 no number is sort of set in stone and you can have really really wide fluctuations depending on what quantity you are looking at all right. What could these? So, if I took two cells let us say two equalized cells cell A and cell B and I say in one there is some 10 to the power of 6 proteins in another there may be a 1000 proteins ok. What sort of processes could give rise to this variability? Any guesses? It is the number of proteins. I can go back and check Rob Phillips and see what the system was. Let us see which figure was this? This is figure 2.6. This is protein senses of E. coli. Yes it is nature biotechnology 2007. I will put that reference in sorry you cannot see anything here. This is mass spectroscopy and fluorescence microscopy. So, I have one simple the answer is of course, complicated, but I will just show one possible cause of this variation which is let us say cell division. So, when you have a cell dividing into two daughter cells each daughter cell will get some copies of the proteins of the mother cell right. So, let me do a very simple very naive calculation. So, you say that a mother cell has some total n protein molecules and the probability of that protein molecule was one protein molecule going to daughter cell 1 is p and the probability of a protein going to daughter cell 2 is q. And I could ask that well what is the probability that daughter cell 1 has some n 1 number of protein molecules. What would be that probability? What distribution is that? The binomial distribution. So, with probability p you send n 1 number of molecules to this daughter 1. Therefore, with probability q you send n minus capital N minus n 1 molecules to daughter cell 2 this is n c n 1. So, that is the probability that daughter cell 1 has n 1 protein molecule. What would be the mean number of protein molecules that this daughter cell would have daughter cell 1 let us say n p? What would be the standard deviation of the variance n p q right. So, if I looked at fluctuations if I compare the fluctuations to the mean I get that the fluctuations are tamped down as 1 over square root of n right. It is a very standard result in binomial. So, the variability can be very large depending on how large your n is. If your n is extremely large then the fluctuations are fluctuations by this process through cell division would be small. However, if the number of copies of the of some protein is small it has 100 copies or 1000 copies you can get very large variation simply due to cell division itself. So, here is one experiment this is one particular protein which has a fluorescent tag fused to it and then you measure the difference in fluorescent intensity between the two daughter cells as a function of the fluorescent intensity of the mother cell. So, you have one cell which divides into two the mother cell has these one particular protein that you are interested in and you fuse a fluorescent tag to it the mother cell divides into two daughter cells. You measure the intensity of the mother cell and the intensity of the two daughter cells and you plot this difference in intensity as a function of the intensity of the mother cell. So, these are all data points. So, it is all over the place, but if you did a mean sort of these points represent the mean. So, if a mother cell has intensity of 50 the difference in the daughter cell intensity is roughly comes out to somewhere 2.5, 2.6 something like that. The solid line is this binomial partitioning that we discussed. So, of course, there is a lot of variability, but if you were just looking at the mean properties the binomial partitioning looks to be not too bad a model. Would this always be true? No, there could be other processes going on that leads to this variability. It so happens that binomial partitioning is one of the factors that play a role. It is not the answer, it is one part of the answer. It so happens that this for this particular protein the variability comes because of this division and that is why you get a reasonably nice agreement with the binomial partitioning model. So, the message is this that well at least one of the messages is this that even though it looks the problem looks complicated you could try very simple models. You could try very sort of naive modeling approaches. They may be enough to answer certain it will not it will not work for any protein and so on, but at least for some cases even naive simplistic modelings might give you a reasonable fit to the experimental data. After all binomial is something that we know for school. So, that is one source of variability. You can think about what other sources of variability there could be alright. For a end I just had this very nice curve which I found interesting. So, it is a distribution of human cell sizes again to show a sort of variability. So, these are different cell types sperm, red blood cell, lymphocyte, neutrosil and so on. You span a whole range of volumes. So, the sperm cell is one of the smallest it is 30 micron cubed. The fat cell or a mousite lies on the other end of the spectrum it is an extremely huge cell. So, again you can plot a histogram of these cell sizes. Well, this is not human this is mouse. I do not think there is one like this for humans, but this is for a mouse lymphoblast cell. And the total number of cells if you estimate for in a human body is around what is this is around 37 trillion cells. So, that is one part. So, we are the two parts. So, we are the two parts. So, we talked about this crowding we talked about this fluctuations or noise yes. In the sense that let us say I have a cell I have a single protein. This cell will divide into two daughter cells. This protein could end up either here or there with some probability. Now, you have many many proteins each of them let us say it is half let us say with equal