Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

A Computational Model of Protein Induced Membrane Morphology with Geodesic Curvature Driven Protein-Membrane Interface

Continuum or hybrid modeling of bilayer membrane morphological dynamics induced by embedded proteins necessitates the identification of protein-membrane interfaces and coupling of deformations of two surfaces. In this article we developed (i) a minimal total geodesic curvature model to describe these interfaces, and (ii) a numerical one-one mapping between two surface through a conformal mapping of each surface to the common middle annulus. Our work provides the first computational tractable approach for determining the interfaces between bilayer and embedded proteins. The one-one mapping allows a convenient coupling of the morphology of two surfaces. We integrated these two new developments into the energetic model of protein-membrane interactions, and developed the full set of numerical methods for the coupled system. Numerical examples are presented to demonstrate (1) the efficiency and robustness of our methods in locating the curves with minimal total geodesic curvature on highly complicated protein surfaces, (2) the usefulness of these interfaces as interior boundaries for membrane deformation, and (3) the rich morphology of bilayer surfaces for different protein-membrane interfaces

Modeling local pattern formation on membrane surfaces using nonlocal interactions

2015 Spring.Includes bibliographical references.The cell membrane is of utmost importance in the transportation of nutrients and signals to the cell which are needed for survival. The magnitude of this is the inspiration for our study of the lipid bilayer which forms the cell membrane. It has been recently accepted that the lipid bilayer consists of lipid microdomains (lipid rafts), as opposed to freely moving lipids. We present two lipid raft models using the Ginzburg-Landau energy with addition of the electrostatic energy and the geodesic curvature energy to describe the local pattern formation of these lipid rafts. The development and implementation of a C⁰ interior penalty surface finite element method along with an implicit time iteration scheme will also be discussed as the optimal solution technique

Advances in Fundamental Physics

This Special Issue celebrates the opening of a new section of the journal Foundation: Physical Sciences. Theoretical and experimental studies related to various areas of fundamental physics are presented in this Special Issue. The published papers are related to the following topics: dark matter, electron impact excitation, second flavor of hydrogen atoms, quantum antenna, molecular hydrogen, molecular hydrogen ion, wave pulses, Brans-Dicke theory, hydrogen Rydberg atom, high-frequency laser field, relativistic mean field formalism, nonlocal continuum field theories, parallel universe, charge exchange, van der Waals broadening, greenhouse effect, strange and unipolar electromagnetic pulses, quasicrystals, Wilhelm-Weber’s electromagnetic force law, axions, photoluminescence, neutron stars, gravitational waves, diatomic molecular spectroscopy, information geometric measures of complexity. Among 21 papers published in this Special Issue, there are 5 reviews and 16 original research papers

