On the Alexandrov Topology of sub-Lorentzian Manifolds

It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian time-separation function. Both lead to the definition of the Alexandrov topology, which is linked to the property of strong causality of a space-time. We studied three possible ways to define the Alexandrov topology on sub-Lorentzian manifolds, which usually give different topologies, but agree in the Lorentzian case. We investigated their relationships to each other and the manifold's original topology and their link to causality.Comment: 20 page

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

Mutation of Archaeal Isopentenyl Phosphate Kinase Highlights Mechanism and Guides Phosphorylation of Additional Isoprenoid Monophosphates

I sopentenyl diphosphate (IPP) and its isomeric part-ner dimethylallyl diphosphate (DMAPP) are precur-sors for a diverse collection of primary and second-ary isoprenoid metabolites in all organisms. Following its formation, successive units of IPP are used together either with DMAPP, formed by the action of types I or II IPP isomerases, or with the IPP extended isoprenoid diphosphate chain, to biosynthesize C10, C15, or C20 oligoprenyl diphosphates known as geranyl diphos-phate (GPP), farnesyl diphosphate (FPP), and gera-nylgeranyl diphosphate (GGPP), respectively, as well as larger isoprenoid diphosphates. In plants and some mi-croorganisms, GPP, FPP, and GGPP also serve as start-ingmaterials for the biosynthesis of a large class of spe-cialized and often cyclic terpene hydrocarbons (1). FPP is the most ubiquitous of the three isoprenoid diphos-phate building blocks, as it resides at the juncture of bi

Metabolism of halophilic archaea

In spite of their common hypersaline environment, halophilic archaea are surprisingly different in their nutritional demands and metabolic pathways. The metabolic diversity of halophilic archaea was investigated at the genomic level through systematic metabolic reconstruction and comparative analysis of four completely sequenced species: Halobacterium salinarum, Haloarcula marismortui, Haloquadratum walsbyi, and the haloalkaliphile Natronomonas pharaonis. The comparative study reveals different sets of enzyme genes amongst halophilic archaea, e.g. in glycerol degradation, pentose metabolism, and folate synthesis. The carefully assessed metabolic data represent a reliable resource for future system biology approaches as it also links to current experimental data on (halo)archaea from the literature

Molecular dynamics of ribosomal elongation factors G and Tu

Translation on the ribosome is controlled by external factors. During polypeptide lengthening, elongation factors EF-Tu and EF-G consecutively interact with the bacterial ribosome. EF-Tu binds and delivers an aminoacyl-tRNA to the ribosomal A site and EF-G helps translocate the tRNAs between their binding sites after the peptide bond is formed. These processes occur at the expense of GTP. EF-Tu:tRNA and EF-G are of similar shape, share a common binding site, and undergo large conformational changes on interaction with the ribosome. To characterize the internal motion of these two elongation factors, we used 25 ns long all-atom molecular dynamics simulations. We observed enhanced mobility of EF-G domains III, IV, and V and of tRNA in the EF-Tu:tRNA complex. EF-Tu:GDP complex acquired a configuration different from that found in the crystal structure of EF-Tu with a GTP analogue, showing conformational changes in the switch I and II regions. The calculated electrostatic properties of elongation factors showed no global similarity even though matching electrostatic surface patches were found around the domain I that contacts the ribosome, and in the GDP/GTP binding region

A modified Ehrenfest formalism for efficient large-scale ab initio molecular dynamics

We present in detail the recently derived ab-initio molecular dynamics (AIMD) formalism [Phys. Rev. Lett. 101 096403 (2008)], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave-functions, which can become the bottleneck for very large systems. Alternatively, one can handle the electron-ion dynamics within the Ehrenfest scheme where no explicit orthogonalization is necessary, however the time step is too small for practical applications. Here we preserve the desirable properties of Ehrenfest in a new scheme that allows for a considerable increase of the time step while keeping the system close to the Born-Oppenheimer surface. We show that the automatically enforced orthogonalization is of fundamental importance for large systems because not only it improves the scaling of the approach with the system size but it also allows for an additional very efficient parallelization level. In this work we provide the formal details of the new method, describe its implementation and present some applications to some test systems. Comparisons with the widely used Car-Parrinello molecular dynamics method are made, showing that the new approach is advantageous above a certain number of atoms in the system. The method is not tied to a particular wave-function representation, making it suitable for inclusion in any AIMD software package.Comment: 28 pages, 5 figures, published in a special issue of J. Chem. Theory Comp. in honour of John Perde

Petrophysical, Geochemical, and Hydrological Evidence for Extensive Fracture-Mediated Fluid and Heat Transport in the Alpine Fault's Hanging-Wall Damage Zone

