Protease-activated receptor 2 (PAR-2) is activated by secreted proteases from immune cells or fungi. PAR-2 is normally expressed basolaterally in differentiated nasal ciliated cells. We hypothesized that epithelial remodeling during diseases characterized by cilial loss and squamous metaplasia may alter PAR-2 polarization. Here, using a fluorescent arrestin assay, we confirmed that the common fungal airway pathogen Aspergillus fumigatus activates heterologously-expressed PAR-2. Endogenous PAR-2 activation in submerged airway RPMI 2650 or NCI–H520 squamous cells increased intracellular calcium levels and granulocyte macrophage–colony-stimulating factor, tumor necrosis factor α, and interleukin (IL)-6 secretion. RPMI 2650 cells cultured at an air–liquid interface (ALI) responded to apically or basolaterally applied PAR-2 agonists. However, well-differentiated primary nasal epithelial ALIs responded only to basolateral PAR-2 stimulation, indicated by calcium elevation, increased cilia beat frequency, and increased fluid and cytokine secretion. We exposed primary cells to disease-related modifiers that alter epithelial morphology, including IL-13, cigarette smoke condensate, and retinoic acid deficiency, at concentrations and times that altered epithelial morphology without causing breakdown of the epithelial barrier to model early disease states. These altered primary cultures responded to both apical and basolateral PAR-2 stimulation. Imaging nasal polyps and control middle turbinate explants, we found that nasal polyps, but not turbinates, exhibit apical calcium responses to PAR-2 stimulation. However, isolated ciliated cells from both polyps and turbinates maintained basolateral PAR-2 polarization, suggesting that the calcium responses originated from nonciliated cells. Altered PAR-2 polarization in disease-remodeled epithelia may enhance apical responses and increase sensitivity to inhaled proteases.

Glial cell line–derived neurotrophic factor (GDNF) is a growth factor that regulates the health and function of neurons and other cells. GDNF binds to GDNF family receptor α1 (GFRa1), and the resulting complex activates the RET receptor tyrosine kinase and subsequent downstream signals. This feature restricts GDNF activity to systems in which GFRa1 and RET are both present, a scenario that may constrain GDNF breadth of action. Furthermore, this co-dependence precludes the use of GDNF as a tool to study a putative functional cross-talk between GFRa1 and RET. Here, using biochemical techniques, terminal deoxynucleotidyl transferase dUTP nick end labeling staining, and immunohistochemistry in murine cells, tissues, or retinal organotypic cultures, we report that a naphthoquinone/quinolinedione family of small molecules (Q compounds) acts as RET agonists. We found that, like GDNF, signaling through the parental compound Q121 is GFRa1-dependent. Structural modifications of Q121 generated analogs that activated RET irrespective of GFRa1 expression. We used these analogs to examine RET–GFRa1 interactions and show that GFRa1 can influence RET-mediated signaling and enhance or diminish AKT Ser/Thr kinase or extracellular signal-regulated kinase signaling in a biased manner. In a genetic mutant model of retinitis pigmentosa, a lead compound, Q525, afforded sustained RET activation and prevented photoreceptor neuron loss in the retina. This work uncovers key components of the dynamic relationships between RET and its GFRa co-receptor and provides RET agonist scaffolds for drug development.

Leukocyte recruitment is a universal feature of tissue inflammation and regulated by the interactions of chemokines with their G protein–coupled receptors. Activation of CC chemokine receptor 2 (CCR2) by its cognate chemokine ligands, including CC chemokine ligand 2 (CCL2), plays a central role in recruitment of monocytes in several inflammatory diseases. In this study, we used phosphoproteomics to conduct an unbiased characterization of the signaling network resulting from CCL2 activation of CCR2. Using data-independent acquisition MS analysis, we quantified both the proteome and phosphoproteome in FlpIn-HEK293T cells stably expressing CCR2 at six time points after activation with CCL2. Differential expression analysis identified 699 significantly regulated phosphorylation sites on 441 proteins. As expected, many of these proteins are known to participate in canonical signal transduction pathways and in the regulation of actin cytoskeleton dynamics, including numerous guanine nucleotide exchange factors and GTPase-activating proteins. Moreover, we identified regulated phosphorylation sites in numerous proteins that function in the nucleus, including several constituents of the nuclear pore complex. The results of this study provide an unprecedented level of detail of CCR2 signaling and identify potential targets for regulation of CCR2 function.

