1,6-hexanediol rapidly immobilizes and condenses chromatin in living human cells

Alcohol, 1,6-hexanediol, is widely used for melting liquid droplets formed by liquid0–liquid phase separation; however, it can also seriously affect cells by immobilizing and condensing chromatin.


Introduction
Some macromolecules self-organize into liquid droplets by a process termed liquid-liquid phase separation (LLPS), which allows specific molecules to be concentrated without a membrane, whereas others are excluded (Hyman et al, 2014;Banani et al, 2017;Shin & Brangwynne, 2017). Cells organize liquid droplet-like condensates/bodies (or compartments), contributing to the spatial and temporal regulation of complex biochemical reactions. However, whether all of these dynamic biomolecular condensates/bodies form by LLPS or some form by another process remains unclear and the subject of debate for many cell biologists (McSwiggen et al, 2019).
LLPS is driven by weak and multivalent interactions between proteins and nucleic acids (Banani et al, 2017;Shin & Brangwynne, 2017). In many cases, proteins in liquid droplet-like condensates/ bodies have intrinsically disordered regions that lack stable folding and often contain stretches of low sequence complexity (Kato et al, 2012;Elbaum-Garfinkle et al, 2015;Nott et al, 2015;Murray et al, 2017). In principle, intrinsically disordered regions mediate multiple weak and transient reversible interactions, unlike the formation of subcellular aggregates. The molecules inside liquid droplet-like condensates/ bodies are highly mobile and can transition in and out of the condensates/bodies (McSwiggen et al, 2019;Taylor et al, 2019).
We investigated how 1,6-HD could influence cellular chromatin behavior in human cells using live-cell single-nucleosome imaging and tracking (Hihara et al., 2012;Lerner et al., 2020;Nagashima et al., 2019;Nozaki et al., 2017), which can sensitively detect change(s) in chromatin state. Although we confirmed several published results that 1,6-HD treatment disrupted nuclear condensates/bodies (Cho et al., 2018;Lin et al., 2016), we found that 1,6-HD drastically and globally suppressed chromatin motion and hyper-condensed chromatin in live HeLa cells. Similar suppression effects were observed in several other human cell lines and these effects were enhanced in a dose-dependent manner. Chromatin was "frozen" when live cells were treated with 5% or higher 1,6-HD for 5 min. Careful consideration is thus needed to interpret all the results of cell biological experiments performed with 1,6-HD treatment.

