Snake Venom Math

Quote of the Day

It is easier to exclude harmful passions than to rule them, and to deny them admittance than to control them after they have been admitted."

— Seneca


Introduction

Figure 1: View from My Hotel.

Figure 1: View from My Hotel.

I was a recently in Barbados doing some field work. Before going anywhere in the field, I like to check to see if there is anything in the area I will be visiting that could hurt me. I have become more careful since a trip to Florida a few years ago where I was warned that an installer had seen a coral snake in one of our enclosures the week before. There are no poisonous snakes in Barbados -- I had nothing to worry about. While doing the research, however, I encountered an interesting table going through the lethality of the most dangerous snake venoms. I thought this table would be interesting to discuss here.

Before I dive into the topic of snake venom, I do want to share a photo from Barbados (Figure 1). It was fun working there and the people could not have been friendlier. If I get to go again, I will bring my wife.

Background

I stumbled upon Table 1 in the Wikipedia on this page. To discuss this table, I first need to define the column headings.

  • "Species" is actually the common name of the snake.
  • LD50 SC is the subcutaneous dose that will kill 50% of the subjects tested.
  • "Dose" is the amount of venom delivered in a strike.
  • "Mice" is the number of mice that could be killed per dose, based on number of mice that would be killed by this dose if it was 100% lethal and equally divided between the mice.
  • "Humans" is the number of humans that could be killed per dose, based on the number of humans that would be killed by this dose, assuming that the dose was
    • equally divided between the humans.
    • the human have the same venom sensitivity as the mice.
    • the dose is 100% lethal.

I find this table interesting for a number of reasons:

  • You can see that there is a wide variation in the lethality of the different types of snake venom.
  • The amount of venom injected varies widely between species.
  • A little bit of calculator work showed that the "Mice killed Per Dose" and "Humans Killed Per Dose" were scaled versions of the LD50 value. The mouse was assumed to have a mass of 20 grams and the human a mass of 75 kg. We can determine the number of animals killed per dose (N) with the equation N=\frac{\frac{Dose}{L{{D}_{50}}}}{m}, where m is the mass of the animal in question.

There were a number of assumptions involved in making this table. I thought it might be interesting to investigate those assumptions.

Table 1: Wikipedia Table on Snake Lethality.

Species

LD50 SC (mg/kg)

Dose (mg)

Mice

Humans

Inland taipan

0.010

110.0

1,085,000

289

Black mamba

0.050

400.0

400,000

107

Forest cobra

0.225

1102.0

244,889

65

Eastern brown snake

0.030

155.0

212,329

59

Coastal taipan

0.106

400.0

208,019

56

Mainland tiger snake

0.190

336.0

138,000

31

Caspian cobra

0.210

590.0

135,556

27

Russell's viper

0.162

268.0

88,211

22

King cobra

1.090

1000.0

45,830

11

Cape cobra

0.400

250.0

31,250

9

Gaboon viper

5.000

2400.0

24,000

6

Saw-scaled viper

0.151

72.0

23,841

6

Fer-de-lance

3.100

1530.0

24,380

6

Jameson's mamba

0.420

120.0

12,709

4

Many-banded krait

0.090

18.4

10,222

3

Analysis

Variations in the Amount of Venom Injected

I assume that the amount of snake venom injected in a strike can vary widely. In fact, some other snake lethality charts actually list the variations. On one web page, they actually show a chart with how the amount of venom injected varies with subsequent strikes. The amount of venom and its potency also varies with the age and size of the snake.

Figure 2: Venom Injection Variation.

Figure 2: Venom Injection Variation.

 

Differences in Mouse and Human Lethality Levels

I have always wondered how well any test results translate from mice to humans. In the case of Table 1, assuming that the mouse and human lethality concentrations are the same is the simplest approach. However, I have no basis on which to believe this assumption is accurate. As a counter-example, consider the case of the Sydney funnel-web spider. It has a venom that is deadly to humans (and other primates), but does not affect other mammals. So I guess I do not really believe the column on human lethality is accurate -- the venom could be more or less lethal than indicated.

Calculation of the Number of Mice and Humans Killed

The lethality of the venom is referred to as LD50, the dose that is lethal to 50% of the subjects exposed. Yet the calculations seem to assume that 100% of those exposed to an equal division of the venom would die. That does not seem correct.

Conclusion

Everyday I see examples of data presented that seem to create more questions than they answer, which is just what Table 1 did for me.

 
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