# Statistically, why is the number of mutated genes in eggs treated with chemical mutagenesis one?

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Excerpted from the Guide to Research Techniques in Neuroscience [1]:

In chemical mutagenesis, a scientist applies a mutagenizing chemical, such as ethyl methane sulfonate (EMS) or N-ethyl-N-nitrosourea (ENU), to thousands of eggs/larvae, which statistically creates lines of ani- mals with mutations in a single gene in the genome.

My hypothesis is that the discrete probability distribution of the number of mutated genes can be approximated by a normal distribution with mean=1, thus it is said statistically the number of mutated genes is one. But how can the scientists know which organism or cells contains only one mutated gene, or for that matter one mutated gene that is caused only by chemical mutagenesis?

[1] Carter, Matt, and Jennifer C. Shieh. Guide to Research Techniques in Neuroscience. Academic Press, 2015. ISBN: 978-0-12-374849-2

The expected number of mutation would not follow normal distribution (ND) as you speculated because a ND would have negative values too as it ranges from \$(-infty,infty)\$, as Remi has also pointed out. In many cases a ND can be approximated because the variance would be so less that you can practically find no negative values. However, it is a wrong assumption to consider all biological statistics as ND by default. Please see this post. Basically, ND approximations can be made on multiple measurements that follow the central limit theorem. Now, in your case of a ND centered at 1, I'll tell you how that is impossible. You can have 2 and more than 2 mutations but you cannot have less than 0 mutations. The distribution is not symmetric and is skewed towards right. You also cannot have fractional mutations and therefore the distribution has to be discrete and not continuous.

Mutagenesis itself can be modelled as a Poisson process. For more information on this please see this post. So the probability of \$k\$ mutations in a time window, \$t\$, can be represented by the following equation:

\$\$P(n=k)=frac{(lambda t)^ke^{-lambda t}}{k!}\$\$

Where \$lambda\$ is the rate of mutagenesis.

The mean number of mutations (and also the variance for a Poisson distribution) would be \$lambda t\$.

Now, the rate of mutagenesis would be proportional to the concentration of the mutagen. I speculate that the relationship between them would follow a saturation kinetics (like Michaelis-Menten) but at lower concentrations it would be essentially linear.

Moreover, the rate of mutagenesis would also depend on the cell type.

Therefore, standardization is required and labs working in this area for a long time develop standardized protocols (with specific mutagen concentrations and treatment times) which would let them avoid multiple mutations. Even then, they have to screen a lot of individuals to filter out the non-mutants.

Basically, there is no magic number.

With the forward genetic screen approach you would treat the organism with your mutagen, and cross them to produce mutants. With forward genetics, you're using a phenotype to map out a gene. You isolate the mutants based on phenotype, and perform a complementation test to determine if the mutation was on the same gene or different genes. This was classically done with Drosophila.

By the classical genetics approach, a researcher would then locate (map) the gene on its chromosome by crossbreeding with individuals that carry other unusual traits and collecting statistics on how frequently the two traits are inherited together. Classical geneticists would have used phenotypic traits to map the new mutant alleles. Eventually the hope is that such screens would reach a large enough scale that most or all newly generated mutations would represent a second hit of a locus, essentially saturating the genome with mutations. This type of saturation mutagenesis within classical experiments was used to define sets of genes that were a bare minimum for the appearance of specific phenotypes. However, such initial screens were either incomplete as they were missing redundant loci and epigenetic effects, and such screens were difficult to undertake for certain phenotypes that lack directly measurable phenotypes. Additionally a classical genetics approach takes significantly longer.

Source: Wikipedia

The reason that I posted this answer is due to the context of chemical mutagenesis, provided on 335 of your source:

Chemical mutagenesis The use of chemical agents, such as EMS or ENU, to mutagenize hundreds or thousands of eggs/larvae for the purpose of performing a forward genetic screen.

What I think the text is saying

The text you quote is a little unclear (note that it is not a peer-reviewed article given the language used). I would think based on the quotation that the treatment is chosen so that the expected number of mutations is 1.

But how can the scientists know which organism or cells contains only one mutated gene?

