Only a subset of proteins in a cell at a given time is expressed. Genomic DNA contains both structural genes , which encode products that serve as cellular structures or enzymes, and regulatory genes , which encode products that regulate gene expression. The expression of a gene is a highly regulated process.
Elucidating the mechanisms controlling gene expression is important to the understanding of human health. Malfunctions in this process in humans lead to the development of cancer and other diseases. Understanding the interaction between the gene expression of a pathogen and that of its human host is important for the understanding of a particular infectious disease.
These interactions lead to the expression of some genes and the suppression of others, depending on circumstances. Prokaryotes and eukaryotes share some similarities in their mechanisms to regulate gene expression; however, gene expression in eukaryotes is more complicated because of the temporal and spatial separation between the processes of transcription and translation. Thus, although most regulation of gene expression occurs through transcriptional control in prokaryotes, regulation of gene expression in eukaryotes occurs at the transcriptional level and post-transcriptionally after the primary transcript has been made.
In bacteria and archaea , structural proteins with related functions are usually encoded together within the genome in a block called an operon and are transcribed together under the control of a single promoter , resulting in the formation of a polycistronic transcript Figure 1. In this way, regulation of the transcription of all of the structural genes encoding the enzymes that catalyze the many steps in a single biochemical pathway can be controlled simultaneously, because they will either all be needed at the same time, or none will be needed.
For example, in E. For this work, they won the Nobel Prize in Physiology or Medicine in Although eukaryotic genes are not organized into operons, prokaryotic operons are excellent models for learning about gene regulation generally. There are some gene clusters in eukaryotes that function similar to operons. Many of the principles can be applied to eukaryotic systems and contribute to our understanding of changes in gene expression in eukaryotes that can result pathological changes such as cancer.
Figure 1. In prokaryotes, structural genes of related function are often organized together on the genome and transcribed together under the control of a single promoter. If a repressor binds to the operator, then the structural genes will not be transcribed. Alternatively, activators may bind to the regulatory region, enhancing transcription.
Each operon includes DNA sequences that influence its own transcription; these are located in a region called the regulatory region. The regulatory region includes the promoter and the region surrounding the promoter, to which transcription factors , proteins encoded by regulatory genes, can bind.
Transcription factors influence the binding of RNA polymerase to the promoter and allow its progression to transcribe structural genes.
A repressor is a transcription factor that suppresses transcription of a gene in response to an external stimulus by binding to a DNA sequence within the regulatory region called the operator , which is located between the RNA polymerase binding site of the promoter and the transcriptional start site of the first structural gene.
Repressor binding physically blocks RNA polymerase from transcribing structural genes. Conversely, an activator is a transcription factor that increases the transcription of a gene in response to an external stimulus by facilitating RNA polymerase binding to the promoter.
An inducer , a third type of regulatory molecule, is a small molecule that either activates or represses transcription by interacting with a repressor or an activator. In prokaryotes, there are examples of operons whose gene products are required rather consistently and whose expression, therefore, is unregulated.
Such operons are constitutively expressed , meaning they are transcribed and translated continuously to provide the cell with constant intermediate levels of the protein products. Such genes encode enzymes involved in housekeeping functions required for cellular maintenance, including DNA replication, repair, and expression, as well as enzymes involved in core metabolism. In contrast, there are other prokaryotic operons that are expressed only when needed and are regulated by repressors, activators, and inducers.
Prokaryotic operons are commonly controlled by the binding of repressors to operator regions, thereby preventing the transcription of the structural genes. Such operons are classified as either repressible operons or inducible operons. Repressible operons, like the tryptophan trp operon, typically contain genes encoding enzymes required for a biosynthetic pathway.
As long as the product of the pathway, like tryptophan, continues to be required by the cell, a repressible operon will continue to be expressed. However, when the product of the biosynthetic pathway begins to accumulate in the cell, removing the need for the cell to continue to make more, the expression of the operon is repressed. Conversely, inducible operons , like the lac operon of E. These enzymes are only required when that substrate is available, thus expression of the operons is typically induced only in the presence of the substrate.
When environmental tryptophan is low, the operon is turned on. This means that transcription is initiated, the genes are expressed, and tryptophan is synthesized. However, if tryptophan is present in the environment, the trp operon is turned off.
