Genome Sequencing, Polymorphisms, and Pharmacogenomics | MIT HST.508

[00:00:00]the following content is provided by mit opencourseware under a creative commons license additional information about our license and mit opencourseware in general is available at ocw.mit.edu ready okay well welcome to uh the third lecture a quick review of what we did last time in the first slide we talked about purification of basically at every level of the hierarchy in complexity from the elements all the way up to organisms and in particular the awesome purification we can contain get by serial dilution down to single molecules recombinant dna molecules in this case embedded in uh e coli cells and how this purification led to a revolution um first pure pure first in biochemistry then recombinant dna molecular biology then led to genome project and systems biology which brings us to models of interconnections and one of the uh to start in with algorithms that are useful in systems biology we start with one of the simplest and most robust ones which is the genetic code shown here in the lower right hand corner but as what looks at the huge diversity in the tree of life you find examples of exceptions to almost everything you can come up with including the genetic code and we and we talked about how to cherish the exceptions as usual here and then getting back to systems biology in terms of how one creates qualitative and quantitative models for functional genomics data and establishes evidence finally we ended on mutations as selection as we have been we will do in all three lectures here this this lecture in particular will focus on mutations and selection so what is today's uh menu we'll start with types of mutants and how they're represented for bioinformatics purposes we'll talk about uh what the three main methods by which mutations occur drift and select so that you can determine these things determine the frequency of different alleles in populations in doing that we'll uh rely on our friend from the first lecture the binomial distribution in the context of an exponentially growing population we have uh then give you some very practical uh training here on association studies where we illustrate it with a very important uh example of hiv resistance and and a very useful statistic easily as useful as the binomial and the gaussian the chi-square statistic and then we'll continue to talk about association in the context of um causative alleles and importance of getting haplotypes and then technologies that are required that have been used to get the the framework first genome and how one might change strategy in getting subsequent genomes in order to make cost-effective these very large association studies and finally in the context of that we'll talk about uh random and systematic errors in more detail so you get lots of examples and ways of dealing with it computationally so just to go from our brief discussion about the our friends the 100 percent dna sequence identity or amino acid sequence identity that you might find in the lens protein and elase enzyme we we can see that even at 100 you can find differences in function and so functional measures are are a good uh adjunct to dna or amino acids identity at 99.9 percent identity we're talking about the level of single nucleotide polymorphisms that might exist between any two positions in your mother and your father's chromosomes in your body or the differences between one of your genomes and one of my genomes about once every kilobase there will be a a polymorphism a difference as often a single nucleotide in a for a g then as we go to 98 differences then we're talking about the differences between one of our genomes and a chimpanzee genome in other words a completely different genus and species however by the criterion we mentioned in a previous lecture about bacterial definitions of species those would be almost identical and you'd have to go to differences identities less than 70 percent in order to call it a new bacterial species so you can see this is a very soft number very dependent upon the context and the and the branch of the trio life that you're working with then uh we have sequence homology and very distant homologues which are only detectable as we'll see when we get to the proteomics section of this course are only detectable um by three-dimensional structures not by sequence and that that switch over between secret homology will be that's the topic of uh next lecture um and the very distant one uh in 3d structures will be later in proteomics but that occurs at about 25 to 30 percent uh this is just a a in a reminder and an introductory slide to the next slide we have the different types of phenotypic different phenotypic effects due to different types of mutations and uh ignoring the phenotypes that we talked about before you have the types of mutations classes are null mutations uh dosage conditional mutations gain of function altered ligand specificity now now that's in broad terms colloquial but how is this achieved on a more molecular level and how do we represent it compactly for bioinformatic discussion so we have single substitutions these can be [Music] a single base pair an at base pair to a cg base pair or a gc base pair to ta base pair and so on um there can be deletions and duplications uh these can range the deletion or duplication can be as large as a chromosome or as small as a single base pair you can delete that a rather than change it into a c and that would be one base up here a very so when you're doing an entire chromosome that's called aneuploidy the expl the example in the previous slide was trisomy 21.

