Systems Biology Lecture 1

Systems Biology Lecture 1

hello everyone and very exciting moment the first class of the systems biology and I want to welcome all of you here I realized that this hall is too small for the number of people here and so we will try to look for a larger place and if we need to and you notice there there was music playing when you came in and in general part of this course talking with distance biologist remember that we're also biological systems with special needs like if you walk into a room with music makes you feel differently and since our objective here is to learn to be concentrated and relaxed we'll try to explore how we can do that together as you know being living organisms it's not just the transfer of information take care of the whole body now I want to also start with introducing the first feedback loop we'll talk about feedback loops in this regard so you know you might be familiar with our state as a human being called the relaxed state where we're open memory works we're not worried and this comes together with many physiological changes among them breathing like what's what's the breathing like when we're relaxed deep and deep and slow right and it turns out research has shown that there's another arrow if you breathe deep and slow you increase the probability that you'll enter the relaxed state and so we're going to experiment with this feedback loop during this class and I'm going to invite you to take a nice deep breath together you don't have to of course but if you do you'll have a good experience the way it's called a deep sigh of relief you take an air and you let out a sound like this so I want to invite you whoever wants to together with me and they take a nice deep sigh of relief good and we'll do that from time to time so on this side of the board I'm writing where we are so welcome to you at the breath my name is Ollie alone and I'm a professor here in molecular cell biology I did my PhD in physics working on hydrodynamics and statistical mechanics and then I got from a friend a biology textbook and I didn't know anything about biology I didn't know the difference between a protein and the only thing I knew about proteins is what I read on a cereal box you know protein and I read this book it was like reading a thriller because I was used to matter that you can describe using you know very well-established mathematical rules and equations and that behaves in kind of pretty predictable ways but when you look inside biology matter you see matter the dances it's completely different it looked to me inside our body inside ourselves millions of times per second these amazing structures form and then they do very precise functions computations even though despite the fact that they're in strong thermal fluctuations do it very precisely and where they're not anymore they go away and this is as absolutely miraculous to me I never saw anything like it and I knew I had to study this so I switched in my postdoc to experimental biology and the remarkable thing is that you can as a physicist as a scientist find very satisfying new kinds of kind of mathematical explanations and regularities and what goes on in biological matter and this wonder is still with me every day when they do research and it's also possible to teach it in a way that's accessible to them audience from many different departments like we are here and my purpose is to share with you this wonder and to my goal is that at the end of this few weeks we have together I don't know 12 weeks you'll know how to take a biological system understand how to make a model that captures some essential features of it use a little bit of math to understand lies the model and concepts that allow you to generalize from one part of biology to many other diverse systems in biology and different scales and I think we can do it this is the eighth time I'm teaching this course I know we can do it so so if I were to say the premise of this course what's the central goal or concept is that going to write it down by the way whenever you need to write a paper or give a talk or teach a course it's very good ahead of time to think what the premise is the one sentence that captures the idea full sentence of what you want to talk about it's not so easy to define it but if you do that your paper or talk or course will be much more unified so that biological principles which we call design principles unify now I told you a little bit about Who I am what the premise of this course is now I want to find out who you are so I want to ask you some questions about who we are the first thing I'd like to ask is what the different backgrounds that you come from so how many people here that I can identify as biologists it looks to me like about half okay and how many people here is physicists so it's like a very little bit less than half and how many people you are come from computer science okay so about 5% 10% and from chemistry oh no what will we do okay and from engineering what kind of engineering chronic engineering electronic engineering the kung-fu it's good because that's engineering is one of the big metaphors will use and anyone from a different background they didn't mention no and another question so I want just to notice to note that we have way it's in one sense a challenge because we have so did so physicists I use one kind of course biologists two different kind of course so you might I might need to ask you for patience when I talk about something that's really very basic for you because for the other people it's not basic at all and on the other hand I want to point out that this actually is a big resource for us because in this course will try to get you to see if you can learn from each other and this whole field starts from people from different disciplines talking to each other and what's easy for you very difficult for the other person and this the way breakthroughs are made so that's another purpose of this course is to find these interdisciplinary connections I want to ask a different question about the where you are in your academic studies so how many people here are first years master students okay that's about it's almost half and second year master students good so we have a majority of master students have said PhD students 20% and post PhD one to good postdocs almost so transition between PhD and postdoc and postdoc Hanna and professors we have people photographing us can you say your name into it sig so thank you for photographing us and the purpose is to put this online and which I did before when I taught in Harvard my sabbatical is very very much used resource and also you maybe will be able to use this if you want to remember what I said or find my error and the last part of who you are I'd like to ask you to turn find somebody from a different background and introduce yourself [Applause] well done always