Antimicrobial resistance (AMR) poses a worldwide threat to human health and biosecurity. The spread of antibiotic resistance genes (ARGs) via conjugative plasmid transfer is a major contributor to the evolution of this resistance. Although permitted as safe food additives, compounds such as saccharine, sucralose, aspartame, and acesulfame potassium that are commonly used as nonnutritive sweeteners have recently been associated with shifts in the gut microbiota similar to those caused by antibiotics. As antibiotics can promote the spread of antibiotic resistance genes (ARGs), we hypothesize that these nonnutritive sweeteners could have a similar effect. Here, we demonstrate for the first time that saccharine, sucralose, aspartame, and acesulfame potassium could promote plasmid-mediated conjugative transfer in three established conjugation models between the same and different phylogenetic strains. The real-time dynamic conjugation process was visualized at the single-cell level. Bacteria exposed to the tested compounds exhibited increased reactive oxygen species (ROS) production, the SOS response, and gene transfer. In addition, cell membrane permeability increased in both parental bacteria under exposure to the tested compounds. The expression of genes involved in ROS detoxification, the SOS response, and cell membrane permeability was significantly upregulated under sweetener treatment. In conclusion, exposure to nonnutritive sweeteners enhances conjugation in bacteria. Our findings provide insight into AMR spread and indicate the potential risk associated with the presence of nonnutritive sweeteners.
Antimicrobial resistance (AMR) is recognized as one of the greatest health threats that human beings face now and in the coming decades [1,2,3]. Globally, 700,000 people die due to infections caused by resistant bacteria every year. It is estimated that 10 million people will be killed by infections due to AMR by 2050 if immediate action is not taken now . The emergence and propagation of antibiotic resistance genes (ARGs) that confer AMR to bacteria is generally attributed to the misuse or overuse of antibiotics [5,6,7]. The spread of ARGs among different bacterial species is mainly driven by horizontal gene transfer (HGT). Conjugation is a significant HGT mechanism, disseminating ARGs by transferring mobile genetic elements (MGEs), including plasmids, integrons, and transposons [8,9,10]. ARGs carried on MGEs can be transferred by cell-to-cell contact through a pilus or pore channel connecting the host and recipient bacteria . This process may occur frequently within genera but also at lower frequency across genera [12, 13].
Nonnutritive sweeteners, approved by the U.S. Food and Drug Administration (FDA), are widely being introduced as safe sugar substitutes in food and beverages as they provide a sweet taste but low calories or energy. The consumption of nonnutritive sweeteners has increased because of their potential to improve the health of individuals suffering from obesity, glucose intolerance, type II diabetes mellitus, and metabolic derangements [14,15,16]. The global consumption of these compounds is estimated to be approximately 117,000 metric tons annually . After intake of food or beverages, these compounds can pass through the human digestive system without being metabolized and their concentration estimates can be as much as tens of mg/L in the human urine [18, 19] and even hundreds of mg/L in the human gastrointestinal tract [20, 21]. With metabolically inert structures, these nonnutritive sweeteners can be directly excreted to the environment from the human body. Currently these compounds are frequently detected in subsurface water, groundwater, and especially, wastewater treatment plants (WWTPs). The concentrations of sweeteners detected can be up to 2.5 mg/L in effluents from WWTPs [22, 23].
Although nonnutritive sweeteners have been developed to allow individuals to avoid the negative effects related to common sugars, a few commonly used nonnutritive sweeteners have recently been associated with health risks. For instance, in vitro tests demonstrated that nonnutritive sweeteners (saccharin (SAC), sucralose (SUC), and aspartame (ASP)) can induce the formation of urinary bladder tumors . In addition, nonnutritive sweeteners are associated with the occurrence of glucose intolerance, which is thought to occur through alterations in the gut microbiota , and there is evidence that SAC, SUC, ASP, and acesulfame potassium (ACE-K) cause DNA damage in bacteria [26, 27]. The latter would likely activate the DNA damage response system (SOS response) of bacteria for remediating the damage. Conjugative ARG transfer has been indicated to be related to the SOS response . Therefore, we hypothesize that these nonnutritive sweeteners may enhance the horizontal transfer of ARGs.
In this study, we tested our hypothesis that the commonly used nonnutritive sweeteners play a role in the spread of AMR. We selected four widely used nonnutritive sweeteners (SAC, SUC, ASP, and ACE-K) to test this hypothesis. We established three model conjugation systems to investigate whether these sweeteners promoted plasmid-mediated conjugative transfer in both environmental and clinical settings. In addition, the dynamic conjugation process at the single-cell level was visualized in real time through microfluidics and confocal microscopy. The underlying mechanisms of conjugative transfer were inferred from changes detected in reactive oxygen species (ROS) production, the SOS response, cell membrane permeability, and transcriptomic responses. These findings show that nonnutritive sweeteners pose an underappreciated ecological risk because they can promote the dissemination of ARGs.
Bacterial strains, growth conditions, and nonnutritive sweeteners
Donor strains E. coli K-12 LE392 and E. coli K-12 MG1655 harbor the plasmid RP4 (carries the ampicillin (Amp), kanamycin (Kan), and tetracycline (Tet) resistance genes) and the plasmid pMS6198A (carries the ampicillin (Amp) resistance gene), respectively. While recipient strains E. coli K-12 MG1655 and P. alloputida, both of which are resistant to chloramphenicol (Chl), were selected as recipients for the conjugation within and across genera, respectively. E. coli strain J53, which is resistent to sodium azide, was also used as another recipient. Strains were cultivated in Luria-Bertani (LB) broth that contained 100 mg/L Amp for the donors, 10 mg/L Chl for P. alloputida, 17 mg/L Chl for E. coli K-12 MG1655, and 100 mg/L sodium azide for E. coli J53. Four nonnutritive sweeteners, saccharine (SAC), sucralose (SUC), aspartame (ASP), and acesulfame potassium (ACE-K) used in this study, were purchased from Sigma-Aldrich (USA).
Determination of MICs against antibiotics
Plate-reader measurements of bacterial growth in the presence of various antibiotic concentrations were used for MIC values. For the strains used in conjugative experiments (both within and across genera) as well as the post-conjugation transconjugants, all dose responses for the four antibiotics (Amp, Kan, Chl, and Tet) were quantified as previously described . Initially, the strains were inoculated in LB media and exponential growth was obtained. Cell concentrations were adjusted to about 105 CFU/mL using LB media and then transferred to 96-well plates. For each well containing 75 µL LB media with different levels of antibiotics, 75 µL of cell suspensions were added. The plates were then incubated at 30 °C for 20 h before measuring the optical density (OD) by a plate reader at a wavelength of 600 nm (Tecan Infinite M200, Swiss). Three replicates per concentration of all antibiotics were prepared and the control containing only sterilized Milli-Q water was simultaneously prepared. MIC90, determined as the antibiotic concentration, at which 90% of cell growth is inhibited, was used in this study.
Mobile plasmid-mediated conjugative transfer models
Since our aim was to unravel whether and how the tested sweeteners (water soluble) would affect the conjugation dynamics in water environment, rather than soil-like environment, we used liquid media (rather than solid media) to do conjugation assays. In this study, three conjugative transfer models were established to evaluate the effects of nonnutritive sweeteners on the conjugative transfer of ARGs. Model I consisted of intra- and inter-genera conjugation process under environmental setting. For the intragenus conjugative transfer, the recipient was selected on the LB agar plates containing 17 mg/L Chl. The intragenus transconjugants were selected on the LB agar plates containing 100 mg/L Amp, 33 mg/L Kan, 17 mg/L Chl, and 20 mg/L Tet. For the intergenus conjugative transfer, the recipient (P. alloputida) was selected from LB broth media containing 10 mg/L Chl. The intergenus transconjugants were selected from LB agar plates containing 100 mg/L Amp, 33 mg/L Kan, 10 mg/L Chl, and 20 mg/L Tet.
After culturing in LB broth media overnight, the bacteria were centrifuged at 5000 rpm for 5 min and washed by substrate-free phosphate-buffered saline (PBS) two times in order to remove the culture media and antibiotic residues. The collected bacteria were then suspended in PBS. The mating system for the conjugative transfer was conducted in a PBS-based solution and consisted of both donor and recipient bacteria at cell densities of 108 CFU/mL with a donor/recipient ratio of 1:1. The mixture (total volume of 1 mL) was then exposed to different concentrations (0, 0.003, 0.03, 0.3, 3, 30, and 300 mg/L) of the four tested nonnutritive sweeteners. These levels of sweeteners cover both environmental and clinical relevant range and were lower than MIC concentrations for the bacteria used in this study (Table S1). Following addition of sweeteners, the mating systems were well mixed by a vortex and subjected to 8-h incubation at 25 °C (the mating process). The system was then mixed again and then poured onto LB agar-selective plates containing antibiotics (prior to selection plating, 100 times dilutions were made for the intragenus conjugation, while no dilution was made for the intergenus conjugation). Separate preparations of the donor and recipients were simultaneously poured onto the transconjugant selective plates in order to measure the background mutation of strains resulting in antibiotic resistance. The plates were incubated at 30 °C for 48 h and then counting of transconjugants and recipients was performed separately. Moreover, the reverse conjugation experiment was also conducted (see the details in Text S1).
