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To Kill a Fish Egg

How much electricity does it take to kill a fish egg, or unhatched embryo? We have mentioned that in classes but have only discussed it in generalities. The purpose of this blog is to look more closely at the question and to quantify it as best we can with the limited information available. It makes sense to look at this from the perspective of egg, or embryo, diameter. Bohl et al. (2010), Electroshock-induced mortality in freshwater fish embryos increases with embryo diameter: a model based on results from 10 species, Journal of Fish Biology 76:975-986 is the source of information for this investigation.

Bohl et al. (2010) combined the results from their own studies and from others to estimate the power density (mW/cc) to kill fish embryos of various species and sizes with direct current (DC) or with pulsed direct current (PDC). Because the results were from multiple studies using different shock times and various PDC waveforms, there must be some flexibility in the comparisons, but these are perhaps the best data available for such an investigation. Below is a summary of the data from their Table 1. Refer to their paper for a list of species. D is power density.

table-1-bohl-et-al-2010

Note that fish response thresholds are typically measured in µW/cc, but here these are fish embryos,  and the objective is to kill them. Small things take more power density for a response, and the desired response here is much more drastic than for taxis or immobilization. Therefore, the power density threshold is reported in mW vs µW per cc.

fig-4-bohl-et-al-2010

The data from their Table 1 were used to construct their Figure 4. The graph above is the same as their Figure 4 except that only the DC data are used here, and a power regression is used here to fit the data.  This regression alone provides useful information for predicting thresholds for killing fish embryos of different sizes.

Embryos are spherical, so diameter can be used to calculate surface area and volume. Other readings reveal that membrane resistance is proportional to the reciprocal of the surface area. Therefore, I began to compute surface areas and current densities (Amperes per surface area) and voltage gradients (V/cm), all in an attempt to answer the initial question above. Of the electrical parameters, we can only directly measure voltage gradient, so I created a graph of voltage gradient VG versus embryo diameter. First, however, I used the power transfer theory model to convert the voltage gradient data from the various studies to what it would be at 100 µS/cm. Use of the PTT model requires knowledge of a fish’s  effective conductivity. Because that is unknown for unhatched embryos, I just used 100 µS/cm as their conductivity. Results in Table 1 for five of the eight species for DC were based on 100 µS/cm, so only three data points on the graph below were adjusted for conductivity.

vg-vs-dia

Because the exponent of the power regression of VG versus diameter was so close to -1, it seemed reasonable to further simplify the predictive equation to some coefficient slightly over 14 divided by embryo diameter in mm. The actual numerator for these data was approximately 14.8, so I rounded it to 15 and compared with the above graph.

vg-15-dia

Thus, the final simplified equation for predicting the voltage gradient required to kill fish embryos with DC is 15 divided by the diameter in mm. That is shown in the red line above whereas the actual fitted regression is indicated by the thin black line. The simplified equation should be quite useful for setting electrofishers to kill fish embryos. In most cases, the embryos were exposed to DC for 20 seconds.

dc-pdc-vs-dia

The results for DC (red line and solid black circles) are as above and are compared to those for PDC (black line and open circles). Results for PDC were more difficult to assess because of different shock times (10 or 20 seconds) and for various duty cycles (18, 24 and 48% current on time), all at 60 Hz. Instead of trying to fit a regression equation, I chose to use the same type of simplified equation as for the DC results. Thus, the equation for PDC threshold voltage gradient is 23 divided by diameter in mm. This is notable because fish immobilization threshold typically is lower for PDC than for DC, so something is fundamentally different about fish embryos. It may be related to the fact that electrical impedance in a fish probably is a combination of resistance and capacitive reactance; the various fish membranes likely act as capacitors. In embryos, the electrical impedance may be more simply resistance which is in turn a function of membrane surface area. For whatever the reason, the threshold voltage gradient for killing embryos was higher for PDC than for DC. This blog roughly quantifies the voltage gradient required to kill fish embryos under these conditions using DC or PDC.

Let me add that the most electrically sensitive phases of embryological development are thought to be generally between fertilization and the eyed-egg stage. More specifically, the most sensitive stage is when the embryo is in epiboly at or near gastrulation. In general, the embryos used in the studies referenced herein were in such an electrically sensitive developmental stage.

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