[00:07:24]um if you remove that chromosome 21 instead of having three copies of it it would be monosomi and these have huge uh consequences even though they're fairly subtle changes in dosage now a special class of deletion and duplication occurs when you have a a tandem repeat of a sequence when you have uh anywhere from a single base repeat aaaa or dinucleotide trinucleotide all the way up those have a tendency a very high tendency for both forward and reverse mutation both deletions and duplications because at the very small level you have polymerase slippage and other uh sort of microscopic events and then uh at the larger level you have some kind of some kind of recombination often homologous recombination that occurs to cause deletions and duplications of tandem repeats now an inversion here this is we're representing a complicated chemical event which involves double stranded dna going five prime to three prime on the top strand from left to right and five from the three from the bottom strand going from right to left and you're taking a little chunk of that and flipping it so that you break some bonds and remake them uh all the five prime to the three prime is is conserved but you've uh done it a reverse complement of the top strand and the bottom strand and that reverse complement you basically turn c's into g's and change the order this is sometimes abbreviated you know for for simple genetic description where let's say we inverted cde you might change the case or add primes to it um color it in some way or you indicate that it's now a reverse complement and of course the gene order or the dna segment order is in is uh is reversed to indicate that inversion uh translocations insertions in recombination have in common that you will make a break betw somewhere and then you will bring in a new piece of dna just like the inversion where you where you inverted in place here involves something acting at more of a distance you'll break between b and c and x and y and you'll in this case do a reciprocal translocation where you conserve all the dna and a and b is now next to y and z and insertion is is like that but now the dna need not be reciprocal in any sense it can come in more or less from outer space uh here it came from greece you can it uh it can it can be a transposable element that uh that came in from who knows where and inserted in between the a and b recombination here i illustrated is homologous recombination and uh you can have non-homologous recombinants but this is by far the most uh common and interesting even some non-homologous combination involves short reasons of homology where you basically have two either two sister chromosomes uh or you know homologs from mother and father or uh paralogs within the genome where you've got a duplicated gene that might even be on the same chromosome arm and now just as with the deletions of duplication where you have tandem repeats you can if you have repeats anywhere in the genome you can um take a small difference we're emphasizing the similarities here but they have a few small differences allow you to track them those can be exchanged by single strand or double-stranded dna various chemistries and you could you can either uh do a nice reciprocal exchange here where you preserve all the dna and the little c gets just replacing the big c by some kind of crossover between d and e somewhere between c and f or you could have a non-reciprocal exchange where you pick up a little bit of c and duplicate it and now there's no big c left over and only little c called gene conversion but you get the ideas that the these are fairly exhaustive lists of the kinds of mutations the kinds of simple elementary mutations you can have now you can pile these in various combinations with each other and over long periods of time you can get completely new sequences uh there's even ways that you can get de novo synthesis of of dna such as uh mechanisms of terminal transferase which is used yes we're going to get to that a little bit later on but i can give you a preview it's uh this uh and say in human genome uh these point mutations occurred about uh 10 to the minus eight um per base pair per generation and um there are deletions and duplications especially in tandem regions can be as much as six orders of magnitude higher frequency than that um so so there's a huge variation from position to position and types of alleles that will determine the mutation rate and you should be quite aware of that as you go through various computational exercises okay this is just a a bit of commonly accepted nomenclature is that mutations and polymorphisms are basically the same thing they're differences between you and me uh they become polymorphisms meaning you know when they're when they are common alleles when their frequency is greater than one percent in a population this is common in the human uh genome community it it may differ for other ones but this this is roughly where you a mutation which is rare less than one percent becomes a polymorphism which is frequent more than one percent as a counterpoint to that i would i would say that uh there is a good chance that every possible single nucleotide polymorphism that could exist does exist in a population as large as ours and mutation rates which are modest but still over long periods of time allow the accumulation of mutations such that rather than having maybe three million commons single nucleotide polymorphisms or snips um we might have 12 billion one at every position and in a lighter slide we'll actually go through and calculate crudely just how many just what those frequent why the frequency should be around 10 to the minus five and why there should be about uh 10 000 of us representing each of these uh so-called rare alleles they're rare individually but they're common as a as a group uh it will make a difference whether we're talking about whether these polymorphisms are linked to your favorite trait or whether they actually cause it whether they're part of the cause no you know no particular one can be said to be one-to-one with a cause it's all a collection of mutations and environment now haplotypes what do we mean by haplotypes we've introduced snips single nucleotide polymorphisms if you have uh a snip that causes let's say is involved in in causing a um apoe4 we'll introduce in just a moment a an allele that is associated with uh increased risk of alzheimer's disease and let's say that protein has it it has a known change in the protein three-dimensional structure and you can call that the bad allele okay or the associated allele now if that were allele word uh that protein will express at a low level for example