You assume they are screening through the lines to find out those who contain a single mutation. This is not what the quoted text is claiming. The quoted text only states that the treatment create mutations at a rate of 1 per genome.

If they would have to screen through the lines to select those that have had one single mutation somewhere, then sequencing would be the only solution.

Note on Stats

The number of mutated genes after treatment is probably Poisson distributed, not normally distributed. A normal distribution is a continuous probability distribution anyway and is bounded between \$-infty\$ and \$+infty\$, while a negative number of mutations makes no sense.

Note on the design of the post

You should link to you source directly. It will be easier for those willing to answer

## Direct quantification of in vivo mutagenesis and carcinogenesis using duplex sequencing

Error-corrected next-generation sequencing (ecNGS) can be used to rapidly detect and quantify the in vivo mutagenic impact of environmental exposures or endogenous processes in any tissue, from any species, at any genomic location. The greater speed, higher scalability, richer data outputs, and cross-species and cross-locus applicability of ecNGS compared to existing methods make it a powerful new tool for mutational research, regulatory safety testing, and emerging clinical applications.

## MATERIALS AND METHODS

Stem population: In October 1998, we started a panmictic laboratory population of D. melanogaster from 50 mated females sampled from a wild population in Ithaca, NY. This population was kept under 16° for three generations before the start of the experiment.

Cultural condition: Unless otherwise specified, flies were grown under a 12/12 light cycle, at 25° and 75% humidity. We used 95 × 25-mm vials with 10 ml of medium containing 10 g agar, 80 g brewer’s yeast, 80 g glucose, and 8 ml propionic acid per liter of water, seeded with few grains of live yeast. CO2 anesthesia was used when handling the flies.

EMS mutagenesis: In January 1999, ∼500 males were sampled from the stem population. Males were kept without food and water for 16 hr and then placed for 20 hr in vials with filter paper soaked with EMS solution (21.2 m m ) in 2% sucrose (A shburner 1989). Six hours after this treatment, these males were “premated” with virgin females, with whom they spent 24 hr, to induce sperm turnover and increase the yield of mutations (A shburner 1989). These females were discarded, and the males were mated again, to produce offspring for further analysis.

Detecting mutations at five eye-color loci: A total of 200 EMS-treated males were mated with 200 females homozygous for the following five recessive alleles that affect eye color: pr 1 , cn 1 , bw 1 , st 1 , and kar 1 . We set up 100 vials, each containing 2 males and 2 females. Once ∼100 eggs were laid in a vial, the parents were discarded. Thus, because the carrying capacity of a vial is ∼300 flies, competition among the offspring was weak. The offspring in each vial were counted daily and screened for eye color mutants.

Production of flies for assaying quantitative traits: A total of 200 EMS-treated males were mated individually and randomly with wild-type virgin females from the stem population (T matings). Simultaneously, 200 untreated males and 200 virgin females from the stem population were also mated individually and randomly (U matings). Parents of T and U matings were removed after 3 days and 3-4 offspring of each sex were collected separately from each sibship. The offspring from different T and U matings were mated individually and randomly to make all four possible types of crosses: T × T, T × U, U × T, and U × U (the first symbol corresponds to the origin of a mother, and the second symbol corresponds to the origin of a father). Also, in some cases we made the crosses between sibs produced in the same U mating (U × UInbr). Parents were kept together for 3 days, after which they were transferred to fresh vials and kept there for 1 day to lay eggs. The offspring from these crosses (F-flies) were used for all fitness assays, except the developmental time. Thus, they were handled with care, using very light CO2 anesthesia.

Developmental time: The parents used to make the four types of crosses (see above) were then merged into sets of 10 females and 10 males per vial, and each group was allowed to lay eggs for 2 hr. These eggs were then put under either 25° or 20° and permanent light. For each vial, we counted the emerging flies every hour.

