 Good morning everybody and welcome to the lecture. This lecture will be on the basis behind the basic idea behind molecular dynamic simulation and on those factors that govern molecular dynamic simulation. My name is Alessandra Villa and I work on the Royal Institute of Technology, Stockholm, in Sweden. So why would we want to do molecular dynamic simulation or molecular simulation in general? Usually, macromolecule are three-dimensional objects so we would like to visualize them and also to visualize their motion and molecular simulation are the best tool to do this. We also like to understand better how molecules interact with each other, how an anti-gene and antibody interact, how the surface model when one comes close to the other. The simulation can also be used to refine structure coming from experimental technique or to complement structural biology experiment. But it can also be useful to refine model coming from docking experiment or modeling experiment. Another field where simulation can be very useful is to understand conformational arrangement, mechanisms that govern macromolecules, how a channel opens and closes for example, how the ion diffuses along the channel, how a ligand can block or open a channel in this case for example. Also simulation allows us to implement small modification, residue mutation and see what is the effect on the structure of the system. Usually when we do simulation we try to simplify the system. For example, if we are interested in wetting of a surface, we will use one drop of water on a surface to see what happens when the drop of water falls on the surface. And so we reduce the system to a dimension that we can simulate. And also here for example we can say what is the effect on the wetting mechanism from different type of surface. We change the surface and we can see how the wetting changes. So also from a medical point of view we can also, we found ourselves in many cases where we need to simplify the system. If we are interested in brain injury or an axonal main injury, we know that at cellular level, in this particular case a neuron level, we found that axon, that is a protuberation of the neuron, gets stress. What happens? So we might, we will address this maybe to looking at the axonal main brain and the main axolema to see what happens to the axolema under stress and at which point of stress for example will disrupt. And then we'll provide us one piece of information about when the axon will disrupt under strain. Of course our system that we use should be close as possible to what is representing this case. For example the lipid composition should resemble the axolema lipid composition. The system should be large enough that we don't have size effect. Why simulation? Atom, everything cannot be seen. Why simulation? Atom cannot be seen. Everything we know about biomolecules at the atomistic level is a model. Structural biology structures are all refined using molecular models. And also sometimes we cannot use structural biologic tools. For example a structure cannot be crystallized. A protein is not soluble so animal cannot, soluble animal cannot be used. The molecule is very small so it has not enough contrast. So cryo-EM cannot be used. And another aspect is that we cannot measure an energy and dynamics at atomistic level. So we are interested that in this case this information can be provided by a molecular simulation. What is the goal of molecular simulation? The goal of molecular simulation is to generate enough representative conformation of our system such a way that an accurate value of a property of interest can be calculated. There are several methods that allowed us to generate representative conformation of our molecular system and one of those is molecular dynamics and is the method that I will treat in this lecture. So one method to generate conformation is molecular dynamic simulation. Molecular dynamic simulation generates conformation applying the Newton equation of motion. So we start from, for example, from a conformation one at time t1 we apply the Newton equation that is a relation between the acceleration acting on the particle, the force on the particle and the mass on the particle and when we get acceleration, if we know the time interval we can get the new velocity and we can get the new position of the atoms of the particle. In this way we can go from conformation one at t1 to conformation two at time t2 where t2 is equal to t1 plus delta t and we go on so. In this way we can generate an ensemble of conformation with a time, also a time dependency. So as you can see in the movie the old step takes place, that takes place, a very tiny step. The Newton equation is, as you can see from the expression here, is a second order partial differential equation so we need it to solve it numerically. The second aspect of this equation you can see we have the acceleration that is equals to the force acting on the particle and the mass acting on the particle. The mass of the particle of the atoms is known but we need to know the force acting. We can get the force if we know the energy function that governs all the interaction in our system and indeed the derivative of this energy function is the force acting on the particle. So this is the second ingredient of molecular dynamics simulation to have the energy function that describes all the interaction in the system. Before I say that we need to generate enough conformation to be able to calculate an accurate value of a property. Why? So experimental measurements are always done in a macroscopic sample. So usually in a macroscopic sample we have a number of avocados of molecules, that means 10 of power 23 molecules. And the