Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.

Molecular Insights of CD4+ T Cell Differentiation, Effector Formation and Helper Function

CD4+ T cells play a crucial in the adaptive immune system. They function as the central hub to orchestrate the rest of immunity: CD4+ T cells are essential governing machinery in antibacterial and antiviral responses by facilitating B cell affinity maturation and coordinating the innate and adaptive immune systems to boost the overall immune outcome; on the contrary, hyperactivation of the inflammatory lineages of CD4+ T cells, as well as the impairments of suppressive CD4+ regulatory T cells, are the etiology of various autoimmunity and inflammatory diseases. The broad role of CD4+ T cells in both physiological and pathological contexts prompted me to explore the modulation of CD4+ T cells on the molecular level.

microRNAs (miRNAs) are small RNA molecules capable of regulating gene expression post-transcriptionally. miRNAs have been shown to exert substantial regulatory effects on CD4+ T cell activation, differentiation and helper function. Specifically, my lab has previously established the function of the miR-17-92 cluster in Th1 differentiation and anti-tumor responses. Here, I further analyzed the role of this miRNA cluster in Th17 differentiation, specifically, in the context of autoimmune diseases. Using both gain- and loss-of-function approaches, I demonstrated that miRNAs in miR-17-92, specifically, miR-17 and miR-19b in this cluster, is a crucial promoter of Th17 differentiation. Consequently, loss of miR-17-92 expression in T cells mitigated the progression of experimental autoimmune encephalomyelitis and T cell-induced colitis. In combination with my previous data, the molecular dissection of this cluster establishes that miR-19b and miR-17 play a comprehensive role in promoting multiple aspects of inflammatory T cell responses, which underscore them as potential targets for oligonucleotide-based therapy in treating autoimmune diseases.

To systematically study miRNA regulation in effector CD4+ T cells, I devised a large-scale miRNAome profiling to track in vivo miRNA changes in antigen-specific CD4+ T cells activated by Listeria challenge. From this screening, I identified that miR-23a expression tightly correlates with CD4+ effector expansion. Ectopic expression and genetic deletion strategies validated that miR-23a was required for antigen-stimulated effector CD4+ T cell survival in vitro and in vivo. I further determined that miR-23a targets Ppif, a gatekeeper of mitochondrial reactive oxygen species (ROS) release that protects CD4+ T cells from necrosis. Necrosis is a type of cell death that provokes inflammation, and it is prominently triggered by ROS release and its consequent oxidative stress. My finding that miR-23a curbs ROS-mediated necrosis highlights the essential role of this miRNA in maintaining immune homeostasis.

A key feature of miRNAs is their ability to modulate different biological aspects in different cell populations. Previously, my lab found that miR-23a potently suppresses CD8+ T cell cytotoxicity by restricting BLIMP1 expression. Since BLIMP1 has been found to inhibit T follicular helper (Tfh) differentiation by antagonizing the master transcription factor BCL6, I investigated whether miR-23a is also involved in Tfh differentiation. However, I found that miR-23a does not target BLIMP1 in CD4+ T cells and loss of miR-23a even fostered Tfh differentiation. This data indicate that miR-23a may target other pathways in CD4+ T cells regarding the Tfh differentiation pathway.

Although the lineage identity and regulatory networks for Tfh cells have been defined, the differentiation path of Tfh cells remains elusive. Two models have been proposed to explain the differentiation process of Tfh cells: in the parallel differentiation model, the Tfh lineage is segregated from other effector lineages at the early stage of antigen activation; alternatively, the sequential differentiation model suggests that naïve CD4+ T cells first differentiate into various effector lineages, then further program into Tfh cells. To address this question, I developed a novel in vitro co-culture system that employed antigen-specific CD4+ T cells, naïve B cells presenting cognate T cell antigen and BAFF-producing feeder cells to mimic germinal center. Using this system, I were able to robustly generate GC-like B cells. Notably, well-differentiated Th1 or Th2 effector cells also quickly acquired Tfh phenotype and function during in vitro co-culture, which suggested a sequential differentiation path for Tfh cells. To examine this path in vivo, under conditions of classical Th1- or Th2-type immunizations, I employed a TCRβ repertoire sequencing technique to track the clonotype origin of Tfh cells. Under both Th1- and Th2- immunization conditions, I observed profound repertoire overlaps between the Teff and Tfh populations, which strongly supports the proposed sequential differentiation model. Therefore, my studies establish a new platform to conveniently study Tfh-GC B cell interactions and provide insights into Tfh differentiation processes.