Numbers of recessive X-linked lethal mutations in F-females

Viability: We followed the procedures of S habalina et al. (1997) with some modifications. Two- to 3-day-old virgin F-flies from the four crosses were mated with males from the stem population and kept at low density for 3 days. The reference line used for competition with all the experimental larvae was marked with the homozygous bw 1 allele, outbred, and was genetically similar to our stem population. Females from the reference line were of the same age and were treated in the same way but were mated with the reference line males. Previously mated 5- to 6-day-old F-females and the reference line females were placed together, without males, for 2 days. Each vial contained either 4 or 8 females of each kind. At noon of day 3, females from each vial were transferred, without anesthesia, into narrow vials (95 × 20 mm) containing poor food (20 g brewer’s yeast, 30 g glucose, 10 g agar and 0.2% propionic acid per liter of water), and allowed to lay eggs for 24 ± 0.1 hr. On day 4 at noon, females from each small vial were again transferred to a big vial (95 × 28 mm) containing the standard good food for 4 ± 0.1 hr to lay eggs before being discarded. When the offspring of these females started to eclose, numbers of wild-type and brown-eyed flies were daily counted and removed from each vial for 3 days.

Fecundity: Virgin F-flies from each of the four crosses were kept under low density (∼25 flies per vial) for 3 days. After this, each female was mated individually with two males from the stem population and kept with them for 3 days. Then, these families were transferred, in the course of 40 min and without anesthesia, into fresh vials and females laid eggs for 24 ± 0.1 hr before being removed. Male and female offspring of each female were counted.

Lethal mutations on X chromosome: The data on fecundity were also used to detect lethal mutations. We concluded that a sibship was produced by a mother heterozygous for an X-linked recessive lethal if the number of male offspring was so low that the hypothesis that the sex ratio is 1:1 can be rejected with 95% confidence.

Longevity: Virgin F-flies were collected and kept separately under low density and optimal conditions for 3-4 days. After this, they were transferred to Plexiglas boxes. Each 150 mm × 150 mm × 150 mm box contained 300 flies of the same sex. Flies were kept at 25° and 70% humidity. The food was provided in a small petri dish at the bottom of the box and changed daily. Dead flies were removed and recorded daily.

Metabolic rates: The 5- to 6-day-old F-flies were anesthetized lightly using N2, sexed, and placed in vials. We then sealed each vial with a rubber stopper. Flies quickly recovered and were able to fly within 5 min of being anesthetized. The vials were flushed for 15 sec at a flow of 90 ml/min with CO2-free water-saturated (100% relative humidity) room air. The flies were left sealed in the chambers for 1 hr at 24.5°. A 1.1-ml (standard temperature and pressure) gas sample was then removed from the vial with a syringe and injected into a Sable System TR-2 carbon dioxide gas respirometry system. The vial was then reflushed with CO2-free air and a second sample was taken 1 hr later. The amount of CO2 produced by each fly was calculated using DATACAN software. The average of these two measurements was used.

Means and standard errors of developmental time (in hours) of F-flies

Motility: F-males were kept under low density and optimal conditions for 3 days, after which their motility was assayed by escape response as described in S habalina et al. (1997). In short, the escape response was measured as follows. A set of 10 males was placed in a small compartment at the top of the experimental tube (500 mm × 40 mm × 40 mm), and 30 sec later the tube was turned upside down, and the sliding wall separating the compartment from the rest of the tube was removed. The time for each male to climb 100 mm was recorded.

—Cumulative frequency distribution of developmental time of F-flies at two temperatures. (A) Females developed at 20° (B) males developed at 20° (C) females developed at 25° and (D) males developed at 25°.

Body weight: The flies used in the metabolic rate study were later weighed to the nearest microgram on a microbalance.

Means and standard errors of viability of offspring of F-flies

Bristle numbers: Numbers of sternopleural (both sides) and abdominal (the fifth segment) bristles of females that were used for fecundity assays were recorded.

Statistical analysis: Distributions of all the traits did not deviate significantly from normality. The only exception was viability, in which case log-transformation was used. The impact of EMS mutagenesis on the mean of each trait was recorded as a regression coefficient of the trait values on the fraction of EMS-treated genome. The confidence limits of these impacts were determined using the t-test. Possible epistasis among mutations could have been detected by significant deviations from linearity in the dependency of the mean value of a trait on the fraction of the genome treated with EMS. The impact of EMS mutagenesis on the variance of a trait shown as the differences in variances of the trait distributions in F-flies obtained in U × U and T × T crosses was compared. The software package JMP was used for most of the analysis.

