Dipolaritons in quantum dots

Abstract. Dipolaritons are quasiparticles that arise in coupled quantum wells embedded in a microcavity, they are a superposition of a photon, a direct exciton and an indirect exciton. An interesting feature of dipolaritons is that their excitons can carry an electric dipole moment. Previous works have found this kind of system suitable for terahertz lasing (Phys. Rev. A 89, 023836) and Bose-Einstein condensation (Phys. Rev. B 90, 125314). In this thesis we study a system that consists of two interacting quantum dots embedded in a microcavity, from the point of view of dipolaritons in direct analogy with the quantum well case. A constant magnetic field is also taken into account. First, the zero temperature case is studied with an exact diagonalization of a finite system hamiltonian in order to find the effects of the magnetic field on the properties of direct and indirect excitons, including their statistics. Then we include light and investigate the properties of a single dipolariton. Next, a variational approach is used to study the many-body problem and we find the effects of the magnetic field on the ground state energy and number of photons. Finally, we consider the problem at finite temperatures and use a self-consistent procedure in a Hartree-Fock-Bogoliubov approximation to find the effect of the magnetic field on the critical temperature for Bose-Einstein condensation.Los dipolaritones son cuasipartículas que surgen en pozos cuánticos acoplados embebidos en una microcavidad; son una superposición de un fotón, un excitón directo y un excitón indirecto. Una característica interesante de los dipolaritones es que sus excitones pueden tener un momento de dipolo eléctrico. Trabajos anteriores han encontrado este tipo de sistemas como candidatos para emisión en terahertz (Phys. Rev. A 89, 023836) y condensación de Bose-Einstein (Phys. Rev. B 90, 125314). En esta tesis se estudia un sistema compuesto de dos puntos cuánticos interactuantes embebidos en una microcavidad, desde el punto de vista de los dipolaritones en analogía directa con el caso de pozos cuánticos. Se incluye, además, un campo magnético constante. Primero, el caso a temperatura cero se estudia con la diagonalización exacta de un hamiltoniano de sistemas finitos, con el objetivo de encontrar los efectos del campo magnético en las propiedades de excitones directos e indirectos, incluyendo su estadística. Luego se incluye la luz y se investigan las propiedades individuales de un dipolaritón. Posteriormente, un tratamiento variacional se desarrolla para estudiar el problema de muchos cuerpos y encontrar los efectos del campo magnético en la energía del estado base y el número de fotones. Finalmente, se considera el problema a temperatura finita y se utiliza un procedimiento autoconsistente en la aproximación de Hartree-Fock-Bogoliubov para encontrar el efecto del campo magnético en la temperatura crítica para la condensación de Bose-Einstein.Maestrí

YukE is the only protein dependent upon YukBA for secretion.

<p>(A). and (B). The relative abundance of proteins detected in the culture supernatant of the wild-type strain (PY79) versus the Δ<i>yukBA</i> strain (A) or the complemented Δ<i>yukBA</i>; <i>yukBA-myc</i> strain (B). Cells were grown in nutrient-limiting 1XMC medium to mid-exponential phase, and the supernatant fractions were filtered through a 0.2 micron filter and TCA precipitated. The proteins in the culture supernatant were analyzed by mass spectrometry. Protein abundance was determined by spectral count analysis; spectral count data are combined totals from three biologically independent samples for each strain. Where no spectra were identified, an arbitrary value of 1 was assigned. The data point for YukE is circled in each graph. The point for YukE is at (95,1) in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0096267#pone-0096267-g002" target="_blank">Figure 2A</a> and at (95, 116) in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0096267#pone-0096267-g002" target="_blank">Figure 2B</a>. The complementation strain was constructed with the ectopically expressed <i>yukBA</i> gene disrupting the native <i>amyE</i> locus. Thus, as expected, AmyE peptides are underrepresented in the complementation strain as compared to both wild-type and Δ<i>yukBA</i> strains; the point located at (77, 1) in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0096267#pone-0096267-g002" target="_blank">Figure 2B</a> corresponds to the peptides assigned to AmyE. High levels of YueB peptides in the Δ<i>yukBA</i> and complement strains is a consequence of strain design; the <i>yuk</i> promoter was reinserted after the <i>yukBA</i> deletion to drive expression of the downstream genes.</p

YukE is secreted, and secretion of YukE depends on other proteins encoded by the <i>yuk</i>/<i>yue</i> locus.

