.42	26.38	-37.46	0.57
0.038	-1.42	30.86	-43.82	0.57
0.038	-1.42	29.27	-41.57	0.57
0.038	-1.42	44.01	-62.49	0.57
0.038	-1.42	26.09	-37.05	0.57
0.038	-1.42	39.23	-55.71	0.57
0.038	-1.42	38.14	-54.16	0.57
0.038	-1.42	27.05	-38.40	0.57
0.038	-1.42	20.23	-28.72	0.57
0.038	-1.42	16.82	-23.88	0.57
0.115	-0.93	15.95	-14.83	0.07
0.115	-0.93	46.01	-42.79	0.07
0.115	-0.93	27.61	-25.67	0.07
0.115	-0.93	50.10	-46.59	0.07
0.115	-0.93	44.09	-41.00	0.07
0.115	-0.93	28.09	-26.13	0.07
0.115	-0.93	32.22	-29.96	0.07
0.115	-0.93	46.37	-43.12	0.07
0.115	-0.93	26.09	-24.27	0.07
0.115	-0.93	41.42	-38.52	0.07
0.115	-0.93	37.59	-34.96	0.07
0.115	-0.93	31.82	-29.59	0.07
0.115	-0.93	25.00	-23.25	0.07
0.115	-0.93	16.00	-15.01	0.07
0.115	-0.93	16.82	-15.64	0.07
0.346	-0.46	51.53	-23.71	0.04
0.346	-0.46	52.15	-23.99	0.04
0.346	-0.46	31.90	-14.67	0.04
0.346	-0.46	54.31	-24.98	0.04
0.346	-0.46	51.30	-23.60	0.04
0.346	-0.46	59.12	-27.19	0.04
0.346	-0.46	40.01	-18.40	0.04
0.346	-0.46	33.99	-15.63	0.04
0.346	-0.46	46.90	-21.57	0.04
0.346	-0.46	60.04	-27.62	0.04
0.346	-0.46	74.27	-34.16	0.04
0.346	-0.46	35.91	-16.52	0.04
0.346	-0.46	30.45	-14.01	0.04
0.346	-0.46	36.59	-16.83	0.04
0.346	-0.46	15.45	-7.11	0.04
1.038	0.02	52.76	0.84	0.47
1.038	0.02	60.12	0.96	0.47
1.038	0.02	53.99	0.86	0.47
1.038	0.02	86.77	1.39	0.47
1.038	0.02	49.50	0.79	0.47
1.038	0.02	63.93	1.02	0.47
1.038	0.02	54.03	0.86	0.47
1.038	0.02	45.78	0.73	0.47
1.038	0.02	49.90	0.80	0.47
1.038	0.02	49.64	0.79	0.47
1.038	0.02	65.51	1.05	0.47
1.038	0.02	59.49	0.95	0.47
1.038	0.02	45.45	0.73	0.47
1.038	0.02	45.45	0.73	0.47
1.038	0.02	16.14	0.26	0.47
1.038	0.02	50.23	0.80	0.47
3.114	0.49	54.60	26.75	1.34
3.114	0.49	63.80	31.26	1.34
3.114	0.49	66.26	32.47	1.34
3.114	0.49	69.94	34.27	1.34
3.114	0.49	61.52	30.15	1.34
3.114	0.49	65.13	31.91	1.34
3.114	0.49	61.10	29.94	1.34
3.114	0.49	58.74	28.78	1.34
3.114	0.49	68.17	33.40	1.34
3.114	0.49	67.70	33.17	1.34
3.114	0.49	68.25	33.44	1.34
3.114	0.49	72.08	35.32	1.34

Legend: Dose (nmol/site); xi: Log of dose (nmol/site); yi: (% of MEP); xiyi: product xi.yi; (xi−)2: (xi –xi averaged)2.

- Linear regression summary:

= -54.8; = 3260; N= 82; = 0.66822; = 40; 2 = 87.4664;

= -1089.7; N.x.y = -2178.55; 2= 0.446517

b= ;

a = - b. thus b = 21.4 (slope) and a = 54.1 (intersept)

- Slope variance = . wherein s2 = Q/(N-2) and Q =

V(b) = 4.9

- Assessment if slope differs from 0:

t = b/{V(b)}1/2; t = 9.64 which exceeds t-table, thus slope differs from zero

t (N-2 degrees of freedom; P=0.05; from t-distribution) = 1.96

- DE20 calculation: DE20 = (20 – a)/b (in log scale); DE20 = −1.59 or 0.025 nmol/site

- Variance of DE20 (VDE20); = s2 / b2 [ 1/N + (x1−x¨)2/ Sxx]; VDE20 = 0.016 (in log scale)

Intraplantar Phα1β

See Table 2.

