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The most critical biochemistry in an organism supports the central dogma of molecular biology: transcription of DNA to RNA and translation of RNA to peptide sequence. Proteins are then responsible for catalyzing, regulating and ensuring the fidelity of transcription and translation. At the heart of these processes lie selective biomolecular interactions and specific dynamics that are necessary for complex formation and catalytic activity. Through advanced biophysical and computational methods, it has become possible to probe these macromolecular dynamics and interactions at the molecular and atomic levels to tease out their underlying physical bases. To the end of a more thorough understanding of these physical bases, we have performed studies to probe the motions and interactions intrinsic to the function of biomolecular complexes: modeling the dual-base flipping strategy of alkylpurine glycosylase D, dynamically tracing evolution and epistasis in the 3-ketosteroid family of nuclear receptors, discovering the allosteric and conformational aspects of transcription regulation in liver receptor homologue 1, leveraging specific contacts in tyrosyl-DNA phosphodiesterase 2 for the development of novel inhibitor scaffolds, and detailing the experimentally observed connection between solvation and sequence-specific binding affinity in PU.1-DNA complexes at the atomic level. While each study seeks to solve system-specific problems, the collection outlines a general and broadly applicable description of the biophysical motivations of biochemical processes.

Introduction Understanding the intricate workings of biological systems at the molecular level is crucial for unraveling the complex mechanisms that underlie Life itself. Proteins and RNA, two essential components of cellular structure and processes, exhibit remarkable structural and functional diversity. Traditional experimental techniques have provided valuable insights into their behaviors; however, they often fall short in capturing the dynamic nature of these biomolecules. Over the past few decades, multiscale molecular dynamics (MD) simulations have emerged as a powerful computational tool to bridge this gap, enabling the study of biological systems at an atomistic resolution. My Ph.D. thesis aims to delve into the realm of multiscale MD simulations to unravel the dynamic landscape of proteins and RNA, shedding light on their folding mechanisms, conformational transitions, and functional dynamics. By integrating the principles of classical, atomistic MD and more advanced modelling techniques, such as coarse-grained models, this research endeavors to highlight and possibly propose ways to overcome the limitations of conventional simulations and offer a comprehensive understanding of the complex dynamics governing these biomolecules. Chapter 1 The first chapter of the thesis provides a comprehensive overview of the theoretical foundations and practical aspects of classical all-atom molecular dynamics (MD) simulations. It begins with a schematic derivation of the all-atom MD equations, emphasizing the integration of electronic degrees of freedom and their contribution to the potential energy. The chapter then focuses on the energy terms utilized in all-atom force fields, highlighting their significance in accurately representing the interactions among atoms. The discussion extends to the theoretical underpinnings of thermostats, drawing from statistical mechanics principles to elucidate their role in controlling temperature during simulations. Furthermore, the use of periodic boundary conditions and the particle mesh Ewald method are discussed, highlighting their importance in simulating (or at least mimicking) large systems and accounting for long-range electrostatic interactions. By delving into these foundational concepts and techniques, this chapter establishes the groundwork for subsequent investigations in multiscale molecular dynamics simulations. Chapter 2 The second chapter focuses on the characterization of the conformational space of the Shwachman-Bodian-Diamond syndrome (SBDS) protein, a critical component involved in cellular processes. Specifically, this research employs all-atom molecular dynamics simulations to study the wild-type SBDS and 12 missense mutations of clinical relevance. The simulations are initiated with two distinct NMR structures representing an open and a closed conformation, respectively, to capture a wide range of conformational variability. Each starting conformation is simulated for the wild type and all 12 mutations, resulting in a total of 26 simulations with a cumulative sampling time of 13$\mu s$. The analyses of these extensive simulations provide valuable insights into the effects of missense mutations on SBDS dynamics and function. The investigation reveals a common trend among all mutations, characterized by increased residue fluctuations in the hinge I-II region. This observation suggests potential interference with the conformational changes involving the reorientation of domains II-III and the detachment of eIF6 from the 60S subunit. Furthermore, the study highlights the structural similarity of the K67E mutation to the wild type, despite a lower exposed positive charge. This finding, supported by free energy analysis, suggests that the pathological mechanism associated with this mutation may be linked more closely to a decrease in binding affinity rather than structural deformation. Additionally, the simulations of R19Q and C84R exhibit lower binding affinity specifically in closed trajectories, corroborating experimental observations regarding their potential impact on RNA binding. Moreover, K151 and R218 reveal importance in stabilizing the conformation assumed by SBDS upon binding with the 60S subunit. Notably, the dynamics-based clustering and free energy analysis highlight the distinct behavior of the K151N mutation, both in open and closed simulations, suggesting that compromised dynamics may hinder the protein's ability to stabilize a functional conformation for effective cooperation with EFL1. Collectively, this chapter