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[Music]

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[Applause]

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so we are interested in the first

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replicating molecules which could well

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have been RNA or something very similar

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and we're imagining there was something

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like a polymerase ribozyme which in our

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we have a pointer okay so in our in our

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cartoonist the red blob is a polymerase

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ribozyme which is functioning as a

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catalyst and it's binding to another

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strand which is the template and we're

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supposing the template is the same

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sequences itself and it's making the

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complementary strand to the template and

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there are ribosomes that work like this

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in the lab so this is a real one that

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came from the 2001 paper here and the

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best ones of this type now go up to 200

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nucleotides so this is good except that

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this one won't work with its own

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sequence as a template so it doesn't yet

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replicate itself so if we think about

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there's three requirements that are that

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a sequence must have in order to sustain

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replication in the RNA world it would

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have to be able to work on its own

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sequence it would have to be able to

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replicate faster than the breakdown rate

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of the same sequence by by hydrolysis

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and it would have to be accurate enough

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to maintain the sequence and roughly

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speaking that means that the numbers of

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the average numbers of errors per whole

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sequence replication is 1 or less so

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that's the error threshold into criteria

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the basic theory of the error threshold

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goes back to I'd encircled ecce de go

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and I'm going to explain it on one slide

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so P is going to be the concentration of

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my functional molecule which is a red a

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red a red square there it can replicate

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at a rate which is R naught and then X

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is the concentration of mutant sequences

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which are black circles on here and they

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replicate at a slow rate R 1 which is

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less than R naught there's a breakdown

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rate which I'll call V and I'm assuming

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for the simple case it's the same for

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all kinds of sequencers so in order to

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survive the good ones must replicate

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faster than V so the red ones have a

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fast replicate faster than V

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and then there's a mutation probability

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M which is the probability of a

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deleterious mutations somewhere in the

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sequence per replication and it turns

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out then that there is a maximum error

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rate that can be sustained that's called

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the error threshold so the red ones

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survive if the error rate is less than

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the maximum M which is called the error

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threshold so this is a very simplest is

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a very simple theory it's a 5-minute

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theory and what comes out of it is this

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if there's no if the error is put if the

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replication is perfect so M is zero then

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I get all red ones as I turn up the

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mutation rate the red ones go down and

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down and there's an as an error

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threshold here which is the maximum

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sustainable error rate and since the in

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this case the this is the case where the

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the black ones the X's cannot replicate

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by themselves the replication rate of

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the the r1 and the replication rate of

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the black ones is less than V so the I

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ones don't die when there's no red ones

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left okay so everything dies when

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mutation is high so that's the basic

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error threshold theory but we we're not

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interested well I'll go back on the this

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this would apply to something like a

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virus that is multiplying inside a cell

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and the cell provides the magical

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ingredients that are necessary for the

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virus to replicate itself but in the RNA

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world there's no magical cell there

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so the what that the RNA ribozyme asked

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to copy itself so now our a reaction

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scheme looks like this a red one meets a

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red one and it makes an orange one the

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orange one is the complementary sequence

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to the red if a red one meets an orange

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one

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replicate but if a mutation happens

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instead of a red a red plus a red should

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make an orange but it makes a black one

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by mistake and a red plus an orange

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should make a red but it makes a black

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one by mistake and if a red meets the

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black it makes another rat another black

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so we're always assuming that mutation

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takes you from the functional ones to

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the non-functional ones because it's

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much easier to go wrong than it is to

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put your mistake right so we just assume

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Mew

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makes the bad ones all the time and so

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now we can do a 5-minute theory of that

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so these these equations are the well

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mixed theory they just tell you what

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would the concentrations of these

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molecules be in a well mixed reaction

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system that's a five minute theory and

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the five minute theory of this says

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everything dies because because the

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parasites take over in this in this case

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the parasites always take over and this

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is accomplice is a a cooperative system

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right one red one can do it by itself

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you need a group of red ones they have

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to cooperate and cooperative systems are

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taken over by parasites in the well

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mixed in the well mixed case so now we

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already know because this is this this

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kind of problem has been studied many

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times before we already know there's two

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ways of saving you from the parasites

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either you have spatial clustering or

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you have protocells so so in a spatial

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clustering model we have they have

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positions now the molecules have

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positions there's still three types of

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strand and what what happens is when you

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have slow diffusion in a spatial model

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you get clusters of functional ones

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together so the functional ones meet the

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other functional ones more more often

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than by chance and therefore they have a

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benefit which is counteracting the

