A simple bijection for classical and enhanced k-noncrossing partitions

In this short note, we give a simple bijection from partitions of subsets of [n] to partitions of [n+1], in which enhanced k-crossings correspond to classical k-crossings. This resolves a recent conjecture of Zhicong Lin involving the binomial transform of the sequence that enumerates enhanced k-noncrossing partitions.Comment: 2 page

From Dyck Paths to Standard Young Tableaux

We present nine bijections between classes of Dyck paths and classes of standard Young tableaux (SYT). In particular, we consider SYT of flag and rectangular shapes, we give Dyck path descriptions for certain SYT of height at most 3, and we introduce a special class of labeled Dyck paths of semilength n that is shown to be in bijection with the set of all SYT with n boxes. In addition, we present bijections from certain classes of Motzkin paths to SYT. As a natural framework for some of our bijections, we introduce a class of set partitions which in some sense is dual to the known class of noncrossing partitions

Chemoenzymatic Labeling of Proteins for Imaging in Bacterial Cells

Reliable methods to determine the subcellular localization of bacterial proteins are needed for the study of prokaryotic cell biology. We describe here a simple and general technique for imaging of bacterial proteins in situ by fluorescence microscopy. The method uses the eukaryotic enzyme N-myristoyltransferase to modify the N-terminus of the protein of interest with an azido fatty acid. Subsequent strain-promoted azide–alkyne cycloaddition allows conjugation of dyes and imaging of tagged proteins by confocal fluorescence microscopy. We demonstrate the method by labeling the chemotaxis proteins Tar and CheA and the cell division proteins FtsZ and FtsA in Escherichia coli. We observe distinct spatial patterns for each of these proteins in both fixed and live cells. The method should prove broadly useful for protein imaging in bacteria

Mechanisms of diffusion in associative polymer networks: evidence for chain hopping

Networks assembled by reversible association of telechelic polymers constitute a common class of soft materials. Various mechanisms of chain migration in associative networks have been proposed; yet there remains little quantitative experimental data to discriminate among them. Proposed mechanisms for chain migration include multichain aggregate diffusion as well as single-chain mechanisms such as “walking” and “hopping”, wherein diffusion is achieved by either partial (“walking”) or complete (“hopping”) disengagement of the associated chain segments. Here, we provide evidence that hopping can dominate the effective diffusion of chains in associative networks due to a strong entropic penalty for bridge formation imposed by local network structure; chains become conformationally restricted upon association with two or more spatially separated binding sites. This restriction decreases the effective binding strength of chains with multiple associative domains, thereby increasing the probability that a chain will hop. For telechelic chains this manifests as binding asymmetry, wherein the first association is effectively stronger than the second. We derive a simple thermodynamic model that predicts the fraction of chains that are free to hop as a function of tunable molecular and network properties. A large set of self-diffusivity measurements on a series of model associative polymers finds good agreement with this model

Mechanisms of diffusion in associative polymer networks: evidence for chain hopping

Networks assembled by reversible association of telechelic polymers constitute a common class of soft materials. Various mechanisms of chain migration in associative networks have been proposed; yet there remains little quantitative experimental data to discriminate among them. Proposed mechanisms for chain migration include multichain aggregate diffusion as well as single-chain mechanisms such as “walking” and “hopping”, wherein diffusion is achieved by either partial (“walking”) or complete (“hopping”) disengagement of the associated chain segments. Here, we provide evidence that hopping can dominate the effective diffusion of chains in associative networks due to a strong entropic penalty for bridge formation imposed by local network structure; chains become conformationally restricted upon association with two or more spatially separated binding sites. This restriction decreases the effective binding strength of chains with multiple associative domains, thereby increasing the probability that a chain will hop. For telechelic chains this manifests as binding asymmetry, wherein the first association is effectively stronger than the second. We derive a simple thermodynamic model that predicts the fraction of chains that are free to hop as a function of tunable molecular and network properties. A large set of self-diffusivity measurements on a series of model associative polymers finds good agreement with this model

Analysis and Control of Chain Mobility in Protein Hydrogels

Coiled-coil domains can direct the assembly of protein block copolymers into physically cross-linked, viscoelastic hydrogels. Here, we describe the use of fluorescence recovery after photobleaching (FRAP) to probe chain mobility in reversible hydrogels assembled from engineered proteins bearing terminal coiled-coil domains. We show that chain mobility can be related to the underlying dynamics of the coiled-coil domains by application of a three-state “hopping” model of chain migration. We further show that genetic programming allows the effective mobility of network chains to be varied 500-fold through modest changes in protein sequence. Destabilization of the coiled-coil domains by site-directed mutagenesis increases the effective diffusivity of probe chains. Conversely, probe mobility is reduced by expanding the hydrophobic surface area of the coiled-coil domains through introduction of the bulky leucine surrogate homoisoleucine. Predictions from the three-state model imply asymmetric sequential binding of the terminal domains. Brownian Dynamics simulations suggest that binding asymmetry is a general feature of reversible gels, arising from a loss in entropy as chains transition to a conformationally restricted bridged state