Model II was set up to test the conjugation process under clinically relevant condition by using clinical relevant plasmid pMS6198A (isolated from the urine of a patient suffering from a urinary tract infection, UTI ). The donor E. coli K-12 MG1655 containing pMS6198A plasmid with Amp resistance gene and recipient E. coli J53 containing resistance to sodium azide were used. Experiments were conducted following the similar procedures as Model I but the mating medium (LB), time condition (37 °C for 2 h), and selective plates (LB agar plates containing 100 mg/L of both Amp and sodium azide) for transconjugants were different.
Model III referred to the single-cell level analysis based on microfluidic system (Text S2). Briefly, overnight cultures of donor (P. alloputida containing gfp-RP4 plasmid; dsRed/GFP-lacIq, red fluorescence) and recipient (wild type of P. alloputida; no fluorescence but green only when the conjugative plasmid was received) were diluted tenfold and were incubated in LB broth media with shaking at 30 °C for 2 h. Afterward, cell suspensions were washed with PBS solution to remove any LB broth residue and were adjusted to an OD600 comprised between 0.7 and 0.8. In total, 300 µL of both donor and recipient cells were mixed (1:1 ratio, v/v) and vortexed before loading onto the B04A microfluidic plate chamber (ONIX, CellASIC®, Merck) with 5 psi for 1 min. Simultaneously, four nonnutritive sweetener solutions were loaded at 1 psi and the temperature was maintained at 25 °C. In total, 100 µM IPTG was also supplied. Cells were imaged at different time intervals for 2–3 h.
Measurement of reactive oxygen species (ROS)
To understand whether oxidative stress has an effect on ARG’s transfer, intracellular ROS concentrations were measured using the 2’,7’-dichlorofluorescein diacetate (DCFDA) cellular ROS detection assay kit (Abcam, UK). Initially, the cell suspensions (initial concentration of about 106 CFU/mL in PBS solution) were incubated with DCFDA at 20 μM for 30 min, at 37 °C in the dark. The sweeteners were then added and incubated for 2 h at room temperature in the dark. After that, the suspensions were analyzed by a CytoFLEX S flow cytometer (Beckman Colter, USA) with excitation at 488 nm and emission at 525 nm. Both positive (3% hydrogen peroxide, final concentration) and negative (Milli-Q water) suspensions were used as controls in the ROS analysis.
Measurement of cell membrane permeability
The condition of cell membranes was examined to explore how they may contribute to the gene transfer. Cell membrane permeability of both donors and recipients was determined using the propidium iodide (PI, Life Technologies, USA) dye at the final concentration of 20 µM, according to the described method [12, 31]. Typically, bacterial cell suspensions of ≈106 CFU/mL in PBS solution were obtained after washing the collected cells that were cultured in LB liquid overnight. Then, for each test, 100 μL of cell solution was added to the 2 mL tubes containing different levels of one of the four sweeteners. These tubes were put at room temperature (25 °C) for 2 h. A control of damaged cells was prepared as described above that was heated at 80 °C for 2 h. Another control of cells was prepared as above, except it had no sweetener treatment. Following the treatments, 1 μL of PI dye (2 mM) was added to the above cell solutions and incubated in the dark for 15 min at 25 °C. Samples of each cell preparation were applied to the flow cytometer that used 488 nm-excitation and 561 nm-emission detection. All samples were prepared in biological triplicates and technical duplicates.
Plasmid extraction, gel electrophoresis, and PCR assays for resistance genes
The donors E. coli K-12 LE392 (RP4) and E. coli K-12 MG1655 (pMS6198A), the recipients P. alloputida, E. coli K-12 MG1655, and E. coli J53, as well as transconjugants (obtained from the transconjugant-selective plates) were cultured in LB broth overnight at 30 °C. Plasmids were extracted from the prepared cultures using the GeneJET Plasmid Miniprep Kit (Life Technologies, Australia), according to the manufacturer’s instructions. Agarose gel electrophoresis was used to confirm the presence of plasmids in the transconjugants. Further, qualitative PCR was employed to confirm whether the amplified ARGs in the transconjugants were the same to their corresponding plasmids (RP4 or pMSA6198). The PCR assays were carried out in a 20-μL volume reaction, which contained 1 μL of DNA sample, 10 μL of Platinum Green Hot Start PCR 2× Master Mix (Invitrogen by Thermo Fisher Scientific), 2 μL of Platinum GC Enhancer, 0.2 μL of forward and reverse primers, and 6.6 μL of Milli-Q water. The information about those primers was shown in Table S2. The amplification process was run on an Applied Biosystems machine in the following conditions: 94 °C for 10 min, followed by 30 cycles of 94 °C for 1 min, 60 °C for 1 min, and 72 °C for 1 min. This was followed by a final extension at 72 °C for 7 min. To confirm whether a specific ARG blaTEM-1 was successfully transferred from donor E. coli K-12 MG1655 to recipient E. coli J53, total DNA was extracted from the donor, recipient, and transconjugants (E. coli J53 with pMS6198A plasmid) using PowerWater® DNA extraction kit (MoBio), according to the manufacturer’s instruction. Afterward, PCR assays were conducted as described above. Visualization of all bands was conducted by SYBR safe DNA gel staining and the GeneRuler 1 kb DNA ladder.
RNA extraction, genome-wide RNA sequencing, and transcriptomic analysis
The intergenera conjugation between E. coli K-12 LE392 and P. alloputida was set up as described above. The mating systems were treated by four types of sweeteners at 0 and 3 mg/L for 2 h and were used for the RNA extractions. Each system was run in biological triplicates. The bacterial cell pellets were collected by centrifugation at 6000 rpm, 4 °C for 6 min. Total RNA was extracted from the pellets using the RNeasy Mini Kit (QIAGEN, Germany) based on the manufacturer’s instructions, with an additional cell lysis step of bead-beating. All RNA samples were then delivered to Macrogen Co. (Seoul, Korea) for construction of strand-specific cDNA library and Illumina sequencing of paired-end genome (HiSeq 2500, Illumina, USA) after passing their quality control. CummeRbund package in R was used to conduct the statistical analysis and visualization. The fragments per kilobase of a gene per million mapped reads (FPKM) was measured to quantify gene expression. The difference in gene expression between the control (without addition of any sweeteners) and the sweetener-treated groups was presented as log2 fold change (LFC). The significance of transcriptome data for expression of genes was determined by a false discovery rate (FDR)-adjusted p value less than 0.05. All samples were prepared in triplicates.
All the experiments were conducted independently at least in biological triplicate. All phenotypic data were expressed as mean ± SD and were analyzed with SPSS 25.0 (SPSS, Chicago, USA). The results were analyzed by Analysis of variance (ANOVA) and Independent-sample t test methods, with the Benjamini–Hochberg correction. The corrected p values less than 0.05 were considered to be statistically significant.
Nonnutritive sweeteners promote conjugative transfer
To test the effect of nonnutritive sweeteners on the conjugative transfer of ARGs, both intra- and intergenus-transfer experiments (model I) were first conducted, in which the bacteria were exposed to various concentrations of four commonly used nonnutritive sweeteners (SAC, SUC, ASP, and ACE-K) for 8 h at room temperature. Notably, in both mating systems, the whole concentration range (from 0.03 to 300 mg/L) of three sweeteners (SUC, ASP, and ACE-K) caused a significant concentration-dependent increase (p = 0.00017 ~ 0.047, Fig. S1a, b); Pearson correlation analysis was shown in Table S3 in conjugative transfer compared to the control (Fig. 1a, b). The intragenus (donor Escherichia coli K-12 LE392 and recipient E. coli K-12 MG1655) spontaneous conjugative transfer frequency was (1.9 ± 0.2) × 10−4 transconjugants per recipient cell (Fig. S2). However, the conjugative transfer frequencies were significantly enhanced by the sweeteners SUC, ASP, and ACE-K at 0.3 mg/L or above. For example, SUC, ASP, and ACE-K at 300 mg/L enhanced the conjugative frequencies by 1.5- (p = 0.00027), 4.1- (p = 0.000000089), and 3.4-fold (p = 0.0000020), respectively (Fig. 1a). In contrast, SAC did not significantly change the conjugative transfer frequency in the conjugation system (p = 0.200 ~ 0.670, Fig. 1a). For intergenus conjugation (donor E. coli K-12 LE392 and recipient Pseudomonas alloputida), all sweeteners at concentrations of 3 mg/L or higher (except for SAC) were seen to promote the conjugative transfer of the donor RP4 plasmid to recipients of different genera (p = 0.000047 ~0.042, Fig. 1b). SUC, ASP, and ACE-K at 300 mg/L caused a great increase in conjugative transfer, by 2.6- (p = 0.0000020), 4.1- (p = 0.000036), and 4.2-fold (p = 0.000019), respectively (Fig. 1b). It should be noted that the enhanced transfer frequencies were associated with the increased number of colonies on selective transconjugant plates, rather than decreased recipient numbers (Fig. S3).
