[MUSIC] Okay, now we're going to do a quantitative analysis of the result obtained by Adriane and his colleagues. This analyses could have been done and actually this is probably what Max Delbrook was hoping for to really believe the answer. As you remember, we had two tubes. We had two tubes in which there was growth of S bacteria. Virulent, deadly bacteria. And two tubes negative. That was a transformation asset with three nanogram of DNA. Now, you may ask, how can I get the number of transformation events? Because when a tube has transformants, this tube could have one transformation event, giving rights to all the transformants, two transformation events, each giving rise to two, to half of it. A million transformation event. You don't know. You just have no way of knowing when you're right at the end of the day. So you have to go to a statistical analysis of the data. Don't worry, the statistics is very simple. Imagine you go to the park, and in your city there is a chess board on the floor, 64 cases, and you have a bag with 64 coins. And you throw the coins, they're all the same weight, the same dimension, etc. Do you think you're going to have one coin per square? If you think so, go and try it. Of course, you will not have one coin per square. You will have some squares that are empty. And some squares that have one coin. And some square that have more than one coin. And it's about one-third, one-third, one-third. So if you want to decide how many coins per square you have in average, you have to use something that is called the Poisson distribution. Poisson was a French physicist in 19th century, and he was asked by the Ministry of Justice to compare the different court systems. One judge, three judge, with jury, without jury, how many appeal level you have, that would give the best and safest system. And he wrote a book called Probability [FOREIGN]. So this book, Probability of Making Mistakes in Penal Justice is a bit surprising that it comes in a course on bacterial genetics. But that Poisson book is very helpful because it is, and I spare you the details but it is the distribution that's most useful for the kind of biological experiment that we're dealing with. And we'll come back to it later. The Poisson distribution says that the only tubes, in this case or cases on the chess board that are informational are the empty one. Now, you may say, come on, this is a joke. It's the cases where I have no event that tell me how many event I have. Yes, because in all the cases that we have no event, no is a solid number, it's zero. When you have events, whether you have one, or two, or three, you cannot say. So they're not informative. So the 0 refraction in this case is 50% or 0.5. If 50% of the chess board cases are empty that means that your average is 0.6. I'm making very crude calculation because they help [INAUDIBLE], that means, of course, you don't have 0.6 coins that you will throw on the case. You have a certain number of coins per case. 60% of 64 is 38, roughly. That means your mom gave you a bag with only 38 coins and not 64 coins. You asked for 64 coins but you only got 38. That's what it means. So we have the average number of transformation. So, with 3 nanogram, we have 0.6 transformants. With 5 nanograms, we have 1 transformant. So, if we had a microgram of DNA, that's 200 x 5 nanogram. You would have 200 transformants. The real numbers 231. That's a 200 roughly. Roughly 200 per microgram of DNA. Now, this is an abysmally low number. It's very inefficient. Today, if you use another system of transformation called electric shock and specially prepared by. You can easily go up to 10 to the 8th per microgram of DNA, okay? 10 to the 8th is 1 million times better than 100. Okay, so now you want to ask yourself how efficient is that in terms of molecules. You have molecules in DNA, right? Molecule of DNA in the paper are roughly 1 kilobase. 1 kilobase is a 1000 base. So one base has a certain weight. A molecular weight of one base pair, because they are pairs, two strands of DNA, is roughly one base pair, is roughly 600 grams per 1 mole. So, if you have one kilo base pair, it's a 1000 times. So it's 6 times 10 to the 5 gram per mole. Now what is a mole? A mole is a unit composed of a certain number of molecules. And the number of molecules was devised by a Italian physicist named Avogadro. Avogadro is one of the few numbers that if you are a chemistry student you just have to know. 1 mole is 6 times 10 to the 23 molecules, that tells you how small the molecules are. So, you have these number, okay. So, you can play with it and you can go down. You remove 6 times 10 to the 5, you have 1, here. You remove the 6 and you have 10 to the 18. 1 gram will be equivalent to 10 to the 18 molecules. 1 nanogram is a billion times less, and so it's 10 to the 9 molecules. So we go back to this, if we have 5 nanogram you'll agree with me that you have five Stanton to the 9 molecule. Now, think about it, it's calculated, it was calculated by armies. That in order to kill a soldier, an enemy soldier you need his weight in bullets, which means many many bullets. Here we're talking about 5 billion. 5 billion is close to the population to the human population of Earth, it's close enough. You need all of these people around to have one that manage to succeed. It's worse than the lotto or playing at the casino. This is really rare. But now you're going to tell me, but this is crap, we don't believe you because if you take DNA from a bacterium like our streptococcus pneumoniae. Streptococcus pneumoniae has other genes. It doesn't have only the gene necessary for making the capsule. It has the genes to make metabolism, it has the genes to make lipids, it has the genes to make DNA, to make RNA, to make proteins, to pump salt in and out of the cell. All these genes are there. So when I make DNA, not all of that DNA will be useful. But only a fraction of it. Do you agree with that? And this fraction can be calculated today we know the genome size of streptococcus, there is about one molecule of interesting DNA. The DNA that called for the capsule, for the enzyme that makes to the capsule out of 2,000 genes. So, 1999 molecules are useless for the transformation. 