4S-Hydroxylation of insulin at ProB28 accelerates hexamer dissociation and delays fibrillation

Daily injections of insulin provide lifesaving benefits to millions of diabetics. But currently available prandial insulins are suboptimal: The onset of action is delayed by slow dissociation of the insulin hexamer in the subcutaneous space, and insulin forms amyloid fibrils upon storage in solution. Here we show, through the use of non-canonical amino acid mutagenesis, that replacement of the proline residue at position 28 of the insulin B-chain (ProB28) by (4S)-hydroxyproline (Hzp) yields an active form of insulin that dissociates more rapidly, and fibrillates more slowly, than the wild-type protein. Crystal structures of dimeric and hexameric insulin preparations suggest that a hydrogen bond between the hydroxyl group of Hzp and a backbone amide carbonyl positioned across the dimer interface may be responsible for the altered behavior. The effects of hydroxylation are stereospecific; replacement of ProB28 by (4R)-hydroxyproline (Hyp) causes little change in the rates of fibrillation and hexamer disassociation. These results demonstrate a new approach that fuses the concepts of medicinal chemistry and protein design, and paves the way to further engineering of insulin and other therapeutic proteins

Controlled Assembly of Macromolecular β-Sheet Fibrils

Construction of functional molecular devices by directed assembly processes is one of the main challenges in the field of nanotechnology. Many approaches to this challenge use biological assembly as a source of inspiration for the build up of new materials with controlled organization at the nanoscale. In particular, the self-assembly properties of β-sheet peptides have been used in the design of supramolecular materials, such as tapes, nanotubes, and fibrils

Cyclometalated iridium(III)-sensitized titanium dioxide solar cells

Ir(III) dyes used as sensitizers in dye-sensitized solar cells produced quantum yields approaching unity for conversion of absorbed photons to current under simulated air mass 1.0 sunlight, with current production resulting from ligand-to-ligand charge-transfer states, rather than the typical metal-to-ligand charge-transfer states in ruthenium-based cells

Selective Proteomic Analysis of Antibiotic-Tolerant Cellular Subpopulations in Pseudomonas aeruginosa Biofilms

Biofilm infections exhibit high tolerance against antibiotic treatment. The study of biofilms is complicated by phenotypic heterogeneity; biofilm subpopulations differ in their metabolic activities and their responses to antibiotics. Here, we describe the use of the bio-orthogonal noncanonical amino acid tagging (BONCAT) method to enable selective proteomic analysis of a Pseudomonas aeruginosa biofilm subpopulation. Through controlled expression of a mutant methionyl-tRNA synthetase, we targeted BONCAT labeling to cells in the regions of biofilm microcolonies that showed increased tolerance to antibiotics. We enriched and identified proteins synthesized by cells in these regions. Compared to the entire biofilm proteome, the labeled subpopulation was characterized by a lower abundance of ribosomal proteins and was enriched in proteins of unknown function. We performed a pulse-labeling experiment to determine the dynamic proteomic response of the tolerant subpopulation to supra-MIC treatment with the fluoroquinolone antibiotic ciprofloxacin. The adaptive response included the upregulation of proteins required for sensing and repairing DNA damage and substantial changes in the expression of enzymes involved in central carbon metabolism. We differentiated the immediate proteomic response, characterized by an increase in flagellar motility, from the long-term adaptive strategy, which included the upregulation of purine synthesis. This targeted, selective analysis of a bacterial subpopulation demonstrates how the study of proteome dynamics can enhance our understanding of biofilm heterogeneity and antibiotic tolerance.IMPORTANCE Bacterial growth is frequently characterized by behavioral heterogeneity at the single-cell level. Heterogeneity is especially evident in the physiology of biofilms, in which distinct cellular subpopulations can respond differently to stresses, including subpopulations of pathogenic biofilms that are more tolerant to antibiotics. Global proteomic analysis affords insights into cellular physiology but cannot identify proteins expressed in a particular subpopulation of interest. Here, we report a chemical biology method to selectively label, enrich, and identify proteins expressed by cells within distinct regions of biofilm microcolonies. We used this approach to study changes in protein synthesis by the subpopulation of antibiotic-tolerant cells throughout a course of treatment. We found substantial differences between the initial response and the long-term adaptive strategy that biofilm cells use to cope with antibiotic stress. The method we describe is readily applicable to investigations of bacterial heterogeneity in diverse contexts