To test whether conjugative transfer would be promoted by the tested compounds under clinical conditions, we used an IncA/C plasmid pMS6198A, which contains multiple clinically relevant resistance genes, in a uropathogenic E. coli strain isolated from a patient who suffered from a urinary tract infection  to conduct a conjugation experiment (model II, donor E. coli K-12 MG1655 and recipient E. coli J53) in liquid culture at 37 °C. Similarly, a significant concentration-dependent increase (p = 0.00017 ~ 0.047, Fig. S4 and Table S3) in pMS6198A transfer was also observed upon exposure to all four sweeteners (Fig. 1c and Fig. S5). This is different from the result in which SAC failed to enhance both intra- and intergenus conjugative transfer of the RP4 plasmid under environmental conditions.
The successful transfer of donor plasmids (RP4 and pMS6198A) to recipients was confirmed by a series of analyses. The MIC levels for transconjugants (recipient with transferred plasmid) were comparable or even higher than those for their corresponding parents that were resistant to all antibiotics (Fig. S6). In addition, plasmid extraction and PCR amplification of related resistance genes showed that all the transconjugants contained the same type of plasmid as the donor did and harbored the corresponding ARGs (Fig. S7). Thus, profiling of all the transconjugants confirmed that the donor plasmid was transferred to the recipient cells and conferred antibiotic resistance.
To understand whether transconjugants were capable of transferring ARGs to other candidates, we performed a reverse conjugation experiment (model III, donor P. alloputida containing the RP4 plasmid and recipient E. coli K-12 MG1655; Methods and Text S1) for 8 h at room temperature. Interestingly, this reverse conjugative transfer occurred and it was enhanced by all nonnutritive sweeteners (p = 0.000033 ~ 0.036, Fig. 1d; Fig. S8 and S9). Specifically, similar to the result of pMS6198A transfer, SAC significantly increased RP4 plasmid transfer (p = 0.036). Thus, the transferred RP4 plasmid in transconjugants maintained its mobility and could be transferred to other potential recipients. Collectively, these results demonstrate that the tested four sweeteners promoted plasmid-mediated conjugation in both nonpathogenic and pathogenic strains.
Real-time visualization of conjugative plasmid transfer
The spread of ARGs by conjugation is a dynamic process. However, clear real-time visualization of the cellular dynamics of conjugative transfer has yet to be obtained. Specifically, little is known about whether nonnutritive sweeteners could speed up the transfer of conjugative plasmids at the single-cell level. To achieve this, we developed an experimental system that is capable of real-time visualization of RP4 plasmid transfer by conjugation at the single-cell level using a fluorescence labeling technique (Methods and Text S2). This method could be useful or inspirational to other ecological studies, such as evolution of antibiotic resistance at a community-wide level. Time-lapse microscopy images showed that in the control group (without the addition of any sweeteners), the RP4 plasmid was successfully transferred to the recipient after 5 min of contact (Fig. 2a; Movie S1). In contrast, under exposure to four sweeteners, the plasmid acquisition process was accelerated, and successful transfer was observed within 5 min (Fig. 2b; Movie S2). Moreover, the number of transconjugants within 150 min were significantly increased under exposure to the tested sweeteners compared to the control (Fig. 2c–g). This was also mathematically supported by single-cell quantitative analysis, which showed higher transfer rates (r) under exposure to the tested sweeteners than in the control (Fig. 2h). A 6.0-, 5.0-, 5.0-, and 7.0-fold increase of transfer rate was induced by SAC, SUC, ASP, and ACE-K, respectively. The fitted maximum number of transconjugants (Nm) showed a more than 2.0- to 4.0-fold increase under treatment with these sweeteners. These results further confirm that nonnutritive sweeteners promote plasmid-mediated conjugation at the single-cell level.
Nonnutritive sweeteners enhance ROS production and the SOS response
It has been reported that nonnutritive sweeteners can cause DNA damage  and induce oxidative stress in bacteria . Thus, we measured ROS production in cells exposed to the tested sweeteners. Notably, in the strains treated with the sweeteners (except for SAC), concentration-dependent increase in ROS was detected (Fig. 3a–c; Fig. S10). For example, under treatment with the sweeteners (except SAC) at 300 mg/L, the relative fold change in ROS production in the donor E. coli K-12 LE392 increased 1.5-fold (p = 0.0010 ~ 0.0070, Fig. 3a). This increase was also observed when both the recipients E. coli K-12 MG1655 and P. alloputida were treated with these sweeteners (Fig. 3b, c). In contrast, exposure to the sweetener SAC did not result in any increase in ROS production in these donor and recipient strains. To further verify the promotion of ROS production by these compounds, thiourea, a scavenger of oxygen-free radicals [33, 34], was added to the mating system together with nonnutritive sweeteners. As expected, significant decrease in ROS production was detected in the three strains treated with SUC, ASP, and ACE-K after thiourea was added (Fig. S11).
To determine whether the increased production of ROS induced by these sweeteners promotes conjugative transfer, thiourea was added to both the intra- and intergenus conjugative systems, together with the sweeteners. Compared to the group without thiourea in both conjugative systems, addition of the scavenger caused no change in the conjugative transfer frequency in the SAC-treated group but significantly decreased the transfer frequency in the SUC-, ASP-, and ACE-K-treated groups (p = 0.000033 ~0.035, Fig. 3d, e). These results suggest that ROS production plays a significant role in the plasmid-mediated conjugation process.
Under oxidative stress caused by the tested sweeteners, bacterial defense may include changed expression of ROS-related genes (or ROS detoxification) as well as changed expression of SOS response-related genes. To track the expression of genes related to ROS production and the SOS response regulated by the tested sweeteners, the mRNA transcription level of genes from both the donor E. coli K-12 LE392 and recipient P. alloputida was measured. The transcripts for genes encoding enzymes involved in ROS detoxification in the donor were increased under exposure to the tested sweeteners (Fig. 3f; Table S4). For example, the gene encoding superoxide dismutase (sodA) exhibited a 1.3- (p = 0.032), 1.8- (p = 0.0052), and 1.8-fold (p = 0.0023) increase in expression in the donor treated with SUC, ASP, and ACE-K, respectively. Accordingly, an SOS response was detected in the donor after exposure to these sweeteners (Fig. 3f; Table S5). Increased transcription was detected for the genes sulA (1.3- to 1.6-fold change, p = 0.0040 ~ 0.036) and umuC (1.6- to 2.1-fold change, p = 0.014 ~ 0.040) after treatment with the three sweeteners. We also found increased expression of ROS detoxification- and SOS response-related genes in recipients treated with SUC, ASP, and ACE-K (Fig. 3g; Tables S6 and S7). In contrast, SAC treatment did not result in significant regulation of the genes mentioned above in the donor or recipient.
It is apparent that SUC, ASP, and ACE-K increased ROS production in both intra- and intergenus conjugative systems, whereas SAC did not induce any change in ROS production in the strains tested. We propose that nonnutritive sweeteners induced ROS overproduction and increased ROS detoxification, and correspondingly stimulated oxidative stress responses (the SOS response) in the strains, eventually contributing to the promotion of intra- and intergenus conjugative transfer.
Nonnutritive sweeteners increased cell membrane permeability
It is worth noting that addition of the scavenger thiourea did not completely reverse the increase in the frequency of conjugative transfer caused by sweeteners (i.e., SUC, ASP, and ACE-K). For example, after addition of thiourea to the mating system that was exposed to 300 mg/L ACE-K, the frequency of conjugative intragenus transfer was (3.5 ± 0.4) × 10–4 transconjugants per recipient cell, which was still significantly (p = 0.0090) higher than the value for the control ((2.0 ± 0.3) × 10–4 transconjugants per recipient cell, Fig. 3d). This indicated that ROS production is not the only mechanism for conjugation.
