TY - JOUR AB - Previously, we reported that the allelic de-etiolated by zinc (dez) and trichome birefringence (tbr) mutants exhibit photomorphogenic development in the dark, which is enhanced by high Zn. TRICHOME BIREFRINGENCE-LIKE proteins had been implicated in transferring acetyl groups to various hemicelluloses. Pectin O-acetylation levels were lower in dark-grown dez seedlings than in the wild type. We observed Zn-enhanced photomorphogenesis in the dark also in the reduced wall acetylation 2 (rwa2-3) mutant, which exhibits lowered O-acetylation levels of cell wall macromolecules including pectins and xyloglucans, supporting a role for cell wall macromolecule O-acetylation in the photomorphogenic phenotypes of rwa2-3 and dez. Application of very short oligogalacturonides (vsOGs) restored skotomorphogenesis in dark-grown dez and rwa2-3. Here we demonstrate that in dez, O-acetylation of non-pectin cell wall components, notably of xyloglucan, is enhanced. Our results highlight the complexity of cell wall homeostasis and indicate against an influence of xyloglucan O-acetylation on light-dependent seedling development. AU - Sinclair, Scott A AU - Gille, S. AU - Pauly, M. AU - Krämer, U. ID - 7417 IS - 1 JF - Plant Signaling & Behavior SN - 1559-2324 TI - Regulation of acetylation of plant cell wall components is complex and responds to external stimuli VL - 15 ER - TY - JOUR AB - For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969). AU - Erdös, László AU - Krüger, Torben H AU - Schröder, Dominik J ID - 6185 JF - Communications in Mathematical Physics SN - 0010-3616 TI - Cusp universality for random matrices I: Local law and the complex Hermitian case VL - 378 ER - TY - THES AB - This thesis is based on three main topics: In the first part, we study convergence of discrete gradient flow structures associated with regular finite-volume discretisations of Fokker-Planck equations. We show evolutionary I convergence of the discrete gradient flows to the L2-Wasserstein gradient flow corresponding to the solution of a Fokker-Planck equation in arbitrary dimension d >= 1. Along the argument, we prove Mosco- and I-convergence results for discrete energy functionals, which are of independent interest for convergence of equivalent gradient flow structures in Hilbert spaces. The second part investigates L2-Wasserstein flows on metric graph. The starting point is a Benamou-Brenier formula for the L2-Wasserstein distance, which is proved via a regularisation scheme for solutions of the continuity equation, adapted to the peculiar geometric structure of metric graphs. Based on those results, we show that the L2-Wasserstein space over a metric graph admits a gradient flow which may be identified as a solution of a Fokker-Planck equation. In the third part, we focus again on the discrete gradient flows, already encountered in the first part. We propose a variational structure which extends the gradient flow structure to Markov chains violating the detailed-balance conditions. Using this structure, we characterise contraction estimates for the discrete heat flow in terms of convexity of corresponding path-dependent energy functionals. In addition, we use this approach to derive several functional inequalities for said functionals. AU - Forkert, Dominik L ID - 7629 SN - 2663-337X TI - Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains ER - TY - THES AB - This thesis concerns itself with the interactions of evolutionary and ecological forces and the consequences on genetic diversity and the ultimate survival of populations. It is important to understand what signals processes leave on the genome and what we can infer from such data, which is usually abundant but noisy. Furthermore, understanding how and when populations adapt or go extinct is important for practical purposes, such as the genetic management of populations, as well as for theoretical questions, since local adaptation can be the first step toward speciation. In Chapter 2, we introduce the method of maximum entropy to approximate the demographic changes of a population in a simple setting, namely the logistic growth model with immigration. We show that this method is not only a powerful tool in physics but can be gainfully applied in an ecological framework. We investigate how well it approximates the real behavior of the system, and find that is does so, even in unexpected situations. Finally, we illustrate how it can model changing environments. In Chapter 3, we analyze the co-evolution of allele frequencies and population sizes in an infinite island model. We give conditions under which polygenic adaptation to a rare habitat is possible. The model we use is based on the diffusion approximation, considers eco-evolutionary feedback mechanisms (hard selection), and treats both drift and environmental fluctuations explicitly. We also look at limiting scenarios, for which we derive analytical expressions. In Chapter 4, we present a coalescent based simulation tool to obtain patterns of diversity in a spatially explicit subdivided population, in which the demographic history of each subpopulation can be specified. We compare the results to existing predictions, and explore the relative importance of time and space under a variety of spatial arrangements and demographic histories, such as expansion and extinction. In the last chapter, we give a brief outlook to further research. AU - Szep, Eniko ID - 8574 TI - Local adaptation in metapopulations ER - TY - THES AB - We study the interacting