Contrary to the traditional structure-function paradigm for proteins, intrinsically disorderedproteins (IDPs) and regions (IDRs) are highly disordered sequences that lack a fixed crystal structure yet perform various biological activities such as cell signaling, regulation, and recognition. The interactions of these disordered regions with water molecules are essential in the conformational distribution. Hence, exploring their solvation thermodynamics is crucial for understanding their functions, which are challenging to study experimentally. In this thesis, classical Molecular Dynamics (MD), 3D-Two Phase Thermodynamics (3D- 2PT), and umbrella sampling have been employed to gain insights into the behaviors of intrinsically disordered proteins (IDPs) and water. In the first project, local and total solvation thermodynamics around the K-18 domain of the intrinsically disordered protein Tau were compared, and simulated with four pairs of modified and standard force fields. In empirical force fields, an imbalance between intramolecular protein interactions and protein-water interactions often leads to collapsed IDP structures in simulations. To counter this, various methods have been devised to refine protein-water interaction models. This research applied both standard and adapted force fields in simulations, scrutinizing the effects of each adjustment on solvation free energy. In the second project, the MD-based 3D-2PT analysis was utilized to examine variations in local entropy and number density of bulk water in response to an electric field, focusing on the vicinity of reference water molecules. In the third project, various peptide sequences were examined to quantify the free energy involved when specific sequences, known as alpha-MoRFs (alpha-Molecular Recognition Features), transition from intrinsically disordered states to structured secondary motifs like the alpha-helix. The low folding free energy penalty of these sequences can be exploited to design peptide-based or small-molecule drugs. Upon binding to alpha-MoRFs, these drugs can stabilize the helix structure through a binding-induced folding mechanism. Alpha-MoRFs were juxtaposed with entirely disordered sequences from known proteins, with findings benchmarked against leading structure prediction models. Additionally, the binding free energies of various alpha-MoRFs in their folded conformation were assessed to discern if experimental binding free energies reflect the separate contributions of folding and binding, as obtained from umbrella sampling simulations.

Computational biophysics is a powerful tool for observing and understanding the microscopic machinery that underpins the biological world. Molecular modeling and simulations can help scientists understand a cell’s behavior and the mechanisms that drive it. Empirical evidence can provide information on the structure and organization of biomolecular machines, which serve as the backbone of biomolecular modeling. Experimental data from probing the cell’s inner workings can provide modelers with an initial structure from which they can hypothesize and independently verify function, complex formation, and response. Additionally, molecular data can be used to drive simulations toward less probable but equally interesting states. With the advent of machine learning, researchers now have an unprecedented opportunity to take advantage of the wealth of data collected in a biomolecular experiment. This dissertation presents a comprehensive review of atomistic modeling with cryo-electron microscopy and the development of new simulation strategies to maximize insights gained from experiments. The review covers the integration of cryo-EM and molecular dynamics, highlighting the evolution of their relationship and the recent history of MD innovations in cryo-EM modeling. It also covers the discoveries made possible by the integration of molecular modeling with cryo-EM. Next, this work presents a method for fitting small molecules into cryo-electron microscopy maps, which uses neural network potentials to parameterize a diverse set of ligands. The method obtained fitted structures commensurate with, if not better than, the structures submitted to the Protein Data Bank. Additionally, the work describes the data-guided Multi- Map methodology for ensemble refinement of molecular movies. The method shows that cryo-electron microscopy maps can be used to bias simulations along a specially constructed reaction coordinate and capture conformational transitions between known intermediates. The simulated pathways appear reversible with minimal hysteresis and require only low-resolution density information to guide the transition. Finally, the study analyzes the SARS-CoV-2 spike protein and the conformational heterogeneity of its receptor binding domain. The simulation was guided along an experimentally determined free energy landscape. The resulting motions from following a pathway of low-energy states show a degree of openness not observed in the static models. This sheds light on the mechanism by which the spike protein is utilized for host infection and provides a rational explanation for the effectiveness of certain therapeutics. This work contributes to the understanding of biomolecular modeling and the development of new strategies to provide valuable insights into the workings of cellular machinery.