if you had a promoter mutation or enhancer mutation then that haplotype that combination promoter mutation and protein mutation is is is a significant more significant predictor than either one of them separately and the fact that they're on the same chromosome is important because if the the promoter enhancer that determines the the level of the protein is in cis meaning on the same dna or in trans makes a huge difference so that's what haplotyping is all about it's determining what mutations are in cis on the same dna in order to make associations biologically meaningful and in terms of systems biology interpreting them in terms of what you know about regulatory elements and protein elements these haplotypes can be inferred indirectly from uh diploid data from how alleles segregate um in in uh small families or or in siblings and so forth or easier to think about and and probably more accurate in general especially limited data sets is direct observation the most extreme direct observation is is you pull out a dna molecule that has say your promoter mutation in your putative uh protein mutation or just a series of linked uh polymorphisms by cl by cloning out or otherwise physically isolating that dna molecule you can uh sequence it and you can determine what by definition if this if they're all in the same sequence uh one then they're on the same molecule but you have to be careful about the sequencing method that you're using there and the specific cloning and or physical separation method because you can there are certain methods where you can get a chimeric sequence either due to kind of cloning of two species together or somehow misassembling them through bioinformatics you can also directly observe it when you go through uh the genetic processes of of mitosis which we've talked about before which is the as the cells divide they split up the chromosomes or meiosis which is the process by which they get prepared for a combination which we'll come back to in a little while okay so when you do want to do it by linkage you want to do a direct observation and you want you need to you need to have uh the best way to to follow the haplotype is if there is a difference at every position um in in both the parents and the child and the child inherits um those differences then it's called informative if if the parents happen to share a single nucleotide polymorphism um even though the child is a heterozygote for one of them it could be that the the parents have additional alleles that can confuse things and it's not informative but the point is if you have enough single lucified polymorphisms you can do a case control study where you have lots of children that are affected for whatever trait you're interested in and hopefully a close to equal number which are in the control group which do not have it an example of that and i'm just trying to give you a flavor for this and where to look rather than to completely empower you on this because that would be an entire separate course but you can look for association and you have to worry about things like structure and admixture where you've had populations that have developed independently in different parts of the world and developed you know have been randomly mixing which is part of the model in these separate populations but then you bring them together very recently and now it looks like uh now it's no longer fair to model it as if it were a uniformly mixing population and the the null hypothesis will refer throughout the course to the null hypothesis which is the the uh thing that you're trying that you're trying to rule out and the probability refers to the the probability that you can reject this null hypothesis and in this case you're trying to reject that the allele frequencies in the candidate locus whatever you picked um do not depend on the phenotype within the subpopulations and that's the way that they deal with these case studies now what are some of the motivations for studying uh either individual polymorphisms or haplotypes combinations of polymorphisms can affect the activity of a protein now i could use hundreds of different examples of well-established and useful um examples but here's one that that hopefully will hit a resonant resonating court in the sense that these are actually used now in certain clinical settings and certainly in clinical research to ask whether a patient population either in the process of developing a new drug or using an established drug to keep the patient toxicity and down and the effectiveness up and so in the far left hand column is the gene or enzyme affected and in the middle is are examples of drugs which interact with this enzyme and then the quantitative effect is in the far right hand side and these for example thiopurine methyltransferase is something which if you have a large amount of the activity whether you have you say that a very active enzyme and or a very active promoter element that causes high levels of it then these various chemotherapeutics that are used for fighting cancers need to be the amount of them need to be adjusted so you have lots of the methyl transfer rates that means you have to give lots of the drug or else you will your drug study will fail or your or your patient will succumb to cancer because it's ineffective you haven't added enough the thiopurine methyltransferase is uh is overcoming the drug so when you on the other hand if you have very low levels of it then you want to give extra dose of it sorry if you have very low levels of the modifying enzyme you want to lower the dose or else you'll have a toxicity okay so that's an example that's actually being used in clinical situations where you can use the information to adjust drug levels or to stratify your patient population so that you put patients into different classes or exclude them from the study altogether because you know that the drug will have some bad effect this increases hopefully decreases the cost on the downside to pharmaceutical development if you do stratify your patient population and you make it through the drug study with that caveat then the fda will require that that you put that proviso in