average that we are doing we take in the measurement is an average of all large number of molecules. While in the simulation we always have one molecule and we let generate conformation involving letting this molecule evolving in time. So how we can combine these two way? So we go back to the statistical mechanics and in this context is very important the ergodic hypothesis. The ergodic hypothesis say that a single system evolving in times is replaced by a large number of replication of the same system that are considered at the same moment. So that means that the average of a large number of conformation is equal to the average of the same property in time. And this is valid when the time is infinite. In our case we have a defined time, a fixed time. When we start the simulation we will always set how long we will simulate. So we have to be sure that the time that we set is large enough to allow us to have enough conformation that are as representative of our system. And in doing that we always have to keep in mind that different type of property have different realization time. So for some property you need a short and sampling time. For other property you need a larger time sampling time. And before setting any project you have to be aware if you can simulate a last time to allow you to get an accurate property. For your system. So here for example are some examples of how we can think about on the time. And also the times relate smaller system equilibrate faster than larger system for some property. And also this has to be taken into account for example. One example is diffusion property. In general if we want to understand the motion of a tiny molecule for example we might need one microseconds a day. But then if we want not only to understand but to predict the whole motion of the molecule or to improve a spirit then we might need longer time per a day. But if at one point we want to get to replace medicine and biology then we have to go to one million seconds a day. If you think about in the cell some conformational rearrangement happens from one from millisecond to seconds. So then you have to account for this when you think to replace medicine and biology experiment. Of course that means that before starting a project you have to see which are your infrastructure. And which is the time simulation time that your infrastructure allowed you to perform a day to have a feeling if you can. You are able to calculate the property that you want. The challenge of molecular simulation. So when we simulate a biophysical process we have 100,000 of atoms. And those atoms have all intricate interaction that we need to simplify to have our energy function. But in the same times are very difficult to simplify it. So this is one challenge. The other challenge is that the process, all those process have a different range of time scale. We have primary events in the order of picoseconds. But then we have enzymatic regulatory process that take milliseconds. And some structural rearrangement or reorganization inside the cell might exceed seconds. And the third aspect and not less important one is that all these biophysical projects, if you can think, binding, folding aggregation are all driven by small force acting one on the other. So it's important that the energy function that we use to describe the system accounts for all this small driving force and is carefully fine tuned. Now we look what govern molecular simulation. We have the choice of the degree of freedom and the connect one, the parameter that we use to describe the interaction between those degree of freedom. Treatment on non-bonded interaction, boundary condition, integration time-strap, temperature pressure, how those are treated, environment, solvent, effect ion and so on. And where we get the starting. One choice that we can do when we start, we have to do when we start a simulation and decide which degree of freedom we want to describe our system. We have different possible options. We can describe our system one particle, one atoms, so what is called all atom description or atomistic level description. Or we can describe our system in more grain way. So we describe, we use one particle that define a group of atoms. And so when we go from an atomistic description to a cos grain description, the number of degree of freedom is reduced and indeed the number of particle is reduced. So it means that you have less particle in the cos grain, so you have less interaction to be calculated. There are sometimes technique that allowed you to simulate in a cos grain model and then to go back to the atomistic description with a procedure called back mapping. And sometimes you have also multi-scale simulation that allowed you to simulate one aspect in a cos grain setting and then move back to the atomistic and then going back again. But another part of the topic of this lecture. So when we choose the degree of freedom, so which number of particle that you want to describe your system is important that you think about which property are you interested. If you are interested of a general behavior or a more atomic based behavior, if you are interested in atomic based behavior, you have to use an atomistic model. Once you have choose which model you use to describe your system, then you have to choose which energy function. I will use to describe all the interaction between those particles. And here in the decision of the energy function, it's very important to consider the real ability of the model that you are using. So one, the model that you choose, whatever the degree of freedom as an energy function has to encompass the property of interest. Second, the model should allow you to simulate enough