homogeneous Bose gas in two spatial dimensions in the thermodynamic limit at fixed density. We shall be concerned with some mathematical aspects of this complicated problem in many-body quantum mechanics. More specifically, we consider the dilute limit where the scattering length of the interaction potential, which is a measure for the effective range of the potential, is small compared to the average distance between the particles. We are interested in a setting with positive (i.e., non-zero) temperature. After giving a survey of the relevant literature in the field, we provide some facts and examples to set expectations for the two-dimensional system. The crucial difference to the three-dimensional system is that there is no Bose–Einstein condensate at positive temperature due to the Hohenberg–Mermin–Wagner theorem. However, it turns out that an asymptotic formula for the free energy holds similarly to the three-dimensional case. We motivate this formula by considering a toy model with δ interaction potential. By restricting this model Hamiltonian to certain trial states with a quasi-condensate we obtain an upper bound for the free energy that still has the quasi-condensate fraction as a free parameter. When minimizing over the quasi-condensate fraction, we obtain the Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity, which plays an important role in our rigorous contribution. The mathematically rigorous result that we prove concerns the specific free energy in the dilute limit. We give upper and lower bounds on the free energy in terms of the free energy of the non-interacting system and a correction term coming from the interaction. Both bounds match and thus we obtain the leading term of an asymptotic approximation in the dilute limit, provided the thermal wavelength of the particles is of the same order (or larger) than the average distance between the particles. The remarkable feature of this result is its generality: the correction term depends on the interaction potential only through its scattering length and it holds for all nonnegative interaction potentials with finite scattering length that are measurable. In particular, this allows to model an interaction of hard disks. AU - Mayer, Simon ID - 7514 SN - 2663-337X TI - The free energy of a dilute two-dimensional Bose gas ER - TY - THES AB - Mrp (Multi resistance and pH adaptation) are broadly distributed secondary active antiporters that catalyze the transport of monovalent ions such as sodium and potassium outside of the cell coupled to the inward translocation of protons. Mrp antiporters are unique in a way that they are composed of seven subunits (MrpABCDEFG) encoded in a single operon, whereas other antiporters catalyzing the same reaction are mostly encoded by a single gene. Mrp exchangers are crucial for intracellular pH homeostasis and Na+ efflux, essential mechanisms for H+ uptake under alkaline environments and for reduction of the intracellular concentration of toxic cations. Mrp displays no homology to any other monovalent Na+(K+)/H+ antiporters but Mrp subunits have primary sequence similarity to essential redox-driven proton pumps, such as respiratory complex I and membrane-bound hydrogenases. This similarity reinforces the hypothesis that these present day redox-driven proton pumps are descended from the Mrp antiporter. The Mrp structure serves as a model to understand the yet obscure coupling mechanism between ion or electron transfer and proton translocation in this large group of proteins. In the thesis, I am presenting the purification, biochemical analysis, cryo-EM analysis and molecular structure of the Mrp complex from Anoxybacillus flavithermus solved by cryo-EM at 3.0 Å resolution. Numerous conditions were screened to purify Mrp to high homogeneity and to obtain an appropriate distribution of single particles on cryo-EM grids covered with a continuous layer of ultrathin carbon. A preferred particle orientation problem was solved by performing a tilted data collection. The activity assays showed the specific pH-dependent profile of secondary active antiporters. The molecular structure shows that Mrp is a dimer of seven-subunit protomers with 50 trans-membrane helices each. The dimer interface is built by many short and tilted transmembrane helices, probably causing a thinning of the bacterial membrane. The surface charge distribution shows an extraordinary asymmetry within each monomer, revealing presumable proton and sodium translocation pathways. The two largest and homologous Mrp subunits MrpA and MrpD probably translocate one proton each into the cell. The sodium ion is likely being translocated in the opposite direction within the small subunits along a ladder of charged and conserved residues. Based on the structure, we propose a mechanism were the antiport activity is accomplished via electrostatic interactions between the charged cations and key charged residues. The flexible key TM helices coordinate these electrostatic interactions, while the membrane thinning between the monomers enables the translocation of sodium across the charged membrane. The entire family of redox-driven proton pumps is likely to perform their mechanism in a likewise manner. AU - Steiner, Julia ID - 8353 SN - 2663-337X TI - Biochemical and structural investigation of the Mrp antiporter, an ancestor of complex I ER - TY - THES AB - The plant hormone auxin plays indispensable roles in plant growth and development. An essential level of regulation in auxin action is