Criteria of Slope and Endogenous Level for Selection of Matrix in the Quantitation of Endogenous Compounds by LC-MS/MS

Figures & data

Figure 1. Background subtraction method.

Using a series of analyte standards spiked to an authentic matrix containing the endogenous analyte, a standard curve equation can be expressed as R = slope × conc. + intercept, where R is the ratio of analyte BM peak area to its internal standard peak area and conc. is concentration. When the endogenous analyte level in the matrix is greater than zero, there is a positive intercept in the standard curve (1). When the endogenous analyte concentration is subtracted from each spiked standard, the intercept is near zero in the standard curve (2). The standard curve (2) can be used for concentration calculation for all unknown samples in the same analytical run.

BM: Biomarker; conc.: Concentration.

Figure 2. Illustration of slope acceptance criteria for a surrogate matrix.

A peak area ratio of 2.25 (analyte to internal standard) from an authentic sample can be calculated with one of the three standard curve slopes. If the interpreted concentration is within ± 15% bias of the true concentration (using authentic matrix slope), that is, % slope difference from the authentic matrix slope (0.00823) ranges from -13.0 to +17.6%, then the standard curve in the surrogate matrix is considered to be parallel to the standard curve in the authentic matrix.

BM: Biomarker; conc.: Concentration.

Figure 3. Illustration of the relationship between endogenous level in a matrix and achievable lower limit of quantitation level.

(A) A high endogenous analyte concentration in the matrix of the standard curve will prevent achieving assay sensitivity (LLOQ). The peak response of matrix A contains the endogenous analyte concentration, 5 parts on the vertical axis. (B) The peak response of spiked LLOQ (only 20% of an endogenous level) onto matrix A. When the ratio of endogenous response (A = 5.0 parts) to net LLOQ response (B-A = LLOQ, 1.0 part) = or >5.0, the desired LLOQ is hard to achieve, as the variability of LLOQ (20%) is the same as the % increase of endogenous concentration in peak B. (C) Matrix C response containing a lower level of endogenous analyte concentration than Matrix A. (D) Spiked LLOQ on matrix C. The endogenous analyte is about 20% lower in matrix C than in matrix A. It will be easy to see enough response difference between peak D and peak C, which is C/(D - C) ≤4.0. Multiple biomarker assay experiments verified that the ratio of endogenous analyte peak response in the matrix to the net LLOQ response must be <4.0, then the desired LLOQ can be achieved or achievable with its precision and accuracy criteria of 20% bias. It can be concluded that assay LLOQ is dependent on the endogenous level of the matrix blank for its standard curve. The higher the endogenous level, the more difficult it is to achieve the desired LLOQ.

LLOQ: Lower limit of quantitation.

Table 1. The % slope difference criteria corresponding to % bias of analyte concentration acceptance criteria.

Bias of concentration criteria (%)	Slope difference criteria (%)
± 5.0	-4.8 to +5.3
± 7.0	-6.5 to +7.5
± 10	-9.1 to +11.1
± 15	-13.0 to +17.6
± 20	-16.7 to +25.0
± 25	-20.0 to +33.3
± 30	-23.0 to +42.8

The % slope difference from the authentic matrix standard curve is based on the accuracy criterion of the assay % bias when an assay has a linear response between its instrument response (like peak area ratio or peak height area) to the analyte concentration. A generic equation for % slope difference criterion is % slope difference = {[1/(1 + B)] - 1} × 100, where B is ± % bias accuracy acceptance criterion for the assay. B can be substituted in the formula with its -value or +value%.

Table 2. Example of relative matrix effect test design.

Sample ID	Surrogate matrix lot	Authentic matrix lot
Low QC	Lot A or more
Spiked	0.300 ng/ml
Mean	0.292
SD	0.0137
% CV	4.7
% bias	-2.8
n	3
Authentic lot		Lot 1	Lot 2	Lot 3	Lot 4	Lot 5	Lot 6
No spike
Mean 1	Measured endogenous conc.	5.65	4.84	4.29	5.16	5.67	3.34
SD		0.216	0.203	0.189	0.050	0.235	0.0310
% CV		3.8	4.2	4.4	1.0	4.1	0.9
% bias		NA	NA	NA	NA	NA	NA
n		3	3	3	3	3	3
Mid QC		Lot 1	Lot 2	Lot 3	Lot 4	Lot 5	Lot 6
Spiked conc.	12.0 ng/ml	12.0	12.0	12.0	12.0	12.0	12.0
Mean 2	Measured total conc.	17.5	16.6	16.3	16.2	17.9	14.9
Theoretical conc.	Measured endogenous + spiked	17.7	16.8	16.3	17.2	17.7	15.3
SD		0.300	0.153	0.416	0.751	1.03	0.551
% CV		2.5	1.3	3.5	6.8	8.4	4.8
% bias		-1.1	-1.2	0.0	-5.8	1.1	-2.6
n		3	3	3	3	3	3
Detected spiked conc.	Mean 2 - Mean 1	11.9	11.8	12.0	11.0	12.2	11.6
Overall % CV among six authentic lots for detected spiked BM1 conc.		3.6 (mean: 11.8; n = 6)

Theoretical conc. = measured endogenous conc. + spiked conc.

