Distinct layers of BRD4-PTEFb reveal bromodomain-independent function in transcriptional regulation.

The BET family protein BRD4, which forms the CDK9-containing BRD4-PTEFb complex, is considered to be a master regulator of RNA polymerase II (Pol II) pause release. Because its tandem bromodomains interact with acetylated histone lysine residues, it has long been thought that BRD4 requires these bromodomains for its recruitment to chromatin and transcriptional regulatory function. Here, using rapid depletion and genetic complementation with domain deletion mutants, we demonstrate that BRD4 bromodomains are dispensable for Pol II pause release. A minimal, bromodomain-less C-terminal BRD4 fragment containing the PTEFb-interacting C-terminal motif (CTM) is instead both necessary and sufficient to mediate Pol II pause release in the absence of full-length BRD4. Although BRD4-PTEFb can associate with chromatin through acetyl recognition, our results indicate that a distinct, active BRD4-PTEFb population functions to regulate transcription independently of bromodomain-mediated chromatin association. These findings may enable more effective pharmaceutical modulation of BRD4-PTEFb activity.

Transcriptional elongation control of hypoxic response.

The release of paused RNA polymerase II (RNAPII) from promoter-proximal regions is tightly controlled to ensure proper regulation of gene expression. The elongation factor PTEF-b is known to release paused RNAPII via phosphorylation of the RNAPII C-terminal domain by its cyclin-dependent kinase component, CDK9. However, the signal and stress-specific roles of the various RNAPII-associated macromolecular complexes containing PTEF-b/CDK9 are not yet clear. Here, we identify and characterize the CDK9 complex required for transcriptional response to hypoxia. Contrary to previous reports, our data indicate that a CDK9 complex containing BRD4 but not AFF1/4 is essential for this hypoxic stress response. We demonstrate that BRD4 bromodomains (BET) are dispensable for the release of paused RNAPII at hypoxia-activated genes and that BET inhibition by JQ1 is insufficient to impair hypoxic gene response. Mechanistically, we demonstrate that the C-terminal region of BRD4 is required for Polymerase-Associated Factor-1 Complex (PAF1C) recruitment to establish an elongation-competent RNAPII complex at hypoxia-responsive genes. PAF1C disruption using a small-molecule inhibitor (iPAF1C) impairs hypoxia-induced, BRD4-mediated RNAPII release. Together, our results provide insight into potentially targetable mechanisms that control the hypoxia-responsive transcriptional elongation.

Somatic mutations of MLL4/COMPASS induce cytoplasmic localization providing molecular insight into cancer prognosis and treatment.

Cancer genome sequencing consortiums have recently catalogued an abundance of somatic mutations, across a wide range of human cancers, in the chromatin-modifying enzymes that regulate gene expression. Defining the molecular mechanisms underlying the potentially oncogenic functions of these epigenetic mutations could serve as the basis for precision medicine approaches to cancer therapy. MLL4 encoded by the KMT2D gene highly mutated in a large number of human cancers, is a key histone lysine monomethyltransferase within the Complex of Proteins Associated with Set1 (COMPASS) family that regulates gene expression through enhancer function, potentially functioning as a tumor suppressor. We report that the KMT2D mutations which cause MLL4 protein truncation also alter MLL4's subcellular localization, resulting in loss-of-function in the nucleus and gain-of-function in the cytoplasm. We demonstrate that isogenic correction of KMT2D truncation mutation rescues the aberrant localization phenotype and restores multiple regulatory functions of MLL4, including COMPASS integrity/stabilization, histone H3K4 mono-methylation, enhancer activation, and therefore transcriptional regulation. Moreover, isogenic correction diminishes the sensitivity of KMT2D-mutated cancer cells to targeted metabolic inhibition. Using immunohistochemistry, we identified that cytoplasmic MLL4 is unique to the tissue of bladder cancer patients with KMT2D truncation mutations. Using a preclinical carcinogen model of bladder cancer in mouse, we demonstrate that truncated cytoplasmic MLL4 predicts response to targeted metabolic inhibition therapy for bladder cancer and could be developed as a biomarker for KMT2D-mutated cancers. We also highlight the broader potential for prognosis, patient stratification and treatment decision-making based on KMT2D mutation status in MLL4 truncation-relevant diseases, including human cancers and Kabuki Syndrome.

