Closing lecture with David Nelson

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Closing lecture with David Nelson
Gene surfing and migrations in structured environments
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Population waves have played a crucial role in evolutionary history, as in the 'out of Africa' hypothesis for human ancestry. Population geneticists and physicists are now developing methods for understanding how mutations, number fluctuations and selective advantages play out in such situations. Once the behavior of pioneer organisms at frontiers is understood, genetic markers can be used to infer information about growth, ancestral population size and colonization pathways. Insights into the nature of competition and cooperation at frontiers are possible. Neutral mutations optimally positioned at the front of a growing population wave can increase their abundance by 'surfing' on the population wave. In addition, obstacles such as lakes, deserts and mountains alter migration fronts and organism geneologies in important and interesting ways, which can be illuminated by a kind of 'Huygens Principle' for biological waves. Experimental and theoretical studies of these effects will be presented, using bacteria and yeast as model systems.
Keywords gene migrations
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only 1 of the last courses conference is my great pleasure to reduce their belts form how about so they got a please United 75 economy rose at the UN Recommendations groups Yuri on critical Solomon was my decision and then basically from 1975 you have been a part of his presidency Solomon professor of biophysics and professor of physics and applied physics at doesn't use a wonderful example that fundamental physics and applied physics don't have to be contradictions the various all officers above the price of for superconductivity is about reprisal soft manpower and whose voters show up the group read all the way which about 10 items a few loose the special almost to talks the moment so the Lorenz was doing professorship enlivened 2006 the there also is a cultural educational and health consultant Dennis was very nice as it moves through items developments and that the other your back Of the logging forward to looked on June softening the migrations instruction environment fuel well it's a it's a great pleasure to be back in the Netherlands that I 1st came in 1974 I think I was a student and wonderful summer school on fundamental problems and statistical mechanics in finding and it was a delightful introduction to the Netherlands and I've been coming back very frequently so what I'd like to do to motivate his talk about 434 physicists in the audience is to summarize the remarkable recent developments in population genetics of use some of you may have heard of the National Gino graphics project which have sequences the genes of indigenous populations typical typically the genes in my country of DNA and deduces various arrival times for the human migration out of Africa there probably were several such migrations but 1 of them was started about 130 thousand years ago and you notice their various arrival times in Asia and Australia and Europe and looking at this from the perspective of the sea physics or chemistry or even biology there's 2 of this 2 striking things 1 is that there's no error bars In this practice I can assure you there are Arab artists and their large and secondly regarded as the Knicks as an experiment as an experiment this is an experiment that's not easy to repeat what you probably wouldn't want to repeat of and so what we got interested in the Oscar halachic an idea of couple years ago was that a kind of simulation all of this kind of range expansion but on a modest selling scale In a laboratory petri dish and the mitochondrial DNA that serve as markers of human range expansions probably had a common ancestor with bacteria like the call I whose migration I'm going to show you here these are odd-shaped organisms there more collide in all of our intestines and there are human beings on the surface of the earth and they go forward in time as well and I'll try to show you that this has really important implications for population genetics and the nice thing about these kinds of experiments is of course they can be repeated and if you don't mind a change in links scale of 10 to the 9th whereas in 500 generations humans are large mammals cane toads invading Australia whether they might expand 10 thousand kilometers these guys and the same number of generations stay on the petri dish the only go centimeters and the aspect of population genetics is interested is in is illustrated in this range expansion which is a work by Kevin Foster on another bacteria called Pseudomonas aeruginosa and here of the 2 there's a mixture of Tubac types of bacteria and they are goal as he could make them but they genetically D max as you go along his outward radial migration from the central area which we call the homeland and you can see that there is an interesting question here why do they do make it's not like oil and water the mixing they they are chemically and and and genetically identical the only differences of fluorescent tags are there is similar as I said that as we could make them of an it's the descendants that'd be mixing and what you see here is an effective fluctuations at the frontier