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We present some properties of a differential sequence prompted by a formula in a paper by Maryna Nesterenko (International Journal of Mathematics and Mathematical Sciences2006 (2006), Article ID 17410) in terms of the symmetry, singularity and integrability properties of the elements of the sequence. [ABSTRACT FROM AUTHOR]

Lie group classification for a diffusion‐type system that has applications in plasma physics is derived. The classification depends on the values of 5 parameters that appear in the system. Similarity reductions are presented. Certain initial value problems are reduced to problems with the governing equations being ordinary differential equations. Examples of potential symmetries are also presented. [ABSTRACT FROM AUTHOR]

In a fairly recent paper (2008 American Control Conference, June 11-13, 1035-1039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent nonlinear evolution partial differential equation was based upon a succession of Ansätze, which can lead to a solution of the terminal-value problem. Through an application of the Lie Theory of Continuous Groups to this equation, we show that the Ansätze are based upon the underlying symmetries of the equation (their (14)). We solve the problem in a more general context by allowing the parameters to be explicitly time dependent. The extension means that more realistic problems are amenable to the same mode of solution. [ABSTRACT FROM AUTHOR]

Derivatives in finance have become pervasive in recent decades. Tremendous impetus was given to this aspect of finance by the pioneering papers of Black and Scholes (1973) and Merton (1973) and has attracted considerable interest since. In general the evolution partial differential equations were solved by means of the traditional methods of partial differential equations and by ansatz previously useful in similar contexts. Here we illustrate the benefits of an algorithmic approach using the method of symmetry analysis introduced by Sophus Lie in the nineteenth century. We demonstrate the utility of this analytic approach with several examples chosen from the field of financial mathematics. [ABSTRACT FROM PUBLISHER]

Canakinumab is an anti–IL-1β antibody that is hypothesized to inhibit protumor inflammation. The CHORUS study tested the efficacy of canakinumab with chemoradiation (cCRT + cana) and consolidation durvalumab (durva + cana) in patients with stage III NSCLC. The primary PFS endpoint is immature. Here, we report an exploratory analysis on circulating tumor DNA (ctDNA) kinetics and imaging response, hypothesizing that associations between both may best predict disease control. This phase I/II trial enrolled 32 patients with stage III NSCLC, treated with canakinumab (200mg every 3 weeks, total of 15 cycles) with standard platinum-based cCRT and durvalumab consolidation. Plasma for ctDNA was analyzed at baseline, weeks 3 (On-Tx1), 7 (On-Tx2) and 16 (On-Tx3) using MSK-ACCESS, a cfDNA assay designed to detect alterations in 129 genes. Patients with matched tumor tissue (n = 24) also underwent sequencing with MSK-IMPACT. Initial surveillance imaging was done 4 weeks post cCRT + cana, after which imaging was every 3 months. Response is per RECIST 1.1 criteria. Between June 2021 and April 2023, 32 patients received cCRT + cana and at least 1 cycle of durva + cana. Median age was 70 years, most patients (n = 22, 69%) had stage IIIB/IIIC disease, adenocarcinoma histology (n = 19, 59%), were female (n = 18, 56%) and had a smoking histology (n = 28, 88%). PDL1-TPS was available for 29 patients (91%) of which 14 (48%) were PDL1 <1%, 7 (24%) were PDL1 ≥1% to <50%, and 8 (28%) were PDL1 ≥ 50%. Median follow-up for all patients was 11.2 months (IQR 8.2-21.1). On initial imaging 4 weeks post cCRT + cana, 23 patients (72%) had a PR/CR, 8 had SD (25%) and 1 was non-evaluable. With 11.2 months of follow-up, 26 patients (81%) had a CR/PR as the best overall response to therapy and 8 patients had confirmed PD. At baseline, all patients (n = 32) had detectable ctDNA. Among patients who also underwent tissue based MSK-IMPACT (n = 24), at baseline, 22 patients (92%) had at least one plasma alteration detected on MSK-ACCESS also detected in tumor tissue. On-Tx1 samples were assessed in 30 patients, of which 10 (33%) had undetectable ctDNA. All 10 patients (100%) with undetectable ctDNA at On-Tx1 had a PR/CR on initial imaging vs patients with detectable ctDNA at On-Tx1 (n = 20) of whom 12 (60%) had a PR/CR on initial imaging (P = 0.029). On-Tx3 samples were assessed in 29 patients of which 20 (69%) had undetectable ctDNA. Among patients with undetectable ctDNA (n = 20) at On-Tx3, 18 (90%) showed a PR/CR as best overall response, and 3 (15%) developed subsequent PD. Among patients with detectable ctDNA (n = 9) at On-Tx3, 6 (67%) showed a PR/CR and 3 (33%) showed SD as best overall response, and subsequently 4 (44%) developed PD. Among patients with both detectable ctDNA at On-Tx3 and best response of SD (n = 3), all (100%) had subsequent PD. Initial imaging response rate to cCRT + cana is encouraging. A combination of both ctDNA dynamics and imaging response appears promising to predict disease control. [ABSTRACT FROM AUTHOR]