probability. So, with half probability it could end up here or it could end up there right. So, when you do it is like a coin toss right. So, if you are. So, if you are tossing 1000 coins on an average you would have 10 to get 500, but you could get 201 and 800 in the other that would cause a variability. But the histogram was according to the size right. The histogram was according to the size of this histogram. The previous one previous one. So, this is the number of proteins. So, when you take an equalized cell the point is that the number of proteins is not fixed right. In some cells you could have 10 to the power of 6 and you take another equalized cell maybe you have 10 to the power of 5 and so on. So, then depending on how it divides or like I said cell division is not the only way it is not even a probably the most important reason of this fluctuation. It is just one case where I can do a very simple modeling and explain try to explain some of the data alright. So, let us 6 ok. So, now that I have done at least a little bit of these two points let me move on and talk a little bit about what sort of spatial scales we are talking about. So, last class we talked about these DNA bases and that was around each base was around 0.33 nanometers right. You can move up scales for example, a viral capsid was roughly around 10 nanometers a bacteriophage is around 0.1 microns if you move up another order of magnitude the E. coli is around 1 microns right. So, here is the bacteriophage sitting on top of the E. coli you can grow go up even more. So, for example, an epithelial cell or may standard human cell the number we take is roughly 10 microns. So, if you take the epithelium as a whole that is around 100 microns tissues you can go up to 1000s of microns and of course, then you go up to organisms. So, you can move up to like meter longs. So, this is whole. So, if you wanted to ask well how exactly does this tissue work, how do the chemical processes the biological processes in this tissue work and if you were looking for a really really comprehensive answer you would need to go back you would need to figure out processes that were happening at all of these scales which is very difficult which is why we generally we do not ask such a broad question like this we restrict ourselves to one sort of scale and because the physics at each of these scales are very different the type of modeling that you would do is very different you try to build put them together as much as you can, but spanning these wide magnitude of spatial scales from nanometers to meters is a really really difficult task. So, it is one of the reasons what makes biology so complicated. So, is another thing. So, this shows variations in cell shapes this over here anyone knows what this is the pretty this is a plasmodium falciparum. So, it is a single celled protozoan the malaria protozoa this over here is a plant cell this over here is an animal cell this is a red blood cell. So, you will see a variation in sort of shapes a plant cell is very sort of rigid it has a cell wall animal cells are sort of fluid they do not have a rigid cell wall these things over here are the chloroplasts I think and here you see this very long objects which are the cytoskeletal filaments the microtubules and a dense actin filaments which again we will talk about. A red blood cell is slightly special in that it does not have at least a mammalian red blood cell does not have a nucleus and that is sort of allows it to squeeze through very narrow capillary spaces, but most cells will have most animals all and other animal cells will have the nucleus. These are still fairly standard cell shapes and you can actually do some amount of mathematics to predict sort of types of cell shapes that you could have that is the next slide, but anyway so you could also have very weird looking cells. So, for example, this is a nerve cell here is the dendrites this is the axon which is the cell body and here are these nerve endings over here. These cells are the rod cells and the cone cells that allow you to see color these are inside your eye and these look extremely weird. As long as you are sort of restricting yourself to sort of basic shapes like these you could try to do sort of theoretical analysis of what sort of shapes would come up. So, this is result of a calculation where you sort of mean you write down a free energy or you write down a Hamiltonian for the sort of various terms that are involved that would go into determining the cell shapes elastic energy bending rigidity and so on. You minimize the free energy and you try to predict depending on what parameter values you have chosen what sort of cell shapes you would get. So, the result of one such analysis and it is it is used for red blood cells and predicts a whole variety of red blood cells. So, this is an equilibrium sort of calculation and even though we know that the body is not really at equilibrium we equilibrium calculations can often work out in different scenarios depending again on what sort of time scales and spatial scales you are talking about. This would not really work for this weird looking cells, but for standard cells this sort of a calculation it is I think it is based on something called the hell fish is based on the hell fish free energy and again we will probably talk about it as we go along in the course. So, I think for the rest of the class let us try to just again get a little bit familiar with what all things are inside the cell. So, what makes up my cell? So, roughly Nelson sort of classifies it into three things small molecules, medium molecules and macro molecules or large molecules. So, the small molecules are water of course, small ions, potassium, sodium, chlorine so on, simple sugars. So, it could be sugars of one ring or two. So, glucose, deoxyribose, ribose