phenomenon and population genetics called genetic drift and you could ask the following question in the spirit of the human range expansions of the around the edge and say counted the number of sectors in this inflating boundary turns in turns out to lock-in eventually after a couple of days or so in this migration and for the few other properties on the boundary could you deduce the size of the homeland because we have a record here of the entire range expansion which can be replicated as I said 40 times were so as we've done in the laboratory that's not what I want talk about so much today that that's that's published work which you could read about if you're interested I'm going to talk about a variants of these range expansions which is range expansions and structured environment so many looking at populations with frontiers just like we saw there but because of course our world is not a featureless landscape and various geographical features can influence biology and population genetics and is a famous example all 1 of these salamanders migrating from north to south of Oakland California of its believe they got separated by this these ranges of mountains and they gradually went their own way on the 2 sides all of this is that this migration events and finally won the their came back together they could no longer make the they were 2 distinct species which illustrates how geography can can affect what's going on so I wanted to talk about how range expansions in inhomogeneously environment influenced the kind of genetic diversity that we saw In those bacteria and will see that will Benchley led to some simplified models of spatial structure of migration around obstacles that that we think of as lakes a desert so they could be mountain ranges and sends them in the Netherlands I I will use Huygens principle to analyze these these range expansions in and help an interesting way so they will also talk about population genetics so that's where we're headed and these are my collaborators of amazing really energetic postdocs who used to be a theoretical physicist he now does both series simulation and also experiments and my colleague in molecular and cellular biology very imaginative colleague named Andrew Murray OK so at
1st I wanted to discuss the will be called the elephant in the room of the elephant in the room here has to do with the nature of physics and biology here I am I was trained as a theoretical physicist as you heard with Michael Fisher at Cornell and again taught that basically this is heavily biological and there's actually an anecdote when the human gene known was of sequence for the 1st draft was announced at a press conference Of course Bill Clinton was there our president at the time and he had an exchange with his science adviser who was a physicist and he said OK you physicists have had years century this was the year 2000 on what are you going to do next and I personally don't believe that is if you start talking about centuries you can say well when went to the chemists have their century and so forth and and and I looked on the internet and there is a "quotation mark it's as if in scientific terms the 20th century's with a century of physics but the 20 1st will surely be the century biology who do you think actually made that "quotation mark Everybody has suggested it wasn't Bill Clinton it was Hillary In her book it Takes a Village how why she put that in there when he's talking about how had lessons children's teachers I don't know but we could also ask Is this really true but have a show of hands how many in his audience ever use the Google and viewer anybody played around with that a couple people is interesting piece of software and it allows you to take based on Google's scanning of all of various people all the books they could be allowed to scare Intel various people stopped them in various languages and so what I did justice give you a sense of how this grandeur works and since we're in the Benelux Hall is I competed other word frequency of Belgium Netherlands and Luxembourg 4 books read written in English over the last 200 years and it's kind of interesting you'll be happy to know that the Netherlands comes out on top eventually despite his presumably due to World War One when Belgium was in the news and many books and so forth Luxembourgers use least noticeable down here the beleaguered also you know following up on Hillary's observation compete a physics and biology so interestingly his physics and blue and and it was around a biology was sort of flat-lined down here it's 0 at about the time of dog when it became its own independent science and it's rising but the gap is seems to be narrowing so something we might want to think about on the other hand it's also instructive to compete physics and biology against DNA for books written in English and I noticed that the NAB it's everybody and I think that's a nice observation because DNA to understand it you need to know polymer physics you need to know chemistry of binding and hydrogen bonds and you cost you need to know biology so it's an inch intrinsically interdisciplinary molecule and the message I would take away from some of the the biology of the biophysics of Physical Biology that we're hearing at this wonderful conference is that perhaps in fact 24 1st century with a century of DNA as revealed by interdisciplinary research so with that links the prelude