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mutational benefit of the parasites so

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clusters of red ones can survive whereas

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similar bit different argument explains

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why replicators in protocells survive

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it's because when we have finite numbers

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of strands in protocells some cells are

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good here's a good one it has only

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functional molecules this one is going

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to multiply fast and divide and produce

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others other prone to cells which will

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also have functional molecules whereas

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something like this is being taken over

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by the black parasites but this one is

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not going to grow and divide so cell

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some cells that are destroyed by

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parasites but not all of them and the

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whole system survives because there are

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some good cells which are not taken over

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by parasites so that's group selection

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right so this is this is group selection

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saying selection works

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the level of cells as well as at the

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level of molecules and it's the group

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selection at the level of the cells that

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favors the survival of the polymer ages

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so all that has been fairly well studied

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but the problem is it's apples and

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oranges right what I what I want to know

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then that the question for this talk is

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which of these two mechanisms is better

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and by better I mean which makes it

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easier for polymerases to survive so

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that means a lower minimum replication

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rate is required in a better model a

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lower replication rate is required so

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it's easier to find a functional

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catalyst that works and in a better

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model the error rate that is tolerated

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is higher that's a higher mutation rate

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a higher error session okay so I want to

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be able to compare spatial models and

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protocell models in a quantitative way

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and then we then we hit this apples and

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oranges problem because they have

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different parameters so then we have to

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do a bit of thinking about what does a

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spatial model mean so in in the simplest

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spatial models we put things on Latin we

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put one strand on each lattice site and

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we say they interact with their

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neighbors and so well maybe that means

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something like a surface and molecules

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are stuck on their surface and two

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molecules next to each other can

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interact with each other but I find that

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hard to believe

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I can't imagine real molecules doing

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this if they're actually stuck to a

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surface right if you know if this is

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going to wrap ups if this is gonna if

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this is going to replicate its neighbor

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well maybe the neighbor needs to move

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somehow so it can't be stuck and if it

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is if it's not stuck then why does it

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not diffuse off into the third dimension

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away from the surface so I can't really

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see these spatial models representing

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really ribosomes that are permanently

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stuck to a surface but what what makes a

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little bit more sense is to think about

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the spatial models representing

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molecules which are in a constrained

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environment so that the diffusion is

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slow so what you what what matters in

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these surface in that in the spatial

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models is diffusion is slow so clusters

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arise and diffusion in

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a 3d open pool is going to be fast so

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you get well mixed and things die right

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so we have to have an advice if the

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spatial model is to be relevant we need

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an environment where diffusion is slow

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and once such might be pause interrupts

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so this is a paper proposed while back

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by cooling and Martin they're imagining

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reactions going on in little pools in

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Iraq little pores in Iraq and each of

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these little pores or crevasses

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molecules in one in one place can

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interact with each other and then they

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move very slowly across the whole

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structure so we so we now study a model

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like this a lattice model where there

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can be many molecules per site and

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things on one site can interact with one

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another and there's some very slow

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hopping from one to the next so this

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this this lattice model is representing

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something like that and the nice thing

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now is that this is this is apples and

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apples right because I can compare this

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lattice model with multiple strands per

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site with a protocell model with

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multiple strands per site and the rules

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of replication inside one cell are the

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same as the rules for replication inside

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one site on the lattice and so those two

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are directly comparable what's different

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is the fact that in the cell model we

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have growth and division of cells in the

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lattice model we have no growth and

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division but we have diffusion between

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neighboring sites so well we do

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simulations of these things we get

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different shapes of the error threshold

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curves but qualitatively similar you

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know if there's no mutation the red ones

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do well you come to a point where

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mutation kills you and this is the error

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threshold and we want to know how do the

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error thresholds compare in these

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different models right I got three

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curves here because there are three

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slightly different proto cell models

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which I'm not going to explain we there

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are different ways of formulating these

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models but all of these three are very

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similar and they're proto cell models

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there's three curves here which are

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slightly different spatial models and

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they're all much worse than the proto

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cell models

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and there's one in the middle which is

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the old our old version of one per site

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on the lattice so this is the this is

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the oranges which we can't really

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compare but these are two lots of apples

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and what we say is protocells are much

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better than spatial models for two

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reasons because the error threshold

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where I should say this is the error

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threshold this is the maximum tolerated

284
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value of the of the error and the error

285
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threshold is much higher for protocells

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and spatial models and then this point

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here is the minimum replication rate

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necessary for survival and the minimum

