 Welcome to this introduction to molecular dynamics simulation. I'm Alessandra Viglia from the Royal Institute of Technology, and I will try to introduce you to the main principle behind molecular dynamics simulation. I think the first question that we have to ask ourselves is why we perform molecular dynamics simulation. I think the main reason is that we cannot see autumn. It's very hard to have an idea where ions are located, for example, in an ion channel, to have a picture of exactly where the membrane is, how the atom moves, and how the protein itself moves. Also, we have to think about that everything that we know on a molecular structure is actually a model. Maybe not always we can have experimental information on the structure. Some molecules cannot be crystallized, some molecules are not soluble, and some other molecules are very small, so also the contrast for cryo-Yam is very hard. If we want to know more about the dynamics of the energy of such an ion channel, it's very hard experimentally. Really, in reality, atoms move. I think in this case, if you want to investigate an ion channel and how it works inside the membrane with the correct ion environment and other small molecule environment, one of the best options is to use molecular simulation. Molecular simulation is not only allowed us to visualize what happens how the atom moves, but also allowed us to have an idea how molecules interact with each other. We can extract information of binding acidity, as you will see later in this school. We will also see how the molecule changes your binding, so how we mimic and we try to promote an interaction process between. In general, when we are performing a simulation, the first step is that we have to simplify our problem. For example, we were asked to understand better brain injury. The brain injury is come from a mechanical insult, so that is the macroscopic, what happens at the macroscopic level. This will cause an injury at the cellular level and the axon level, but we want to understand exactly what happens inside this cell. We cannot simulate the old cell. We don't have the information of all the molecules that are inside the cell, but we want to start to see what happens to the subcomponent of this cell. What happens to the axonal membrane when it's under stress? Will it be broken? Which strain will be broken? Will it be formed a pore? Which strain will not? Of course, this is a no-local event that we can perform with molecular description, and we need the molecular description to perform properly, but we also needed to put this local deformation inside the large contrast of the cell. Deformation may occur in a different way along, for example, the axon. For this problem, we have simplified our description, we have combined the results of this Simpson with other techniques that allowed us to account for the rest of the cellular environment, so in a sort of multi-scale approach. In this case, specifically, we will combine molecular dynamics results with fine element description of the axonal model. What is the main goal of a molecular simulation? I will say that the molecular simulation in general is main goal is to generate a self-representative conformation of the molecular system in such a way that we can extract a property. One of the approaches is molecular dynamics that allowed us. Molecular dynamics is based on the Newton equation. So what tells us the Newton equation? The Newton equation is a relation between the acceleration that is acting on one atom and the force acting on the atom and the mass acting on the atom. We can speak about atom because here I have an atomistic representation, but we can speak a general on a particle. So we can retain the acceleration on a particle if we know the force on that particle and the mass of the particle. This is a second-order differential equation. It can be solved in an analytical way. So what usually we do, we have a step. We use a step in time. So we move from one conformation where for each particle we know the position and the velocity. We integrate the Newton equation and we get a following position and the following velocity for all the atoms. So the simulation proceeds in a very small step. Those steps are usually for an atomistic model in the order of femtoseconds. And these also reflect in a very, very small step in the movement of the molecule. And the molecules are moving a small step that very small compared to actually the human step. To apply the Newton equation, we need an information. It's the force acting on the atoms, the mass usually we know. And the force is related to the potential that define all the interaction inside our system. And indeed, the potential is defined as V is in function of the position of all the atoms. We can let our system move in a discrete step. So we have information at different time point. How we calculate the property? So in molecular dynamic simulation, we can take the average over the time and that will provide an average value of the property that we are interested to calculate. It is valid if we have sample, we have enough conformation of our system that are generated in time. But what happens in a macroscopic level? When usually we do an experiment that we experimentally measure a property, this property is the average of a large number of molecules. Usually in a cuvette and when we perform an experiment, we speak about millimolar. So it's something in the order of 10 of more than power 20 molecules. And also this property probably is the average of the time that the measurement took. So it's an average, a large number of molecules and an average of the measurement time. So how we can compare those two? Average. We can compare them. And that is thanks to statistical mechanics, and particularly to develop by Boltzmann and Gibbs. And here we come to the ergodic hypothesis that states that the average of an ensemble, so a large amount of conformation, is equal to the average in time. So if we have sample long enough, our simulation, we can calculate the average, and this average is equal to the sample. But we have to be sure that we have a sample enough conformation, such a way that our ensemble is ergodic, and that the average value is comparable to an ensemble average. In doing that, we have to pay attention that not... If we were simulating an infinitive time, then we will be sure that we all are convergent. But since we cannot simulate at an infinitive time, we have to assume that we simulate enough time that the property is converged. In doing that, we have to be aware that different properties have different range of time in which they achieve convergence. Another aspect that we have to consider from simulation is that we can start equilibrium property from a simulation, but since we anyway generate the conformation in time, that allowed us also to extract time-dependent property. So with time-dependent, I mean property like diffusion, or property or kinetic property. So as I mentioned, there is a key factor in a simulation, the time. We have always to simulate long enough