let's get down to business and I know their contributions in the audience that he actually supplied some strains of the call life for these range expansions or just remind you what was on that 1st slide in the context of the collide these were 2 are nearly identical equalize except that this the main chromosomes were the same these little plasmids were more or less the same except there was 1 change in the amino acid of a fluorescent expressed protein that change the color of safe from yellow to sign an experiment was so simple that even I a card-carrying theoretical physicists could do it mainly makes these things up overnight I'm 50 50 proportions let's say pipette them down in a little section 4 To Michael leader "quotation mark the carrier fluid dried out leaving behind these bacteria wait for days and this is 1 quarter other calling sized but colony in white light that that that appeared but this looks tired and all of last year really love of microbiology but in fact under fluorescent excitation it looks like that and here's a more global view
but change colors is to make it a little more visible this is the homeland and these are these service sectors radiating out I'm not gonna talk so much about them until the very end 1 of focus now on the homeland and see if we could use the homeland and exploit its properties To make a structured environment and In fact here are some homelands that displayed at various densities 50 50 concentrations but different densities of 1 of the initial occupant on the petri dish and they're going from 25 to 250 to 2 thousand 500 of each of the founder of the the colonies his colleagues in the interior in his homeland are additionally the founders separated and they come crashing together To make these these beautiful fractal patterns and the and what would cost like to do is to regard these homelands as a kind of ecological landscape occurring on mm scale through which we could have populations migrate and so here a blowup of this little region here looks like 1 of these maps that you might find in the Game of Thrones there's something in the back of the book and you can imagine that these are inlets and Israel land masses and ask what what would it be like to live in such a such a complicated set of estuaries and for a course we need to have something to live there and
what we decided to study was of the spread of a virus Of the particular virus was 37 it infects call it's a well-studied virus here some of its properties and basically what it does here's users has I costing he grows symmetry this virus seems to know about the Platonic solids of and 1 it's as many of you know when interjects it's it's small modest complement of DNA into a bacterium it takes over the reproductive machinery and reproduces itself maybe 30 or 50 fold this is it's Gino To that end with with with with its various genes not too many indicated by the CBI flags in this picture and I the here is a picture of a different virus but this if you feel don't like getting up bitten by mosquitoes in dense forests and so forth I think of this poor bacterium being attacked speak by all the virus is trying to use their their are some hybrid almond needle-like projections to get the DNA inside this is a movie Wolfram actually made this a couple of amounted to after you arrived in it's it's actually kind of fun to watch because the collider growing up and you can see them elongating the rod shape their undergo cell division there's happily about to collide is little the cloning founders everything seems to be fine except he mixed in a little virus into the Aguilar it took a while for the virus to diffuse in and you can see it's a disaster all these bacteria are exploding and then once a little plaque which is the region of exploded bacteria and an excess virus this produced the viruses to fuse to a fresh region of bacterial 1 and exploded over there as well you don't think this is a little chemical reaction where the virus jumps onto a bacterium it and may jump on and off irreversibly producing some infected thing but once it gets into the interior with some other rate constant K 2 it multiplies itself but by a factor why why integer like 30 or 40 others since the proliferate of power 1 of these some of these viruses and this is 37 a well-studied example union the Gaskell studied these objects as kind of population ways and what what happens is you end up with a concentration of viruses which are based on a piece of this equation that looks like diffusion just ordinary diffusion of diffusion constant of the virus In some bacterial 1 as it meanders around exploding things reproducing itself the rate and is just the the carrying capacity here and so the question is how many of you have encountered this parabolic but nonlinear differential equation before not many physicists have have usually run across it but it has wonderful properties and I'll show you that if you want to know about the properties 1 way is to read a lot of beautiful Review article by women themselves and now director of the following however this does have almost 200 pages is extremely methodical and and thorough or you could look at the next slide books that the Amigo back here next
slide is he is not
