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# Fibril formation and therapeutic targeting of amyloid-like structures in a yeast model of adenine accumulation

## Abstract

The extension of the amyloid hypothesis to include non-protein metabolite assemblies invokes a paradigm for the pathology of inborn error of metabolism disorders. However, a direct demonstration of the assembly of metabolite amyloid-like structures has so far been provided only in vitro. Here, we established an in vivo model of adenine self-assembly in yeast, in which toxicity is associated with intracellular accumulation of the metabolite. Using a strain blocked in the enzymatic pathway downstream to adenine, we observed a non-linear dose-dependent growth inhibition. Both the staining with an indicative amyloid dye and anti-adenine assemblies antibodies demonstrated the accumulation of adenine amyloid-like structures, which were eliminated by lowering the supplied adenine levels. Treatment with a polyphenol inhibitor reduced the occurrence of amyloid-like structures while not affecting the dramatic increase in intracellular adenine concentration, resulting in inhibition of cytotoxicity, further supporting the notion that toxicity is triggered by adenine assemblies.

## Introduction

The canonical amyloid hypothesis attributed the formation of nano-scale fibrillar assemblies exclusively to proteins and polypeptides1,2. However, a paradigm for the pathophysiology of inborn error of metabolism disorders significantly extended the original hypothesis, showing that at millimolar pathological concentrations, the single phenylalanine amino acid can form nanofibrillar structures in aqueous solution and neutral pH in vitro3. These nonproteinaceous assemblies exhibit typical apple-green birefringence and clear fluorescence signal upon Congo red staining when examined under cross-polarized light and fluorescent microscopy, intense fluorescence following thioflavin T staining, and cell culture cytotoxicity3,4. Using electron microscopy, a fibrillar morphology of the phenylalanine assemblies was observed, showing physical properties characteristic of protein amyloids. As opposed to single crystals that show regular geometrical shapes consisting of flat faces, amyloid structures have a fibrillar morphology. Based on the similar characteristics to amyloid proteins, these nonproteinaceous assemblies were suggested to display ‘amyloid-like’ properties.

The notable toxicity of the assemblies was suggested to be associated with the neurological damage observed in non-treated patients suffering from the phenylketonuria (PKU) error of metabolism disorder, in which phenylalanine accumulates due to metabolic pathway alteration. Histological post-mortem staining of brain tissues of human PKU patients, as well as of PKU model mice, using specific antibodies raised against phenylalanine fibrils, demonstrated the specificity of the antibodies and the formation of metabolite amyloid-like assemblies in the disease state3. Follow-up studies supported the notion that the single phenylalanine amino acid can form amyloid-like nanofibrillar structures, established the mechanism of oligomerization, and determined the ability of the phenylalanine assemblies to interact with phospholipid membranes, similar to protein amyloids5,6,7,8,9,10,11,12,13. Furthermore, doxycycline, epigallocatechin gallate, and tannic acid (TA), known inhibitors of amyloid fibril formation, were shown to counteract both phenylalanine aggregation and cytotoxicity of the assemblies in vitro14,15. Moreover, the amyloid hypothesis was significantly extended by demonstrating that several other metabolites, including additional amino acids and nucleobases, could form such archetypical nanofibrils in vitro, displaying amyloid-like properties4,16,17,18,19,20,21. The alanine amino acid shows none of the above characterizations, as well as no toxic effect when added to cultured cells at high concentrations3,4. Furthermore, differential flexibility properties might explain the resistance of alpha-phenylglycine, that differs from phenylalanine by the absence of an additional flexible carbon extension, to fibril formation12. Thus, fibril formation and toxic effect are believed to occur due to structures formed by only certain metabolites.

## Results

### In vivo model for adenine accumulation and toxicity

Altogether, the presence of adenine at the normal concentration used for wild-type yeast growth leads to a significant cell growth decrease in a strain that is defective in the biosynthesis downstream to adenine. This is indeed an unusual phenomenon as in most cases (excluding mutations in transport systems) the absence of a given metabolite, rather than its presence in the physiological concentration needed for normal yeast growth, serves as a limiting factor of wild-type yeast growth34. This is analogous to the toxicity of normal metabolite concentrations observed in some inborn error of metabolism disorders, such as PKU and tyrosinemia35, where the RDA for the general population is actually toxic to the affected individuals, due to accumulation of the metabolites in the absence of salvage. The effect indeed appears to reflect toxicity, as increasing adenine levels in the medium led to decreased cell growth in a dose-dependent manner (Fig. 1c, d), similar to the toxic effect previously observed in in vitro cell culture studies4. It should be noted that the toxic effect on cell growth due to adenine accumulation is very similar to the outcome of protein amyloid expression in yeast cells26,28,29.

### Non-linear response to adenine feeding

The dose–response curve of cell growth as a function of adenine concentration was fitted using a four-parameter logistic equation (4PL), producing a typical-sigmoidal shaped curve, with no effect at lower concentrations and a sharp increase in the inhibitory effect upon reaching a critical concentration threshold (Fig. 1d). Thus, cell growth appears to be affected by adenine levels in a non-linear cooperative manner. This is consistent with the mechanism of nucleation-growth as observed in micelle formation (assembly above a critical micelle concentration, CMC) or the formation of amyloids by the assembly of protein monomers36,37,38. Indeed, in vitro studies also showed non-linear self-assembly of adenine at different concentrations (Supplementary Fig. 3 and Supplementary Methods). Thus, we present in vitro as well as in vivo data regarding adenine accumulation at different concentrations and the possible correlation between the assembly mechanism of fibril formation and cellular growth. Our results imply that above a critical concentration, the favorable energetic state dictates the formation of the toxic assemblies, while at lower concentrations the metabolites are most likely at the normal physiological state.