and that makes the the size of the population that will be buying the drug smaller which makes the since the costs of developing the drug are fairly fixed it decreases the profit now uh i pointed out that there may be a very large number of rare single nucleotide polymorphisms but in terms of common ones there's you know we're getting pretty close to saturating the common ones now these and their databases of these just like their databases almost everything you can imagine some of them better than others uh the uh the common ones will of course be the ones that tend either are neutral with respect to their phenotypic effect that is to say they it doesn't really matter whether they're uh one common allele or the other one you know the one allele might be at 30 percent the other one is 70 percent but they're both fairly neutral with respect to function or it could be that they both provide different advantages in different scenarios or the heterozygote where you have one over the other provide some advantage and that's kept it in the population but it's unlikely that they're highly deleterious because the highly deleterious alleles are going to be rare they're going to be selected against and we're going to fully model that in just a moment now say that we could uh somehow anybody who wanted their genome could have their genome tomorrow you could have your complete genome sequence how would you then as computational biologists prioritize those single nucleotide polymorphisms you find in there relative to the whole genome sequence which is in gen pang now this would be an excellent project for you to do for the term project but what you might say first of all uh well actually anybody what what what single nuclear type only misses would you throw out for example or deep put low on your priority list or which one should you put high on your priority list okay um no that's that's fine i mean you could you everybody has their own pet part of the genome they don't like introns almost sunk the genome project they said why are we going to speak with the 98 of the genome that doesn't code for proteins fortunately we went ahead and sequenced it anyway another favorite thing that people mentioned that is is repetitive dna that was another part of the genome they didn't actually sequence it from drosophila the repetitive dna and uh and it's considered also not protein coding and uh and i'm gonna give you a couple examples as we go through here to illustrate other points but also to illustrate that repetitive regions that are not in protein coding regions whether introns or other non-coding regions can be important and here's an example this is one of the most repetitive elements in the human genome it's called an alloy repeat as you as those of you who have done bioinformatics before realize that it's the bane of our existence uh in terms of assembling and searching and so forth but it here's an example of a single base mutation in this repeat there's about 500 000 copies of the human genome scattered about it's called an intersperse repeat as a consequence and this a to g transition is found upstream from the myeloperoxidase enzyme encoding gene it is uh so how do we find out whether this is important in any sense first of all the observation is it it is associated with a several-fold less transcriptional activity it it that particular position creates binding sites or creates or destroys binding sites for these um transcription elements and that might be the reason that it has lower transcriptional activity and finally it is over represented in a particular type of cancer and we're going to go through the the ways that we that we take an observation like a polymorphism move to an association like here with cancer then take it to a mechanism such as here with the transcriptional uh regulators i think that's that's what this is about it's not sufficient to observe the polymorphism you can't say a priori whether it's important or not whether it's it's alley repeats are not conserved that's another thing that people say throw out all the non-conserved uh single nucleotide polymorphisms it's not conserved it's not present in mouse for example uh it's non-coding and it's repetitive now in addition to the types of mutations we have the modes of inheritance that is to say the different ways in which a change a polymorphism can be transmitted and i include this kind of broaden your perspective rather than getting in entirely fixated on the three million dna snips let's broaden the discussion here a little bit you can have not only dna polymorphisms but you can have rna polymorphisms which are heritable for example and i use this as a extreme case rnai 22 nucleotide or so probably a variety of mechanisms bits of rna can uh be induced in various ways and once induced they can they can uh replicate essentially within a cell and between cells they can spread throughout an organism and probably be be propagated over generations between different generations organisms so this is heritable and you can consider it epigenetic or genetic polymorphism depending on the nomenclature that you adopt even a protein confirmation can be considered a polymorphism that is heritable the central dogma tells us this protein is encoded by a nucleic acid and that certainly is still the case even the these heritable uh polymorphisms and proteins but it has a different conformation and that conformation recruits other conformations and so and so is inherited not only within a cell but between cells and between organisms and as the causation of things like mad cow disease so on and finally modifications of biopolymers such as methylation can occur and this is not formally a dna sequence change but it is uh either it's a it's a heritable change that can have very significant effects on things like cancer and other and gene expression in general okay now that's these are not these is the broadening of the definition of polymorphisms and now let's talk in uh thoroughly about the different of the ways it can be inher inherited as horizontal or vertical okay horizontal typically means between species but in a certain sense it could be it could