KOBRA: a fluctuating elastic rod model for slender biological macromolecules

Computational Biophysics lies at the intersection between biology, physics, applied mathematics and software engineering. Some of the most burning questions in molecular biology are concerned with biomechanical systems, the dynamics of which are driven by chemistry and physics. Unfortunately, we have extremely limited means to observe these dynamics experimentally. In the past, this problem has been solved with the use of molecular dynamics, sometimes referred to as a `computational microscope'. Studying biomolecules in silico can provide a wealth of new information at temporal and spatial resolutions far beyond any current imaging modality. But molecular dynamics algorithms are limited by current computing power, and by the assumptions used to construct them. The kinetochore, a supramolecular structure crucial to the process of cell division, operates on time and length scales outside the reach of atomistic molecular dynamics with current computing power. To overcome this limitation, we propose a new, coarse-grained algorithm, which allows for a more computationally inexpensive representation of the biomolecules that comprise the kinetochore. This algorithm, KOBRA (KirchOff Biological Rod Algorithm) is designed to perform dynamical simulations of elongated biomolecules such as those containing alpha-helices and coiled-coils. It represents these as coarsely-discretised Kirchoff rods, with linear elements that can stretch, bend and twist independently. These rods can have anisotropic and inhomogeneous parameters and bent or twisted equilibrium structures, allowing for a coarse-grained parameterisation of complex biological structures. Each element is non-inertial and subject to thermal fluctuations. This coarse-grained representation allows for simulations of extremely large, long-lived systems at the biological mesoscale. KOBRA has been extended with a parameterisation scheme that allows for rod parameters (in terms of stretching, bending and twisting constants) to be extracted from all-atom simulation trajectories. An all-atom representation of Ndc80C - a sub-unit of the kinetochore - was constructed, and the KOBRA parameters for the molecule were extracted from its trajectory. The KOBRA algorithm is validated against both the physics of elastic rods and the biology of Ndc80C and the kinetochore. A partial kinetochore system was constructed and simulated using KOBRA and FFEA (Fluctuating Finite Element Analysis). The resulting trajectories were analysed and used to investigate the microtubule-binding ability of Ndc80C in a variety of configurations. A C++ implementation of KOBRA is available under the GNU GPLv3 free software licence, and can http://ffea.bitbucket.io

Towards a Unification of Supercomputing, Molecular Dynamics Simulation and Experimental Neutron and X-ray Scattering Techniques

Molecular dynamics simulation has become an essential tool for scientific discovery and investigation. The ability to evaluate every atomic coordinate for each time instant sets it apart from other methodologies, which can only access experimental observables as an outcome of the atomic coordinates. Here, the utility of molecular dynamics is illustrated by investigating the structure and dynamics of fundamental models of cellulose fibers. For that, a highly parallel code has been developed to compute static and dynamical scattering functions efficiently on modern supercomputing architectures. Using state of the art supercomputing facilities, molecular dynamics code and parallelization strategies, this work also provides insight into the relationship between cellulose crystallinity and cellulose-lignin aggregation by performing multi-million atom simulations. Finally, this work introduces concepts to augment the ability of molecular dynamics to interpret experimental observables with the help of Markov modeling, which allows for a convenient description of complex molecule dynamics as transitions between well defined conformations. The work presented here suggests that molecular dynamics will continue to evolve and integrate with experimental techniques, like neutron and X-ray scattering, and stochastic models, like Markov modeling, to yield unmatched descriptions of molecule dynamics and interpretations of experimental data, facilitated by the growing computational power available to scientists

Molecular Simulations of Protein-Induced Membrane Remodeling

Membranes organize much of the cell and host a great deal of molecular machinery required to integrate signals from the outside, regulate the surrounding matrix, change shape, move, and grow. Understanding how a dense forest of proteins, sugars, and biomarkers modulates the shape of the cell is necessary to produce more detailed, accurate predictions of cell behavior, particularly in the studies of cell signaling processes that lead to oncogenesis. In this dissertation, I will present a series of molecular models which, when combined with continuum models and both in vitro and in vivo experiments, describe the molecular basis for membrane morphology changes. In particular, we investigate the mechanisms by which proteins assemble on a bilayer undergoing thermal fluctuations. This work serves to quantify and explain a series of biophysical experiments in molecular detail, and contributes to the development of multiscale models for predicting cell fate

Knowledge-based identification of functional domains in proteins

The characterization of proteins and enzymes is traditionally organised according to the sequence-structure-function paradigm. The investigation of the inter-relationships between these three properties has motivated the development of several experimental and computational techniques, that have made available an unprecedented amount of sequence and structural data. The interest in developing comparative methods for rationalizing such copious information has, of course, grown in parallel. Regarding the structure-function relationship, for instance, the availability of experimentally resolved protein structures and of computer simulations have improved our understanding of the role of proteins' internal dynamics in assisting their functional rearrangements and activity. Several approaches are currently available for elucidating and comparing proteins' internal dynamics. These can capture the relevant collective degrees of freedom that recapitulate the main conformational changes. These collective coordinates have the potential to unveil remote evolutionary relationships between proteins, that are otherwise not easily accessible from purely sequence- or structure-based investigations. Starting from this premise, in the first chapter of this thesis I will present a novel and general computational method that can detect large-scale dynamical correlations in proteins by comparing different representative conformers. This is accomplished by applying dimensionality-reduction techniques to inter-amino acid distance fluctuation matrices. As a result, an optimal quasi-rigid domain decomposition of the protein or macromolecular assembly of interest is identified, and this facilitates the functionally-oriented interpretation of their internal dynamics. Building on this approach, in the second chapter I will discuss its systematic application to a class of membrane proteins of paramount biochemical interest, namely the class A G protein-coupled receptors. The comparative analysis of their internal dynamics, as encoded by the quasi-rigid domains, allowed us to identify recurrent patterns in the large-scale dynamics of these receptors. This, in turn, allowed us to single out a number of key functional sites. These were, for the most part, previously known -- a fact that at the same time validates the method, and gives confidence for the viability of the other, novel sites. Finally, for the last part of the thesis, I focussed on the sequence-structure relationship. In particular, I considered the problem of inferring structural properties of proteins from the analysis of large multiple sequence alignments of homologous sequences. For this purpose, I recasted the strategies developed for the dynamical features extraction in order to identify compact groups of coevolving residues, based only on the knowledge of amino acid variability in aligned primary sequences. Throughout the thesis, many methodological techniques have been taken into considerations, mainly based on concepts from graph theory and statistical data analysis (clustering). All these topics are explained in the methodological sections of each chapter