1,6-HD rapidly suppresses chromatin motion in living human cells
To investigate how 1,6-HD treatment affects chromatin behavior in living cells, we performed single-nucleosome imaging and tracking Figure 1. 1,6-hexanediol (1,6-HD) dissolves nuclear droplets/bodies. (A) Chemical structure of 1,6-HD. (B) Effects of 2.5%, 5%, and 10% 1,6-HD treatments on Cajal bodies labeled with EGFP-coilin in HeLa cells. First row, DNA staining with DAPI; second-row, fluorescent images of EGFP-coilin; third row, magnified images of the boxed regions in the second-row images. (C) The quantification of the number of foci per cell is shown as a bar graph. Data are mean ± SEM. The mean number of foci per cell: 2.98 (n = 85 cells) in control; 1.64 (n = 80 cells) in 2.5%; 0.84 (n = 92 cells) in 5%; 0.20 (n = 90 cells) in 10% 1,6-HD. ***P < 0.0001 by the Welch's t test for control versus 2.5% (P = 1.47 × 10 −8 ), for control versus 5% (P = 1.31 × 10 −21 ), and for control versus 10% (P = 1.31 × 10 −29 ). (D) Effects of 2.5%, 5%, and 10% 1,6-HD treatments on transcription foci/condensates fluorescently labeled by mClover-MED14 in HCT116 cells. First row, DNA staining with DAPI; second-row fluorescent images of mClover-MED14; third row, magnified images of the boxed regions in the second-row images. (E) The quantification of the number of foci per cell is shown as a bar graph. Data are mean ± SEM. The mean number of foci per cell: 6.14 (n = 87 cells) in control; 0.71 (n = 99 cells) in 2.5%; 0.05 (n = 95 cells) in 5%; 0.00 (n = 30 cells) in 10% 1,6-HD. ***P < 0.0001 by the Welch's t test for control versus 2.5% (P = 2.14 × 10 −24 ), for control versus 5% (P = 3.46 × 10 −27 ), and for control versus 10% (P = 2.15 × 10 −27 ).  (Hihara et al., 2012;Lerner et al., 2020;Nagashima et al., 2019;Nozaki et al., 2017) by oblique illumination microscopy (Fig 2A). This imaging illuminates a thin area within a single nucleus to improve the level of background noise observed (Tokunaga et al, 2008). Our technique sensitively and accurately measures local chromatin dynamics in a whole nucleus and provides new information on how chromatin organizes in living cells. Histone H2B tagged with HaloTag (H2B-Halo) was stably expressed in HeLa cells (Fig S2A). H2B-Halo can be specifically labeled with HaloTag ligand tetramethylrhodamine (TMR) for live-cell imaging ( Fig S2B). Cells were treated with very low concentrations of TMR to obtain sparse labeling (Fig 2B). We recorded the TMR-nucleosome dots (left, Fig 2C) at 50 ms/frame (~100 frames, 5 s total) (Video 1). The dots showed a single-step photobleaching profile (right, Fig 2C), which suggested that each dot represents a single H2B-Halo-TMR molecule in a single nucleosome. The individual dots were fitted with a 2D Gaussian function to estimate the precise position of the nucleosome (Betzig et al, 2006;Rust et al, 2006;Selvin et al, 2007) and were tracked using u-track software ( Fig 2D) (Jaqaman et al, 2008) (the position determination accuracy is 15.55 nm). Notably, we tracked only the signals of TMR-labeled H2B-Halo in the nucleosomes ( Fig 2C) because free H2B-Halo moved too fast to detect as dots and track under our imaging conditions. From the nucleosome tracking data, we calculated mean square displacement (MSD), which shows the spatial extent of motion in a certain time period . The plots of calculated MSD appeared to be sub-diffusive ( Fig 2E). Chemical fixation of the cells with formaldehyde (FA) or methanol (MeOH) almost completely immobilized TMR-labeled nucleosomes (Fig 2E), indicating that most of the observed movement was derived from real nucleosome movements in living cells.
Higher concentrations of 1,6-HD "freeze" chromatin in living human cells 1,6-HD treated cells were extensively washed and chromatin movements were remeasured to determine if the motion suppression effects were reversible or not. The washing step did not The fluorescent intensity of each dot was~50, and in the single-step photobleaching profile, the intensity dropped to around 10, suggesting that each dot represents a single H2B-Halo-TMR molecule in a single nucleosome. (D) Three representative trajectories of the tracked single nucleosomes in HeLa cells. (E) Mean square displacement plots (± SD among cells) of single nucleosomes in interphase HeLa cells (Control, black), FA-fixed (pink), and cold methanol-fixed (light blue) HeLa cells. For each condition, n = 10 cells. The average numbers of nucleosome trajectories used per cell, 1,300-1,800. ***P < 0.0001 for control versus FA-fixed cells (P = 1.1 × 10 −5 ), and for control versus MeOH-fixed cells (P = 1.1 × 10 −5 ). (F) Mean square displacement plots (±SD among cells) of nucleosomes in HeLa cells treated with 2.5% (light blue), 5% (purple), or 10% (pink) of 1,6-HD for 5-30 min. For each condition, n = 8-10 cells. The average numbers of nucleosome trajectories used per cell, 800-1,800. **P < 0.01 for untreated control versus 5% (P = 1.6 × 10 −4 ). ***P < 0.0001 for untreated control versus 2.5% (P = 4.6 × 10 −5 ), and for untreated control versus 10% (P = 4.6 × 10 −5 ). Statistical significance in this figure was determined by the Kolmogorov-Smirnov test. affect chromatin motion in untreated cells ( Fig S2C). MSD levels from cells treated with 2.5% 1,6-HD were comparable to untreated cells around 90 min after washing (Fig 3A), suggesting that the effects induced by low levels of 1,6-HD are reversible. However, in treatments with 5% or 10% of 1,6-HD, the reduced MSD values did not change 90 min after washing (Fig 3B and C). These results indicate that a high concentration of 1,6-HD "froze" chromatin and affected chromatin to be similar to that observed in MeOH-fixed cells ( Fig 2E).
Cell viability remained comparably high after cells were treated for 30 min with 2.5% or 5% 1,6-HD. However, the viability decreased to about 2% in cells following a 30-min treatment with 10% 1,6-HD (Table 1). These results suggest that our observation of chromatin "freezing" by 1,6-HD treatment was not a direct consequence of cell death, whereas the treatment has considerable cell toxicity.