<p>A: Schematic depicting the <i>yuk</i>/<i>yue</i> locus and surrounding genes. Currently, there are five annotated genes in the <i>yuk</i> operon: <i>yukE, yukD, yukC, yukBA</i>, and <i>yueB </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0096267#pone.0096267-Barbe1" target="_blank">[31]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0096267#pone.0096267-SaoJose1" target="_blank">[32]</a>. Recent high throughput transcriptomics data implicates <i>yueC</i> and/or <i>yueD</i> as potential members of the <i>yuk</i>/<i>yue</i> locus as well <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0096267#pone.0096267-Nicolas1" target="_blank">[33]</a>. The predicted promoter (<i>Pyuk</i>) is indicated with an arrow. Homology to genes of other ESX/Ess systems is indicated below the corresponding <i>yuk</i>/<i>yue</i> gene name. B: Secretion assay for YukE. Cells were grown in LB medium to OD600nm of approximately 1.0–1.3. The cell pellet (P) was separated from the culture supernatant (S) by centrifugation. The pellet fractions were prepared into whole cell lysates and the supernatant fractions were filtered through a 0.2 micron filter and TCA precipitated. Samples were analyzed by SDS-PAGE under reducing conditions and immunoblot analysis with an α-YukE antibody and an α-SigmaA antibody as a loading/lysis control. The supernatants are shown in two exposures; the overexposed α-YukE blot (OE) allows visualization of faint bands. Data are representative of at least three biologically independent experiments. Pellet samples are equivalent to 0.1 OD and twenty-fold more was loaded for supernatant samples. Equivalent loading of precipitated supernatant samples was confirmed by densitometry of the Coomassie-stained gel.</p

<i>yuk</i>/<i>yue</i> knockout strains do not have a growth or competition defect compared to the wild-type strain.

<p>A: Growth curve of the wild-type strain (PY79) and <i>yuk</i>/<i>yue</i> knockout strains grown in LB medium shaking at 37°C. The OD600nm was taken every 30 minutes for a total of 540 minutes. The following <i>yuk</i>/<i>yue</i> knockout strains were tested: Δ<i>yukE</i>, Δ<i>yukD</i>, Δ<i>yukC</i>, Δ<i>yukBA</i>, Δ<i>yueB</i>, and Δ<i>yukEDCBAyueBCD</i>. B: The results of a representative competition experiment between Δ<i>yukEDCBA</i> (light gray) versus the wild-type reporter strain (dark gray) in nutrient-rich LB medium. This competition had a starting ratio of 10% Δ<i>yukEDCBA</i> cells to 90% wild-type cells. The percentages were determined by counting the number of blue and white colonies on a single plate each day (typically 150–250 colonies per plate) and then calculating the percentage of colonies from each strain. Shown are the mean percentages averaged from triplicate platings for each day.</p

Small protein ORFs are frequently coupled to the ORF downstream.

<p>(A) <i>M</i>. <i>tuberculosis</i> leaderless transcripts initiate unannotated small protein ORFs that terminate at the start of the annotated gene downstream more often than expected. All small protein ORF stop codons within 100 nucleotides of an annotated gene start are shown relative to that start codon (0 = coupled RTGA overlap). Three structural classes are identified: uORFs (the small ORF terminates upstream of the annotated start), coupled ORFs (linked by an RTGA tetramer), and overlapping ORFs. The y-axis shows the fraction of small ORFs that terminate a specified distance (x-axis) from the annotated start codon of the downstream gene. (B) One example of a coupled small protein in <i>M</i>. <i>tuberculosis</i> and <i>M</i>. <i>smegmatis</i>, upstream of orthologous genes. The primary sequence of the encoded small protein is not conserved, but the leaderless initiation and coupled linkage is maintained.</p

A translational reporter system identified leaderless and leadered initiation codon preferences.