reflect some of the things that are going on here with rna and protein inheritance in the sense that is being horizontally transmitted between different cells within the same organism but generally it's it's uh it's a mechanism that does not involve mitosis or meiosis of of the nuclear or or organeller genomes and this the natural processes are transduction and transformation uh being distinguished but transduction typically involves a viral or protein coat for the nucleic acid and transformation involves something closer to naked nucleic acids transgenic is a completely laboratory based version of these two more natural methods i think vertical we've already talked about this is what we normally think of inheritance rather for a horizontal we saw in the in the tree of life is very common even in the late branches in the early branches vertical though is what we normally think about when we're doing crosses in laboratory some of these are maternally inherited like mitochondria and chloroplasts but it's still the same kind of process mitosis segregation of dna okay so now we've got types of mutations we want to talk about mutation drift and selection as the main source of uh the frequencies that we that we find in populations we want to know where do allele frequencies come from and i will maintain that that generally speaking in almost all living systems whether they're cells from organisms that are mutating or whole organisms whether they do recombination or not they will do mutation selection and drift now to develop a fairly rigorous model here yet simple we have some assumptions we always have assumptions and models if people tell you that there's no assumptions then you need to you need to dig a little further the con that the functions that we'll make here for a little while and and then i'll give you a nice example that undermined them all but it's constant population size n um that you have random mating remember we were talking about admixture before we have everything every every member of the population randomly made they're non-overlapping generations this is a convenience we are not making any assumptions about the population allele frequencies being at equilibrium this is something those of you have taken biology courses with hardy weinberg makes that assumption here this is a much more general model it includes non-equilibrium and equilibrium can be a special case so this is relatively minor non-assumption but but we are assuming that we do not have an infinite number of alleles nor an infinite number of population size okay so now ignore everything on this slide but the upper left-hand corner of slide 15 here is this should look familiar this should look somewhat like the uh logistic map where we had the incremental exponent slow exponential increase of one allele in a population over another or one organism over another based on the different selection coefficients of those organisms and you know this could be a very small difference say a one percent increase per generation will uh will dominate after a thousand generations or so um quite definitely and so that's what you're seeing the exponential curve and the plateaus um as it gets uh to 100 percent allele frequency that that's the full range on the vertical axis of zero to 100 percent wheel frequency and generation goes from zero to fourteen hundred now what it actually represents in this particular case is closely related a little more complicated than just one allele replacing another because here we have um diploids that is to say not a halfway that just has one allele like in in the bacterial species that we've kind of implicitly been talking about but you can have here now three combinations of alleles you can have say the the reference genotype of of capillae a which we just call uh 100 percent of fitness so we have fitness and selection coefficient which are interchangeable terms that are very trivial mathematical relationship between them so we'll use w and s in different contexts here it just does population geneticists do then you can have big a big a little a little a and big a little a as the heterozygote and we're assuming an additive model here where you get a little more selection with one allele of little a and then two alleles of little a results in 2s one plus 2s and uh and this has a very similar curve to uh the logistic map if you had a simple allele replacement on the other hand and and what you tend to have in this population since a thousand generations in the big scheme of things it may seem like a lot to you but the big scheme is it's a very short period of time and so you tend to have alleles at frequency of zero and uh 100 on the other hand if you have over dominant mode where the heterozygote has the highest fitness of the three possibilities where one plus s is larger than one or one plus t then you aim for equilibrium whether you're in starting at close to zero percent or close to 100 percent the allele frequency will converge on some equilibrium point um in this case somewhere around 0.6 to 0.4 0.6 for 1 allele 1.4 for the other and it could be anywhere it depends on the relative fitnesses s and t okay this is just a reminder slide combining two slides from before just to connect that slide connects the logistic map from lecture one to uh the selection coefficients we've been talking about in lecture two to the the diploids that we're mainly talking about in this lecture because humans are diploids and here's just to just connect this um to the fact that the selection coefficients s or the fitness w is relevant to different environments and the different times that organisms spend in those different environments and all mutants are tagged by their dna and they're pooled and they're selected and you can read them out in a variety of methods so now let's dig down into where the allele frequencies come from based on uh mutation migration and selection i'm sorry mutation or migration which we'll lump together here as m selection and drift now the mutation will have a forward rate constant and a reverse this is this should remind you the conversation we just had about of the different kinds of alleles