Fault rock assemblages reflect interaction between deformation, stress, temperature, fluid, and chemical regimes on distinct spatial and temporal scales at various positions in the crust. Here we interpret measurements made in the hanging-wall of the Alpine Fault during the second stage of the Deep Fault Drilling Project (DFDP-2). We present observational evidence for extensive fracturing and high hanging-wall hydraulic conductivity (∼10−9 to 10−7 m/s, corresponding to permeability of ∼10−16 to 10−14 m2) extending several hundred meters from the fault's principal slip zone. Mud losses, gas chemistry anomalies, and petrophysical data indicate that a subset of fractures intersected by the borehole are capable of transmitting fluid volumes of several cubic meters on time scales of hours. DFDP-2 observations and other data suggest that this hydrogeologically active portion of the fault zone in the hanging-wall is several kilometers wide in the uppermost crust. This finding is consistent with numerical models of earthquake rupture and off-fault damage. We conclude that the mechanically and hydrogeologically active part of the Alpine Fault is a more dynamic and extensive feature than commonly described in models based on exhumed faults. We propose that the hydrogeologically active damage zone of the Alpine Fault and other large active faults in areas of high topographic relief can be subdivided into an inner zone in which damage is controlled principally by earthquake rupture processes and an outer zone in which damage reflects coseismic shaking, strain accumulation and release on interseismic timescales, and inherited fracturing related to exhumation

The Emergence and Early Evolution of Biological Carbon-Fixation

The fixation of into living matter sustains all life on Earth, and embeds the biosphere within geochemistry. The six known chemical pathways used by extant organisms for this function are recognized to have overlaps, but their evolution is incompletely understood. Here we reconstruct the complete early evolutionary history of biological carbon-fixation, relating all modern pathways to a single ancestral form. We find that innovations in carbon-fixation were the foundation for most major early divergences in the tree of life. These findings are based on a novel method that fully integrates metabolic and phylogenetic constraints. Comparing gene-profiles across the metabolic cores of deep-branching organisms and requiring that they are capable of synthesizing all their biomass components leads to the surprising conclusion that the most common form for deep-branching autotrophic carbon-fixation combines two disconnected sub-networks, each supplying carbon to distinct biomass components. One of these is a linear folate-based pathway of reduction previously only recognized as a fixation route in the complete Wood-Ljungdahl pathway, but which more generally may exclude the final step of synthesizing acetyl-CoA. Using metabolic constraints we then reconstruct a “phylometabolic” tree with a high degree of parsimony that traces the evolution of complete carbon-fixation pathways, and has a clear structure down to the root. This tree requires few instances of lateral gene transfer or convergence, and instead suggests a simple evolutionary dynamic in which all divergences have primary environmental causes. Energy optimization and oxygen toxicity are the two strongest forces of selection. The root of this tree combines the reductive citric acid cycle and the Wood-Ljungdahl pathway into a single connected network. This linked network lacks the selective optimization of modern fixation pathways but its redundancy leads to a more robust topology, making it more plausible than any modern pathway as a primitive universal ancestral form

Feasibility studies for the measurement of time-like proton electromagnetic form factors from p¯ p→ μ+μ- at P ¯ ANDA at FAIR

This paper reports on Monte Carlo simulation results for future measurements of the moduli of time-like proton electromagnetic form factors, | GE| and | GM| , using the p¯ p→ μ+μ- reaction at P ¯ ANDA (FAIR). The electromagnetic form factors are fundamental quantities parameterizing the electric and magnetic structure of hadrons. This work estimates the statistical and total accuracy with which the form factors can be measured at P ¯ ANDA , using an analysis of simulated data within the PandaRoot software framework. The most crucial background channel is p¯ p→ π+π-, due to the very similar behavior of muons and pions in the detector. The suppression factors are evaluated for this and all other relevant background channels at different values of antiproton beam momentum. The signal/background separation is based on a multivariate analysis, using the Boosted Decision Trees method. An expected background subtraction is included in this study, based on realistic angular distributions of the background contribution. Systematic uncertainties are considered and the relative total uncertainties of the form factor measurements are presented

Towards Comprehensive Foundations of Computational Intelligence

Abstract. Although computational intelligence (CI) covers a vast variety of different methods it still lacks an integrative theory. Several proposals for CI foundations are discussed: computing and cognition as compression, meta-learning as search in the space of data models, (dis)similarity based methods providing a framework for such meta-learning, and a more general approach based on chains of transformations. Many useful transformations that extract information from features are discussed. Heterogeneous adaptive systems are presented as particular example of transformation-based systems, and the goal of learning is redefined to facilitate creation of simpler data models. The need to understand data structures leads to techniques for logical and prototype-based rule extraction, and to generation of multiple alternative models, while the need to increase predictive power of adaptive models leads to committees of competent models. Learning from partial observations is a natural extension towards reasoning based on perceptions, and an approach to intuitive solving of such problems is presented. Throughout the paper neurocognitive inspirations are frequently used and are especially important in modeling of the higher cognitive functions. Promising directions such as liquid and laminar computing are identified and many open problems presented.