 Putting that, we will have the questions for 15 minutes. OK, thanks. Thanks, Ancona, for this nice introduction. I have to say it's a big pity I cannot be in India. Last time I visited Kerala, it was really wonderful. And it was an amazing experience. So it's a pity I cannot come again and meet with friends and students and colleagues. So, yeah, before I start, I would like to also thank the organizers for putting this amazing program together and for inviting me over in Zoom. So today I'm going to talk about the photochemistry of retinal proteins. And the outline of my talk is the following. So in introduction, I will talk about different photoreceptor proteins. And then I will briefly mention rhodopsins. And then I have two aspects of the photochemistry. First, I will talk about spectral tuning. And the models involved there. And then I will talk about the photoism mutation. OK, so let's just start with a general introduction. So what are photoreceptor proteins? Well, typically a photoreceptor protein is composed of an apoprotein. It means composed just of regular amino acids. And then it has some cofactor, or we call it a chromophore, because it interacts with light in the visible. And so what happens at chromophore makes this protein sensitive to light. And when you shine light, this chromophore absorbs light in the visible range. And then it undergoes some change. It can be a photoismization or proton transfer or some other rearrangement. And then in the second step, after the absorption and after the conversion, it transduces the light energies from molecular energy to the protein. And as a consequence, the protein changes its shape. So this happens at the, this is from the biological level. But if you look at it from the technological perspective, these proteins are basically energy converters, because they take a photon and then they produce molecular energy or even, as you will see later, even electrical energy. So when they convert the energy, the output from the protein is a signal. And so that's why these photoreceptor proteins have been utilized in many, in various applications. So for example, if the photoreceptor protein happens to be also fluorescent, it can be nicely used in super resolution microscopy. You see on the left side, this is a regular microscopy. And on the right side, this is the same cell visualized using super resolution microscopy. Here, photoreceptor proteins are used to be quickly switched on and off. Mainly fluorescence. And by switching on and off the fluorescence, they can allow to make a sharp contrast and increase the resolution. The other field where photoreceptor proteins have been used is optogenetics. Optogenetics combines the two is a combination of opto, meaning light control and genetics. And here, the genes of a photoreceptor proteins are inserted in the living organism. And these genes usually encode a retinal protein. But it can be also other proteins. And then they make cells where they are inserted, light sensitive. So here you see this famous experiment of a living mouse, which has in the neural cells a light sensitive retinal protein. And then there is this optical fiber cable, which guides the light through the skull inside the head. And then makes it controllable by light. OK, so what are the common photoreceptor proteins? So here is an overview of the major families in plants and in fungi, taking from the review from Heinzen. So we have, for example, tryptophan, which is present in a protein called UVR8. We have Flavin, which is found in the light oxygen voltage-sensing protein called Lofdomein. We have another family of proteins called cryptochromes. They also have Flavin chromophore. And then we have my favorite, my family, which is Rodopsin, so also called retinal proteins, because all of them have the retinal chromophore. And then we have phytopromes, which are predominantly found in plants. The chromophore in this set of proteins is linear tetrapyrus. So there are four rings, and they are called pyros. They are also propionates, and they are metabolized from chlorophyll or from hems. So you also have an indication here in this graph on the top, the range of the absorption from different photoreceptor proteins. So all of them have the same, I mean, in each respective family, they have the same chromophore, but the protein apparently is tuning. It allows to cover a wide range of light. And while this figure was from 2011, 10 years ago, the Rodopsins were found to be covering a range from 475 to 570 nanometers. But in the recent years, they have been new discoveries. And the range of retinal proteins has been extended to 690 nanometers. So and I'm going to explain to you how this tuning process takes place. But first I want to give a short introduction to Rodopsin. One of the most studied members of this family is the animal Rodopsin, or the visual Rodopsin, is found in our eye. So we have in the backside of our eye, we have a layer called retina. And on this layer, we have visual cells. They're called rod cells or cone cells. Here you see a representation of the rod cell. It has this elongated shape. It looks like an antenna. And then in the outer compartment of this rod cell, you have a large number of so-called disks. And then inside the membrane of each disk, you'll find the transmembrane protein, Rodopsin. This is the visual Rodopsin. And inside the membrane, we have seven helices. And these seven helices, they form a barrel type structure. And in the middle of this barrel, you have the chromophore, which is the, in case of this visual Rodopsin, it's 11 cis retinal. It has six conjugated double bonds. One, two, three, four, five, six. And only the one from the carbon 11, carbon 12 has the cis configuration. OK, so all the Rodopsins have in common that they have this retinal chromophore. It's not always cis. Sometimes it's in trans, depending on the type of Rodopsin. They also have in common this seven transmembrane protein structure, which sits inside the membrane. So now the first part that I want to address in this tutorial is how can we rationalize the tuning of the absorption maximum, which is both also spectral tuning or in some researchers call it color tuning in retinal proteins. So I think this goes back to the work of Salem and Brugman in 1975, who have investigated the isomerization of retinal. And they notice that inside, in the excited state, there was some rearrangement of the charges in retinal. And this was then later substantiated in 1993 years later by Arya Warshall, who said that actually there is a charge transfer. If you look here on the top graph, the positive charge sits here on one end of the retinal, which is called the shift base. And then upon excitation, this charge moves to the other end of the retinal, which is located at the better end. So this charge transfer inside retinal chromophore was established in the end of the 70s. And then Barry Honig, together with the experimental group of Kijinakanishi, they came up with the external point charge model for the spectral tuning in the redopsis. And I mean, interesting, it's an interesting fact that actually Barry