To quantify the intracellular concentrations of adenine, gas chromatography mass-spectrometry (GC–MS) was used. Analysis of the cellular adenine concentrations under different conditions indicated that on SD media in the presence of the metabolite, adenine levels were indeed significantly higher in the salvage mutant as compared to the wild-type strain (×45 fold; Fig. 1e), suggesting a clear correlation between the feeding amounts of adenine and growth inhibition. Similarly, when not following a very strict diet, inborn error of metabolism patients have 1–2 orders of magnitude higher concentrations of metabolites, as compared to the general population10.

### Visualization of adenine accumulation by Raman imaging

To detect the accumulation of adenine in vivo, we utilized Raman microspectroscopy. Raman spectroscopy coupled with microscopy has recently emerged as a promising tool to trace intracellular processes in vivo and was successfully used in yeast to follow glucose assimilation into intracellular components39. Raman spectrum provides rich and highly specific chemical information and thus intracellular molecular distribution can be visualized at a sub-μm spatial resolution by Raman microspectroscopy. Moreover, being a vibrational spectroscopic technique, label-free imaging could be performed, as it requires no exogenous dye probe. Space-resolved Raman spectra obtained at three different points in salvage mutant single cells (aah1Δ apt1Δ) in the presence of adenine showed Raman bands characteristic to proteins (Fig. 2a, c). Major features included 1004 cm−1 [phenylalanine ring breathing], 1250 cm−1 [amide III], 1340 and 1448 cm−1 [C–H bend], and 1655 cm−1 [amide I]40,41,42. By carefully examining the region between 800 and 700 cm−1, we could observe a band at 785 cm−1 corresponding to ring breathing modes of nucleobases such as uracil, cytosine, thymine, and nucleic acid backbone vibration (Fig. 2b). Additionally, we also observed a band at 724 cm−1 corresponding to adenine ring breathing modes (Raman band of adenine in solid and solution forms are shown in Supplementary Fig. 4). According to these observations, we chose the 785 cm−1 band as a marker of nucleic acids in general while 724 cm−1 served as an adenine marker43,44,45. As expected, the intensities of these two bands varied depending on the location in the cell. As shown in Fig. 2b, while the red and black spectra showed intense adenine marker with very low nucleic acid band (indicating high prevalence of adenine), respectively, the spectrum in green showed comparable intensities of these two bands, which is typical of nucleic acids. Thus, these bands can be used to study adenine accumulation.

### Amyloid-like assemblies formation upon adenine accumulation

To examine whether the observed non-linear behavior of the dose-dependent toxicity is indeed associated with self-organization of the metabolites into amyloid-like assemblies in vivo, the cells were stained with ProteoStat, an amyloid-specific fluorescent dye. This reagent was previously shown to facilitate specific and sensitive detection of amyloid aggregates in living cells46. To validate the possible identification of amyloid fibrils by ProteoStat staining in yeast, detection of the prion protein Sup35 was examined (Supplementary Fig. 5), showing significant and gradual increase in the staining of [psi] compared to two types of [PSI+] aggregates, weak [PSI+] and strong [PSI+]. Flow cytometry and confocal microscopy were then employed to detect the presence of intracellular amyloid-like adenine aggregates. Both techniques clearly indicated the presence of amyloid-like structures in the adenine salvage mutant. Flow cytometry showed a higher degree of aggregation in the mutant compared to wild-type cells in the presence of the metabolite (Fig. 3a). Moreover, consistent with the indicated adenine sensitivity (Fig. 1a), removal of adenine from the medium reduced the level of aggregation in the mutant cells (Fig. 3a). Confocal microscopy further allowed the identification of the intracellular localization of the adenine aggregates, showing clearly stained dots only in the salvage mutant and specifically following the addition of adenine (Fig. 3b). Z-stack followed by 3D reconstruction (Fig. 3c), as well as projection of a single section of the Z-stack (Fig. 3d), showed that the stained dots were localized inside the cell, excluding the possibility of their attachment to the outer membrane or cell wall. Furthermore, Hoechst staining showed no co-localization, ruling out the possibility that the stained dots were inside the nucleus (Fig. 3e).

The Hsp104 chaperon was previously shown in yeast to play a pivotal role in the formation of numerous aggregates by structurally unrelated proteins and its deletion partially restored the viability of cells expressing Aβ and polyQ in yeast models for Alzheimer’s disease and Huntington’s disease, respectively47,48. To test whether the toxicity following adenine accumulation in the salvage mutant is mediated by Hsp104, cell growth upon adenine addition was examined in the presence of guanidine hydrochloride that was repeatedly shown to inhibit Hsp104 activity, as well as in a hsp104Δ mutant background (Supplementary Fig. 6a, b). No Hsp104 dependency was observed, suggesting that the toxicity induced by adenine accumulation involves a different mechanism than the Hsp104-associated one. To further validate this observation, the chaperon response was examined using a Hsp104-mCherry strain49 (Supplementary Fig. 6c). While Hsp104 recruitment and accumulation was observed under heat shock stress and in the presence of adenine both in wild-type and in the salvage mutant cells, no such dots appeared under optimal growth temperature, suggesting a different mechanism other than the Hsp104-associated one that was previously reported.

### In vivo formation of adenine amyloid-like assemblies

To confirm that the staining with the ProteoStat dye specifically identifies adenine amyloid-like structures, antibodies against adenine fibril structures were generated, as we have previously described for phenylalanine and tyrosine fibrils3,50. After staining with the anti-adenine fibril antibodies, fluorescent dots could be detected only in the salvage mutant in the presence of adenine (Fig. 3f). This result suggests that the observed cellular toxicity is directly linked to self-assembled amyloid-like adenine structures.

### Inhibition of adenine toxicity by TA

In order to ascertain that the inhibition by TA represents a general phenomenon applicable for other known amyloid inhibitors, baicalein, an additional polyphenolic inhibitor of protein amyloid formation, that was recently shown to bear therapeutic potential for Alzheimer’s and Parkinson’s disease56 was examined. Indeed, the use of this inhibitor resulted in a significant effect on yeast cell growth (Supplementary Fig. 8a, b) and on adenine aggregation (Supplementary Fig. 8c), as well as in a dose-dependent inhibition of adenine self-assembly in vitro (Supplementary Fig. 8d).