time, so that means that the time that you simulate is larger of the approaches that you want to investigate. Like we will say enough and fulfill the ergonomic, ergodic hypothesis. And also you have to pay attention to the size of your system, so to avoid that you have a final size effect. So your simulation size should be enough to avoid size effect for the property that you want to calculate. And also consider all the aspects of the simulation, all the aspects of the molecule and of the system that you want to simulate. There is a strict relation between how you describe the degree of freedom that you use to describe your system, atomistic or coarse grain. Coarse grain, they are different levels, so coarse grain, they are fine coarse grain, they are more grain, coarse grain. But anyway, there is a relation between how you describe the degree of freedom that you describe your system, the simulation time that you can achieve, and the dimension of the system that you can use. Then we go to the energy function, so you find yourself to choose this energy function. That is called also force field, and there are several parameters that are inside this energy function. One of the challenges of molecular simulation was to have a simplified model for this integrated interaction, and why we need a simplified model. So this has come from the lecture of the Nobel Prize in 2013, make a levite, when he will say in his introduction lecture that a simplified representation of molecular systems should be as simple as possible. The reason why? That I think is applied to any model, and I think the more easy way to understand why is if you think about the weather forecast. You have a model, and the model can be very accurate, very complex, but you have always to keep in mind that you want the weather forecast of tomorrow to day. So you cannot apply a too complex model that provides you the weather forecast of tomorrow, the day after tomorrow. Because then your results, your prediction, are too old, are not any more useful. And the same is for molecular model, you want a molecular model that is simple enough so that it allows us to compute something in a reasonable time. So not in years, but probably in a span of PhD approaches. How they look like this force field? This force field, these are usually called molecular mechanics force field. When a particle base, all the interactions are interaction between pair particles, usually. And they are divided, the energy functions are divided in components that are characterized, define the bonded interaction and the non-bonded interaction. So the formula that you see here is a common formula among the atomistic force field used for biomolecules. Each force field is characterized by having analytical function, describe all the type of interaction. And those analytical functions most come from classical mechanics. For example, you can see the bones are exactly an oak potential. And then a set of parameter that take in the potential, all the chemical components of your aspect of your atoms. And the other characteristic of this potential is, like I will say, mainly a pair potential because it makes it easy to calculate pair interaction. So these are molecular force fields that might have mixed term or three-body term that slow down all the computation. So these force field and molecular force field are usually atomic base. And usually we have deep atom types that describe, more atom types describe the same elements. It depends a lot where this element, in which functional group is this element. For example, an oxygen in an ATAR group or an oxygen in a carbosyl group might be described by a different atom type. There is a strict relation between the parameter and the functional form. So you cannot use a set of parameter with a different functional form that will provide the wrong results. Also, there is a relation not only between the parameter, the functional form, but also the philosophy that has been used to parameterize the force field. So you cannot take a parameter from force field A and move to force field B. No. If some parameters are missing in your force field, you need to reparameterize or parametrize those parameters in line with the parametrization strategy of the force field that we are using. The most common biological force field in biomolecule simulation are amber, charm, grommos, or PLS. And for the coarse-grained setting, martini force field. We have also several online server and offline tools that allowed us to parametrize some extra parameter in line with the force field. Where the parameters in the force field come from, usually? They can have two different sources. One can be that they come from experimental or ab initio study and of small compounds. For example, bond angle can come from crystal data, force constant might come from spectroscopy data, charge might come from quantum mechanic electrostatic potential. Then there is another approach. You don't take directly the value from experimental ab initio study, but you just set up a fitting procedure to get the best set of parameters that reproduce an experimental value. And this usually is applied if you want to reproduce thermodynamic data or kinetic property. One example is ion usually are parametrized against not only their structure with water, but also the solvation in water. And they exchange with water. Most of the parametrization are done on small model compounds. And one of the property of those molecular mechanics force field is that parameter developed for small compounds should be transferable to a larger set of molecules. That means similar molecule with similar functional group also larger set of larger molecule like macromolecule.