[SOUND] Hello. In this lecture, I'm gonna continue with my description of emergent properties. And the first part, I will deal with ultrasensitivity. In the second part, I'm gonna deal with robustness, and also deal a little bit with the role of scaffolds in sort of enabling emergent properties. So what is ultrasensitivity? The term was originally coined actually by in a newspaper by Goldbeter and Koshland, and I think their description of this term is a really, pretty good one. And since I couldn't do better, I just sort of cut and pasted what this said in their paper, and I shall just read it to you. And it says, we shall use the term ultrasensitivity to describe the output response that is more sensitive to change in stimulus than the hyperbolic Michaelis-Menten equation. And what this means is that when one studies enzyme activity and there is a stimulus, and the stimulus can produce sort of a standard response query should the Michaelis-Menten, when the system is hypersensitive the response would be far steeper. Pasted below is a couple of sentences from their abstract, and I think it's a very nice and concise description of ultrasensitivity. So I thought even for folks who didn't want to read the whole paper, looking at these words would give you a clear definition on what ultrasensitivity is. So why is this an emergent property? Actually, ultrasensitivity is among the most elemental of emergent properties, because it's a property that can be possessed by a system of just two enzymes acting on a single substrate. Neither enzyme by itself is ultrasentitive which means the reaction would be Michaelis-Menten, however, together the system can shield this ultrasensitive response. So let's go and look at the paper that the studies that go better, and caution conducted, and also the classic work of Jim Farrell and his colleagues, and we can better understand how ultrasensitivity works. So here, is a description of an ultrasensitive system that Goldbeter and Koshland used. Consider a substrate W, which could be a protein that's phosphorylated and becomes W star. The kinase E1 that phosphorylates it is involved in these forward reactions, and W star is dephosphorylated by these reverse reactions shown in the equation two. Together, one can then calculate, and the various forward and reverse rates are given here. Together, one can calculate values which are called K1 and K2. And when these values for K1 and K2, and they are defined out here, are close to 1 and follow Michaelis-Menten kinetics, the system behaves like a normal system. As K1 and K2 reach smaller values, the response becomes progressively more steeper, and this is the normal system shown here. The response becomes progressively more steeper, such that when K1 is equal to K2 is equal to 0.01, the system has a very steep response and it has a hill coefficient of, in this case, 13. Some of you may remember that I had introduced the Stirum hill coefficient. Way back in lecture two or three, to describe to you how allosteric regulation works. It's a versatile concept or number that can be use to describe the steepness of this response. Out here is the definitions of V1 and V2. And you can see that V1 and V2 represent the sort of a product of the rate constant of the total enzymes involved in these two steps. And you can plot, and what they have plotted here is the ratio of V1 to V2 as a function of the either active or inactive proteins. So this behavior arises from the relative kinetics of the two enzymes, E1 and E2. And it works, that work in opposite directions at a fixed substrate concentration and sort of works and it works at a level when W is much greater than E1 and E2, and so the system is called zero order ultrasensitivity. The zero order ultrasensitivity can work not only on a single cascade as I showed you before, but you can also work on a bicyclic cascade and this was described again by a good veteran in the original paper. And here, they have the standard one that they showed before W going to W star and W star can be now considered an active. If you consider it an active enzyme that converts the protein Z into Z star and the reverse reaction is catalyzed by this enzyme E3 here. So in their system they called, back then, they called the input, which we could call a receptor or a signal, they called it an effector, S. And they looked at various concentrations of S, and how the system would respond to this differing stimulus as S up here. So the effect of S on the first enzyme as you can see is relatively a standard Michaelis-Menten response and this is shown out here. But due to the coupling of these reactions, of E1 and E2, and E2 to E3 with W star being intermediate as the signal progresses down the system, the response is far more sort of switch like, and you can see that the ratio of W star to W total or Z's total is much sharper than the original response. So the hill coefficient for the original curve was 1, the Hill coefficient for the W star curve is 3.5, and the hill coefficient for the Z star curve is 7.5, thus you can see that these are very sharp responses. There are some kinetic restrictions for this kind of coupler systems to work. In reality, not all enzymes have to be in the zero-order regime, but at least some of the enzymes, such as for instance, maybe the first enzyme E1 and E2, need to be in the zero-order regime such that the total W plus W star is much greater than E1 or E2. So then, back in 1981 when Goldbeter and Koshland first proposed this, they did not have any real systems where they could study the theoretical concept of ultrasensitivity. In 1996, Huang and Ferrell published what is now a classic paper that they showed in the MAP-kinase pathway is ultrasensitive. So here, is the typical MAP-kinase that with three different kinases. MAP, kinase, kinase, kinase, MAP, kinase, kinase, and then MAP, kinase as the output, and one can ask the question, as signals flows from the top, so think of the standard