Table 2

Dose-effect data Phα1β (i.p.) on capsaicin-induced nociception.

Dose	xi	yi	xiyi	(xi−X̅)2
0.01	-2.00	19.51	-39.02	1.00
0.01	-2.00	27.44	-54.88	1.00
0.01	-2.00	46.34	-92.68	1.00
0.01	-2.00	0.33	-0.66	1.00
0.01	-2.00	6.23	-12.46	1.00
0.01	-2.00	-36.30	72.61	1.00
0.01	-2.00	20.49	-40.98	1.00
0.01	-2.00	12.31	-24.63	1.00
0.03	-1.52	18.90	-28.73	0.27
0.03	-1.52	31.71	-48.20	0.27
0.03	-1.52	18.69	-28.41	0.27
0.03	-1.52	44.92	-68.28	0.27
0.03	-1.52	7.54	-11.46	0.27
0.03	-1.52	30.51	-46.38	0.27
0.03	-1.52	30.51	-46.38	0.27
0.03	-1.52	-15.59	23.70	0.27
0.10	-1.00	64.63	-64.63	0.00
0.10	-1.00	26.22	-26.22	0.00
0.10	-1.00	50.61	-50.61	0.00
0.10	-1.00	48.17	-48.17	0.00
0.10	-1.00	8.20	-8.20	0.00
0.10	-1.00	14.10	-14.10	0.00
0.10	-1.00	35.74	-35.74	0.00
0.10	-1.00	37.05	-37.05	0.00
0.10	-1.00	25.84	-25.84	0.00
0.10	-1.00	29.18	-29.18	0.00
0.10	-1.00	38.53	-38.53	0.00
0.30	-0.52	54.27	-28.22	0.23
0.30	-0.52	44.51	-23.15	0.23
0.30	-0.52	43.61	-22.68	0.23
0.30	-0.52	20.00	-10.40	0.23
0.30	-0.52	30.49	-15.86	0.23
0.30	-0.52	45.88	-23.86	0.23
0.30	-0.52	55.23	-28.72	0.23
0.30	-0.52	5.12	-2.66	0.23
0.50	-0.30	67.68	-20.30	0.49
0.50	-0.30	68.29	-20.49	0.49
0.50	-0.30	62.20	-18.66	0.49
0.50	-0.30	62.80	-18.84	0.49
0.50	-0.30	65.85	-19.76	0.49
0.50	-0.30	30.49	-9.15	0.49
0.50	-0.30	35.08	-10.52	0.49
0.50	-0.30	41.64	-12.49	0.49
0.50	-0.30	41.64	-12.49	0.49
0.50	-0.30	41.87	-12.56	0.49
0.50	-0.30	58.57	-17.57	0.49
0.50	-0.30	56.57	-16.97	0.49

Legend: Dose (nmol/site); xi: Log of dose (nmol/site); yi: (% of MEP); xiyi: product xi.yi; (xi−)2: (xi –xi averaged)2.

Linear regression summary:

= -46.92; = 1589.6; N= 47; = -0.99; = 33.82; 2 = 64.72;

= -1175.24; N.x.y = -1586.9; 2= 0.99

b= ;

a = - b. thus b = 23.2 (slope) and a = 57.1 (intercept)

Slope variance = . wherein s2 = Q/(N-2) and Q =

V(b) = 18.1

- Assessment if slope differs from 0:

t = b/{V(b)}1/2; t = 5.40 which exceeds t-tabulated, thus slope differs from zero

t (N-2 degrees of freedom; P=0.05; from t-distribution) = 1.96

- DE20 calculation: DE20 = (20 – a)/b (in log scale); DE20 = −1.60 or 0.025 nmol/site

- Variance of DE20 (VDE20); = s2 / b2 [ 1/N + (x1−x¨)2/ Sxx]; VDE20 = 0.025 (in log scale)

Intrathecal Phα1β

See Table 3.

