Analysis of protein dynamics using local-DME calculations

Flexibility and dynamics of protein structures are reflected in the B-factors and order parameters obtained experimentally with X-ray crystallography and Nuclear Magnetic Resonance (NMR). Methods such as Normal Mode Analysis (NMA) and Elastic Network Models (ENM) can be used to predict the fluctuations of protein structures for either atomic level or coarse-grained structures. Here, we introduce the Local-Distance Matrix Error (DME), an efficient and simple analytic method to study the fluctuations of protein structures, especially for the ensembles of NMR-determined protein structures. Comparisons with the fluctuations obtained by experiments and other by computations show strong correlations

Porphyrin as a Spectroscopic Probe of Net Electric Fields in Heme Proteins

Heme proteins have diverse functions as well as varied structures but share the same organic, conjugated cofactor. Similarly varied approaches have been taken to deduce how heme can take on different roles based on its protein environment. A unique approach is to view the protein matrix as a constellation of point charges that generates a defined, reproducible, net internal electric field that has influence over the electronic properties of the heme cofactor. This work considers how porphyrins, the basic chromophore building block of heme, can be used as a native spectroscopic sensor of internal electric field at the active site of heme proteins. First, a number of approaches to model the electrostatic nature of protein structure are described. One approach based on Coulomb’s law is used to estimate the net electric field in myoglobin, easily placing the internal electric field on the order of MV/cm. A closer inspection of myoglobin structure reveals that slight changes in position or strategic mutations can cause appreciable change in the field magnitude and direction. Then, the idea of a porphyrin probe is further developed, followed by a theoretical and spectral characterization of porphyrins substituted into heme proteins for use in emission spectroscopy as non-emissive heme must be replaced by other porphyrin analogs with higher quantum yield. Once the porphyrin–protein system has been established as the guest–host system of interest, the hole-burning Stark spectroscopy method was used to quantitatively measure the magnitude and direction of the internal electric field vector generated by the protein. The collected Stark spectra had a more established classical analysis method for analysis, but a major aspect of this work is a quantum-mechanical analysis method that has been advanced for more practical and widespread usage. This novel quantum-mechanical approach to the method has promise for greater accuracy for internal electric field determination as well as the ability to resolve the field into spatial components in order to determine not just field magnitude but also direction. The results from the new analysis of experimental data for myoglobin of the in-plane components of the field places both at 1.7 MV/cm. Finally, two ab initio excited-state methods, CIS and TDDFT, were used to calculate electronic state energies and transition dipole moment values in support of this new quantum-mechanical analysis method. The two methods are described thoroughly with presentation of benefits and drawbacks to each method

Doctor of Philosophy

dissertationA new quantum chemistry-based, atomic point polarizable dipole potential was developed for molecular dynamic (MD) simulations of poly (ethylene oxide) (PEO) and poly (propylene oxide) (PPO) aqueous solutions employing a modified version of a single water molecule with four interaction sites and Drude polarizability (SWM4-DP). A twoextended charge ether model has been chosen as best describing electrostatic potential of DME. Ether/water interactions were parameterized to reproduce the binding energy of water with 1,2-dimethoxyethane (DME) that was determined from high-level quantum chemistry calculations. The DME/water nonbonded parameters were found to be transferrable to 1,2-dimethoxypropane (DMP). An accuracy of the developed force field was justified by comparing thermodynamics properties obtained from molecular dynamics simulations with experimental data including free energy, enthalpy, and entropy of DME solvation. Free energy of DME solvation in water was obtained employing a new interface transit method (ITM) followed by calculations using perturbation theory. Simulations of DME/water solutions at room temperature using the new polarizable force field yielded enthalpy of solvation in a good agreement with experiment. Simulations of PEO/water and PPO/water solutions improved ability of the new force field to capture, at least qualitatively, low critical solution temperature (LCST) behavior in these solutions. The predicted miscibility of PEO and water as a function of temperature was found to be strongly correlated with the predicted free energy of solvation of DME in water for the various force fields investigated. Intermolecular pair correlations are employed to analyze phase behavior of nonionic polymers in aqueous solution

Development of an Accurate and Efficient Method for Normal Mode Analysis in Extended Molecular Systems: the Mobile Block Hessian Method

