 So, what I will do today is that I will give an introduction to this molecular motors. I will not do a lot of maths today I will keep that for next class, but I thought I will just introduce what motors are and in what contexts we want to study them ok. So, here is one of the most famous examples of a molecular motor. This is the kinesin motor which is walking on a microtubule. So, this orange thing over here is kinesin, this green track over here is the microtubule and this darker green sphere of which you can only see apart is the cargo that this motor is carrying. So, it is very nice in that. So, this is a protein basically, it walks along this microtubule track by using ATP to bind and unbind this microtubule binding domain. So, which are let us say its legs ok. So, it places its legs one after another and it walks and on its head it is attached again chemically to this cargo. In this case of vesicle it can attach to different types of cargo and it transports this cargo. Inside this vesicle you might have different proteins or whatever that needs to be transported from one end of the cell to another. So, it just carries this cargo along these tracks and it does so processively and repetitively many many times over the life cycle of the cell. So, it takes in what it does is that it takes in chemical energy in the form of ATP hydrolysis. So, these are active processes they require an input of energy. So, ATP binds it hydrolyzes forming ADP plus phosphate plus energy that energy is utilized into converted into this mechanical energy which results in this directed non-random motion. So, this is not like a random walk where this motor you know sort of does takes one step this way or the other another step the other way. These motors move along because these microtubules remember have a polarity it has a minus end and a plus end. So, there is a directionality to the railway track of this microtubules and then they move directly on this on the line railway track. So, this is one motor. There can be other types of motors for example, this RNA polymerase motor. So, again there is this nice video. So, here is my DNA. The DNA is wrapped around these histone proteins forming the nucleosome right. If you do not remember this you should go back and recall it it is also part of the quiz question. So, when this DNA needs to be transcribed you need to form the mRNA then this RNA polymerase will comes and binds to this DNA. It first opens up from the histones so that it can be read then this RNA polymerase comes and binds to this and then it moves along this DNA track while forming this mRNA by reading the sequence. And again this movement of this RNA polymerase is an energy driven process. It takes in chemical energy in the form of ATP it converts it to directed motion as it moves along the DNA backbone and it produces this RNA transcript. So, again this is an example of a motor. So, anything that takes in this chemical energy and converts into some sort of mechanical word is what I will call a biological motor and they can be of different types as we will see as we go along. But for this RNA polymerase which we have seen in the context of this DNA transcription that also fits our definition of the motor. So, for the first part what I will try to focus on are these translational motors families of translational motors. There can be other types although I will talk I will do not think I will talk about them today. Let me just say that rough or broadly you can say that I will categorize my motors into maybe three classes transcriptional motors like this kinesin or this RNA polymerase motor that we saw or these other motors which I will discuss kinesin dyneins, myosins whatever. So, these are motors that takes in chemical energy and it sort of uses that chemical energy to produce directed motion along different substrates in different contexts, but produce directed motion. Linear sort of motion along a track something like this. So, that is one sort of motor. Another sort of motor could be rotatory motors rotatory motors. And where have we seen a rotatory motor? The helical flagella for example, in the E. coli where the motor that rotates the helical flagellum that is an example of a rotatory motor. Again it takes in chemical energy, but it converts that not into linear motion, but into rotational motion. So, that is a different class of motors. Or you could think of stuff like polymerization motors for example, microtubules and actins themselves. They can take in energy, they polymerize and in the process of that polymerization they can do some work by exerting forces on different substrates. So, that is a different class of motor that is called polymerization motors. So, this would be actins, microtubules and so on. So, all of these are motors because broadly they fall under the class of active processes. So, these are systems, protein complexes that take in chemical energy in the form of ATP or GTP or something and converts into some sort of motion. So, for today what I will deal with is mostly these translational motors and in particular motors that walk on microtubules and on actin. So, here are three representative motors. So, this motor over here is what is called the is example of a myosin category of motors. So, myosins are motors that walk along actin filaments. So, myosins will walk only along actins, myosins these walk along actin filaments. If you see the structure there is the stock of the motor, then over here are these two head domains and over here there is something called the tail domain. The tail domain is the one that binds the cargo. So, the vesicle like the vesicle in the previous animation, the head domain is what binds the stock or the track along which the motor walks. Here in the middle is something that is it is a example for kinesin motor and kinesins as opposed to myosins they walk along microtubules, they walk along microtubule filaments and not only that they walk in a specific direction along microtubule filaments. The microtubule remember has a minus and a plus depending on whether alpha tubulin is exposed or beta tubulin is exposed it is a chemical polarity and then kinesins walk towards the plus end of microtubules always. Whenever you have a kinesin motor, they will walk towards the plus end of from the minus end towards the plus end. And again it is roughly similar, it has these head domains. So, the head domains are much smaller, the tail domains look different. So, structurally this is different from the myosin family, but functionally it is somewhat the structure is somewhat conserved in that you have this head domains which bind to the track, microtubule in this case, the tail domains which bind to the cargo. And finally, there is this other class which is dynines which is dynines these also walk along microtubule filaments. This also walk along microtubule filaments except they walk in the reverse direction. So, they walk from the plus end of microtubules towards the minus end as opposed to kinesins. The dynine structure is somewhat