Honig, when he did this research, he was also the Hebrew University in Jerusalem like my current affiliation. So what is this point charge model actually predict and how does it work? So as I mentioned, in the ground state, this is the structure of the old trans retinal. The positive charge is located on the shift base nitrogen. And then upon excitation in S1 in the excited state, this positive charge moves to the better end honoring. So there is this charge transfer. Now, if you look at the energies associated with this state, so the ground state energy is here, the excited state energy is here, and the difference between them is determining the absorption wave. So now what happens in the protein environment? In the protein environment, you can have neutral amino acids. You can have polar amino acids. You can also have charged amino acids. So if you place an amino acid, which is charged next to the shift base, what's going to happen is that here in the ground state where the positive charge is closed, we are going to have a large stabilization, because here's the positive and here's the counter and there's a negative charge. Now, in the excited state, the charge moves further away. So the excited state will be stabilized less than the ground state. And therefore, if you look here in the scheme, the excited state is stabilized less and the ground state is stabilized more. So it means that the energy gap between the ground and excited state is going to increase. And now you can also imagine the opposite scenario. If you're going to put a negative charge here close to the better known rate, then the excited state is going to be stabilized more than the ground state. So then we have opposite effects. So the energy gap is going to, instead of increasing, is going to decrease. So now, basically, biologists have this kind of, thanks to this point charge model, they have a handle of how to control the absorption maximum in the residual proteins. So they can simply introduce a mutation in the protein. And this mutation can carry a charge or it can be without a charge. And this can influence the absorption spectrum, the maximum of the absorption spectrum. Now, you can also ask, is there actually experimental evidence for this? Well, in a few years ago, the group of Lars Andersen from Denmark and Joni Topper, who is also in Israel, they have studied retinal isolated in gas phase. So it's retinal completely without the protein environment. And if you look here in the scheme, they studied this retinal analog. So here we have the large portion of the license side chain connected to the shift phase. This is called 1 plus. Then they replace it with two method groups called 2 plus. And then they added different counterimes. So here's, I think, this D is called betaine. And here is another sweet ionic counterime. And when you look at the experimental results, there is a spectra here. And then we also contributed with simulations. These are the sticks. You see clearly that if you go from the isolated compound in blue, when you introduce the counterime, you move in the spectrum towards shorter wave. So when you introduce this betaine, which has a smaller charge separation, you shift it by 0.2 electron volts to the blue. And if you introduce the bigger counterime, then you shift it by 0.4. OK, so now what can we do today? Well, today we have a high-level QMM simulation. So we can not only produce these qualitative pictures, where we have a point charge moving from one end to another. We can map out the entire protein. We can map out the whole hydrostatic potential from the protein and have an accurate map of how to change or how to tune the wavelengths. So here you see the old trans-retinal. Now what we can do is we can put a van der Waals sphere around each atom. And then we have this surface. And on this surface, we can now project the charges from the protein environment. So here you see an example of the proteorhodopsin. You see here in the cartoon representation, the helices. And here you see key residues. There are two counterimes. And then there is this one important residue, which is responsible for the color switch in proteorhodopsin, which I'm going to cover in the second part of my talk. But what I wanted to show you is that now we can take all the charges from the protein and project it on this van der Waals sphere. And what we have now is we can see exactly how the protein environment is interacting with the retinal form. So here you see a very strong red color. This indicates the negative interaction coming from the two counterimes, which are negative recharge. And here on the other end, on the top part of the better non-ring, you see almost a blue color. This indicates that there is some positive amino acid or neutral amino acid close by in the vicinity. OK, so now we can use these maps from the protein electrostatics and combine it with knowledge about the charge distribution in retinal and get a very accurate prediction of the absorption maximum. And this is going to be the subject of my research talk. So I'm going to show you how we started different mutants of proteorhodopsin. And as I show you here in this preview, we will introduce a mutation to different residues. And they will change the electrostatic potential on the retinal. OK, so now this was the first part. This was the tutorial about the spectral tuning in retinal proteins. Now I'm going to talk about the second part, which is about the photoisomerization. So once retinal absorbs a photon, it undergoes a conformational change in the visual retopsin where you start with 11 states. You go to actually all trans. So this bond is going from cis to trans. And now if you want to study the most accurate way to do it is to run a molecular dynamic simulation. So why do we choose a molecular dynamic simulation? Because it allows you to predict time-dependent properties. For example, we want to see the mechanism of this photoisomerization. In classical dynamics, it allows you to equilibrate the structure of geometry. And it actually is the most realistic type of simulation. So what are the requirements to run an MD? So we have three quantities that we need. We need the coordinates. This is basically the structure of the protein or the retinal. Then for each atom, we need velocities. And we need to calculate. We need to be able to calculate the forces. The forces are the negative of the gradient. So if you have the energy, by deriving the energy, we can get the gradient. Now, how does it work? Well, we have a potential energy surface. This is a scheme. And we have our coordinates, which define this point here on the surface. And we have a time 0. This is the starting of our simulation. So we want to move forward from one time point to the next. And the way how we do it is it's first, for a given set of coordinates at time 0, we calculate the potential energy. And in this case, we're using a quantum chemical method. So we have a wave function. And we calculate the expectation value of this wave function. And then we get the potential energy. And then we make a derivative with respect to all coordinates. I'm not sure