 So, what we will look at today is sort of how to write down dynamics of cytoskeletal polymerization. So, dynamics. So, yesterday or rather last class I was discussing a little bit about these cytoskeletal actins and microtubules. So, we will sort of look at different levels of models actins or microtubules and we will look at models of different levels of complexity to sort of see what we can understand about polymerization and depolymerization of such a. So, before I start I thought I will just give brief introduction once more. So, we have all seen actins and microtubules, but maybe in a just a little bit of more detail what these polymers are ok. So, here is actin. So, this over here is what is called G actin or globular actin, the globular monomeric form of actin. This is a single monomer of this G actin protein. So, it is a protein consisting of these four subdomains 1, 2, 3 and 4. And if you see over here in the middle there is an ATP molecule sitting over there right. So, this is the molecule that can hydrolyze. So, it can hydrolyze and form an ADP binding over there and that releases some energy that goes into stabilizing the structure of this filament. So, these monomers assemble together to form this actin filament. This is called F actin or filamentous actin. So, G actin is the monomeric form, F actin is the filamentous form. And the filamentous form consists of two sort of filaments wrapping coiling around each other in a helical form to give what is called this actin polymer or this actin filament. Because these the way this subunits assemble is such that there is a structural asymmetry and one end of these actins will look slightly different from the other end. If you were to look at it in an electron microscope for example, and that leads to a sort of identification of two different ends one end is called the plus end, another end is called the minus end. And often in literature the plus end is called the barbed end and the pointed the minus end is called the pointed end. So, when these actins are in solution the globular actins the monomeric forms of actin are in solution they generally. So, here is my actin monomer, here is my G actin G actin when they are in solution it comes associated with an ATP molecule. Then when it polymerizes so, when many of these G actins polymerizes to form your actin polymer as it were these ATPs will hydrolyze to form ADPs. So, the more you go towards the intake let us say this is the plus end of the micro T of the actin over here is the minus end on this side. So, the more you go away from the plus end the more likely are you that the ATP has hydrolyzed to become ADP. So, these are the two states that we were talking about the previous class. What does this do? This ATP to ADP conversion it introduces a structural conformational change in the protein state. It introduces a conformational change in the protein state. I do not know if you can see. So, over here in the middle is this ATP binding domain of this globular actin. The black versus the white shaded parts show the change in the positions of the different amino acids of this G actin when ATP is bound versus when ADP is bound. So, this G actin one says it can exist in two states open or closed open or closed. These are two conformational states depending on whether ATP is bound or ADP is bound. So, if you go back and think in terms of these multi state models that we did for example, this MWC model for hemoglobin and so on those often existed in multiple states. So, this is another example of a protein that exists in two such states open or closed. And these two states have slightly different structures that leads to different stability. Similarly, if you look at this G actin in solution versus a G actin on the filament, again you will see that there are certain structural differences. I think I may be wrong, but I think the yellow one is the positions of the amino acids in the globular form and the white one is the position of the amino acids when this actin is polymerized to form their factor. So, again this polymerization leads to certain structural changes and that again contributes to the stability of this filamentous assembly. So, you have this G actin which can exist in two states ATP or ADP consistent with two sort of conformational states of this actin open or closed. It then assembles to form a filament, this filament to the structural polarity with a plus end and a minus end and that is how this is sort of a cartoon of this actin filament. These are two sort of strands intertwined with each other giving rise to a helical pattern. The two ends look structurally different and this one end is called the plus the other end is called the minus. As far as actin goes, you can have monomers being added, you can have monomers being added or taken out. So, these are G actins from both ends both the plus end and the minus end. So, you can have monomers being added both to the plus end or monomers being taken off both from the plus end and the minus end. These are the rates of these processes are different. Let us say it comes it attaches with some rate k on plus and dissociates with some rate k on minus where sorry k on k off plus that is it and in the minus end it is on and off rates which you call k on minus and k off minus. So, generically these are different and for actins generally the growth is faster at the plus end. So, on on an average you will have things that are being added in the plus end and on on an average you will have things that are being removed from the minus end ok. So, that is this phenomenon of tread milling. So, here is sort of the picture that these globular actins. So, this is my plus end that is my