Bacterial cell membranes act as a barrier against horizontal transfer of ARGs , and the permeability of this barrier could play a significant role in the transport of substances into or outside of cells. Therefore, we tested whether nonnutritive sweeteners could change the cell membrane permeability. To examine this concept, we treated both the donor E. coli LE392 and the two recipients (E. coli K-12 MG1655 and P. alloputida) with different concentrations of the four sweeteners. After 2 h of treatment, the cell membrane permeability was increased by up to 3.7-fold (p = 0.000047 ~ 0.0019) in the donor by all the sweeteners (300 mg/L) except SAC (Fig. 4a; Fig. S12). This increase was also observed in the two recipients treated with all sweeteners (Fig. 4b, c), exhibiting an increase of up to 1.5- and 1.6-fold, respectively (p = 0.0010 ~ 0.028), under exposure to all tested sweeteners at 300 mg/L. In addition, we found that SAC, together with the other three sweeteners, significantly increased the permeability of another donor strain, E. coli K-12 MG1655 (p = 0.00024 ~ 0.0082, Fig. S13a). Similar results were also found for the permeability of the recipient strain E. coli J53 (p = 0.000088 ~ 0.0074, Fig. S13b).
Our results showed that the SAC failed to enhance ARG transfer from E. coli LE392 to either E. coli K-12 MG1655 and P. alloputida but enhanced conjugative transfer between E. coli K-12 MG1655 and E. coli J53, as well as between the strain P. alloputida containing the RP4 plasmid and the strain E. coli K-12 MG1655 (i.e., reverse conjugation). This raises the question of whether the permeability of the donor or recipient (or both) is important for conjugative transfer. To this end, we performed different pre-exposure to separately increase the cell membrane permeability of the donor (E. coli LE392) and two recipients (E. coli K-12 MG1655 and P. alloputida) before mixing for conjugation experiments (Text S3; Table S8). We treated each strain with 3 mg/L SUC, which significantly increased the permeability of the donor and recipient (Fig. 4a–c). The results showed that there was no significant change in conjugation frequency when the recipients were pre-exposed to SUC (p = 0.078 ~ 0.19, Fig. 4d, e; Fig. S14). This indicates that the increased permeability of the recipient did not guarantee enhanced conjugative transfer. In contrast, both intra- and intergenus conjugation frequencies were significantly (p = 0.00000000034 ~ 0.040) promoted when the permeability of the donor was significantly increased. Overall, these results indicate that cell membrane permeability is positively mediated by nonnutritive sweeteners in mating systems and that donor permeability plays a more critical role than recipient permeability in the conjugation process.
We tested whether genes that mediate membrane permeability at the molecular level were upregulated in the donor and recipient (P. alloputida) after treatment with the tested sweeteners at 3 mg/L. Genes related to cell membrane permeability in both donor and recipient cells were upregulated after exposure to the tested sweeteners (Fig. 4f, g). For instance, fecA, which encodes an outer membrane transporter, and ybgE, which encodes an inner membrane protein, were significantly upregulated (1.5- to 7.0-fold (p = 0.0020 ~0.037) and up to 2.7-fold (p = 0.0060 ~0.044), respectively, Table S9) in the donor cells treated with SUC, ASP, and ACE-K (Fig. 4f). In contrast, SAC did not induce significant changes in the expression of cell membrane-related genes in the donor. These findings are consistent with the results showing that all sweeteners, except SAC, increased the membrane permeability of the donor. Nevertheless, cell membrane-related genes in the SAC-treated recipient showed increased expression, as seen in the other sweetener-treated recipient groups (Fig. 4g; Table S10).
These results confirm that the tested sweeteners increased the expression of cell membrane-related genes, and then increased the cell membrane permeability of the donors or both parents to promote the conjugative transfer of plasmids between strains.
Nonnutritive sweeteners upregulate the expression of conjugation-related genes on the RP4 plasmid
The process of conjugative transfer mediated by the RP4 plasmid requires the regulation of global regulatory genes and conjugative transfer-related genes [35, 36]. After treatment with 3 mg/L SUC, ASP, and ACE-K, we found that the core global regulatory gene korC was repressed in comparison with the control group. Accordingly, the conjugative transfer regulator gene traG (which connects the relaxosome and mating pair formation complex) and DNA transfer and replication (Dtr) genes traC1 and traC2 exhibited increased expression compared with the mRNA expression detected in the control group (Fig. 5). During the conjugation process, the plasmid is thought to be transferred via a pilin bridge between donor and recipient cells . The expression levels of pilin formation-related genes, including traA, traB, traF, and trap, were also upregulated in the sweetener-treated groups (Fig. 5). These genes also contribute to the formation of the mating pair formation (Mpf) system. For example, compared to the control, mRNA expression of gene traB (encoding a conjugative transfer protein) was significantly upregulated by more than 1.5- (p = 0.0046), 1.4- (p = 0.047), and 2.1-fold (p = 0.000050) under exposure to SUC, ASP, and ACE-K, respectively (Fig. 5a; Table S11). Together, these results reveal that these sweeteners (except for SAC) cause increased mRNA expression levels of genes related to RP4 plasmid transfer and replication (Dtr genes) and then promote the formation of the pilus channel in the Mpf system to allow RP4 plasmid transfer from the donor to the recipient.
The conjugation process also requires direct cell-to-cell contact. This can be achieved by the periplasmic pilin of donor cells. In the donor E. coli K-12 strain, pili operons have been found to play roles in cell adhesion and colonization . In the present study, the expression of genes in these adhesion-relevant operons was upregulated. For example, the expression of gene ecpA was upregulated by 1.8- (p = 0.035), 4.2- (p = 0.0070), and 2.1-fold (p = 0.033) after treatment with SUC, ASP, and ACE-K, respectively (Fig. 5b; Table S12).
Based on the three established conjugation models and a real-time dynamic conjugation system at the single-cell level, our work for the first time demonstrates that four commonly used nonnutritive sweeteners can promote ARG transfer by conjugation at environmentally and clinically relevant concentrations. Multiple pieces of evidence were gathered, including from measurement of ROS production, cell membrane permeability, and whole-genome RNA sequencing analysis, to elucidate the underlying mechanisms. These measurements, coupled with the real-time dynamic analysis of conjugation process, enable the identification of key factors in HGT and quantitative estimates of the extent of HGT in diverse microbial communities. Although the enhanced conjugative frequency could be significantly decreased after adding the scavenger thiourea, nonnutritive sweetener (SUC, ASP, and ACE-K)-treated groups still showed higher frequencies of conjugative transfer than the control group. These results suggest that ROS production induced by nonnutritive sweeteners plays a significant role in the promotion of conjugative transfer but is not the only underlying mechanism.
As a permeable barrier controlling the entry of extracellular substances, the cell membrane also plays a role in the conjugative transfer of ARGs [12, 38, 39]. Our results demonstrate that in addition to increased ROS production, cell membrane permeability, especially that of the donor, also plays an important role in the conjugative transfer frequency of the RP4 plasmid. Specifically, SAC increased the cell membrane permeability of both recipients (E. coli MG1655 and P. alloputida) but failed to increase that of the donor E. coli LE392. This might be why SAC did not increase the conjugative transfer frequency of the RP4 plasmid in mating model I. In contrast, SAC can increase the conjugative transfer frequency of the RP4 plasmid (reverse conjugation), the GFP-labeled RP4 plasmid in P. alloputida, and the pMS6198A plasmid, since the cell membrane permeability of the donor P. alloputida (Fig. 4c) or E. coli K-12 MG1655 (Fig. S13a) increased significantly. We further verified this hypothesis, based on experiments, with the exposure of different donors and recipients to nonnutritive sweeteners. When the permeability of the donor was increased but that of the recipient was not, conjugative transfer was significantly promoted. In contrast, when the permeability of the recipients was increased but that of the donor was not, both intra- and intergenus conjugative transfer showed insignificant changes. It has been reported that in the transfer of ARGs, donors with high expression of the conjugation machinery were shown to be associated with low-receptivity recipients . Thus, the increased permeability of the donor may cause increased ARG transfer to the recipient and result in increased conjugative transfer frequency.
As aforementioned, we suggest that the mechanisms (Fig. 6) underlying the tested sweetener-promoted conjugative transfer include increased ROS production and detoxification, and increased cell membrane permeability of the parent bacteria. In addition, the tested sweeteners promote increased expression levels of conjugative transfer-related genes and activate plasmid DNA processing (Tra1) and mating pair formation (Mpf or Tra2) to enhance the intercellular transfer of the RP4 plasmid through a pilus channel.
As the environment and human gut system are reservoirs of various microbes, the emergence of nonnutritive sweeteners can be a driving force to shape these microbial communities. Specifically, nonnutritive sweeteners might play a significant role in the dissemination of ARG transfer in both environmental and clinical settings.