Transcription does not occur and tryptophan is not synthesized. When tryptophan is not present in the cell, the repressor by itself does not bind to the operator; therefore, the operon is active and tryptophan is synthesized. However, when tryptophan accumulates in the cell, two tryptophan molecules bind to the trp repressor molecule, which changes its shape, allowing it to bind to the trp operator.
This binding of the active form of the trp repressor to the operator blocks RNA polymerase from transcribing the structural genes, stopping expression of the operon. Thus, the actual product of the biosynthetic pathway controlled by the operon regulates the expression of the operon. Figure 2. The five structural genes needed to synthesize tryptophan in E.
When tryptophan is absent, the repressor protein does not bind to the operator, and the genes are transcribed. When tryptophan is plentiful, tryptophan binds the repressor protein at the operator sequence. This physically blocks the RNA polymerase from transcribing the tryptophan biosynthesis genes.
The lac operon is an example of an inducible operon that is also subject to activation in the absence of glucose Figure 3. The lac operon encodes three structural genes necessary to acquire and process the disaccharide lactose from the environment, breaking it down into the simple sugars glucose and galactose.
For the lac operon to be expressed, lactose must be present. This makes sense for the cell because it would be energetically wasteful to create the enzymes to process lactose if lactose was not available. In the absence of lactose, the lac repressor is bound to the operator region of the lac operon, physically preventing RNA polymerase from transcribing the structural genes.
However, when lactose is present, the lactose inside the cell is converted to allolactose. Allolactose serves as an inducer molecule, binding to the repressor and changing its shape so that it is no longer able to bind to the operator DNA. Removal of the repressor in the presence of lactose allows RNA polymerase to move through the operator region and begin transcription of the lac structural genes. Figure 3. The three structural genes that are needed to degrade lactose in E. When lactose is absent, the repressor protein binds to the operator, physically blocking the RNA polymerase from transcribing the lac structural genes.
These in silico evolved promoter functions, however, still behaved bistably with respect to artificial inducers. Indeed, the in silico evolved promoter function resembled the experimentally measured promoter function. Here we study how noise in gene expression influences the adaptation of the lac operon promoter function, both on a physiological and an evolutionary time scale.
We use a computational approach to tackle this problem. We modified the previously developed deterministic model [ 10 ] for the evolution of the lac operon to include stochasticity in gene expression. This model is spatially explicit and consists of cells that grow on glucose and lactose, divide, and die.
The intracellular model consists of detailed differential equations describing lac operon transcription, translation, and metabolism, with parameters taken from literature. The cells evolve the parameters which determine the lac operon promoter function and in this way adapt to the fluctuating environment.
Importantly, the cells can in this way also adapt to the constraints that are imposed by the fixation of the other parameters.
In our view, this is a good way to cope with the inevitable parameter uncertainty. See Materials and Methods for a more detailed description of the model. We added stochasticity in gene expression on the protein level. We assumed that protein production occurs in bursts, as is experimentally observed [ 7 ]. The amount of protein produced per burst i. This observation suffices to make our deterministic model stochastic, as is explained in the Materials and Methods section. Protein degradation is modeled binomially.
When a cell divides, the number of proteins is divided between the two cells in a binomial way. In this way we added stochasticity without introducing any unknown parameter. By comparing the deterministic and stochastic models, we can directly observe the consequences of stochasticity on the lac operon, which is experimentally difficult, because the lac operon is inherently stochastic.
We compared the amount of noise in gene expression in our model with experimentally observed values of noise for the lac operon [ 2 ] and found that noise in gene expression in our model is comparable to the experimentally observed noise. These noise values were measured using IPTG. The positive feedback loop is much weaker for lactose than for artificial inducers such as IPTG. Accordingly, we find that noise values for lactose are much lower than for IPTG. Therefore, the effect of stochasticity on evolution of the lac operon might be lower than what would be expected from these experiments.
In experiments where stochasticity in gene expression is measured, isogenic populations in well-mixed systems are considered in order to exclude all other sources of population heterogeneity. When we want to investigate the importance of stochasticity in gene expression in natural circumstances, we should, however, also take these other sources of population heterogeneity into account.