### TA mechanism of action

In order to examine the in vivo mechanism underlying the inhibition of adenine amyloid-like formation by TA, the inhibitor was added at different time points of yeast growth. TA was found to hinder the formation of adenine amyloid-like assemblies when added at earlier time points of yeast growth, while it had no effect on their growth when added at later stages, suggesting that TA is most effective at the nucleation and early oligomerization stage of the metabolite self-assembly (Fig. 5a). These results further support a correlation between adenine aggregation into ordered structures and growth inhibition, suggesting that the toxic effect is induced by adenine accumulation into amyloid-like species. This effect can be rescued by either removal of adenine from the medium or addition of the amyloid inhibitor, thereby modulating the assembly process.

Finally, we examined whether the dramatic effect of the inhibitor on the viability of the mutant cells actually reflects a change in the concentration of adenine in the metabolite salvage model, in addition to the inhibition of amyloid-like structure formation. For this purpose, the intracellular concentrations of adenine with and without the inhibitor were compared using mass spectrometry. Evidently, while the addition of the inhibitor drastically improved cell growth, the intracellular levels of adenine remained constant (Fig. 5b). Thus, the change in cell growth appears to occur specifically due to the inhibition of adenine aggregate formation, and not as a result of a decrease in adenine levels, ruling out the possibility of an indirect effect of TA on adenine availability in the medium. This result, in addition to studies demonstrating the ability of TA to inhibit amyloid-like fibrillation of adenine in vitro15, further implies that the assemblies, rather than free metabolite molecules, mediate cell toxicity (as modeled in Fig. 5c).

## Discussion

The ability of metabolites to form ordered amyloid-like assemblies in vitro represents a significant extension to the “amyloid hypothesis” and provides a paradigm for the etiology of inborn error of metabolism disorders. The current study offers an in vivo demonstration and key experimental tools for the study of metabolite aggregation phenomena in living systems. One of the most intriguing results is the non-linear dose-dependency of the salvage mutant growth inhibition upon external addition of adenine (Fig. 1d). This type of cooperative behavior is typical of the well-coordinated self-assembly processes of protein and peptide amyloids. Significant effort was invested in order to understand the organization of amyloids formed by the assembly of various disease-related protein building blocks including the deciphering of primary and secondary nucleation events and the resulting fibril growth57,58. While these highly important studies were performed in vitro, the analysis of such processes in living cells has so far been hampered. The established model could provide an invaluable, yet simple, in vivo system to determine amyloid nucleation and assembly in living eukaryotic cells. In the current work (Fig. 5c), adenine aggregation and the formation of adenine amyloid-like structures inside the cell were demonstrated, as well as the suppression by well-known amyloid inhibitors.

The stereotypical cell-to-cell cerebral spreading of neurodegenerative disorders, such as Alzheimer’s disease, Parkinson’s disease, and amyotrophic lateral sclerosis (ALS) has recently been suggested to be propagated in a prion-like manner59,60,61. Given the remarkable similarities between protein and metabolite amyloids, prion-like features of metabolite assemblies cannot be ruled out. In fact, such a behavior may provide insights into surprising phenomena, including the maternal error of metabolism disorders, in which the newborn has normal metabolism but might still suffer from neurodevelopmental aberrations due to maternal effects10,62. Yeast have been successfully used to study cell-to-cell spreading of yeast prions63,64. The current system should allow to reveal any possible prion-like effects of nonproteinaceous aggregates. This will extend not only the definition of amyloids, but also the definition of metabolite prion-like entities, or ‘metions’ (metabolite infectious particles).

The yeast model could also serve as the perfect platform for high throughput screening of therapeutic agents to target metabolite aggregation, as previously demonstrated for yeast models of protein amyloid self-assembly28. Yeast mutations, resulting in the accumulation of given metabolites, as observed in various human metabolic diseases, may be utilized in a simple yet robust way. The ability of TA to reverse the growth inhibition without an effect on metabolite concentration (Fig. 5b) provides a proof of concept for a large-range screen of potential drugs that could target the aggregation process, as well as possible nucleating seeds.

Finally, the current work provides a clear indication that the assembly of metabolites into ordered amyloid-like structures, rather than merely their amount, mediates growth inhibition. Indeed, excessive concentrations of adenine caused a complete growth inhibition, which was rescued with pharmacological intervention. This further raises the question regarding the natural mechanisms that help unicellular and multicellular organisms to avoid aggregation upon temporary or chronic surge in the concentration of a given metabolite. Presumably, similar to the proteostasis machinery65,66, there are cellular mechanisms aimed to avoid metabolite aggregation or clear preformed metabolite nuclei. Such a ‘metabostasis’ mechanism appears to be crucial, as many of the essential components of life, including aromatic amino acids and purine nucleobases, appear to be highly aggregative. The use of these molecular components is essential to maintain functional biological systems, while safety mechanisms should be available to prevent unwanted association of these aggregation-prone entities.

## Methods

### Strains and culture

Yeast strains, plasmids, and primers used in this study are listed in Supplementary Tables 1, 2 and 3, respectively. Strains were cultured in SD media consisting a defined mixture of amino acids and nucleobases. Adenine (adenine hemisulfate salt, Sigma-Aldrich) was supplemented in the indicated concentrations.

### Construction of aah1Δapt1Δ strain

The kanMX6 cassete in the apt1::kanMX6 strain was replaced by a PCR product of the HygromycinR cassette using U2/D2 oligonucleotides that contain a homology sequence for homologous recombination. Cells were grown in rich medium (YPD) for ~24 h before plating on YPD plates containing Hygromycin (200 mg/L). The double mutant strain apt1::hphMX6 aah1::kanMX6 was generated by transforming a PCR product of the KanMX cassette with 5′ and 3′ flanking sequences of AAH1 into the apt1::hphMX6 strain. Cells were grown in YPD for ~24 h before plating on YPD plates containing G418 (200 mg/L). Genetic disruptions were confirmed by PCR using an oligonucleotide upstream of the deletion and a reverse oligonucleotide within the HygR or the KanMX gene.