The RNA pseudoknots in foot-and-mouth disease virus are dispensable for genome replication, but essential for the production of infectious virus.

Non-coding regions of viral RNA (vRNA) genomes are critically important in the regulation of gene expression. In particular, pseudoknot (PK) structures, which are present in a wide range of RNA molecules, have a variety of roles. The 5' untranslated region (5' UTR) of foot-and-mouth disease virus (FMDV) vRNA is considerably longer than in other viruses from the picornavirus family and consists of a number of distinctive structural motifs that includes multiple (2, 3 or 4 depending on the virus strain) putative PKs linked in tandem. The role(s) of the PKs in the FMDV infection are not fully understood. Here, using bioinformatics, sub-genomic replicons and recombinant viruses we have investigated the structural conservation and importance of the PKs in the FMDV lifecycle. Our results show that despite the conservation of two or more PKs across all FMDVs, a replicon lacking PKs was replication competent, albeit at reduced levels. Furthermore, in competition experiments, GFP FMDV replicons with less than two (0 or 1) PK structures were outcompeted by a mCherry FMDV wt replicon that had 4 PKs, whereas GFP replicons with 2 or 4 PKs were not. This apparent replicative advantage offered by the additional PKs correlates with the maintenance of at least two PKs in the genomes of FMDV field isolates. Despite a replicon lacking any PKs retaining the ability to replicate, viruses completely lacking PK were not viable and at least one PK was essential for recovery of infections virus, suggesting a role for the PKs in virion assembly. Thus, our study points to roles for the PKs in both vRNA replication and virion assembly, thereby improving understanding the molecular biology of FMDV replication and the wider roles of PK in RNA functions.

Incidence and Factors Associated With Acne in Transgender Adolescents on Testosterone: A Retrospective Cohort Study.

OBJECTIVE: This retrospective cohort study aimed to assess incidence and predictors of acne among transgender adolescents receiving testosterone. METHODS: We analyzed records of patients aged <18 years, assigned female at birth, seen at Children's Healthcare of Atlanta Pediatric Endocrinology clinic for testosterone initiation between January 1, 2016, and January 1, 2019, with at least 1-year follow-up documented. Bivariable analyses to determine the association of clinical and demographic factors with new acne diagnosis were performed. RESULTS: Of 60 patients, 46 (77%) did not have baseline acne, but of those 46 patients, 25 (54%) developed acne within 1 year of testosterone initiation. Overall incidence proportion was 70% at 2 years; patients who used progestin prior to or during follow-up were more likely to develop acne than nonusers (92% vs 33%, P <.001). CONCLUSION: Transgender adolescents starting testosterone, particularly those taking progestin, should be monitored for acne development and treated proactively by hormone providers and dermatologists.

Re-thinking Stepfathers' Contributions: Fathers, Stepfathers, and Child Wellbeing.

Using data from a contemporary cohort of children, we revisit the question of whether children benefit from being close to and engaging in activities with a stepfather. We deploy the Fragile Families and Child Wellbeing Study, a birth cohort study of nearly 5000 children born in US cities in 1998-2000, with a large oversample of nonmarital births. We explore the relationships between stepfathers' closeness and active engagement and youth's internalizing and externalizing behaviors and school connectedness at ages 9 and 15 for between 550 and 740 children (depending on the wave) with stepfathers. We find that the emotional tenor of the relationship and level of active engagement between youth and their stepfathers are associated with reduced internalizing behaviors and higher school connectedness. Our findings suggest that stepfathers' roles seem to have evolved in ways that are more beneficial to their adolescent stepchildren than was previously the case.