% bias = (measured total conc.)/theoretical conc. × 100%.

Detected spiked conc. = measured total conc. - measured endogenous conc.

The spiked analyte conc. should be no more than half (0.5×) to five (5×) fold of the endogenous level in all lots. Otherwise, it is hard to test whether the endogenous level in each lot can be added correctly with the spiked analyte. All concentrations were regressed with a surrogate matrix standard curve. The surrogate matrix was tested with the slope acceptance criterion and was within -13.0% to +17.6% difference of the slope of the authentic matrix standard curve.

BM: Biomarker; conc.: Concentration; CV: Coefficient of variation; ID: Identifier; NA: Not applicable; QC: Quality control; SD: Standard deviation.

Table 3. Selection of surrogate matrix using slope criteria and endogenous criteria in LC-MS/MS assays.

Case no. (LLOQ)	Matrix ID	Slope	Intercept	r-value^†	Assay name	Slope difference (%)^‡	Ratio of endogenous conc.^§ to LLOQ	Ratio^¶ <4.0?	Comment
1 (0.1 μg/ml)	Pooled hPL	0.06766	0.32721	0.9979	Plasma GL-1	NA	48.4	No	Authentic matrix, not achievable at LLOQ, 0.1 μg/ml
	0.3% HSA in PBS 10×	0.10971	0.00161	0.8952	Plasma GL-1	62.1	0.147	Yes	r <0.990, reject matrix
	Artificial plasma	0.07222	0.00559	0.9469	Plasma GL-1	6.7	0.774	Yes	r <0.990, reject matrix
	dPL, lot 1	0.06841	0.00510	0.9983	Plasma GL-1	1.1	0.746	Yes	Accept the lot
	Pooled dPL	0.07386	0.00456	0.9979	Plasma GL-1	9.2	0.617	Yes	Accept the lot
	dPL, lot 2	0.05467	0.00373	0.9997	Plasma GL-1	-19.2	0.682	Yes	Reject the matrix, failed slope criteria, not parallel
	dPL, lot 3	0.06762	0.00435	0.99562	Plasma GL-1	0.0	0.643	Yes	Accept the lot
	dPL, lot 4	0.05908	0.00475	0.99948	Plasma GL-1	-12.6	0.804	Yes	Accept the lot
2 (5 pg/ml)	hCSF (vendor 1)	0.0541	0.0513	0.9989	CSF BM2	NA	0.474	Yes	Authentic matrix (costly)
	hCSF (vendor 2)	0.0532	0.0633	0.9989	CSF BM2	NA	0.595	Yes	Authentic matrix (costly)
	aCSF	0.0535	0.0147	0.9996	CSF BM2	1.1, 0.6	0.137	Yes	Accept the lot
3, first test (5 ng/ml)	hCSF, lot 1	0.00436	0.14997	0.9946	CSF BM3	NA	6.879	No	Authentic matrix (costly and preventing LLOQ at 5 ng/ml)
	aCSF	0.00517	0.04827	0.9984	CSF BM3	18.6	1.867	Yes	Reject the matrix, failed slope criteria, not parallel
	50% aCSF/50% hCSF, lot1	0.00474	0.09204	0.9986	CSF BM3	8.7	3.884	Yes	Accept the lot
3, second test (5 ng/ml)	hCSF, lot 2	0.00514	0.09695	0.9978	CSF BM3	NA	3.772	Yes	Authentic matrix (costly)
	aCSF	0.00605	0.00264	0.9984	CSF BM3	17.7	0.087	Yes	Reject the matrix, failed slope criteria, not parallel
	50% aCSF/50% hCSF, lot 2	0.00527	0.06146	0.9993	CSF BM3	1.9	2.332	Yes	Accept the lot
4 (100 μg/ml)	Pooled hPL	0.001428	0.3817	0.9981	Plasma BM1	NA	2.67	Yes	Accept the lot
	Pooled dPL	0.001517	0.02604	0.9990	Plasma BM1	6.2	0.172	Yes	Accept the lot
	50% dPL/50% hPL	0.001390	0.2491	0.998	Plasma BM1	-2.7	1.79	Yes	Accept the lot

† Criterion for a linear standard curve is set at r ≥0.990 for accepting a run.

‡ (Tested matrix slope - authentic matrix slope)/authentic matrix slope × 100%.

§ Intercept/slope.

¶ If the ratio of endogenous conc. to LLOQ conc. <4.0, then the desired LLOQ is achievable; either lower endogenous level in the matrix for the standard curve or raise LLOQ conc. to make the ratio <4.0.

aCSF: Artificial cerebrospinal fluid; BM: Biomarker; conc.: Concentration; CSF: Cerebrospinal fluid; dPL: Delipidized plasma; HSA: Human serum albumin; hCSF: Human cerebrospinal fluid; hPL: Human plasma; ID: Identifier; LLOQ: Lower limit of quantitation; NA: Not applicable; PBS: Phosphate-buffered saline.