—Cumulative frequency distribution of viability of offspring of F-flies under four kinds of conditions. (A) High density and poor food (B) high density and good food (C) low density and poor food and (D) low density and good food.

## Contents

There are different kinds of mutagenic breeding such as using chemical mutagens like ethyl methanesulfonate and dimethyl sulfate, radiation or transposons to generate mutants. Mutation breeding is commonly used to produce traits in crops such as larger seeds, new colors, or sweeter fruits, that either cannot be found in nature or have been lost during evolution. [6]

Exposing plants to radiation is sometimes called radiation breeding and is a sub class of mutagenic breeding. Radiation breeding was discovered in the 1920s when Lewis Stadler of the University of Missouri used X-rays on maize and barley. In the case of barley, the resulting plants were white, yellow, pale yellow and some had white stripes. [7] In 1928, Stadler first published his findings on radiation-induced mutagenesis in plants. [8] During the period 1930–2004, radiation-induced mutant varieties were developed primarily using gamma rays (64%) and X-rays (22%). [4] : 187

Radiation breeding may take place in atomic gardens [8] and seeds have been sent into orbit in order to expose them to more cosmic radiation. [9]

High rates of chromosome aberrations resulting from ionizing radiation and the accompanied detrimental effects made researchers look for alternate sources for inducing mutations. As a result, an array of chemical mutagens has been discovered. The most widely used chemical mutagens are alkylating agents. Ethyl methanesulfonate (EMS) is the most popular because of its effectiveness and ease of handling, especially its detoxification through hydrolysis for disposal. Nitroso compounds are the other alkylating agents widely used, but they are light-sensitive and more precautions need to be taken because of their higher volatility. EMS has become a commonly used mutagen for developing large numbers of mutants for screening such as in developing TILLING populations. [10] Although many chemicals are mutagens, only few have been used in practical breeding as the doses need to be optimised and also because the effectiveness is not high in plants for many.

According to garden historian Paige Johnson

After WWII, there was a concerted effort to find 'peaceful' uses for atomic energy. One of the ideas was to bombard plants with radiation and produce lots of mutations, some of which, it was hoped, would lead to plants that bore more heavily or were disease or cold-resistant or just had unusual colors. The experiments were mostly conducted in giant gamma gardens on the grounds of national laboratories in the US but also in Europe and countries of the former USSR. [11]

In the debate over genetically modified foods, the use of transgenic processes is often compared and contrasted with mutagenic processes. [12] While the abundance and variation of transgenic organisms in human food systems, and their effect on agricultural biodiversity, ecosystem health and human health is somewhat well documented, mutagenic plants and their role on human food systems is less well known, with one journalist writing "Though poorly known, radiation breeding has produced thousands of useful mutants and a sizable fraction of the world's crops. including varieties of rice, wheat, barley, pears, peas, cotton, peppermint, sunflowers, peanuts, grapefruit, sesame, bananas, cassava and sorghum." [7] In Canada crops generated by mutation breeding face the same regulations and testing as crops obtained by genetic engineering. [13] [14] [15] [16] Mutagenic varieties tend to be made freely available for plant breeding, in contrast to many commercial plant varieties or germplasm that increasingly have restrictions on their use [4] : 187 such as terms of use, patents and proposed genetic user restriction technologies and other intellectual property regimes and modes of enforcement.