The experiences of people with disability and their families/carers navigating the NDIS planning process in regional, rural and remote regions of Australia: Scoping review.

BACKGROUND: Australia's National Disability Insurance Scheme (NDIS) was launched in 2013 to provide financial support packages for people with disability to purchase supports and services to enhance independence. People with disability are required to develop a plan with the National Disability Insurance Agency (NDIA), the government department responsible for managing the NDIS. This scoping review aims to ascertain the level of research into people's experience of the NDIS planning process in these geographic areas. METHODOLOGY: Research publication databases were searched using a specific search string to identify research about people with disability and their families/carer's experiences of the NDIS planning process in regional, rural and remote regions of Australia. The Mixed Methods Appraisal Tool (MMAT) was adopted to appraise the quality of the research publications. Research publications focused on Aboriginal and Torres Strait Islander people were additionally appraised using the Aboriginal and Torres Strait Islander Quality Appraisal Tool developed by the Centre for Excellence in Aboriginal Chronic Disease Knowledge Translation and Exchange. A thematic synthesis of the publications' contents was undertaken to ascertain people with disabilities and carers experience of the NDIS planning process. RESULTS: Ten (N = 10) research papers were found that met the inclusion criteria. Two papers were policy reviews and reported on the improvements of the NDIS planning process since its conception. The analysis found the research archive focused on five themes: (1) healthcare workforce and NDIA staff; (2) NDIS package holders and carers lack of awareness of the NDIS; (3) cultural/socio-economic barriers; (4) travel funding; and (5) emotional burden of the NDIS planning process. CONCLUSION: There are limited papers available that explore people's experiences of the NDIS planning process in regional, rural and remote regions of Australia. This systematic review illuminates the difficulties, barriers and concerns of people with disability and their carers about the planning process.

Disability workforce and the NDIS planning process in regional, rural and remote regions of Australia: Scoping review.

BACKGROUND: The Australian geographically rural and remote disability workforce has historically demonstrated difficulties to keep up with the demand for quality services and supports for people with disability. In 2013, the National Disability Insurance Scheme (NDIS) was launched to provide individualised disability support packages to meet people's needs. To receive funding, people with disability are required to develop a NDIS plan. That plan is then funded by the National Disability Insurance Agency (NDIA), the government agency responsible for managing the NDIS. Although the NDIS has been operating for almost 10 years, there is limited research into the planning experiences of the workforce in regional, rural and remote regions of Australia. This review aims to ascertain the level of scholarly investigation into workers' experiences of NDIS planning. METHODOLOGY: Research publication databases were searched using a specific search string to identify publications that included reference to the workforce's experiences of the NDIS planning process in regional, rural and remote regions of Australia. The Mixed Methods Appraisal Tool (MMAT) was adopted to appraise the quality of the research publications. Research publications that focused on those working with Aboriginal and Torres Strait Islander people were also appraised using the Aboriginal and Torres Strait Islander Quality Appraisal Tool developed by the Centre for Excellence in Aboriginal Chronic Disease Knowledge Translation and Exchange. A thematic synthesis of the publications was undertaken to ascertain disability and health workforce experiences of the NDIS planning process. RESULTS: Seven papers met the selection criteria. Two papers were policy reviews and reported the improvements of the NDIS planning process since its inception. These studies reported four reoccurring themes: (1) cultural/socioeconomic and geographical factors; (2) administrative burden and bureaucracy; (3) values, culture and geography; and (4) burden on allied health workers. CONCLUSION: The NDIS planning process has developed and progressed since its rollout in 2013. There are limited research papers available that describe the workforce's experience of the planning process in regional, rural and remote regions. More research in this area is needed to identify the experiences of the disability workforce in relation to the NDIS planning process.

Acute care utilization and housing hardships in American children.

