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Variational Metadynamics

Periodic Reporting for period 4 - VARMET (Variational Metadynamics)

Reporting period: 2020-07-01 to 2020-12-31

Molecular dynamics and Monte Carlo methods based on an atomistic description of matter are indispensable tools in modern science. Thanks to their ability of simulating the microscopic behavior of matter, they help interpret experimental results, provide insight, predict new phenomena, and replace costly or impossible experiments. Atomistic simulations find application in almost all areas of science and help design new drugs, discover new materials, find greener chemical processes, and address the energy problem.

The overall aim of the project is to extend the scope of atomistic simulations by removing one of its most significant limitations, namely the limited time scale that can be investigated in standard simulations. The methods that we have developed for this purpose are based on the construction of an external bias that is added to the Hamiltonian to remove kinetic bottlenecks. One first defines a set of collective coordinates that are functions of the atomic coordinates and then builds a bias that is a function of the collective coordinates.

The project was centered on the application of a variational principle to determine the bias. We were able to achieve all the methodological objectives of the project. This has allowed us to gain a deeper insight not only on the variational method but also on how collective variable based sampling methods work. This has led to the development of a novel, highly efficient and simple to use sampling method that we call OPES that is on the flight probability enhanced sampling. This has offered the possibility of putting many different and apparently unrelated sampling methods under the same umbrella. During the project powerful machine learning based methodologies have also been developed enhancing the power of our approach.
The development of method has gone hand in hand with applications in the area of chemical reactions, crystallization, and ligand-protein binding.
Following closely the project timeline we have implemented the variational enhanced sampling (VES) and have improved its efficiency in different ways. In addition, we found that the use of a neural network to represent the bias was extremely beneficial. We have also realized that in the VES scheme it is possible to implement a multithermal multibaric simulation. This allows simulations in a wide range of temperatures and pressures to be simulated at a cost comparable to that of a standard simulation at a fixed temperature and pressure. This capability is very handy when it comes to studying phase diagrams.

As mentioned earlier, for the success of our enhanced sampling method it is necessary to identify good collective variables. Thus, a considerable effort has been devoted to the development of efficient collective variables. We have followed two strategies; one is based on physics considerations the other instead relies on machine learning methodologies. In particular, in this context nonlinear discrimination methodologies and signal analysis methods were found to be very useful.

In an enhanced sampling run the presence of the bias affects the dynamics of the system and therefore dynamical properties are modified. However, from a biased run rates of transitions between different metastable states can be computed, provided that the bias is null in the transition state region. We have devised three new methods to achieve this result. One is based on VES and it is described in the proposal. The second called Gaussian Mixture Biased Enhanced Sampling (GAMBES) is based on a different concept. For each metastable state we perform an unbiased run. From these data we model the local probability density with a Gaussian mixture. From the Gaussian mixture a local bias is computed that is by construction null in the transition state. Finally, the third method is based on a combination of enhanced sampling and path sampling. This implies that rather than sampling configurations we sample trajectories in an enhanced sampling framework.

Possibly the most important outcome of the project is what we have learned from the VES experience about enhanced sampling. In VES one must introduce a target distribution and the bias is such that at convergence the biased system reaches such a distribution. We realized that most the sampling methods can be formulated as a way of sampling some kind of target distribution. Making use of this observation, we formulated a unified approach to sampling whereby different sampling methods can be formulated in a unified way. The implementation of this approach is based on a novel enhanced sampling method that aims at reconstructing the probability distribution and not the bias. This method, based on metadynamics and VES has proven to be very efficient and easy to use.

Crystallization is an intense area of applications and a testing and a source of inspiration for new developments. We have applied our methods to of one component, multicomponent and molecular system. We have also developed the unique possibility of studying crystallization processes in solution.

In the field of protein-ligand interaction wea have applied our most advanced techniques for the determination of collective variable and for performing enhance sampling and set up a very accurate protocol for computing ligand protein free energy of binding We have underlined in this context the role of water and found innovative ways of incorporating its effect.
We have implemented the Variational Enhanced Sampling (VES) method into the plug in PLUMED that has been developed for standard metadynamics. PLUMED can be interfaced with many of the most popular ab-initio and standard MD codes thus it allows an easy access to the VES method. In order to facilitate even more the diffusion of the method we have used non-ERC funds to run a very successful workshop aimed at young people. The course was followed by 51 participants most of whom (48) were from European research institutions.

All the results presented are novel and have pushed the state of the art. As discussed above we have made the code available to a vast community of users including the industrialist. The wide variety of possible applications ensure that the project has having and will have a lasting impact in many areas of science like material science, chemistry, biology, and drug design.
Free-energy surface profile , F(s), and flooded surface, F(s) +V(s), for the asymmetric CH3F + Cl- -