here years OK so let's take a look at this next like this is this is a world population ways for Dummies and so here's here's the idea parabolic differential equation in 1 dimension over short times of just well rises up and go back here here rises up exponentially at the origin spreads out like the square root of time it's that that's the result of the linear terminus effusive terms so that's pretty standard but remarkably once is now the near-term gets into play when it reaches the carrying capacity over some region of this one-dimensional illustration of this this wave equation this becomes a wave like the actually a propagating front velocity not a solid conference but it has a velocity of and the velocity depends in this way on the diffusion constant growth and also a well-defined interface which so it's not the conventional wave of crests and troughs as we as we familiar with in linear wave mechanics and nonlinear phenomenon but it still has a constant way velocity and you can actually model these viral plaques bite
something precisely like this and so here we have an example of infection in the homeland of this about by this virus several actually are going to take off here so I inoculate and you can see and the timescales hours I think in the end said this is what's going on and all I also notice that there's refraction that is this circular waves the propagating out these these Fisher waves of end of the year but eventually the waves on the edge start to go faster so look up here is in homogeneous wastes be here at approximately a flat-front but you'll see it start curving around and so we seem to have a viral analog of refraction why would a wave wanted to on Monday's population ways here's another
example of this is now getting to our structured environment where Wilson took a homeland with the yellow and and red organisms but they haven't quite grown together that's why you see these black gaps and now he introduced of virus this this is not shown to scale on the on the right side there around 3 o'clock 3 o'clock and the notice of preferentially attacking the yellow susceptible strains but it sort of avoiding at least initially the the resistant strain of this bacterial this virus however can mutate so fast it eventually will attack the red as well so this is the kind of model of Epidemiology where you can do replicates 40 replicates on a petri dish and try study what's going on with these population waves in homogeneous structured environment so you can see it eventually attacks the Redbud preferentially at least initially goes for the yellow and there's a lot of interesting science here from related to percolation related to waves in inhomogeneously media is a great tradition in the Netherlands of studying anomalous back scattering of light and threw in homogeneous random frozen dielectric landscapes and bond facial depend delicate consensus something similar but with a very different kind of way so that's what I want to talk about and while we
eventually decided to do was to 1st simplify the problem printing our own bacterial and so what Wolfram realize was that he could take on an ordinary inkjet printer like this 1 by its original purpose in life was to print labels on CDs and and then persuaded to print bacteria of different shapes and colors and so here's the any coal line and you can see it's preferentially rather than the yellow part of this city in the call I is being chewed up turned into plaque which has just been exceeded exploded of cells and then the virus that came with it and we were we 1st thought we would look away happens when these obstacles the regard them as lakes and deserts in an ecological context that would that would confront a a wave of of of viral plaque spreading so that's the idea
and so the 1st thing we looked at was a diamond and what's shown down here at the bottom is out of piece of the virus soaked filter paper which allows us to launch a linear way well away when you lay it down on this Petri dish so it's a long and yellow resistance of susceptible bacteria and orange resistant bacteria and Alice watches go around noticed that of incipient costs that seems to form on the far side of the diamond so that's 1 of the interesting phenomena that we'd like to to understand and it turns out that there for us anyway the ways to do it is to sing in a kind of inspiration from Christian Huygens OK so you know more about his work I'm sure than I do but his famous in all levels of education science in the United States not quite so famous as fair met them but he also had a good nite interesting ideas and so I'd like to ask in the context of his population waves what can we learn of from these gentlemen other than the fact that the French flag is the Dutch flag rotated by 90 degrees and well here's agents