what is wrong here. It's supposed to be a nabla operator. So it's derivative in x, y, and z. And the negative of the derivative is the force. And now, according to Newton's law, from the force, we can extract, because the force is nothing else but the mass times the acceleration, we can extract the acceleration. And then the acceleration, we multiply it with the time step, delta t. This is the time difference between two consecutive steps. And we get the change in the velocity. OK. And then once we get the new velocities, we can propagate from 0 to 0.1 and get the next point and repeat the whole cycle again. So what I wanted to show on this slide is actually that molecular dynamics is not only associated with a classical force field. It can use, in principle, any energy and then the related gradients in order to propagate a chemical system or a molecule in time. Now, there are different time integration schemes. And one of the most popular families, so-called the Verlet family of algorithm. So because I see that now I'm running out of time, so I'm not going to go into detail. I'm just going to mention briefly. So there are three forms. This is the original form. Then there is the leapfrog form. And both of them have the problem that there is no velocity. So here you see coordinates are velocities and accelerations. In the original valet, there are no velocities. In the leapfrog, the velocities are not available at the same time as the acceleration and the coordinates. They are only available for the half step. Now, in the velocity extension of the valet algorithm, the velocities, the coordinates and the acceleration are obtained for the same time point. So that helps you to evaluate the potential energy and kinetic energy for the same time. And here I prepared the slide to show how it works. So it works in two steps. Velocity valet, you need the coordinates. You go to the next step. You get the coordinates for the next step by using the coordinates. Velocities and acceleration. And then you also calculate the half step velocities. And then using in the second step, so between the first and the second, you evaluate the gradients one more time. And then in the second step, you actually take the half step velocities in the new acceleration to get the full step velocities. Okay, so what's the advantage of having molecular dynamics simulation? So here's work by a Bill Hayes group. They have this study where they start from a transition state. And in this example, there is this methane peroxide where which interacts with the fluorine ion and they have used two different methods to continue the simulation from the transition state. So the black line follows the molecular dynamics trajectory versus the red line, which follows the minimum energy pass optimization. So you see that actually following the optimization where you don't have kinetic energy, you end up having a D alcohol in complex with the fluoride. But if you run a molecular dynamics from the same transition state, you will end up in a dissociation in a three-body dissociation. So the molecule falls apart in three pieces. And for both simulations, they use exactly the same electronic structure method. Just the type of the simulation was different. So it tells you that actually with molecular dynamics, you can get very different answers. Now this was a ground state simulation, but I mentioned that in retinal proteins, we are studying the photochemistry. So in photochemistry, actually it becomes much more complicated and that's why molecular dynamics is important. So instead of having a transition state which connects A, the reactant to B, the product, okay, and which is a stationary point and is characterized by a transition vector which leads to only one product. In photochemistry, we are facing so-called conical intersection. Now conical intersection in contrast to transition state is not a stationary point, it's a singularity because the derivative here is not determined. And instead of one transition vector, we have two vectors which form the so-called branching plane. So they're shown here as X1 and X2. And they actually can also go back to the reactant or move forward to the product. So it allows to reach one or more products. Okay, I think I'm going to skip this slide. So how do we describe this conical intersection? So the electronic structure method in order to, the most basic way to describe such a conical intersection is the use of the complete active space self-consistent field method. How does this method work? So first we have our chemical system. Let's say we have here a six orbitals. Okay, one, two, three, four, five, six. This is the energy level. And then the lowest three are W-operates. So in the CASA CF method, you describe the wave function as a linear combination from different configurations. And each configuration is weighted by coefficients. So how do we generate these configurations? Well, we choose three- Igor, you have five more minutes for you to- Okay, thanks. Thanks. We are choosing three different orbital spaces. One is the inactive space. And here is shown in green. The orbitals are always W-occupied. In a second, the great so-called active space, we allow all possible configurations. So we have two orbitals here and we have two electrons. So we allow one electron. Okay, we allow, for example, a transition from this electron to this orbital, or we can promote both electrons to this orbital. So here in the active space, we are generating all these configurations. Okay, so the active space is defined by the number of orbitals and the number of electrons. In this case, the active space is two electrons and two orbitals. Okay, so when we look at the retinal protein, okay, this is the retinal protein. So how would you select an active space? Is there maybe someone in the audience who has an idea what would be the active space for the retinal? So the active space, in this case, if you want to study the excitations in retinal, then we need to include the pi-conjugated system. And I mentioned that it has six double bonds. So the six double bonds are formed from in total 12 p-orbitals. They form six pi and six pi star. So in total we have six, 12 orbitals and 12 electrons. This will be the active space. Here, these are the bonding pi orbitals. One, two, three, four, five, six. And these are the anti-bonding. One, two, three, four, five, six. So in all, in total 12. So this CASACF method is actually quite expensive because the number of the possible configuration is increasing very rapidly with the size of the active space. The more the more electrons and the more orbitals you have, the larger is the number of the permutation that you can achieve inside the active space. However, it's really important to describe this conical dissection correctly. Here's another example why we need, in particular CASACF and why we need to do excited state molecular dynamics. So here is a study of ethylene. And this was done by the group of Todd Martinez. So they showed that actually transitions from the excited to the ground state take place at energy gaps, which are larger than zero. So it doesn't