Unlike genetically modified crops, which typically involve the insertion of one or two target genes, plants developed via mutagenic processes with random, multiple and unspecific genetic changes [17] have been discussed as a concern [18] but are not prohibited by any nation's organic standards. Reports from the US National Academy of Sciences state that there is no scientific justification for regulating genetic engineered crops while not doing so for mutation breeding crops. [5]

Several organic food and seed companies promote and sell certified organic products that were developed using both chemical and nuclear mutagenesis. [19] Several certified organic brands, whose companies support strict labeling or outright bans on GMO-crops, market their use of branded wheat and other varietal strains which were derived from mutagenic processes without any reference to this genetic manipulation. [19] These organic products range from mutagenic barley and wheat ingredient used in organic beers [20] to mutagenic varieties of grapefruits sold directly to consumers as organic. [21]

### Restriction endonucleases Edit

Interest in the use of bacterial restriction endonucleases (RE) to study double-stranded breaks in plant DNA began in the mid-nineties. These breaks in DNA, otherwise known as DSBs, were found to be the source of much chromosomal damage in eukaryotes, causing mutations in plant varieties. REs induce a result on plant DNA similar to that of ionizing radiation or radiomimetic chemicals. Blunt ended breaks in the DNA, unlike sticky ended breaks, were found to produce more variations in chromosomal damage, making them the more useful type of break for mutation breeding. While the connection of REs to chromosomal aberrations is mostly limited to research on mammalian DNA, success in mammalian studies caused scientists to conduct more studies of RE-induced chromosomal and DNA damaged on barley genomes. Due to restriction endonucleases' ability to facilitate damage in chromosomes and DNA, REs have the capability of being used as a new method of mutagenesis to promote the proliferation of mutated plant varieties. [22]

## Results

### Estimating fitness in the mutagenic environment: Deleterious mutations confound the baseline estimate

The fitnesses in Equations 1a and 1b apply to the environment in which the virus is grown while being subjected to mutation. Thus, it is necessary to measure both the baseline fitness, W0, and the final fitness, , in that environment. With T7 and virtually all viruses subjected to mutagenic drugs clinically, that environment is one in which the cells are exposed to mutagen. The problem this presents when parameterizing the model is that measuring W0 in the mutagenic environment introduces mutations, during the assay, that confound a precise estimate of W0.

The fitness consequences of viral growth in the mutagenic environment may be partitioned as follows:

Mutagen impairs bacterial physiology and growth, reducing the number of phage progeny produced by the cell although fewer progeny are produced, the progeny produced are not affected by this mechanism.

Progeny viruses from hosts grown in mutagen potentially have structural defects in their virions these effects are not heritable but they do affect the ability of those progeny to initiate infections.

Replication of viruses in hosts grown in mutagen introduces nonlethal mutations in progeny viral genomes these effects are heritable, affecting fitness across future generations.

Viral replication in hosts grown in mutagen introduces lethal mutations in some progeny progeny with lethal mutations leave no descendants and cannot be counted.

The difficulty is that the nonheritable effects are confounded with heritable effects when measuring (initial) fitness, but the model requires that only the nonheritable effects be included. Suppose the burst size (fitness in this example) of the wild-type genome in the absence of mutagen is 100. The fitness assay conducted in the presence of mutagen reveals a (viable) burst of 30 for the wild type, giving the impression that W0 is 30. However, suppose the host has reduced ability to support phage growth—effects 1 and 2 in the list above—and that the true W0 is 50 lethal mutations kill all but 60% of those progeny. The value of W0 is thus 50, not 100 nor 30. Yet there is no obvious way to disentangle the nonheritable effects of mutagen on the host from the effect of mutagen in killing 40% of the actual progeny. Ignoring the problem and treating the observed 30 as W0 leads to predicting too low of a final fitness hence the model would be rejected even if it was correct. In the case of T7, the initial fitness W0 was based on an assay spanning six generations, so the effect is possibly substantial. How serious, then, is the expected impact of the early mutations?

### The decline in fitness with continual mutagenesis

The fitness impact of mutagenesis is easily calculated under the Poisson model. Johnson (1999) provided a set of recursions by which the impact of progressive mutation may be calculated iteratively, although the formula we need remains to be derived. Let all mutations be deleterious. Within the set of deleterious mutations there are n classes according to their effect size: those with deleterious effect si arise at genomic rate Ui. The combined deleterious rate across all mutations is . We further assume the convenient property that a genome’s fitness declines multiplicatively with its set of mutations. Mean fitness after k generations of mutation and selection is (2) (Appendix). Mean fitness in the first two generations of exposure and selection follows and (for ). is always smaller than except in the extreme case that all mutations are either neutral or lethal. With appropriate limits on the mean and higher-order moments of s, mean fitness declines approximately as the power k early in the process.

