On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

Quorum sensing in the plant pathogen Erwinia carotovora subsp. carotovora

Erwinia carotovora subsp. carotovora (Ecc) is a Gram-negative enterobacterium that causes soft-rot in potato and other crops. The main virulence determinants, the extracellular plant cell wall -degrading enzymes (PCWDEs), lead to plant tissue maceration. In order to establish a successful infection the production of PCWDEs are controlled by a complex regulatory network, including both specific and global activators and repressors. One of the most important virulence regulation systems in Ecc is mediated by quorum sensing (QS), which is a population density -dependent cell-to-cell communication mechanism used by many Gram-negative bacteria. In these bacteria N-acylhomoserine lactones (AHSL), act as diffusible signaling molecules enabling communication between bacterial cells. The AHSLs are structurally diverse and differ in their acyl chain length. This gives the bacteria signaling specificity and enables the recognition and communication within its own species. In order to detect and respond to the AHSLs the bacteria use QS regulators, LuxR-type proteins. The aim of this study was to get a deeper understanding of the Ecc QS system. In the first part of the study we showed that even different strains of Ecc use different dialects and of physiological concentrations, only the cognate AHSL with the correct acyl chain is recognized as a signal that can switch on virulence genes. The molecular basis of the substrate specificity of the AHSL synthase ExpI was investigated in order to recognize the acyl chain length specificity determinants of distinct AHSL synthases. Several critical residues that define the size of the substrate-binding pocket were identified. We demonstrated that in the ExpISCC1 mutations M127T and F69L are sufficient to change the N-3-oxohexanoyl-L-homoserine lactone producing ExpISCC1 to an N-3-oxooctanoyl-L-homoserine lactone (3-oxo-C8-HSL) producing enzyme. In the second study the means of sensing specificity and response to the AHSL signaling molecule were investigated. We demonstrated that the AHSL receptor ExpR1 of Ecc strain SCC3193 has strict specificity for the cognate AHSL 3-oxo-C8-HSL. In addition we identified a second AHSL receptor ExpR2 with a novel property to sense AHSLs with different acyl chain lengths. In the absence of AHSLs ExpR1 and ExpR2 were found to act synergistically to repress the virulence gene expression. This repression was shown to be released by addition of AHSLs and appears to be largely mediated by the global negative regulator RsmA. In the third study random transposon mutagenesis was used to widen the knowledge of the Ecc QS regulon. Two new QS-controlled target genes, encoding a DNA-binding regulator Hor and a plant ferredoxin-like protein FerE, were identified. The QS control of the identified genes was executed by the QS regulators ExpR1 and ExpR2 and as expression of PCWDE genes mediated by the RsmA repressor. Hor was shown to contribute to bacterial virulence at least partly through its control of PCWDE production, while FerE was shown to contribute to oxidative stress tolerance and in planta fitness of the bacteria. In addition our results suggest that QS is central to the control of oxidative stress tolerance in Ecc. In conclusion, these results indicate that Ecc strain SCC3193 is able to react and respond both to the cognate AHSL signal and the signals produced by other bacterial species, in order to control a wide variety of functions in the plant pathogen Ecc.

Mu in vitro transposition applications in protein engineering

Transposons, mobile genetic elements that are ubiquitous in all living organisms have been used as tools in molecular biology for decades. They have the ability to move into discrete DNA locations with no apparent homology to the target site. The utility of transposons as molecular tools is based on their ability to integrate into various DNA sequences efficiently, producing extensive mutant clone libraries that can be used in various molecular biology applications. Bacteriophage Mu is one of the most useful transposons due to its well-characterized and simple in vitro transposition reaction. This study establishes the properties of the Mu in vitro transposition system as a versatile multipurpose tool in molecular biology. In addition, this study describes Mu-based applications for engineering proteins by random insertional transposon mutagenesis in order to study structure-function relationships in proteins. We initially characterized the properties of the minimal Mu in vitro transposition system. We showed that the Mu transposition system works efficiently and accurately and produces insertions into a wide spectrum of target sites in different DNA molecules. Then, we developed a pentapeptide insertion mutagenesis strategy for inserting random five amino acid cassettes into proteins. These protein variants can be used especially for screening important sites for protein-protein interactions. Also, the system may produce temperature-sensitive variants of the protein of interest. Furthermore, we developed an efficient screening system for high-resolution mapping of protein-protein interfaces with the pentapeptide insertion mutagenesis. This was accomplished by combining the mutagenesis with subsequent yeast two-hybrid screening and PCR-based genetic footprinting. This combination allows the analysis of the whole mutant library en masse, without the need for producing or isolating separate mutant clones, and the protein-protein interfaces can be determined at amino acid accuracy. The system was validated by analysing the interacting region of JFC1 with Rab8A, and we show that the interaction is mediated via the JFC1 Slp homology domain. In addition, we developed a procedure for the production of nested sets of N- and C-terminal deletion variants of proteins with the Mu system. These variants are useful in many functional studies of proteins, especially in mapping regions involved in protein-protein interactions. This methodology was validated by analysing the region in yeast Mso1 involved in an interaction with Sec1. The results of this study show that the Mu in vitro transposition system is versatile for various applicational purposes and can efficiently be adapted to random protein engineering applications for functional studies of proteins.