The heterodimeric cytokine interleukin-23 (IL-23 or IL23A/IL12B) is produced by dendritic cells and macrophages and promotes the proinflammatory and regenerative activities of T helper 17 (Th17) and innate lymphoid cells. A recent study has reported that IL-23 is also secreted by lung adenoma cells and generates an inflammatory and immune-suppressed stroma. Here, we observed that proinflammatory tumor necrosis factor (TNF)/NF-κB and mitogen-activated protein kinase (MAPK) signaling strongly induce IL23A expression in intestinal epithelial cells. Moreover, we identified a strong crosstalk between the NF-κB and MAPK/ERK kinase (MEK) pathways, involving the formation of a transcriptional enhancer complex consisting of proto-oncogene c-Jun (c-Jun), RELA proto-oncogene NF-κB subunit (RelA), RUNX family transcription factor 1 (RUNX1), and RUNX3. Collectively, these proteins induced IL23A secretion, confirmed by immunoprecipitation of endogenous IL23A from activated human colorectal cancer (CRC) cell culture supernatants. Interestingly, IL23A was likely secreted in a noncanonical form, as it was not detected by an ELISA specific for heterodimeric IL-23 likely because IL12B expression is absent in CRC cells. Given recent evidence that IL23A promotes tumor formation, we evaluated the efficacy of MAPK/NF-κB inhibitors in attenuating IL23A expression and found that the MEK inhibitor trametinib and BAY 11–7082 (an IKKα/IκB inhibitor) effectively inhibited IL23A in a subset of human CRC lines with mutant KRAS or BRAFV600E mutations. Together, these results indicate that proinflammatory and mitogenic signals dynamically regulate IL23A in epithelial cells. They further reveal its secretion in a noncanonical form independent of IL12B and that small-molecule inhibitors can attenuate IL23A secretion.

Pyruvate kinase muscle isoform 2 (PKM2) is a key glycolytic enzyme involved in ATP generation and critical for cancer metabolism. PKM2 is expressed in many human cancers and is regulated by complex mechanisms that promote tumor growth and proliferation. Therefore, it is considered an attractive therapeutic target for modulating tumor metabolism. Various stimuli allosterically regulate PKM2 by cycling it between highly active and less active states. Several small molecules activate PKM2 by binding to its intersubunit interface. Serine and cysteine serve as an activator and inhibitor of PKM2, respectively, by binding to its amino acid (AA)-binding pocket, which therefore represents a potential druggable site. Despite binding similarly to PKM2, how cysteine and serine differentially regulate this enzyme remains elusive. Using kinetic analyses, fluorescence binding, X-ray crystallography, and gel filtration experiments with asparagine, aspartate, and valine as PKM2 ligands, we examined whether the differences in the side-chain polarity of these AAs trigger distinct allosteric responses in PKM2. We found that Asn (polar) and Asp (charged) activate PKM2 and that Val (hydrophobic) inhibits it. The results also indicate that both Asn and Asp can restore the activity of Val-inhibited PKM2. AA-bound crystal structures of PKM2 displayed distinctive interactions within the binding pocket, causing unique allosteric effects in the enzyme. These structure-function analyses of AA-mediated PKM2 regulation shed light on the chemical requirements in the development of mechanism-based small-molecule modulators targeting the AA-binding pocket of PKM2 and provide broader insights into the regulatory mechanisms of complex allosteric enzymes.