Droplet interface bilayers (DIBs) are model membranes formed between lipid monolayer-encased water droplets in oil. Compared to conventional methods, one of the most unique properties of DIBs is that they can be connected together to generate multi-layered 'tissue-like' networks, however introducing communication pathways between these compartments typically relies on water-soluble pores that are unable to gate. Here, we show that network connectivity can instead be achieved using a water-insoluble membrane protein by successfully reconstituting a chemically activatable mutant of the mechanosensitive channel MscL into a network of DIBs. Moreover, we also show how the small molecule activator can diffuse through an open channel and across the neighbouring droplet to activate MscL present in an adjacent bilayer. This demonstration of membrane protein mediated bilayer communication could prove key toward developing the next generation of responsive bilayer networks capable of defining information flow inside a minimal tissue., Competing Interests: Competing interests The authors declare no competing interests.

The aim of the present study was to examine the existing association between mindfulness, impulsivity, moral disengagement, and bullying experiences at school. Longitudinal data were collected in three points in time (T1, T2, T3) with 6 months interval between them. Participants were 558 adolescents attending secondary schools in Cyprus, with their ages ranging from 14 to 17 years (M = 15.3; standard deviation = 0.69). Through structural equation modeling, it was found that mindfulness at T1 had a significant negative effect on both impulsivity and moral disengagement at T2 and these, in turn, had a positive effect on bullying and victimization at T3. Thus, mindfulness had an indirect effect on both bullying and victimization, fully mediated by impulsivity and moral disengagement., (© 2019 Wiley Periodicals, Inc.)

To date, reconstitution of one of the fundamental methods of cell communication, the signaling pathway, has been unaddressed in the bottom-up construction of artificial cells (ACs). Such developments are needed to increase the functionality and biomimicry of ACs, accelerating their translation and application in biotechnology. Here, we report the construction of a de novo synthetic signaling pathway in microscale nested vesicles. Vesicle-cell models respond to external calcium signals through activation of an intracellular interaction between phospholipase A2 and a mechanosensitive channel present in the internal membranes, triggering content mixing between compartments and controlling cell fluorescence. Emulsion-based approaches to AC construction are therefore shown to be ideal for the quick design and testing of new signaling networks and can readily include synthetic molecules difficult to introduce to biological cells. This work represents a foundation for the engineering of multicompartment-spanning designer pathways that can be utilized to control downstream events inside an AC, leading to the assembly of micromachines capable of sensing and responding to changes in their local environment., Competing Interests: The authors declare no conflict of interest.