Studies on the function of PRG2/PLPPR3 in neuron morphogenesis

Neuron development follows a multifaceted sequence of cell migration, polarisation, neurite elongation, branching, tiling, and pruning. The implementation of this sequence differs between neuronal cell types and even in individual neurons between sub-compartments such as dendrites and axons. Membrane proteins are at a prime position in neurons to couple extrinsic morphogenetic signals with their intrinsic responses to orchestrate this defined morphological progression. The Phospholipid phosphatase-related / Plasticity-related gene (PLPPR/PRG)-family comprises five neuron-enriched and developmentally regulated membrane proteins with functions in cellular morphogenesis. At the start of this project, no publication had characterised the function of PLPPR3/PRG2 during neuron development. The presented work describes PLPPR3 as an axon-enriched protein localising to the plasma membrane and internal membrane compartments of neurons. Mutagenesis studies in cell lines establish the plasma membrane localisation of PLPPR3 as a regulator of its function to increase filopodia density (Chapter 2). Furthermore, the generation of a Plppr3-/- mouse line using CRISPR/Cas9 genome editing techniques (Chapter 3) enabled characterising endogenous phenotypes of PLPPR3 in neurons. In primary neuronal cultures, PLPPR3 was found to specifically control branch formation in a pathway with the phosphatase PTEN, without altering the overall growth capacity of neurons (Chapter 4). Loss of PLPPR3 specifically reduced branches forming from filopodia without affecting the stability of branches. This precise characterisation of PLPPR3 function unravelled the existence of parallel, independent programs for branching morphogenesis that are utilised and implemented differentially in developing axons and dendrites (Chapter 5). Furthermore, this thesis establishes multiple tools to study PLPPR3, the membrane lipid phosphatidylinositol-trisphosphate, and neuron morphogenesis by providing molecular tools, protocols, and semi-automated and automated image analysis pipelines (Appendix Chapter 7) and discusses experiments to test, refine and extend models of PLPPR3 function (Chapter 6). In summary, this thesis generated and utilised several tools and a Plppr3-/- mouse model to characterise PLPPR3 as a specific regulator of neuron branching morphogenesis. This precise characterisation refined and expanded the understanding of axon-specific branching morphogenesis.Nervenzellen entwickeln ihre komplexe Morphologie durch das Zusammenwirken diverser molekularer Entwicklungs-Programme der Zellkörper-Migration, der Polarisierung und der Morphogenese durch Wachstum, Verzweigung, Stabilisierung und Koordinierung ihrer Neuriten. Dabei unterscheidet sich die exakte Implementierung zwischen Nervenzell-Typen und selbst innerhalb einzelner Zellen zwischen Axonen und Dendriten. Diese unterschiedliche Morphogenese wird dabei speziell durch Membranproteine stark beeinflusst, die durch ihre Präsenz an der Plasmamembran Zell-extrinsische Signale mit den Zell-intrinsischen Morphogeneseprogrammen verbinden und beeinflussen. Die Familie der Phospholipid phosphatase-related / Plasticity-related gene (PLPPR/PRG) Proteine umfasst fünf Nervenzell-spezifische Membranproteine mit Effekten auf die Morphologie von Zellen. Zu Beginn dieses Projektes hatte noch keine Studie die Funktion des Familienmitglieds PLPPR3/PRG2 in Nervenzellen untersucht. Diese Dissertation beschreibt die Lokalisation von PLPPR3 an der Plasmamembran und in Zell-internen Membranstrukturen von Nervenzellen. Experimente in Zellkultur zeigen eine erhöhte Filopodien-Dichte nach Überexpression von PLPPR3, Mutagenese-Studien deuten eine strikte Kontrolle der Plasmamembran-Lokalisation an (Kapitel 2). Die Generierung einer Plppr3 Knockout Mauslinie mittels CRISPR/Cas9 Genom-Modifizierung (Kapitel 3) erlaubte eine Charakterisierung der endogenen Funktion von PLPPR3 in Nervenzellen. In Primärzellkultur von Nervenzellen des murinen Hippocampus zeigte sich, dass PLPPR3 im Zusammenspiel mit der Phosphatase PTEN spezifisch die Verzweigung von Nervenzellen kontrolliert, ohne deren Wachstumspotential global zu verändern (Kapitel 4). Dadurch kann PLPPR3 als ein Schalter zwischen Verzweigung und Verlängerung eines Nervenzell-Fortsatzes agieren. Der Verlust von PLPPR3 verursachte reduzierte spezifisch die Anzahl an Verzweigungen, die aus Filopodien entstanden, ohne dabei die Stabilität dieser Verzweigungen zu beeinflussen. Die präzise Charakterisierung dieser Funktion von PLPPR3 deckte auf, dass Verzweigungen von Nervenzell-Fortsätzen durch voneinander unabhängige Entwicklungsprogramme ausgebildet und stabilisiert werden können (Kapitel 5). Diese Programme werden von Axonen und Dendriten in unterschiedlicher Weise eingesetzt. Zusätzlich etabliert diese Arbeit sowohl diverse molekulare Werkzeuge und Visualisierungs-Protokolle zur Analyse von PLPPR3 und dem Membranlipid Phosphatidylinositol-Trisphosphat, als auch automatisierte Quantifizierungssoftware zur Studie der Nervenzellmorphologie (Appendix-Kapitel 7). Abschließend entwickelt und verfeinert die Dissertation mögliche Modelle zur PLPPR3-Funktion und zeigt experimentelle Strategien auf, um diese Modelle besser charakterisieren zu können (Kapitel 6). Zusammenfassend wurden in dieser Promotionsarbeit diverse Experimental- und Analyse-Strategien und eine Plppr3-/- Mauslinie entwickelt und genutzt, um PLPPR3 als einen spezifischen Regulator der Nervenzell-Morphogenese zu etablieren. Diese präzise Charakterisierung des PLPPR3 Phänotyps erlaubte zusätzlich eine Verfeinerung und Erweiterung der Erkenntnisse zur Axon-spezifischen Entwicklung von Verzweigungen

The 2018 biomembrane curvature and remodeling roadmap

The importance of curvature as a structural feature of biological membranes has been recognized for many years and has fascinated scientists from a wide range of different backgrounds. On the one hand, changes in membrane morphology are involved in a plethora of phenomena involving the plasma membrane of eukaryotic cells, including endo-and exocytosis, phagocytosis and filopodia formation. On the other hand, a multitude of intracellular processes at the level of organelles rely on generation, modulation, and maintenance of membrane curvature to maintain the organelle shape and functionality. The contribution of biophysicists and biologists is essential for shedding light on the mechanistic understanding and quantification of these processes. Given the vast complexity of phenomena and mechanisms involved in the coupling between membrane shape and function, it is not always clear in what direction to advance to eventually arrive at an exhaustive understanding of this important research area. The 2018 Biomembrane Curvature and Remodeling Roadmap of Journal of Physics D: Applied Physics addresses this need for clarity and is intended to provide guidance both for students who have just entered the field as well as established scientists who would like to improve their orientation within this fascinating area

Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems

This report advances the hypothesis that multifunctional systems may be associated with multifunnel potential and free energy landscapes, with particular focus on biomolecules. It compares systems that exhibit single, double, and multiple competing structures, and contrasts multifunnel landscapes associated with misfolded amyloidogenic oligomers, which presumably do not arise as an evolutionary target. In this context, intrinsically disordered proteins could be considered intrinsically multifunctional molecules, associated with multifunnel landscapes. Potential energy landscape theory enables biomolecules to be treated in a common framework together with self‐organizing and multifunctional systems based on inorganic materials, atomic and molecular clusters, crystal polymorphs, and soft matter.epsr

Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems

This report advances the hypothesis that multifunctional systems may be associated with multifunnel potential and free energy landscapes, with particular focus on biomolecules. It compares systems that exhibit single, double, and multiple competing structures, and contrasts multifunnel landscapes associated with misfolded amyloidogenic oligomers, which presumably do not arise as an evolutionary target. In this context, intrinsically disordered proteins could be considered intrinsically multifunctional molecules, associated with multifunnel landscapes. Potential energy landscape theory enables biomolecules to be treated in a common framework together with self‐organizing and multifunctional systems based on inorganic materials, atomic and molecular clusters, crystal polymorphs, and soft matter.epsr