Millions of families in the United States are economically vulnerable: one shock can lead to hardship. We use data from the Fragile Families and Child Wellbeing Study to examine the association between acute healthcare utilization - emergency room visits or hospitalizations - and subsequent housing hardships, such as being evicted for financial reasons. Further, we explore whether this association differs by who in the family utilized the care and whether perceived social support protects against hardship when these experiences occur. Using lagged dependent variable regression models, we find that families that visited the emergency room or were hospitalized, regardless if it was a child or parent with this experience, were five percentage points more likely to experience any housing hardship than families that did not use acute care. Among families in which a child utilized acute care, perceived social support buffered the impact of using acute care. That perceived social support is associated with a lower likelihood of housing hardship among families that experienced acute care utilization for a child, but not parent, suggests that social support may be able to offset the challenges arising from children's, but not adults', use of acute care. In the face of economic precarity, informal safety nets may be insufficient to reduce the impact of acute care utilization on housing hardships.

Government Assistance Protects Low-Income Families from Eviction.

A lack of affordable housing is a pressing issue for many low-income American families and can lead to eviction from their homes. Housing assistance programs to address this problem include public housing and other assistance, including vouchers, through which a government agency offsets the cost of private market housing. This paper assesses whether the receipt of either category of assistance reduces the probability that a family will be evicted from their home in the subsequent six years. Because no randomized trial has assessed these effects, we use observational data and formalize the conditions under which a causal interpretation is warranted. Families living in public housing experience less eviction conditional on pre-treatment variables. We argue that this evidence points toward a causal conclusion that assistance, particularly public housing, protects families from eviction.

Single-Molecule Stretching Shows Glycosylation Sets Tension in the Hyaluronan-Aggrecan Bottlebrush.

Large bottlebrush complexes formed from the polysaccharide hyaluronan (HA) and the proteoglycan aggrecan contribute to cartilage compression resistance and are necessary for healthy joint function. A variety of mechanical forces act on these complexes in the cartilage extracellular matrix, motivating the need for a quantitative description that links their structure and mechanical response. Studies using electron microscopy have imaged the HA-aggrecan brush but require adsorption to a surface, dramatically altering the complex from its native conformation. We use magnetic tweezers force spectroscopy to measure changes in extension and mechanical response of an HA chain as aggrecan monomers bind and form a bottlebrush. This technique directly measures changes undergone by a single complex with time and under varying solution conditions. Upon addition of aggrecan, we find a large swelling effect manifests when the HA chain is under very low external tension (i.e., stretching forces less than ∼1 pN). We use models of force-extension behavior to show that repulsion between the aggrecans induces an internal tension in the HA chain. Through reference to theories of bottlebrush polymer behavior, we demonstrate that the experimental values of internal tension are consistent with a polydisperse aggrecan population, likely caused by varying degrees of glycosylation. By enzymatically deglycosylating the aggrecan, we show that aggrecan glycosylation is the structural feature that causes HA stiffening. We then construct a simple stochastic binding model to show that variable glycosylation leads to a wide distribution of internal tensions in HA, causing variations in the mechanics at much longer length scales. Our results provide a mechanistic picture of how flexibility and size of HA and aggrecan lead to the brush architecture and mechanical properties of this important component of cartilage.

Standing MRI lesions of the distal interphalangeal joint and podotrochlear apparatus occur with a high frequency in warmblood horses.