have one rings, sucrose is two rings. It could be this screen is not very good at least the screen over there is somewhat better. You could have you could have the four nucleotide bases thymine cytosine adenine guanine and again thymine and cytosine are the pyrimidines which contains one ring, the adenine and guanine are the purines which contains two rings. So, these are some small molecules you could take one of these nucleotide bases thymine cytosine adenine guanine, add a sugar to it one of these look ox ribose, deoxyribose and so on, add a phosphate. So, if you take this adenine you add three sugars you add a ribose and you sorry you add one ribose and you add three phosphate bonds that gives you what is called adenosine triphosphate or ATP you have heard of ATP that is like the energy currency of the cell. So, that is where the cell stores its energy. This ATP can hydrolyze one of these phosphate bonds to give ADP adenosine diphosphate where you have only two phosphate molecules plus it releases some energy. This energy the cell uses to perform whatever actions it needs to perform. Similarly, you could have guanine triphosphate hydrolyzing to guanine syn triphosphate hydrolyzing to guanine syn diphosphate plus energy. So, this is the sort of energy currency of the cell ATP, GTP and so on. So, you take a base a nucleotide base you add a sugar you add some number of phosphates and that stores some energy. The other sort of small molecule are these fatty acids which are chains of carbon atoms with a carboxyl group at the end and then depending on how long this chains are you have different fatty acids, pomatic fatty acid, steric arctic and so on. And the final category are what we already talked about these amino acids. The amino acids you put group into three classes charged amino acids, hydrophobic amino acids and polar amino acids and depending on whether they are charged or not whether they are hydrophobic or they are hydrophilic it will it will sort of reflect on the secondary structure how they assemble whether they want to stay in contact with water or whether they want to repel water and so on. So, these are roughly my small molecules. Then you move into medium range molecules. So, for example, one is phospholipids where you take a fatty acid chain which we talked about you add a glycerol, a phosphate and a head group and you get a phospholipid. So, the name sort of encodes it for example, if you have phosphatidyl choline it means that the head group is choline. If you have phosphatidyl serine the head group is serine and this is sort of a representation. So, there here is your head which is hydrophilic here are your fatty acid tails which are hydrophobic and this phospholipids are found where this phospholipids are found in various membranes. So, they assemble the self assemble into sort of bilayers. So, if you have this sort of a phospholipid here is your head group which is hydrophobic here are your fatty acid tails and you put many of them together they will try to expose the hydrophobic heads and protect their sorry they will try to expose the hydrophilic heads and try to protect their hydrophobic tails. So, you get a bilayer like this. So, this is what the cell membrane is sort of made up of. Then another category of medium molecules is what you would call fats. So, there you take 3 fatty acid chains you add glycerol that is what is called triglyceride depending on whether you have double bonds or single bonds you could have saturated fats and unsaturated fats you should eat one you should not eat the other all right what else then you have these large molecules. So, the macromolecules. So, for example, RNA you have DNA you could have proteins you could have polysaccharides like Lycogen. So, here again is the difference in the basis between RNA and DNA is that in RNA the thymine is replaced with uracil like we talked last class. So, these are one category of large molecules you could also have macromolecular assemblies. So, for example, if you remember this picture of the cell you had these very long sort of objects which span all of the cell. So, this is what is called a microtubule and the microtubule is made up of a very basic protein unit which is called dimer it is called the tubulin dimer which contains an alpha tubulin and a beta tubulin it contains a tubulin dimer many such tubulin dimers join together in a cylindrical fashion to form this microtubule. So, each green and blue together forms a single unit the tubulin dimer consisting of alpha tubulin and a beta tubulin it comes together to form this large macromolecular assembly which is called the microtubule. The microtubule has various functions it acts as the sort of the railroad of the cell things get transported from one end of the cell to another by piggybacking on this microtubule network. It lends the cell some sort of structural rigidity in fact it is a part of a class of objects which are called the cytoskeletal filaments cytoskeletal filaments in that they form sort of the skeleton of the cell. So, microtubule is one of these things. So, if we look at the micrograph of the cell this microtubule this microtubule network spans this sort of whole cell. An interesting thing about microtubules is that these are not static objects they are not fixed they polymerize and depolymerize. So, here is here is my microtubule you could add tubulin subunits to the end and cause this polymer to grow which is this polymerization. You could also remove tubulin subunits and you would get depolymerization it happens in a very sort of signature way which is called when it goes from polymerization to this it is called microtubule dynamic instability dynamic it is called the dynamic instability of microtubules and again we will sort of look at this in more detail as the course goes on. So, I