when I do this kind of thing to see people tend to smile after talking to somebody new before we start talking about an overview of the course it's I think it will be a good time to practice again take a nice deep sigh of relief so I invite you if you'd like to alright so what will we talk about this so we have all these lists of words here that we need to by the end of this course cover this course this lecture and I you know some people here I just want to stress people from biology background know very well the difference between these two words and in biology so if you know very well the difference between these two words could you raise your hand that's really majority and I want to also ask you to feel free to say I don't know because otherwise I don't know if you to teach you so if you don't know in biology the difference between these words please raise your hand thank you very much and then there are other people here for whom it's very easy to know by heart the solution for this equation so if you do can you raise your hand it's not a test okay just for me to know and if you'd like more to refresh yourself about math more can you raise your hand or if you don't want to know anything about math but you don't know so I want just to set your expectations you learn people don't know about this you learn about these you also people don't know you learn about these the level of the math with this for at least the first half of the course will be linear ordinary differential equations then we'll go into more complicated equations if you're the kind of physicists that wants a course with a lot of equations it's not the course for you but if you do want to learn how to take a complicated system and throw away the what's non-essential ed up with a model that's useful it gives you intuition it is the course for you so just want to explain that this is the solution to this equation and we'll use it today also and we'll talk about this in a second again I just want to make the sense that if you don't know either of these you always have the person you just met to tell you so in this course we're going to talk about several principles it's organized by principles the first part of the course will talk about the brain of the cell how cell thinks about its environment quote/unquote represents the world and makes decisions and the brain of the cell turns out to be made of a small set of recurring circuit elements will understand the second part of the course we'll talk about robustness this principle is there's this biological material one of its properties is it's very very noisy every year some things in it can never be determined precisely concentration of a certain component could be 1,000 in one cell and 2,000 is sister cell and can't do anything about it how can we make a circuit 3 that can work precisely despite this inherent variability and that constrains biology to very elegant and aesthetic designs a very small number of them which define if you want to say the manifold in which biological systems reside as the second principle we'll talk about robustness we'll talk about how a single cell evolves to a baby and adult with all these patterns this beautiful patterning problem and how could be robust we'll talk about error correction information processing in biology and we'll talk about optimality how evolution can find solutions that are optimal and how we can use optimality as a principle to understand biology so all these things are also a little bit different from if you're used to physics because evolution is at play and this will create some shocks for you it cries a little bit a different way of thinking good and so let's begin maybe I should ask at this point if there's any questions yes what the question is what about the course requirements so how many people you are actually signed up for the course now many people are just listen so you're welcome to come I didn't forget to say how many people come from a different University one where you come from thank you for making all this way and this is my right you live here yeah okay honesty is hey hey hey so the requirements at this point a I'd like to introduce Olin so Val will be the course teaching assistant Owen is the one here yeah so can you give me say a few words so I'm Owen and I will be teaching assistant ta there would be a two we had two beginning week or two we'll see how it goes but we have to differ to separate study groups like to total goon and Monday and on Wednesday you saw that on the final website and on Monday between one and two the group focus more on studying or feeding principles of biology so for the non biologist and on Wednesday with more focused on mathematics or the guys that are mobile resistant another flash the exponential automatics and those are the requirements and there will be a weekly exercise starting form next week and again the purpose is to know the material not to test your abilities it shouldn't be two things should narrow something like that's okay between our two week that's the workload for you should be we want to make it about an hour two hours because they really recognize that a lot of you have a lot of course loads already but if we don't have exercises I think it will be a shame yeah and one on the fight vulgar website the clap the will there is a class website will post the exercises on there and we have our details and have my email and feel free to email me and would you be able to write the email address you know so when we talked about exercises an exam final exam any more questions about requirements percentage of the score we didn't decide yet so we'll let you know about percentage of the score we don't know yet books great question oh thank you so this book will follow this book and and this book is I wrote this book based on the courses I taught at the course I taught here again after four times I want to have something organized so I wrote the book and it's really very useful for me and I and I can other I'm going to pass it around we reserved the six copies in the physical library and six copies in the biology library and if there's not enough you please let me know so I'm going to let you pass it around so you can take a look and book yeah that's the book it's I think it should be enough it has some terms and has some math at the back and it has and today there's also Wikipedia as a huge resource people about biology you can just if you don't know a word you can find they're good explanations more questions about structure good okay and so what I'll start start to get into our subject today our first subject not because the dynamics response time in action so what you find the term etc we'll think about for the purpose of this introduction about the one of the best understood organisms a living cell it's just one cell unlike us which are made of 10 to the 14 cells this cell this