principle and he thought of the little wavelets any superimpose them and got beautiful diffraction or and fractions all talk about refraction here but and we could regard these as individual founder of the clonal bacteria or virus plaques all along this line going into a different medium with a different velocity and if you do this nice superposition of origins of then you fact a bending of refraction as you would all of affair man who formulated principle of least time and then we'll see how that comes into play in a minute but the formal realization of this principle this time it's an elementary exercise in the calculus of variations that a complicated medium here a past parameterize by clings take my word for it all of this equation down here where I have a position dependent velocity .period describes the the principle of least time and question is does that work for these nonlinear wave equations I'm not saying interference that would involve Crescent Frost fees are not present Frost deserved reserve game of solitaire on our way from coming coming by with maybe a similar principle could be applied and if I have a diamond we could head implement collegians and mad by saying OK here's a little plot virus on infected cell right at the front here's from it's going to be sweeping by this diamond of size and we can ask Is this person the year following hypothetical question that person but seller virus where did your ancestors come from and clearly the ancestors that were most likely to get there 1st is summarized up here it's survival the fastest and so the ancestor probably came from here on the other hand for on this little point on the front this emerging from the shaper trying to calculate but presumably because of the shortest path it's coming up straight here and analysts bending somewhere on the arc of a circle and so that's the idea and notice it leads naturally to a cost at the tip of the diamond no we have to be a little careful but we can go through his little calculation I did of the shape of the cost downstream of the diamond This is the angle the opening angle of the of the cast and it gradually flattens and it starts off a diamond like like a 90 degree costs gradually flattens out his 0 like 1 over time so it's not exponential it's pretty slow that's 1 the interesting observations this is like geometrical optics geometrical optics works when the scale of the variation of the objects that you're refracting around or large compared the wavelength of light for example here requirement is that the object the large compared to the width of that Fisher but other than that the front the frontier aware it that I was talking about earlier however I want to mention this will come in at the very end of we have to be careful .period information but neglects the discrete missile viruses themselves and it's a good it is reasonable 1st approximation but the idea is that is a simple computer simulation of the infected cell giving rise to another infected cells and so forth and in the simple lattice context you can program this on your laptop yourself you can actually look at what happens when you go by diamond and you can see here now the lineages the actual lineages of who begat Homer who destroyed home coming up here matters of viral lineage for example here's the cast but you can see that the friend is Ross that's 1 difference that's an important difference but also the pastor not straight lines their wiggling their jiggling around due to a phenomenon called genetic drift in population genetics here there's no genetic differences that I'm mindful attracting but these patterns that look like that the Nile River delta and so forth are lineages that server reminiscent of a kind of Fineman path integral approach but understanding complicated dynamical problems and in general he'd have to some over overpass but there's certainly something very interesting but vaguely reminiscent of Loijens Informatics notices a curved path here and except for these fluctuations which are quite interesting I think of that might be a good 1st step 1st cut at what's going on just like geometrical optics is the good news was 1st cut off for flu-like phenomenon that although it neglects the wave nature and so forth OK so Our here's we have are aware of Fisher equation and what we can do actually what sort of test origins and then and Fairmont is too solve this fisher equation with an obstacle and while we do is we take the growth rate to be 0 inside the obstacle although the viruses can still diffuse and so here I have a diamond-shaped object on a wider got obsessed with diamonds but there is a cost that he also and if you think the diamond especially over here is an ellipse or I think it was originally a circle and now there is again a cost and the cost we've we've checked numerically seem in experiments to heal like 1 over time and costs understanding as we think we now do a single
obstacles ultimately we want to look at multiple obstacles to here's an interesting array of squares a diamonds the purple here shows where the wave would have gone in the absence of the obstacles is like a lattice of square like the wintry model of statistical mechanics it's a lattice of of Lake and on this this is the front end of the 1st work this is where the front would have been in the absence of diamonds this is where actually is and you can see it slowing down so there's an index of refraction that describes these complicated media at least under some circumstances OK but on the other hand if I move the square is a little further apart as well from did and now you can see that you get cast but the costs and the develop overall velocity is unchanged and this is a big difference from way phenomena were there'd be back scattering and was probably slowed down a bit but even then and this expanded geometry of so we're still trying to track it down but they're there at least under some circumstances can be reduced velocity and hence the bending an index of refraction OK so now I want to conclude by talking about population genetics and ideally we would have been able to make