am just throwing various things out there just to get you familiar with the names and the terms as the course progresses we look at all of this in much greater detail and see how to model these various things. So, when it switches from a polymerization state to a depolymerization state it is called the catastrophe when it switches back from a depolymerization to a polymerization state it is called a rescue event and again this is an energy driven event. So, when it attaches it has GTP once it attaches it hydrolyzes and the GTP becomes a GDP. So, that is one macromolecular assembly another example is another class of cytoskeletal filaments which are called the actin filaments and here again the subunit is something that is the actin protein many such actin proteins joined together to form this actin filament. Again this is a energy driven process it is driven by this hydrolysis of ATP to ADP. Again these are dynamic in that for actins you will get subunits being added to one end and being removed from the other end. So, for actin the process is specifically called treadmilling it is called treadmilling. So, these objects both microtubules and actin actually has a structural polarity one end looks different from the other and one end is called a plus end one end is called a minus end these units get added to the plus end they get removed from the minus end. So, again if you look at the micrograph of an animal cell these green things these long green things are these microtubules this red objects which are near the periphery of the cell they are the actin filaments. So, if you have this animal cell you will have microtubules spanning throughout this microtubule network then over here in the ends you will get your actins mostly. So, here you would form you would see these actins. So, again actin is another part of the cytoskeletal filaments. Another example of this macromolecular assemblies is this bacterial flagellum which again is made up of many different proteins and it is a really fascinating thing which we will again look at when we look at hydrodynamics. So, bacteria like the E.coli has many flagella this phospholipid drawing is actually a good drawing for E.coli flagella as well. So, here if this is my E.coli it has many flagella when an E.coli wants to move in a particular direction all of these flagellas come together and they start to rotate in one direction in a coordinated fashion. So, it like a corkscrew it rotates and that causes the E.coli to move. When the E.coli does not want to move all of this flagella move apart from one another. So, they are not bunched together anymore and the E.coli just drifts around. It is called two different phases of the E.coli motion run and tumble. So, here is when the all these flagellas are sort of bunched together they move in this corkscrew fashion and that propels the E.coli through the media. When you say animal cell what animal are we drawing? E.coli and the slide we had a. Oh, long back I do not know which particular you are asking which particular cell type this is I have to look up. Of which animal? Of which animal I have to look up this is a very generic picture in that sense in that it is if you look at the outer membrane it is sort of flexible it is not. So, the difference that I wanted to point out is that the plant cell is sort of roughly rigid it looks like the rectangle whereas, an animal cell would look roughly like this. As to exactly which cell this is a picture of I forgot I will look up and tell you. But any generic animal cell will roughly tend to look like this sort of fluid floppy elastic membrane a nucleus in the middle and then a lot of these microtubules and actin filaments all over the place. So, bacterial flagellum it is really the motor the bacterial flagellar motor is really a marvel of nature we will try to talk about this in a little more detail later ok. Again sticking with this sort of the theme of diversity here are a variety of viral capsids for from different viruses here is the influenza virus here is the HIV virus here is the tobacco mosaic virus and so on. So, you will see a lot of so, this is again another sort of macromolecular assembly different proteins come together they assemble the self assemble to form this sort of capsids. Some again some amount of modeling has been done in order to understand what sort of forces causes this self assembly hydrophobic forces are important electrostatic interactions are very important. These individual protein subunits can be charged they interact with the DNA inside the viral capsids which are negatively charged and this DNA can often cause a self aggregation of these viral capsids at least for some viruses. Yes, someone good question hold on to that in a couple of slides I will come to timescales of the self assembly of capsids. I will talk a little bit when I come to that. These are different types of viruses the nomenclature of viruses mostly I think based on the disease, but I am not sure if there is some so, I do not want to answer mostly based on disease for example, this virus causes influenza this causes HIV and so on. But may not be true for example, I different people have named it differently I guess this is a lambda phage it is a random sort of. So, here is one more so, another assembly so, this is the plasma membrane again this picture is so, bad. So, this is what I was trying to draw over there the phospholipids form a bilayer such that the hydrophilic parts are exposed to water, the hydrophobic parts are sort of protected inside you get various sort of transmembrane proteins that are embedded into this plasma membrane you get other things like iron channels. So, this is one iron channel which allows things to move in and out of the plasma membrane these are roughly around 4 nanometers thick and surface area of the