Molecular Dynamics Simulation

Condensed matter systems, ranging from simple fluids and solids to complex multicomponent materials and even biological matter, are governed by well understood laws of physics, within the formal theoretical framework of quantum theory and statistical mechanics. On the relevant scales of length and time, the appropriate ‘first-principles’ description needs only the Schroedinger equation together with Gibbs averaging over the relevant statistical ensemble. However, this program cannot be carried out straightforwardly—dealing with electron correlations is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the many-body problem can be effectively reduced to one of independent particles or quasi-particles. [...

Nonlinear machine learning of macromolecular folding and self-assembly

High performance computation and sophisticated machine learning algorithms have emerged as new tools for studying biological, physical and chemical systems at the atomistic scale. In this thesis, I report several applications of molecular dynamics simulation and machine learning in the study of the macromolecular folding and assembly. In the first aspect, I employ molecular simulation and non-linear manifold learning to explore the dynamics and configuration of linear and ring polymers. Integrating statistical mechanics with dynamical systems theory, I establish a means to determine single molecule folding funnels from univariate time series in experimentally accessible observables. In the second aspect, I utilize coarse grained molecular simulation to explore the self-assembly of hundreds of asphaltene molecules over micro-second time scales to reveal the aggregation phase behavior as a function of temperature, pressure and solvent conditions. I then employ graph matching and non-linear manifold learning to obtain asphaltene folding and assembly free energy landscapes. This thesis establishes new fundamental understanding of the folding and assembly of macromolecules, builds connections between computer simulation and experimental measurements, and provides new routes to the rational design of functional molecular materials

Probing Local Atomic Environments to Model RNA Energetics and Structure

Ribonucleic acids (RNA) are critical components of living systems. Understanding RNA structure and its interaction with other molecules is an essential step in understanding RNA-driven processes within the cell. Experimental techniques like X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy, and chemical probing methods have provided insights into RNA structures on the atomic scale. To effectively exploit experimental data and characterize features of an RNA structure, quantitative descriptors of local atomic environments are required. Here, I investigated different ways to describe RNA local atomic environments. First, I investigated the solvent-accessible surface area (SASA) as a probe of RNA local atomic environment. SASA contains information on the level of exposure of an RNA atom to solvents and, in some cases, is highly correlated to reactivity profiles derived from chemical probing experiments. Using Bayesian/maximum entropy (BME), I was able to reweight RNA structure models based on the agreement between SASA and chemical reactivities. Next, I developed a numerical descriptor (the atomic fingerprint), that is capable of discriminating different atomic environments. Using atomic fingerprints as features enable the prediction of RNA structure and structure-related properties. Two detailed examples are discussed. Firstly, a classification model was developed to predict Mg$^{2+}$ ion binding sites. Results indicate that the model could predict Mg$^{2+}$ binding sites with reasonable accuracy, and it appears to outperform existing methods. Secondly, a set of models were developed to identify cavities in RNA that are likely to accommodate small-molecule ligands. The models were also used to identify bound-like conformations from an ensemble of RNA structures. The frameworks presented here provide paths to connect the local atomic environment to RNA structure, and I envision they will provide opportunities to develop novel RNA modeling tools.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163135/1/jingrux_1.pd

Mass & secondary structure propensity of amino acids explain their mutability and evolutionary replacements

Why is an amino acid replacement in a protein accepted during evolution? The answer given by bioinformatics relies on the frequency of change of each amino acid by another one and the propensity of each to remain unchanged. We propose that these replacement rules are recoverable from the secondary structural trends of amino acids. A distance measure between high-resolution Ramachandran distributions reveals that structurally similar residues coincide with those found in substitution matrices such as BLOSUM: Asn Asp, Phe Tyr, Lys Arg, Gln Glu, Ile Val, Met → Leu; with Ala, Cys, His, Gly, Ser, Pro, and Thr, as structurally idiosyncratic residues. We also found a high average correlation (\overline{R} R = 0.85) between thirty amino acid mutability scales and the mutational inertia (I X ), which measures the energetic cost weighted by the number of observations at the most probable amino acid conformation. These results indicate that amino acid substitutions follow two optimally-efficient principles: (a) amino acids interchangeability privileges their secondary structural similarity, and (b) the amino acid mutability depends directly on its biosynthetic energy cost, and inversely with its frequency. These two principles are the underlying rules governing the observed amino acid substitutions. © 2017 The Author(s)