The mutation load experienced in the kth generation of mutagenesis is . The residual load, i.e., that experienced beyond generation k, is thus . This residual load is what is measurable in protocols that assay initial fitness during exposure to mutagen, for assays lasting k generations. As , the residual load vanishes even at low k because the full effect of mutation is experienced after few generations of mutagenesis.

From (2), there are important consequences of a mutagenesis protocol using fitness measured in the mutagenic environment. Overall, the observed decline in fitness between the initial and final estimates will be less than the true negative impact of mutations on fitness, as given by (1b). The observational bias is worse still if the “final” population has not attained equilibrium. This bias arises because the observed initial fitness is confounded by deleterious mutations accumulating during the assay, and the bias increases the larger the mutational effects and the longer the assay continues. Failure to account for this bias—by assuming that the initial fitness estimate represents W0 instead of —will overpredict the expected fitness decline from a high mutation rate. The theory would then be tested inappropriately.

A few comments about model (2) are warranted. First, the model assumes an infinite number of sites in each class i. Thus a genome can theoretically experience and accumulate infinitely many mutations in each class. Second, the model admits beneficial mutations (sj < 0), but with even a single class of beneficial mutations, fitness increases without bound as k increases to infinity (Uj(1 − sj) k → ∞). The unbounded fitness is due to the infinite sites assumption, which allows genomes to accumulate ever-increasing numbers of beneficial mutations (as favored by selection). Consequently, use of (2) with beneficial mutations should be limited to the initial generations of mutagenesis. The long-term equilibrium may be calculated for a finite number of beneficial mutations by assuming that initial genotype has already acquired the beneficial mutations (with W0 adjusted accordingly).

The average effect of a random deleterious mutation (including lethals) has been estimated as ∼ 0.68 in VSV (vesicular stomatitis virus, calculated from Table 1 in Sanjuán et al. 2004) and as 0.40 3 and 0.45 in two phages (Domingo-Calap et al. 2009). With these values, approximately half the long-term deleterious fitness effect of a high mutation rate is experienced in the first generation and will not be detectable by many methods that assay fitness in the mutagenic environment. The average fitness effect of all mutations is −0.3 and −0.36 for the two phages, and even more negative for VSV. By this measure as well, there should be a substantial fitness decline in the first few generations.

### T7 revisited

In the study of bacteriophage T7 mutagenesis, initial growth rate of the wild-type virus in the mutagenic environment was 18.3 doublings/hr (Springman et al. 2010). From a directly measured 4.3 viable mutations per genome per generation, the viable deleterious mutation rate was converted to 2.6 by assuming a deleterious fraction of 0.6 (based on direct estimates from other viruses). A model similar to that in Equation 1b but tailored to viral growth rate gave a predicted equilibrium of 8.6 doublings/hr. The observed fitness after 200 generations of propagation was 21.9, higher than fitness of the initial virus and a profound failure of the theory. Per 20 min viral generation, the difference between 21.9 and 8.6 is equivalent to a 20-fold difference in number of offspring.

Several possibilities were addressed in attempting to account for those results (Springman et al. 2010):

The phage may have evolved a lower mutation rate during the adaptation. T7 encodes its own DNA polymerase (DNAP) for genome replication, and resistance to mutagen could easily have evolved in that gene. However, a replicate evolution in which the phage DNAP was prevented from evolving exhibited a similar lack of fitness decline.

Deleterious fitness effects may be too small to expect a fitness drop in 200 generations. This possibility is inconsistent with the fitness effects of mutations reported in other viruses.

With 200 generations of evolution, beneficial mutations may have been able to ascend and offset the decline. The trajectory of fitness evolution supported this possibility, but with only a small magnitude of effect: fitness at 15 generations was not significantly below that of the estimated W0, but fitness at 80 generations showed a significant but small decline of about one doubling per hour below that of W0. Fitness at generation 200 thus implied a rise from generation 80 of about four doublings per hour. The question was why fitness exhibited such a modest decline at the earlier time points.