1 in 2,000. So we have to divide this by 2,000. If we divide this by 2,000 we arrive at 2.5 divided by 2 times 10 to the 6. So now we have 2 million people. Okay, 2 million people is probably something like 20% or 25% of Manhattan population. 2 million people is a lot, but still it becomes a bit more reasonable, because you can say that all the other molecules will get lost in the water. God knows why. 200 molecules are needed now. 2 million molecule are needed to make 1 transformation. 2 million molecule of the gene, right? That single gene that was sufficient. Okay now, the calculation that Hammerstein and other critics were doing, where they say, okay, how do you deal with that? Think about it yourself. How do you deal with the criticism? It must be a DNA, a protein contaminant in the DNA. Well, you can have a religious attitude and say I believe because it's written somewhere, you can have a casino attitude and say I flip the coin and I believe either one of the two parties, or you can be a scientist. And you try to make it seriously. So you say okay, because you always have to make assumptions, working hypothesis, let's assume that in this 5 nanogram of DNA, I have some protein. Now the question is, how much? As a first step, it's not going to be 100% protein, right? It's bound to be less than some number. Let's assume to be very conservative that Avery was absolutely maniac in his work to refine the DNA and he only had open 1% contamination. 1 in a 1000 in weight, so this is 5 picogram is protein. So far, you agree. Now, let's make another assumption, which is the worst case. The worst case is that this is a single protein, the protein that makes a capsule. That sneaked through the DNA. And let's make an assumption that this is an average protein, which is roughly has a molecular weight of roughly 30,000. 30,000 gram per mole, okay. So, 30,000 per mole. That means that 3 x 10 to the 4th, this is just re-writing 30,000, is equal to 1 mole 6 x 10 to the 23 individual molecules. I shouldn't put an equal because those are not the same units. But corresponds to, and bear with me that I put equal. So you can play with the number, right? You go down to 1 picogram, which is 10 to the minus 12 gram, correspond to 2 times 10 to the 7 molecules. But we have 5 picogram of protein, so that is 10 to the 8th protein molecules. Of course, we have made an assumption. We made three assumptions. It's a single protein. It's mass is 38,000. And it is present at 0.1% contamination. But now if you remember the previous drawing, in the previous calculation, 5 nanogram of DNA is 2.5 x 10 to the 6th molecules of the gene. 2.5 million in 100 million. So even if the contamination is very, very low, there are more protein molecules than DNA molecules. So the criticism raised by Hammerstein and the others was not unreasonable. Now, of course, it becomes unreasonable to suppose that it's a single protein, that's the most unreasonable part of our three assumptions. But the criticism is a valid criticism. And it's very hard to say what is pure. Pure is a notion that is used in lots of different contexts. Pure water, pure water, if you talk to a chemist, pure water from a well is everything but pure. Unless you really distill it a certain number of times, you pass it through a filter and blaby and blah, blah, your water's not pure. As soon as it stays in contact with air for an hour, it's no longer pure water because CO2 has dissolved in it. So that's the term of purity. Purity is also a term used in your pure angel, yes. Since we don't exactly know what an angel is, we don't care whether we know or not what pure mean. Pure in terms of biology and biochemistry. Pure in terms of biology has been used by Nazi eugenics, who claim to have to prepare, pave the way for a pure race. And we all know that this is absolute crap and unscientific. Pure at the time of a microbiologist, a microbiologist claims that if you have isolated a colony on a plate it's a pure strain. But even that pure strain contains mutants. So it's not 100%. Probably, physicists would agree that a beam of electron is a pure contains pure particles. Even though their speed, their energy, and whatever is not the same, everybody would probably agree that an electron is equal to another electron is equal to a third electron as a first approximation. Pure for the biochemist was crystallize. If you remember this was the time where x-ray crystallography was really very strongly developed, and extremely useful, and imaginative, and give a lot of information. Geologists knew about crystals. So crystal, pure for the people of the time, was an enzyme that has been crystallized, that is pure. Today, when we buy enzymes we consider the purest form of enzyme is not that it has been crystallized because that takes too much time and is too expensive. The purist form of enzyme is recombinant. That's pure rate. Well, it is pure, but it still comes from a living organism. Of course, if you've taken bacterium and you add the human gene and you produce a human protein. That protein would be the only human protein producing this bacterium. But once you extract it, you have to get rid of all the bacteria proteins, because they are there. They're more or less prevalent, but they're there. So purity is a very difficult term, or it is a term that you can use, as long as you are aware of the limits of this purity.