organism called is a bacteria called Ecoline and its size is 1 micron more or less and it can do a lot of the functions of life you give it some water with sugar and salt and it can divide you can replicate itself in a order of half an hour make it 2 4 8 16 until food runs out and you can calculate in a day with this process you can get if you didn't run the food didn't run out to get well you can calculate how much how many bacteria will get it to astronomical volume now this bacterium is also thinking all the time it's knows about the environment it can detect things about the chemical environment and make decisions change its composition in response to the changes in environment so we'll do a lot talk a lot about how the cell thinks and what how it can store information and make sense of the world and it can move put some food here it'll grow propellers with electrical motors it's been at 100 Hertz and move towards the food very efficiently but run away from toxins cetera communicate cells communicate with each other this little creature is amazing and the amount of things that can do that carry out up carry and a lot of things about it are also applied to ourselves so it's one of the favorite organisms because it grows so quickly biologists have been able to analyze it in great detail now the interesting thing we'll focus about any coli how it does all its functions if we look inside the cell we'll see that it's a it's a dense gel of the most important molecules we'll be talking about proteins this is one cell the next level of resultant proteins which are molecular machines I'm going to draw in like a pacman here it's good it's almost it's almost like a living molecule it's it's size is about 10 to the 4 atoms net one nanometer so you can fit a thousand from side to side this is the scale and these proteins are are the things that do things in the cell they're the ones who build the parts of the cell they're the ones who do the chemistry breaking down sugar is taking the carbon atoms and making the rest of the cell they're the ones who some are like antennae that are half outside the cell half inside the cell and read what's going on the external world some of them are information processing devices that can be mcclee modified and then become active and chemically modify other proteins forming circuits of information processing 30 ones who bind to the DNA to write to control when other proteins are made carry out functions so equally so when I say the cognitive problem of the cell is to react appropriately to changes the environment in the world could be inside the cell or outside the cell what do I mean by that when we supply a sugar that the cell can use to grow so makes a protein that can break down the sugar into carbon right you use it up so this is a 1960s more or less biologists in Paris mano and Jacob this is the 50th anniversary of that actually figure it out how this works the basis of how it this piece of information from the outside sugar converts to an action which makes the protein that's acts on this sugar in a useful way that's or if the cell is damaged it may it senses it and it makes proteins and then repair the damage or commit suicide like ourselves you know in there damage sometimes the commit suicide so we don't get cancer very important this happens on the order of a million times a day a second cells make the right decision in our body it's very be very grateful for this right well we can so I'm going to talk about a little bit of this fungus problem it turns out that the cell so you know the chemical environment the things can happen is infinite and in different dimensional space of of it took a toll so you know the problem the the world it can be tremendously complicated there's many things that can change temperature pressure many kinds of chemicals cells can use or toxic etc the cell is able to represent which is better represent the world using about 300 internal degrees of freedom these are molecular states that are the internal representation of what's going on in the world one internal representation says my DNA is damaged another obsession says oh there is this particular sugar out there and at this particular concentration there's 300 like that in e : there are just 300 transcription factors of E coli or or less talk okay so oh good so first I want to say this is another first question it's the first question about biology or thank you matter so thank you for asking it how did they come to the number 300 in a second I'll talk about the molecules that do these called transcription factors and we know from the fully sequenced genome of E coli every every single protein and we know that about 300 of them are transcription factors that's the number did I answer your question yes yeah we have freedom here yeah let me define it for you in a second it's concentration of Amalek particular molecular species I goes from 1 to 300 so we'll analyze this with this example supplies sugar and cell makes a protein that can break down the sugar into carbon so to understand that we need to talk a little bit more biology and what I can tell you now is like very very very basic biology and that applies virtually to all the kinds of organisms we know so inside e.coli is the DNA molecule we've all heard of DNA which stores the information needed to produce each one of the different proteins this DNA is a molecule that is made of repeating elements you all heard I think about these letters ATGC t a is for it's a polymer made of four kinds of chemical letters with this you can write the instructions needed to make proteins the number of base pairs in E coli DNA is known precisely in fact we know every letter there so it's a polymer and size is about five million and letters which is the E coli DNA and it's organized into genes gene is a piece of DNA that encodes for one particular kind of protein of course again for biologists here you'll recognize it every statement I say here has many exceptions for example in our body a gene can code for several proteins the splice variants etcetera so we recognize that I'm using a language that I hope they will be understandable to everyone and that captures the main main part of the story and this gene has can be read and the way it's read so how does this information turn into protein is by a special protein so DNA in order to make meaning has to be read by a protein the protein raises information there and and proteins end up making the new proteins encoded there in the gene DC and the way this works is again I'm just the basics there's a special protein that knows how to read a certain sequence of letters the tells that this is the start of the gene and then it starts taking this DNA run across the DNA and making another polymer that's just a copy of this DNA this is like a little like transcribing the skull transcription the information there into a chemical