### Yeast growth assays

Strains were grown over night at 30 °C in SD medium without adenine. For spotting assays, strains were diluted to 6.25*107 cells/mL and were then five-fold serially diluted and spotted on SD media with the indicated concentrations of adenine or TA (Sigma-Aldrich). Plates were incubated at 30 °C for 2 days. The results displayed are representative of three biological experiments.

For OD600 measurements, strains were diluted to OD600 0.01. 200 µL of cells were platted on 96 wells plates and incubated at 30 °C for 25 h with continuous shaking. OD600 was measured using TecanTM SPARK 10M plate reader. The results displayed are representative of three biological experiments performed in triplicate.

For the dose–response curve of WT and aah1Δapt1Δ cell growth (Fig. 1d), strains were cultured in SD media containing different concentrations of adenine (from 0.03 µg/L to 40 mg/L) and OD600 measurements were performed when the cells reached log phase (1*107 cells/mL). The results displayed are representative of three biological experiments. Results were fitted to a standard logistic four-parameter equation using the OriginLab software using the following equation:

$${y} = {d} + \frac{{{a} - {d}}}{{\left( {1 + \left( {\frac{{x}}{{{c}^{b}}}} \right)} \right.}}$$
(1)

where y is the OD600 value, d is the maximum OD600 value, a is the minimum OD600 value, x is adenine concentration (µg), c is the point of inflection, and b is the slope factor of the curve.

For the percentage of growth analysis (Figs. 4b and 5a), OD600 was measured when cells reached log phase. The percentage of growth represents the growth with TA compared to the growth without TA. The results displayed are representative of three biological experiments performed in triplicate.

### GC–MS

The protocol was adapted from Tu, B. P. et al.67. Four milliliters of 60% methanol/10 mM Tricine (pH 7.4) that was maintained at −20 °C were added to 2 mL of logarithmic cells. The number of cells was counted using a hemocytometer. Cells were incubated for 5 min at −20 °C, centrifuged at 1000×g for 3 min at 4 °C, washed with 1 mL of the same buffer and resuspended in 1 mL of 75% ethanol/0.5 mM Tricine (pH 7.4). Intracellular metabolites were extracted by incubating at 80 °C for 3 min and then at 4 °C for 5 min. Samples were centrifuged at 20,000×g for 1 min, and 0.9 mL of the supernatant was transferred to a new tube, centrifuged again for 10 min and 0.8 mL was transferred to a new tube. Samples were stored at −80 °C until analysis. For each strain and/or condition, seven samples were extracted: three samples for measurement and four samples for spiking adenine standard. Matrix-matched standard curves for each cell pool were constructed68. Stock solution of adenine (1 mg/mL in 1 M HCl) was sequentially diluted 10-fold, 100-fold, and 1000-fold into solutions that were spiked to four samples of the same group of extracts plus one blank in amounts providing final exogenous adenine concentrations of 1, 5, 10, and 50 µg/mL after derivatization. All samples were evaporated in N2-flow and then lyophilized for 2 h. Each sample was derivatized by adding 30 µL of MSTFA (Restek, #35600) and shaking at 60 °C for 1 h. The mixtures were transferred to 2 mL autosampler glass vials with 100 µL glass inserts. Acquisition was performed in GC–MS system comprising an Agilent 7890A gas chromatograph and LECO Pegasus HT Time-of-Flight Mass Spectrometer (MassBank Record: OUF00096) using a Rxi-5Sil MS (Restek) column. Samples were analyzed using the splitless mode; the temperature of injector was set to 230 °C and the transfer line to 250 °C. The injected analytes were separated using the following chromatographic conditions: 1 mL/min of helium as a carrier gas was held at 80 °C for 2 min, ramped to 330 °C at 15 °C/min, and then held at this temperature for another 6 min. For mass-spectrometry, electron impact mode with ionization voltage was 70 eV, mass range 85–500m/z and acquisition rate of 20 spectra per second. The ion source chamber was set to 200 °C, and the detector voltage was 1650V. LECO ChromaTOF software was used for acquisition control and data processing with 264m/z at 722-s peak for quantitation, with the limit of quantitation being 0.01 µg/mL. Adenine concentration was normalized to the number of cells per each sample and divided by 108 cells. The results displayed are representative of three biological experiments performed in triplicate. Values are the mean ± s.d. of three independent experiments.

### Flow cytometry

One milliliter of logarithmic cells were washed with PBS buffer and sonicated using 15 s pulses at 20% power. For each sample, 2*106 cells were resuspended with ProteoStat dye (Enzo Life Sciences) diluted 1:3000 in ProteoStat assay buffer. Cells were incubated for 15 min at room temperature protected from light. Flow cytometry was preformed using Stratedigm S1000EXi and the CellCapTure software (Stratedigm, San Jose, CA). Live cells were gated (P1) by forward scatter and side scatter. Fluorescence channels for FITC (530/30) and PE-Cy5 (676/29) were used utilizing a 488 nm laser source. A total of 50,000 events were acquired for each sample. Analyses were performed using FlowJo software (TreeStar, version 10). The results displayed are representative of three biological experiments performed in triplicate.

### Confocal microscopy

One milliliter of logarithmic cells were washed with PBS buffer, sonicated using 15 s pulses at 20% power and resuspended in 50 µL of ProtesoStat dye diluted 1:250 in ProteoStat assay buffer. Cells were incubated for 15 min at room temperature protected from light. 10 µL of each sample was deposited on poly-lysine-coated glass slides (Sigma-Aldrich). Cells were imaged using Leica TCS SP8 laser confocal microscope with ×63 1.4 NA or ×100 1.4 NA oil objectives. To visualize the nuclei, Hoechst (33342; ImmunoChimestry) was used. An argon laser with 488 excitation line was used for ProteoStat (emission wavelength, 500–600 nm), and a 405 UV laser was used to excite Hoechst fluorescence (emission wavelength, 415–450 nm). The results displayed are representative of three biological experiments.

