TY - THES
AB - A search problem lies in the complexity class FNP if a solution to the given instance of the problem can be verified efficiently. The complexity class TFNP consists of all search problems in FNP that are total in the sense that a solution is guaranteed to exist. TFNP contains a host of interesting problems from fields such as algorithmic game theory, computational topology, number theory and combinatorics. Since TFNP is a semantic class, it is unlikely to have a complete problem. Instead, one studies its syntactic subclasses which are defined based on the combinatorial principle used to argue totality. Of particular interest is the subclass PPAD, which contains important problems
like computing Nash equilibrium for bimatrix games and computational counterparts of several fixed-point theorems as complete. In the thesis, we undertake the study of averagecase hardness of TFNP, and in particular its subclass PPAD.
Almost nothing was known about average-case hardness of PPAD before a series of recent results showed how to achieve it using a cryptographic primitive called program obfuscation.
However, it is currently not known how to construct program obfuscation from standard cryptographic assumptions. Therefore, it is desirable to relax the assumption under which average-case hardness of PPAD can be shown. In the thesis we take a step in this direction. First, we show that assuming the (average-case) hardness of a numbertheoretic
problem related to factoring of integers, which we call Iterated-Squaring, PPAD is hard-on-average in the random-oracle model. Then we strengthen this result to show that the average-case hardness of PPAD reduces to the (adaptive) soundness of the Fiat-Shamir Transform, a well-known technique used to compile a public-coin interactive protocol into a non-interactive one. As a corollary, we obtain average-case hardness for PPAD in the random-oracle model assuming the worst-case hardness of #SAT. Moreover, the above results can all be strengthened to obtain average-case hardness for the class CLS ⊆ PPAD.
Our main technical contribution is constructing incrementally-verifiable procedures for computing Iterated-Squaring and #SAT. By incrementally-verifiable, we mean that every intermediate state of the computation includes a proof of its correctness, and the proof can be updated and verified in polynomial time. Previous constructions of such procedures relied on strong, non-standard assumptions. Instead, we introduce a technique called recursive proof-merging to obtain the same from weaker assumptions.
AU - Kamath Hosdurg, Chethan
ID - 7896
TI - On the average-case hardness of total search problems
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
TI - Biochemical and structural investigation of the Mrp antiporter, an ancestor of complex I
ER -
TY - THES
AB - Cytoplasm is a gel-like crowded environment composed of tens of thousands of macromolecules, organelles, cytoskeletal networks and cytosol. The structure of the cytoplasm is thought to be highly organized and heterogeneous due to the crowding of its constituents and their effective compartmentalization. In such an environment, the diffusive dynamics of the molecules is very restricted, an effect that is further amplified by clustering and anchoring of molecules. Despite the jammed nature of the cytoplasm at the microscopic scale, large-scale reorganization of cytoplasm is essential for important cellular functions, such as nuclear positioning and cell division. How such mesoscale reorganization of the cytoplasm is achieved, especially for very large cells such as oocytes or syncytial tissues that can span hundreds of micrometers in size, has only begun to be understood.
In this thesis, I focus on the recent advances in elucidating the molecular, cellular and biophysical principles underlying cytoplasmic organization across different scales, structures and species. First, I outline which of these principles have been identified by reductionist approaches, such as in vitro reconstitution assays, where boundary conditions and components can be modulated at ease. I then describe how the theoretical and experimental framework established in these reduced systems have been applied to their more complex in vivo counterparts, in particular oocytes and embryonic syncytial structures, and discuss how such complex biological systems can initiate symmetry breaking and establish patterning.
Specifically, I examine an example of large-scale reorganizations taking place in zebrafish embryos, where extensive cytoplasmic streaming leads to the segregation of cytoplasm from yolk granules along the animal-vegetal axis of the embryo. Using biophysical experimentation and theory, I investigate the forces underlying this process, to show that this process does not rely on cortical actin reorganization, as previously thought, but instead on a cell-cycle-dependent bulk actin polymerization wave traveling from the animal to the vegetal pole of the embryo. This wave functions in segregation by both pulling cytoplasm animally and pushing yolk granules vegetally. Cytoplasm pulling is mediated by bulk actin network flows exerting friction forces on the cytoplasm, while yolk granule pushing is achieved by a mechanism closely resembling actin comet formation on yolk granules. This study defines a novel role of bulk actin polymerization waves in embryo polarization via cytoplasmic segregation. Lastly, I describe the cytoplasmic reorganizations taking place during zebrafish oocyte maturation, where the initial segregation of the cytoplasm and yolk granules occurs. Here, I demonstrate a previously uncharacterized wave of microtubule aster formation, traveling the oocyte along the animal-vegetal axis. Further research is required to determine the role of such microtubule structures in cytoplasmic reorganizations therein.