note that soon will be thrown into the weight baskets but just for a little while it has information ready to G this process called transcription this RNA a is then goes into a chemical in into huge protein factory and here at Weitzman you know this Factory the ribosome structure was figured out by other unit who won the Nobel Prize in 2009 this is a huge achievement in biology to understand this Factory in the cell that takes the RNA and makes reads the letters and understand how to link together a chemicals in order to make protein this is called translation so here you know the difference between transcription translation right you can congratulate ourselves of course in a very superficial level so that's that's what it is how many genes are there any coli you coli has about 4,000 genes he has about 4,000 genes and therefore we know it has it can make 4,000 different kinds of proteins some of them repair the DNA damage some of them break down sugar others make the cell wall others are in the ribosome to make new proteins others are special regulatory proteins that tell jeans when to turn on and turn off etc itself 4,000 biological functions like this total number of proteins in the cell is about three million let's make it four million okay therefore on average each protein is found at about a thousand copies so how did I get this number I just divided four million like four thousand kinds of proteins but again there's a bigwig range some proteins are found at just a few copies per cell and others are found at hundreds of thousands like the proteins of the ribosome that's the machine that makes new proteins are among the most common protein so there's a big big range if proteins are found just a few per cell it's if I tell you there's ten per cell you already understand that there is a randomness going on here because ten percent have precisely ten per cell some cells will have five some cells about fifteen did put some statistics when the cell divides those proteins will go half and half it's not five and five times six and four etcetera so I want to tell you already that for in biology you can't escape from the inherent randomness because you're always dealing with small numbers there's only one copy of the gene for example there's a few copies of the RNA for each gene so you go through bottlenecks of small numbers and randomness so Casta city is built in we'll get back to that later this by the way is called the central dogma of biology this transcription translation information flows from DNA to protein it's now as I mentioned before but the cognitive problem of the cell protein for example the protein that breaks down sugar particularly is not made all the time it's only made when it's needed it's only made when the sugar is around so how does that happen how does that happen and the answer and we already talked about gene now we need to talk about what what turns this process on and off that the switches switches so invite M environmental signals for example sugar is present affect regular regulatory proteins so these are special proteins whose job is to turn genes on and off they're called transcription factors I realize I'm telling you a lot of for some of you new concepts here for some of you very old topics and these transcription factors this is special proteins so for example in the case of the sugar we're going to write down in general we're going to write down these signals as s and the signal for regulatory protein X we're going to call s X and the sugar binds to this protein the protein is this molecule right 10,000 atoms it's a very very big molecule but it's folded into very precise shape that we can now know using x-ray crystallography it's another and this sugar the signal binds a specific place on this protein and this protein is designed to go it's like a machine that changes its shape and when it changes its shape it becomes possible for it to do something new for example to bind to a specific sequence of letters on the DNA that's inside this protein is a lot of cleverness it's recognized specifically the signal and changes shape in order to specifically recognize a piece of the DNA so it's kind of a way to connect those those words and it went in it's an active form it it can recognize it's a binding site some sequence of letters usually a palindromic sequence of letters by the way because they work in dimers you can kill is no matter and when and when it binds to this physically bind here it can activate this protein to make to transcribe so when we add the signal protein switches its active shape binds the DNA and starts transcription and we get the protein if we call this protein why we're going to summarize this entire molecular series of events in the symbol X arrow Y x activates the production of protein why now why itself in some cases is also a regulatory protein it's also a transcription factor and it goes to Z and Z can if it's a regulatory protein can activate W and you etc and so you can get a whole network of interactions like this in fact that's what you do find slightly Cola so there's a whole series of events it's started by a signal allowing you to make quite sophisticated computations we'll talk about transcription factors and signals this this is the gene the part here next to the gene where all the regulation goes on is called the promoter just part of the DNA so you know in the DNA there's parts that encode for protein and there's quite large parts that are there just to regulate how much and when this protein is made and in fact if you look at different organisms like a human being and a monkey the genes that they say the kinds of proteins we make is virtually identical and then pointed point of view of letters 98% identical and when people found that out they said wait what's the difference between a human being and a monkey and a mustard plant and it turns out that the fundamental differences here actually when and where and how much is the logic or the computation when and where and how much to make these proteins we'll talk about that logic is very very important I want to talk a little about time scales before I erase this how long does each of these reaction takes and and here in biology we found find something very very useful which is called a known separation of time scales that each step here happens on a very very different time scale and for theorists that means that you can average out the fast reactions when you're considering the slower reactions and make really much much simpler models than you otherwise would have to do so this active inactive transitions take place on the microsecond time scale when it's active this protein diffuses in the cell or slides along the DNA to find its binding sites and this takes let's say one second transcription takes 100 seconds you see the vast separations of time scales here and then the protein is around