Table 3

Dose-effect data of Phα1β (i.t.) on capsaicin-induced nociception.

Dose	xi	yi	xiyi	(xi- X̅)2
0.0003	-3.52	39.54	-139.20	2.47
0.0003	-3.52	-25.58	90.05	2.47
0.0003	-3.52	31.40	-110.50	2.47
0.0003	-3.52	-4.65	16.37	2.47
0.0003	-3.52	41.29	-145.30	2.47
0.0003	-3.52	13.11	-46.15	2.47
0.0003	-3.52	4.50	-15.84	2.47
0.0003	-3.52	-0.98	3.44	2.47
0.0003	-3.52	13.82	-48.64	2.47
0.0003	-3.52	12.88	-45.34	2.47
0.0003	-3.52	-1.17	4.12	2.47
0.0003	-3.52	20.38	-71.72	2.47
0.0003	-2.52	50.00	-126.00	0.33
0.003	-2.52	24.63	-62.06	0.33
0.003	-2.52	39.55	-99.67	0.33
0.003	-2.52	34.18	-86.13	0.33
0.003	-2.52	65.40	-164.80	0.33
0.003	-2.52	20.37	-51.33	0.33
0.003	-2.52	24.07	-60.67	0.33
0.003	-2.52	17.44	-43.95	0.33
0.003	-2.52	23.26	-58.60	0.33
0.003	-2.52	20.93	-52.74	0.33
0.003	-2.52	27.20	-68.55	0.33
0.003	-2.52	63.47	-159.90	0.33
0.003	-2.52	42.86	-108.00	0.33
0.003	-2.52	37.24	-93.84	0.33
0.01	-2.00	19.84	-39.68	0.00
0.01	-2.00	-30.95	61.91	0.00
0.01	-2.00	47.76	-95.52	0.00
0.01	-2.00	50.00	-100.00	0.00
0.01	-2.00	96.27	-192.50	0.00
0.01	-2.00	40.08	-80.17	0.00
0.01	-2.00	33.33	-66.67	0.00
0.01	-2.00	26.58	-53.16	0.00
0.01	-2.00	26.19	-52.38	0.00
0.01	-2.00	41.67	-83.33	0.00
0.01	-2.00	37.96	-75.93	0.00
0.01	-2.00	35.19	-70.37	0.00
0.01	-2.00	43.52	-87.04	0.00
0.01	-2.00	43.52	-87.04	0.00
0.01	-2.00	45.37	-90.74	0.00
0.01	-2.00	50.00	-100.00	0.00
0.10	-1.00	50.00	-50.00	0.90
0.10	-1.00	36.51	-36.51	0.90
0.10	-1.00	39.55	-39.55	0.90
0.10	-1.00	69.40	-69.40	0.90
0.10	-1.00	68.66	-68.66	0.90
0.10	-1.00	29.11	-29.11	0.90
0.10	-1.00	40.93	-40.93	0.90
0.10	-1.00	28.27	-28.27	0.90
0.10	-1.00	33.33	-33.33	0.90
0.10	-1.00	58.33	-58.33	0.90
0.10	-1.00	42.59	-42.59	0.90
0.10	-1.00	66.67	-66.67	0.90
0.10	-1.00	55.56	-55.56	0.90
0.10	-1.00	59.26	-59.26	0.90
0.10	-1.00	69.44	-69.44	0.90
0.30	-0.52	57.14	-29.71	2.04
0.30	-0.52	-3.97	2.06	2.04
0.30	-0.52	58.21	-30.27	2.04
0.30	-0.52	71.64	-37.25	2.04
0.30	-0.52	67.91	-35.31	2.04
0.30	-0.52	45.15	-23.48	2.04
0.30	-0.52	51.06	-26.55	2.04
0.30	-0.52	29.96	-15.58	2.04
0.30	-0.52	36.91	-19.19	2.04
0.30	-0.52	60.71	-31.57	2.04
0.30	-0.52	51.85	-26.96	2.04
0.30	-0.52	75.93	-39.48	2.04
0.30	-0.52	55.56	-28.89	2.04
0.30	-0.52	62.96	-32.74	2.04
0.30	-0.52	77.78	-40.44	2.04

Legend: Dose (nmol/site); xi: Log of dose (nmol/site); yi: (% of MEP); xiyi: product xi.yi; (xi−)2: (xi –xi averaged)2.