the duplications and deletions how they can have different rates if they're tandem duplication then that has a great tendency to delete if it deletes down to a single repeat there's now no longer any repeat and so the chance of generating the exact duplicate is low so that the forward in reverse here the frequency of forward and reverse mutation is represented by f and r respectively now what you'll see we're going to walk through this starting with a a frequency t sub i for where i is the uh number of mutants in a population size n so here and down at the bottom is i mutants have population size then and we'll see that applying the mutation applying the selection and applying the drift are all applications of binomial distributions when we're talking about this discrete population of individuals it makes remember that the three bell-shaped curves are curves that can be bell-shaped here it's clearly a discrete uh population because we have in individuals taking i mutants at a time so we have so the binomials that we'll be using all all three processes have the same form where you have a combination of of some population n and a sub population i and of course the recipe the remainder is n minus i and that comp the different combinations are times some probability this probability is the is the last parameter in the binomial here which a binomial is a function of the n i and p the population size sub population size and some frequency it can be either a forward or reverse mutation frequency it can be a selection probability or it can be a drift probability and we'll see how each of these work out so let's we start with a a frequency of i you can have i ranges from 0 to n you could have if i is 0 then the frequency is zero over n or zero if i is n it's n over n or frequency is a hundred percent just that same vertical axis we had in all previous slides the starting frequencies have some distribution t t sub i for i going from one zero to n and we want now i want to derive a new uh vector of frequencies which would be m and all we do is we apply the binomial distribution for the forward process of forward mutation and then once we're done with that we apply uh we now use the new the m's and adjust it so that's now give a chance to do the reverse mutation because you'll generate this binomial distribution forwards and then you'll give them a chance to to revert then you apply selection a new binomial now here the probability of a transition from your mutants starting with t then you go to m now to get to s the transition probability is a function of this fitness remember w and s fitness and selection um here the the fitness determines a probability of a transition in a in a binomial distribution and there's there's two slightly different uh equations that you use depending on whether the fitness is uh greater than one or less than one in other words whether it has a tendency to increase um with time due to selection or to decrease that allele with time as a function of selection and then that's what these two cases are here and then finally you have after you've applied forward inverse mutation and selection whether it's more fit or less fit than then you apply drift now drift just means that if you have a small popular think of if you have a small population of uh individuals let's say they're you know a set of colored balls in a jar in front of us here it's a small number and i pull a handful out because in each generation you're gonna you're gonna duplicate the population but remember the assumption of constant population size if i pull out the new generation and forget about the the rest of the duplicated they could all be the same color and that's the chance you could drift to fixation where one of them now dominates not because it's superior from a selection standpoint not because it's been uh you know mutated in a directed way to that point but just because of random drift that you have a constant population and uh and you and so you can see how that would depend on how many are in the in the jar if i take half of them out of the jar and and the jar only has five in it then it's a hot much higher chance it will go to fixation quickly than if the jar has millions in it if i take half of half a million out it's very likely that it will still be the more or less the same ratios and this is exactly how it plays out when you look at random genetic drift it's very dependent on population size so here here are simulations going out to say 150 generations on the horizontal axis and the allele frequency as usual going from zero to 100 percent and they we start with a population with 50 50 ratio of two alleles and what you see is if the population the number of individuals is only 25 then you quickly fix maybe in a few generate maybe uh 30 generations you can and this this is anecdotal of get fixation as it goes up to a population size of 2500 you can see it for all intensive purposes it's flat it will eventually fix i assure you this simulation if you run it long enough it one of the two alleles will go to zero and the other one will go to 100 percent and you do another simulation and it may be the other one because this is random drift not selection uh so you can see the final frequencies are going to be some complicated function of mutation rates and selection rates and drift rates and pop which and that last one is a function of population size when the drift when the population size is very very large you can see that's going to be constant enough that's why you can see very subtle differences in selection coefficient okay now we're going to come back to the mutation selection and drift in the context of human genetics in just a moment but first i want to tell you the last uh component of population genetics that we'll be talking about which is recombination now this doesn't occur in every biological system i made the argument before that mutation selection and drift occurs in every biological system from cells to organisms of all types those that in those biological systems where dna can be exchanged by transduction transformation meiotic fusion and so forth then you can get recombination and