Foot pain is a common presenting complaint in Warmblood horses. The aim of this retrospective, cross-sectional study was to determine the spectrum of foot lesions detected by magnetic resonance imaging (MRI) in Warmblood horses used for dressage, jumping, and eventing. The medical records of 550 Warmblood horses with foot pain that were scanned using standing MRI were reviewed and the following data were recorded: signalment, occupation, lameness, diagnostic analgesia, imaging results, treatments, and follow-up assessments. Associations between standing MRI lesions and chronic lameness following treatment were tested. Abnormalities of the navicular bone (409 horses, 74%), distal interphalangeal joint (362 horses, 65%), and deep digital flexor (DDF) tendon (260 horses, 47%) occurred with the highest frequency. The following abnormalities were significantly associated (P < .05) with chronic lameness following conservative therapy: moderate to severe MRI lesions in the trabecular bone of the navicular bone, mild or severe erosions of the flexor surface of the navicular bone, moderate sagittal/parasagittal DDF tendinopathies, and moderate collateral sesamoidean desmopathies. Also, identification of concurrent lesions of the DDF tendon, navicular bone, navicular bursa, and distal sesamoidean impar ligament was associated with chronic lameness after conservative therapy. Development of effective treatment options for foot lesions that respond poorly to conservative therapy is necessary.

Is Housing Hardship Associated with Increased Adolescent Delinquent Behaviors?

Housing-related hardships, ranging from an inability to pay full housing costs to being evicted, are common experiences for families in the U.S. Despite the frequency of these hardships, little is known about their relationships with adolescent behaviors. The current paper uses longitudinal data on births in large U.S. cities from all six waves of the Fragile Families and Child Well-being Study to explore the association between childhood experiences of housing hardships and delinquent behaviors in adolescence. About 60% of the sample experiences housing hardship at one or more waves. Inabilities to meet housing costs are common among the sample: over 40% are unable to pay their full rent or mortgage payment. Results from multivariate regression and residualized change models indicate that children who experience any housing hardship are more likely to engage in delinquent behaviors than children who do not experience hardship. Exposure to higher average levels of hardship and more waves of hardship are both associated with increased delinquency. Childhood poverty does not moderate the relationship between housing hardship and delinquency suggesting that housing hardship is associated with delinquent behaviors for poor and non-poor children alike. This research builds on existing literature highlighting the importance of examining hardship as a measure of family wellbeing. It also suggests that preventing common housing-related hardships can be beneficial for youth behavioral outcomes.

Picornavirus RNA is protected from cleavage by ribonuclease during virion uncoating and transfer across cellular and model membranes.

Picornaviruses are non-enveloped RNA viruses that enter cells via receptor-mediated endocytosis. Because they lack an envelope, picornaviruses face the challenge of delivering their RNA genomes across the membrane of the endocytic vesicle into the cytoplasm to initiate infection. Currently, the mechanism of genome release and translocation across membranes remains poorly understood. Within the enterovirus genus, poliovirus, rhinovirus 2, and rhinovirus 16 have been proposed to release their genomes across intact endosomal membranes through virally induced pores, whereas one study has proposed that rhinovirus 14 releases its RNA following disruption of endosomal membranes. For the more distantly related aphthovirus genus (e.g. foot-and-mouth disease viruses and equine rhinitis A virus) acidification of endosomes results in the disassembly of the virion into pentamers and in the release of the viral RNA into the lumen of the endosome, but no details have been elucidated as how the RNA crosses the vesicle membrane. However, more recent studies suggest aphthovirus RNA is released from intact particles and the dissociation to pentamers may be a late event. In this study we have investigated the RNase A sensitivity of genome translocation of poliovirus using a receptor-decorated-liposome model and the sensitivity of infection of poliovirus and equine-rhinitis A virus to co-internalized RNase A. We show that poliovirus genome translocation is insensitive to RNase A and results in little or no release into the medium in the liposome model. We also show that infectivity is not reduced by co-internalized RNase A for poliovirus and equine rhinitis A virus. Additionally, we show that all poliovirus genomes that are internalized into cells, not just those resulting in infection, are protected from RNase A. These results support a finely coordinated, directional model of viral RNA delivery that involves viral proteins and cellular membranes.

Structures of foot and mouth disease virus pentamers: Insight into capsid dissociation and unexpected pentamer reassociation.