contributes to our understanding of SBDS dynamics and the effects of missense mutations, paving the way for further investigations into the molecular mechanisms underlying Shwachman-Diamond syndrome. Chapter 3 The third chapter explores the principles and applications of coarse-graining (CG) and multiscale modeling techniques in computational biophysics. After providing a theoretical foundation for CG, the chapter presents several examples of CG models employed in the research. This includes the implementation of Elastic Network Models (ENMs), which capture the essential dynamics of proteins by simplifying their atomistic representation. Additionally, the oxRNA model, designed specifically for RNA molecules, and the CANVAS multi-resolution model for proteins are introduced, showcasing their ability to capture the key features of the molecular system while significantly reducing computational complexity. Furthermore, the chapter delves into the theory of implicit solvation, as it plays a crucial role in some of the aforementioned models. Implicit solvation methods enable the efficient treatment of solvent effects without explicitly simulating water molecules, thereby reducing computational costs. Notably, the chapter sets the stage for the subsequent chapter by introducing the concept of implicit solvation, as chapter 5 presents a novel technique for implicit solvation based on Artificial Neural Networks. By providing an in-depth exploration of CG and multiscale modeling techniques, along with their associated solvation models, this chapter equips readers with the necessary tools to understand the methods developed to effectively study large-scale biological systems with reduced computational demands. Chapter 4 The fourth chapter, extracted from the paper \textit{``In search of a dynamical vocabulary: a pipeline to construct a basis of shared traits in large-scale motions of proteins'', published in Applied Sciences, introduces a structure-based pipeline for capturing the main features of large-scale protein motions. The pipeline aims to provide a general description of protein motion, not only for those proteins whose structures are used as input but also for structurally similar proteins that were not included in the initial dataset. To demonstrate the effectiveness of the pipeline, the research applied it to a set of 116 chymotrypsin-related proteases. By employing the presented workflow, the study successfully captured dynamical features of proteins that are structurally similar to, but not part of, the input structures used to build the basis set of the dynamical space of the proteins. This allows a comprehensive understanding of the shared traits in large-scale motions, facilitating the characterization of protein dynamics beyond the limitations of specific protein structures. Overall, this chapter highlights the development and application of a structure-based pipeline that enables the extraction of essential dynamic features from proteins, contributing to the establishment of a comprehensive dynamical vocabulary in the study of protein motion. Chapter 5 The fifth chapter introduces a novel method for implicit solvation of biomolecules in molecular dynamics simulations, leveraging the power of artificial neural networks (ANN). The chapter begins by formally describing the methodology, starting with the architecture of ANN. The latter are trained to predict the free energy of solvation for each atom in the system at every time step of the simulation. The inputs to the network are derived from special symmetry functions, which capture the local environment of each atom. The output of the ANN provides the necessary information to extract forces, which are subsequently integrated into the equations of motion. Moreover, the chapter presents the algorithmic implementation of the method into the LAMMPS molecular dynamics software package, enabling its practical application to a wide range of molecular systems. To assess the performance and accuracy of the method, three test cases are examined: the alanine dipeptide, the icosalanine (a polymer composed of 20 alanine amino acids), and a small RNA fragment containing approximately 1000 atoms. The results of the tests indicate that the method performs well in describing general macroscopic features of the molecules. However, it exhibits limitations in accurately predicting high-resolution properties, such as specific minima in the Ramachandran space of dihedral angles for the alanine dipeptide or the precise hydrogen bond network among the bases in the RNA fragment. Despite these limitations, the method demonstrates promising computational performance and scalability, making it a valuable tool for efficient implicit solvation simulations. Overall, this chapter presents a new approach to implicit solvation using artificial neural networks, showcasing its potential for accurately describing general molecular features while highlighting areas for further refinement. The method holds promise for enabling large-scale simulations with reduced computational costs, thereby expanding the scope of molecular dynamics studies. Chapter 6 The sixth chapter presents the results of a comprehensive and multi-resolution molecular dynamics study focusing on a virion particle of the Chlorotic Cowpea Mottle Virus (CCMV) and its constituent molecules. The chapter encompasses various MD simulations, each offering unique insights into the dynamics and behavior of the viral components. The first set of simulations investigates the coarse-grained folding and relaxation of the RNA2 viral single-stranded RNA (ssRNA) fragment. The simulations start with a free, rod-like polymer chain configuration, and the subsequent folding and relaxation processes are examined. Furthermore, non-equilibrium squeezing of the folded RNA structure into a spherical region of space, mimicking the confinement within the capsid, is explored. These simulations are aimed at shedding light on the structural and dynamic aspects of viral RNA during the self-assembly process of the virus. The chapter then proceeds to present multi-resolution equilibrium simulations of a trimer, which consists of