Therefore, by using a spatially explicit model of cells that evolve their lac operon promoter function, spatial and genetic heterogeneity are automatically taken into account. We find that both genetic and spatial heterogeneity contribute more to population heterogeneity than stochasticity in gene expression. To explore the effect of stochasticity on evolution of the lac operon, we compared the results of the evolutionary simulations between the stochastic and the deterministic models [ 10 ].
We found that in the stochastic simulations, cells evolve a higher repressed transcription rate than in the deterministic model. Therefore, the promoter functions that evolved in the deterministic model experience more stochasticity when placed in the stochastic model than the promoter functions that evolved in the stochastic model.
We show that this causes a reduction of fitness compared with the promoter functions evolved in the stochastic model, due to an increase in delay in lactose uptake. We conclude that in the stochastic model, the promoter functions evolve to minimize stochasticity in gene expression. Indeed, stochasticity, when growing on lactose, is relatively unimportant for the dynamics of these evolved promoter functions, except sometimes at high glucose, low lactose concentrations.
The dynamics when growing on lactose can well be described using a deterministic model. When modeling the dynamics of induction with artificial inducers, stochasticity, however, is much more important, due to the stronger positive feedback, and should be incorporated. First we studied how stochasticity in gene expression influences noise in gene expression. The promoter function of the cell in large part determines the amount of stochasticity a cell experiences, because stochasticity is higher at low protein levels.
Therefore, promoter functions with low repressed transcription rates experience more noise than promoter functions with high repressed transcription rates. It has been shown that noise in gene expression can be split up into two orthogonal components, intrinsic and extrinsic noise, such that [ 11 ].
Extrinsic noise is all noise that would affect two identical, independent copies of one gene in a single cell in exactly the same way, and intrinsic noise is noise that causes differences in expression levels of identical copies in a single cell. The amount of intrinsic and extrinsic noise of lac -repressible promoters in different E.
This was done by placing two genes, coding for two fluorescent proteins, which are controlled by identical promoters, in an E. The intrinsic and extrinsic noise can now be simultaneously measured, by measuring how the protein levels fluctuate. We performed similar simulations to validate the stochastic model with these experiments. We initiated a population of induced or repressed cells solid and dotted lines, respectively, in Figure 1 in a homogeneous environment with a certain extracellular inducer concentration.
As in the experiments, spatial and genetic heterogeneity are absent. We waited for 41 hours, more than enough time for cells to go to equilibrium in the deterministic model. Then we calculated the noise in the protein number in the population. Noise levels were obtained in the same way as in the experiments. We kept track of the activity of two independent, identical lac -repressible genes that do not have a function in lactose uptake.
The red lines indicate intrinsic noise, the green lines extrinsic noise, and the blue lines total noise. The filled dots indicate the experimentally observed noise levels, adapted from [ 2 ]. Solid lines indicate that cells are initially induced, dotted lines that cells are initially repressed. The maximum in the extrinsic noise is shifted to lower protein numbers. C Noise levels in the model using lactose as inducer default model , leading to much lower extrinsic noise.
Inducer concentrations are scaled relative to the binding affinity of the inducer with LacI, the repressor protein of the operon. The black curves indicate the mean protein number. Because we did not introduce any free parameter in the model when introducing stochasticity, noise levels only depend on the promoter function used. As a comparison, for the wild-type lac promoter function, the repression rate has been reported to be [ 9 ].
Furthermore, we used a Hill-coefficient of 4. For the growth rate, we took 0. The induced transcription rate of the operon in these simulations is equal to the maximal transcription rate we imposed during the evolutionary experiments. The experiments were done using IPTG, an artificial inducer of the lac operon. This changes the dynamics, hence the noise, of the system considerably. Our model describes operon dynamics with lactose as inducer.
It is known that IPTG also enters the cell in the absence of permease. This is not taken into account in our model describing lactose dynamics and hence we add a permease-independent influx term for IPTG see Materials and Methods. The amount of permease independent influx we chose is such that the maximum in the total noise is similar to that in the experiments. The intrinsic noise found in our simulations is almost identical to the experimentally observed intrinsic noise.
Intrinsic noise levels in the model only depend on the number of proteins. This figure also confirms that the induced transcription rate we used has the right order of magnitude.
It has been reported that the maximal in vitro transcription rate is approximately 0. Qualitatively, the extrinsic noise corresponds with the experimentally observed noise. The maximum in the extrinsic noise is caused by the positive feedback loop in the lac operon. Fluctuations due to the intrinsic noise are amplified by the positive feedback, but only at intermediate inducer hence protein concentrations, where the promoter function is steepest.