As a multi-faceted concept, health literacy concerns the capacities of people to meet the complex demands of health in a modern society, starting with basic skills and ending with active citizenship. The importance of advancing health literacy in Europe was recognised by the European Commission in various communications and initiatives and most recently by the OECD. However, a strategic approach combined with a long-term action plan is still missing. This commentary advocates for an EU strategy on health literacy to fully take into account the partnership of citizens and patients with professionals and decision-makers in health and health care to promote health literate societies., Competing Interests: Not applicableNot applicableThe authors declare that they have no competing interests.Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Membrane proteins must be inserted into a membrane and folded into their correct structure to function correctly. This insertion occurs during translation and synthesis by the ribosome for most α-helical membrane proteins. Precisely how this co-translational insertion and folding occurs, and the role played by the surrounding lipids, is still not understood. Most of the work on the influence of the lipid environment on folding and insertion has focussed on denatured, fully translated proteins, and thus does not replicate folding during unidirectional elongation of nascent chains that occurs in the cell. This review aims to highlight recent advances in elucidating lipid composition and bilayer properties optimal for insertion and folding of nascent chains in the membrane and in the assembly of oligomeric proteins., (© 2018 The Author(s). Published by Portland Press Limited on behalf of the Biochemical Society.)

Correctly folded membrane proteins underlie a plethora of cellular processes, but little is known about how they fold. Knowledge of folding mechanisms centres on reversible folding of chemically denatured membrane proteins. However, this cannot replicate the unidirectional elongation of the protein chain during co-translational folding in the cell, where insertion is assisted by translocase apparatus. We show that a lipid membrane (devoid of translocase components) is sufficient for successful co-translational folding of two bacterial α-helical membrane proteins, DsbB and GlpG. Folding is spontaneous, thermodynamically driven, and the yield depends on lipid composition. Time-resolving structure formation during co-translational folding revealed different secondary and tertiary structure folding pathways for GlpG and DsbB that correlated with membrane interfacial and biological transmembrane amino acid hydrophobicity scales. Attempts to refold DsbB and GlpG from chemically denatured states into lipid membranes resulted in extensive aggregation. Co-translational insertion and folding is thus spontaneous and minimises aggregation whilst maximising correct folding.

Molecular diagnostics can offer important benefits to patients and are a key enabler of the integration of personalised medicine into health care systems. However, despite their promise, few molecular diagnostics are embedded into clinical practice (especially in Europe) and access to these technologies remains unequal across countries and sometimes even within individual countries. If research translation and the regulatory environments have proven to be more challenging than expected, reimbursement and value assessment remain the main barriers to providing patients with equal access to molecular diagnostics. Unclear or non-existent reimbursement pathways, together with the lack of clear evidence requirements, have led to significant delays in the assessment of molecular diagnostics technologies in certain countries. Additionally, the lack of dedicated diagnostics budgets and the siloed nature of resource allocation within certain health care systems have significantly delayed diagnostics commissioning. This article will consider the perspectives of different stakeholders (patients, health care payers, health care professionals, and manufacturers) on the provision of a research-enabled, patient-focused molecular diagnostics platform that supports optimal patient care. Through the discussion of specific case studies, and building on the experience from countries that have successfully integrated molecular diagnostics into clinical practice, this article will discuss the necessary evolutions in policy and health technology assessment to ensure that patients can have equal access to appropriate molecular diagnostics., (© 2016 S. Karger AG, Basel.)

Small-molecule amphiphilic species such as many drug molecules frequently exhibit low-to-negligible aqueous solubility, and generally have no identified transport proteins assisting their distribution, yet are able to rapidly penetrate significant distances into patient tissue and even cross the blood-brain barrier. Previous work has identified a mechanism of translocation driven by acid-catalysed lipid hydrolysis of biological membranes, a process which is catalysed by the presence of cationic amphiphilic drug molecules. In this study, the interactions of raclopride, a model amphiphilic drug, were investigated with mixtures of biologically relevant lipids across a range of compositions, revealing the influence of the chain-melting temperature of the lipids upon the rate of acyl hydrolysis.