necessarily go through the conical dissection. Already in the vicinity it can make a transition. And then on the right side, you also see that this transition occurs up several electron volts above the optimized minimum energy conical section. So it means that the dynamics using kinetic energy leads to different paths compared to optimization. Okay, I think that's about it. So I just listed few references for the CASACF method. And if I just have like one minute, I want to mention that a most common method to study excited state is time dependent density functional theory. And it works very well for excitation energy. And it's a very popular method. However, if you're talking about this photoisomerization and other photo processes, it has a severe shortcoming. It doesn't correctly describe conical dissection. So if you see here in the comparison to a, okay, this is a slightly more advanced improved CASACF version where perturbation is added. Instead of having a conical dissection in case of this multi-configuration message, TDDFT does not describe the two branching pin vectors. It describes the degeneracy only in one degree of freedom. So it fails to describe the dimensionality of the conical dissection. And therefore it's not recommended to use it to study photo processes which goes through a conical dissection. Okay, I think with this I'm finished. I finished the tutorial part. And if there are any questions, I will be happy to answer them. Yes, thank you for a very nice tutorial. And if people have questions, either raise your hands or type them in the chat and unmute you so that we can ask your questions. So while we wait for people to ask questions, Igor, maybe I can start out with a few questions that I had. One is do we, oh, there's already one. So we'll just take it from the audience first. So can somebody help unmute Fabio, which you need to ask a question? Yeah, I mean, I can read the question. Okay, I can read three. Why is the positive charge localized rather than delocalized in the chromophore? Okay, yeah, that's a good question. So I mean, it's not, so the positive charge is not like, I mean, okay, so it's not like, it's not, they're not too extreme. Okay, localized and delocalized. It is, you're right, it is slightly delocalized, but the major part of the charge is on the more electronegative, on the more electronegative nitrogen, just simply because it's more electronegative than carbons. But you're right, because you can nicely draw resonance formulas and you can see that you can rearrange the conjugated double bonds and the positive charge will be also partially distributed on the poly-inchain. Right, okay, so this was one question and I had one question, we did it to the first part of your talk before where you were showing the spectral tuning of retinal in the S0 and S1 state. In the S0 state, you had the protonated, I mean, right, the shifts, I mean, kind of shift-based, yeah, the shift-based, but so wouldn't this user proton, I mean, is this proton also lost from the S1 state? It's not lost, so yeah, that's a very good question. So in the early days, like in the, once after retinal was discovered and the first spectroscopic study started, there was a dispute whether the primary event in the redoxin is photoisomerization or photoactivated proton transfer or excited state proton transfer. And it turns out there's photoisomerization because the process is just much faster than the proton, than excited state proton transfer. However, they are like, there is the photoisomerization is triggering like a cascade of processes in the ground state. And then along this cascade in the so-called M intermediate, the retinal indeed loses the proton. So it happens later in the ground state, but it's not, it doesn't happen in the excited state. Okay, okay, so there is another question by Priyanka Pushparajan. I'm not sure if she's able to unmute herself, but I can read the question for you. Yeah. Priyanka, okay, yeah. If not TDDFT, which method best describes conical intersections, does TDDFT fail only in the case of retinal? Okay, yeah, this is a good question. I have to say that also in my department here, we have also Hardy Gross, who is the, basically the series who developed this formalism of TDDFT. And he always tells me TDDFT in principle is exact. So I have to make, I forgot to make another statement that actually the failures that I showed is for linear response TDDFT. So there are other ways of formula TDDFT more accurate, which include double excitation. They can indeed treat conical intersections, but the most common one, like the ones that you have in the most common packages like implemented like Gaussian or Orca or Turbomol, they have linear response TDDFT and that fails for all conical intersections. So if you want to describe conical intersection, and then I recommend to use multi-reference methods such as CASSACF or CASPD2 or there are other methods like NAFPD2. So there are multi-reference methods and they can treat these conical sections correctly. And so TDDFT or I should say linear response TDDFT fails in all cases, not only greater than that. Okay, there's another question by Fabio. How many A-residues, amino acid residues are included in the Q&A part? Yeah, okay. This is also a very good technical question. So it depends, I mean, it depends on the problem. So if you're talking now specifically about, if you're asking specifically about retinal proteins. So we are like in the most recent study that we did on channel reduction, we included retinal and then, ah, the amino acids are two counterins and then asparagene and I think two water molecules. So in total, three amino acids are included. But this is for calculation of the excitation. If you do dynamics, then we usually include only the retinal because the calculations are too expensive. Okay, great. I don't see any more questions in this. Okay, hope that answered your question, Fabio. May I ask a question? Sure, please go ahead, Mahesh. Igor, I have a question. When you have this point charge model, let us say buried inside a protein pocket versus the point charge model when treated in polar solvents, how do we go about selecting the method? Would that be the same or like, you know, would that be different? So the question is how do we select the method for treating this? For using it in protein or in a polar solvent? Yeah, yeah. Yeah, so, okay, so routinely I would say like, nowadays it's almost routine to use to use a classical force field with static charges for the protein and the same can be also used for solvent. And then the MM and the QM part interacts through so-called electrostatic embedding. But if you have like a highly polar solvent, which I mean, in principle, you also have highly polar residues. So there is a more recent development of using polarizable force fields. Or if you can afford it, as Fabio said, you can include more residues in the surrounding in the QM region. Then you can use polarizable embedding or extend the QM region to take an account of this. I'll take a look at that method you were talking about. Thanks, Evo. Okay, great. Are there any more questions