Note that the cell cycle and the intracellular inducer concentration are the only extrinsic noise sources we included in the model. The maximum in the extrinsic noise is located at lower protein concentrations in the data than in our model.
This is because the extrinsic noise is high if the positive feedback is strong. Sufficient positive feedback can only be accomplished if the protein-dependent and protein-independent inducer influx are of the same order of magnitude. Therefore, when the protein-independent inducer influx is high, the maximum in the extrinsic noise will be located at high protein concentrations.
We can reproduce the experimental data better if we assume a lower growth rate or a higher protein-dependent inducer efflux.
Both these changes diminish the positive feedback and therefore we need a smaller protein-independent influx to fit the maximum amount of extrinsic noise. Therefore, the maximum in extrinsic noise will also be shifted to lower protein concentrations.
We obtained these curves for a protein-independent inducer influx k IPTG of 0. For lactose as inducer, the picture is very different Figure 1 C. The intrinsic noise remained unchanged, but extrinsic noise changed considerably. There is still a maximum in extrinsic noise, but this is barely visible. Indeed, the operon used is monostable for lactose. For lactose, we found that extrinsic noise is almost completely determined by the cell cycle for all protein numbers, instead of only for high protein numbers as we found for IPTG.
We conclude that the results of the experiments can only be understood when we realize that IPTG was used as an inducer. When lactose as inducer is used, extrinsic noise levels as high as in the experiments can in our model only be observed when the repressed transcription rate is considerably lower.
Finally, we tried to simulate noise in gene expression for TMG, another artificial inducer. Therefore, the positive feedback loop is stronger for TMG. We observe that the extrinsic noise increases drastically Figure 1 D , while the intrinsic noise again remains unchanged. Indeed, the stronger positive feedback loop increases extrinsic noise.
For IPTG, however, bistability is expected to be much less severe [ 9 ]. We find that the experimentally observed noise can best be described by a promoter function that is just bistable for IPTG. This can be seen when we compare the amount of noise for initially induced and repressed cells. Although all individual cells are in equilibrium, the results are different when we start with an initially induced population or an initially repressed population.
For TMG, we also find that the promoter function is much more bistable. The hysteresis-loop, indicating that for certain extracellular inducer concentrations the amount of proteins is dependent on the history of the cells, is clearly visible. Furthermore, we see that when inducer concentrations are low, transitions from the induced to the repressed equilibrium are more likely, and vice versa.
In the previous section, we showed that stochasticity in gene expression can cause significant amounts of noise when the operon is repressed. These experiments and simulations were done using cells with identical promoters in a well-mixed environment.
In natural and evolving populations, different cells will have slightly different promoter functions, due to genetic variation, and the environment will not be well-mixed [ 17 , 18 ]. Both these factors can cause population heterogeneity, but are neglected in almost all experiments.
This makes sense if we want to study whether stochasticity in gene expression occurs at all. Stochasticity in gene expression can only be proven when gene expression is different in two identical cells in an identical environment.
For the importance of stochasticity in natural circumstances, however, other factors causing population heterogeneity need to be considered. We embedded the intracellular stochastic model of lac operon dynamics in an evolutionary, spatial context, as described in the Materials and Methods section and in more detail in [ 10 ]. We used this stochastic model and the deterministic model [ 10 ] to unravel the contributions of the various factors on population heterogeneity.
To this end, we performed evolutionary simulations in both a spatial and a well-mixed environment, for both the stochastic model and the deterministic model. In these simulations, cells evolve their promoter function in an environment in which the glucose and lactose concentrations fluctuate. To understand the effect of genetic diversity, we also performed simulations using a genetically identical population. We used the last common ancestor the last individual cell that had the whole population at the end of a simulation as offspring of each evolutionary simulation for this.
In this way, we can compare the effects when genetic variation, spatial variation, both, or none are incorporated, in both the deterministic model Figure 2 A and the stochastic model Figure 2 B , yielding eight different simulations.
Different colors represent different simulations. All dots indicate the population heterogeneity at certain equally spaced timepoints. Solid lines give the result of a power-law regression between these dots. Black: an evolutionary simulation in a spatial environment, both genetic and spatial heterogeneity, evolutionary timescale.