289
00:11:51,050 --> 00:11:47,709
replication rate for the protocells is

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less than it is for the spatial models

291
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meaning that for both of those reasons

292
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it's easier for replicators to survive

293
00:12:04,530 --> 00:12:00,610
in protocells so why do protocells work

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better because group selection works in

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00:12:09,000 --> 00:12:07,269
protocells cells with good teams of

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molecules grow and divide and they

297
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replace the slow-growing cells and

298
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either we keep the cell constant and

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when one cell multiplies another one is

300
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removed or we keep the number of strands

301
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limited which then leads to an effective

302
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amudha love the cells with no strands so

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so so one way or another there's group

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selection in proto cells which is not

305
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really happening spatial models because

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in spatial models when we have good

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combination of when we have a good team

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of molecules on one side it fills up

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that site and stops itself replicating

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it can only continue by sending by

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diffusing molecules out of that site to

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its neighbors so that mechanism works

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but it works less whoops but it's less

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well than the proto salt this is Madhu

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this is this is just to say so far I've

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been assuming that the rate of

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replication of the parasites was the

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same as the replication of the of the

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functional molecules so the parasites

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were not adapted they were just

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non-functional now I want to say what if

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the parasites were adapted they're

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adapted to be good templates and they

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and they multiply faster than they

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than the functional molecules so the

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blue curves are my old protocell and

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spacial case where the replication rate

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of the parasite is the same as the as

329
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the polymerase okay those two and now I

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00:13:41,650 --> 00:13:39,620
have a new version the red and the pink

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where the replication rate of the

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parasite is now twice as much as the

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replication rate of the polymerase and

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so the answer is both of these Mollett a

335
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protocell and spatial models still

336
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survive even when you have adapted

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parasites okay so the parasites can

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adapt to be better than the protein the

339
00:14:02,590 --> 00:13:59,300
polymerizes themselves and this

340
00:14:05,140 --> 00:14:02,600
mechanism of protocells or spatial

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00:14:07,450 --> 00:14:05,150
models both save you from being killed

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by the parasites but what happens then

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is that the error thresholds come down

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relative to the red curve is below the

345
00:14:17,710 --> 00:14:16,250
blue curve in both cases right but the

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difference between the red and the pink

347
00:14:21,640 --> 00:14:19,730
is actually larger than the difference

348
00:14:24,700 --> 00:14:21,650
between the blue and there than the blue

349
00:14:25,810 --> 00:14:24,710
and the two blues okay so the when

350
00:14:28,030 --> 00:14:25,820
parasites are better

351
00:14:29,650 --> 00:14:28,040
the advantage of Perl to cells is larger

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than it was when they weren't then we

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00:14:33,760 --> 00:14:32,390
were neutral parasites so so I'm arguing

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00:14:36,010 --> 00:14:33,770
that this advantage that we see for

355
00:14:38,080 --> 00:14:36,020
protocells is robust to different ways

356
00:14:40,110 --> 00:14:38,090
of formulating the model and to the and

357
00:14:42,550 --> 00:14:40,120
to different rates of parasite

358
00:14:46,840 --> 00:14:42,560
multiplication so what what does all

359
00:14:49,150 --> 00:14:46,850
this mean it probably means that

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00:14:52,450 --> 00:14:49,160
compartments like protocells came very

361
00:14:56,860 --> 00:14:52,460
early in evolution so so Damon diamond

362
00:14:58,870 --> 00:14:56,870
is a Jing replicating sequences inside

363
00:15:00,790 --> 00:14:58,880
visa calls that are formed when we

364
00:15:04,960 --> 00:15:00,800
fought when we have ripped wetting and

365
00:15:09,040 --> 00:15:04,970
drying of of shallow pools in the

366
00:15:11,020 --> 00:15:09,050
presence of lipids okay so there so the

367
00:15:12,850 --> 00:15:11,030
environment provided by the lipids is

368
00:15:17,170 --> 00:15:12,860
good for polymerization maybe we get

369
00:15:20,440 --> 00:15:17,180
sandwich RNAs inside inside membranes

370
00:15:22,090 --> 00:15:20,450
and it also creates visa calls okay so

371
00:15:24,010 --> 00:15:22,100
maybe they were present all along maybe

372
00:15:25,300 --> 00:15:24,020
that maybe the lipid membranes and the

373
00:15:28,240 --> 00:15:25,310
reason fuels were present all along

374
00:15:31,260 --> 00:15:28,250
maybe the first replicators involved

375
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inside cells okay was that time okay so