The question raised by the preceding analysis is whether the predicted impact of mutations was affected by a biased estimate of W0. It is of course not possible to explain a fitness increase from this bias, but an upward correction of the predicted final fitness certainly helps reduce the discrepancy. The solution suggested by (2) is to correct for the early accumulation of deleterious mutations. However, if the distribution of deleterious fitness effects is not known, the correction is not straightforward.

As one approach, Springman et al. (2010) developed a model that partitioned lethals separately from other deleterious mutations and then parameterized the model so that the predicted fitness drop was restricted to the nonlethal component. This correction mirrors the one suggested above—the fitness impact of lethals on mean fitness is the same from the first generation onward so is independent of the duration of the fitness assay. In contrast, the fitness impact of nonlethals accumulates gradually and is thus possibly detectable when comparing assays of different durations.

Partitioning the deleterious mutation rate U into a lethal rate (UL) and a nonlethal rate (UnL), Equation 1b may be rewritten as . The product in parentheses is the initial viable fitness. This value corresponds to the 30 in our example three sections above and is easily measurable. Using this adjusted fitness as initial fitness, the predicted decline from other deleterious mutations is now the component due to nonlethals, . This decline should accumulate gradually and thus be detectable with the methods used in the study, to the extent that the average effect of nonlethal, deleterious mutations is small. Of course, this drop does not represent the full negative impact of deleterious mutations, but understanding its magnitude could facilitate resolving the enigma of T7 evolving higher fitness under mutagenesis.

As the standard fitness assay spans several generations and thus might have partitioned some of the nonlethal component into , the T7 study estimated initial fitness in two ways. One method directly measured fitness (growth rate) from viral titers compared between three and six generations, so that estimate would indeed have been depressed below its true value by the early accumulation of nonlethal mutations. The other estimate, which avoids this problem, parameterized a fitness function using fitness components obtained during the first generation of mutagen exposure. This latter method should avoid the effects of deleterious mutations, save for lethal mutations (which were already accounted for by using the viable burst size).

The two fitness estimation methods gave broadly similar values, albeit variance in the fitness function estimate was not quantified. Consequently, there was no obvious bias attributable to nonlethals accumulated during the first six generations of mutagenic growth. For both fitness estimates, the long-term predicted fitness decline was the component based on the nonlethal mutation rate, and a directly measured nonlethal mutation rate was used to parameterize that component. The predicted decline was substantial and profoundly at odds with the fitness increase observed at the end of the experiment. Thus it does not seem that the failure of the theory is due to a biased initial fitness estimate.

### A surrogate fitness measure in T7

To test the model appropriately, the assays used to estimate fitness must represent fitness as it applies during the mutagenic evolution thus the most appropriate fitness assay environment would use mutagenic growth. For short-term evolution, however, fitness measured in a nonmutagenic environment may correspond to fitness in the mutagenic environment so that alternative fitness assays are acceptable. Specifically, if most mutations deleterious in the mutagenic environment are also deleterious in a surrogate environment, the fitness decay over a few generations of mutagenesis may parallel each other in the two environments. A fitness decline may then be more easily documented in a nonmutagenic environment and be free of the estimation biases noted above. In the long term, adaptive evolution specific to the mutagenic environment may destroy any correspondence in fitness between the two environments, but this problem will not arise in the very short term.

We thus attempted an alternative fitness assay of T7 exposed to mutagen to shed light on these anomalies of initial fitness measures. As in prior work, T7 was grown on cells exposed to nitrosoguanidine to introduce mutations, but here fitnesses of those stocks were assayed in the absence of mutagen. We obtained samples of phage exposed for zero generations (mutagen-free control), exposed for one generation, or exposed for three generations. These phage were then added to separate, mutagen-free cultures of cells, with titers determined at 2 min and 13 min the sample at 2 min represents the number of viable parent phage and the sample at 13 min represents the number of progeny after a single infection cycle. For the mutation-free control, burst occurs at just under 11 min (Heineman and Bull 2007), so the titer at 13 min should be an effective burst size. For mutated genomes, the effective burst may be reduced by three mechanisms—reduced adsorption rate, reduction of progeny in the cell, and delay of burst (an infected cell not yet burst plates as a single progeny phage). If there is a rapid accumulation of deleterious, nonlethal mutations during the first few generations of mutagenesis, these effective burst sizes should decline progressively with the number of generations of exposure.