the lifetime of the proteins is around hours for days so again so this separation physical you can say is this my chance or is this how come we have a separation of time scale and how does whole this thing come around about I mean how did this start yeah you're right yes yes here there's there's no turf separation of time scales or we can say this whole this whole step takes on the order order of 100 SEC a few minutes of course this can change from organisms organisms there's a lot of complications I'm not I'm not talking about the e.coli that's the promoter how does this whole thing how did this happen how does it's quite miraculous in fact too too remote to remember that these cells ecoli are living organisms than they are made or the change by a process of natural selection the Darwin talked about in 1860 he wrote in his book right 1867 and the idea is that when ecoli divides makes a baby makes exciting facts these duplicates itself also duplicates the DNA precisely so again exactly four point seven times ten to the six letters exactly exactly copied correctly duplicated with an error rate of 10 to the minus 9 that means to say takes a thousand duplications before you get a change what changes still occur and if that bacteria has a change somewhere for example a letter here that changes the shape of this protein eventually and usually this is a bad news for this bacterium and that removes a change that mutant doesn't reproduce as much as the other bacteria and this change is lost but sometimes it's an improvement under the particular conditions of bacterial lives and that improvement therefore makes that Baqir makes a little bit more babies and that piece of DNA replicates more and so these changes are kept and that's how by this process believe it or not you get all of these 4,000 genes promoters the right place the right time bacteria became multicellular animals fish reptiles mammals monkeys humans and this is accelerating pace evolution worked took about a billion years to go from bacteria to more complicated organism so nucleus another half a billion years to multicellular organisms and then on another and you know quarter of a billion years to get too complicated animals and they're not humans diverged from monkeys a few million years ago it's accelerating the pace of what we might look at is the increase in complexity in something so that's something to understand by the way a lot of things are open questions how this scale of evolution works complexity builds etc there's a lot in this field it's like we know the tip of the iceberg there's a lot a lot to discover and want to also tell you that so this is about natural selection just just a small taste of it so am I right in asking are you asking why there are so many proteins 4000 kinds of proteins in the cell you're asking for one kind so for instance the protein that breaks down the sugar why do we have about a thousand copies of it why not one so that's a very good question that amounts the concentrations of these proteins are also quite well determined by natural selection and they're determined usually according to what they need to do so think about the protein that needs to cut the sugar it needs to produce enough carbon atoms to make a entire new cell in 30 minutes now each one of those proteins works let's say a hundred times per second producing 10 car new carbon atoms for the cell now you can calculate how long you need to work in order to produce the 10 to the 12 carbon atoms in the cell 10 to the 12 I think is the right number there's 10 to the not 10 to the 6 proteins each one has about 100 amino acids each one of which made made up let's say 10 carbon atoms but so I don't know maybe it's 10 to the nine carbons that you have to check that so it turns out when you do all the calculations that you need for that sugar cutting enzyme of almost a hundred thousand copies that's how much the cell makes if you have a less sugar it makes less of it so I'd like to tell you that the amounts made also depend on the intensity of the signal and that function is itself under natural selection and as I'll tell you words then you can from optimality arguments calculate sometimes how much the protein should be in the stuff that's refer ecoli the amount of proteins in our cells it's still under debate what whether there's the silk errors if you take away half of them or not the answer your question great so very very good questions I want to encourage you to ask questions especially questions when you don't understand something you're helping other people who don't understand probably the same thing the same time it's super-super we're making excellent product progress before we take a break you want to draw for you the upshot of what I just said about X arrow y ecoli as a transcription Network made out of settar a with about 300 transcription factors and about 10,000 arrows where the arrows mean transcription factor X turn transcript factories 4,000 nodes each node is a protein 300 of them or transcription factors or regulatory proteins that are able to change the production rate of other protein so 303 are driven have arrows going out of them and there's about 10,000 arrows so this is the brain we're going to discuss and because we're working in e.coli we know the shape of the brain we know each and every interaction to first approximation who talks to whom so we have an object here of high complexity carries out very important functions for the cells figuring out how to change the cell's composition in response to the environment and we have a chance to do something that I think is the first time in science to understand an object of this complexity because you know a network of nonlinear interactions with tenth that with you know a few thousand variables is impossible to understand generic network is impossible to understand you know this equation but because it's an evolved Network we'll see that it's special its biological biological networks are simpler than the generic case and then there have principles because they've evolved that actually make it possible for human beings to understand them that's deeply satisfying that's they'll be a big part of the first third of the course I think this is a good time to take a break we'll come back at 3:20 you so it looks like there's a creation of free seats so people if you want if you want to sit more comfortably there's one there and two there if you guys are you over there there's three seats here for example but I do not treat not free passing out a phone chicken design your name email and if you are interested or not to the class because you to know we were sending out to find of each everybody so we're going to send some you know that another just make sure you want your emails early so we can get some materials they will send yeah we can join them good so let's begin by taking together a nice deep