to generate enough conformation that are representative for our system. And there is a strict relation between the dimension of the system and how long we can simulate. So a small system, we can simulate longer and longer for a more simple system than a complex system. So here I just put the feeling, of course, we want to simulate and to get results usually in a reasonable time, and we have always to consider this. Understanding a small movement of a small molecule, for example, we might want to have a one microsecond a day, it is now a day possible for a small molecule. But if we want to go a step further to understand and predict the motion, then we will need longer time. We will need events, repeat more than one time, and we might be to consider also better the environment so the complexity of the system become larger, and then also the system become larger. And that means that the simulation time increase. So more the system increase, more we need to answer to our question longer time. Here I report the time that we wish to one, if we want for a small molecule at a one microsecond per day, that means that as a whole time we need to have 400 microsecond each step. We want to have each step in 400 microseconds. You have to read this slide in this way. Okay, so now we have seen the base, the principle behind molecular simulation, how we can extract property from molecular simulation. And now we can see what government the simulation. There are different... I will divide this in three parts. There is the choice of the molecular model that will govern your MD. There is the choice of the molecular condition and also there is the choice that you make to set the system, the environment of the system where you set your system. We start with the choice, the molecular model. So we have different aspect here. We have to choose the degree of freedom that we want to use in our system. We probably want to use which type of potential we use to describe the interaction between our particle in the system. So the first, the degree of freedom. We can describe our system at the domestic level. That means one particle is one atom. But we could also decide to describe our system using one particle corresponding to a group of atoms. That is called also at the cross-grain level. In some cases we have a relation between the cross-grain definition of the bit and the atomistic description. So that means that we know in the position of the bit we can back-met the position of the atom, respect the position of the bit. This relation is peculiar for some cross-grain model but not for all of the cross-grain model. It is clear that when we decide the degree of the cross-grain or atomistic model we also decide for an atomistic model we have more particles, so our time. Why our simulation time? Maybe we might need more time to simulate our system. In the cross-grain model we have a less number of particles so that maybe the simulation is somehow it takes less time for the same simulation time. But we reduce the degree of freedom and so we reduce also the details. How to choose which type of description? When we decide the description we have to decide the degree of freedom. So which particle we will use to describe our system and also which energy function we will use to describe the interaction between the particle and our system. How we make this choice? Probably we will make this choice based on these three criteria. The model that you will use should encompass the property of interest. These are all what we use in molecular simulation or an empirical model so you have to be sure that it is appropriate to describe what you want, the property that you want. The other things that you have to think about that the simulation time that you can achieve with that model, with that description of the system should be larger than the time scale of the process that you want to investigate. That is the second important point. And the third point, that the dimension that you can describe with that molecular model should be larger of the size of the system that you want to simulate. If you can see if we move from different level of description starting from a quantum chemistry base description to an atomistic description to cos-grain description some people will say that an atomistic description is already a cos-grain description of a quantum chemistry description. When we move from quantum chemistry description to cos-grain we see that we have a change in the dimension of the system that we can simulate and the time, the simulation time that we can achieve. When we have chosen our model also there is another aspect we can also decide to build to construct our model. And doing that and also what people have done before one has to think about very basic things that a simplified representation of a molecular system should be as simple as possible. That is very important. I will let you think about why or if you are curious you can have a look to the Nobel lecture of Michael Leavitt. Martin Campos, Michael Leavitt and Ariel Burscher got the Nobel Prize in Chemistry in 2030. And I think their lecture are very nice to follow. So the potential energy can be seen depending on the position of the system or all the particles in the system and can be divided, factorized in the same way in one body term, two body term, three body term, four, five and body term. Usually more will increase the body term more costly is the calculation and also high level body term are usually a minor contribution so they weaken in your... So usually in molecular simulation we know everything that is... we take an account up to three body term but in some particular way in the sense that we base of our potential are base pair potential so we are transmitting the potential in one body that usually we ignore and in two body potential but we include in these two body potential the average effect of the three body potential that means that that is the reason why the potential that we are using in molecular simulation is an effective potential. What is the consequence of this approximation that our effective potential depends on somehow on the density, on the temperature rather factor and it is not a true two body potential. So which are the components of this potential are all based on pair interaction we have seen but which are the components. So usually potential are divided in different type of interaction and to see the interaction we can have a quick look to how the movement that we will have in a molecule. So we have a vibration of the bond we have a sort of vibration of the angle and we have the rotation of the torch plus we have all the non-bonded interaction that avoid the molecule penetrating to each other but also account how the molecules interact with each other. They like each other, they don't dare to pull each other. So in classical we divide the potential so if we think about in terms that are bonded term where we include bond angle torsion and non-bonded term where we include Lenard-Jones interaction and electrostatic interactions. So this is a