three capsid molecules. The trimer is studied using five different approaches: all-atom representation in explicit solvent, all-atom representation in implicit solvent employing Debye-Huckel electrostatics, and three different applications of the CANVAS model. The latter is a model multi-resolution for proteins, developed in my group, which combines atomistic force fields together with an elastic network model to describe protein dynamics with manually deployed levels of resolution. These simulations allow for a comprehensive analysis of the trimer's dynamics and interactions, highlighting the influence of different models on the observed behavior, as well as testing the applicability of the CANVAS model to this kind of system. Additionally, all-atom simulations are performed for both the capsid and the virion, which includes the RNA2 fragment within the capsid, in explicit solvent. These simulations provide detailed information about the structural and dynamic properties of the viral capsid and the interactions between the capsid and the encapsulated RNA2 fragment. By leveraging multi-resolution approaches and conducting various simulations at different levels of detail, this chapter offers a comprehensive understanding of the RNA dynamics, folding, relaxation, and interactions within the virion particle of CCMV. These findings contribute to our knowledge of viral assembly and the behavior of viral constituents, facilitating further insights into the functioning and stability of viral systems.

This is a problem of sampling. The number of classical states of an N-body system grows with O( 3 ^ N ). To sample this space, advanced techniques are required. Replica Exchange (RE), also known as parallel tempering, is an example that uses parallelization, and Hamiltonian Replica Exchange is a subset of RE that scales the energy of the replicas. The number of simulations required grows at O( N^(1/2) ), where N is number of atoms in the system. Replica Exchange with Dynamical Scaling (REDS) attempts to address this problem to decrease computational cost. It has been shown to increase efficiency 10-fold. We implemented REDS in GROMACS 2018. (Abraham 2015) All changes to the source code were written in the form of parallel methods. Scripts were written in Python and Perl to automate the experiment entirely. An exchange connects a region of high energy space, far above the surface of the landscape, to low energy space, which approaches the surface of the landscape, which represents the natural conformational progression of the molecule. Using REDS we were able to achieve exchanges at temperatures spaced too far apart to exchange using normal RE. Ergo, the flexibility of dynamical scaling allowed regions of phase space that would have gone unsampled to be mapped, addressing our initial problem of sampling.

abstract: Proteins are essential for most biological processes that constitute life. The function of a protein is encoded within its 3D folded structure, which is determined by its sequence of amino acids. A variation of a single nucleotide in the DNA during transcription (nSNV) can alter the amino acid sequence (i.e., a mutation in the protein sequence), which can adversely impact protein function and sometimes cause disease. These mutations are the most prevalent form of variations in humans, and each individual genome harbors tens of thousands of nSNVs that can be benign (neutral) or lead to disease. The primary way to assess the impact of nSNVs on function is through evolutionary approaches based on positional amino acid conservation. These approaches are largely inadequate in the regime where positions evolve at a fast rate. We developed a method called dynamic flexibility index (DFI) that measures site-specific conformational dynamics of a protein, which is paramount in exploring mechanisms of the impact of nSNVs on function. In this thesis, we demonstrate that DFI can distinguish the disease-associated and neutral nSNVs, particularly for fast evolving positions where evolutionary approaches lack predictive power. We also describe an additional dynamics-based metric, dynamic coupling index (DCI), which measures the dynamic allosteric residue coupling of distal sites on the protein with the functionally critical (i.e., active) sites. Through DCI, we analyzed 200 disease mutations of a specific enzyme called GCase, and a proteome-wide analysis of 75 human enzymes containing 323 neutral and 362 disease mutations. In both cases we observed that sites with high dynamic allosteric residue coupling with the functional sites (i.e., DARC spots) have an increased susceptibility to harboring disease nSNVs. Overall, our comprehensive proteome-wide analysis suggests that incorporating these novel position-specific conformational dynamics based metrics into genomics can complement current approaches to increase the accuracy of diagnosing disease nSNVs. Furthermore, they provide mechanistic insights about disease development. Lastly, we introduce a new, purely sequence-based model that can estimate the dynamics profile of a protein by only utilizing coevolution information, eliminating the requirement of the 3D structure for determining dynamics. / Dissertation/Thesis / Doctoral Dissertation Physics 2016

A new metric for the quantitative and qualitative evaluation of bone stiffness is introduced. It is based on the spectral decomposition of stiffness matrix computed with finite element method. The here proposed metric is defined as an amplitude rescaled eigenvalues of stiffness matrix. The metric contains unique information on the principal stiffness of bone and reflects both bone shape and material properties. The metric was compared with anthropometrical measures and was tested for sex sensitivity on pelvis bone. Further, the smallest stiffness of pelvis was computed under a certain loading condition and analyzed with respect to sex and direction. The metric complements anthropometrical measures and provides a unique information about the smallest bone stiffness independent from the loading configuration and can be easily computed by state-of-the-art subject specified finite element algorithms.