sigh of relief you know so we're going to talk about soon about the dynamics and response time of one arrow like this and we started talking that you know the jeans have their this complicated the series of event for transcription factors become active defuse bind the particular site just maybe 10 10 20 letters inside this millions of letters in front of the gene start transcription translation and make a protein this stuff is summarized by one letter arrow X arrow Y X changes many different marker before production rate of protein why so make it bigger letters and by the way there's another ritual I want to tell you about a when people come in late which is fine we welcome them with a nice deep sigh of relief let's welcome them that way we're going to get get to breathe a lot which is very very good again the purpose is not to not to humiliate anyone it's just that when something happens in the class we all notice it and if we just recognize it since again we're human beings we can it's fit just feels better yeah size consideration the sizes of protein versus decided to sell has it fit a million of them in there with the DNA it still leave room for things to move around so great so the question is I told you the size is one micron and those silent proteins one nanometer how can you make fit a million proteins into this membrane enclosed capsule and indeed if you this equalize one this dimension is about 0.1 micrometer so the volume of this is about 10 to the minus 2 micrometers cubed and that means there's room for about ten to the seven nanometer cubed proteins because this is one thousandth of a micrometer so it's one billionth of a micro meter cubed is the one protein we have ten to the minus seven nano meter cube and what the result is that the cells just as you suspected are are densely packed with proteins it's not a dilute gas of proteins it bump into each other and the DNA like in a ideal gas this is like this and cell is volume fraction of proteins is very high like close to 50% and the DNA is a tiny tiny part of that volume fraction if you take the DNA of the bacteria and stretch it out it will be much larger than micron will be I am a thousand times longer than the cell it's coiled coiled coil or like this and everything is very packed so the proteins are moving like this and still need to find that piece of DNA and the right search around among the millions of letters for their letter how can it happen and like I told you in a second ten seconds good physics problems right the a lot of this has been worked out before a lot of love things they're letting to stir it till we can talk later about diffusion constants inside the cell inside of it it's a non-trivial crowded environment in there mmm answer your question and thanks for asking it you asked me during the break and I wanted you to ask here because anyway I want to encourage you guys to ask if you don't if something is bothering you or don't understand because that means helps me it helps me explain better just a few more details about this brain what we know is that there it isn't brain or the transcription network there are two signs possible signs on the arrows positive and negative positive means x increases the production of Y and negative means X decreases the production of Y the way you can write if you help you remember but everything I'm saying is it is also in the book you want it just not right it's also a good option and and our symbols for activation we have special symbol for this decreasing thing is this is for the positive interaction and for negative we use this kind of sign it's like a arrow like this this is for X decreases the production of Y X is like this are called activators and X is like this are called repressors more words and we know that any co light network there are about 50% activators and 50% repressors and in e.coli and in human beings it's about 80% 20% and by the way in another kind of biological network neuronal networks where X is neuron cells and this is a synapse and neural cells there's also 80 percent more or less activating and 20 percent inhibiting interactions is that a coincidence or not we'll talk about later our brains of course have many more than four thousand nodes our brain as you know how many neurons do we have 10 to the 11 10 to the 10 to the 11 neurons and this brain has only 4,000 nodes and 300 of them are the ones that activate and regulate so it's smaller it's more it's a good place to start the signs on the outgoing arrows from a transcription factor usually have the same signs outgoing arrows are usually all plus or minus if X is activator all plus effects as a repressor all minus the incoming arrows to a given node are mixed usually incoming arrows are mixed science mixed class – this property also happens in neural net newer onal networks the outgoing connections of the neuron cells usually have the same effect because it's kind of neurotransmitters they have the incoming have different effects that's called Dale's rule in neurosciences same thing in transcription factor networks so the comment here is there are transcription factors it could be both activators and repressors absolutely right so a some set X can also repress some specific genes absolutely right so let's make it more precise they have correlated correlated sign mostly plus and these are less correlated yeah I think reproduction reproduction rings so the portray the rate of production thank you very much and that's something we'll talk about now when you change the rate of production what's the dynamics of the change of the concentration of the protein why that's exactly what we'll talk about in this lecture absolutely good comments all right when two inputs go into the same and do the same note interesting things can happen for example we'll see later that they can act as and gates you need both of these inputs x1 and x2 to be active because act as or gates either one is enough in order to act change production rate of the gene it could be more complicated functions I'll talk about that later but genes that have two different transcription factors for example this is first signal to the second thing binding to their own each one to its own site can act together as add Gates or gates other functions and that's a lot of where the information in animals comes from which cells will become a brain cell which will become a muscle cell why this makes muscle proteins this makes brain proteins at particular Speight places particularly time determined by the logic on the promoter that piece of DNA that controls how much of sections you prefer to make in the developing embryo which changes the signals have to do with where that cell is and the transcription factors make this computation and so this carries through to very profound things about about our biology too not only in e : of course our biology much much more