### Confocal Raman microscopy

All Raman spectroscopic and imaging experiments were performed with a laboratory-made confocal Raman microscope, details of which can be found elsewhere41. A He–Ne laser with an output wavelength of 632.8 nm was used for excitation. Laser power of 5 mW was used at the sample point with an exposure of 0.5 s per point. For Raman imaging experiments, a step size of 0.6 µm was used. The results displayed are representative of three biological experiments.

Adenine at a final concentration of 8 mg/mL was dissolved in PBS at 90 °C, followed by overnight gradual cooling for the formation of adenine fibrils. These structures served as antigens in a series of seven immunization cycles in rabbit followed by purification of polyclonal IgG antibodies using protein G column. The antibodies were supplied by Adar Biotech (Rehovot, Israel).

### Indirect immunofluorescence

Eight milliliters of yeast cells at the logarithmic phase were fixed for 2 h with formaldehyde (3.7% final) and potassium phosphate buffer (100 mM final, pH 6.5), washed and resuspended in sorbitol buffer (1.2 M sorbitol and 100 mM potassium phosphate, pH 6.5). Sorbitol buffer supplemented with β-mercaptoethanol (20 mM) and zymolyase 20T (12.5 mg/mL) was added for 1.5 h at 37 °C to digest the cell wall. The cells were then fixed on poly-l-lysine-coated glass slides and permeabilized with PBT (PBS with 1% BSA and 0.05% Triton X-100). Immunofluorescence directed against adenine amyloid-like structures was performed using the anti-ADE antibody described above at a dilution of 1:200 for 2 h followed by three washes (PBT) and incubation with Cy3-conjugated anti-rabbit diluted 1:200 for an additional 1.5 h followed by three washes (PBS). DNA was stained with 4′,6-diamidino-2-phenylindole (DAPI). Cells were imaged using Leica TCS SP8 laser confocal microscope with ×63 1.4 NA oil objective. The results displayed are representative of three biological experiments.

### Reporting summary

Further information on experimental design is available in the Nature Research Reporting Summary linked to this article.

## Data availability

Journal peer review information: Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work.

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Zaguri, D., Kreiser, T., Shaham-Niv, S. & Gazit, E. Antibodies towards tyrosine amyloid-like fibrils allow toxicity modulation and cellular imaging of the assemblies. Molecules 23, 1273 (2018).

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Porat, Y., Abramowitz, A. & Gazit, E. Inhibition of amyloid fibril formation by polyphenols: structural similarity and aromatic interactions as a common inhibition mechanism. Chem. Biol. Drug Des. 67, 27–37 (2006).

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Meng, F., Abedini, A., Plesner, A., Verchere, C. B. & Raleigh, D. P. The flavanol (−)-epigallocatechin 3-gallate inhibits amyloid formation by islet amyloid polypeptide, disaggregates amyloid fibrils, and protects cultured cells against IAPP-induced toxicity. Biochemistry 49, 8127–8133 (2010).

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Ebrahimi, A. & Schluesener, H. Natural polyphenols against neurodegenerative disorders: potentials and pitfalls. Ageing Res. Rev. 11, 329–345 (2012).

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Verges, K. J., Smith, M. H., Toyama, B. H. & Weissman, J. S. Strain conformation, primary structure and the propagation of the yeast prion [PSI+]. Nat. Struct. Mol. Biol. 18, 493–499 (2011).

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Tartaglia, G. G., Pechmann, S., Dobson, C. M. & Vendruscolo, M. Life on the edge: a link between gene expression levels and aggregation rates of human proteins. Trends Biochem. Sci. 32, 204–206 (2007).

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Tu, B. P. et al. Cyclic changes in metabolic state during the life of a yeast cell. Proc. Natl Acad. Sci. USA 104, 16886–16891 (2007).

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## Acknowledgements

We thank A. Brandis for GC–MS analysis, E. Haimov and B. Redko for LC–MS analysis, A. Lichtenstein for confocal microscopy analysis, O. Sagi-Assif for the fluorescence-activated cell sorting analysis, B. Lifshitz and L. Gershon for assistance with plasmids cloning, K. Simpson-Lavy for assistance with the Hsp104 experiments, T. Guterman for assistance in Fig. 1d, S. Rencus-Lazar for proofreading the article. We thank A. Parket and members of the Gazit, Adler-Abramovich, and Kupiec laboratories for helpful discussions. This work was supported by the Israel Science Foundation (Grant no. 802/15; E.G.) and by the Adelis Forever Foundation (E.G.). This research was a collaboration with the BCDD, funded by Len Blavatnik and the Blavatnik Family Foundation. This work is dedicated to the memory of Prof. Susan L. Lindquist (1949–2016), a pioneer and visionary in the establishment of yeast models of neurodegenerative amyloid disorders and their therapeutic treatment.

## Author information

### Affiliations

1. #### Department of Molecular Microbiology and Biotechnology, George S. Wise Faculty of Life Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

• Dana Laor
• , Shira Shaham-Niv
• , Dor Zaguri
• , Myra Gartner
• , Vasantha Basavalingappa
•  & Ehud Gazit
2. #### BLAVATNIK CENTER for Drug Discovery, Tel Aviv University, 6997801, Tel Aviv, Israel

• Avi Raveh
• , Edward Pichinuk
• , Hamutal Engel
•  & Ehud Gazit
3. #### Faculty of Life and Environmental Science, Shimane University, Matsue, 690-8504, Japan

• Keita Iwasaki
•  & Tatsuyuki Yamamoto
4. #### Raman Center for Medical and Biological Applications, Shimane University, Matsue, 690-8504, Japan