Transition metal ions such as Zn2+, Mn2+, Co2+, and Fe2+ play crucial roles in organisms from all kingdoms of life. The homeostasis of these ions is mainly regulated by a group of secondary transporters from the cation diffusion facilitator (CDF) family. The mammalian zinc transporters (ZnTs), a subfamily of CDF, have been an important target for study as they are associated with several diseases, such as diabetes, delayed growth and osteopenia, Alzheimer’s disease, and Parkinsonism. The bacterial homolog of ZnTs, YiiP, is the first CDF transporter with a determined structure and is used as a model for studying the structural and mechanistic properties of CDF transporters. On the other hand, Molecular dynamics simulation has emerged as a valuable computational tool for exploring the physical basis of biological macromolecules' structure and function with atomic precision at femtosecond resolution. This work aims to elucidate the roles of the three Zn$2+ binding sites found on each YiiP protomer and the role of protons in the transport process of CDFs, which remain under debate despite previous thermodynamic and structural studies on YiiP. Cryo-EM, microscale thermophoresis (MST) and molecular dynamics (MD) simulations were used to address these questions. With a Zn2+ model that accurately reproduces experimental structures of the binding clusters, the dynamical influence of zinc binding on the transporter was accessed through MD simulations, which was consistent with the new cryo-EM structures. Zinc binding affinities obtained through MST were used to infer the stoichiometry of Zn2+/H+ antiport in combination with a microscopic thermodynamic model and constant pH simulations. The most likely microstates of H$^+$ and Zn2+ binding indicated a transport stoichiometry of 1 Zn2+ to 2-3 H+ depending on the external pH. A model describing the entire transport cycle of YiiP was finally built on these findings, providing insight into the structural and mechanistic properties of CDF transporters.

As a rapidly evolving field, nucleic acid nanotechnology focuses on creating functional nanostructures or dynamic devices through harnessing the programmbility of nucleic acids including deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), enabled by the predictable Watson-Crick base pairing. The precise control over the sequence and structure, along with the development of simulation softwares for the prediction of the experimental implementation provides the base of designing structures or devices with arbitrary topology and operational logic at nanoscale. Over the past 40 years, the thriving field has pushed the boundaries of nucleic acids, from originally biological macromolecules to functional building blocks with applications in biomedicine, molecular diagnostics and imaging, material science, electronics, crystallography, and more have emerged through programming the sequences and generating the various structures or devices. The underlying logic of nucleic acid programming is the base pairing rule, straightforward and robust. While for the complicated design of sequences and quantitative understanding of the programmed results, computational tools will markedly reduced the level of difficulty and even meet the challenge not available with manual effort. With this thesis three individual projects are presented, with all of them interweaving theory/computation and experiments. In a higher level abstraction, this dissertation covers the topic of biophysical understanding of the dynamic reactions, designing and realizing complex self-assembly systems and finally super-resolutional imaging. More specifically, Chapter 2 describes the study of RNA strand displacement kinetics with dedicated model extracting the reaction rates, providing guidelines for the rational design and regulation of the strand displacement reactions and eventually biochemical processes. In chapter 3 the platform for the design of complex symmetry of the self-assembly target and first experimental implementation of the assembly of pyrochlore lattices with DNA origamis are presented, which potentially can be applied to manipulate lights as optical materials. Chapter 4 focuses on the in solution characterization of the periodicity of DNA origami lattices with super-resolutional microscopy, with algorithms in development for three dimensional structural reconstruction.

Understanding solvent-mediated interactions in biomolecular systems at the molecular level is important for the development of predictive models for processes such as protein folding and ligand binding to a host biomolecule. Solvent-mediated interactions can be quantified as changes in the solvation free energy of solvated molecules. Theoretical models of solvent-mediated interactions thus need to include ensemble-averaged solute-solvent interactions. In this thesis, molecular dynamics simulations were coupled with the 3D-2PT method to decompose solvation free energies into spatially resolved local contributions. In the first project, this approach was applied to benzene derivatives to guide the development of efficient and predictive models of solvent-mediated interactions in the context of computational drug design. Specifically, the effects of carboxyl and nitro groups on solvation were studied due to their similar sterical requirements but distinct interactions with water. A system of solvation free energy arithmetics was developed and showed that non-additive contributions to the solvation free energy originate in electrostatic solute-solvent interactions, which are qualitatively reproduced by computationally efficient continuum models. In the second project, a simple model system was used to analyze hydrophilic water-mediated interactions (water-mediated hydrogen bonds), which have been previously suggested to play a key role in protein folding. Using the spatially resolved analysis of solvation free energies, the sites of bridging water molecules were identified as the primary origin of solvent-mediated forces and showed that changes in hydration shell structure can be neglected. In the third project, the analysis of solvation free energy contributions is applied to proteins in inhomogeneous electric fields to explore water-mediated contributions to protein dielectrophoresis. The results provide a potential explanation for negative dielectrophoretic forces on proteins, which have been observed experimentally but cannot be explained with previous theoretical models.

