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20 Years of Polarizable Force Field Development

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20 Years of Polarizable Force Field Development 20 YEARS OF POLARIZABLE FORCEFIELDDEVELOPMENTfor biomolecular systems thor van heesch Supervised by Daan P. Geerke and Paola Gori-Giorg 1 contents 2 1 Introduction 3 2contentsForce fields: Basics, Caveats and Extensions 4 2.1 The Classical Approach . 4 2.2 The caveats of point-charge electrostatics . 8 2.3 Physical phenomenon of polarizability . 10 2.4 Common implementation methods of electronic polarization . 11 2.5 Accounting for anisotropic interactions . 14 3 Knitting the reviews and perspectives together 17 3.1 Polarizability: A smoking gun? . 17 3.2 New branches of electronic polarization . 18 3.3 Descriptions of electrostatics . 19 3.4 Solvation and polarization . 20 3.5 The rise of new challenges . 21 3.6 Parameterization or polarization? . 22 3.7 Enough response: how far away? . 23 3.8 The last perspectives . 23 3.9 A new hope: the next-generation force fields . 29 4 Learning with machines 29 4.1 Replace the functional form with machine learned force fields . 31 4.2 A different take on polarizable force fields . 33 4.3 Are transferable parameters an universal requirement? . 33 4.4 The difference between derivation and prediction . 34 4.5 From small molecules to long range interactions . 36 4.6 Enough knowledge to fold a protein? . 37 4.7 Boltzmann generators, a not so hypothetical machine anymore . 38 5 Summary: The Red Thread 41 introduction 3 In this literature study we aimed to answer the following question: What has changedabstract in the outlook on polarizable force field development during the last 20 years? The theory, history, methods, and applications of polarizable force fields have been discussed to address this question. This investigation showed that the quality of the force field potential is detrimental for any type of atomistic sampling technique. If the underlying energy function contains flaws, these flaws are one way or another embedded in the fast amount of data we seek to understand to repro- duce a wide range of quantifiable observables accurately. Subsequently, we identi- fied two key challenges associated with the development of polarizable force fields: First, how to determine transferable and accurate parameters sets, and second, how to advance the underlying physical model without computational overhead. Af- ter twenty year the classical avenue of force field development has the modeling community finally made the transition towards a general acceptance of the need to develop more physically sound models. During the last 5 years machine learning techniques emerged to provide new means to remove bottlenecks in the current process towards the development of an accurate force field potential. Next-generation atomistic force fields include polarization effects for the simula- tion1 ofintroduction biomolecular systems. How this apparent change happened is a different story, to explain this generational transition we begin our study in the late 1950s. Physicists Bernie Alder and Thomas Wainwright were the first to translate digital computation into the study of many particle systems.[1] Eventually, the offspring of their research brought the simulation method called molecular dynamics (MD) to reality. Currently, classical MD simulation methods are being applied to study a multitude of physical, chemical, and biological systems, ranging from pure liquids to large complex systems such as proteins and cell membranes. [2, 3] As a result atomistic simulations have become an important tool to understand fundamental processes of biological systems. Since the pioneering work of Alder and Wainwright, computing performance has increased by more than trillion fold.[4] This rapid development of digital machines lead to the expansion of system sizes and increase of timescales. As this was not the only advancement, since technological advancement inspired in an equal man- ner the drive to search for faster, more efficient and accurate underlying physical models for our simulation methods. In response a diverse set of atomistic sim- ulations methods developed (co-)independently for the simulation of electrolytes, ionic liquids, metal organic frame works, biomolecular systems, and other types of nano-materials. In this study we will keep our attention focused on the simulation of biomolecular systems. For this particular simulation field, the inclusion of explicit polarization effect has dominated the evolutionary process towards obtaining an improved de- scription of the systems under investigation. To understand the reasons why the biomolecular simulation community chose to include polarization effects into the force fields: basics, caveats and extensions 4 atomistic model, we will let ourselves get inspired by the following remarkable ob- servation: The number of reviews that specifically address recent developments in polarizable force fields is numerous: [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. This (incomplete) selection of publications account together for more than 2000 citations according to Google Scholar. The period over which these reviews span, from 2001 till the present, amounts to almost two decades. Therefore, it might be fruitful to ask ourselves the following question: what has changed in the outlook on polarizable force field development during the last 20 years? First, this approach will allow us to assess the progress made and may show us the edge of where polarizable force fields are right now. Second, this method could expose whether there are persistent factors that hamper our progress towards a po- larizable force field for general use in biomolecular simulation. After the evaluation of this question we will discuss the open ends and look forward to how these new challenges can be solved. This will include the exploration of how Machine Learn- ing (ML) methods and novel sampling techniques can aid towards the development of general use biomolecular force fields. Finally, we will summarise these efforts and provide an outlook on the current status of polarizable force field development for biomolecular simulations. Before we will proceed with an analysis of the aforementioned reviews we will provide2 force the necessary fields: background basics, information caveats to understand and extensions what is about to be discussed. The next sections will therefore explain the basics behind force fields together with the caveats of choosing a model that is based on fixed point charges, i.e., a non-polarizable force field. The first section discusses the components of the potential-energy function in terms of bonded and non-bonded interactions and seemingly continues with the caveats related to this classical approach. This next section will focus on the methods used to refine the model for its intent and purpose. Finally, the contributions of anisotropic charge distributions are discussed in the last section. In2.1 molecularThe Classical dynamics Approach (MD) simulations are the atoms more often than not treated as point-like particles. Their reciprocal interactions in combination with the dy- namic equations of motion determine how the system will evolve over time. This simple approach is well suited to simulate the collective behavior of atoms in molec- ular structures and ensembles. Moreover, when a few assumptions are set aside, this level of theory can determine both the micro- and macroscopic properties of the respective system within the line of expectations. [17] However, there is still plenty of room for uncertainty to develop during the course of the simulation. The biggest assumption that makes atomistic simulations to some extent a conjecture is the lack of an explicit expressions for electrons. In addition, the lack hereof assumes that the system is always in the electronic ground state. force fields: basics, caveats and extensions 5 As it where, these factors seem like a major shortcoming for creating a faithful molecular model. But, the simplicity of the atomistic model is also its greatest strength. Accounting for the electronic behavior implicitly allows for long simula- tion times up to the regime of µs, while maintaining relative low computational cost.[18, 19, 20] Given the reason for treating atoms as simple particles, how do we resolve the need for inclusion of fundamental electrostatic effects without turning to on-the-fly quantum mechanical calculations? Atomistic simulation methods have developed an implicit way to account for the existence and effects of electrons. The electronic energy is formulated as a para- metric function of the nuclear coordinates and corresponding parameters are sub- sequently fitted to experimental or higher level computational data. Such a param- eterised potential that describes all forces in the system is called a force field. This description allows us to think more pragmatic about what chemistry conveys in molecular simulations. Simply put, chemistry becomes the knowing of the energy as a function of nuclear coordinates and molecular properties become the knowing of how the energy changes upon adding a perturbation to the system. [17] Deter- mining the physics using this approach is justified in classical mechanics, because this is the basis of methods that give access to the Boltzmann weighted ensembles from which macroscopic properties of the system directly follow. [21] Still, there are numerous ways to construction of such energy functions. In the following section we will therefore discuss the most important components for the construction of a force field. An atomistic-potential energy function 2.1.1 Schematic illustration of the terms in a classical fixed-charge
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