related to the first part of the talk? Yeah, hello. Can I have one more? Hi, Fabio. Yeah, sure, you can. You can take one last question. Yeah, thank you. Very interesting, Igor, about your explanation. What about the preparation of the system? I mean, you start from a crystal structure, I think, and then I guess you have to probably adjust and check the hydrogens and then some residues are not complete. So I think that's also quite a lot of work to prepare the system. Can you say something about it? Yes, precisely. Yeah, this is indeed a very challenging part because most of the times the crystal structures are not complete. And this is due to maybe flexible side chains like outside of the membrane. There are loops which move freely. And so sometimes we have to use homology model to complete missing residues. And then even though if you have a complete structure, you're right that we need to protonate because the crystal structure usually, unless it's super resolution crystal structure, below one axon usually it doesn't have protons. So we need to protonate all the residues. And then we need to take special care of tetratable residues. So we need, for example, glutamic acids or aspartic acids. We need to know in the protonate form or the deprotonate because they carry a charge. And the same also for histidine. So we need to take some time to carefully prepare the structure. And then one goes through the classical protocol of heating up the protein. If necessary, embed it in the protein and then equilibrate it and check that the RMSD is not changing. And then eventually what we are doing now is once we have the full classical system, so using classical force to equilibrate it, we usually go then from the classical simulation to QMM. And we do a sampling using QMM in the ground. And then from there we start the excited state calculation and also the dynamics. OK, thank you very much. For the answer to your question. And so with that, Igor, we can move now on to your research talk, which is a little bit before 30 minutes. OK. I'm going to switch the slides just to give me a moment. Almost there. OK, here we go. So now I'm going to talk about our recent studies on a specific type of retinal protein, which is called proteadobsin. So proteadobsin was discovered in the gamma proteobacteria in 2000 in the Monterey Bay in California. Now, proteadobsin turns out is the most abundant microbial redoxins, microbial redoxins. And because it's found in the ocean and the ocean powers most of the earth, the proteadobsin is also responsible for 50% of the photosynthesis on the surface of the ocean. This was quite a surprising discovery because people have believed that chlorophyll is making most of the photosynthesis. So what is the function of the proteadobsin? It acts as a light driven protoprop inside the cell. So basically it takes the protons from inside the cell and pumps them outside. Now, the interesting thing is that this proteobacteria, which carry the protein, are distributed in the ocean. So they are found in different depths. And in order to account for these depths in the ocean, proteadobsin is undergone some adaptation to the light condition. So here you see on the right side the light penetration through water. And you see that on the surface, the whole spectrum is available. But if you go deeper, then you see that the red part, the UV part is eliminated. And 200 meters, only the blue part can effectively penetrate. So proteadobsin is undergone some adaptation. And there are two variants or two subfamilies. There's one subfamilie which absorbs blue light at 490 nanometers. And the other one absorbs green light at 525 nanometers. So and the major difference between them is the mutation of the residue in position 105. So in the blue proteadobsin, this residue is a glutamine. While in the green absorbing proteadobsin, this residue is a lucid. So glutamine is polar and lucidness neutral. So when you just take and mutate this amino acid from lucid to glutamine, you can recover most of the shift. You can go from 500 to 520. You get 20 of the certain nanometer shift. Now, in order to study it, we have used QMM. But in addition, we have used sampling. And I want to explain to you why we use sampling. So typically, if you study a molecular system using quantum chemistry and the system is isolated, you can easily locate a minimum on the potential image surface. You locate a minimum, and then you do a vertical excitation. So you don't change the geometry, and you calculate the excited state energy. And this is called the vertical excitation approximation. But in the protein, like membrane protein, proteadobsin, you have a very highly complex potential energy. There are many minima. And there is not one minima that is the lowest. There are several minima which are quite low. So in order to make sure that we cover all of them, because different minima might have different excitation energies, we are doing sampling. So basically, we are making a QMM molecular dynamics, like I just said, to Fabio. So we have this one nanosecond QMM using a semi-empirical method in order to be able to sample for a long time. Then we take 100 snapshots, and we use both ADC2 and campus relief. And then we describe both electrostatic embedding and polarizable embedding. This was the question from Mahesh. So we take static charges, and we take also an improved model where we have polarizable charges. And this was done in collaboration with Magnus, who developed this polarizable embedding. So now here are the results. We have started the wild type. OK, so you see, first of all, you see relative changes. So 0 is the wild type. And then you see differences between the wild type and the protonated counter ion, D97 is here. Then you see the mutant of the Q105, which is the color switch residue here. And then you see double mutants, or basically a Q10, let's say a variant. Q105 was mutated to L, and the counter ion was protonated. And then here we mutated a 97 counter ion D97 to aspargin. And we mutated the Glutamine 105 to Lucine. And this is a different type of blue proteadobs. So these are the different types. And this is the relative change with respect to the wild type of this blue proteadobs. So you see experimentally, there is a strong shift. And this value is given in electron volts. So the absorption maximum is getting smaller in electron volts, so it means it's a red shift. And then if you mutate this counter ion to a neutral residue, it has the same effect. If you mutate only Glutamine, then the red shift is smaller. And then again, double mutants make the shift even bigger. And now you see the simulations. In red you see TDDFT with electrostatic embedding and polarizable embedding. You see also ADC2, which is the algebraic diagrammatic construction to second order. So it's some wave function method combined with linear response theory. And here we use both electrostatic and polarizable embedding. And you see that although we don't match exactly the spectroscopy, the trend is reproduced with all the methods. So we have the same behavior that for the protonated counter ion and the mutated