Vibrational spectroscopy is an important technique for the structural characterization of (bio)molecules and (nano)materials. For example, it is particularly suited for studying proteins in their natural environment (i.e., in aqueous solution), and can be used in many cases where other techniques such as Xray crystallography and nuclear magnetic resonance spectroscopy cannot be employed. In particular infrared (IR) and Raman spectroscopy have been used extensively for gaining information on the secondary structure of polypeptides and proteins. Also in other fields, these techniques help to identify the functional groups in the material, or provide a unique “fingerprint” of the material, the so-called skeleton vibrations. A frequently encountered problem in spectroscopy is the precise interpretation of the obtained experimental spectra. Many of these nanostructured systems are characterized by very complex vibrational spectra and the assignment of specific bands to particular vibrations is difficult if based solely on experimental techniques. In this field theoretical predictions form an undeniable complement to the measured spectra. Each observed band in the spectrum consists of a number of close-lying normal modes, which result from normal mode analysis (NMA). This is the diagonalization of the full mass-weighted molecular Hessian matrix, which contains the second derivatives of the total potential energy with respect to Cartesian nuclear coordinates, evaluated in an equilibrium point on the potential energy surface (PES). By performing NMA, the system is approximated as a set of decoupled harmonic oscillators. The frequencies and modes contain information on the curvatures of the PES and the mass distribution in the system. NMA is a static approach that samples the PES exactly, if higher order derivatives, i.e. anharmonic corrections, are neglected, and is therefore an approximate analysis method complementary to molecular dynamics and Monte Carlo simulations. In extended molecular systems (like polypeptides, polymer chains, supramolecular assemblies, systems embedded in a solvent or molecules adsorbed within porous materials etc.), this procedure poses two major problems. First, the size of the relevant systems can easily reach a few hundreds or several ten thousands of atoms, and full calculations of such large systems are computationally demanding if not impossible with accurate methods. Second, even if possible, such calculations provide a large amount of data that will be increasingly difficult to interpret. Here lies the scope of this PhD work: The aim of this PhD is the calculation of accurate frequencies and modes in extended molecular systems in an efficient manner. Mainly two categories of approximate normal mode calculations can be identified: (1) the PES description is simplified; (2) the description of the PES is unchanged, but only a subset of the modes is calculated in an approximate way. This PhD work focuses on the latter category and presents the new Mobile Block Hessian (MBH) method and its variants. The key concept is the partitioning of the system into several blocks of atoms, which move as rigid bodies during the vibrational analysis with only rotational and translational degrees of freedom. The MBH has several variants according to the block choice and the way blocks are adjoined together. The MBH is currently implemented in the last upgrade of CHARMM and Q-Chem and the method will be available too in the next release of ADF. Outline PhD thesis In the introductory Chapter 1, normal mode analysis is presented as a technique to scan the potential energy surface within the harmonic oscillator approximation. The standard NMA equations with the full Hessian are revised. The problems brought up by nonstationary points motivate the necessity of a profound theoretical study of the NMA of partially optimized geometries as is the case for MBH. Chapter 2 elaborates the MBH theory in two sets of coordinates: internal coordinates and block parameters. For the extension of the MBH to all kind of blocks (including linear, single-atom blocks) and adjoined blocks (linked by a common “adjoining” atom), the general formulation in block parameters is also linked to Cartesian quantities (Cartesian Hessian, gradient). Five practical implementation schemes for MBH conclude this chapter. In Chapter 3, the MBH is assessed in its performance to reproduce accurate frequencies and normal modes. During my PhD, a large test set has three examples are outlined. The thanol molecule shows how MBH yields physical frequencies for a partially optimized structure, and that MBH is an improvement with respect to the Partial Hessian Vibrational Analysis (PHVA) because of the correct mass description of the block. The MBH is capable of reproducing accurate reaction rate constants given an acceptable block choice, as is illustrated with an aminophosphonate reaction in solvent. The usefulness of adjoined blocks is demonstrated with the calculation of the lowest normal modes of crambin, a small protein. Finally Chapter 4 gives some concluding remarks on the MBH’s performance. Perspectives for the further improvements of MBH include the optimization of the implementation in frequently used program packages, as well as several combined models for advanced NMA. Besides MBH there are other models in literature for the calculation of frequencies in extended systems. In particular, the vibrational subsystem analysis (VSA) method by B. R. Brooks is a competitive scheme. A comparative study of NMA methods based on Hessians of reduced dimension (partial Hessians) has been accomplished very recently in collaboration with prof. B. R. Brooks of the Laboratory of Computational Biology (National Institutes of Health) in Bethesda (Maryland). PHVA is found to be capable of reproducing localized modes. In addition to localized modes, the MBH can reproduce more global modes. VSA is most suited for the reproduction of the modes and frequencies in the lower spectrum. In partially optimized structures, PHVA and MBH can still yield physical frequencies. Moreover, by varying the size of the blocks, MBH can be used as an analysis tool of the spectrum. The comparative study is added in the Appendix. This PhD work has resulted in eight papers, six related to MBH – published, in press, or submitted – and two papers not directly related to MBH. All publications are included in the Appendix

Cofilin is a pH sensor for actin free barbed end formation: role of phosphoinositide binding

Newly generated actin free barbed ends at the front of motile cells provide sites for actin filament assembly driving membrane protrusion. Growth factors induce a rapid biphasic increase in actin free barbed ends, and we found both phases absent in fibroblasts lacking H+ efflux by the Na-H exchanger NHE1. The first phase is restored by expression of mutant cofilin-H133A but not unphosphorylated cofilin-S3A. Constant pH molecular dynamics simulations and nuclear magnetic resonance (NMR) reveal pH-sensitive structural changes in the cofilin C-terminal filamentous actin binding site dependent on His133. However, cofilin-H133A retains pH-sensitive changes in NMR spectra and severing activity in vitro, which suggests that it has a more complex behavior in cells. Cofilin activity is inhibited by phosphoinositide binding, and we found that phosphoinositide binding is pH-dependent for wild-type cofilin, with decreased binding at a higher pH. In contrast, phosphoinositide binding by cofilin-H133A is attenuated and pH insensitive. These data suggest a molecular mechanism whereby cofilin acts as a pH sensor to mediate a pH-dependent actin filament dynamics

Neuronal (Bi)Polarity as a Self-Organized Process Enhanced by Growing Membrane

Early in vitro and recent in vivo studies demonstrated that neuronal polarization occurs by the sequential formation of two oppositely located neurites. This early bipolar phenotype is of crucial relevance in brain organization, determining neuronal migration and brain layering. It is currently considered that the place of formation of the first neurite is dictated by extrinsic cues, through the induction of localized changes in membrane and cytoskeleton dynamics leading to deformation of the cells' curvature followed by the growth of a cylindrical extension (neurite). It is unknown if the appearance of the second neurite at the opposite pole, thus the formation of a bipolar cell axis and capacity to undergo migration, is defined by the growth at the first place, therefore intrinsic, or requires external determinants. We addressed this question by using a mathematical model based on the induction of dynamic changes in one pole of a round cell. The model anticipates that a second area of growth can spontaneously form at the opposite pole. Hence, through mathematical modeling we prove that neuronal bipolar axis of growth can be due to an intrinsic mechanism