more complicated than the kinesins or the myosins and as a result its functionality also has some complications we will come to that later. But at the simplest level it is again the same, you have these head domains which will bind to the track, the microtubule in this case and the tail domains which will bind to the cargo. I call it examples of myosin kinesin and dynine because these are basically not a single motor, but these are a family of motors ok. So, for example, if I think of myosin here is the myosin super family of motors. So, these are all different proteins all different myosin like proteins occurring in different organisms or in even in the same organism in different cell types ok. So, there are myosin 1, myosin 2 and so on and even within one there are subclasses of myosin motors they might differ by amino acid residues, but they will all roughly do the same thing in that they will bind to an actin filament and they will walk along the actin filament. The actin the myosin have not written whether it is a plus walking motor or a minus walking motor because in myosins there are categories which walk towards the plus end of actin and categories which walk towards the minus end, but they are not different proteins as such unlike in the case of kinesins and dinins. So, even kinesin you would have a super family like this there are different types of kinesins of what is shown here is a particular kinesin kinesin 1. There can be other types of kinesins, but again and they will differ in the sort of cargos they can bind, they will differ in the organisms in which they are formed, but they will all bind to microtubules and they will all walk from the minus end to the plus end. Similarly, there will be different types of dinins, but again they will all bind the microtubules and walk from the plus end to the minus end. So, these are if you think about the diversity these are quite complicated objects, but as long as we are talking in terms of a modeling context I will often use kinesin as something that just you know I do not care about what particular cargo it binds and so on I will just consider it to be a motor that binds to microtubules and walks along the plus end. How do I say that these motors are different? One is of course, by looking at the structure and the minus end residue and so on. So, at a chemical level you can see that these this protein is different from this protein is different from that protein ok, but physically one can also show that these motors behave differently by using different experiments. For example, one common experiment that is used to characterize the properties of a motor or what I call these force velocity curves. So, you apply a sort of force. So, let us say this here is my kinesin let us say here is my microtubule on which I have this kinesin it is a very bad kinesin, but this kinesin motor binding here is my cargo. And what I can do is that I can it walks with some velocity some average velocity it will walk along the microtubule. What I could do is that I could pull back on this cargo with some force let us say the cargo is let me just draw it on the cargo. So, let us say I pull back on the cargo with some force generally these experiments are done using optical traps. So, you trap the cargo bead and you pull on it with some opposing force and you see how this velocity changes as a function of force. How does this velocity change as a function of the force that you apply? And if you look at it for different motors this curve will look different. So, these are all the force axes are all normalized by the force at the half maximal velocity because the forces that are produced by these different motors are very different, but I have just normalized it. So, that when f is equal to 0 whatever it is it is y axis is normalized with a maximum velocity. So, that all points on the y axis for these different motors all fall on one. So, this is data for three different motors one is this kinesin motor that we have been talking about. The second is the blue curve is this RNA polymerase motor that I showed and the third one is this phage packaging motor ok. The phage packaging motor is in viruses like bacteriophage you need to package your DNA inside this viral capsid and that again happens through a motor. So, that is the phage packaging motor. So, that is the one shown in the red curve. And of course, when force is very high all of these velocities will drop to 0. So, if you apply a counter you apply an opposing force eventually provided you apply a large enough force all of these motors will stop ok. And so, the velocity in each will drop to 0, but how it drops to 0 is very different for different classes of motors. So, kinesin so, for example, RNA polymerase has this very strong sigmoidal curve. So, for small forces it does not really affect the velocity that much then beyond a certain this critical force it sort of very quickly and very sharply drops to 0. Kinesin is somewhat of a more of a less steeper sigmoid whereas, this phage packaging motor it sort of drops linearly with force almost for a very long range. The more force you apply the more the slower the velocity and then it slowly drops to 0. If you were to do it for different motors you will see different sorts of curves that emerge and you can use this sort of force velocity curves to characterize. So, the internal working of all of these motors are different and what this force velocity curve shows you is sort of a macroscopic manifestation of the differences in this internal architecture of the internal machinery of this motor. So, it is a reflection of the fact that these different motors have different mechanisms ok. So, how do I how can I characterize motors for example, what are the different quantities that I can use. So, one is this thing that we have been talking about direction of motion right. So, for example, kinesin is plus and directed on microtubules whereas, dynines are minus and directed. I could talk about the speed of the motor. So, for the speed of course, depends on the depends on the force as we saw. So, these v is a function of f, but I could talk about the 0 force velocity right. So, in the absence of any opposing load how does this what is this velocity with which the motor moves. So, for kinesin for example, the step size is 8 nanometers and this 8 nanometer step size is nothing but the size of the underlying lattice basically. You remember this microtubule consists of this alpha beta dimers right and the size of this alpha beta dimers is 8 nanometers. What it means is that this kinesins bind hopped from one of these alpha beta tubulin subunits to the next one and therefore, the step size of these kinesin motors is 8 nanometers. The speed is some of the order of microns per second. So, some 6 microns per second for the case of kinesins. Again these are all sort of typical numbers in the sense that if you did different if you looked at different kinesin motors for example, you would maybe find some differences, but roughly of that order.