1,6-HD has similar effects on several human cells
We investigated chromatin motion in three other human cell lines: RPE-1 (Bodnar et al, 1998), HCT116, and DLD-1 to exclude the possibility that the 1,6-HD chromatin effects were unique to HeLa cells.
We performed single-nucleosome imaging and tracking for RPE-1, HCT116, and DLD-1 cells, all of which stably expressed H2B-Halo. Similar to HeLa cells treated with 1,6-HD, suppression of chromatin motion was observed in a dose-dependent manner in RPE-1, HCT116, and DLD-1 cells treated with 1,6-HD (Fig 4A-C). Whereas the potency at each concentration varied at lower doses, treatments of 10% 1,6-HD seemed equivalent among all cell lines tested. Collectively, effects by 1,6-HD on chromatin motion appear to be general, not specific to particular cell types.

1,6-HD condenses chromatin structure in live cells
We investigated how 1,6-HD influences chromatin structure/ organization in living cells because motion suppression effects described above should be reflected in structural changes of chromatin when cells are treated with 1,6-HD. For this purpose, we used photoactivated localization microscopy (PALM) (Betzig et al, 2006;Manley et al, 2008;Nozaki et al, 2017) to perform superresolution live-cell imaging of HeLa cells expressing histone H2B tagged with photoactivatable (PA)-mCherry (Subach et al, 2009). We reconstructed the spatial organization of nucleosomes from the obtained PALM images (Fig 4D).
Cells were treated with 2.5%, 5%, or 10% of 1,6-HD for 5 min before PALM imaging and reconstructing the high-resolution chromatin images (Fig 4D). We found that chromatin seemed more condensed with increasing amounts of 1,6-HD (Fig 4D). L function, L(r), was used to quantitate nucleosome clustering (Fig S3A) (Nozaki et al, 2017). The L-function plot (L(r)-r versus r plot) gives a value of 0 for the random distribution (blue, Fig S3A), and deviation from zero provides an intuitive measure of the size of the cluster and the degree of accumulation (red, Fig S3A) (Nozaki et al, 2017). The L-function plot peak provides good approximations of the size and compaction state of the nucleosome clusters (or chromatin domains). The L-function plots (Fig 4E) suggest that 5% and 10% 1,6-HD both caused chromatin hyper-condensation, whereas cells treated with 2.5% 1,6-HD had a somewhat similar nucleosome clustering to that in untreated control cells (Fig 4E). The hyper-condensation effects of 5% and 10% 1,6-HD could be correlated to their observed immobilization effects on nucleosomes (Fig 3B and C).

1,6-HD facilitates chromatin condensation in vitro
We examined the effects of 1,6-HD on Mg 2+ -dependent chromatin condensation in vitro to further investigate how 1,6-HD induces hyper-condensation of chromatin. Chromatin, which is negatively charged and repulses other chromatin in the absence of cations, is neutralized by Mg 2+ and condensed in a dose-dependent manner ( Fig S3B) (Hansen, 2002;Maeshima et al, 2016Maeshima et al, , 2018. Purified chicken native chromatin was used for our study (Fig S3C and D). We observed condensates (~1 μm in size) when purified chromatin was mixed with 2.5 mM Mg 2+ and stained with 49,6-diamidino-2-phenylindole (DAPI) (Fig 5A). To quantitate the chromatin condensation process, we performed a static light scattering assay (Dimitrov et al, 1986) with a titration of Mg 2+ . Dramatic chromatin condensation was observed in the range of 1.5-2 mM Mg 2+ (Fig 5B). When increasing concentrations of 1,6-HD were added, the scattering plots were shifted to the left (Fig 5B). This shift indicated that Cell viability after treatment of the indicated concentration of 1,6-HD is given as the mean ± standard deviation following treatment with increasing concentrations of 1,6-HD. Experiments were performed in triplicate with~3 × 10 5 cells/each experiment.
These results indicate that 1,6-HD directly acts on chromatin and promotes chromatin condensation in vitro, consistent with the previous microscopic observations in live cells (Fig 4D and E).

