Protein therapeutics and their lessons: Expect the unexpected when inhibiting the multi-protein cascade of the complement system.

Over a century after the discovery of the complement system, the first complement therapeutic was approved for the treatment of paroxysmal nocturnal hemoglobinuria (PNH). It was a long-acting monoclonal antibody (aka 5G1-1, 5G1.1, h5G1.1, and now known as eculizumab) that targets C5, specifically preventing the generation of C5a, a potent anaphylatoxin, and C5b, the first step in the eventual formation of membrane attack complex. The enormous clinical and financial success of eculizumab across four diseases (PNH, atypical hemolytic uremic syndrome (aHUS), myasthenia gravis (MG), and anti-aquaporin-4 (AQP4) antibody-positive neuromyelitis optica spectrum disorder (NMOSD)) has fueled a surge in complement therapeutics, especially targeting diseases with an underlying complement pathophysiology for which anti-C5 therapy is ineffective. Intensive research has also uncovered challenges that arise from C5 blockade. For example, PNH patients can still face extravascular hemolysis or pharmacodynamic breakthrough of complement suppression during complement-amplifying conditions. These "side" effects of a stoichiometric inhibitor like eculizumab were unexpected and are incompatible with some of our accepted knowledge of the complement cascade. And they are not unique to C5 inhibition. Indeed, "exceptions" to the rules of complement biology abound and have led to unprecedented and surprising insights. In this review, we will describe initial, present and future aspects of protein inhibitors of the complement cascade, highlighting unexpected findings that are redefining some of the mechanistic foundations upon which the complement cascade is organized.

Triple-fusion protein (TriFu): A potent, targeted, enzyme-like inhibitor of all three complement activation pathways.

The introduction of a therapeutic anti-C5 antibody into clinical practice in 2007 inspired a surge into the development of complement-targeted therapies. This has led to the recent approval of a C3 inhibitory peptide, an antibody directed against C1s and a full pipeline of several complement inhibitors in preclinical and clinical development. However, no inhibitor is available that efficiently inhibits all three complement initiation pathways and targets host cell surface markers as well as complement opsonins. To overcome this, we engineered a novel fusion protein combining selected domains of the three natural complement regulatory proteins decay accelerating factor, factor H and complement receptor 1. Such a triple fusion complement inhibitor (TriFu) was recombinantly expressed and purified alongside multiple variants and its building blocks. We analyzed these proteins for ligand binding affinity and decay acceleration activity by surface plasmon resonance. Additionally, we tested complement inhibition in several in vitro/ex vivo assays using standard classical and alternative pathway restricted hemolysis assays next to hemolysis assays with paroxysmal nocturnal hemoglobinuria erythrocytes. A novel in vitro model of the alternative pathway disease C3 glomerulopathy was established to evaluate the potential of the inhibitors to stop C3 deposition on endothelial cells. Next to the novel engineered triple fusion variants which inactivate complement convertases in an enzyme-like fashion, stoichiometric complement inhibitors targeting C3, C5, factor B, and factor D were tested as comparators. The triple fusion approach yielded a potent complement inhibitor that efficiently inhibits all three complement initiation pathways while targeting to surface markers.

DeepProjection: specific and robust projection of curved 2D tissue sheets from 3D microscopy using deep learning.

The efficient extraction of image data from curved tissue sheets embedded in volumetric imaging data remains a serious and unsolved problem in quantitative studies of embryogenesis. Here, we present DeepProjection (DP), a trainable projection algorithm based on deep learning. This algorithm is trained on user-generated training data to locally classify 3D stack content, and to rapidly and robustly predict binary masks containing the target content, e.g. tissue boundaries, while masking highly fluorescent out-of-plane artifacts. A projection of the masked 3D stack then yields background-free 2D images with undistorted fluorescence intensity values. The binary masks can further be applied to other fluorescent channels or to extract local tissue curvature. DP is designed as a first processing step than can be followed, for example, by segmentation to track cell fate. We apply DP to follow the dynamic movements of 2D-tissue sheets during dorsal closure in Drosophila embryos and of the periderm layer in the elongating Danio embryo. DeepProjection is available as a fully documented Python package.

The Complement-Targeted Inhibitor Mini-FH Protects against Experimental Periodontitis via Both C3-Dependent and C3-Independent Mechanisms.