- Linear regression summary:

= -132.32; = 2787; N= 72; = -1.84; = 38.72; 2 = 320.64;

= -4120; N.x.y = -5123; 2= 3.38

b= ;

a = - b. thus b = 12.9 (slope) and a = 62.5 (intercept)

- Slope variance = . wherein s2 = Q/(N-2) and Q =

V(b) = 4.9

- Assessment if slope differs from 0:

t = b/{V(b)}1/2; t = 5.84 which exceeds t-tabulated, thus slope differs from zero.

t (N-2 degrees of freedom; P=0.05; from t-distribution) = 1.96

- DE20 calculation: DE20 = (20 – a)/b (in log scale); DE20 = −3.28 or 0.5 pmol/site

- Variance of DE20 (VDE20); = s2 / b2 [ 1/N + (x1−x¨)2/ Sxx]; VDE20 = 0.09 (in log scale)

Calculation of the proportion of constituents in the mixture

.

a + b = c. wherein:

a = the quantity (in nmol) of SB366791

b = quantity (nmol) of Phα1β

c = sum (in nmol) of quantities of Phα1β and SB366791 in the mixture

The proportion of a and b was fixed and calculated according to the formulae below:

a = A x f

b = (1-f) x B; wherein:

A = DE20 of SB366791

B = DE20 of Phα1β

f = proportion factor.

The factor f was calculated based on the variances of the DE20 values from SB366791 (A) and Phα1β (B) according to the formula:

f = V (B) / V (A) + V (B); wherein:

V (A) = variance of DE20 of SB366791 and

V (B) = variance of DE20 of Phα1β;

For combination of intraplantar Phα1β with SB366791. f = 0.38

For combination of intraplantar SB366791 with intrathecal Phα1β. f = 0.69 (Table 4, Table 5).

Table 4

Doses used in the dose-response curve for intraplantar combination of SB366791 and Phα1β.

Drug pair	SB366791 (nmol/site)	Phα1β (nmol/site)	Composed drug pair (nmol/site)
1	0.012	0.0006	0.013
2	0.037	0.001	0.038
3	0.11	0.005	0.115
4	0.33	0.016	0.346
5	0.99	0.048	1.038
6	2.97	0.144	3.114

Table 5

Doses used in the dose-response curve for concurrent treatment with SB366791 (i.p.) and Phα1β (i.t.).

Drug pair	SB366791 (nmol/site)	Phα1β (nmol/site)	Composed drug pair (nmol/site)
1	0.022	0.00000048	0.02200048
2	0.066	0.0000014	0.0660014
3	0.2	0.0000043	0.2000043
4	0.60	0.00013	0.60013
5	1.8	0.00039	1.80039
6	5.4	0.00117	5.40117

Summary of linear regression analyses for the agents administered in combination

Phα1β (i.p.) combined with SB366791 (i.p.)

See Table 6.

Phα1β (i.t.) combined with SB366791 (i.p.)

See Table 7.

Table 7

Dose-effect data Phα1β (i.t.) and SB366791 (i.p.) on capsaicin-induced nociception.