NAD+ is a central metabolite participating in core metabolic redox reactions. The prokaryotic NAD synthetase enzyme NadE catalyzes the last step of NAD+ biosynthesis, converting nicotinic acid adenine dinucleotide (NaAD) to NAD+. Some members of the NadE family use l-glutamine as a nitrogen donor and are named NadEGln. Previous gene neighborhood analysis has indicated that the bacterial nadE gene is frequently clustered with the gene encoding the regulatory signal transduction protein PII, suggesting a functional relationship between these proteins in response to the nutritional status and the carbon/nitrogen ratio of the bacterial cell. Here, using affinity chromatography, bioinformatics analyses, NAD synthetase activity, and biolayer interferometry assays, we show that PII and NadEGln physically interact in vitro, that this complex relieves NadEGln negative feedback inhibition by NAD+. This mechanism is conserved in distantly related bacteria. Of note, the PII protein allosteric effector and cellular nitrogen level indicator 2-oxoglutarate (2-OG) inhibited the formation of the PII-NadEGln complex within a physiological range. These results indicate an interplay between the levels of ATP, ADP, 2-OG, PII-sensed glutamine, and NAD+, representing a metabolic hub that may balance the levels of core nitrogen and carbon metabolites. Our findings support the notion that PII proteins act as a dissociable regulatory subunit of NadEGln, thereby enabling the control of NAD+ biosynthesis according to the nutritional status of the bacterial cell.

8 January 2020 , Volume 96, Number 1

21 April 2020

This article is part 3 of a series on Fantasy Fortifications by Toni Šušnjar.

The design of a fortification depends on its purpose and on the threats it is expected to face. A fortification facing only infantry-held weapons, one facing mechanical artillery, and one facing gunpowder artillery will all significantly differ in design characteristics. Some characteristics however will be the same – geography will always provide advantage (or disadvantage) in defending a fort or a city, and thus location has to be carefully chosen. In some cases, location may be good enough to allow the defender to skimp on certain design features – as seen with e.g. Klis fortress, where northern wall is waist-tall at best, thanks to its position on an inaccessible cliff (clissa). In other cases, disadvantageous terrain may have to be compensated with by massive man-made features.

General Design

In order to cope with development of artillery, design of fortifications changed with time. First fortifications, which only had to deal with handheld weapons, were simple wooden palisades. These were later supplemented with earthen ramparts

As siege weapons developed, fortifications grew both in height and thickness.

Continue reading Fantasy Fortifications — Part 3: Design at Mythic Scribes.

George H. Rothblat
May 1, 1999; 40:781-796
Reviews

ATP plays important roles outside the cell, but the mechanism by which it is arrives in the extracellular environment is not clear. Dunn et al. now show that decreases in cellular cholesterol levels mediated by the ABCG1 transporter increase ATP release by volume-regulated anion channels under hypotonic conditions. Importantly, these results may imply that cells that handle cholesterol differently might experience differential extracellular ATP release during hypotonicity.

Purinergic signaling by extracellular ATP regulates a variety of cellular events and is implicated in both normal physiology and pathophysiology. Several molecules have been associated with the release of ATP and other small molecules, but their precise contributions have been difficult to assess because of their complexity and heterogeneity. Here, we report on the results of a gain-of-function screen for modulators of hypotonicity-induced ATP release using HEK-293 cells and murine cerebellar granule neurons, along with bioluminescence, calcium FLIPR, and short hairpin RNA–based gene-silencing assays. This screen utilized the most extensive genome-wide ORF collection to date, covering 90% of human, nonredundant, protein-encoding genes. We identified two ABCG1 (ABC subfamily G member 1) variants, which regulate cellular cholesterol, as modulators of hypotonicity-induced ATP release. We found that cholesterol levels control volume-regulated anion channel–dependent ATP release. These findings reveal novel mechanisms for the regulation of ATP release and volume-regulated anion channel activity and provide critical links among cellular status, cholesterol, and purinergic signaling.

Heterotrimeric G proteins mediate a variety of signaling processes by coupling G protein–coupled receptors to intracellular effector molecules. In Drosophila, the Gαq gene encodes several Gαq splice variants, with the Gαq1 isoform protein playing a major role in fly phototransduction. However, Gαq1 null mutant flies still exhibit a residual light response, indicating that other Gαq splice variants or additional Gq α subunits are involved in phototransduction. Here, we isolated a mutant fly with no detectable light responses, decreased rhodopsin (Rh) levels, and rapid retinal degeneration. Using electrophysiological and genetic studies, biochemical assays, immunoblotting, real-time RT-PCR, and EM analysis, we found that mutations in the Gαq gene disrupt light responses and demonstrate that the Gαq3 isoform protein is responsible for the residual light response in Gαq1 null mutants. Moreover, we report that Gαq3 mediates rhodopsin synthesis. Depletion of all Gαq splice variants led to rapid light-dependent retinal degeneration, due to the formation stable Rh1-arrestin 2 (Arr2) complexes. Our findings clarify essential roles of several different Gαq splice variants in phototransduction and retinal integrity in Drosophila and reveal that Gαq3 functions in rhodopsin synthesis.