schematic representation of the molecular mechanics force field and you can see that if the force field can be defined with a set given set of particles a force field is the potential function described the interatomic interaction between all those particles. Force fields are characterized by having a functional form and a set of parameter. Here is an example, a general example of a force field and its analytical functions not all the force fields have the same analytical function one has to check, this is just an example and you can see that you have term for bonds, angle, torsion and we always have a sum of all the contribution on it and then we have a term for non-bonded interaction. What we can say more on force field so usually force fields are based on atom types that means that those atoms might be more than the normal number of elements for example for the oxygen in water we might have one atom type and for the oxygen in a carboxyl group we will have a different atom type even if they are both of the same atom type atom, element, same, they are both of oxygen. All the parameter that were generated in a force field depends on the functional form that is used in that force field. That means that you cannot use a parameter for a bond interaction with another functional form. There is a strict link between the functional form and the parameters. Another thing is that if a parameter is developed inside a force field it cannot be used in another force field. So when you want to add a new parameter in a force field you have to perform a parameterization in line with the philosophy of the strategy of the force field. So these are four things pay attention when one handles with force field. We have a biomolecular field we have different force fields that are mainly used these are Humber, Char, Promo, so PLS speaking about Colesgrave model Martini force field. We have also a series of here a list series of server online or offline tools that can help in parameterize new molecule for some of those force fields. But where I actually come from the parameter force that are in the force field they come from very different source for this reason I will always say check how the force field that you decide to use has been parameterized. So parameter can come from experimental data or they can also come from a binitial study in particular a small molecule usually we use a small molecule that represents a functional group we use that one to parameterize and then we hope that parameter developed for those molecules can be transferred to a larger, the same functional group in a larger molecular context. We can have information and angle of bonds for example for crystallographic crystal data we can have the constant the bond and angle force constant they can come from here or Raman spectroscopy charge usually come from quantum mechanics calculation but we have also different approach where we decide to parameterize this is always usually we parameterize non-bonded interaction based on observer data like thermodynamic or kinetic property and with a sort of fitting procedure we try to reproduce those observable that is frequently done for example reproduce salvation free energy partition property or kinetic property like water exchange for example so in this way a pool of parameter are redeveloped and this as I told before is linked to the functional form and so it's linked to the force field within its parameterize there's another aspect that is also linked when you choose a force field you don't not only choose the how the potential to describe the interaction between your particle but you also somehow make also choice on how you will treat for example long range interaction because this is also how they are you have to look how the parameter parameterize in which environment and also you will also know already which type of time step that we will be in the future will be used and probably which type of bond constraint these three aspects are also strictly linked to the choice of the force field so we will say no bonded interaction in particular no bond long range interaction why we are describing short range and long range no bonded interaction in different way the reason is that more than 90% of the computational time is spent in calculating no bonded interaction the number of the non bonded interaction is increased with the number of atoms square and that so that means that we always like to decrease our computational time because we will need to sample longer so it was observed that both the function used to describe the Lena-Jones interaction and the Letro-State interaction are decay they are relative fast Lena-Jones decay is 1 over R power 6 Coulomb decay is 1 over R that means that a longer and longer range the contribution of this interaction may be very small and that can be somehow in your so for this reason we thought about cutting the potential at some point with a cutoff and you will notice that each force field different force field may use different cutoff and different way to treat how they switch between the cutoff and the long range interaction and for this reason it is very important when you run a simulation to account to check how the long range interaction in the force field parameterization so we will say we cut this kind of problem, we cannot ignore what is after after the cutoff we have to consider it so we use other methods some force field use reaction field other force field use particle mesh shiver to account for the interaction or long range so we have seen the base idea behind molecular dynamic simulation we see molecular model that is also what is part and here I want you a little to think about which you think are the challenge for molecular biomolecular simulation so I try to list the one that I think are the main three challenge maybe you think about other but usually in biomolecular simulation we want to reproduce biophysical approaches biophysical approaches involve hundreds of thousands of atoms and those atoms have in intricate interaction that are difficult to simplify and this I think is a big challenge the other challenge that we have in biomolecular simulation that we still want to reproduce biophysical approaches can spam with a very large time scale we have events very fast like photosynthesis that occur in the range of picoseconds we have enzymatic and regulatory approaches that might take in the order of millisecond and some structural organization might exceed seconds and I think the third challenge is that we have actually the force acting between the atom a very small force a small driving force are really small driving force are the force causing the molecular change in all this project we don't involve large change but very tiny change and these change results are results of large opposite energetic effect so it means that all the force field has to be tiny tuned such a way to describe the small driving force so these are I think for me the big challenge for molecular simulation maybe you have another one and I will be happy to discuss with you in a Q&A