In the environmental setting, although various techniques, including adsorption, advanced oxidation processes, and biological treatment, are used to remove nonnutritive sweeteners, the removal efficiency of these sweeteners is generally low (less than 30%) [41,42,43]. We also found that nonnutritive sweeteners used were metabolically resistant to the tested bacterial strains (p = 0.062 ~ 0.700; see in Text S4; Fig. S15). Noticeably, the concentrations of nonnutritive sweeteners used in this study were environmentally relevant (e.g., 0.03 ~ 3 mg/L) . Moreover, previous studies found that WWTPs served as hotspots harboring antibiotic- resistant bacteria (ARB) and ARGs due to HGT among indigenous bacterial species [45, 46]. Upon exposure to these compounds, it is reasonable to assume that the transfer frequency of ARGs would be promoted in WWTPs. In addition, our results show that the ARGs on the RP4 plasmid from transconjugants can also be transferred to other candidates (Fig. 1d) and the transfer rate can be facilitated by the four commonly used nonnutritive sweeteners (Fig. 2). It is possible that these sweeteners could cause a cascading spread of ARGs in the WWTPs, thus facilitating increased development of antibiotic resistance in downstream environmental bacteria. However, it should be noted that our work highlighted the results of conjugation between pure cultures. Further studies could be carried out to test whether these sweeteners could promote conjugation in mixed culture-based systems (e.g., activated sludge). In addition, our work highlighted the results of an acute exposure (~8 h) to the tested four sweeteners, rather than a chronic exposure. Considering that these compounds are being soaringly consumed and can exist in the environment for a long period, a chronic exposure to the tested sweeteners may induce an accumulative effect on the spread of antibiotic resistance, as antibiotics or heavy metals did [47,48,49]. Thus, it is meaningful and necessary to study the long-term effect of these sweeteners at lower concentrations (e.g., ng/L) on the spread of antibiotic resistance.
On the other hand, our work provided evidence that the four commonly used nonnutritive sweeteners (at 3 mg/L or above) significantly promoted conjugative transfer of plasmid pMS6198A that was isolated from the urine of a patient suffering from UTI (Fig. 1c). Considering that the concentrations of the tested sweeteners can be higher than 30 mg/L in urine , our result indicates that these nonnutritive sweeteners might enhance plasmid conjugation in the human urinary system. In addition, it is estimated that the human gut microbiota is composed of as many as 1014 bacteria , which are involved in multiple interactions relevant to host health  and serve as a transporter  and even a reservoir of ARGs . In fact, the levels of consumed nonnutritive sweeteners in the human gastrointestinal tract are likely to be far higher than the ones used in the present study [20, 21]. The highest concentration (300 mg/L) of these compounds is also within the dosage range for average daily intake (i.e., 5 mg/kg/d sucralose) suggested for an individual with a body weight of 60 kg by the U.S. FDA and is also lower than the threshold concentrations (>1000 mg/L) regulated by the Codex General Standard for Food Additives (CODEX STAN 192-1995). Moreover, our study did in vitro assays of plasmid conjugation driven by the tested sweeteners in PBS or LB media, which were not totally clinically relevant to the human urinary and gut system conditions. In the future, it is worthwhile to validate whether these nonnutritive sweeteners could promote conjugative plasmid transfer in animal or human gut microbiomes, which will provide more concrete evidence.
Collectively, the findings of the present study provide evidence that four commonly used nonnutritive sweeteners can promote the horizontal transfer of ARGs via conjugation in both environmental and clinical settings. The establishment of a real-time dynamic analysis of conjugation process in this study will advance the ecological studies such as the spread of AMR in diverse conditions. Considering the substantial application of these sweeteners in food industry (over 117,000 metric tons globally consumed per year), our findings are a wake-up call to start evaluating the potential antibiotic-like roles induced by nonnutritive sweeteners. In vivo assays could be further applied to test whether nonnutritive sweeteners are able to promote conjugation in human urinary and gut systems in the long-term run.
All RNA sequencing data have been deposited to the Gene Expression Omnibus of National Center for Biotechnology Information (NCBI) and are accessible through the GEO series (GSE139245).
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This study was financially supported through Australian Research Council Future Fellowship (FT170100196) awarded to JG and the UQ Foundation Research Excellence Awards. ZY also thanks UQ Research Training Scholarship for the financial support. We thank Dr. Uli. Klümper (Technical University Dresden) for sharing GFP-labeled strains and Prof Mark Schembri (The University of Queensland) for the donation of pMS6198A plasmid and E. coli J53 strain. We also thank Dr. Michael Nefedov (The University of Queensland) for flow cytometer analysis, Dr. Likai Mao (The University of Queensland) for assisting with mRNA data analysis, Mr. Nigel Dawson and Nathan Clayton (The University of Queensland) for quantitative LC–MS analysis of nonnutritive sweeteners, and Dr. Steven Mason (The University of Queensland) for microscopy and imaging.
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Yu, Z., Wang, Y., Lu, J. et al. Nonnutritive sweeteners can promote the dissemination of antibiotic resistance through conjugative gene transfer. ISME J 15, 2117–2130 (2021). https://doi.org/10.1038/s41396-021-00909-x
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Squaring the Square
N 1936, FOUR STUDENTS AT TRINITY COLLEGE, Cambridge-Brooks, Smith, Stone, and Tutte--considered the problem of cutting up a rectangle into squares of unequal size (no two alike). It was known, at that time, that a rectangle 32 by 33 could be "squared" as shown in Figure 7.1.
Stone became particularly interested in trying to prove that it was impossible to cut a given square into unequal squares. While not able to do this, he did discover a squaring of another rectangle (see Figure 7.2).
One way of attacking the problem of finding rectangles that can be squared is to make a sketch of a proposed partition into squares, labelling the edge-length of each square, writing down all the relations that the edge-lengths must satisfy in order to fit into the rectangle, and solving the system of equations thus obtained.
We shall carry this out for some examples. Instead of carrying as many unknowns as there are squares in the subdivision, we shall try to label neighbouring squares so that they fit together in the sketch; thus we shall have fewer unknowns to eliminate later.
In Figure 7.3, we label the neighbouring squares x, y and z, as shown. Then it is easy to label the remaining squares in the order
x + y, 2x + y, y - z, y - 2z, y - 3z, 2y - 5z.
Next, we obtain relations between our unknowns; for example, we can equate the lengths of opposite sides of the containing rectangle The horizontal sides yield
2x + y + x + y = 2y - 5z + y - 2z + y - z,
that is, (1)
3z - 2y + 8z = 0;
and the vertical sides yield
2y - 5z + 2x + y = y - z + y + x + y,
x - 4z = 0.
x = 4z and Y = 10Z.
We observe that if we set z = 1, we obtain the tiling shown in Figure 7.1; if we set z equal to any other positive quantity, we obtain the same configuration, blown up (or shrunk) by the factor z. If we prescribe the length of the horizontal edge, say 64", then z would be 2" and the figure would be completely determined.
In Figure 7.4, two unknowns, x and y, suffice to express the edgelengths of all compartments.
Equating the lengths of the horizontal sides of the containing rectangle, we obtain
9x - 5y + 6x - 2y = 2x + 5y + x + 2y + x + y + 2x + y,
that is, 9x - 16y = 0, whence (3) X 16 -- = -- Y 9
The values x = 16, y = 9 yield Stone's tiling of the 177 X 176 rectangle (see Figure 7.2), and other values satisfying (3) would give a similar figure.
To show that such schemes do not always yield feasible results, we give another example.
Starting with x and y as shown in Figure 7.5, we can label the other squares
X + Y, 2x + y, 3x + y;
and equating lengths of the vertical borders, we get
2x + y + 3x + y=x + y + y
our middle square turns out to be a point and the remaining four squares axe equal. We have merely quartered the given rectangle, which must have been a square!
Our examples indicate that the system of linear equations we get from an arbitrary sketch of a partition seems to have a unique solution (except for a scaling factor), although the solution is not necessarily geometrically feasible. It could happen, for example, that some of the edge-lengths turn out to be negative, and that would not make sense in the context of our tiling problem.From our previous experience with systems of linear equations we know that there may be too many equations (in which case there is no solution) or there may be too few (in which case there are infinitely many solutions) or the number of equations may bejust right, that is, they are satisfied by exactly one set of numbers. In all our examples, the number of equations obtained by prescribing the length of one pair of edges of the containing rectangle, but not the length of the other, was just right; i.e., each system had a unique solution. Was this just a happy accident? We shall show, by appealing to electrical network theory, that a system of linear equations obtained from a sketched partition always has a unique solution.
To make things more precise, consider a given subdivision of a rectangle into squares. With respect to each horizontal segment of the partition (see Figure 7.6) we have a relation
a + b = c + d + e
telling us that the sum of the lengths of the edges of squares bordering the segment on one side is equal to the sum of the lengths of the edges of squares bordering the segment on the other side. We shall call all such relations horizontal compatibility relations. Similarly, the analogous relations obtained from vertical segments will be called vertical compatibility relations. Clearly, the set of all compatibility relations forms a system S of linear equations.
THEOREM. If one of the two dimensions of a partitioned rectangle is prescribed, the system S of compatibility relations always has a unique Solution (though not necessarily geometrically meaningful).