Glial cell line–derived neurotrophic factor (GDNF) is a growth factor that regulates the health and function of neurons and other cells. GDNF binds to GDNF family receptor α1 (GFRa1), and the resulting complex activates the RET receptor tyrosine kinase and subsequent downstream signals. This feature restricts GDNF activity to systems in which GFRa1 and RET are both present, a scenario that may constrain GDNF breadth of action. Furthermore, this co-dependence precludes the use of GDNF as a tool to study a putative functional cross-talk between GFRa1 and RET. Here, using biochemical techniques, terminal deoxynucleotidyl transferase dUTP nick end labeling staining, and immunohistochemistry in murine cells, tissues, or retinal organotypic cultures, we report that a naphthoquinone/quinolinedione family of small molecules (Q compounds) acts as RET agonists. We found that, like GDNF, signaling through the parental compound Q121 is GFRa1-dependent. Structural modifications of Q121 generated analogs that activated RET irrespective of GFRa1 expression. We used these analogs to examine RET–GFRa1 interactions and show that GFRa1 can influence RET-mediated signaling and enhance or diminish AKT Ser/Thr kinase or extracellular signal-regulated kinase signaling in a biased manner. In a genetic mutant model of retinitis pigmentosa, a lead compound, Q525, afforded sustained RET activation and prevented photoreceptor neuron loss in the retina. This work uncovers key components of the dynamic relationships between RET and its GFRa co-receptor and provides RET agonist scaffolds for drug development.

Mass spectrometry (MS)-based proteomics has great potential for overcoming the limitations of antibody-based immunoassays for antibody-independent, comprehensive, and quantitative proteomic analysis of single cells. Indeed, recent advances in nanoscale sample preparation have enabled effective processing of single cells. In particular, the concept of using boosting/carrier channels in isobaric labeling to increase the sensitivity in MS detection has also been increasingly used for quantitative proteomic analysis of small-sized samples including single cells. However, the full potential of such boosting/carrier approaches has not been significantly explored, nor has the resulting quantitation quality been carefully evaluated. Herein, we have further evaluated and optimized our recent boosting to amplify signal with isobaric labeling (BASIL) approach, originally developed for quantifying phosphorylation in small number of cells, for highly effective analysis of proteins in single cells. This improved BASIL (iBASIL) approach enables reliable quantitative single-cell proteomics analysis with greater proteome coverage by carefully controlling the boosting-to-sample ratio (e.g. in general <100x) and optimizing MS automatic gain control (AGC) and ion injection time settings in MS/MS analysis (e.g. 5E5 and 300 ms, respectively, which is significantly higher than that used in typical bulk analysis). By coupling with a nanodroplet-based single cell preparation (nanoPOTS) platform, iBASIL enabled identification of ~2500 proteins and precise quantification of ~1500 proteins in the analysis of 104 FACS-isolated single cells, with the resulting protein profiles robustly clustering the cells from three different acute myeloid leukemia cell lines. This study highlights the importance of carefully evaluating and optimizing the boosting ratios and MS data acquisition conditions for achieving robust, comprehensive proteomic analysis of single cells.

Signaling networks process intra- and extracellular information to modulate the functions of a cell. Deregulation of signaling networks results in abnormal cellular physiological states and often drives diseases. Network responses to a stimulus or a drug treatment can be highly heterogeneous across cells in a tissue because of many sources of cellular genetic and non-genetic variance. Signaling network heterogeneity is the key to many biological processes, such as cell differentiation and drug resistance. Only recently, the emergence of multiplexed single-cell measurement technologies has made it possible to evaluate this heterogeneity. In this review, we categorize currently established single-cell signaling network profiling approaches by their methodology, coverage, and application, and we discuss the advantages and limitations of each type of technology. We also describe the available computational tools for network characterization using single-cell data and discuss potential confounding factors that need to be considered in single-cell signaling network analyses.