complicated but principles are very carried and one more thing I'd like to tell you about this is that the design here this design promoter gene this design is highly modular or if you want to call it plug-and-play I can take a piece of DNA from a jellyfish at that piece of DNA makes the protein that makes this jellyfish green fluorescent it's the gene called that makes a protein green fluorescent protein so I take just this part gene from jellyfish that encodes green fluorescent protein and using the tools of microbiology which are extremely powerful every lab here at the Wilson building has the technology to take that piece of DNA and glue it into the DNA of e.coli precisely glue it into a coli DNA next to let's say a sugar controlled promoter so this is genetic engineering I think a piece of DNA from the jellyfish and I'm combining it with a piece of DNA from E coli and what do you get you get eco light the turns green when you add sugar it's a seamless modular design Oh light turns green when you end so you can also ask this all evolved by these random mutations random letter changes that select four and then the Equality supplicating more babies survives there how does this get you to this modularity design why shouldn't it just change for each organism has its own machinery specialized machinery what keeps it like that that jellyfish and e-coli they have diverged to billions of years ago there are the last common ancestor why should it be that their genes work in each other and that's that's very very interesting project question it has to do with things like evolved ability the ability for organisms to change this modularity affects a lot the ability to recombine parts just like we have an electronic engineering plug-and-play elements make allow us to make engineering much much much quicker we don't need to reinvent the wheel every time right have you served mechanisms for example promoting motors like that also helps it we say conserved is just the words it says how similar between different kinds of animals and organism is the so the question is the converse experiment if I take this the regular piece of DNA from jellyfish and I stick it into E coli in front of a gene from E coli that won't work anymore because equality doesn't doesn't make the regulatory proteins that can recognize the jellyfish signals how far away do I have to go the question is how far away the Tree of Life can I go before promoters start losing their ads especially so I don't know the answer and that's a nice research question so here we we are touching the boundary of the unknown please the unknown to me let's call it and by the way I think that'll be nice for us they take a lot of your questions will generate things we just don't know I don't know for sure but maybe even feel so I want you to get the message that it's a very fresh fresh fresh field more less known then still to be discovered by some of you lady all right now let's let's talk about dynamics in response time so I'm going to erase this but this gives this piece of biology and we're going to think about just out of this whole network we're just going to take X arrow Y and analyze its simplest dynamics in the simplest case to get a sense of timescales and by the way this lecture is unusual because I told you a lot of biological words but next lecture that's it more or less will work with this for a while think if you know think all these words are what we need for the first third of the course more or less okay so we're going to talk about X or Y and we're going to calculate the dynamics of the concentration protein Y which will the notice wife so I want to write down the equation for the rate of change what that equation is very simple it's a first-order rate equation it's the rate of change of Y this is the production rate and in general it's a function of how much active transcription factor x7 to sell if X is an activator beta will be an increasing function if X is a repress or better will be a decreasing function we're not going to worry about that right now we're going to make better constant this is the removal rate and it's the rate at which protein Y concentration goes away and this removal rate has made two processes degradation and dilution degradation is the active destruction of Y so the cells know how to make machines to take protein and cut it up at a certain rate alpha dehghan you see it's a first order process it's just like radioactive decay – the probability per unit time for y – and the aleutian is the reduction due to cell growth so because concentration is the number of proteins divided by the volume of the cell we didn't make or destroy any proteins but just increase the size of the cell by growth concentration would go down that's what's called dilution so this is a very good comic the comment is that this equation means that a change in X star in the active transcription leads immediately to change in production rate whereas in the scheme that I showed you the central dogma the central dogma the there's delays so it takes a microsecond for the signal to change X star then in about let's say seconds to find the DNA then minutes to produce protein Y so that's a production rate may be ordered mine two seconds said and here thanks for this question because I didn't explain myself that well I'm using separation of time scales so I what I'm doing here here is physics the favorite topic is to neglect some of the complexities of the real world and in the hope that you get a model that can make nothing to it of sense that you can go back and understand so I'm going to write it down I used used separation of time skills to write an equation where a change in X star makes instantaneous change in better production rate a more real more realistic model would have let's say equations for RNA for binding of X star etc all these are on the art 10 to 100 seconds time scale but changes in Y will see our order of magnitude faster more so I'm going to neglect these and assume they're instantaneous on the time scales we're talking about this very important point and of course in the homework assignments you'll be able to write the second-order equation that's the kind of things as you can now good question yeah right there's a separate the question of why do you consider degradation vector separate equation for X and that's going to change this as a function of time and that means this this thing can be a function of time then we need to solve this and it's possible to solve I'm still going to solve it assuming X is constant like in a idealized situation the answer your question good good good good good yeah can we go on great great we're going to make it so so we're going to solve this equation and the first situation is case one said state so beta has been constant for a long time why no longer changes so dy DT is equal to zero and then we can solve this and we