Spontaneous Unfolding and Refolding of FNIII Domains Assayed by Thiol Exchange

Fibronectin (FN) is a large extracellular matrix (ECM) protein that is made up of

type I (FNI), type II (FNII), & type III (FNIII) domains. It assembles into an insoluble

supra-­‐‑molecular structure: the fibrillar FN matrix. FN fibrillogenesis is a cell‐‑mediated process, which is initiated when FN binds to integrins on the cell surface. The FN matrix plays an important role in cell migration, proliferation, signaling & adhesion. Despite decades of research, the FN matrix is one of the least understood supra-­‐‑molecular protein assemblies. There have been several attempts to elucidate the exact mechanism of matrix assembly resulting in significant progress in the field but it is still unclear as to what are FN-­‐‑FN interactions, the nature of these interactions and the domains of FN that

are in contact with each other. FN matrix fibrils are elastic in nature. Two models have been proposed to explain the elasticity of the fibrils. The first model: the ‘domain unfolding’ model postulates that the unraveling of FNIII domains under tension explains fibril elasticity.

The second model relies on the conformational change of FN from compact to extended to explain fibril elasticity. FN contain 15 FNIII domains, each a 7-­‐‑strand beta sandwich. Earlier work from our lab used the technique of labeling a buried Cys to study the ‘domain unfolding’ model. They used mutant FNs containing a buried Cys in a single FNIII domain and found that 6 of the 15 FNIII domains label in matrix fibrils. Domain unfolding due to tension, matrix associated conformational changes or spontaneous folding and unfolding are all possible explanation for labeling of the buried Cys. The present study also uses the technique of labeling a buried Cys to address whether it is spontaneous folding and unfolding that labels FNIII domains in cell culture. We used thiol reactive DTNB to measure the kinetics of labeling of buried Cys in eleven FN III domains over a wide range of urea concentrations (0-­‐‑9M). The kinetics data were globally fit using Mathematica. The results are equivalent to those of H-­‐‑D exchange, and

provide a comprehensive analysis of stability and unfolding/folding kinetics of each

domain. For two of the six domains spontaneous folding and unfolding is possibly the reason for labeling in cell culture. For the rest of the four domains it is probably matrix associated conformational changes or tension induced unfolding.

A long-­‐‑standing debate in the protein-­‐‑folding field is whether unfolding rate

constants or folding rate constants correlate to the stability of a protein. FNIII domains all have the same ß sandwich structure but very different stabilities and amino acid sequences. Our study analyzed the kinetics of unfolding and folding and stabilities of eleven FNIII domains and our results show that folding rate constants for FNIII domains are relatively similar and the unfolding rates vary widely and correlate to stability. FN forms a fibrillar matrix and the FN-­‐‑FN interactions during matrix fibril formation are not known. FNI 1-­‐‑9 or the N-­‐‑ terminal region is indispensible for matrix formation and its major binding partner has been shown to be FNIII 2. Earlier work from our lab, using FRET analysis showed that the interaction of FNI 1-­‐‑9 with a destabilized FNIII 2 (missing the G strand, FNIII 2ΔG) reduces the FRET efficiency. This efficiency is restored in the presence of FUD (bacterial adhesion from S. pyogenes) that has been known to interact with FNI 1-­‐‑9 via a tandem ß zipper. In the present study we

use FRET analysis and a series of deletion mutants of FNIII 2ΔG to study the shortest fragment of FNIII 2ΔG that is required to bind FNI 1-­‐‑9. Our results presented here are qualitative and show that FNIII 2ΔC’EFG is the shortest fragment required to bind FNI 1-­‐‑9. Deletion of one more strand abolishes the interaction with FNI 1-­‐‑9.