Question

A novel chimeric monoclonal antibody (Nocatmab) has been developed for the treatment of tetanospasmin toxicity, one of the most potent and dangerous toxins known in modern medicine. Each molecule of Nocatmab inactivates four molecules of tetanospasmin. Knowing that the lethal dose for tetanospasmin is 2.5 ng/kg for a human adult, and that the MW (Molecular Weight) of tetanospasmin is 150,020 amu, can you calculate the minimal dose of Nocatmab (MW 348,055 amu) required to treat a subject who weighs 63 kg and has recieved a lethal dose of tetanospasmin?

Answer 1

Solution :-

Lets first calculate the mass of the tetanospasmin in 63 kg adult

63 kg * 2.5 ng per kg = 157.5 ng

157.5 ng * 1 g / 1*10^9 ng = 1.575*10^-7 g

Lets calculate the moles

Moles = mass/ molar mass

Moles of tetanospasmin = 1.575*10^-7 g * 1 mol / 150020 g per mol

                                            = 1.05*10^-12 mol

1 molecule of Nocatmab inactivates four molecules of tetanospasmin

So moles of the nocatmab needed are

1.05*10^-12 mol tetanospasmin * 1 mol Nocatmab / 4 mol tetanospasmin = 2.625*10^-13 moles

Now lets convert the moles of the Nocatmab to its mass

Mass= moles * molar mass

         = 2.625*10^-13 mol * 348055 g per mol

         = 9.14*10^-8 g

Lets convert the g to ng

9.14*10^-8 g * 1*10^9 ng / 1 g = 91.4 ng

So to treat the 63 kg adult it need 91.4 ng of the Nocatmab