neutral residue, we have the large shift for the Q105L, this color switch residue. We have a smaller shift, but it's the correct shift in agreement with experiment. And then again, we increase the shift. OK, so what we have done now, we just established a simulation protocol and we said that indeed we can qualitatively get the same shifts so we get the trends correctly with both methods. And now the next step is to understand and to check what happens, what is really the origin of this. What is really the origin of this shift? So what we have done, we have done something that cannot be done in experiment. We have repeated the simulation but without the protein. So on the right side, you see the same spectroscopy but without the protein. And the trend looks actually the same. It looks very similar. However, if you look carefully, there is a different scale. Now the spectral shifts are much, much smaller. Here we're going from 0 to almost half an electron volt, this is the range scale. Here the scale, if I put it on the same scale like on the left, the shift is almost gone. So it means that the geometry alone, the geometry distortion alone is not responsible for the shift because there was a study from a group in Frankfurt in Germany. And they have said that when they do an MR study, they measure a significant stretch in the retinal carbon-14, carbon-15 bond. And they say that this stretch in the bond is responsible for the shift. But we showed, by calculating the retinal in the gas phase, that actually the shift without the protein is very, very small and it's actually negligible. So it's not the single bond which makes the shift. So what we did instead, we checked. So what we did, in addition, we carefully checked the bond order alternation. So it's the difference between the average double bonds and the average single bonds. This is the value for the six variants that I showed you before. This is the wild type. This is the protonated counter ion, the mutated counter ion, the color switch mutation, and so on. And we also looked just at this bond. And we looked at its value. And indeed, the value is really changing quite a lot. And then what we did, we correlated. We made a correlation between the snapshots, between the excitation energy, and the geometry. So if you remember, each absorption maximum that we got was based on 100 snapshots. So for each of these 100 snapshots, we compared the correlation between the absorption maximum and the parameters. So you see here, bond order alternation compared to the absorption maximum, or the bond lengths compared to absorption maximum. And indeed, we found a very good, very high correlation coefficient. So it was very high. It was high with the proton environment. And without the proton environment, it gets slightly lower. OK, so oh, OK. So I think there is a mix. I'm missing one slide. Sorry, just a second. I think there is a mix up. I think I moved it by chance to the end. Oh, yeah, this is the slide. Sorry about it. OK. So we showed that there is a high correlation. But if you remove the protein, then the shift becomes very small. So now what we have done is we did this map of the electrostatic potential of the protein. We mapped it on the whole, on the van der Waals spheres of the retinal. And we did it for the Q105L mutant and for the Q105. And if you look at this map, I mean, it's very difficult to find a difference. They are almost the same. And the reason for this is because the counter-line, according to the point charge model that I presented in the tutorial, has the strongest effect. If you see, this is the scale for the electrostatic interaction. There is a highly red area here in both cases. So what we did next is we put all the charges to 0 except for this residue in position 105. Because you see that here it is some kind of greenish. Here it is slightly bluish. So if you put all the charges to 0 instead of 105, we'll see the pure effect of this residue in position 105. And indeed, the polar glutamine in position 105 make has a strong positive interaction with the positive electrostatic effect on the retina. So what we say, what we have found is that it's not the double bond, sorry, not the single bond that is affecting the spectrum, but it's more the electrostatic effect from this polar residue. So now the question is, and why is the shift, so why is it a redshift exactly in this position? So here, in order to explain why the shift occurs exactly for the interaction with the position 105 in this location of retina, well, we have calculated the difference between the excited state and the ground state electron density. This is reporting the charge transfer. So we see here blue, and we see here red. This is the electron density, so it's opposite to the positive charge that I showed you before. So it's a slightly different picture. So positive charge was sitting here on the shift base and moving to the better known rate. It means there is more electron density here now. So blue is a positive difference. So there is an additional density now here upon excitation, and red is less electron density. So because this area here is rich in electrons in the excited state, and now there is this positive interaction coming from glucin, this explains the qualitative shift from the glucin, sorry, from the glutamine to glucin. OK, so this was the first part addressing the spectral tuning in proteardopsin, but now I also mentioned that we studied the photoisomerization. So here I'm going to show you how we studied the photoisomerization of proteardopsin. So this was done not for the blue proteardopsin, but we used the green proteardopsin. So here we also used the sampling to get initial geometries and velocities, and here we used CASACF average for the ground state in the excited state with active space of 12 electrons and 12 orbitals and a double-zeta basis set. We used for the protein the ember force field, and then we launched 100 trajectories in the excited state. So this is what we found from 100 trajectories, because we need to make sure that we are not running only one trajectory, we are running more, because we want to get some statistics. So from the 100 trajectories we found the following, that within the simulation time of one picosecond, 29 of them remained in the excited state, while the majority, 71, have relaxed to the ground state as through a conical intersection. And when they relaxed 42, basically the majority have successfully summarized to 13 states, while 29 have returned back to the old trans. So now if you look, the calculated yield of the successfulization relation is 59%. The experimental one was 66%. So it's kind of, it's in the same, let's say qualitatively it's very similar. Okay, so then we decided to analyze what is the reason why some of them isomerized and some of them return. And here I'm showing you the movie. So you see the protein environment represented by a force field. And here you see the retinal chromophore. And this is the double bond which is going to rotate. This is carbon-13, carbon-14. And here you will see that it rotates. Now on the bottom you see the energy evolution. This