Foot-and-mouth disease virus (FMDV) belongs to the Aphthovirus genus of the Picornaviridae, a family of small, icosahedral, non-enveloped, single-stranded RNA viruses. It is a highly infectious pathogen and is one of the biggest hindrances to the international trade of animals and animal products. FMDV capsids (which are unstable below pH6.5) release their genome into the host cell from an acidic compartment, such as that of an endosome, and in the process dissociate into pentamers. Whilst other members of the family (enteroviruses) have been visualized to form an expanded intermediate capsid with holes from which inner capsid proteins (VP4), N-termini (VP1) and RNA can be released, there has been no visualization of any such state for an aphthovirus, instead the capsid appears to simply dissociate into pentamers. Here we present the 8-Å resolution structure of isolated dissociated pentamers of FMDV, lacking VP4. We also found these pentamers to re-associate into a rigid, icosahedrally symmetric assembly, which enabled their structure to be solved at higher resolution (5.2 Å). In this assembly, the pentamers unexpectedly associate 'inside out', but still with their exposed hydrophobic edges buried. Stabilizing interactions occur between the HI loop of VP2 and its symmetry related partners at the icosahedral 3-fold axes, and between the BC and EF loops of VP3 with the VP2 ßB-strand and the CD loop at the 2-fold axes. A relatively extensive but subtle structural rearrangement towards the periphery of the dissociated pentamer compared to that in the mature virus provides insight into the mechanism of dissociation of FMDV and the marked difference in antigenicity.

Genetic economy in picornaviruses: Foot-and-mouth disease virus replication exploits alternative precursor cleavage pathways.

The RNA genomes of picornaviruses are translated into single polyproteins which are subsequently cleaved into structural and non-structural protein products. For genetic economy, proteins and processing intermediates have evolved to perform distinct functions. The picornavirus precursor protein, P3, is cleaved to produce membrane-associated 3A, primer peptide 3B, protease 3Cpro and polymerase 3Dpol. Uniquely, foot-and-mouth disease virus (FMDV) encodes three similar copies of 3B (3B1-3), thus providing a convenient natural system to explore the role(s) of 3B in the processing cascade. Using a replicon system, we confirmed by genetic deletion or functional inactivation that each copy of 3B appears to function independently to prime FMDV RNA replication. However, we also show that deletion of 3B3 prevents replication and that this could be reversed by introducing mutations at the C-terminus of 3B2 that restored the natural sequence at the 3B3-3C cleavage site. In vitro translation studies showed that precursors with 3B3 deleted were rapidly cleaved to produce 3CD but that no polymerase, 3Dpol, was detected. Complementation assays, using distinguishable replicons bearing different inactivating mutations, showed that replicons with mutations within 3Dpol could be recovered by 3Dpol derived from "helper" replicons (incorporating inactivation mutations in all three copies of 3B). However, complementation was not observed when the natural 3B-3C cleavage site was altered in the "helper" replicon, again suggesting that a processing abnormality at this position prevented the production of 3Dpol. When mutations affecting polyprotein processing were introduced into an infectious clone, viable viruses were recovered but these had acquired compensatory mutations in the 3B-3C cleavage site. These mutations were shown to restore the wild-type processing characteristics when analysed in an in vitro processing assay. Overall, this study demonstrates a dual functional role of the small primer peptide 3B3, further highlighting how picornaviruses increase genetic economy.

Polyelectrolyte Conformation Controlled by a Trivalent-Rich Ion Jacket.

The configuration of charged polymers is heavily dependent on interactions with surrounding salt ions, typically manifesting as a sensitivity to the bulk ionic strength. Here, we use single-molecule mechanical measurements to show that a charged polysaccharide, hyaluronic acid, shows a surprising regime of insensitivity to ionic strength in the presence of trivalent ions. Using simulations and theory, we propose that this is caused by the formation of a "jacket" of ions, tightly associated with the polymer, whose charge (and thus effect on configuration) is robust against changes in solution composition.