Red: an evolutionary simulation in a well-mixed environment, genetic heterogeneity, but no spatial heterogeneity, evolutionary timescale.
B Population heterogeneity in the stochastic simulations. All colors are as in Figure 2 A, except yellow: regression curve of intrinsic noise versus average protein number from Figure 1. Of the four sources of population heterogeneity in our model, spatial, genetic, stochastic, and cell cycle related, we can exclude all, except for the cell cycle. When all these three noise sources were excluded, we still observed some population heterogeneity, but it was completely independent of protein number Figure 2 A, blue dots.
The population heterogeneity varied wildly over time, due to the partial synchronization of the cells. Sometimes all cells have just divided, and population heterogeneity is very low. When only half of the population has recently divided, population heterogeneity is maximal.
This explains the extremely broad distribution of blue dots in Figure 2 A. When genetic or spatial heterogeneity was present, very low values of population heterogeneity did not occur anymore Figure 2 A, red, green, and black dots. When these sources of population heterogeneity were present, population heterogeneity became inversely correlated with protein number. It is clear that in our model, space has a larger effect on population heterogeneity than genetic variation see Figure 2 A, red and green dots.
When we compare population heterogeneity in the deterministic model Figure 2 A with the population heterogeneity in the stochastic model Figure 2 B , we find, as expected, the largest difference when spatial and genetic heterogeneity are both absent. Intrinsic noise Figure 2 B, yellow line gives a lower boundary to the population heterogeneity in the stochastic model. The mean population heterogeneity is increased considerably by stochastic gene expression.
When genetic or spatial heterogeneity was present in the stochastic model Figure 2 B, red and green , we observed, however, that much of the difference in population heterogeneity between the deterministic model and the stochastic model disappeared. Population heterogeneity due to stochastic gene expression, therefore, apparently is small compared with population heterogeneity due to spatial and genetic variation.
Intrinsic noise, as shown in the previous section, follows power law behavior with respect to protein number, with a coefficient of 0. Surprisingly, both in the deterministic model Figure 2 A and the stochastic model Figure 2 B we see that if spatial or genetic variation is present, the data can still reasonably be described using a power law. In Table 1 , we give the regression and correlation coefficient of a power law regression of the data.
Regression and Correlation Coefficients. The regression coefficient indicates how strong population heterogeneity and protein number are correlated. The more sources causing population heterogeneity, the higher the regression coefficient is. Genetic heterogeneity correlates with protein number because the selection pressure on the induced operon is higher than on the repressed operon. The reason for this is that the cost for promoter activity is much more important for the induced operon than for the repressed operon.
This appears to be a reasonable assumption that is likely to hold in the natural environment of E. Population heterogeneity due to space is largest at intermediate extracellular inducer concentrations. At very high inducer concentrations, noise in the inducer concentrations does not cause noise in gene expression, because of the sigmoid shape of the promoter function.
This also holds for very low extracellular inducer concentrations. For intermediate inducer concentration, gene expression is very much influenced by spatial heterogeneity. We observed, however, a monotonic relationship between protein number and noise due to spatial heterogeneity.
This is because when the promoter activity of cells becomes low, cells stop lactose consumption, and therefore cells never experience very low lactose concentrations. This effect is likely to play a role in the natural environment, but in the natural environment, lactose degradation is probably not only due to E. From all this we expect that only in a monomorphic population, living in a well-mixed environment, does stochasticity in gene expression play an important role.
Whether stochasticity influences evolution, however, is therefore doubtful. To study whether stochasticity does or does not play an important role in evolution, in the next section we compare evolution of the lac operon in the stochastic and deterministic models. We do this in a well-mixed environment, because there stochasticity is expected to have the largest influence. Fecal samples were collected and weighed daily. When grown in MacConkey, E.
To assess if the lac operon confers an advantage to E. For the remaining colonizations, the first 3 days were considered. As for the number of generations per day, we considered this value to be 18 based on the previous estimation of min generation time for E. Deblur was used for quality filtering and denoising Amir et al. The generated table of ASVs was then used in the R package phyloseq McMurdie and Holmes, to determine the Bray-Curtis dissimilarity index, using rarefaction based on the sample with the lowest sequencing depth.