Imagine that the rectangle is a plate of uniform thickness made of some conducting metal. Suppose all points of the upper edge of the rectangle were given the same electric potential V, and all points on the lower edge had a lower constant potential V'. (This could be accomplished by coating these edges with some perfect conductor.) Because of the prescribed potential difference V - V', there will be a steady flow of current through the rectangle, in the vertical direction. The rate at which electrons cross over a horizontal interval is proportional to the length of that interval. Thus, if I is the current crossing over a horizontal interval of unit length, then the current flowing across an interval of length I is 11. The resistance of such a rectangle to electric current is directly proportional to its vertical height L (to the distance the current must traverse) and inversely proportional to its horizontal width W (the distance along which the current may enter); i.e., resistance = (RL/W). Thus, if the rectangle happens to be a square (L = W ), then its resistance is R and does not depend on the size of the square.
Now suppose that such a current-carrying rectangle has been partitioned into squares. Since the flow is vertical (there is no flow in the horizontal direction), we may cut through vertical segments without interfering with the current. Now regard the cut-up plate as a network where the constituent squares are identified with conducting wires and where horizontal segments axe identified with points, or vertices at which the conducting wires meet. (See Figure 7.7, where the vertices A, B, - - . in the network correspond to horizontal segments at levels a, b, . . . of the rectangle, wires AB, AC, correspond to squares extending from levels a to b, a to c,
The magnitude of the current flowing through each wire is proportional to the length of the side of the square represented by that wire.
The law of conservation of current states that, at each vertex of the graph, the total amount of current flowing in equals the total amount of current flowing out. For example, the vertex C (corresponding to the horizontal segment at level c) receives current tI + wl through wires AC and BC (corresponding to squares t and w) and C loses current xI + zI through wires CD and CE (corresponding to squares x and z). The law cited above yields the relation
t + w = X + z
which is just one of our horizontal compatibility relations.
Since current flows in at the upper edge of the plate, moves down vertically and flows out at the lower edge, we see that every point at the same horizontal level is at the same potential, and points at higher horizontal levels have higher potentials than points at lower horizontal levels. According to Ohm's law, the difference in potential between two Points of the network joined by a wire is equal to the product of the current through that wire and the resistance offered by it. For example, the Potential difference between B said C (representing levels b and c of the plate) is wI x R (wI being the current entering at the upper edge of the square w, and R the resistance of any square; see p. 52). Moreover, the potential difference is additive; that is, if A and D are two vertices in the network connected by a path AB, BD through B, then the difference in potentials between A and D is the sum of the differences in potentials between A, B and B, D: sI.R + vI.R in our illustration. As a consequence, for any closed path in the
network, say ABDCA, the corresponding sum is zero+, and for any two paths from the same beginning point to the same end point, the corresponding sums are the same. Thus for ABD and ACD, we have
sI.R + vI-R = tI.R + xl.R
which reduces to
s + V = I + X.
This is one of our vertical compatibility relations.
The law of conservation of current and Ohm's law yield a system of linear equations equivalent to the system S of compatibility relations. Now it seems plausible that if a difference in potential is prescribed for a network such as ours (say the potentials at vertices A and E are given, or equivalently, at the top and bottom edges of the plate) then the current flowing in each wire is determined. This, in fact, is the content of the celebrated theorem by Kirchhoff:
If a potential difference between any two points of a network is prescribed, then the laws of conservation and Ohm determine -uniquely the flow in each wire.
Since these physical laws axe equivalent with the geometrical compatibility relations (the prescribed potential difference corresponding to the vertical dimension of the rectangle), the assertion that the system S has a unique solution (see p. 52) is seen to be just a corollary of Kirchhoff's theorem.
A rigorous proof of Kirchhoff's theorem is beyond the scope of this essay.$
Let us now re-examine the problem of partitioning a rectangle into squares.
First we note that a solution of the linear system S may include
non-positive quantities. These cannot be made to correspond to lengths of sides
of subdivision squares, so such solutions of the system S are not solutions
of the tiling problem.
We might try to attack the rectangle-tiling problem by first devising a systematic method of enumerating all possible partitions into n squares and letting the integer n increase. We might then solve the system S for each partition and discard all partitions with geometrically non-feasible solutions. Even among the feasible solutions, many would be uninteresting (i.e., partitions into equal squares, etc.). Requirements such as (a) no two squares in the partition may be congruent, or (b) the partitioned rectangle may not contain a smaller rectangle, impose further conditions on the solutions of S. Perhaps we can approach the problem simultaneously from the other direction; that is, weed out all networks about which we know a priori that the solutions of the associated system S are either geometrically not feasible or produce unwanted partitions of types (a) or (b) above.t
A squaring or tiling in which no two squares are the same size is said to be "perfect". Tutte and his friends were chiefly after perfect tilings. They wanted to find a "perfect square", that is, a square with a perfect tiling. All their results involved non-square rectangles. And so they began to think that a perfect square did not exist. However, in 1939 Roland Sprague of Berlin found one, and, since then, many others have been discovered.
Attention was then turned to finding the perfect square with the smallest number of squares in it (i.e., of lowest order). The record to date is one of order 24, found by an amateur mathematician, T. H. Willcocks of Bristol, England. (See Figure 7.8.)
Figure 7.8 (Compound) perfect square of order 24.
A tiling tiling is said to be "simple" if the arrangement of the squares does not form any smaller squared rectangle inside the original. Willcocks' perfect square is compound, not simple. Accordingly, attention was focussed on the simple perfect square of lowest order. Until recently, Willcocks also held this record with a square of order 37. However, in. 1964 Dr. John Wilson of the University of Waterloo (a student of Tutte), using an electronic computer, found one of order 25 (see Figure 7.9), and he is the record-holder at present.
It has been shown, using computers, that there is no perfect square of order less than 20, simple or otherwise. Consequently, there is not much room for improvement in the above records.
So many perfect squares have been found that experts in the field suspect that tiled rectangles of unequal sides are the harder to come by.
We close this essay with the following easy-to-prove theorem: It is impossible to fill a rectangular box with a finite number of unequal cubes.
Figure 7.9. Simple perfect square of order 25
Proof: Any successful packing of the box provides a perfect tiling of the bottom of the box by those cubes which rest on the bottom. Now the smallest cube S among those lining the bottom certainly could not touch an upright side of the box; for then there would have to be an even smaller one touching the bottom. (See Figure 7.10.)
Figure 7.10. View of bottom rectangle of the box.
This smallest cube on the bottom, being out in the middle part of the bottom, must be bordered on every side by a bigger cube (it is the smallest). Its upper surface, then, is completely walled in; see Figure 7.11. In order to cover this upper surface, even smaller cubes must be used.
Among the cubes on the upper surface of S, the smallest, again occurring in the middle part, is surrounded by bigger ones. Consequently, even smaller ones still must occur in a third layer on the top of this walled-in cube. This argument continues without end, implying that there is no end to the number of cubes that must be employed.
Prove that there exists some rectangle which can be tiled into N unequal squares for each value of N greater than 8, i.e., for N = 9, 10, 11, . . .
In tiling an equilateral triangle with unequal equilateral triangles, prove:
(b) the smallest
tile, T, touching the top of S meets the top of S in just
(c) Does this lead to an endless tower of little triangles, providing a proof of the theorem "it is impossible to tile an equilateral triangle with unequal equilateral triangles (no two alike)", which was first proved by Tutte around 1948?
+ Some headway in this direction has been made, for example, by applying Euler's formula to the graphs of our networks.
+ A path in our network leads from a vertex along an edge in the direction of a next vertex, etc. We take these directions into account by using signed quantities in this sum. For example, A C corresponds to tI, and CA corresponds to - 11.
$The interested reader may look it up, for example, in R, E. Scott, Elements of Linear Circuits, Addison-Wesley, 1965, Reading, Mass.
J. Bouwkamp, On the Dissection of Rectangles into Squares, Kon. Ned.
Ak. van Wet.,
1946, Vol. 49, pp. 1176-1188; 1947, Vol. 50, pp. 1296-1299.


In 1980 Francis Shaeffer and J. P. Moreland published a book entitled “He Is There and He Is Not Silent”. The title of that work suggested something profound about the existence of God and his self-disclosure.
There are of course, many things about God and his ways that he has chosen not to reveal. But God has not been silent about gender roles. His actions have been recorded, his commands have been preserved and at least some of his reasons have been revealed. Taken together, these move us toward a theology of gender roles.
We begin this discussion by noting that the bible as a whole treats the Genesis account of creation as an historical record. It is neither myth nor metaphor. Luke’s genealogy traces the ancestry of Jesus back to the first man Adam who was not an imaginary figure.
One can scarcely begin to read the bible before coming to the creation of Man. The scriptures affirm that God created a single humanity, composed of two people with two distinct genders each of whom was made in the image of God. Genesis chapter two expands this story, explaining that God made the man first and then made the woman from a body-part of the man (Genesis 2, 1st Tim. 2:13). Once created, the woman was brought to the man and presented to him as a companion and a wife. Adam called her ‘woman’ for she was taken from man (Gen. 2).