Low-resolution, coarse-grained models are powerful computational tools to investigate the behavior of biological systems over time and length scales that are not accessible to all-atom Molecular Dynamics simulations. While several algorithms exist that aim at constructing accurate coarse-grained potentials, few works focus on the choice of the reduced representation, or mapping, to be employed to describe the high-resolution system with a lower number of degrees of freedom. This thesis proposes a series of approaches to investigate and characterise the representation problem in coarse-grained modelling of proteins. This is achieved by employing a collection of diverse methods, including statistical mechanics, machine learning algorithms and information-theoretical tools. The central mathematical object of this work is the mapping entropy, a Kullback-Leibler divergence that measures the intrinsic quality of a given reduced representation. When this quantity is minimised, we obtain the maximally informative coarse-grained mappings of a biomolecule, which cover the structure with an uneven level of detail. Tests conducted over a set of well-known proteins show that regions preserved with high probability are often related to important functional mechanisms of the molecule. Applications of the mapping entropy outside of the field of structural biology show promising results, leading to the identification of those combinations of features that retain the maximum amount of information about the high-resolution system. Additionally, a purely structural notion of scalar product and distance between coarse-grained mappings is introduced, which allow to analyse the metric and topological properties of the mapping space. The thorough exploration of such space leads to the discovery of qualitatively different reduced representations of the biomolecule of interest.

Proteins are one of the most studied biological molecules of the last decades. A great amount of experimental techniques provide to researchers direct or indirect informations on proteins structure and function. In silico simulations can be used as a “computational microscope” giving the possibility to observe protein dynamic properties at atomistic resolution. In this work, various applications of computational methods to biological systems are presented. In particular, all-atom Molecular Dynamics (MD) simulations were employed to investigate the behaviour of proteins at atomstic resolution. The term “Molecular Dynamics” is usually referred to computational methods used for the simulation of classical many-body systems. These techniques are applied to microscopic systems and they represent a powerful approach for the study of physical processes, providing a tool for their interpretation. They have been widely used in the past decades to elucidate a large variety of molecular processes in different fields such as solid state physics, material science, chemistry, biochemistry and biophysics. Here, all-atom MD simulations were employed to observe equilibrium properties of several biologically relevant proteins. This allowed us to direct perform a comparison of molecular mechanisms occurring at the atomistic level as obtained from in silico studies with experimental data, which usually describe processes at larger length and time scales. These MD simulations were also meant as a starting point for the construction of simplified models, as they were processed through coarse-graining procedures to extrapolate crucial systems features, such as informative protein sites, on the basis of information theory approaches. Specifically we studied the dynamics of pembrolizumab, a humanized immunoglobulin of type G4 (IgG4) used as a therapeutic antibody. It is employed for the treatment of lung cancer, melanoma, stomach and head cancer and Hodgkin’s lymphoma. This antibody interacts with the programmed cell death protein 1 (PD-1) receptor, blocking the suppression of the immune response during cancer development. The studied systems are three: the apo state of pembrolizumab, the holo state (i.e. pembrolizumab bound to PD-1) and the glycosylated apo configuration. Each configuration was simulated for 2μs, for a total of 6μs. The analysis of the trajectories was carried out by combining standard structural analysis techniques and information theory-based measures of correlation. From MD trajectories we could extract valuable informations on the connectivity that exists among the structural domains that compose the antibody structure. Moreover, it was possible to infer which regions are involved in the structural rearrangement in the case of the antigen binding. We could observe that the presence of the antigen reduces the conformational variability of the molecule giving a greater stability to it. The second studied system is the P53 protein complex. In this case we focused on the tetramerization domain (TD) region that is composed by 2 identical dimers and has the function of bringing together the four monomers of the p53 complex. Starting from the observation that in case of the mutation of residue R337 several pathologies are developed in humans, we constructed computational models to reproduce the dynamics of the mutants and investigate their behaviour