Mechanical properties of biological membranes are known to regulate membrane protein function. Despite this, current models of protein communication typically feature only direct protein-protein or protein-small molecule interactions. Here we show for the first time that, by harnessing nanoscale mechanical energy within biological membranes, it is possible to promote controlled communication between proteins. By coupling lipid-protein modules and matching their response to the mechanical properties of the membrane, we have shown that the action of phospholipase A(2) on acyl-based phospholipids triggers the opening of the mechanosensitive channel, MscL, by generating membrane asymmetry. Our findings confirm that the global physical properties of biological membranes can act as information pathways between proteins, a novel mechanism of membrane-mediated protein-protein communication that has important implications for (i) the underlying structure of signaling pathways, (ii) our understanding of in vivo communication networks, and (iii) the generation of building blocks for artificial protein networks.

Modelling the urban water balance enables the understanding of the interactions of water within an urban area and allows for better management of water resources. However, few models today provide a comprehensive overview of all water sources and uses. The objective of the current paper was to develop a user-friendly tool that quantifies and visualizes all water flows, losses and inefficiencies in urban environments. The Urban Water Flow Model was implemented in a spreadsheet and includes a water-savings application that computes the contributions of user-selected saving options to the overall water balance. The model was applied to the coastal town of Limassol, Cyprus, for the hydrologic years 2003/04-2008/09. Data were collected from the different authorities and hydrologic equations and estimations were added to complete the balance. Average precipitation was 363 mm/yr, amounting to 25.4 × 10(6)m(3)/yr, more than double the annual potable water supply to the town. Surface runoff constituted 29.6% of all outflows, while evapotranspiration from impervious areas was 21.6%. Possible potable water savings for 2008/09 were estimated at 5.3 × 10(3) m(3), which is 50% of the total potable water provided to the area. This saving would also result in a 6% reduction of surface runoff.

Contamination with the multidrug transporter AcrB represents a potential pitfall in the structural analysis of recombinant membrane proteins expressed in Escherichia coli, especially when high-throughput approaches are adopted. This can be a particular problem in two-dimensional (2-D) crystallization for electron cryomicroscopy since individual crystals are too small for compositional analysis. Using a broad 'sparse matrix' of buffer conditions typically used in 2-D crystallization, we have identified at least eight unique crystal forms of AcrB. Reference to images and projection maps of these different forms can greatly facilitate the early identification of false leads in 2-D crystallization trials of other membrane proteins of interest. We illustrate the usefulness of such data by highlighting two studies of membrane proteins in our laboratories. We show in one case (a bacterial sodium channel, NaChBac) how early crystallization 'hits' could be attributed to contaminating AcrB by comparison against our AcrB crystal image database. In a second case, involving a member of the monovalent cation/proton antiporter-1 family (MPSIL0171), a comparison with the observed AcrB crystal forms allowed easy identification of reconstituted AcrB particles, greatly facilitating the eventual purification and crystallization of the correct protein in pure form as ordered helical arrays. Our database of AcrB crystal images will be of general use in assisting future 2-D crystallization studies of other membrane proteins., (Copyright © 2011 Elsevier Inc. All rights reserved.)

In excitable cells, the main mediators of sodium conductance across membranes are voltage-gated sodium channels (Na(V)s). Eukaryotic Na(V)s are essential elements in neuronal signaling and muscular contraction and in humans have been causally related to a variety of neurological and cardiovascular channelopathies. They are complex heavily glycosylated intrinsic membrane proteins present in only trace quantities that have proven to be challenging objects of study. However, in recent years, a number of simpler prokaryotic sodium channels have been identified, with NaChBac from Bacillus halodurans being the most well-characterized to date. The availability of a bacterial Na(V) that is amenable to heterologous expression and functional characterization in both bacterial and mammalian systems has provided new opportunities for structure--function studies. This review describes features of NaChBac as an exemplar of this class of bacterial channels, compares prokaryotic and eukaryotic Na(V)s with respect to their structural organization, pharmacological profiling, and functional kinetics, and discusses how voltage-gated ion channels may have evolved to deal with the complex functional demands of higher organisms.