Now when we first read this, there do not appear to be any self-evident conclusions. The bare facts do not really speak for themselves. The theological significance of the order of creation emerges only as we read further. It becomes quickly apparent that Adam is in charge. By giving her a name, Adam relates from a position of leadership and headship. God reinforced that headship by making what had been implicit, explicit, reminding Eve that despite her desire to the contrary, her husband would rule over her (Gen. 3:16).
The apostle Paul explained the significance of the creation order by stating that the man is the head of the woman, for the man was not made for the woman but the woman for the man. For the man was not made from the woman but the woman from the man (1st Cor. 11:3, 9). God gave Adam authority over his wife and that aspect of the husband-wife relationship remains in place.( Eph. 5:23 1st Pet. 3:1)
What Paul means to say is that God did this deliberately. It did not happen because He was inattentive or somehow distracted. God did precisely what he set out to do. He created a single humanity made up of two separate people, two distinct genders for which he had in mind two distinctly separate roles. He signaled this by creating one first and then the other.
The Old Testament consistently reflects this headship in the covenants and ordinances of God. Men were called to act as the head of their families and to lead in spiritual matters.
This arrangement persists as we enter the New Testament. When God came to earth in human form, he came as a man. When Jesus chose those who would lay the foundation for the church he chose twelve men from among his disciples to serve as apostles. (Matt. 10:1-4, Luke 6:12-16, Mark 3:13-18). When the apostles organized the church according to the will of Jesus, they appointed men to serve as evangelists, elders, deacons and teachers. When the gospel came to the egalitarian culture of Greece, the apostle Paul reminded the Corinthian church about the headship of the man and the distinct leadership roles given to men and not to women. (1st Cor. 11:1-17, 14:34-40). He repeated these instructions to Timothy, serving in a very different culture in Asia. (1st Tim. 2:8-15) The roles that Paul identified applied equally to the church in each and every culture of the ancient world. (1st Cor. 11:16)1. Paul makes it clear that distinct gender roles find their source and parallel in the makeup of the godhead and in God’s plan for our salvation. (1st Cor.11:3)
The fact is that the order of God’s creation cannot be undone. Nor can the theological significance of this creation-order be removed from scripture. To do so does great violence to the Biblical doctrine of Man and even greater violence to the doctrine of the Godhead.
The scriptures teach that there is one and only one God. They further affirm that there are three members of the godhead. These are identified for us as the Father, the Son and the Holy Spirit. All are equally God. All are equal in essence and being. Theirs’ is a shared divinity whose sum is; one God.
What emerges within scripture as further revelation about God is that the persons of the godhead have voluntarily assumed distinct and separate roles. These roles predate creation and remain beyond The Judgment. They act as bookends for our existence2.
There are three prominent features attending these divine roles.
- The first is organizational. The godhead functions as a hierarchy. God the Father has had authority over God the Son and God the Holy Spirit. Thus, the father sent the Son to be the savior of the world. And God the Father sent the Holy Spirit to empower the Son and to indwell His people. The Son in turn sends the Holy Spirit to dwell within and to be with his people. Though equally divine, these three do not act – for the present – from a position of equal authority.
- The second thing about these roles is that they have been voluntarily entered into. Jesus agreed to the incarnation. He agreed to submit to the Father while on earth.
- There is every indication that these roles are not interchangeable. God the Father has at no time ever been the Son or fulfilled the role of the Son. In Gethsemane, the Son did not implore the Father to change places with him. All three persons of the godhead have been true to their roles no matter the cost.
It is reasonable therefore to conclude, that at the very core – at the very essence of the being of God, there is a nature of humility and condescension. No one could have suspected it. There is no apparent reason why God should be humble. Nor can we conceive why it could ever be right for God to submit. What we learn from the godhead is a unique truth about God that is found nowhere else.
While the doctrine of the godhead is 2000 years old, it is hard to find anyone marching in the streets, demanding equal rights for the Son. The theological form that this protest is taking is to deny the doctrine of the godhead altogether. After all, one cannot reasonably worship a god of submission and humility while promoting ‘egalitarianism’. What is truly alarming is that this denial has even surfaced within the churches of Christ.
The bible teaches, that what God is in his essence and in the godhead, is reflected in creation. There is only one God and only a single humanity. But being made in the image of God also suggests that mankind must reflect the truth about the godhead. To that end, God has made a distinction between men and women from the very beginning, giving to each a uniquely separate role. He served notice of this by creating one first and then the other. Like the roles of the godhead, human roles cannot be exchanged. They are God’s doing and not our own.
Denying that such roles exist denies the essential truth about God. It disowns the God who in three persons created the world. It is ashamed of the God who from eternity purposed to save us from sin by taking upon himself our humanity. And it renounces the God who condescends to dwell within us, sent by both the Father and Son. The great irony is that God is willing to do what we are not.
Should the church renounce these roles it will cease to reflect the true nature of the godhead. The writers of the New Testament knew this and made it very clear that in God’s new creation, the roles of men and women have not changed.
We are very much aware that the world is watching us. The great danger is that we will be embarrassed by the gospel of Jesus Christ and decide to preach another. The great privilege remains for us to conform to the image of God himself, honoring him from within the roles that He has given.
This alone puts the wisdom of God on display. It elevates God’s will above our own and invites the world to ask why? To which we must reply “I’m glad you asked; let me tell you about my God”.
1 These roles should therefore never be confused with or compared to those things that human beings have put in place within culture. God created Mankind (male & female) in his own image. Male and female he created them. He did not create women with veils on nor did he create some men as masters or others as slaves. The presence or absence of these human practices has no bearing on the subject of God-given roles for men and women.
2 The Apostle Paul states that all (created) things are from God the father for whom we exist and all things are through our Lord Jesus Christ, through whom we exist (1st Cor. 8:6). John expresses this same distinction between the roles of God (the Father) and the Word (the Son) in John 1:1-3. The separate roles of Father and Son predate creation. 1st Corinthians 15:28 explains that at the end of time, “The Son himself will be subjected to him who put all things under him, that God may be all in all.” Having ruled and reigned until he has put every enemy under his feet, the Son will hand the kingdom over to the Father, placing himself in subjection again to the Father. No terminal point to the fatherhood of God or the son-ship of Jesus is indicated in this text.
Editor’s Note: this article was first published in the Gospel Herald in the December issue in 2007 and is being republished with the encouragement that congregationss who have dismissed or downgraded the significance of Biblical gender roles will reconsider these in light of their theological roots.


Smartplanet is reporting that current models of 3D printers are emitting concerning quantities of ultrafine particles (UFPs). The news comes on the back of a recent study in Atmospheric Environment on the topic. The study reported emission ranges of 20–200 billion UFPs per minute, depending on the feedstock used.
These levels of emissions are a cause for concern, but come with two caveats. The first is that there isn’t a lot of toxicology information on feedstocks studied, polylactic acid or acrylonitrile butadiene styrene. Second, there are coagulation effects that may reduce the reactivity of the emitted UFPs.
Though these qualifications are signs that we need more research on the topic, the article serves as an important reminder that distributing scientific and manufacturing power also distributes the health and safety issues that come with those tools. There isn’t yet good evidence that with the gradual erosion of economies of scale in manufacturing comes a reduction in the impact of manufacturing. Even if it does, there are still important health issues to be considered when it comes to 3D printing, of which current consumers may not be aware.
This is only going to get more serious. As 3D printing expands, along with DNA synthesis and chemical micro-process devices (subject of a recent, excellent paper by Amy E. Smithson), chemical and biological foundries will continue to miniaturise and find their way into homes. It is alarming that we’re already seeing health concerns with 3D printers, much less these more advanced applications.
We should continue to investigate the health and security impacts of citizen manufacturing, and how we approach the design and sale of these devices in the future. We should also look to consumer education about filtration and air ventilation as these devices continue to device to proliferate. 3D printers and their ilk are likely here to stay, but we should work to make them as safe to use as possible.
- B. Stephens, P. Azimi, Z.E. Orch, and T. Ramos, “Ultrafine particle emissions from desktop 3D printers,” Atmospheric Environment 79 (2013): 334–339. ↩
- For those interested, the updated version of this paper and its companions was published in J.B. Tucker (2012) Innovation, Dual Use, and Security: Managing the Risks of Emerging Biological and Chemical Technologies (Cambridge, MA: MIT Press). ↩


The Bakken Pipeline, also known as the Dakota Access Pipeline (DAPL) is a very controversial oil pipeline that is currently being constructed, that is being fought for the endangerment of water and soil resources, its proximity to the Standing Rock Reservation of the Sioux Tribe and its cultural resources, and the improper use of eminent domain. Thousands of people have gathered in protests along the pipeline, especially in North Dakota and Iowa. The pipeline is being built across four states, from North Dakota, where shale oil is being extracted, and pumped through South Dakota, Iowa and Illinois, where it will be hooked to an existing pipeline to deliver oil to the Gulf of Mexico.