is the simulation time from zero to 400 femtoseconds. This is the ground state. This is the excited state. And this green line is the moment where there is transition from the excited state to the ground state. So we have a transition through a conical intersection or in the vicinity of the conical section. Now I'm going to play the movie and you see here the evolution in the energy. And you see also here the geometry. So when we come closer to the transition, you see now the hydrogen starts to move and now we have a rotation. So after something like 400 femtoseconds, we have now formed the cis bond. Before we started from trans, now from the molecular dynamics we formed. You see again, this is the trans. And now you'll see that we formed in this particular trajectory, we formed a successful product, which is certain cis. So the question is what makes retinal isomerase successfully and what makes it go back? But before I show you this mechanism and before I explain it, we have done another check. We looked at the change in the excited state population. Okay, so this is our, the blue one is the average excited state population and we use refitted it. Refitted this decay in the population and it was found to be calculated was 279 femtoseconds, experimented it was 350 seconds. So not only the yield, but also the excited state lifetime was found to be in good agreement with experiment. So now what we have done, we have grouped all the 40 trajectories, which were successfully isomerized and those 30 which did not isomerize. And then we looked at the evolution of the bonds. So you see the color coded bonds, purple double bond, green single bond, orange double bond, pink single bond, brown double bond. And you see indeed these double bonds are quite, sorry, these double bonds are quite short and the single bonds are long, but once we excite, then the bonds are inverted. And this is due to the charge transfer, the charge going from the shift phase to the better in on ring. It makes the double bonds rearrange. So now the double bonds are becoming long like single bonds and the single bonds are short like double bonds. And this continues until we have the transition to the ground state. And then it again, the double bond becomes short and the single bond becomes long. And the same happened also if you look at the behavior of the non isomerized. So so far we couldn't find the difference. Now in those trajectories which remained for the entire simulation in the excited state, we saw only one change so that the bonds became, double bonds became longer, single bonds become shorter, but it didn't revert because there was no, no transition to the ground state. So then we looked further and we looked at the hydrogen out of plane mode. So the hydrogen out of plane mode is defined usually by two hydrogen atoms. Okay, and if they're in plane, then it's the value is either 180 or zero. But if they move out of plane, then the value is significantly deviating from zero or 180. So now in this plot, these are the trajectories which I summarized and this one which I did not summarize. You see that the hydro angle from purple, blue and green, the hydros. And you see that the nitrogen 15 and 1112, they did not change, but the entire change comes from the 1340 which goes from trans to cis. In the other case, we saw that actually there is some large fluctuation but there is no significant change. If you consider that the range here is like something like 20, 30 degrees, this is just regular fluctuation. And, but of course this is a non-isomerized subset of the trajectories. So that's why we don't expect to see large changes. Now, when we have no hope, then the fluctuation becomes even smaller. The fluctuation around the hydro angle is now in the range of five or 10 degrees. So we still didn't find, we still didn't find the reason for this successful or unsuccessful as a relation. So then we decided to look at the point charge, sorry, on the molecular charge. As I said in the tutorial, the positive charge in the ground state is localized on the shift base. Upon excitation, there is the charge transfer and now the positive charge is located on the better end on it. So what we did, we divided, because this bond is the one which is isomerizing, we divided the original in two fragments. The fragments starting from carbon-14 and the other one including all the atoms until carbon-13. And then we summed up all the charges for the better end on part and for the shift base part. And then we plotted them for the isomerized subset and for the non-isomerized. So here you see the plot of the one part charge and here's the other one. So what we see basically, zero now is the time of the transition. And now we start to see a remarkable, some noticeable difference. So when we have this approach and there is a transition at time zero, then the charge, which was originally very like localized on this unit, okay, starts to decrease and then it increases again. The same also if you look on the other half, it starts to increase and then it decreases again. But for those which are non-isomerized, we notice that even after the transition, okay, the charges for the ground and excited state, for the ground and excited state, they are still somehow coupled. So after the transition at time zero, they are first the same and then there is slight difference, but they are not like at the beginning of the trajectory clearly separate. They have the same sign. So here in this case, for the better non-part both are negative, for the shift base part both are positive. So there is some change in the charge distribution. And so what can cause this change in the charge distribution? And as I showed in the tutorial, they can be a residue close by. So for example, negative charge residue, which can stabilize the positive charge in the area outside of the better anodic. So in the excited state, if you have a counter ion which is close to carbon-13, then it will stabilize the positive charge in this carbon-13. And so what we have done then is we have looked at the distance from this counter on 97 to the atoms of carbon-13, 14, and 15 and the nitrogen. And we saw that actually in case of the isomerized bond, sorry, in case of the isomerized trajectories, the distance has dramatically changed. So it was just before the transition, the distance from carbon-15 and the nitrogen was large and the nitrogen carbon-13 and 14 was close, but immediately after the approach, sorry, after the transition, then carbon-14 and carbon start to move away while carbon-13 was still kind of close. Now, in case of the non-isomerized, you see that carbon-14 did not move far away and instead carbon-13 was approaching this counter ion. So that's why it did not isomerized because this carbon-13 was, the positive charge was stabilized on the, by the counter and 97. So to cut the long story short. We found that this counter ion has a profound impact on the outcome of the photoisomerization because in some trajectories it comes close to the retinal and then it stabilizes the positive charge. Now, this is a hypothesis that we have obtained from the simulation. So