Collectively, these studies provide further evidence for the coupling between cell cytoskeleton and cell cycle machinery, which can underlie a core self-organizing mechanism for orchestrating large-scale reorganizations in a cell-cycle-tunable manner, where the modulations of the force-generating machinery and cytoplasmic mechanics can be harbored to fulfill cellular functions.
AU - Shamipour, Shayan
ID - 8350
TI - Bulk actin dynamics drive phase segregation in zebrafish oocytes
ER -
TY - THES
AB - Algorithms in computational 3-manifold topology typically take a triangulation as an input and return topological information about the underlying 3-manifold. However, extracting the desired information from a triangulation (e.g., evaluating an invariant) is often computationally very expensive. In recent years this complexity barrier has been successfully tackled in some cases by importing ideas from the theory of parameterized algorithms into the realm of 3-manifolds. Various computationally hard problems were shown to be efficiently solvable for input triangulations that are sufficiently “tree-like.”
In this thesis we focus on the key combinatorial parameter in the above context: we consider the treewidth of a compact, orientable 3-manifold, i.e., the smallest treewidth of the dual graph of any triangulation thereof. By building on the work of Scharlemann–Thompson and Scharlemann–Schultens–Saito on generalized Heegaard splittings, and on the work of Jaco–Rubinstein on layered triangulations, we establish quantitative relations between the treewidth and classical topological invariants of a 3-manifold. In particular, among other results, we show that the treewidth of a closed, orientable, irreducible, non-Haken 3-manifold is always within a constant factor of its Heegaard genus.
AU - Huszár, Kristóf
ID - 8032
SN - 2663-337X
TI - Combinatorial width parameters for 3-dimensional manifolds
ER -
TY - THES
AB - Synthesis of proteins – translation – is a fundamental process of life. Quantitative studies anchor translation into the context of bacterial physiology and reveal several mathematical relationships, called “growth laws,” which capture physiological feedbacks between protein synthesis and cell growth. Growth laws describe the dependency of the ribosome abundance as a function of growth rate, which can change depending on the growth conditions. Perturbations of translation reveal that bacteria employ a compensatory strategy in which the reduced translation capability results in increased expression of the translation machinery.
Perturbations of translation are achieved in various ways; clinically interesting is the application of translation-targeting antibiotics – translation inhibitors. The antibiotic effects on bacterial physiology are often poorly understood. Bacterial responses to two or more simultaneously applied antibiotics are even more puzzling. The combined antibiotic effect determines the type of drug interaction, which ranges from synergy (the effect is stronger than expected) to antagonism (the effect is weaker) and suppression (one of the drugs loses its potency).
In the first part of this work, we systematically measure the pairwise interaction network for translation inhibitors that interfere with different steps in translation. We find that the interactions are surprisingly diverse and tend to be more antagonistic. To explore the underlying mechanisms, we begin with a minimal biophysical model of combined antibiotic action. We base this model on the kinetics of antibiotic uptake and binding together with the physiological response described by the growth laws. The biophysical model explains some drug interactions, but not all; it specifically fails to predict suppression.
In the second part of this work, we hypothesize that elusive suppressive drug interactions result from the interplay between ribosomes halted in different stages of translation. To elucidate this putative mechanism of drug interactions between translation inhibitors, we generate translation bottlenecks genetically using in- ducible control of translation factors that regulate well-defined translation cycle steps. These perturbations accurately mimic antibiotic action and drug interactions, supporting that the interplay of different translation bottlenecks partially causes these interactions.
We extend this approach by varying two translation bottlenecks simultaneously. This approach reveals the suppression of translocation inhibition by inhibited translation. We rationalize this effect by modeling dense traffic of ribosomes that move on transcripts in a translation factor-mediated manner. This model predicts a dissolution of traffic jams caused by inhibited translocation when the density of ribosome traffic is reduced by lowered initiation. We base this model on the growth laws and quantitative relationships between different translation and growth parameters.
In the final part of this work, we describe a set of tools aimed at quantification of physiological and translation parameters. We further develop a simple model that directly connects the abundance of a translation factor with the growth rate, which allows us to extract physiological parameters describing initiation. We demonstrate the development of tools for measuring translation rate.
This thesis showcases how a combination of high-throughput growth rate mea- surements, genetics, and modeling can reveal mechanisms of drug interactions. Furthermore, by a gradual transition from combinations of antibiotics to precise genetic interventions, we demonstrated the equivalency between genetic and chemi- cal perturbations of translation. These findings tile the path for quantitative studies of antibiotic combinations and illustrate future approaches towards the quantitative description of translation.
AU - Kavcic, Bor
ID - 8657
SN - 978-3-99078-011-4
TI - Perturbations of protein synthesis: from antibiotics to genetics and physiology
ER -