these two figures illustrate that on the left-hand side of slide 19 is the non-recombination scenario and on the right hand side is the sexual or recombination mediated gene change in gene combinations so let's look at this time is going horizontally and you can see at the very begi at the very left-hand side the beginning of each of these scenarios you get a certain rate of occurrence of mutations this is based on the forward mutation rate in our previous um equations and they occur very early on a b and c all occur but they tend to die out because of because of drift okay and the population size is small enough that this is about that that half of them die out and one of them fixes okay and a is destined to fix it but it takes some time for it to fix and until it's you know a huge front it starts at a frequency close to zero and by the time it's fifty percent to a hundred percent it's ready to start picking up a second mutation at the same frequency they were occurring before now you can pick up the b mutations while the c dies off you know it comes and goes due to drift and finally once a b fixes then you can pick up the c and you get abc that was a long slow serial process on the right hand side we see the what can happen in the in the case of of exchange of genetic material in a freely mixing population is now that a b and c all occur at the same frequency as on the left but now because they're exchanging information very early on before b has a chance to die off due to drift it combines its dna with a and you get a b and some of the small a population is destined to be fixed anyway but happens to combine with c and again before before drift can wipe them out selection the very small selection that you have that couldn't overcome drift in the in the left-hand panel now fixes them all the really favorable combination of a b and c very early on and so there is there's a whole series of arguments and counter arguments in the population genetics literature about why is there sex of course you know we all know uh we have our own reasons but but in here they say there's a huge cost the count the counter argument is there's a there's a huge cost of having two genders uh maybe as much as fifty percent possibly higher uh because they don't they have uh they have different morphologies and different capabilities and so on um but then there's this benefit this is the risk and the benefit is the earlier recombination but then there's counter arguments and so forth that we won't go into oh yeah what if actually random what is it that causes either a real fix if you have two different elements why wouldn't it just eventually come back well it can you can see here uh that it's it's starting to head so that it's fixing uh on on one allele and it changes direction and it fixes the other one so it can it can go all the way down to to to close to zero and then bounce back up and it's all this is just some typical simulations here uh if you do enough of these you'll find every possible behavior um it's cool basically eventually it will fix you can't necessarily predict which one will fix on half you know if there's no selection half the time it will fix on one half on the other if they start out at a frequency of 50 50.

[00:48:01]but you have to think of it in the context of mutation and selection too because they're all acting there and when you say that something is selectively neutral what you really mean i mean everything has some very very tiny selective coefficient but if that is if it's tiny enough then drift and the population size is small enough then drift will blind you and you can't see it but if you get really big populations then you'll get small drift and then you'll see subtle more subtle selection you know the human population is very large some of the oceanic species are truly enormous so you need to think about that as a possibility so now let's talk about common diseases we have the question is uh our common diseases really to what extent are they caused by common variants clearly some of them are caused by common variants and we've said that well common variants really shouldn't be deleterious um because they would be wiped out by selection they they could be very very mildly deleterious such that drift will cause them to get fixated or persist but they really they can't be really noticeably they get they you know selection coefficients of 10 to the minus 4 very very tiny effects can be uh wiped out in in populations sort of normal size populations so here are three examples of common variants that almost certainly are associated with common diseases so why are these special cases rather than in my opinion rather than the general case apoe4 i only alluded to is associated with alzheimer's dementia it's involved in lipid transport and metabolism and this particular allele the the uh the e4 allele is uh present 20 percent in humans about 80 percent is the other allele the most second most common allele is the three allele and so you might say well this this battle theolous e4 is uh you know it's the one that should be present in the common ancestors of humans uh it should be if sorry the e3 the good one should be present the common ancestors and this ae4 is a recent aberration um it's it's somehow getting into human population but actually the e4 is the ancestral one presumably due to some difference in diet or some other selective effects the e4 which is currently bad for us we think is really good for some of our related species and so we need to think very carefully before we do anything drastic about eliminating this allele from say the human population hemoglobin sickle cell the sickle cell allele is probably the oldest and most famous of the molecularly characterized alleles such a london polling made this famous many decades ago and it exists in 17 of the human population and this is uh responsible for oxygen transport in red blood cells and we saw you saw in one of the earlier slides today those sickled shaped cells which have a huge effect on the hemodynamics of the red blood cell well another red blood cell component an enzyme g6pd which is involved in maintaining the redox