A minimized version of complement factor H (FH), designated mini-FH, was previously engineered combining the N-terminal regulatory domains (short consensus repeat [SCR]1-4) and C-terminal host-surface recognition domains (SCR19-20) of the parent molecule. Mini-FH conferred enhanced protection, as compared with FH, in an ex vivo model of paroxysmal nocturnal hemoglobinuria driven by alternative pathway dysregulation. In the current study, we tested whether and how mini-FH could block another complement-mediated disease, namely periodontitis. In a mouse model of ligature-induced periodontitis (LIP), mini-FH inhibited periodontal inflammation and bone loss in wild-type mice. Although LIP-subjected C3-deficient mice are protected relative to wild-type littermates and exhibit only modest bone loss, mini-FH strikingly inhibited bone loss even in C3-deficient mice. However, mini-FH failed to inhibit ligature-induced bone loss in mice doubly deficient in C3 and CD11b. These findings indicate that mini-FH can inhibit experimental periodontitis even in a manner that is independent of its complement regulatory activity and is mediated by complement receptor 3 (CD11b/CD18). Consistent with this notion, a complement receptor 3-interacting recombinant FH segment that lacks complement regulatory activity (specifically encompassing SCRs 19 and 20; FH19-20) was also able to suppress bone loss in LIP-subjected C3-deficient mice. In conclusion, mini-FH appears to be a promising candidate therapeutic for periodontitis by virtue of its ability to suppress bone loss via mechanisms that both include and go beyond its complement regulatory activity.

Gliosis-dependent expression of complement factor H truncated variants attenuates retinal neurodegeneration following ischemic injury.

Inherited, age-related, and acute retinal diseases are often exacerbated by an aberrant or excessive activity of the complement system. Consequently, cells not directly affected by an acute event or genetic variants may degenerate, resulting in enhanced visual impairment. The therapeutic potential of supplementation of complement factor H (FH), a key regulator of the complement cascade, is therefore particularly promising in the context of retinal diseases caused by complement activation. In this study, we engineered adeno-associated viruses (AAVs) containing sequences of two truncated human FH variants. The expression of these variants was regulated by the glial fibrillary acidic protein (GFAP) promoter, which is selectively active in gliotic Müller cells. Both FH variants consisted of FH domains 19-20, which were connected to domains 1-4 and 1-7, respectively, by a polyglycine linker. These AAVs were intravitreally injected following ischemic injury of C57BL/6J mouse retinas. We observed transgene expression in gliotic Müller cells and to some extent in astrocytes. The expression correlated directly with damage severity. Interventions resulted in decreased complement activation, accelerated normalization of microglia activity and morphological improvements. Reduced levels of C3 transcripts and C3d protein in conjunction with higher transcript levels of inhibitory regulators like Cfi and Cfh, hinted at attenuated complement activity. This study demonstrates the great potential of complement regulatory gene addition therapy. With further in vivo testing it could be applied to treat a wide range of retinal diseases where no causative therapies are available.

Complement and the prothrombotic state.

In 2007 and 2009, the regulatory approval of the first-in-class complement inhibitor eculizumab revolutionized the clinical management of 2 rare, life-threatening clinical conditions: paroxysmal nocturnal hemoglobinuria (PNH) and atypical hemolytic uremic syndrome (aHUS). Although being completely distinct diseases affecting blood cells and the glomerulus, PNH and aHUS remarkably share several features in their etiology and clinical presentation. An imbalance between complement activation and regulation at host surfaces underlies both diseases precipitating in severe thrombotic events that are largely resistant to anticoagulant and/or antiplatelet therapies. Inhibition of the common terminal complement pathway by eculizumab prevents the frequently occurring thrombotic events responsible for the high mortality and morbidity observed in patients not treated with anticomplement therapy. Although many in vitro and ex vivo studies elaborate numerous different molecular interactions between complement activation products and hemostasis, this review focuses on the clinical evidence that links these 2 fields in humans. Several noninfectious conditions with known complement involvement are scrutinized for common patterns concerning a prothrombotic statues and the occurrence of certain complement activation levels. Next to PNH and aHUS, germline-encoded CD59 or CD55 deficiency (the latter causing the disease complement hyperactivation, angiopathic thrombosis, and protein-losing enteropathy), autoimmune hemolytic anemia, (catastrophic) antiphospholipid syndrome, and C3 glomerulopathy are considered. Parallels and distinct features among these conditions are discussed against the background of thrombosis, complement activation, and potential complement diagnostic and therapeutic avenues.