This map shows the precise location of the pipeline and allows you to locate your current position, shows the current construction progress, properties it crosses and taken by eminent domain, and property owners in a lawsuit with Dakota Access LLC. The diameter of the pipeline is 30 inches, and the 50 ft easement is shown, as well as the temporary 150 ft right of way.
The map is an effort coordinated by Nitin Gadia, a resident of Ames, Iowa, in an effort to support the efforts to inform people about the pipeline, and support the efforts to resist the pipeline, who develops content with mapstory.org, a website dedicated to open mapping data.
Efforts in North Dakota to obtain map data were denied when Dakota Access requested that authorities restrict the data. People have had to rely on hard copies of maps to see where the pipeline lies, and the map was drawn using hundreds of public record maps from each of the states.
The pipeline has been mostly constructed in all states. Construction progress is only reported in Iowa, and was previously updated weekly; since the pipeline has mostly been laid since the last update on 11/16/2016, all of the pipeline has been marked as "mostly complete". Weekly construction maps have been required to be provided to Dakota Access to the Iowa Utilities Board (IUB). Users are encouraged to crowdsource information, like locations of protests and events. For more information about the map and how participate, read the About page and blog post written by Gadia.
For more on the motivation and issues surrounding this map, and to view and obtain an embed, check out the blog post:
Mapping the Bakken Pipeline and Our “Secret” Infrastructure
This map could use your help. It needs to add the precise locations of protests and events. If you're interested in helping, contact Nitin below.
Map license: CC-BY. Credits can be listed as: bakkenpipelinemap.com, Nitin Gadia of MapStory.org, Carl Sack
Github page (for sources, data, collaboration):
nittyjee at gmail dot com


Is it important if you want to impress your significant other on the dance floor? Absolutely. Could it be relevant in other instances? Based on recent research, it sure seems like it!
124 high school students were studied at Northwestern University and the surprising link between music, rhythmic abilities and language skills was published in The Journal of Neuroscience.
Dr. Nina Kraus works shows, for the first time, biological evidence linking the ability to keep a beat to the neural encoding of speech sounds as it has significant implications for reading.
Dr. Kraus was able to demonstrate that accurate beat keeping involves synchronization between the parts of the brain responsible for hearing as well as movement.
Hearing sounds of speech and associating them with the letters comprising written words is crucial to learning how to read, say the Northwestern researchers. They reasoned that the association between reading and beat synchronization likely has a common basis in the auditory system.
Two tests were performed on the subjects. In the first test, they were asked to listen to a metronome and tap their finger along to it on a special tapping pad. Tapping accuracy was computed based on how closely their taps aligned in time to the tick-tock of the metronome.
In the second test, a “brainwave test”, the subjects were fitted to electrodes measuring the consistency of their brain response to a repeated syllable.
The more accurate the subjects were at tapping along to the beat, the more consistent their brain response was to the speech syllable.
Kraus says that rhythm is an integral part of both music and language.
Could it be then that, if we improve coordination and balance, we can improve cognitive performance?


Cleanup work of any kind can be dangerous, but flood conditions make this work even harder. However, following the recommendations set by the Occupational Safety and Health Administration (OSHA) will help keep you safe and healthy while cleaning up. After natural disasters excessive moisture, flooding, and standing water can cause mold growth in buildings. When returning home be aware that mold may be present and can be a health risk.
Cleaning Up Mold:
Porous items, such as, carpeting, carpet padding, upholstery, wallpaper, drywall, ceiling tiles, insulation material, some clothing, leather, paper, some wood and wood products and food, must be removed if they have been wet for more than 48 hours. These items must be removed as these items can remain a source of mold growth. Other wet items and surfaces must be cleaned with detergent and water to prevent mold growth. Do not mix cleaning products together. DO NOT mix bleach and ammonia because it can create toxic vapors. If there is excessive mold, professional cleaners must be hired. When hiring contractors make sure that they are experienced in cleaning mold and are licensed by your state. Check references and ask the contractor to follow the recommendations in the guidelines of the American Conference of Governmental Industrial Hygienists (www.ACGIH.org) or other guidelines from professional organizations or state agencies. Contact your state health department’s website for information about state licensing requirements for contractors in your state.
Other Mold Removal Tips:
- Use fans and dehumidifiers to remove moisture. Do not use fans if mold has already started to grow, because they may spread the mold.
- Ensure that laundry is washed in safe water. If the items are only wet, they can be laundered normally. Adding chlorine bleach to the wash cycle can remove most mildew and sanitize the clothing.
- Nonporous items (e.g., dishes, pots, glass items, and hard plastic items) can be salvaged. However, because floodwaters are contaminated, nonporous items should be washed by hand in a disinfectant and then air-dried. Do not use a dish towel.
- All surfaces of an HVAC system and all its components that were submerged during a flood are potential reservoirs for dirt, debris, and microorganisms, including bacteria and mold. Therefore, all flood water-contaminated and moisture-laden components of the HVAC system should be thoroughly inspected, cleaned of dirt and debris, and disinfected by a qualified professional.
- Take frequent rest breaks when lifting heavy, water-laden objects. Avoid overexertion and practice good lifting techniques. Also, consider using teams of two or more to move bulky items that weigh more than 50 pounds. Or, use a proper automatic lifting assistance device, if practical.
- When working in hot environments, have plenty of water available to drink, use sunscreen and take frequent rest breaks out of the sun. Wear light-colored, loose-fitting clothing.
- Be sure that a first aid kit is available in case of cuts or other small injuries. If you do get hurt while working, protect the injury with waterproof gloves and dressings.
- Wash your hands often during the day, especially before eating, drinking, touching your face or applying cosmetics.
- Before entering a flooded area, use a wooden stick or pole to check for pits, holes and protruding objects.
- Ensure that all ladders and scaffolds are properly secured prior to use.
- Conduct a preliminary worksite inspection to verify stability before entering a flooded or formerly flooded building, or before operating vehicles over roadways or surfaces.
- Do not work in or around any flood damaged building until it has been examined and certified as safe for work by a registered professional engineer or architect.
- Washouts, trenches, excavations and gullies must be supported or their stability should be verified prior to entry. All trenches should be supported with a trench box.
- Establish a plan among employees for contacting medical personnel in the event of an emergency.
- Report any obvious hazards (downed power lines, frayed electric wires, gas leaks or snakes) to the appropriate authorities and your supervisor.
- Use fuel-powered generators outdoors only, as they present a carbon monoxide hazard.
- Use life vests when engaged in activities that could result in deep water exposure.
- Use extreme caution when handling containers holding unknown substances or known toxic substances. If you see any of these hazards, alert your supervisor so he/she can contact the Environmental Protection Agency (EPA) for disposal information.
Personal Protective Equipment (PPE) and Clothing
- Always wear watertight boots with a steel toe and insole, gloves, long pants and safety glasses during cleanup operations; street shoes should not be worn because they cannot protect against punctures, bites or crush injuries. Also wear a hardhat if there is a risk of falling debris.
- Wear a NIOSH-approved dust respirator, if you are working with moldy building materials or with vegetable matter (hay, stored grain or compost).
- When handling bleach or other chemicals, follow the directions on the package and wear eye, hand and face protection. Also have plenty of clean water available for emergency eye washing or other first aid.
- Do not touch downed power lines or any object or water they may be in contact with.
- Treat all power lines as if they are energized until you have specific confirmation that they have been deenergized.
- Beware of overhead and underground power lines when clearing debris. Extreme caution is necessary when moving ladders or other equipment near overhead power lines to avoid accidental contact.
- If damage to an electrical system is suspected (examples: wiring has been under water, you can smell burning insulation, wires are visibly frayed or you can see sparks), turn off the electrical system in the building and follow all lockout/tagout procedures. Do not turn the power back on until the electrical equipment has been inspected by a qualified electrician.
- When using a generator, be sure that the main circuit breaker is OFF and is locked out prior to starting. This will prevent unintentional energization of power lines from back feed electrical energy and will help protect utility line workers from possible electrocution.
- Be aware that de-energized power lines may become energized by a secondary power source.
- Any electrical equipment used in wet environments must be marked for use in wet locations and must be undamaged. Be sure that all connections are out of water.
- All cord-connected, electrically operated tools and equipment must be grounded or double-insulated.
- Ground-fault circuit interrupters (GFCIs) must be used in all wet locations.
- Immediately evacuate any building that has a gas leak until it is controlled and the area is ventilated.
- Be sure that an adequate number of fire extinguishers are available. Be sure that all fire exits are clear of debris and sandbags.