find that why steady state made over alpha so what this equation tell us is that at steady state nothing's changing the amount of protein we find is the ratio of production to removal rates a double production a double why steady state if I double remove all a half why steady state case two suddenly theta becomes zero though I started at y equals y 67 for a long time I had the sugar around and made the protein now the sugar is gone maybe all the cells ate it up or I move to a new place it's it what's going to happen to the protein concentration it's no longer produced so it'll just be removed solution for this equation like I wrote down in the first lesson in the first part is an exponential decay the rate of this exponential decay is given by the removal rate just like in radioactive decay you want to plot it out here can you see the mister camera yeah time 5 T concentration versus time we start out at Y steady state and it looks like this doesn't reach 0 of course I want to introduce so we talked about the gradation we steady-state I want you to use this concept of response time concept actually comes from engineering response time tells us how quickly things happen in a dynamical system response time is the time to reach halfway from initial to final in general so we could ask what is the response time in this simple case need to calculate it so the question is when do we start from we start from Y steady-state and the response time is the time to reach Y steady-state divided by 2 this is we call t 1/2 so let's solve it from our solution here so Y of T 1/2 is 1/2 Y steady state that's equal Y steady state e to the minus alpha T 1/2 I plugged in T 1/2 here so Y steady state it doesn't matter what Y steady state is the answer is that T 1/2 – love to over alpha I'm going to fast with the math I suggest you try it out after after the class now what does this mean here this means that the time it takes for the for the protein to go away half to half where it started is governed is inversely proportional to the removal rate alpha the faster I remove the proteins the faster they go down but it is independent on the production rate better of course there's no production rate in this situation because they stopped production to zero just dependent it's important to me for me to say that and this will use later most ecoli proteins have no degradation or degradation alpha'd egg is much smaller than alpha dilution SEC over the times we're so growing divide these proteins are stable so that alpha is alpha dilution I just want to tell you that what this means is that the response time which is log 2 over alpha is equal to 1 cell generation let's say about 30 minutes to a few hours depending on how much sugar there is around 70 how do I know this the reason is very simple if I have a protein that's not actively destroyed it just diluted out by cell growth and they start with a cell now I let it grow to twice the size and it divides that protein which started at a certain amount now divides half and half into the two guard cells so after one cell generation its concentration in each cell is now half of what it started with if there's no degradation after one cell generation which means I started from a cell it grew to twice the size and then split into two cells this is one cell generation right this is 30 minutes you have half in each yourself half of what you started in other words alpha dilution is log2 over the generation time and that is cells by the way the volume grows exponentially until they divide it grow exponentially did it bind that's true also for ourselves they grow exponentially and divide to go as much one second I ever kind of can take a question right now so this is actually quite slow it means that you have to wait a few generations to get rid of this protein what about the case where you start producing what's the response time when you start producing a protein response time is important if you want to fast responses organisms sometimes one case three start with y equals zero and suddenly increase beta so better the production rate the time T equals zero starts reaching from zero to a value certain value the solution of the equation in this case is this you can verify by taking the derivative of this function by time a derivative of e to the minus alpha T is minus alpha e to the minus alpha T because there's a minus here it's a plus and beta over alpha cancels the Alpha and you get this equation let's plot it out looks like this at long times when T is very long e to the minus something large is 0 we're left with beta over alpha which is why steady state good so we have have to go bye-bye and we reach the steady state it's good whatabout in the beginning in the beginning this slope here is better T you can do the Taylor expansion here and see that in the beginning this looks like betta T so production rate is this slope here so X proteins get produced until there's enough of them where removal balances production so what's happening what's the response time so we reach Y steady state over to this is what is y steady state 1 minus e to the minus alpha T 1/2 and if you solve this equation you find the t 1/2 is exactly the same at this t 1/2 so the halfway point here does not depend on production rate production rates if increase production rate increases the steady state but due time to reach halfway to that new steady state doesn't depend on production rate it only depends on removal rate now removal rate is slow for its stable protein no matter what dr. Ralph or these cases of activating or deactivating the betta is slow whatever you buy slow about one cell generation for most of equalized proteins what does that mean it means that if I let's say I have some damage and I want to recur it quickly and I want to make a lot of proteins I don't it takes for my daughters and granddaughters only they get that amount now since again we're living organisms that could be a disadvantage so the question is is there a way to overcome this this response time of course is the eigenvalue of this dynamic equation so you can't play around with that too much you can of course increase the destruction rate the act of destruction rate like degradation destroy the proteins that means to reach a certain steady-state you need to make more of the proteins which is a cost energetically costly so you can make what's called a futile cycle which is make a lot and break a lot make a lot and break Cola whose payoff is faster response time but if you're limited for resources that's not a very good solution so are there ways to get around this response time and the thing we'll do in the next class is look at some circuitry part of that network that I showed you that can speed up the dynamics so I invite you all to take a nice deep sigh of relief and they'll see you next week you

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