Validation of a methylation-based signature for subventricular zone involvement in glioblastoma.

PURPOSE: Glioblastomas (GBM) with subventricular zone (SVZ) contact have previously been associated with a specific epigenetic fingerprint. We aim to validate a reported bulk methylation signature to determine SVZ contact. METHODS: Methylation array analysis was performed on IDHwt GBM patients treated at our institution. The v11b4 classifier was used to ensure the inclusion of only receptor tyrosine kinase (RTK) I, II, and mesenchymal (MES) subtypes. Methylation-based assignment (SVZM ±) was performed using hierarchical cluster analysis. Magnetic resonance imaging (MRI) (T1ce) was independently reviewed for SVZ contact by three experienced readers. RESULTS: Sixty-five of 70 samples were classified as RTK I, II, and MES. Full T1ce MRI-based rater consensus was observed in 54 cases, which were retained for further analysis. Epigenetic SVZM classification and SVZ were strongly associated (OR: 15.0, p = 0.003). Thirteen of fourteen differential CpGs were located in the previously described differentially methylated LRBA/MAB21L2 locus. SVZ + tumors were linked to shorter OS (hazard ratio (HR): 3.80, p = 0.02) than SVZM + at earlier time points (time-dependency of SVZM, p < 0.05). Considering the SVZ consensus as the ground truth, SVZM classification yields a sensitivity of 96.6%, specificity of 36.0%, positive predictive value (PPV) of 63.6%, and negative predictive value (NPV) of 90.0%. CONCLUSION: Herein, we validated the specific epigenetic signature in GBM in the vicinity of the SVZ and highlighted the importance of methylation of a part of the LRBA/MAB21L2 gene locus. Whether SVZM can replace MRI-based SVZ assignment as a prognostic and diagnostic tool will require prospective studies of large, homogeneous cohorts.

Upregulation of Checkpoint Ligand Programmed Death-Ligand 1 in Patients with Paroxysmal Nocturnal Hemoglobinuria Explained by Proximal Complement Activation.

Paroxysmal nocturnal hemoglobinuria (PNH) is a rare hemolytic disease driven by impaired complement regulation. Mutations in genes encoding the enzymes that build the GPI anchors are causative, with somatic mutations in the PIG-A gene occurring most frequently. As a result, the important membrane-bound complement regulators CD55 and CD59 are missing on the affected hematopoietic stem cells and their progeny, rendering those cells vulnerable to complement attack. Immune escape mechanisms sparing affected PNH stem cells from removal are suspected in the PNH pathogenesis, but molecular mechanisms have not been elucidated. We hypothesized that exuberant complement activity in PNH results in enhanced immune checkpoint interactions, providing a molecular basis for the potential immune escape in PNH. In a series of PNH patients, we found increased expression levels of the checkpoint ligand programmed death-ligand 1 (PD-L1) on granulocytes and monocytes, as well as in the plasma of PNH patients. Mechanistically, we demonstrate that complement activation leading to the decoration of particles/cells with C3- and/or C4-opsonins increased PD-L1 expression on neutrophils and monocytes as shown for different in vitro models of classical or alternative pathway activation. We further establish in vitro that complement inhibition at the level of C3, but not C5, inhibits the alternative pathway-mediated upregulation of PD-L1 and show by means of soluble PD-L1 that this observation translates into the clinical situation when PNH patients are treated with either C3 or C5 inhibitors. Together, the presented data show that the checkpoint ligand PD-L1 is increased in PNH patients, which correlates with proximal complement activation.

Bi-allelic loss-of-function variants in KIF21A cause severe fetal akinesia with arthrogryposis multiplex.