Discussion
Our single-nucleosome imaging/tracking revealed that the aliphatic alcohol 1,6-HD, which has been widely used for LLPS studies, can immobilize chromatin motion and hyper-condense chromatin in live cells. Single-molecule imaging is sufficiently sensitive to detect possible change(s) of local chromatin environments when treated in real time in live cells, which other imaging or genomic techniques might not see. Interestingly, another aliphatic alcohol, 2,5-HD, which has a much lower melting activity of droplets formed by LLPS (Lin et al, 2016), had a comparable motion suppression effect to 1,6-HD (Fig 3D). This finding indicates that the observed 1,6-HD "freezing" action on chromatin organization is distinct from its disruption activity of liquid droplets formed by LLPS.
To better understand what may be happening in a cell when it is treated with 1,6-HD, it is useful to discuss the general properties of alcohols. Alcohol concentrations above 40% denature protein structure by strengthening intramolecular hydrogen bonds (Shiraki et al, 1995), whereas a low percentage of alcohol does not affect the protein structure or solubility (Chin et al, 1994). However, these low concentrations of alcohol weaken the hydrophobic interactions between proteins, allowing alcohol to dissolve or melt the protein droplets without protein denaturation. Indeed, the more hydrophobic 1,6-HD is known to dissolve protein droplets better than 2,5-HD in vitro (Lin et al, 2016).
Although the mechanism on how 1,6-HD acts on chromatin remains unclear, we consider that alcohols such as 1,6-HD might remove water molecules around chromatin and locally condense chromatin as condensates (right, Fig 5C) because each nucleosome binds~3,000 water molecules (Davey et al, 2002) and the surrounding chromatin environment is highly hydrophilic (left, Fig 5C). This notion reminds us of "ethanol precipitation" to recover purified plasmid or genomic DNAs (Sambrook & Russell, 2001). Indeed, 5% of 1,6-HD "froze" chromatin motion in live cells and the suppressed motion did not recover over 90 min after washing out 1,6-HD (Fig 3B). This situation appears to be similar to that observed with methanol fixation (Fig 2E). Another mechanism of how 1,6-HD acts on chromatin in the cell is also possible, and further investigation is warranted to gain added mechanistic insight into this intriguing issue.
As discussed above, the effect of 1,6-HD on chromatin in living cells is distinct from the melting activity of liquid droplets or disruptions of weak hydrophobic interactions between proteins/RNAs/DNAs in droplets. Dissolving LLPS driven formation of cytoplasmic/nuclear condensates/bodies was previously reported to be the main action of 1,6-HD in biological studies (Lin et al, 2016). Although we agree that the use of 1,6-HD is remarkably effective for simplified in vitro experiments, caution should be used as 1,6-HD treatment can, directly or indirectly, affect various kinds of interactions between DNAs/RNAs/proteins. Thus, careful interpretation of the results obtained from cell biological experiments using 1,6-HD treatment should be done. Our study also suggests that 1,6-HD-sensitivity cannot be evidence for proving that cellular condensates/bodies of protein/DNA complexes, including chromatin, are formed by LLPS. More quantitative analyses of the molecular behavior in condensates/bodies in living cells would be required (
Z-stack images (every 0.2 μm in the z direction, 20-25 sections in total) of the cells were obtained using DeltaVision Elite microscopy (Applied Precision) with an Olympus PlanApoN 60× objective (NA 1.42) and a sCMOS camera. InsightSSI light (~50 mW) and the fourcolor standard filter set were also equipped. DeltaVision acquisition software, Softworx, was used to project deconvolved z-stacks to cover the whole nucleus (seven images) because the signals were not distributed homogeneously across all the z-stacks.
Optical sectioning images were recorded with a 400 nm step size using a DeltaVision microscope (Applied Precision) as described above. Softworx was used to project acquired images over the whole nucleus (usually five images). The projected images were deconvolved and used as source images. Nucleoplasm regions were extracted on the basis of the DNA (DAPI) staining regions.
A median filtered image (radius = 8 pixel) was subtracted from the source image using ImageJ software (NIH) to count the number of fluorescent foci/condensates/bodies. The processed image was smoothed by adding a Gaussian blur (σ = 1 pixel). Then, a threshold was applied to count the number of local maxima above background in cells (Cho et al, 2018).
The live-cell chamber INU-TIZ-F1 (Tokai Hit) and GM-8000 digital gas mixer (Tokai Hit) were used to maintain cell culture conditions (37°C, 5% CO 2 , and humidity) during microscopy. Single nucleosomes were observed by using an inverted Nikon Eclipse Ti microscope with a 100-mW Sapphire 561-nm laser (Coherent) and sCMOS ORCA-Flash 4.0 camera (Hamamatsu Photonics). Live cells fluorescently labeled with H2B-Halo-TMR or PA-mCherry were excited by the 561-nm laser through an objective lens (100× PlanApo TIRF, NA 1.49; Nikon) and detected at 575-710 nm. An oblique illumination system with the TIRF unit (Nikon) was used to excite fluorescent molecules within a limited thin area in the cell nucleus and reduce background noise. Sequential image frames were acquired using MetaMorph software (Molecular Devices) at a frame rate of 50 ms under continuous illumination.