• Tatsuyuki Yamamoto
•  & Hemanth Noothalapati

• Ehud Gazit

### Contributions

D.L., S.S.-N., D.S., A.R., H.N., and E.G. designed the experiments. D.L. planned and performed most of the experiments. Metabolites and tannic acid extraction using GC–MS and LC–MS were planned and performed by D.L., A.R., M.G., and V.B. Raman microspectroscopy experiments were planned and performed by K.I., T.Y., and H.N. In vitro thioflavin T fluorescence measurements were planned and performed by S.S.-N. Anti-adenine fibril antibodies production procedure was planned and validated by S.S.-N. and D.Z. Indirect immunofluorescence assay was planned and performed by D.S. and D.L. D.L., H.E., and E.P. participated in finding the polyphenolic inhibitors and D.L. and M.G. preformed the cell growth assays. D.L. and E.G. wrote the paper. All authors discussed the results and provided critical revisions of the manuscript.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to Ehud Gazit.


text:
A 1.6 M Tall Girl Stands at a Distance of 3.2 M from a Lamp-post and Casts a Shadow of 4.8 M on the Ground. Find the Height of the Lamp-post by Using (I) Trigonometric Ratios (Ii) Property of Similar Triangles. - Mathematics

A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts a shadow of 4.8 m on the ground. Find the height of the lamp-post by using (i) trigonometric ratios (ii) property of similar triangles.

Solution

Let AC be the lamp post of height h

We assume that ED 1.6 m, BE = 4.8 m and EC = 3.2 m

We have to find the height of the lamp post

Now we have to find the height of lamp post using similar triangles.

Since triangle BDE and triangle ABC are similar.

(AC)/(BC) = (ED)/(BE)

h/(4.8 + 3.2) = 1.6/(BE)

h =  8/3

Again, we have to find height of lamp post using trigonometric ratios.

=> tan theta = 1.6/4.8

=> tan theta  = 1/3

Again in  ΔABC

=> tan theta = h/(4.8 + 3.2)

=> 1/2  = h/8

h = 8/3

Hence the height of lamp post is 8/3 m

Concept: Heights and Distances
Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 10 Maths
Chapter 12 Trigonometry
Exercise 12.1 | Q 21 | Page 31

format: plain


text:
Rs Aggarwal 2020 2021 Solutions for Class 7 Maths Chapter 23 Probability are provided here with simple step-by-step explanations. These solutions for Probability are extremely popular among Class 7 students for Maths Probability Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2020 2021 Book of Class 7 Maths Chapter 23 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2020 2021 Solutions. All Rs Aggarwal 2020 2021 Solutions for class Class 7 Maths are prepared by experts and are 100% accurate.

#### Page No 283:

Total number of trials = 300
Number of times a head is obtained = 136
Number of times a tail is obtained= 164

(i) Probability of getting head ==$\frac{136}{300}=\frac{34}{75}$

(ii) Probability of getting a tail ==$\frac{164}{300}=\frac{41}{75}$

#### Page No 283:

Total number of trials = 200
Number of times 2 heads are obtained = 58
Number of times one head is obtained  = 83
Number of times no head is obtained = 59

(i) Probability of getting 2 heads =  = $\frac{58}{200}=\frac{29}{100}$

(ii) Probability of getting 1 head = = $\frac{83}{200}$

(iii) Probability of getting 0 head =  = $\frac{59}{200}$

#### Page No 283:

Total number of trials = 100
Number of times 3 is obtained = 18
Number of times 6 is obtained = 9
Number of times 4 is obtained = 15
Number of times 1 is obtained =  21


text:
# Irreducible polynomials: one of them must be of degree zero

I have the following definition of irreducible polynomials, given by my professor:

If $p = f * g$ , where $f, g \in F[x]$ then $degree(f) = 0 \ \ or \ \ degree(g) = 0$

And then the following sentence: it is always possible to represent a polynomial as $p = f*g$, where $deg(f) = 0$ (like this: $p = a * (a^{-1}*p)$)

I am confused, need your help. If every polynomial can be represented as such product with $deg(f) = 0$, given the definition of irreducible polynomials above, doesn't it mean every polynomial is irreducible? (I know, this is false).

F.e., I have a polynomial f = (x+2)(x-5). Well, I can represent it as $a*(a^{-1}*(x+2)(x-5)$ and say that it's irreducible as $deg(a) = 0$.

Do you see what I mean, where my problem is? Would you please help me to understand, what my prof. wanted to tell us?

• Irreducible means that the only way to write it as a product is that one of the factors is a unit. You can of course write everything as "unit times whatever", but irreducibles, you can write in only that way as a product. Nov 8 '13 at 20:10
• Try to work out some examples to get a handle on the definition. For example, try to prove that $x^3 - 1$ is not irreducible in $\mathbb{R}[x]$. However, you can try to show that $x^2 + 1$ is irreducible in $\mathbb{R}[x]$. Play around with these examples to make sure you see what part of the definition is being used. Nov 8 '13 at 20:17
• @Daniel, that means we talk about writing them exactly as a product of two polynomials.. I guess I see now what I overlooked. Nov 8 '13 at 20:21
• @tylerco816, $x^3 - 1 = (x-1)(x^2+ab+b^2)$. So we can represent it as a product of exactly two polynomials and non of them is of degree 0. But x-1 must have a zero point, as well as $(x^2+ab+b^2)$. So in $\Bbb R$ they both have. Am I going in the right direction? Or I could say $x^3 = 1$, i.e. $x=1$ is a zero point for $x^3 -1$... And I don't know how to continue. Nov 8 '13 at 20:26
• Got it.. that means I can factor it and get what I've just written above. So we have a product of two polynomials and non of them is of degree zeor. :) Nov 8 '13 at 20:32


text:
# Does this “extension property” for polynomial rings satisfy a universal property?

On page 151 of Paolo Aluffi's Algebra: Chapter 0, an important property of the polynomial ring $\mathbb{Z}[x_1, \cdots, x_n]$ is introduced, namely that it's initial in the category of set functions from a fixed $n$-element set $A$ to commutative rings. (Or, to put it another way, a set function $f: A \to R$ with $R$ an arbitrary commutative ring factors uniquely through $\mathbb{Z}[x_1, \cdots, x_n]$.)