BACKGROUND: Fetal akinesia (FA) results in variable clinical presentations and has been associated with more than 166 different disease loci. However, the underlying molecular cause remains unclear in many individuals. We aimed to further define the set of genes involved. METHODS: We performed in-depth clinical characterisation and exome sequencing on a cohort of 23 FA index cases sharing arthrogryposis as a common feature. RESULTS: We identified likely pathogenic or pathogenic variants in 12 different established disease genes explaining the disease phenotype in 13 index cases and report 12 novel variants. In the unsolved families, a search for recessive-type variants affecting the same gene was performed; and in five affected fetuses of two unrelated families, a homozygous loss-of-function variant in the kinesin family member 21A gene (KIF21A) was found. CONCLUSION: Our study underlines the broad locus heterogeneity of FA with well-established and atypical genotype-phenotype associations. We describe KIF21A as a new factor implicated in the pathogenesis of severe neurogenic FA sequence with arthrogryposis of multiple joints, pulmonary hypoplasia and facial dysmorphisms. This hypothesis is further corroborated by a recent report on overlapping phenotypes observed in Kif21a null piglets.

Complement inhibition at the level of C3 or C5: mechanistic reasons for ongoing terminal pathway activity.

Blocking the terminal complement pathway with the C5 inhibitor eculizumab has revolutionized the clinical management of several complement-mediated diseases and has boosted the clinical development of new inhibitors. Data on the C3 inhibitor Compstatin and the C5 inhibitors eculizumab and Coversin reported here demonstrate that C3/C5 convertases function differently from prevailing concepts. Stoichiometric C3 inhibition failed to inhibit C5 activation and lytic activity during strong classical pathway activation, demonstrating a "C3 bypass" activation of C5. We show that, instead of C3b, surface-deposited C4b alone can also recruit and prime C5 for consecutive proteolytic activation. Surface-bound C3b and C4b possess similar affinities for C5. By demonstrating that the fluid phase convertase C3bBb is sufficient to cleave C5 as long as C5 is bound on C3b/C4b-decorated surfaces, we show that surface fixation is necessary only for the C3b/C4b opsonins that prime C5 but not for the catalytic convertase unit C3bBb. Of note, at very high C3b densities, we observed membrane attack complex formation in absence of C5-activating enzymes. This is explained by a conformational activation in which C5 adopts a C5b-like conformation when bound to densely C3b-opsonized surfaces. Stoichiometric C5 inhibitors failed to prevent conformational C5 activation, which explains the clinical phenomenon of residual C5 activity documented for different inhibitors of C5. The new insights into the mechanism of C3/C5 convertases provided here have important implications for the development and therapeutic use of complement inhibitors as well as the interpretation of former clinical and preclinical data.

Moving into the cell: single-molecule studies of molecular motors in complex environments.

Much has been learned in the past decades about molecular force generation. Single-molecule techniques, such as atomic force microscopy, single-molecule fluorescence microscopy and optical tweezers, have been key in resolving the mechanisms behind the power strokes, 'processive' steps and forces of cytoskeletal motors. However, it remains unclear how single force generators are integrated into composite mechanical machines in cells to generate complex functions such as mitosis, locomotion, intracellular transport or mechanical sensory transduction. Using dynamic single-molecule techniques to track, manipulate and probe cytoskeletal motor proteins will be crucial in providing new insights.

Firms' responses to the COVID-19 pandemic.

The COVID-19 pandemic requires firms to adequately respond. In this study, we first explore in our empirical data how firms responded to the COVID-19 crisis and identify five tactical response types, operational, digitalization, financial, supportive, and organizational responses. Furthermore, our findings indicate that responses vary in scope; Some firms act on their own, while others engage in collaborations. Finally, we find that the response angle is different across firms, as some firms leverage potential and others primarily mitigate risk. Second, we follow an event study design to measure the financial implications of these responses. We find that responses to the COVID-19 pandemic generally entail a positive stock market reaction. Financial and digitalization responses, as well as risk mitigation responses, are consistently evaluated positively. We discuss our findings in context of different theoretical lenses, substantiating the emerging literature on the COVID-19 crisis, and the established literature on crisis response management.

Mapping Activity-Dependent Quasi-stationary States of Mitochondrial Membranes with Graphene-Induced Energy Transfer Imaging.

Graphene-induced energy transfer (GIET) was recently introduced for sub-nanometric axial localization of fluorescent molecules. GIET relies on near-field energy transfer from an optically excited fluorophore to a single sheet of graphene. Recently, we demonstrated its potential by determining the distance between two leaflets of supported lipid bilayers. Here, we use GIET imaging for mapping quasi-stationary states of the inner and outer mitochondrial membranes before and during adenosine triphosphate (ATP) synthesis. We trigger the ATP synthesis state in vitro by activating mitochondria with precursor molecules. Our results demonstrate that the inner membrane approaches the outer membrane, while the outer membrane does not show any measurable change in average axial position upon activation. The inter-membrane space is reduced by ∼2 nm. This direct experimental observation of the subtle dynamics of mitochondrial membranes and the change in intermembrane distance upon activation is relevant for our understanding of mitochondrial function.