Single-nucleosome tracking analysis
Image processing, single-molecule tracking, and singlenucleosome movement analysis were performed as previously described (Nagashima et al., 2019;Nozaki et al., 2017). Sequential images were converted to 8-bit grayscale, and the background noise signals were subtracted with the rolling ball background subtraction (radius, 50 pixels) of ImageJ. The nuclear regions in the images were manually extracted. Following this step, the centroid of each fluorescent dot in each image was determined, and its trajectory was tracked with u-track (MATLAB package; [Jaqaman et al, 2008]). To generate photoactivated localization microscopy (PALM) images, the individual nucleosome positions were mapped using R software (65 nm/pixel) on the basis of the u-track data, and then a Gaussian blur (σ = 1 pixel) was added to obtain smoother rendering using ImageJ. For single-nucleosome movement analysis, the MSD of the fluorescent dots was calculated on the basis of their trajectory using a Python program (Nagashima et al, 2019). The originally calculated MSD was in 2D. To obtain the 3D value, the 2D value was multiplied by 1.5 (4-6 Dt). Statistical analyses of the obtained single-nucleosome MSD between various conditions were performed using R.

Clustering analyses of nucleosomes in PALM images
The methods for clustering analyses of nucleosomes in PALM images were described previously (Nozaki et al, 2017). Ripley's K function is given by where (N − 1)/S is the average particle density of area S, and N is the total number of particles contained in the area. The δ function is given by where r i,j is the distance between r i and r j . The L function is given by The area S of the total nuclear region was estimated using the Fiji plugin Trainable Weka Segmentation, and the area of the whole region was measured by Analyze Particles (ImageJ).

RNA interference and α-amanitin (α-AM) treatment
siRNA transfection into HeLa S3 cells grown on poly-L-lysine coated glass-based dishes was performed using Lipofectamine RNAiMAX (13778-075; Invitrogen) according to the manufacturer's instructions. The medium was changed to a fresh medium 16 h after transfection. The transfected cells were used for subsequent studies 48 h after transfection. The siRNA oligonucleotide targeting RAD21 sequence (Sense: 59-CAGCUUGAAUCAGAGUAGAGUGGAA-39; Invitrogen) was used. As a control, an oligonucleotide (4390843; Ambion; the sequence is undisclosed) was used. For double treatment with RAD21-KD and 2.5% 1,6-HD, cells were cultured for 48 h after RAD21 siRNA transfection and then treated with 2.5% 1,6-HD as described above.
For transcription inhibition, cells were treated for 4 h with the transcription inhibitor, 100 μg/ml α-AM (A2263-1MG; Sigma-Aldrich). Cells were imaged or chemically fixed in FA after the treatment. For double treatment with α-AM and 2.5% 1,6-HD, cells were treated with 1 ml medium containing 100 μg/ml α-AM for 4 h, then an equal volume of medium containing 5% 1,6-HD was added on to the glassbased dish on the microscope just before observation.