Pyruvate kinase muscle isoform 2 (PKM2) is a key glycolytic enzyme involved in ATP generation and critical for cancer metabolism. PKM2 is expressed in many human cancers and is regulated by complex mechanisms that promote tumor growth and proliferation. Therefore, it is considered an attractive therapeutic target for modulating tumor metabolism. Various stimuli allosterically regulate PKM2 by cycling it between highly active and less active states. Several small molecules activate PKM2 by binding to its intersubunit interface. Serine and cysteine serve as an activator and inhibitor of PKM2, respectively, by binding to its amino acid (AA)-binding pocket, which therefore represents a potential druggable site. Despite binding similarly to PKM2, how cysteine and serine differentially regulate this enzyme remains elusive. Using kinetic analyses, fluorescence binding, X-ray crystallography, and gel filtration experiments with asparagine, aspartate, and valine as PKM2 ligands, we examined whether the differences in the side-chain polarity of these AAs trigger distinct allosteric responses in PKM2. We found that Asn (polar) and Asp (charged) activate PKM2 and that Val (hydrophobic) inhibits it. The results also indicate that both Asn and Asp can restore the activity of Val-inhibited PKM2. AA-bound crystal structures of PKM2 displayed distinctive interactions within the binding pocket, causing unique allosteric effects in the enzyme. These structure-function analyses of AA-mediated PKM2 regulation shed light on the chemical requirements in the development of mechanism-based small-molecule modulators targeting the AA-binding pocket of PKM2 and provide broader insights into the regulatory mechanisms of complex allosteric enzymes.

Cytochrome c oxidase (CcO) reduces O2 to water, coupled with a proton-pumping process. The structure of the O2-reduction site of CcO contains two reducing equivalents, Fea32+ and CuB1+, and suggests that a peroxide-bound state (Fea33+–O−–O−–CuB2+) rather than an O2-bound state (Fea32+–O2) is the initial catalytic intermediate. Unexpectedly, however, resonance Raman spectroscopy results have shown that the initial intermediate is Fea32+–O2, whereas Fea33+–O−–O−–CuB2+ is undetectable. Based on X-ray structures of static noncatalytic CcO forms and mutation analyses for bovine CcO, a proton-pumping mechanism has been proposed. It involves a proton-conducting pathway (the H-pathway) comprising a tandem hydrogen-bond network and a water channel located between the N- and P-side surfaces. However, a system for unidirectional proton-transport has not been experimentally identified. Here, an essentially identical X-ray structure for the two catalytic intermediates (P and F) of bovine CcO was determined at 1.8 Å resolution. A 1.70 Å Fe–O distance of the ferryl center could best be described as Fea34+ = O2−, not as Fea34+–OH−. The distance suggests an ∼800-cm−1 Raman stretching band. We found an interstitial water molecule that could trigger a rapid proton-coupled electron transfer from tyrosine-OH to the slowly forming Fea33+–O−–O−–CuB2+ state, preventing its detection, consistent with the unexpected Raman results. The H-pathway structures of both intermediates indicated that during proton-pumping from the hydrogen-bond network to the P-side, a transmembrane helix closes the water channel connecting the N-side with the hydrogen-bond network, facilitating unidirectional proton-pumping during the P-to-F transition.