The composition of the lipid bilayer is increasingly being recognised as important for the regulation of integral membrane protein folding and function, both in vivo and in vitro. The folding of only a few membrane proteins, however, has been characterised in different lipid environments. We have refolded the small multidrug transporter EmrE in vitro from a denatured state to a functional protein and monitored the influence of lipids on the folding process. EmrE is part of a multidrug resistance protein family that is highly conserved amongst bacteria and is responsible for bacterial resistance to toxic substances. We find that the secondary structure of EmrE is very stable and only small amounts are denatured even in the presence of unusually high denaturant concentrations involving a combination of 10 M urea and 5% SDS. Substrate binding by EmrE is recovered after refolding this denatured protein into dodecylmaltoside detergent micelles or into lipid vesicles. The yield of refolded EmrE decreases with lipid bilayer compositional changes that increase the lateral chain pressure within the bilayer, whilst conversely, the apparent rate of folding seems to increase. These results add further weight to the hypothesis that an increased lateral chain pressure hinders protein insertion across the bilayer. Once the protein is inserted, however, the greater pressure on the transmembrane helices accelerates correct packing and final folding. This work augments the relatively small number of biophysical folding studies in vitro on helical membrane proteins.

Voltage-gated sodium channels are dynamic membrane proteins essential for signaling in nervous and muscular systems. They undergo substantial conformational changes associated with the closed, open and inactivated states. However, little information is available regarding their conformational stability. In this study circular dichroism spectroscopy was used to investigate the changes in secondary structure accompanying chemical and thermal denaturation of detergent-solubilised sodium channels isolated from Electrophorus electricus electroplax. The proteins appear to be remarkably resistant to either type of treatment, with "denatured" channels, retaining significant helical secondary structure even at 77 degrees C or in 10% SDS. Further retention of helical secondary structure at high temperature was observed in the presence of the channel-blocking tetrodotoxin. It was possible to refold the thermally-denatured (but not chemically-denatured) channels in vitro. The correctly refolded channels were capable of undergoing the toxin-induced conformational change indicative of ligand binding. In addition, flux measurements in liposomes showed that the thermally-denatured (but not chemically-denatured) proteins were able to re-adopt native, active conformations. These studies suggest that whilst sodium channels must be sufficiently flexible to undergo major conformational changes during their functional cycle, the proteins are highly resistant to unfolding, a feature that is important for maintaining structural integrity during dynamic processes.

The NaChBac sodium channel from Bacillus halodurans is a homologue of eukaryotic voltage-gated sodium channels. It can be solubilized in a range of detergents and consists of four identical subunits assembled as a tetramer. Sodium channels are relatively flexible molecules, adopting different conformations in their closed, open and inactivated states. This study aimed to design and construct a mutant version of the NaChBac protein that would insert into membranes and retain its folded conformation, but which would have enhanced stability when subjected to thermal stress. Modelling studies suggested a G219S mutant would have decreased conformational flexibility due to the removal of the glycine hinge around the proposed gating region, thereby imparting increased resistance to unfolding. The mutant expressed in Escherichia coli and purified in the detergent dodecyl maltoside was compared to wildtype NaChBac prepared in a similar manner. The mutant was incorporated into the membrane fraction and had a nearly identical secondary structure to the wildtype protein. When the thermal unfolding of the G219S mutant was examined by circular dichroism spectroscopy, it was shown to not only have a Tm approximately 10 degrees C higher than the wildtype, but also in its unfolded state it retained more ordered helical structure than did the wildtype protein. Hence the G219S mutant was shown to be, as designed, more thermally stable.

