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ScientificWorldJournal
2014 Jan 01;2014:936202. doi: 10.1155/2014/936202.
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Oversimplification and overstandardization in biological methods: sperm bioassays in ecotoxicology as a case of study and a proposal for their reformulation.
Murado MA
,
Prieto MA
.
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An interesting toxicological bioassay (fertilization inhibition in sea urchin) uses as assessment criterion a variable (fertilization ratio) whose variation with time creates two types of difficulties. First, it fails to distinguish between the toxic effect and the spontaneous decline in the sperm activity, causing some inconsistencies. Second, the sensitivity of the fertilization ratio to many other variables of the system requires a complex standardization, constraining the achievement of the method without solving its main problem. Our proposal consists of using a parameter (sperm half-life) as the response of the assay, and describing explicitly the behavior of the system as a simultaneous function of dose and time. This new focus is able to solve the problematic character of the results based on the fertilization ratio and by using the same data set which is required by the conventional approach; it simplifies the protocol, economizes experimental effort, provides unambiguous and robust results, and contributes to the detection of an artefactual temperature effect, which is not very evident under the usual perspective. Potential application of this new approach to the improvement of other formally similar bioassays is finally suggested.
Figure 1. Effect of the parameters β and β
0 from (2) on the fertilization kinetics for a constant value of S
0 (1,000/μL) and increasing values of O
0 (1, 2,…,6/μL). (b) Parametric values (β = 3.8 × 10−6; β
0 = 3.3 × 10−4 mm3·s−1) from Vogel et al. [27]; at left and right, results of dividing by 4 the value of β and multiplying by 4 the value of β
0, respectively.
Figure 2. Fertilization ratio as a function of gamete concentrations in Paracentrotus lividus ((2) with the central parametric values from Figure 1) at 2 (a) and 10 minutes (b). (c) Values along the diagonal of the S
0
O
0 plane in (a) (∙) and (b) (∘), illustrating the effect of the absolute gamete population for a single S
0/O
0 ratio.
Figure 3. (a) Spermatic lifespan (Paracentrotus lividus) in sea water at 18–20°C, pH = 8.2-8.3, diluted “dry” sperm (1/3,000). Data from Vogel et al. [27] (points), adjusted to (5) (line). (b) Relationships between the maxima corresponding to the fertilization kinetics (left) and the spermatic lifespan (right).
Figure 4. Different perspectives of the relationships among dose (D), exposure time (t), fertilization ratio (F), and response (R), this last one defined as (increasing) decrease of τ or F, as a function of the dose with respect to the control. Simulations from model (7) with the parametric values are specified in Table 1, supposing a negligible error (σ = 5 × 10−4). The closed symbols in subfigures (B2) and (B3) correspond to the control time course and the complete dose series at time zero, respectively. The open symbols in subfigures (B2) and (B3) correspond to the different response at different doses of toxic and the different exposure times, respectively. See text and Table 1 for details.
Figure 5. Effect of the observational error on the parametric estimates of model (7) (τ: ▵, v: ▿, K: ⋄, m: ∘, a: □) and their confidence intervals under the specified conditions. Dotted lines indicate parametric true values.
Figure 6. Simulation (points) of a single assay (σ = 0.100, 2 replicates, no smoothing) and its fitting (lines) to models (1) (U series) and (7) (B series). In B series, correlation between simulated and predicted results (B2), residuals as a function of the dose (B3) and dr relationships (U and B) according to the univariate (dotted lines) and bivariate (solid line) approaches are also shown. Acceptable fittings were not possible at t
1 and t
6 (omitted points at t
6 were located outside the represented domain) (The rest of keys as in Figure 2). See also text and Table 2.
Figure 7. Distributions of the parametric estimates obtained with models (1) (white) and (7) (grey) in 2,000 repetitions of an assay with σ = 0.100, 2 replicates and smoothed data along the variable D. Dotted lines indicate parametric true values.
Figure 8. Effect of the spermatic half-life (τ) on the estimation of the parameter m
F (ED50) by means of model (1) at different times, supposing observations with a negligible error (σ = 5 × 10−4). Simulations with model (7), combining the following pairs of true parametric values: □: τ = 0.6, m
τ = 0.25; ■: τ = 0.6, m
τ = 0.35; ◯: τ = 0.4, m
τ = 0.25; ●: τ = 0.6, m
τ = 0.35 (the rest of the parametric values as in Table 1). Bars indicate the confidence intervals (α = 0.05) of the estimates.
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