order of micron. Finally, this is one more example this is an example of a molecular motors so, I am just showing sort of a random collection of things I find interesting. So, these are molecular motors which are proteins which walk on these microtubules and they transport stuff from one end of the cell to another right. So, I said that these microtubules form like a railroad for the cell and the railway carriage as it were are powered by these molecular motors they are powered by ATP consumption. So, they consume ATP these subunits of the motors this head domains. So, this is these are three types of molecular motors myosin, kinesin and dynein I will just explain in a bit what the differences are, but this cartoon is for kinesin. So, you will see that these there are two head domains over here these head domains attached to the microtubule and one by one they unbind and they sort of walk. So, it is literally like walking on these tracks the other the tail domains bind to cargo. So, that is what is being transported. So, here it is a vesicle inside this vesicle might be different proteins that has been synthesized at one end of the cell maybe a protein was synthesized here, but it is required for some function over here how would it go from here to here it uses this railroad network. So, it latches it goes inside a vesicle the vesicle is carried by these motor proteins which are walking on these railroad tracks kinesins. So, this is a kinesin motor this is a dynein motor kinesins and dyneins walk on microtubules kinesins walk on actin filaments and again this is only one type there can be different subgroups of this. So, there are kinesin 1 kinesin 2 and so on similarly, kinesin 1 kinesin 2 this is one particular type called kinesin 5, but the basic structure is the same you will have a head domain which will bind to the filament whether it be microtubule or whether it be actin you will have a tail domain which will bind to the cargo and that will transport the cargo from one end to another. These are intrinsically driven processes these are non-equilibrium processes driven by the consumption of energy you need ATP or GTP or some sort of an energy currency in order to transport these in order for these motor proteins to function properly. In fact, this sort of concept of non-equilibrium is something that we look at in little bit of detail towards post myths and basically you most processes inside the cells are non-equilibrium processes at some level they are driven by energy. In fact, they like this quote that if you are if as a biological system you are in equilibrium that basically means that you are dead. Anything in order to be living you need to be consuming energy you take in food that gets converted to all of this ATP GTP which the cell uses to perform all of these tasks. Does that mean that whatever equilibrium calculations that we will do pre myths and are not correct of course not you just have to be aware of the limitations of that and that is something that we do not in biology but everywhere for example, if I were to say that what is the temperature of this room I do not know maybe it is 24 25 degrees right, but it is not really the depends on what time scale you are talking about. If you are saying what is the temperature of this room over a scale of 24 hours the temperature is not constant right it is changing. So, the room is a non-equilibrium system it is exchanging energy with the surroundings and so on and it is changing temperature, but if you are looking at a period of time where that non-equilibrium properties are not important you can define a temperature. Similarly, you can do equilibrium calculations depending on what the time scales and the spatial scales are and that is what we will spend our time in the pre myths and part of the course we will look at equilibrium keeping in mind in the background yes consuming and the species in a chemical biochemical reaction networks are always changing I mean the concentrations are always changing. So, is that why those do not go to equilibrium. So, I did not understand the cell has biochemical reaction yes inside right. So, is it because the cell is always getting species inside and that is why it is not reaching equilibrium. It is a non-equilibrium system because in order to maintain the proper functioning of the cell which is all of this the chemical reactions, reproductions or DNA duplication and so on and so forth protein production all of this required energy the moment you stop producing stop providing energy to a cell the cell would stop performing all of these things it will stop the biochemical reactions it would stop protein production and so on and so forth the cell would die. So, what basically what is equilibrium you take a system you leave it to itself it reaches a nice happy state on its own right if you took a cell and you did that the cell would die you would have to constantly supply an input of energy in order for the cell to perform its functions. So, in that sense the cell is intrinsically a non-equilibrium system does that mean that whenever we talk about any chemical reaction that is going on we will never use equilibrium approximations no ok we will use keeping in mind that these are small subset that we are looking at the whole network if you were to look at the whole systems biology of all of these reactions going on overall it is a non-equilibrium system some small part maybe some small constituent part maybe in a maybe in equilibrium for a small duration of time for the duration of time of that reaction ok. So, that is what so we will talk about equilibrium and we will try to clarify when the equilibrium approximation is appropriate and when it is not and when it is not we will try to see what sort of we will try to see to a small extent what sort of things we can do.