Experimental and Theoretical Validation of System Variables That Control the Position of Particles at the Interface of Immiscible Liquids.

We construct a mathematical model describing the equilibrium flotation height of a spherical particle at the interface of immiscible liquids. The behavior of such a system depends on several experimentally measurable parameters, which include surface tensions, densities of all phases, and system scale. These parameters can be absorbed into three quantities that entirely determine the equilibrium position of the particle: the contact angle between the interface and particle, the Bond number, and the ratio of particle buoyant density to liquid phase densities-a new, dimensionless number that we introduce here. This experimentally convenient treatment allows us to make predictions that apply generally to the large parameter space of interesting systems. We find the model is in good agreement with experiments for particle size and interfacial tension spanning 3 orders of magnitude. We also consider the low interfacial tension case of aqueous two-phase systems (ATPSs) theoretically and experimentally. Such systems are more sensitive to changes in density than higher-tension aqueous/organic two-phase systems; we experimentally demonstrate that a millimeter-sized bead in an ATPS can be controllably positioned with between 5.9 and 95.1% of its surface area exposed to the bottom phase, whereas the same bead in an aqueous/organic system is limited to a range of 18.2-61.6%. Finally, we discuss the potential for wettability-based control for micron length-scale particles, which are not sensitive to changes in density. Our results can be used to simply define the experimentally controllable parameters that affect the equilibrium position and the length scales of a particle over which such parameters can be effectively tuned. A complete understanding of these properties is important for a number of applications including colloidal self-assembly and chemical patterning (e.g., formation of desymmetrized or Janus particles). By considering ATPSs, we broaden the potential uses to biological applications such as cell separation and interfacial tissue assembly.

Surface-induced effects in fluctuation-based measurements of single-polymer elasticity: A direct probe of the radius of gyration.

Single-molecule measurements of polymer elasticity are powerful, direct probes of both biomolecular structure and principles of polymer physics. Recent work has revealed low-force regimes in which biopolymer elasticity is understood through blob-based scaling models. However, the small tensions required to observe these regimes have the potential to create measurement biases, particularly due to the increased interactions of the polymer chain with tethering surfaces. Here, we examine one experimentally observed bias, in which fluctuation-based estimates of elasticity report an unexpectedly low chain compliance. We show that the effect is in good agreement with predictions based on quantifying the exclusion effect of the surface through an image-method calculation of available polymer configurations. The analysis indicates that the effect occurs at an external tension inversely proportional to the polymer's zero-tension radius of gyration. We exploit this to demonstrate a self-consistent scheme for estimating the radius of gyration of the tethered polymer. This is shown in measurements of both hyaluronic acid and poly(ethylene glycol) chains.

Geometrically controlled snapping transitions in shells with curved creases.

Curvature and mechanics are intimately connected for thin materials, and this coupling between geometry and physical properties is readily seen in folded structures from intestinal villi and pollen grains to wrinkled membranes and programmable metamaterials. While the well-known rules and mechanisms behind folding a flat surface have been used to create deployable structures and shape transformable materials, folding of curved shells is still not fundamentally understood. Shells naturally deform by simultaneously bending and stretching, and while this coupling gives them great stability for engineering applications, it makes folding a surface of arbitrary curvature a nontrivial task. Here we discuss the geometry of folding a creased shell, and demonstrate theoretically the conditions under which it may fold smoothly. When these conditions are violated we show, using experiments and simulations, that shells undergo rapid snapping motion to fold from one stable configuration to another. Although material asymmetry is a proven mechanism for creating this bifurcation of stability, for the case of a creased shell, the inherent geometry itself serves as a barrier to folding. We discuss here how two fundamental geometric concepts, creases and curvature, combine to allow rapid transitions from one stable state to another. Independent of material system and length scale, the design rule that we introduce here explains how to generate snapping transitions in arbitrary surfaces, thus facilitating the creation of programmable multistable materials with fast actuation capabilities.