Cell-surface signaling (CSS) in Gram-negative bacteria involves highly conserved regulatory pathways that optimize gene expression by transducing extracellular environmental signals to the cytoplasm via inner-membrane sigma regulators. The molecular details of ferric siderophore-mediated activation of the iron import machinery through a sigma regulator are unclear. Here, we present the 1.56 Å resolution structure of the periplasmic complex of the C-terminal CSS domain (CCSSD) of PupR, the sigma regulator in the Pseudomonas capeferrum pseudobactin BN7/8 transport system, and the N-terminal signaling domain (NTSD) of PupB, an outer-membrane TonB-dependent transducer. The structure revealed that the CCSSD consists of two subdomains: a juxta-membrane subdomain, which has a novel all-β-fold, followed by a secretin/TonB, short N-terminal subdomain at the C terminus of the CCSSD, a previously unobserved topological arrangement of this domain. Using affinity pulldown assays, isothermal titration calorimetry, and thermal denaturation CD spectroscopy, we show that both subdomains are required for binding the NTSD with micromolar affinity and that NTSD binding improves CCSSD stability. Our findings prompt us to present a revised model of CSS wherein the CCSSD:NTSD complex forms prior to ferric-siderophore binding. Upon siderophore binding, conformational changes in the CCSSD enable regulated intramembrane proteolysis of the sigma regulator, ultimately resulting in transcriptional regulation.

Hippo pathway signaling limits cell growth and proliferation and maintains the stem-cell niche. These cellular events result from the coordinated activity of a core kinase cassette that is regulated, in part, by interactions involving Hippo, Salvador, and dRassF. These interactions are mediated by a conserved coiled-coil domain, termed SARAH, in each of these proteins. SARAH domain–mediated homodimerization of Hippo kinase leads to autophosphorylation and activation. Paradoxically, SARAH domain–mediated heterodimerization between Hippo and Salvador enhances Hippo kinase activity in cells, whereas complex formation with dRassF inhibits it. To better understand the mechanism by which each complex distinctly modulates Hippo kinase and pathway activity, here we biophysically characterized the entire suite of SARAH domain–mediated complexes. We purified the three SARAH domains from Drosophila melanogaster and performed an unbiased pulldown assay to identify all possible interactions, revealing that isolated SARAH domains are sufficient to recapitulate the cellular assemblies and that Hippo is a universal binding partner. Additionally, we found that the Salvador SARAH domain homodimerizes and demonstrate that this interaction is conserved in Salvador's mammalian homolog. Using native MS, we show that each of these complexes is dimeric in solution. We also measured the stability of each SARAH domain complex, finding that despite similarities at both the sequence and structural levels, SARAH domain complexes differ in stability. The identity, stoichiometry, and stability of these interactions characterized here comprehensively reveal the nature of SARAH domain–mediated complex formation and provide mechanistic insights into how SARAH domain–mediated interactions influence Hippo pathway activity.

Cholesterol/sphingolipid-rich membrane domains, known as lipid rafts or membrane rafts, play a critical role in the compartmentalization of signaling pathways. Physical segregation of proteins in lipid rafts may modulate the accessibility of proteins to regulatory or effector molecules. Thus, lipid rafts serve as sorting platforms and hubs for signal transduction proteins. Cancer cells contain higher levels of intracellular cholesterol and lipid rafts than their normal non-tumorigenic counterparts. Many signal transduction processes involved in cancer development (insulin-like growth factor system and phosphatidylinositol 3-kinase-AKT) and metastasis [cluster of differentiation (CD)44] are dependent on or modulated by lipid rafts. Additional proteins playing an important role in several malignant cancers (e.g., transmembrane glycoprotein mucin 1) are also being detected in association with lipid rafts, suggesting a major role of lipid rafts in tumor progression. Conversely, lipid rafts also serve as scaffolds for the recruitment and clustering of Fas/CD95 death receptors and downstream signaling molecules leading to cell death-promoting raft platforms. The partition of death receptors and downstream signaling molecules in aggregated lipid rafts has led to the formation of the so-called cluster of apoptotic signaling molecule-enriched rafts, or CASMER, which leads to apoptosis amplification and can be pharmacologically modulated. These death-promoting rafts can be viewed as a linchpin from which apoptotic signals are launched. In this review, we discuss the involvement of lipid rafts in major signaling processes in cancer cells, including cell survival, cell death, and metastasis, and we consider the potential of lipid raft modulation as a promising target in cancer therapy.

