Lusztig Induction, Unipotent Supports, and Character Bounds

Recently, a strong exponential character bound has been established in [3] for all elements $g \in \mathbf{G}^F$ of a finite reductive group $\mathbf{G}^F$ which satisfy the condition that the centraliser $C_{\mathbf{G}}(g)$ is contained in a $(\mathbf{G},F)$-split Levi subgroup $\mathbf{M}$ of $\mathbf{G}$ and that $\mathbf{G}$ is defined over a field of good characteristic. In this paper, assuming a weak version of Lusztig's conjecture relating irreducible characters and characteristic functions of character sheaves holds, we considerably generalize this result by removing the condition that $\mathbf{M}$ is split. This assumption is known to hold whenever $Z(\mathbf{G})$ is connected or when $\mathbf{G}$ is a special linear or symplectic group and $\mathbf{G}$ is defined over a sufficiently large finite field.Comment: 35 pages; v2. minor improvements to abstract and introduction; v3. further improvements to the exposition; v4. significant changes. Main result now works for special linear and symplectic groups. Added results on groups of type A generalising results of Hildebrand; v5. post referee repor

Non-abelian Littlewood-Offord inequalities

In 1943, Littlewood and Offord proved the first anti-concentration result for sums of independent random variables. Their result has since then been strengthened and generalized by generations of researchers, with applications in several areas of mathematics. In this paper, we present the first non-abelian analogue of Littlewood-Offord result, a sharp anti-concentration inequality for products of independent random variables.Comment: 14 pages Second version. Dependence of the upper bound on the matrix size in the main results has been remove

Design and Optimization of Nanoformulations for Stability and Sustained Release of Therapeutic Compounds

Due to the complexity of physiological conditions inside the human body, therapeutic compounds often face challenges such as short half-life in plasma, fast enzymatic metabolism and degradation. Nanocarriers such as liposomes and polymeric nanoparticles offer solutions to improve the stability and sustain the release of therapeutic compounds. However, the development of such vehicles often requires careful optimization. We demonstrated that by using X-ray techniques integrated with the Langmuir trough, the liposomal development process can be shortened significantly through the understanding of the molecular interaction between our prodrug 5-FCPal, a capecitabine analogue, with our model lipids and the effects of 5-FCPal on the lipid packing structure at the air-liquid interface. Additionally, the X-ray techniques can be used as a new platform to predict the drug loading in liposomes by increasing the molar fraction of the prodrug in the monolayer and observing the changes in molecular interaction. It was revealed that 5-FCPal interacted strongly with cationic lipids through electrostatic interaction of the head groups and caused the molecular packing to be tighter while the prodrug exhibited weak interaction with neutral and anionic lipids. Proof-of-concept nanoformulations were prepared and found that cationic lipids were able to form 100 nm vesicles while neutral lipids formed large aggregates with 5-FCPal. Utilizing a unique flash nanoprecipitation (FNP) process, polymeric particles were optimized to sustain the release of pazopanib for the treatment of osteoarthritis (OA). The results showed that the release of pazopanib strongly depended on the degradation rate of the polymer matrix and pH conditions. In vivo efficacy evaluation found that after single injection, the pain reduction effect lasted up to 16 weeks in mice with partial medial meniscectomy (PMM)-induced knee. FNP was also optimized to produce PLGA polymeric nanoparticles encapsulating emricasan, a peptide compound with poor pharmacokinetics property. The nanoparticles stability in aqueous condition was tracked for 6 hours. Our results indicated that the nanoparticles were more stable with shorter sonication time and lower concentration of trehalose (added as cryoprotectant). These results lay the important groundwork for future direction of designing stable nanoparticles systems to improve emricasan pharmacokinetics and enhance its cancer treatment property

Activity of moxifloxacin against biofilms formed by clinical isolates of Staphylococcus aureus differing by their resistant or persister character to fluoroquinolones

Staphylococcus aureus biofilms are poorly responsive to antibiotics. Underlying reasons include a matrix effect preventing drug access to embedded bacteria, or the presence of dormant bacteria with reduced growth rate. Using 18 clinical isolates previously characterized for their moxifloxacin-resistant and moxifloxacin-persister character in stationary-phase culture, we studied their biofilm production and matrix composition and the anti-biofilm activity of moxifloxacin. Biofilms were grown in microtiter plates and their abundance quantified by crystal violet staining and colony counting; their content in polysaccharides, extracellular DNA and proteins was measured. Moxifloxacin activity was assessed after 24 h of incubation with a broad range of concentrations to establish full concentration-response curves. All clinical isolates produced more biofilm biomass than the reference strain ATCC 25923, the difference being more important for those with high relative persister fractions to moxifloxacin, most of which being also resistant. High biofilm producers expressed icaA to higher levels, enriching the matrix in polysaccharides. Moxifloxacin was less potent against biofilms from clinical isolates than from ATCC 25923, especially against moxifloxacin-resistant isolates with high persister fractions, which was ascribed to a lower concentration of moxifloxacin in these biofilms. Time-kill curves in biofilms revealed the presence of a moxifloxacin-tolerant subpopulation, with low multiplication capacity, whatever the persister character of the isolate. Thus, moxifloxacin activity depends on its local concentration in biofilm, which is reduced in most isolates with high-relative persister fractions due to matrix effects, and insufficient to kill resistant isolates due to their high MIC

The Persister Character of Clinical Isolates of Staphylococcus aureus Contributes to Faster Evolution to Resistance and Higher Survival in THP-1 Monocytes: A Study With Moxifloxacin

Staphylococcus aureus may cause relapsing infections. We previously showed that S. aureus SH1000 surviving intracellularly to bactericidal antibiotics are persisters. Here, we used 54 non-duplicate clinical isolates to assess links between persistence, resistance evolution, and intracellular survival, using moxifloxacin throughout as test bactericidal antibiotic. The relative persister fraction (RPF: percentage of inoculum surviving to 100× MIC moxifloxacin in stationary phase culture for each isolate relative to ATCC 25923) was determined to categorize isolates with low (≤10) or high (>10) RPF. Evolution to resistance (moxifloxacin MIC ≥ 0.5 mg/L) was triggered by serial passages at 0.5× MIC (with daily concentration readjustments). Intracellular moxifloxacin maximal efficacy (Emax) was determined by 24 h concentration-response experiments [pharmacodynamic model (Hill-Langmuir)] with infected THP-1 monocytes exposed to moxifloxacin (0.01 to 100× MIC) after phagocytosis. Division of intracellular survivors was followed by green fluorescence protein dilution (FACS). Most (30/36) moxifloxacin-susceptible isolates showed low RPF but all moxifloxacin-resistant (n = 18) isolates harbored high RPF. Evolution to resistance of susceptible isolates was faster for those with high vs. low RPF (with SOS response and topoisomerase-encoding genes overexpression). Intracellularly, moxifloxacin Emax was decreased (less negative) for isolates with high vs. low RPF, independently from resistance. Moxifloxacin intracellular survivors were non-dividing. The data demonstrate and quantitate persisters in clinical isolates of S. aureus, and show that this phenotype accelerates resistance evolution and is associated with intracellular survival in spite of high antibiotic concentrations. Isolates with high RPF may represent a possible cause of treatment failure not directly related to resistance in patients receiving active antibiotics