Background: Membrane proteins are influenced by their surrounding lipids. We investigate the effect of bilayer composition on the membrane transport activity of two members of the small multidrug resistance family; the Escherichia coli transporter, EmrE and the Mycobacterium tuberculosis, TBsmr. In particular we address the influence of phosphatidylethanolamine and anionic lipids on the activity of these multidrug transporters. Phosphatidylethanolamine lipids are native to the membranes of both transporters and also alter the lateral pressure profile of a lipid bilayer. Lipid bilayer lateral pressures affect membrane protein insertion, folding and activity and have been shown to influence reconstitution, topology and activity of membrane transport proteins., Results: Both EmrE and TBsmr are found to exhibit a similar dependence on lipid composition, with phosphatidylethanolamine increasing methyl viologen transport. Anionic lipids also increase transport for both EmrE and TBsmr, with the proteins showing a preference for their most prevalent native anionic lipid headgroup; phosphatidylglycerol for EmrE and phosphatidylinositol for TBsmr., Conclusion: These findings show that the physical state of the membrane modifies drug transport and that substrate translocation is dependent on in vitro lipid composition. Multidrug transport activity seems to respond to alterations in the lateral forces exerted upon the transport proteins by the bilayer.

NaChBac from Bacillus halodurans is a bacterial homologue of mammalian voltage-gated sodium channels. It has been proposed that a NaChBac monomer corresponds to a single domain of the mammalian sodium channel and that, like potassium channels, four monomers form a tetrameric channel. However, to date, although NaChBac has been well-characterized for functional properties by electrophysiological measurements on protein expressed in tissue culture, little information about its structural properties exists because of the difficulties in expressing the protein in large quantities. In this study, we present studies on the overexpression of NaChBac in Escherichia coli, purification of the functional detergent-solubilized channel, its identification as a tetramer, and characterization of its secondary structure, drug binding, and thermal stability. These studies are correlated with a model produced for the protein and provide new insights into the structure-function relationships of this sodium channel.

The ability of multidrug transport proteins within biological membranes to recognise a diverse array of substrates is a fundamental aspect of antibiotic resistance. Detailed information on the mechanisms of recognition and transport can be provided only by in vitro studies in reconstituted bilayer systems. We describe the controlled, efficient reconstitution of the small multidrug transporter EmrE in a simple model membrane and investigate the effect of non-bilayer lipids on this process. Transport activity is impaired, in line with an increase in the lateral pressure within the bilayer. We demonstrate the potential of this lateral pressure modulation method as a general approach to the folding and assembly of membrane proteins in vitro, by recovering functional transporter from a partly denatured state. Our results highlight the importance of optimising reconstitution procedures and bilayer lipid composition in studies of membrane transporters. This is particularly pertinent for multidrug proteins, and we show that the use of a sub-optimal lipid bilayer environment or reconstitution method could lead to incorrect information on protein activity.

Although calcium plays an important role in the activation of leukocytes for such processes as eicosanoid biosynthesis, secretion of granular constituents and superoxide generation, sustained high levels of intracellular calcium ions may be toxic. We have previously found that high concentrations of calcium ionophores induce a rapid-onset "calcium overload" toxicity in rat peritoneal leukocytes, in which functional responses such as beta-glucuronidase secretion, superoxide generation and leukotriene B4 synthesis are greatly attenuated, and some leakage of cytoplasmic LDH occurs. We have now compared this phenomenon in peritoneal leukocytes elicited from animals pretreated in three ways: glycogen, interleukin-1 beta (IL-1 beta) alone or glycogen plus IL-1 beta. Peritoneal administration of IL-1 beta caused elicitation of cells which were enriched in eosinophils; however, the functional responses of the cells in all three groups were broadly similar in terms of the ability of the agonists FMLP, PMA and A23187 to initiate superoxide generation, beta-glucuronidase secretion and leukotriene generation. Cells from all three treatment groups showed diminished responsiveness at 10(-5) M A23187, indicative of calcium overload toxicity. This was most evident for the superoxide and beta-glucuronidase responses. Some quantitative differences observed between treatment groups may reflect the different sensitivities of the various cells contained in the mixed leukocyte preparations. We conclude that IL-1 beta induces leukocyte emigration into the peritoneal cavity but that the cell population is different from that induced by glycogen. However, the cells retain susceptibility to calcium overload toxicity.