function in the cell is as high as 40 percent the the mutant whichever one you want they're so close to 50 they're just they're just two alleles um and one of them is a deleterious in a certain sense a biochemical sense but both of these have a heterozygote advantage in being malarial resistant and so probably that's the reason it is common in the population and this uh is well probably proving to be the rule that that these are examples of that convergence that we saw in the case of balanced polymorphisms where the heterozygote has some advantage and so you get a balanced point rather than one or the other dominating through the drift or selection and the third example is which we will develop in much more detail a ccr5 there's a deletion of 32 base pairs which confers resistance to one of the greatest plagues in the history of uh human race which is uh to the aids virus and its frequency is nine percent caucasians i think we wish that it were 100 uh when we worry about hiv but we need to wonder why it's not 100 there may be some other reason for it being a non-deleted version in so many humans and we need to understand that and as far as i know we don't understand that okay now uh this is the last slide before the break i want to now that i promised you that we would take that simple mathematical treatment of mutation selection and drift and show that it actually has some impact that is actually used in uh in human genetics now i must warn you that that this is not a consensus view this is a view that i find appealing in slide 21 that uh john pritchard has has authored and he titled it in a uh provocative way are rare variants responsible for susceptibility to complex diseases and uh this is a quote that cust it's customary and theoretical work relating to complex diseases that the allele frequencies are treated as parameters of the model and then typically in models you'll have derived uh values and parameters which are input the things that you that the user is expected to provide and and you don't want to have to be guessing at all frequencies and having those parameters so what's new here is that that using an evolutionary process which includes you guessed it selection mutation and genetic drift they can we can learn or as they model the underlying allele frequencies they can be derived rather than being required as an input and so i think this this um and this is illustrated here um with uh a model which which you know this is entirely theoretical but it is based the parameters that are used are based on some genetic studies that have been done for example on autism and so let me just define some of the terms here we have this risk ratio is related in a certain sense to the selection and fitness coefficient we were talking about before now selection and fitness coefficients refer to reproductive fitness and in human genetics we're much more we're we have broader interests and all sorts of things that that either don't affect reproductive fitness or or we don't know how it affects people but it affects some kind of medical or just uh just some trait of interest in this case um the the risk ratio replaces the selection coefficient and this is basically saying my brother or sister has also if if they did then i would have a 75 fold higher chance of having it than someone selected randomly from the same population as i come from so this 70 fold increase is a very high heritability for this particular example also in this example through some genetics we won't discuss it it seemed reasonable that the number of loci involved might be much great you know might be a large number on the order of 100 or so and you can think that a lot of common diseases when you start listing the the the well characterized ones we start losing the number of genes that are either known or plausible like cancer or uh you know walking down the street or whatever these really complicated traits involve a very large number of uh cell types a large number of cell components and hence a large number of genes so here they've assumed a model with 100 loci 100 different genes and they have multiplicative effects of the of the polymorphisms in those genes between loci that is to say you need to have gene one working and gene two and gene three so that's multiplicative but then the polymorphisms you introduce into a gene you could think there are a lot of genes involved and there are a lot of different positions within the gene that can be involved and each of those is additive you have a little uh reduction in activity due to first mutation and then a second mutation the third each of those is a this or this or this or this and so that's an additive effect and so they they have various you know historical justifications for having additive penetrance within the gene and multiplicative um across different loci different genes in the genome now for these hundred loci there will be a top five five that affect the relative risk the most and that's what's been plotted here where we have uh the zero curve you see is in the in the absence of any of these multiplicative effects this is if you had no loci that were affecting the frequency of susceptibility alleles and so as in most unselective populations you'll have somewhere you'll have mostly alleles being either zero frequency or 100 percent basically the zero representing you know the absence of the the the other the alternatives the 100 that's there but if you have this this uh these uh the top five loci out of 100 that contribute to the risk ratio then those are represented by these four curves which which say this frequency of susceptibility alleles which range along the horizontal axis now from zero to 100 percent have what he calls a probability density i mean it's it's clearly not a probability density because it's not going to integrate to one but here it's the the probability uh the sort of the histogram of risk ratios okay so let's take a break and uh we'll pick up uh on our on an exact i will go drill down on the association study in a very interesting case anybody who any problem sets to hand in can put them here during the break so i understand about modeling mutations