in silico. We performed simulations for a total of 16 μs divided in 8 different cases. In the first part of the study the wild type (WT) protein was compared to the R337C and the R337H mutant in three different protonation states: delta protonated Histidine, epsilon protonated Histidine ad double protonated Histidine. In the second part of the study we highlighted the differences between the WT configuration and three rationally designed mutants: R337D-352D, 337R-D352R, R337D-D352R. In this part of the investigation, the importance of the electrostatic interaction between residues R337 and D352 in the stability of the tetramerization do- main was discussed. Furthermore, we matched the obtained computational results of p53 tetramerization domain with functional experiments in yeasts (performed in collaboration with the CIBIO department) of all the simulated forms. The third simulated protein is the zinc sensing transcriptional repressor (CzrA), an homodimeric protein that binds DNA in Staphylococcus aureus. All-atom MD simulations of two different configurations were performed for a total of 4μs, the first one is the WT apo protein while the second is the WT holo system, where the protein is complexed with two Zn ions. In this case, in addition to standard analysis techniques, we applied the mapping entropy minimization protocol to highlight the most informative protein regions, from the perspective of information theory. Finally, our in silico results were compared to available NMR data of the protein itself.

The 20th century saw the first revolution of quantum mechanics, setting the rules for our understanding of light, matter, and their interaction. The 21st century is focused on using these quantum mechanical laws to develop technologies which allows us to solve challenging practical problems. One of the directions is the use quantum devices which promise to surpass the best computers and best known classical algorithms for solving certain tasks. Crucial to the design of realistic devices and technologies is to account for the open nature of quantum systems and to cope with their interactions with the environment. In the first part of this dissertation, we show how to tackle classical optimization problems of interest in the physical sciences within one of these quantum computing paradigms, known as quantum annealing (QA). We present the largest implementation of QA on a biophysical problem (six different experiments with up to 81 superconducting quantum bits). Although the cases presented here can be solved on a classical computer, we present the first implementation of lattice protein folding on a quantum device under the Miyazawa-Jernigan model. This is the first step towards studying optimization problems in biophysics and statistical mechanics using quantum devices. In the second part of this dissertation, we focus on the problem of excitonic energy transfer. We provide an intuitive platform for engineering exciton transfer dynamics and we show that careful consideration of the properties of the environment leads to opportunities to engineer the transfer of an exciton. Since excitons in nanostructures are proposed for use in quantum information processing and artificial photosynthetic designs, our approach paves the way for engineering a wide range of desired exciton dy- namics. Finally, we develop the theory for a two-dimensional electronic spectroscopic technique based on fluorescence (2DFS) and challenge previous theoretical results claiming its equivalence to the two-dimensional photon echo (2DPE) technique which is based on polarization. Experimental realization of this technique confirms our the- oretical predictions. The new technique is more sensitive than 2DPE as a tool for conformational determination of excitonically coupled chromophores and o↵ers the possibility of applying two-dimensional electronic spectroscopy to single-molecules.

During tissue invasion individual tumor cells exhibit two interconvertible migration modes, namely mesenchymal and amoeboid migration. The cellular microenvironment triggers the switch between both modes, thereby allowing adaptation to dynamic conditions. It is, however, unclear if this amoeboid-mesenchymal migration plasticity contributes to a more effective tumor invasion. We address this question with a mathematical model, where the amoeboid-mesenchymal migration plasticity is regulated in response to local extracellular matrix resistance. Our numerical analysis reveals that extracellular matrix structure and presence of a chemotactic gradient are key determinants of the model behavior. Only in complex microenvironments, if the extracellular matrix is highly heterogeneous and a chemotactic gradient directs migration, the amoeboid-mesenchymal migration plasticity allows a more widespread invasion compared to the non-switching amoeboid and mesenchymal modes. Importantly, these specific conditions are characteristic for in vivo tumor invasion. Thus, our study suggests that in vitro systems aiming at unraveling the underlying molecular mechanisms of tumor invasion should take into account the complexity of the microenvironment by considering the combined effects of structural heterogeneities and chemical gradients on cell migration.