376
00:15:47,020 --> 00:15:41,870
the other thing I just want to say half

377
00:15:48,370 --> 00:15:47,030
a minute about is what we really need is

378
00:15:51,580 --> 00:15:48,380
something like this we need multiple

379
00:15:53,680 --> 00:15:51,590
genes so we don't just want one kind of

380
00:15:55,600 --> 00:15:53,690
replicator that replicates itself we

381
00:15:58,210 --> 00:15:55,610
want that replicator then to be able to

382
00:16:02,740 --> 00:15:58,220
replicate other genes with different

383
00:16:05,140 --> 00:16:02,750
functions so cells also have an

384
00:16:07,060 --> 00:16:05,150
advantage in that if you have molecules

385
00:16:09,130 --> 00:16:07,070
with different functions inside a cell

386
00:16:11,410 --> 00:16:09,140
then group selection and light enables

387
00:16:15,480 --> 00:16:11,420
the survival of unlinked molecules with

388
00:16:20,990 --> 00:16:15,490
different functions finished

389
00:16:25,490 --> 00:16:22,879
all right so it looks like we have time

390
00:17:03,710 --> 00:16:25,500
for a few quick questions just so we'll

391
00:17:04,370 --> 00:17:03,720
start with Dave and back right so I see

392
00:17:06,439 --> 00:17:04,380
what you're saying

393
00:17:09,260 --> 00:17:06,449
what what you what you mean in these

394
00:17:13,370 --> 00:17:09,270
molecules is very slow diffusion like

395
00:17:15,500 --> 00:17:13,380
you need you need the desk the basically

396
00:17:18,620 --> 00:17:15,510
they move by an amount of order their

397
00:17:20,510 --> 00:17:18,630
own size in their own lifetime right so

398
00:17:23,090 --> 00:17:20,520
in terms of a lattice they can hop once

399
00:17:25,250 --> 00:17:23,100
to a neighboring lattice site in their

400
00:17:28,580 --> 00:17:25,260
own lifetime and if they go faster than

401
00:17:30,289 --> 00:17:28,590
that they end up being mixed and then

402
00:17:37,940 --> 00:17:30,299
you lose the advantage of the clustering

403
00:17:50,100 --> 00:17:47,940
yes right really what I'm trying to say

404
00:17:51,919 --> 00:17:50,110
is you need to have very slow diffusion

405
00:17:54,299 --> 00:17:51,929
so you need to have strong binding and

406
00:17:56,159 --> 00:17:54,309
if you have strong binding you mess

407
00:18:03,390 --> 00:17:56,169
things up right you messed you mess up

408
00:18:27,779 --> 00:18:03,400
the template okay I maybe we can quickly

409
00:18:31,720 --> 00:18:30,669
okay I know that policing comes up when

410
00:18:35,710 --> 00:18:31,730
you're talking about evolution of

411
00:18:37,570 --> 00:18:35,720
cooperation in Pilar in organisms what

412
00:18:39,970 --> 00:18:37,580
does a policing molecule tell me what's

413
00:19:03,580 --> 00:18:39,980
a police molecule is and I don't know

414
00:19:05,409 --> 00:19:03,590
what it is something that comes to mind

415
00:19:07,510 --> 00:19:05,419
there is this idea that you can have

416
00:19:09,789 --> 00:19:07,520
tags on molecules which indicate that

417
00:19:11,710 --> 00:19:09,799
this is a functional molecule and it

418
00:19:13,810 --> 00:19:11,720
must must be present in order for the

419
00:19:16,029 --> 00:19:13,820
polymerase to replicate this this

420
00:19:18,669 --> 00:19:16,039
sequence right so that can that can

421
00:19:22,779 --> 00:19:18,679
eliminate parasites which don't have the

422
00:19:24,639 --> 00:19:22,789
tag but doesn't eliminate mutations

423
00:19:26,230 --> 00:19:24,649
occurring in the functional molecule

424
00:19:27,580 --> 00:19:26,240
such that the functional bit is no

425
00:19:30,639 --> 00:19:27,590
longer functional and the tag is still

426
00:19:32,110 --> 00:19:30,649
present so there's a little bit along

427
00:19:33,519 --> 00:19:32,120
the lines that you're talking about but

428
00:19:36,220 --> 00:19:33,529
I don't think it saves you from the

429
00:19:37,720 --> 00:19:36,230
probe so it's basically there's a there

430
00:19:41,500 --> 00:19:37,730
is a problem here of parasites which