<p>(A) Libraries of leader sequences were generated using two overlapping oligonucleotides, each with a single randomized codon positioned either at the leaderless position (+1) or the leadered position (+30), in-frame with the zeocin-resistance (<i>zeo</i>^r) gene. Self-primed heterodimers were inserted between the promoter and the <i>zeo</i>^r gene and transformed into <i>E</i>. <i>coli</i>. The library was electroporated into <i>M</i>. <i>smegmatis</i>. Hygromycin selection allowed maintenance of the complete library, while zeocin selection required translation initiation at either one of the randomized codon sites. Following selection in zeocin, plasmids were recovered and the leader regions amplified for Ion-Torrent sequencing. Deep sequencing of amplicon libraries allowed the unbiased identification and estimation of relative efficiency of initiation codons. (B) A Shine-Dalgarno site was omitted to facilitate direct comparison between leaderless and leadered architectures. Read counts were compiled for each of the 64 possible codons at the leaderless position (columns) and leadered position (rows). Heat map indicates read counts of each combinatorial leaderless/leadered codon pair, from 10⁰ (blue) through 10⁴ (yellow). Only ATG or GTG at the leaderless position were capable of initiating translation of <i>zeo</i>^r. At the leadered codon position, no enrichment indicated that translation initiation did not occur at any of the possible codons. A further reduction of the expected stop codons suggested that they prevented read through of leaderless ribosomes into the <i>zeo</i>^<i>r</i> ORF. (C) A Shine-Dalgarno sequence enables efficient use of diverse leadered initiation codons. A consensus Shine-Dalgarno (SD) element was placed upstream of the randomized leadered codon position. Zeocin-resistant pools showed a complex pattern of active translation initiation codons at both the leaderless and leadered positions. The presence of a Shine-Dalgarno supported translation initiation activity of ATG and GTG triplets in the leadered position, as well as the less common TTG and ATT triplets.</p

Definition of <i>cis</i> elements that support translation initiation in mycobacteria.

<p>(A) Zeo-seq viability reporter libraries were generated to determine the sequence context preferences for a SD upstream of a leadered initiation codon. Randomized nucleotides were positioned upstream of a leadered initiation codon, and zeocin selection enriched for Shine-Dalgarno-like sequences, indicating that mycobacteria adhere to this canonical translation criterion. (B) Leaderless translation initiation exhibits no sequence preference in the adjacent mRNA. A block of 6 nt was randomized immediately downstream of a leaderless initiation zeocin reporter construct. Sequences in the recovered pools of zeocin-resistant <i>M</i>. <i>smegmatis</i> were not enriched in composition or motifs in this region. The absence of any detectable enrichment in the randomized region for the leaderless pool indicates that there are no nucleotide preferences for efficient leaderless initiation in mycobacteria downstream of the RTG codon.</p

Leaderless gene architectures bring promoters and ORFs together.

<p>(A) Logo plot of TSS and proximal promoter region of traditional leadered genes. A purine (A or G) is favored at the +1 nucleotide, and an AT rich -10 element appears upstream. The 5’ UTR downstream of the transcription start site shows no sequence constraints or enrichment. (B) A Logo plot of the 5’ UTR from the translation initiation codon shows a Shine-Dalgarno-like AGGAGG sequence enrichment, centered 9–10 nt upstream (positions 10–11). From the initiation codon, the coding sequence downstream shows the wobble bias of the G-C rich mycobacterial genome. (C) The proximal promoter regions of leaderless genes have a -10 sequence of similar composition and spacing to that of leadered genes (compare to 2A). The TSS is also the first nucleotide of the translation initiation codon. There is no evidence of Shine-Dalgarno sequence enrichment upstream. The ORF initiated by leaderless codons shows the same wobble bias as seen in leadered ORFs.</p

Leaderless and leadered genes produce distinct RNA-seq and ribosome profiling 5’ boundaries.

<p>(A) The transcription start site (TSS) and translation initiation site are the same in leaderless genes. No 5’ UTR and no Shine-Dalgarno (SD) sequence imply that an assembled 70S ribosome engages the 5’ terminal initiation codon directly, followed by elongation to translate the ORF. Individual sequence reads from RNA-seq (green) and ribosome profiling (Ribo-seq, orange) analyses were mapped to the genome, and the abundance of the individual reads is indicated by the height of the peaks. In leaderless translation RNA-seq and ribosome profiling have coincident 5’ boundaries. The 5’ triplet is nearly always ATG or GTG and, in the typical example shown, corresponds to the predicted N-terminus of the annotated ORF. (B) Traditional gene structures generate nested ribosome profiling profiles, with a 5’ UTR that includes an SD ribosome-binding site upstream of the initiating methionine codon (ATG). The 30S and 50S ribosomal subunits assemble at the SD to form a complete 70S ribosome that begins translation at the adjacent AUG with an N-terminal formylated methionine (fM) amino acid residue. RNA-seq reads (green) indicate positive-strand transcription at this locus, and upstream of an annotated ORF. Mapped ribosome profiling reads (orange) begin downstream of the onset of RNA-seq reads, and ~17–35 nt upstream of the initiation codon of the annotated ORF. In both examples, JCVI correctly predicted the respective ORFs (black).</p