Expert

Cytochrome c oxidase (CcO) reduces O2 to water, coupled with a proton-pumping process. The structure of the O2-reduction site of CcO contains two reducing equivalents, Fea32+ and CuB1+, and suggests that a peroxide-bound state (Fea33+–O−–O−–CuB2+) rather than an O2-bound state (Fea32+–O2) is the initial catalytic intermediate. Unexpectedly, however, resonance Raman spectroscopy results have shown that the initial intermediate is Fea32+–O2, whereas Fea33+–O−–O−–CuB2+ is undetectable. Based on X-ray structures of static noncatalytic CcO forms and mutation analyses for bovine CcO, a proton-pumping mechanism has been proposed. It involves a proton-conducting pathway (the H-pathway) comprising a tandem hydrogen-bond network and a water channel located between the N- and P-side surfaces. However, a system for unidirectional proton-transport has not been experimentally identified. Here, an essentially identical X-ray structure for the two catalytic intermediates (P and F) of bovine CcO was determined at 1.8 Å resolution. A 1.70 Å Fe–O distance of the ferryl center could best be described as Fea34+ = O2−, not as Fea34+–OH−. The distance suggests an ∼800-cm−1 Raman stretching band. We found an interstitial water molecule that could trigger a rapid proton-coupled electron transfer from tyrosine-OH to the slowly forming Fea33+–O−–O−–CuB2+ state, preventing its detection, consistent with the unexpected Raman results. The H-pathway structures of both intermediates indicated that during proton-pumping from the hydrogen-bond network to the P-side, a transmembrane helix closes the water channel connecting the N-side with the hydrogen-bond network, facilitating unidirectional proton-pumping during the P-to-F transition.

8 January 2020 , Volume 96, Number 1

As difficult as it is to do the census, the ensuing process of determining the number of congressional seats for each state can be even harder. The basic premise, that the proportion of each state's delegation in the House should match its proportion of the U.S. population, is simple enough. The difficulty arises when deciding what to do with the fractions that inevitably arise (e.g., New York can't have 28.7 seats). Over the past 200 years, several methods of apportioning seats have been used. Many sound good but can lead to paradoxes, such as an increase in the total number of House seats actually resulting in a reduction of a state's delegation. The method used since the 1940s, whose leading proponent was a mathematician, is one that avoids such paradoxes. A natural question is Why 435 seats? Nothing in the Constitution mandates this number, although there is a prohibition against having more than one seat per 30,000 people. One model, based on the need for legislators to communicate with their constituents and with each other, uses algebra and calculus to show that the ideal assembly size is the cube root of the population it represents. Remarkably, the size of the House mirrored this rule until the early 1900s. To obey the rule now would require an increase to 670, which would presumably both better represent the population and increase the chances that the audience in the seats for those late speeches would outnumber the speaker. For More Information: "E pluribus confusion", Barry Cipra, American Scientist, July-August 2010.

As difficult as it is to do the census, the ensuing process of determining the number of congressional seats for each state can be even harder. The basic premise, that the proportion of each state's delegation in the House should match its proportion of the U.S. population, is simple enough. The difficulty arises when deciding what to do with the fractions that inevitably arise (e.g., New York can't have 28.7 seats). Over the past 200 years, several methods of apportioning seats have been used. Many sound good but can lead to paradoxes, such as an increase in the total number of House seats actually resulting in a reduction of a state's delegation. The method used since the 1940s, whose leading proponent was a mathematician, is one that avoids such paradoxes. A natural question is Why 435 seats? Nothing in the Constitution mandates this number, although there is a prohibition against having more than one seat per 30,000 people. One model, based on the need for legislators to communicate with their constituents and with each other, uses algebra and calculus to show that the ideal assembly size is the cube root of the population it represents. Remarkably, the size of the House mirrored this rule until the early 1900s. To obey the rule now would require an increase to 670, which would presumably both better represent the population and increase the chances that the audience in the seats for those late speeches would outnumber the speaker. For More Information: "E pluribus confusion", Barry Cipra, American Scientist, July-August 2010.

Researcher: Meredith Greer, Bates College. Going Over the Top Description: Meredith Greer talks about math and roller coasters.

Researcher: Jim Papadopoulos, Northeastern University
Description: Jim Papadopoulos talks about his years of research analyzing bicycles.