the directional auxin transport within cells. The establishment of auxin gradient in plant tissue has been attributed to local auxin biosynthesis and directional intercellular auxin transport, which both are controlled by various environmental and developmental signals. It is well established that asymmetric auxin distribution in cells is achieved by polarly localized PIN-FORMED (PIN) auxin efflux transporters. Despite the initial insights into cellular mechanisms of PIN polarization obtained from the last decades, the molecular mechanism and specific regulators mediating PIN polarization remains elusive. In this thesis, we aim to find novel players in PIN subcellular polarity regulation during Arabidopsis development. We first characterize the physiological effect of piperonylic acid (PA) on Arabidopsis hypocotyl gravitropic bending and PIN polarization. Secondly, we reveal the importance of SCFTIR1/AFB auxin signaling pathway in shoot gravitropism bending termination. In addition, we also explore the role of myosin XI complex, and actin cytoskeleton in auxin feedback regulation on PIN polarity. In Chapter 1, we give an overview of the current knowledge about PIN-mediated auxin fluxes in various plant tropic responses. In Chapter 2, we study the physiological effect of PA on shoot gravitropic bending. Our results show that PA treatment inhibits auxin-mediated PIN3 repolarization by interfering with PINOID and PIN3 phosphorylation status, ultimately leading to hyperbending hypocotyls. In Chapter 3, we provide evidence to show that the SCFTIR1/AFB nuclear auxin signaling pathway is crucial and required for auxin-mediated PIN3 repolarization and shoot gravitropic bending termination. In Chapter 4, we perform a phosphoproteomics approach and identify the motor protein Myosin XI and its binding protein, the MadB2 family, as an essential regulator of PIN polarity for auxin-canalization related developmental processes. In Chapter 5, we demonstrate the vital role of actin cytoskeleton in auxin feedback on PIN polarity by regulating PIN subcellular trafficking. Overall, the data presented in this PhD thesis brings novel insights into the PIN polar localization regulation that resulted in the (re)establishment of the polar auxin flow and gradient in response to environmental stimuli during plant development. AU - Han, Huibin ID - 8589 SN - 2663-337X TI - Novel insights into PIN polarity regulation during Arabidopsis development ER - TY - JOUR AB - Multiple resistance and pH adaptation (Mrp) antiporters are multi-subunit Na+ (or K+)/H+ exchangers representing an ancestor of many essential redox-driven proton pumps, such as respiratory complex I. The mechanism of coupling between ion or electron transfer and proton translocation in this large protein family is unknown. Here, we present the structure of the Mrp complex from Anoxybacillus flavithermus solved by cryo-EM at 3.0 Å resolution. It is a dimer of seven-subunit protomers with 50 trans-membrane helices each. Surface charge distribution within each monomer is remarkably asymmetric, revealing probable proton and sodium translocation pathways. On the basis of the structure we propose a mechanism where the coupling between sodium and proton translocation is facilitated by a series of electrostatic interactions between a cation and key charged residues. This mechanism is likely to be applicable to the entire family of redox proton pumps, where electron transfer to substrates replaces cation movements. AU - Steiner, Julia AU - Sazanov, Leonid A ID - 8284 JF - eLife TI - Structure and mechanism of the Mrp complex, an ancient cation/proton antiporter VL - 9 ER - TY - THES AB - In the thesis we focus on the interplay of the biophysics and evolution of gene regulation. We start by addressing how the type of prokaryotic gene regulation – activation and repression – affects spurious binding to DNA, also known as transcriptional crosstalk. We propose that regulatory interference caused by excess regulatory proteins in the dense cellular medium – global crosstalk – could be a factor in determining which type of gene regulatory network is evolutionarily preferred. Next,we use a normative approach in eukaryotic gene regulation to describe minimal non-equilibrium enhancer models that optimize so-called regulatory phenotypes. We find a class of models that differ from standard thermodynamic equilibrium models by a single parameter that notably increases the regulatory performance. Next chapter addresses the question of genotype-phenotype-fitness maps of higher dimensional phenotypes. We show that our biophysically realistic approach allows us to understand how the mechanisms of promoter function constrain genotypephenotype maps, and how they affect the evolutionary trajectories of promoters. In the last chapter we ask whether the intrinsic instability of gene duplication and amplification provides a generic alternative to canonical gene regulation. Using mathematical modeling, we show that amplifications can tune gene expression in many environments, including those where transcription factor-based schemes are hard to evolve or maintain. AU - Grah, Rok ID - 8155 SN - 2663-337X TI - Gene regulation across scales – how biophysical constraints shape evolution ER - TY - JOUR AU - Han, Huibin AU - Rakusova, Hana AU - Verstraeten, Inge AU - Zhang, Yuzhou AU - Friml, Jiří ID - 7643 IS - 5 JF - Plant Physiology SN - 0032-0889 TI - SCF TIR1/AFB auxin signaling for bending termination during shoot gravitropism VL - 183 ER -