bacteria that were different cut Missouri viruses that were different colors and and track the different viral species we weren't successful you least yet in doing that maybe someone the audience to do it all he cited do instead was to now instead of having viruses growth through bacterial ones to let bacteria just grown on a petri dish just like in the original experiment that I showed you and this is a again bacteria so soaked filter paper 3 different colors but is a great deal of chaos and fighting dominance or whatever you want call these proximately neutral strains of red a blue and yellow in the early days but eventually there's local fixation genetic the mixing of these 3 colors and I want to ask what happens when we had an obstacle so obstacle in this case was simply out of a circular of very fine mesh piece of filter paper so that it can date vaguely see hear and see here heroes as a kind of black circle and nutrients couldn't get up to the egg are allowed to feed these these bacteria that were coming coming down from above and so if I take a take a look here so you can see the effect of the obstacle on the population genetics it's not very visible but there was a cost saying cuts we had before but right at the cusp at 6 o'clock to genetic variants come together and this only happens when the neutral if there was a selective advantage they would this meeting would have been shifted to 7 o'clock but over here or 5 o'clock let's say so this is a kind of selective advantage meter and notice that this boundary as much straighter than that of the Wiggles that you have over here so there is a scar in the genetic landscape of this obstacle this lake like obstacle that seems to persist for a very long time and here's a radial of range expansion version of the same thing again but in this case the yellow and blue strains meet at least approximately at 6 o'clock may be a little more more courts 7 and out of the system shows these obstacles to really have we think a pretty important role in the population genetics and has assembled from strained as a theoretical physicist and so on he got beautiful results she just went simulated and what he did was to simulate not 3 colors but essentially an infinite number of colors 1 1 color every bacteria has its own distinct Gino and that's all that's true humans to an excellent approximation of and I can be implemented actually using something called the Brando technology in molecular biology we may or may not do ourselves but here's a whole bunch of colors migrating around elliptical object and you see pretty much the same thing you'll see a cost when things come together right now almost in a vertical slope and then with these fluctuations we see the blue and the green on the genetic boundary that it is inherited by the passage around the obstacle and and you can think of this as a kind of selections but by geometry because notice the very fortunate bacteria that just grazed the the Ellipse up here the green and then there's this blue strain which almost got squeezed out but basically had his Open Range downstream and were able to it's sort of takeover and that's the other thing that we're following up on which we think is it quite interesting disorders experiment again here's a simulation going around a diamond-shaped obstacles so you can see that dozens of shape doesn't matter that much there's the cast there's the boundary in this case purple and green and there are other lineages and notice that you go up here to the frontier and all of origins and pheromone you ask Where did your ancestors come from most of the time those ancestors just grazed the corner of the this this little rumpus this time and so on it's the kind of selection it's like a population bottleneck but it half faced only that is the nature of the construction of and we think it's very interesting to try to do so coalescence theory and look at these lineages and how they branch and how that branching is influenced by these obstacles so am I. I'd like
to conclude there was some reason and 1 last night's experiment but this is what I was just talking about their these unlucky genotypes that goes smashing into the obstacle so this service light blue turquoise it's it's all over for them they did they could go anywhere obviously have to only can get across by diffusion if they could defuse at all but then the the the fortunate that types that that actually just grazing along the edges of obstacles reduced genetic diversity of the but by these unfortunate extinct new strains here there are the lucky genotypes as well and the costs eventually deal with the sector boundary seems to persist indefinitely on the
1 hand with a view to full experiment it's more of a facetious expected experiment from which Wolfram did it and he can print anything and so why not print a map of the world so here the comments are a susceptible strains of bacteria and the oceans are resistant strain where to inoculate 37 well where else but the Rift Valley and so here's an inoculation in this artificial geography in a petri dish and I'm not saying No I think what will often say that human range expansions can be compared to viruses but it does show the geography matters there as well from who helped movement many of the key ideas here and
I'd like to close and thank you for your attention


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