Indirect immunofluorescence
To verify RAD21-depletion and transcription inhibition, immunostaining was performed as described previously (Hihara et al, 2012), and all processes were performed at room temperature. Cells on the coverslips were fixed and permeabilized as described above. After washing twice with HMK for 5 min, the cells were incubated with 10% normal goat serum (NGS; 143-06561; Wako) in HMK for 30 min. The cells were incubated with diluted primary antibodies: mouse anti-RAD21 (1:1,000 dilution, 05-908; Upstate) or mouse anti-phosphorylated Ser5 of RNA Polymerase II (RNAPII) (1:1,000, RNAPII-Ser5P provided by Dr. H Kimura; clone CMA603 described in Stasevich et al 2014) in 1% NGS in HMK for 1 h. After being washed with HMK four times, the cells were incubated with diluted secondary antibodies: goat antimouse IgG Alexa Fluor 488 (1:500, A11029; Thermo Fisher Scientific) in 1% NGS in HMK for 1 h followed by a four washes with HMK. DNA staining and mounting were performed as described above. Optical sectioning images were recorded with a 200 nm step size using a DeltaVision microscope (Applied Precision) as described in the section "Cell lines, DNA construction, and establishment of stable cell lines." For RAD21 and RNAPII-Ser5P staining, the mean intensities of the nuclear signals after background subtraction (the signals outside nuclei) were calculated and plotted.
Chromatin isolation, condensate imaging, and condensation assay by static light scattering Fresh chicken blood was obtained from the wing vein of Tosa-jidori. Briefly, 1 ml of fresh chicken blood was lysed with 10 ml of MLB (60 mM KCl, 15 mM NaCl, 15 mM Hepes, pH 7.3, 2 mM MgCl 2 , 0.1% NP-40, and 1 mM PMSF) for 10 min on ice. After centrifugation at 1,200g at 4°C for 5 min, the supernatant was removed and resuspended in 10 ml of MLB. This step was repeated four times before the samples were ready for chromatin purification. Chromatin purification was carried out as described by Ura and Kaneda (2001), with some modifications. The nuclei (equivalent to~2 mg of DNA) in nuclei isolation buffer (10 mM Tris-HCl, pH 7.5, 1.5 mM MgCl 2 , 1.0 mM CaCl 2 , 0.25 M sucrose, and 0.1 mM PMSF) were digested with 50 U of micrococcal nuclease (Worthington) at 30°C for 2 min. The reaction was stopped by adding ethylene glycol tetraacetic acid to a final concentration of 2 mM. After being washed with nuclei isolation buffer, the nuclei were lysed with lysis buffer (10 mM Tris-HCl, pH 8.0, 5 mM EDTA, and 0.1 mM PMSF) on ice for 5 min. The lysate was dialyzed against dialysis buffer (10 mM HEPES-NaOH, pH 7.5, 0.1 mM EDTA, and 0.1 mM PMSF) at 4°C overnight using Slide-A-Lyzer (66380; Thermo Fisher Scientific). The dialyzed lysate was centrifuged at 20,400g at 4°C for 10 min. The supernatant was recovered and used as the purified chromatin fraction. The purity and integrity of the chromatin protein components were verified by 14% SDS-PAGE ( Fig  S3C). To examine average DNA length of the purified chromatin, DNA was isolated from the chromatin fraction and electrophoresed in 0.7% agarose gel (Fig S3D).
Samples of chicken chromatin (2 μg) were incubated with 0.5 or 2.5 mM of MgCl 2 for 15 min on ice and spun onto poly-Llysine-coated coverslips by centrifugation at 2,380g at 4°C for 15 min. The chromatin was gently fixed with 2% FA in the same buffer. After DNA staining (DAPI), the coverslips were sealed with nail polish. Optical sectioning images were recorded with a 200-nm step size using a DeltaVision microscope and deconvolved to remove out-of-focus information. Projected images from five sections were shown as described previously (Maeshima et al, 2016).
To analyze static light scattering by chicken chromatin, diluted chicken chromatin was centrifuged at 20,400g for 1 min, then supernatant (200 μl) was used for analysis. Static light scattering at 90°angle was measured using a fluorescence spectrophotometer (F-4500; HITACHI) at a wavelength of 350 nm. A 10 mM solution of MgCl 2 was titrated into the samples containing indicated concentrations of 1,6-HD to obtain the desired final Mg 2+ concentrations. The value measured at 0 mM was subtracted from all other measurements as background. After background subtraction, the resultant values were normalized to the peak value. Mean values from four experiments were plotted with their SDs.

Data Availability
All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.