為什麼 OD 不能直接報告？
抗原—抗體結合是「飽和反應」，劑量反應呈 sigmoidal（S 形）而非線性。把 OD 拿去算濃度，必須先以標準品擬合曲線。Findlay & Dillard (2007) 與 FDA Bioanalytical Method Validation Guidance (2018) 都把 4-PL（四參數對數）列為配體結合分析的預設方法；競爭型與 multiplex ELISA 因曲線不對稱，須改用 5-PL（多一個 asymmetry 參數 g）。
2023-2024 年 YCharOS / eLife 研究指出 50% 以上市售抗體在至少一種應用上失敗，因此抗體驗證（KO/KD 對照）已是審稿必問題。
Antigen–antibody binding saturates, so dose-response is sigmoidal, not linear. To convert OD to concentration you must fit a calibration curve. Findlay & Dillard (2007) and FDA Bioanalytical Guidance (2018) both set the 4-PL (four-parameter logistic) as the default for ligand-binding assays; asymmetric (competitive / multiplex) curves need 5-PL (extra asymmetry parameter g).
YCharOS / eLife studies in 2023-2024 show that >50% of commercial antibodies fail in at least one application — so antibody validation (KO / KD controls) is now a standard reviewer question.
一、四參數 (4-PL) 公式
4-PL：Y = D + (A − D) / (1 + (X/C)^B)，其中 A 為下平台、D 為上平台、C 為 EC50/IC50、B 為 Hill slope。5-PL 額外引入不對稱參數 g。
4-PL: Y = D + (A − D) / (1 + (X/C)^B) where A = lower asymptote, D = upper asymptote, C = EC50/IC50, B = Hill slope. 5-PL adds an asymmetry parameter g.
LOD
= blank mean + 3·SD
能可靠偵測但不一定能定量的最低濃度。
= blank mean + 3·SD
Lowest concentration reliably detected (not necessarily quantified).
LOQ
= blank mean + 10·SD（且 CV ≤ 20%）
能可靠定量的最低濃度。
= blank mean + 10·SD (with CV ≤ 20%)
Lowest concentration reliably quantified.
Parallelism
樣品序列稀釋曲線需與標準曲線平行（F-test 或 RSSE）；非平行 = matrix effect 或抗體交叉反應。
Sample dilution curve must run parallel to the standard curve (F-test or RSSE); non-parallelism = matrix effects or antibody cross-reactivity.
4-PL 標準曲線擬合器
調整四個參數，觀察曲線形狀。綠色區段是可定量範圍 (ED20-ED80)，橘色為樣品 OD，計算對應濃度。
Tune the four parameters and watch the curve. Green region = quantifiable range (ED20-ED80); orange line shows your sample OD and back-calculated concentration.
X：log10(concentration pg/mL) | Y：OD
二、R 與 Python 擬合 4-PL
# R: drc 套件 — Ritz 2015 PLOS ONE library(drc) std <- read.csv("std.csv") # conc, OD fit <- drm(OD ~ conc, data=std, fct=LL.4(names=c("B","A","D","C"))) summary(fit) plot(fit, log="x", type="all") # 反算未知樣品濃度 unk <- read.csv("samples.csv") # OD conc <- ED(fit, respLev=unk$OD, type="absolute", interval="delta")
import numpy as np from scipy.optimize import curve_fit def four_pl(x, A, B, C, D): return D + (A - D) / (1 + (x/C)**B) std_conc = np.array([3.9,7.8,15.6,31.25,62.5,125,250,500]) std_od = np.array([0.08,0.12,0.22,0.45,0.91,1.55,2.10,2.40]) popt,_ = curve_fit(four_pl, std_conc, std_od, p0=[0.05,1,100,2.5]) # 反推：給 OD 解出 conc def inverse_4pl(y, A, B, C, D): return C * ((A - D)/(y - D) - 1) ** (1/B) unk_od = np.array([0.4, 1.2, 2.0]) print(inverse_4pl(unk_od, *popt))
三、何時用哪一種擬合？
四、reviewer 必問清單
❌ 線性硬套 S 曲線
把整條 S 曲線塞進線性回歸，導致兩端非線性區外推完全錯誤。
Forcing linear regression on the full sigmoid extrapolates the non-linear plateaus completely wrong.
❌ 未做 spike-and-recovery
不同 matrix（血漿 vs 細胞培養液）可能造成 30-50% 偏差。Recovery 應在 80-120% 區間。
Different matrices (plasma vs media) cause 30-50% bias. Recovery should be 80-120%.
❌ 抗體未驗證
商用抗體在 KO 細胞失敗率 > 50%。檢查 YCharOS / Antibodypedia / 期刊 RRID。
Commercial antibodies fail in KO controls > 50% of the time. Check YCharOS / Antibodypedia / journal RRIDs.
❌ 不報告 inter-plate CV
同樣品在不同盤的 CV 應 < 15%。跨盤分析需在每盤放入 QC 樣品做漂移校正。
Same sample across plates should have CV < 15%. For cross-plate analyses, include QC samples on every plate for drift correction.
🎯 章末小測驗
1. LOQ 的定義最接近？
2. 競爭型 ELISA 通常使用？
3. 樣品 OD 高於最高標準品時應？