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Nanocarbon structures, such as fullerenes and nanotubes, have generated considerable interest and research, due to their unique properties and potential applications. In this thesis, we present a study of the phase transition properties of nanocarbon clusters,in particular, we pay special consideration to fullerenes. The work presented in this thesis is largely theoretical and computational in nature, employing as a tool, molecular dynamics simulations to probe the dynamic stability of fullerenes and associated nanocarbon structures such as graphenes and nanotubes.
Specific functions of biological systems often require conformational transitions of macromolecules. Thus, being able to describe and predict conformational changes of biological macromolecules is not only important for understanding their impact on biological function, but will also have implications for the modelling of (macro)molecular complex formation and in structure-based drug design approaches. The “conformational selection model” provides the foundation for computational investigations of conformational fluctuations of the unbound protein state. These fluctuations may reveal conformational states adopted by the bound proteins. The aim of this work is to incorporate directional information in a geometry-based approach, in order to sample biologically relevant conformational space extensively. Interestingly, coarse-grained normal mode (CGNM) approaches, e.g., the elastic network model (ENM) and rigid cluster normal mode analysis (RCNMA), have emerged recently and provide directions of intrinsic motions in terms of harmonic modes (also called normal modes). In my previous work and in other studies it has been shown that conformational changes upon ligand binding occur along a few low-energy modes of unbound proteins and can be efficiently calculated by CGNM approaches. In order to explore the validity and the applicability of CGNM approaches, a large-scale comparison of essential dynamics (ED) modes from molecular dynamics (MD) simulations and normal modes from CGNM was performed over a dataset of 335 proteins. Despite high coarse-graining, low frequency normal modes from CGNM correlate very well with ED modes in terms of directions of motions (average maximal overlap is 0.65) and relative amplitudes of motions (average maximal overlap is 0.73). In order to exploit the potential of CGNM approaches, I have developed a three-step approach for efficient exploration of intrinsic motions of proteins. The first two steps are based on recent developments in rigidity and elastic network theory. Initially, static properties of the protein are determined by decomposing the protein into rigid clusters using the graph-theoretical approach FIRST at an all-atom representation of the protein. In a second step, dynamic properties of the molecule are revealed by the rotations-translations of blocks approach (RTB) using an elastic network model representation of the coarse-grained protein. In the final step, the recently introduced idea of constrained geometric simulations of diffusive motions in proteins is extended for efficient sampling of conformational space. Here, the low-energy (frequency) normal modes provided by the RCNMA approach are used to guide the backbone motions. The NMSim approach was validated on hen egg white lysozyme by comparing it to previously mentioned simulation methods in terms of residue fluctuations, conformational space explorations, essential dynamics, sampling of side-chain rotamers, and structural quality. Residue fluctuations in NMSim generated ensemble is found to be in good agreement with MD fluctuations with a correlation coefficient of around 0.79. A comparison of different geometry-based simulation approaches shows that FRODA is restricted in sampling the backbone conformational space. CONCOORD is restricted in sampling the side-chain conformational space. NMSim sufficiently samples both the backbone and the side-chain conformations taking experimental structures and conformations from the state of the art MD simulation as reference. The NMSim approach is also applied to a dataset of proteins where conformational changes have been observed experimentally, either in domain or functionally important loop regions. The NMSim simulations starting from the unbound structures are able to reach conformations similar to ligand bound conformations (RMSD < 2.4 Å) in 4 out of 5 cases of domain moving proteins. In these four cases, good correlation coefficients (R > 0.7) between the RMS fluctuations derived from NMSim generated structures and two experimental structures are observed. Furthermore, intrinsic fluctuations in NMSim simulation correlate with the region of loop conformational changes observed upon ligand binding in 2 out of 3 cases. The NMSim generated pathway of conformational change from the unbound structure to the ligand bound structure of adenylate kinase is validated by a comparison to experimental structures reflecting different states of the pathway as proposed by previous studies. Interestingly, the generated pathway confirms that the LID domain closure precedes the closing of the NMPbind domain, even if no target conformation is provided in NMSim. Hence, the results in this study show that, incorporating directional information in the geometry-based approach NMSim improves the sampling of biologically relevant conformational space and provides a computationally efficient alternative to state of the art MD simulations.
This work presents a contribution to the literature on methods in search of lowdimensional models that yield insight into the equilibrium and kinetic behavior of peptides and small proteins. A deep understanding of various methods for projecting the sampled configurations of molecular dynamics simulations to obtain a low-dimensional free energy landscape is acquired. Furthermore low-dimensional dynamic models for the conformational dynamics of biomolecules in reduced dimensionality are presented. As exemplary systems, mainly short alanine chains are studied. Due to their size they allow for performing long simulations. They are simple, yet nontrivial systems, as due to their flexibility they are rapidly interconverting conformers. Understanding these polypeptide chains in great detail is of considerable interest for getting insight in the process of protein folding. For example, K. Dill et al. conclude in their review [28] about the protein folding problem that "the once intractable Levinthal puzzle now seems to have a very simple answer: a protein can fold quickly and solve its large global optimization puzzle simply through piecewise solutions of smaller component puzzles".
This thesis contributes to the field of soft matter research and studies the importance of hydrodynamic interactions during free-solution electrophoresis of linear polyelectrolytes by means of coarse-grained molecular dynamics simulations including full electro-hydrodynamic interactions. The center of attention is the specific role of hydrodynamic interactions on the electrophoretic behaviour of charged macromolecules. Points of interest are the dependence of hydrodynamic interactions on the chain length, the chain flexibility and the surrounding counterions, and their combined influence on important observables such as the static chain conformations and the dynamic transport coefficients, i.e., the diffusion and the electrophoretic mobility. These problems are addressed by extensive computer simulations that are quantitatively matched with experimental results. Existing theoretical predictions are carefully examined and are augmented by the observations in this thesis.