After establishing this property, two examples are given; the first, a special case when $n=1$, proves the existence of a unique ring homomorphism $\mathbb{Z}[x] \to S$ sending $x$ to an element $s \in S$ and extending the unique homomorphism from $\mathbb{Z} \to S$. So far so good.

The author then goes on to give a second example:

Let $a : R \to S$ be a fixed ring homomorphism, and let $s \in S$ be an element commuting with $a(r)$ for all $r \in R$. Then there is a unique ring homomorphism $\bar{a} : R[x] \to S$ extending $a$ and sending $x$ to $s$.

It is an exercise to provide the details of this construction. It's not hard to show what this map must be and prove that it's unique by "naive" methods, but, given its placement and the pedagogical bent of the text in general, I assume that there's a slicker way to define this map based solely on categorial considerations.

So: does this "extension homomorphism" satisfy a universal property?

(I've thought vaguely about this question for a little while but didn't hit upon anything; hints or full explanations would be much appreciated.)

-

HINT $\:$ An $\:R$-algebra $\:A\:$ is a ring that contains a homomorphic image of $\:R\$ in the center of $\:A\:$. The universal property at hand is that $\: R[x_1,\cdots,x_n]\:$ is the universal $\:R$-algebra on $n$ generators. Since every ring is a $\:\mathbb Z$-algebra, the first case is simply the special case $\:R = \mathbb Z\:$. This should be mentioned in your textbook. Indeed, it is, see Proposition 6.4 p. 168.


text:
Visual Insight

I have another blog, called Visual Insight. Over here, our focus is on applying science to help save the planet. Over there, I try to make the beauty of pure mathematics visible to the naked eye.

I’m always looking for great images, so if you know about one, please tell me about it! If not, you may still enjoy taking a look.

Here are three of my favorite images from that blog, and a bit about the people who created them.

I suspect that these images, and many more on Visual Insight, are all just different glimpses of the same big structure. I have a rough idea what that structure is. Sometimes I dream of a computer program that would let you tour the whole thing. Unfortunately, a lot of it lives in more than 3 dimensions.

Less ambitiously, I sometimes dream of teaming up with lots of mathematicians and creating a gorgeous coffee-table book about this stuff.

Schmidt arrangement of the Eisenstein integers

This picture drawn by Katherine Stange shows what happens when we apply fractional linear transformations

$z \mapsto \frac{a z + b}{c z + d}$

to the real line sitting in the complex plane, where $a,b,c,d$ are Eisenstein integers: that is, complex numbers of the form

$m + n \sqrt{-3}$

where $m,n$ are integers. The result is a complicated set of circles and lines called the ‘Schmidt arrangement’ of the Eisenstein integers. For more details go here.

Katherine Stange did her Ph.D. with Joseph H. Silverman, an expert on elliptic curves at Brown University. Now she is an assistant professor at the University of Colorado, Boulder. She works on arithmetic geometry, elliptic curves, algebraic and integer sequences, cryptography, arithmetic dynamics, Apollonian circle packings, and game theory.

{7,3,3} honeycomb

This is the {7,3,3} honeycomb as drawn by Danny Calegari. The {7,3,3} honeycomb is built of regular heptagons in 3-dimensional hyperbolic space. It’s made of infinite sheets of regular heptagons in which 3 heptagons meet at vertex. 3 such sheets meet at each edge of each heptagon, explaining the second ‘3’ in the symbol {7,3,3}.

The 3-dimensional regions bounded by these sheets are unbounded: they go off to infinity. They show up as holes here. In this image, hyperbolic space has been compressed down to an open ball using the so-called Poincaré ball model. For more details, go here.

Danny Calegari did his Ph.D. work with Andrew Casson and William Thurston on foliations of three-dimensional manifolds. Now he’s a professor at the University of Chicago, and he works on these and related topics, especially geometric group theory.

{7,3,3} honeycomb meets the plane at infinity

This picture, by Roice Nelson, is another view of the {7,3,3} honeycomb. It shows the ‘boundary’ of this honeycomb—that is, the set of points on the surface of the Poincaré ball that are limits of points in the {7,3,3} honeycomb.

Roice Nelson used stereographic projection to draw part of the surface of the Poincaré ball as a plane. The circles here are holes, not contained in the boundary of the {7,3,3} honeycomb. There are infinitely many holes, and the actual boundary, the region left over, is a fractal with area zero. The white region on the outside of the picture is yet another hole. For more details, and a different version of this picture, go here.

Roice Nelson is a software developer for a flight data analysis company. There’s a good chance the data recorded on the airplane from your last flight moved through one of his systems! He enjoys motorcycling and recreational mathematics, he has a blog with lots of articles about geometry, and he makes plastic models of interesting geometrical objects using a 3d printer.

7 Responses to Visual Insight

1. John Baez says:

This is a test to see if you can now use Markdown in comments, for example to create links, italicized or boldface text, or quotes:

Markdown is not a replacement for HTML, or even close to it. Its syntax is very small, corresponding only to a very small subset of HTML tags. The idea is not to create a syntax that makes it easier to insert HTML tags. In my opinion, HTML tags are already easy to insert. The idea for Markdown is to make it easy to read, write, and edit prose. HTML is a publishing format; Markdown is a writing format. Thus, Markdown’s formatting syntax only addresses issues that can be conveyed in plain text.

For any markup that is not covered by Markdown’s syntax, you simply use HTML itself. There’s no need to preface it or delimit it to indicate that you’re switching from Markdown to HTML; you just use the tags.

The only restrictions are that block-level HTML elements — e.g. <div>, <table>, <pre>, <p>, etc. — must be separated from surrounding content by blank lines, and the start and end tags of the block should not be indented with tabs or spaces. Markdown is smart enough not to add extra (unwanted) <p> tags around HTML block-level tags.

• John Baez says:

2. arch1 says:

Thanks for sharing these, John. They are beautiful! In the 3rd picture above, using Chrome in Win7, I see circles filled with at least 3 different shades of blue, while in your AMS article they are all shaded identically; unless I’m missing something you may want to delete the qualifier “light-colored” in the description, or tweak the shading.