Dose	xi	yi	xiyi	(xi−X̅)2
0.022	-1.66	2.00	-3.07	1.50
0.022	-1.66	-33.77	56.06	1.50
0.022	-1.66	32.95	-54.70	1.50
0.022	-1.66	-34.79	57.76	1.50
0.022	-1.66	29.24	-48.54	1.50
0.022	-1.66	32.19	-53.43	1.50
0.022	-1.66	49.14	-81.57	1.50
0.022	-1.66	5.42	-9.00	1.50
0.022	-1.66	23.73	-39.39	1.50
0.022	-1.66	37.13	-61.64	1.50
0.022	-1.66	52.16	-86.59	1.50
0.022	-1.66	34.40	-57.10	1.50
0.066	-1.18	15.30	-18.06	0.56
0.066	-1.18	51.72	-61.02	0.56
0.066	-1.18	50.92	-60.09	0.56
0.066	-1.18	25.35	-29.91	0.56
0.066	-1.18	-29.95	35.35	0.56
0.066	-1.18	34.40	-40.59	0.56
0.066	-1.18	39.56	-46.68	0.56
0.066	-1.18	49.14	-57.99	0.56
0.066	-1.18	24.75	-29.20	0.56
0.066	-1.18	32.88	-38.80	0.56
0.066	-1.18	34.40	-40.59	0.56
0.066	-1.18	26.88	-31.72	0.56
0.200	-0.69	27.18	-18.75	0.07
0.200	-0.69	5.01	-3.46	0.07
0.200	-0.69	54.88	-37.87	0.07
0.200	-0.69	14.98	-10.33	0.07
0.200	-0.69	-2.30	1.59	0.07
0.200	-0.69	50.23	-34.66	0.07
0.200	-0.69	52.09	-35.94	0.07
0.200	-0.69	46.93	-32.38	0.07
0.200	-0.69	68.30	-47.13	0.07
0.200	-0.69	31.86	-21.99	0.07
0.200	-0.69	40.00	-27.60	0.07
0.200	-0.69	59.32	-40.93	0.07
0.200	-0.69	35.08	-24.21	0.07
0.200	-0.69	34.00	-23.73	0.07
0.200	-0.69	55.58	-38.35	0.07
0.600	-0.22	62.01	-13.64	0.05
0.600	-0.22	37.47	-8.24	0.05
0.600	-0.22	35.88	-7.89	0.05
0.600	-0.22	70.28	-15.46	0.05
0.600	-0.22	54.38	-11.96	0.05
0.600	-0.22	53.69	-11.81	0.05
0.600	-0.22	54.30	-11.95	0.05
0.600	-0.22	53.56	-11.78	0.05
0.600	-0.22	65.36	-14.38	0.05
0.600	-0.22	41.02	-9.02	0.05
0.600	-0.22	36.95	-8.13	0.05
0.600	-0.22	59.32	-13.05	0.05
0.600	-0.22	52.16	-11.48	0.05
0.600	-0.22	41.23	-9.07	0.05
0.600	-0.22	56.95	-12.53	0.05
1.800	0.25	81.00	20.25	0.47
1.800	0.25	71.50	17.88	0.47
1.800	0.25	52.51	13.13	0.47
1.800	0.25	71.66	17.91	0.47
1.800	0.25	57.14	14.29	0.47
1.800	0.25	59.22	14.80	0.47
1.800	0.25	74.20	18.55	0.47
1.800	0.25	54.30	13.57	0.47
1.800	0.25	67.57	16.89	0.47
1.800	0.25	52.20	13.05	0.47
1.800	0.25	43.05	10.76	0.47
1.800	0.25	63.39	15.85	0.47
1.800	0.25	44.65	11.16	0.47
1.800	0.25	48.75	12.19	0.47
1.800	0.25	63.78	15.95	0.47
5.400	0.73	77.88	56.85	1.36
5.400	0.73	57.83	42.22	1.36
5.400	0.73	68.89	50.29	1.36
5.400	0.73	76.41	55.78	1.36
5.400	0.73	56.51	41.25	1.36
5.400	0.73	69.78	50.94	1.36
5.400	0.73	65.42	47.76	1.36
5.400	0.73	52.20	38.11	1.36
5.400	0.73	67.46	49.24	1.36
5.400	0.73	57.63	42.07	1.36
5.400	0.73	61.05	44.56	1.36
5.400	0.73	65.15	47.56	1.36

Legend: Dose (nmol/site); xi: Log of dose (nmol/site); yi: (% of MEP); xiyi: product xi.yi; (xi−)2: (xi –xi averaged)2.

- Linear regression summary:

= -35.22; = 3614; N=81; = -0.43481; = 45; 2 = 64.9758;

= -573.761; N.x.y = -1571.51; 2= 0.1890

b= ;

a = - b. thus b = 20.1 (slope) and a = 53.4 (intersept)

- Slope variance = . wherein s2 = Q/(N-2) and Q =

V(b) = 5.1

- Assessment if slope differs from 0:

t = b/{V(b)}1/2; t = 7.99 which exceeds t-tabulated. Thus, slope differs from zero

t (N-2 degrees of freedom; P=0.05; from t-distribution) = 1.96

- DE20 calculation: DE20 = (20 – a)/b (in log scale); DE20 = -1.66 or 0.022 nmol/site

- Variance of DE20 (VDE20); = s2 / b2 [ 1/N + (x1−x¨)2/ Sxx]; VDE20 = 0.033 (in log scale)

Statistical comparisons between experimentally obtained DE20 (Zmix) and Theoretical additive DE20 (Zadd)

.