Transportation of material across a cell membrane is a vital process for maintaininghomeostasis. Na+/H+ antiporters, for instance, help maintain cell volume and regulate intracellular sodium and proton concentrations. They are prime drug targets, since dysfunction of these crucial proteins in humans is linked to heart and neurodegenerative diseases. Due to their placement in a cell membrane, their study is particularly difficult compared to globular proteins, which is likely the reason the transport mechanisms for these proteins are not entirely known. This work focuses on the electrogenic bacterial homologs Thermus thermophilus NapA (TtNapA) and Echerichia coli NhaA (EcNhaA), each transporting one sodium from the interior of the cell for two protons on outside of the cell. Even though X-ray crystal structures for both of these systems have been resolved, their study through molecular dynamics (MD) simulations is limited. The dynamic protonation and deprotonation of the binding site residues is a fundamental process in the transport cycle, which currently cannot be explored intuitively with standard MD methodologies. Apart from this limitation, simulation performance is only a fraction of what is needed to understand the full transport process, particularly when it comes to global conformational changes. This work seeks to overcome these limitations through the development and application of a multiscale thermodynamic and kinetic framework for constructing models capable of predicting experimental observables, such as the dependence of transporter turnover on membrane voltage. These models allow interpretation of the effects of individual processes on the function as a whole. This procedure is demonstrated for TtNapA and the connection between structure and function is shown by computing cycle turnover across a range of non-equilibrium conditions.

Biopolymers perform the majority of essential functions necessary for life. From a small amount of components emerges considerable complexity in both structure and function. The separated timescales of dynamic processes and intricate intra- and inter-molecular interactions of these molecules necessitate the development and utilization of computational approaches for biopolymer study and nanotechnology applications. Biopolymer nanotechnology exploits the natural chemistry of biopolymers to perform novel functions at the nanoscale. Molecular dynamics is the numerical simulation of chemical entities according to the physical laws of motion and statistical mechanics. The number of atoms in biopolymers require coarse-grained methods to fully sample the dynamics of the system with reasonable resources. Accordingly, a coarse-grained molecular dynamics model for the characterization of hybrid nucleic acid-protein nanotechnology was developed. Proteins are represented as an anisotropic network model (ANM) which show good agreement with experimentally derived protein dynamics for a small computational cost. The model was subsequently applied to hybrid DNA-protein cages systems and exhibited excellent agreement with experimental results. Ongoing development efforts look to apply network models to oxDNA origami to create multiscale models for DNA origami. The network approximation will allow for detailed simulation of DNA origami association, of concern to DNA crystal and lattice formation. Identification and design of target-specific binders (aptamers) has received considerable attention on account of their diagnostic and therapeutic potential. Generated in selection cycles from extensive random libraries, biopolymer aptamers are of particular interest due to their potential non-immunogenic properties. Machine learning leverages the use of powerful statistical principles to train a model to transform an input into a desired output. Parameters of the model are iteratively adjusted according to the gradient of the cost function. An unsupervised and generative machine learning model was applied to Thrombin aptamer sequence data. From the model, sequence characteristics necessary for binding were identified and new aptamers capable of binding Thrombin were sampled and verified experimentally. Future work on the development and utilization of an unsupervised and interpretable machine learning model for unaligned sequence data is also discussed.

The purpose of this project was to compare the different physical models behind four algorithms in computational chemistry: Molecular dynamics with a thermostat (specifically simple velocity rescaling, Berendsen, and Nosé-Hoover), Langevin dynamics, Brownian dynamics, and Monte Carlo. These algorithms were programmed in C and the impact of specific parameters, such as the coupling parameter and time step, were studied. Their results were compared based on their radial distribution functions and, when the thermostats were in use, fluctuations in temperature.

Barnase-Barstar is a protein complex that has a strong association constant. The purpose of this research is to investigate the effects of conformational fluctuations on protein-water interactions, resulting water-mediated interactions, and the binding free energy of the protein complex. Using all-atom molecular dynamics simulations, the sets of simulations for flexible and rigid proteins to identify the effects on water-mediated interactions were prepared for analysis. To analyze the properties and interactions that result in the strong association of the Barnase-Barstar protein complex, the molecular dynamics simulations were prepared. A thorough review of the GROMACS manual and completion of the GROMACS Lysozyme in Water tutorial was completed to understand the steps and commands to write and run molecular dynamics simulations. The preliminary data investigated the impact of water-mediated interactions on the solvation free energy in the Barnase-Barstar protein complex where the proteins are kept rigid. This was achieved by observing the change in solvation free energy with respect to separation distance. From the data obtained, it is concluded that solvent-mediated interactions do not contribute to the negative binding free energy. With increasing separation distance, the change in solvation free energy decreased. Therefore, thermodynamically, water-mediated interactions destabilize the protein complex, while the binding free energy is dominated by direct protein-protein interactions. The follow-up simulations of flexible proteins with controlled protein-protein separation distances, for which a fully automated simulation and analysis protocol has been prepared in this project, will allow us to quantify the impact of conformational fluctuations on water-mediated interactions and the binding free energy of the protein complex by comparison to the simulations of rigid proteins.