Human α-Defensin-6 Neutralizes Clostridioides difficile Toxins TcdA and TcdB by Direct Binding.

Rising incidences and mortalities have drawn attention to Clostridioides difficile infections (CDIs) in recent years. The main virulence factors of this bacterium are the exotoxins TcdA and TcdB, which glucosylate Rho-GTPases and thereby inhibit Rho/actin-mediated processes in cells. This results in cell rounding, gut barrier disruption and characteristic clinical symptoms. So far, treatment of CDIs is limited and mainly restricted to some antibiotics, often leading to a vicious circle of antibiotic-induced disease recurrence. Here, we demonstrate the protective effect of the human antimicrobial peptide α-defensin-6 against TcdA, TcdB and the combination of both toxins in vitro and in vivo and unravel the underlying molecular mechanism. The defensin prevented toxin-mediated glucosylation of Rho-GTPases in cells and protected human cells, model epithelial barriers as well as zebrafish embryos from toxic effects. In vitro analyses revealed direct binding to TcdB in an SPR approach and the rapid formation of TcdB/α-defensin-6 complexes, as analyzed with fluorescent TcdB by time-lapse microscopy. In conclusion, the results imply that α-defensin-6 rapidly sequesters the toxin into complexes, which prevents its cytotoxic activity. These findings extend the understanding of how human peptides neutralize bacterial protein toxins and might be a starting point for the development of novel therapeutic options against CDIs.

Multiscale Microrheology Using Fluctuating Filaments as Stealth Probes.

The mechanical properties of soft materials can be probed on small length scales by microrheology. A common approach tracks fluctuations of micrometer-sized beads embedded in the medium to be characterized. This approach yields results that depend on probe size when the medium has structure on comparable length scales. Here, we introduce filament-based microrheology using high-aspect-ratio semiflexible filaments as probes. Such quasi-1D probes are much less invasive than beads due to their small cross sections. Moreover, by imaging transverse bending modes, we simultaneously determine the micromechanical response of the medium on multiple length scales corresponding to the mode wavelengths. We use semiflexible single-walled carbon nanotubes as probes that can be accurately and rapidly imaged based on their stable near-IR fluorescence. We find that the viscoelastic properties of sucrose, polyethylene oxide, and hyaluronic acid solutions measured in this way are in good agreement with those measured by conventional micro- and macrorheology.

Self versus Nonself Discrimination by the Soluble Complement Regulators Factor H and FHL-1.

The plasma proteins Factor H (FH) and its alternate splice variant FH-like protein 1 (FHL-1) are the major regulators of the complement alternative pathway. The indiscriminate nature of alternative pathway activation necessitates the regulators to be host selective, but the underlying principles of selectivity remained largely elusive. By analyzing human FH and FHL-1 for protection of different host and foreign cells (rabbit and yeast), we uncovered a 2-fold discriminatory mechanism of FH in favor of self: relative to FHL-1, FH exhibits a regulatory benefit on self but importantly, also, a regulatory penalty on nonself surfaces, yielding a selectivity factor of ∼2.4 for sialylated host surfaces. We further show that FHL-1 possesses higher regulatory activity than known but is relatively unselective. The reason for this unexpected high activity of FHL-1 is the observation that the complement regulatory site in FH exceeds the established first four domains. Affinity for C3b, cofactor and decay-accelerating activities, and serum assays demonstrate that the regulatory site extends domains 1-4 and includes domains 5-7. But unlike FH, FHL-1 exhibits a fast plasma clearance in mice, occurs sparsely in human plasma (at one fortieth of the FH concentration), and resists deregulation by FH-related proteins. These physiological differences and its late phylogenetic occurrence argue that FHL-1 is crucial for local rather than systemic compartments. In conclusion, we demonstrate a 2-fold discriminatory power of FH to promote selectivity for self over foreign and show that FHL-1 is more active than known but specialized for regulation on local tissues.