The observed ASVs were also calculated in QIIME2 with diversity core-metrics-phylogenetic and diversity alpha-group-significance , also using rarefaction based on the sample with the lowest sequencing depth. All graphical representations were performed in GraphPad Prism 8. The detailed statistics and sample size for each experiment are described in the figure legends.
The selective advantage conferred by the ability to metabolize a given nutrient is expected to change with its relative abundance, its energetic potential, and the amount of competition for that nutrient. Here we evaluated the selective advantage conferred by the lac operon to an E. This procedure maintains a complex microbiota while allowing for E. Figure 1. The advantage of the lac operon is dependent on diet and the microbiota composition.
Figure 2. The selective advantage provided by the lac operon in the presence of lactose increases with microbiota complexity. The effect of the chosen antibiotic regime was assessed by estimating the Bray-Curtis beta diversity, a measure of group heterogeneity, before and after antibiotic treatment in an independent set of 5 animals. These results led us to conclude that the lac operon can afford a significant advantage to an E.
To isolate the effect of lactose and test for the influence of a microbiota diversity to the selective coefficient of the lac operon, we engaged in a series of colonizations within a range of microbiota diversities. These comprised a mono, double and a triple colonization. A group of animals continuously treated with antibiotic 7 days was further included, representing a complex yet simpler microbiota than the group treated only for a short period 1 day. Although not statistically significant, after antibiotic treatment the two regimes differed in microbiota richness, with an average of 20 continuous regime and 26 1 day regime ASVs Supplementary Figure 1C and Supplementary Table 1.
These microbiota compositions likely represent different levels of competition to E. Interestingly we observed that when E. Though it could be hypothesized that in this simple environment the available glucose could preclude the expression of the lac operon by catabolite repression this seems unlikely since glucose is less abundant in the cecum of monocolonized than in SPF mice Barroso-Batista et al. We proceeded by co-colonizing GF animals with E.
As before, the lac operon conferred no particular advantage both in the presence or absence of lactose Figures 1E,F , 2. Therefore, to further increase the competition level, we performed a triple colonization of GF animals with equal amounts of E. Nevertheless, we cannot rule out the possibility that B. Coherently, in the context of continuously antibiotic treated mice and in the presence of lactose, the effect of the lac operon was further increased showing a mean advantage of 4. Globally, these experiments demonstrate that the benefit of the lac operon is potentiated by the presence of lactose and increases with the number of co-colonizers Figures 2B,C.
Increasing microbiota diversity likely promotes competition but it also raises the probability of synergism, e. Here we observe that E. Specifically, when comparing the double with the mono colonization we observed a non-significant but sustained increase in the average loads of E. Upon 5 days of colonization E. Figure 3. The total E. Average E. The effects of the microbiota composition and time on the total E. In day 5, E. In day 6, E. These data suggest that E.
In contrast, the expansion of E. The nearly ubiquitous presence of the lac operon in E. In contrast, it has it has been shown that lactose consumption is not essential for E. Therefore, our results suggest that the strong interspecies competition for nutritional resources that occurs in these settings Coyte et al. The emergence of constitutive mutants for lactose consumption during the first days of life was observed in a controlled experiment Ghalayini et al. Besides the presence of lactose, the fitness advantage of the lac operon for E.
One way to interpret this result is to consider that an increasing number of species increases the opportunity for more competitive interactions. Thus, the ability to consume lactose would become a bigger advantage as other nutritional sources get depleted by the growing number of competitors. On the other hand, as the number of species increases, so does the opportunity for synergism, with the absolute success of E.
The observation that the population size of E. This is consistent with the notion that E. This seems to occur regardless of the ability to metabolize lactose, and it is independent of the availability of that additional carbohydrate. In contrast to our findings, in a scenario of DSS-induced colitis E. Here the oral administration of these species was enough to reduce the overgrowth of E.
The higher microbiota complexity of the animals in the referred study when compared to ours, as well as potentially different strains, may account for this difference. Conversely, in the presence of a complex microbiota several tens of species , its absolute success decreased and the most likely scenario was one dominated by competition Coyte et al. A scenario where the population size of E. Surprisingly, when comparing the mono with the triple colonization, lactose showed to be more advantageous in the situation where E.
Future work should address this issue, possibly through investigating the geographic distribution of bacteria abundances and possible differences in the lac operon selective advantage along the intestinal tract.
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