minus end. I have now forgotten about the structure of just everything is shown as balls. This globular actin comes with ATP this binds the ATP then hydrolyzes to form ADP and this phosphate is released. So, in the interior of this filament most of these actins will have an ADP bound to them. So, when stuff dissociates from the minus end what you are getting is this globular actin with an ADP bound to it ok. And then in solution this ADP will again convert this ADP actin will again convert to ATP actin and it will again come and bind ok. So, it is a cyclical process right. And that will give rise to this cartoon that we saw the other day this actin tread milling where things on an average will add on at the plus end they will dissociate from the minus end and you will get this phenomenon called tread mill. So, it is not simply it is a complicated process it is not simply monomers being added and taken off there are these various internal states that you need to take care of if you were to do a full modeling. The picture is sort of similar for microtubules ok. So, the situation is somewhat similar for microtubules except here the constituent monomer that makes up this microtubule polymer is actually a dimer. So, it consists of two proteins alpha tibulin and beta tibulin that form a dimer like this and then this dimer is the basic building block that forms your microtubules. Again here both of these alpha and beta subunits the alpha tibulin and the beta tibulin has a domain that binds GTP in this case instead of ATP both over here and here. And this GTP at this beta subunit that can again hydrolyze to form GTP and release energy exactly like ATP hydrolyzes and releases energy for actin. So, this dimer is then the basic building block of this microtubule the microtubule. So, it it forms filaments like this which are called proto filaments and then 13 of these proto filaments form this hollow tube which is which is my microtubule. So, the structure is little more complicated than actin it is not just two filaments winding in the helix it is like this hollow tube made up of these alpha beta tibulin heterodynes. And again there is a structurally symmetry because in one end you will always see a beta tibulin exposed at the other end you will always see an alpha tibulin exposed and that is why we again say that for microtubules it is structurally polar object it again has a plus end and it has a minus end. And again if you look at studies when you have this hydrolyzed hydrolysis of GTP to GTP there is consequently a change in structure this picture has not come very well, but if you see so this is a unhydrolyzed sort of alpha beta alpha beta chain this is a hydrolyzed alpha beta chain this one you will see is slightly more compressed. So, there are changes in the conformation again of this tubulin heterodymer as a result of this hydrolysis. So, again there are distinct conformation of states that occur as a result of this GTP to GTP hydrolysis yes 2. So, in a given heterodymer in a given heterodymer the GTP on the beta subunit that hydrolyzes to give GTP this one stays as GTP why I have no clue why, but it is just that the as far as I remember I think it is the beta one that hydrolyzes to give GTP. So, the same sort of unit of currency that you gain on polymerization it can. So, in principle you could say that I have a k on rate which has ATP for ATP bound subunits like you could also say that I have a k on plus D for GTP bound G actin and similarly 2 dissociation rates as well. It is just that this rate is known experimentally to be much smaller than this rate. So, for most modeling purposes we do not really take this into account and we say that only the ATP or the GTP form attaches and only the ADP or the GTP form detaches from the other, but in principle you should consider all four rates. So, you can also see that this sort of structural this conformational change is present which is there in the monomers for this alpha beta tbilin. There is also sort of manifested in this macroscopic structure of the microtubule polymer itself. During hydrolysis when things are being added things add more or less is a straight this microtubule looks like sort of a straight cylinder. During disassembly the different protofilaments sort of peel off like flaws. So, there is sort of some intrinsic curvature to these protofilaments and they peel off like this sort of curved sort of segments. And the one of the major or one of the leading hypothesis is that at this leading edge you have the subunits that are attaching on these GTP bound subunits which are shown in the CLO and cyan and in the interior they are all this GTP bound. And this GTP bound sort tubulin acts as a stabilizing cap which sort of prevents this disassembly. So, if ever all of these were to be hydrolyzed into the GDP form you would switch from this growth stage to this shrink shrinkage stage through a catastrophe and then the microtubule would start to depolymerize. And here the sort of instability manifests not as thread milling, but as this dynamic instability where. So, here generally for microtubules you could of course, polymerize them in vitro if you left solution of free tubulence and you waited long enough you would see that after sometime it would start to grow. But inside the cells there is the structure called the microtubule organizing center in the interior of the cell and things microtubules nucleate from there. So, the minus ends are sort of bound to this and they do not have much binding and binding. Most of the binding and binding happens at the plus end. So, things attach and fall off at the plus end for microtubules unlike for actin where it actually happens from both ends.