now the question is how can we prove it? So we have a very good question. So, how can we prove it? So, how can we prove it? The question is how can we prove it? So we have repeated the simulation in the gas phase. So now we have done it outside of the protein simulation and what we found is now that the yield of the isomerization has gone significantly down. It's now instead of 60, it's 30%, 37 and the excited state lifetime has almost doubled from 250 to 560 seconds. Now, interestingly, in the gas phase, 63% of the trajectories, they go through the CI and they twist around the 1112 W1, not 1314. And we found even 37% were the twist around the 912 W1. So therefore we found that actually the protein environment is not only responsible for the success, meaning if it goes from trans to cis or trans and then back to trans, but it also selects the bond for isomerization cis. It also tells you which bonds will I summarize. Okay, so here's the conclusion. I showed you that the spectral tuning in proterodopsin is due to the polarization from the amino acid in position 105. And I showed you in the second part of the isomerization that the counter and plays an important role in determining the outcome of the excited state dynamics. It does select the double bond for isomerization and it causes the trajectories to isomerize successfully. So with this, I'm coming to the end of my talk and I would just like to show the acknowledgement to give acknowledgement. So all of this research would have not been possible without excellent coworkers in my group. So the first part is about the spectral tuning. This is research carried out by Gil Amoyar who was a bachelor's student in my lab and John Church who was the postdoc who did these analysis of the charge distribution. And the second part about the photoisomerization in proterodopsin was carried out by Sarmic who was also postdoc and who is now continuing his research in the Paul Sherry Institute in Switzerland. And last but not least, I would also like to acknowledge funding bodies which have allowed me to get computer resources and also finance the group and also collaborations in this project. So thank you also for your attention and I will be happy to take any question. Thanks a lot. I got this. This is really fascinating with the molecular insights that you have been able to gain on this system. So the floor is now open for questions and you can either use the reactions box to put your hands up or raise your hands up or write questions in the chat box. Okay. I have, we have already one question from Imol. Imol, you can unmute yourself now and ask the question. Yeah. Nice talk, you got. And so my question is like the counter anions like aspartate, mostly aspartate I think those are also incorporated in the QM region or those are just taken care of with the amber force field. Yeah. Hi, Imol. Thanks. This is a great question. So in this simulation, the aspartate was outside of the QM region. So it has carries a negative charge and yeah. So it's just a charge effect, not anything. Yeah, exactly. The charge of this counter and it's static it does not change due to polarization. Yeah. Okay, yeah. Thank you. Can I ask one more leg? Sure. Yes. I don't see any other hands raised so you can go ahead. So if you change it with a polarization model do you think that the percentage of cis trans isomerization will change? Okay. Yeah. This is an excellent question as well. Thank you. I mean, I am, I mean, we have to do the simulation to give a definite answer. But at the current stage, I think it wouldn't change the result. And the reason is because the distance, I mean it's, because the distance is not, I mean it's what I think two, between two and three amps so from such a long distance, I mean, what matters is the fact that it carries a negative charge. So I think that the polarization effect on this range will be probably minor effect. Okay. Yeah. Thank you. Okay. Thank you. So I don't see any more questions in the chat box but in the meantime, since we have some time I have to ask the question and if somebody else has a question, please raise your hands. So Ibar, when you were doing the initial calculations for the shift in the mutants, when you remove the protein, did you just look at the geometries? I mean, how would you then incorporate mutations? You didn't have the protein at all. The initial graphs that you showed, is Igor around or did Igor lose his connection? Yes. Yes. It looks like there was a break in his connection. Okay. We will wait. Hopefully he's going to try to reconnect back. And if there are any other questions, people can start thinking in the meantime. Here he is. Okay. He's back. Igor, there was a break in your connection I think. You need to unmute yourself. Hi. Hi. I think there was a break in your connection. My laptop crashed and I had a blue screen and I'm restarting, so I can't, sorry about it. Okay. Okay. I think I heard your question before I got out. So you were asking me, how we did the gas phase simulation? Yes, when you removed the protein. So initially you did the simulations with the protein and then you removed the protein and showed that the changes were very low. I mean, that's the extent of changes, well, that's it. Yes. Because of the absorption shift. So what we did, we kept the retinal geometry, like in the protein, we didn't change, we didn't touch the geometry. We took it from the same snapshots, but then we just removed the protein. So for us, in the simulation, it's very easy to do. You just delete the atoms of the protein or you put the charges to zero. So it was not such a big thing. And but it helped us to understand the spectral tuning because what we found was that if you remove the protein, then the spectral shift is becoming much, much smaller. So it means that it's not just by the retinal geometry. It must come from the protein. Okay. But then the important thing about these two mutants is that the leucine has been mutated to glutamine. And you're even removing that leucine and the glutamine, right? Exactly, yes, exactly, precisely. Wait a moment, wait a moment. You're talking about the calculation of the excitation energy, which changed the shift in the gas phase, or you mean this visualization? Yes, the initial graph that you showed where you were calculating the shifts. Oh, okay. Yeah, so we removed everything. Yeah, we removed everything, all the residues. No, because, I mean, sorry, maybe I didn't explain it well. There was this claim by the group in Frankfurt. They say that there is some stretch of the C14, C15 bond. So if this claim is true, then we can remove the protein and the bond stretch alone would explain the difference. So when we did this comparison, then we saw that the shift also was removed. So that's why, that's how we could exclude this bond stretch as an explanation. Okay, are there any more questions from the audience? I don't see any more questions in the chat box, but if there are no more questions, then let us please use the reactions box to appreciate the talk. And I can of course clap for you both. Thank you, Gaurav, thanks. Fascinating results.