Length-Selective Dielectrophoretic Manipulation of Single-Walled Carbon Nanotubes.

Single-walled carbon nanotubes (SWNTs) possess unique physical, optical, and electrical properties with great potential for future nanoscale device applications. Common synthesis procedures yield SWNTs with large length polydispersity and varying chirality. Electrical and optical applications of SWNTs often require specific lengths, but the preparation of SWNTs with the desired length is still challenging. Insulator-based dielectrophoresis (iDEP) integrated into a microfluidic device has the potential to separate SWNTs by length. Semiconducting SWNTs of varying length suspended with sodium deoxycholate (NaDOC) show unique dielectrophoretic properties at low frequencies (<1 kHz) that were exploited here using an iDEP-based microfluidic constriction sorter device for length-based sorting. Specific migration directions in the constriction sorter were induced for long SWNTs (≥1000 nm) with negative dielectrophoretic properties compared to short (≤300 nm) SWNTs with positive dielectrophoretic properties. We report continuous fractionation conditions for length-based iDEP migration of SWNTs, and we characterize the dynamics of migration of SWNTs in the microdevice using a finite element model. Based on the length and dielectrophoretic characteristics, sorting efficiencies for long and short SWNTs recovered from separate channels of the constriction sorter amounted to >90% and were in excellent agreement with a numerical model for the sorting process.

Complement therapeutic strategies in trauma, hemorrhagic shock and systemic inflammation - closing Pandora's box?

After severe trauma, the immune system is challenged with a multitude of endogenous and exogenous danger molecules. The recognition of released danger patterns is one of the prime tasks of the innate immune system. In the last two decades, numerous studies have established the complement cascade as a major effector system that detects and processes such danger signals. Animal models with engineered deficiencies in certain complement proteins have demonstrated that widespread complement activation after severe injury culminates in complement dysregulation and excessive generation of complement activation fragments. Such exuberant pro-inflammatory signaling evokes systemic inflammation, causes increased susceptibility to infections and is associated with a detrimental course of the disease after injury. We discuss the underlying processes of such complementopathy and recapitulate different intervention strategies within the complement cascade. So far, several orthogonal anti-complement approaches have been tested with varying success in a large number of rodent, in several porcine and few simian studies. We illustrate the different features among those intervention strategies and highlight those that hold the greatest promise to become potential therapeutic options for the intricate disease of traumatic injury.

Pellicle Modification with Casein and Mucin Does Not Affect Surface Loss from Erosion and Abrasion.

AIM: A combination of the proteins casein and mucin is known to modify the salivary pellicle and improve its protection of the underlying enamel from erosion. It is so far not known if this protection is confined solely to erosion, or if it also extends to abrasion, and this in vitro study aimed at investigating this question. METHODS: A total of 72 human enamel specimens were prepared and randomly assigned to four groups: pellicle (P), casein/mucin (CM), pellicle + casein/mucin (PCM), and control (Ctrl). Each specimen underwent five cycles, each cycle consisting of a pellicle/treatment part, an erosion part (3 min in 1% citric acid, pH 3.6, 25°C, 70 rpm), and an abrasion part (50 toothbrush strokes within 25 s in toothpaste slurry with a 200-g load). The pellicle/treatment part consisted of 2 h of incubation in whole human saliva for group P, 2 h of incubation (25°C, 70 rpm) in a protein mixture of 1% casein and 0.27% mucin for group CM, and 2 h of incubation in saliva followed by 2 h of incubation in the protein mixture for group PCM. The fourth group (Ctrl) served as the control and was kept in a humid chamber without saliva or protein treatment. The enamel surfaces were scanned with an optical profilometer initially and after the final cycle, and surface loss was analyzed. Furthermore, the surface microhardness (SMH) was measured initially, after each pellicle/treatment part and each erosion cycle, and after the final abrasion cycle. The results were analyzed with Kruskal-Wallis and Wilcoxon tests with Bonferroni corrections. RESULTS: The different treatments did not show differences in surface loss and therefore did not protect enamel from surface loss by abrasion. Nonetheless, we observed differences in the SMH values, namely the Ctrl group being significantly softer than the experimental groups. CONCLUSION: The observed differences in SMH suggest that a different abrasion protocol could lead to differences in surface loss, and further investigation of whether and under which conditions pellicle modification leads to increased resistance to abrasion remains worthwhile.