Zadd = f.A + (1-f). B wherein:

f = the proportion factor (obtained from topic B);

A = DE20 of SB366791;

B = DE20 of Phα1β.

Variance of Zadd = f2. V(A) + (1-f)2. V(B). wherein

f = proportion factor;

V(A) and V(B) = Variances of the DE20 of SB366791 and Phα1β, respectively.

Comparison test

t = (x-y)/[(SEx)2+(SEy)2]1/2; wherein:

x = Log of Zadd

y = Log of Zmix

(SEx)2 = V(Zadd)

(SEy)2= V(Zmix)

T = [tadd(SEx)2+tmix(SEy)2]/[(SEx)2+(SEy)2]; where in:

tadd = tabular value of t based on N´-2 degrees of freedom for 95% of significance

tmix = tabular value of t based on N-2 degrees of freedom for 95% of significance

(SEy)2= Variance of Zmix

Interpretation: If tT, Z is significantly smaller (95% of confidence) than the Zadd, which implies a synergistic effect of combined drugs (Table 8).

Table 8

Compilation of the comparison test.

Route of combined agents	Zadd(nMol)	Zmix (nMol)	tcritical	Ttabulated	Statistical significance
Intraplantar/Intraplanar	0.35	0.025	6.37	1.96	Yes
Intraplantar/Intrathecal	0.34	0.022	5.44	1.96	Yes

Experimental design, materials and methods

Capsaicin-induced nociceptive responses

This test was conducted essentially as described previously [1]. Briefly, individual animals were placed in transparent acrylic square boxes (20 cm per side) immediately after the capsaicin injection (1 nmol/paw i.p.), and nociceptive behaviours were recorded continuously for 300 s. Behaviours were quantified by recording the time spent licking, biting or flinching (nociceptive time) the paw injected with capsaicin. Phα1β (i.t. or i.p), SB366791 (i.p.), combined Phα1β + SB366791 or their respective vehicles were injected 10 min before the capsaicin injection. The initial dose ranges of Phα1β and SB366791 were selected based on previous data [1]. Antinociceptive effects were measured as a percentage of the maximum possible (% MPE) effect according to the formula: % MPE = 100*(A – B / A), where A is the averaged nociceptive time of the vehicle group and B is the nociceptive time of each animal in the treated group (drugs alone or in combination) [2].

Experimental design and statistical isobolographic analysis

Experimental design and statistical analyses were conducted essentially as previously described [3], [4], [5]. Briefly, dose-response curves were first obtained for Phα1β and SB366791 administered alone. Line equations, slope values and respective variances were obtained using linear regression [3]. DE20 values and 95% confidence limits were calculated using probit analysis. DE20 values (doses that exhibit 20% MPE) were used to assess whether the dose-effect of these drugs alone exhibited a constant potency ratio, which is necessary to perform fixed dose-pair combination of drugs [4].

Drug doses in association studies were determined as a proportion of their DE20 values. This proportion was constant and estimated based on a factor derived from the individual variances of the DE20 values. This fixed proportion of agents was necessary to assess whether the combination displayed enhanced potency indicative of synergism. Dose-response curves of associated drugs were constructed to obtain the doses that achieved the same effect level (20% MPE) compared to drugs given alone. This experimentally obtained DE20 (here called Zmix) was compared to theoretically calculated DE20 value for additive interactions (Zadd). The criterion for establishing a statistical significance was P < 0.05. Graphical assessments of synergy are also presented using isobolographic analyses. Measurement of the interaction index (α) was obtained by dividing experimentally obtained DE20 of the drug pair by the theoretical additive DE20 of the drug pair. The α interaction index provides a measure of the degree of synergism.

Subject area	Biology
More specific subject area	Neuropharmacology, pain management
Type of data	Table, text file
How data was acquired	Experimental observation of nociceptive behavior in mice by using a chronometer.
Data format	Raw and analyzed
Experimental factors	Dose response curves for Single drug administration of combined drugs, given at the same of at different sites
Experimental features	Isobolographic analysis using a fixed proportion ratio of two drugs.
Data source location	N.A.
Data accessibility	Data is with this article.