Rolling tachyons, random matrices, and Coulomb gas thermodynamics

Time-dependent backgrounds in string theory provide a natural testing ground for physics concerning dynamical phenomena which cannot be reliably addressed in usual quantum field theories and cosmology. A good, tractable example to study is the rolling tachyon background, which describes the decay of an unstable brane in bosonic and supersymmetric Type II string theories. In this thesis I use boundary conformal field theory along with random matrix theory and Coulomb gas thermodynamics techniques to study open and closed string scattering amplitudes off the decaying brane. The calculation of the simplest example, the tree-level amplitude of n open strings, would give us the emission rate of the open strings. However, even this has been unknown. I will organize the open string scattering computations in a more coherent manner and will argue how to make further progress.

Markov random fields and spatial smoothing in improving of forest inventory estimates

Markov random fields (MRF) are popular in image processing applications to describe spatial dependencies between image units. Here, we take a look at the theory and the models of MRFs with an application to improve forest inventory estimates. Typically, autocorrelation between study units is a nuisance in statistical inference, but we take an advantage of the dependencies to smooth noisy measurements by borrowing information from the neighbouring units. We build a stochastic spatial model, which we estimate with a Markov chain Monte Carlo simulation method. The smooth values are validated against another data set increasing our confidence that the estimates are more accurate than the originals.

Light scattering in random media with wavelength-scale structures : astronomical and industrial applications

Light scattering, or scattering and absorption of electromagnetic waves, is an important tool in all remote-sensing observations. In astronomy, the light scattered or absorbed by a distant object can be the only source of information. In Solar-system studies, the light-scattering methods are employed when interpreting observations of atmosphereless bodies such as asteroids, atmospheres of planets, and cometary or interplanetary dust. Our Earth is constantly monitored from artificial satellites at different wavelengths. With remote sensing of Earth the light-scattering methods are not the only source of information: there is always the possibility to make in situ measurements. The satellite-based remote sensing is, however, superior in the sense of speed and coverage if only the scattered signal can be reliably interpreted. The optical properties of many industrial products play a key role in their quality. Especially for products such as paint and paper, the ability to obscure the background and to reflect light is of utmost importance. High-grade papers are evaluated based on their brightness, opacity, color, and gloss. In product development, there is a need for computer-based simulation methods that could predict the optical properties and, therefore, could be used in optimizing the quality while reducing the material costs. With paper, for instance, pilot experiments with an actual paper machine can be very time- and resource-consuming. The light-scattering methods presented in this thesis solve rigorously the interaction of light and material with wavelength-scale structures. These methods are computationally demanding, thus the speed and accuracy of the methods play a key role. Different implementations of the discrete-dipole approximation are compared in the thesis and the results provide practical guidelines in choosing a suitable code. In addition, a novel method is presented for the numerical computations of orientation-averaged light-scattering properties of a particle, and the method is compared against existing techniques. Simulation of light scattering for various targets and the possible problems arising from the finite size of the model target are discussed in the thesis. Scattering by single particles and small clusters is considered, as well as scattering in particulate media, and scattering in continuous media with porosity or surface roughness. Various techniques for modeling the scattering media are presented and the results are applied to optimizing the structure of paper. However, the same methods can be applied in light-scattering studies of Solar-system regoliths or cometary dust, or in any remote-sensing problem involving light scattering in random media with wavelength-scale structures.