pathway where RAF would be activated by RAS, so the signal would come from out here. And as it flows down this pathway, how does the response look like? And this is plotted here again, and you can see that the stimulus is ones a product on the linear scale up here, and on the log scale here. And let's just consider the log scale, because it's easier to see. The MAP, kinase, kinase kinase, where the stimulus just it shows the standard Michaelis-Menten sort of curve. However, when you go just one step below due to the coupling, the map kinase kinase orderly starts to show some positive cooperative like cooperated with the light phenomenon, with a Hill coefficient of 1.7. That's right at the margins of where you're starting to get a switch-like behavior. But when you get two steps down, and now look at MAP-kinase, you can see that the Hill coefficient is more in the four region, showing that there is a very sharp response of MAP-kinase to a sort of relatively standard stimulus at the level of the MAP-kinase cascade. So in the paper by Huang-Ferrel, they actually verified this theoretical prediction shown in the previous slide using the frog oocyte system. The frog oocyte extracts, these are frog egg extracts, contain Map kinase and MAP kinase, kinase, and to this they add in the activated MAP, kinase kinase, kinase. In the frog system it's called Mos, and this is a recombinant version of Mos for malE, malE-Mos. So this enzyme was added to the extract, and then MAP-kinase activity or MAP-kinase and MAPK activity was measured by immunoblotting, and the plot is shown here. As you can see that the MAP, kinase, kinase, as you can see that the MAP plot, because it's MAPKKK is just activated the MAP, kinase, kinase kinase and shows a relatively standard Michaelis-Menten kinetics. Well, the MAP-kinase activity shows a very clear positive cooperative dividing the Hill coefficient of 4.9 and switching-like behavior. This is the standard prod and the MAPK prod for activity is actually measured as shown down here, and you can see that this is very similar to the standard Michaelis-Menten prod down here. So by doing these experiments they were able to show that as predicted by the model there are signal travels down from MAP, kinase, kinase, kinase to MAP, kinase, kinase to MAP, kinase. The MAP-kinase activity shows switch-like response to the upstream signal. So it has ultrasensitive behavior. Many years later, in like 2008 and 9, Ozzy Lipshtat, a post doc in my laboratory, did further studies along the same line of reasoning to ask the question whether small GTPase systems would also show ultrasensitivity. So in addition to asking whether GTPase showed ultrasensitivity, he was interested in understanding whether one could get ultrasensitivity even if the system was in the first-order regime, and what that means in this case, is that, the levels of the GTPases are similar to the levels of the GEF or the GAP. Remember, in the previous case, when we had zero order ultrasensitivity, the level of the substrate was in far excess of that of the enzyme. And indeed, I'm only gonna show you one equation from his paper. Indeed, what he found was, that the level of activation of the small GTPase was also had ultrasensitive properties and they could be described by this equation shown here. Graphically, this is very nicely explained out here. So what as it shows here is a graph of the gap. So in this particular case the signal is one that degrades the gap for the system. And since the negative regulator is degraded, it allows for activation on the GTPase. And here, are four different stimulus strength. And they are plotted on a Michaelis-Menten curve of a of GAP degradation. And as this GAP is degraded, if one calculates the ratio of the activated to total small GTPase, one can see where each of the stimulus lands you in the GTPase activity curves. When this is plotted in the In the log format, you can see clearly that one gets like a very sharp response here in terms of signal strength with respect to GTPase activity. So this is a case where under first-order regimes, that a continuous signal can produce a sharp switch-like response or an ultrasensitive response for GTPase. As he and his colleagues conducted experiments to show that this behavior that he found by modeling computational models was observable in real life. And this shows the change in the GTPase activity at the small GTPase Rap which is activated by the receptor cannabinoid-1 receptor CBR1. CBR1 activates the G-protein to stimulate the degradation of Rap-GAP and this reduction of Rap-GAP results in activation of Rap. You can see from the experiments here that increasing the concentration of the ligand or the active receptor gives you a sharp stimulus with a Hill coefficient of five. And similarly, there is also a duration dependent switching of the Rap-GTP's activity, and there the Hill coefficient is actually 8.6 showing that in a time dependent manner, there is a sharp switching of the GTP's activity as Rap-GAP gets degreed. So why is ultrasensitivity important in cellular regulation? Phosphorylation and dephosphorylation and GTPase cycles. Phosphorylation, dephosphorylation, and the GTPase cycles are the two major modes of cellular regulation. So that, both of these systems has switching capability, allows the system to play a very broad regulatory row within the cell. One advantage of ultrasensitive systems is that ultrasensitivity can be found in pathways, sometimes linear pathways or the pathways, the relationship will be nonlinear. But nevertheless in these pathways and it does not require the presence of loops. As Ozzy showed in his paper, ultrasensitivity is versatile and can respond in a switch-like fashion to stimulus strength, stimulus duration and even the space dependent switching. So ultrasensitivity can provide switch-like behavior in a variety of conditions, and hence can be widely used to obtain regulatory control within sets. [SOUND] [BLANK AUDIO]