• arch1 says:

Correction – I’m using IE9 in Win7, not Chrome in Win7.

• John Baez says:

Well, the circles are always lighter blue than their surroundings, but they get darker as they get smaller. I suppose I can just drop “light-colored” and it will be less confusing.

I went with Roice’s black-and-white image on Visual Insight because it lets you see more fine detail, and it looks spooky—a nice change from the colorful pictures that I usually feature:

3. tcmJOE says:

I learned that Danny Calegari was a professor at Caltech JUST AFTER he left, much to my chagrin. I really wanted to put a poster next to his office that said “Du musst Calegari werden”.

• John Baez says:

Is there some cultural reference or joke I’m missing? I understand German, but not why you’d write a poster in German saying this.


text:
# If one mole of ammonia and one mole of hydrogen chloride is mixed in a closed container to form ammonium chloride gas, then:[A]$\Delta H>\Delta U$[B]$\Delta H=\Delta U$[C]$\Delta H<\Delta U$[D] There is no relationship

Verified
146.4k+ views
Hint: We can solve this by using the equation which gives us the relation between change in internal energy and enthalpy. From the ideal gas law equation we can replace the pressure and volume and get the equation in terms of number of moles and temperature. By putting the number of moles of reactant and product, we can find the change in the number of moles and use that to assume whether $\Delta H$is positive, negative or equal to change in internal energy.

$\Delta$H is the enthalpy. It is the amount of heat released or evolved in a reaction at a constant pressure.
A negative value of enthalpy means heat is released in the reaction and positive value of enthalpy means energy was required to carry out the reaction.
It is related to internal energy and change in volume as-
$\Delta H=\Delta U+P\Delta V$
Where, $\Delta U$ is the change in internal energy of the system and
$\Delta V$is the change in volume,
P is the pressure.
For an exothermic reaction, change in enthalpy is negative and for an endothermic reaction, the change in enthalpy is positive.
As we can see, the reaction given to us in the question is occurring in a closed container. When a reaction takes place in a closed container, it means neither the product nor the reactant can escape from the system i.e. the reaction is taking place in a closed system.
Therefore, in a closed system the volume will be fixed.
As we know, PV=nRT, which is the ideal gas law.
We can also solve this by replacing PV by nRT in the equation.
We can write that, $\Delta H=\Delta U + \Delta nRT$where,
$\Delta n$ is the change in the number of moles,
R is the universal gas constant and T is the temperature.
We can write the given reaction as-
$N{{H}_{3}}(g)+HCl(g)\to N{{H}_{4}}Cl(g)$
$\Delta n$ = number of moles of product – number of moles of reactant = 1 - 2 = -1.
Therefore, $\Delta H=\Delta U+(-1)RT = \Delta U-RT$
As we know R has a fixed positive value for every gas and temperature also has a fixed value. Therefore, a positive quantity is subtracted from the change in internal energy to get the change in enthalpy which means $\Delta$H is less than$\Delta U$.
Therefore, the correct answer is option [C]$\Delta H<\Delta U$.

Note: In a closed system, there is no exchange of matter with the surrounding but there can be change in energy as heat or work. Whereas in an open system there can be exchange of matter as well as energy. This is the first law of thermodynamics.


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# type similar to union

This topic is 3724 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

i need some kind of type that is like "union" that can store classes and when called returns the actual type that is currently set... for example class Base { union xtype { class1 A; class1 B; class1 C; } xtype U; void class_function(class1 a){} void class_function(class2 b){} void class_function(class3 c){} } main() { Base X; X.U = class1(somevalue); Base.class_function(X.U); // call the apropriate function } how can i do this? ive looked at boost::variant but i dont think it allows me to call function inside the same class as the variable... since i have to make a "visitor" class which cant access variables in the class (which i need to).

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I don't know the answer to your question, but maybe you could settle for something like the State pattern or the Strategy pattern?

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Would using inheritance work for you instead?

__declspec(novtable) class Base{  virtual void class_function() = 0;};class A : public virtual Base //, other base classes{  virtual void class_function() {}};class B : public virtual Base //, etc{  virtual void class_function() {}};

main()
{
A a1;
Base *base = &a1;

base->class_function();
}

[Edited by - Nypyren on January 8, 2008 3:45:05 PM]

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Quote:
 Original post by NypyrenWould using inheritance work for you instead?

im sorry i forgot to mention the regular types should also be used... i could make wrappers for all the types that i need though... but it seems like a quite ugly solution.. or?

EDIT:: Im using C++

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Why?

It's pointless to talk about solution without knowing the problem it's trying to solve.

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Is the type X.U compile time constant?

[Edited by - King Mir on January 8, 2008 3:05:08 PM]

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heh... well i guess soo... seems like i have a habit of simplifying my questions as much as possible...

i have a class which should store alot of objects/variables with different types and have "Set" functions for each type...

one way i could do this is to create on std::list<> for each type... but its a bit unpractical and ugly way to do it... also a bit slow where i have to decide which list to put new variables in...

what id like is a general type soo i can put all of them in the same list...

one way ive tried is to use boost::any... which works great except when i have to use "Set"... i have to first check which type it is than convert it to that type and call the appropriate "Set" function... which is kinda slow...

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Quote:
 Original post by King MirIs the type X.U compile time constant?

im unsure what you mean...

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Quote:
Original post by Dragon_Strike
Quote:
 Original post by NypyrenWould using inheritance work for you instead?

im sorry i forgot to mention the regular types should also be used... i could make wrappers for all the types that i need though... but it seems like a quite ugly solution.. or?

EDIT:: Im using C++

You'll have to make a separate class_function for every single type anyway, so making wrappers isn't THAT ugly.

Quote:
 Original post by AntheusWhy?It's pointless to talk about solution without knowing the problem it's trying to solve.

Actually, talking about it helps a person understand available options so that they can make better decisions for totally different problems in the future.

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Quote:
 Original post by Dragon_StrikeWhat I'd like is a general type so I can put all of them in the same list...

This is precisely the case where you'd want to use inheritance.