Figure 1 reveals that the highest effective burst size is with no exposure (red squares), but no further decline is seen between 1 and 3 generations of exposure (solid blue and open black circles). There is thus an apparent contradiction here: from Equation 2, a decline in the first generation should be followed by additional declines in the next few generations unless is near 1. Herein lies a methodological problem, however. The observed decline in the first generation need not be due to classic mutations it could be due to mutagen effects on the nongenomic part of the virion or to epigenetic effects on the genome (see the following section for an example of the former). Thus these data fail to provide clear evidence of a short-term fitness decline from nonlethal mutations. These results are consistent with those of Springman et al. (2010), whose assay of initial fitness based on six generations of mutagenic growth matched the estimate based on one generation. The failure of T7 fitness to decline on long-term mutagenic propagation appears to reside at a fundamental level of evolution, such as neglecting beneficial mutations or overestimating the deleterious fraction of mutations, not to a confounded estimate of W0.

Effective burst sizes after exposure to nitrosoguanidine for zero, one, and three generations. Across three trials, there is a clear pattern of decline from zero- to one-generation exposure and no evident decline from one- to three-generations exposure. For each trial (conducted with a different, freshly mutagenized phage stock) the three pairs of values exhibit statistically significant heterogeneity. Methods: Populations of T7Hi from Heineman and Bull (2007) were grown in 10 μg/ml of the mutagen nitrosoguanidine for a single infection cycle (one generation, or 1 g), or for 70 min (three generations) or grown without mutagen (zero generations) and collected over chloroform to kill cells. These phage stocks were then added to mutagen-free cells that had been grown for 1 hr to a density of 1 × 10 8 cells/ml and plated at 2 min and 13 min after infection without killing cells. Burst size was calculated as the phage titer at 13 min divided by the titer at 2 min. Points shown are the raw data. Broth was LB and cells Escherichea coli IJ1133 methods, bacterial strain genotype and recipes otherwise follow Springman et al. (2010).

### Avoiding problems with in vivo mutagenesis: Virions exposed to mutagen

If viral growth in the presence of mutagen confounds mutagenic effects on the virus with impairment of host, one solution is to mutate the genome separately from the host, by treating free virus particles (virions) with mutagen. The fitness of both the wild-type and mutated viruses can be measured in the mutagen-free environment, fully avoiding the estimation biases highlighted in the preceding section. If sequencing is employed to measure the average mutation rate, and a Poisson distribution is assumed for the incidence of mutations per genome, the surviving fraction of virions can be used to calculate the lethal mutation rate. An average burst size among the survivors may even be used to estimate an average fitness effect of nonlethal mutations.

Virion survival upon exposure to mutagens was assayed extensively nearly half a century ago (e.g., Benzer 1961 Tessman et al. 1964, 1965 Tessman 1968 Botstein and Shortle 1985). For chemicals supposedly creating base changes (hydroxylamine, nitrous acid, EMS, MMS), the typical decay in viability was log-linear with time of exposure. Log-linear decay is expected if there is a constant rate of lethal mutations per unit time, even if the fraction of mutations that are lethal differs across genes. For example, if the mutation rate per unit time is Ui for gene i (U is the total genomic rate and Ui = piU) and the lethal fraction within that gene is Li, the viable fraction of genomes viable (V) under a Poisson model is (3) where . is independent of the total mutation rate, so if the mutation rate U is linear with time of exposure, the plot of log(V) will decline linearly with time, as commonly reported. In phage T4, for example, the log linearity spans the entire viability plot, nearly 6 orders of magnitude survival (Tessman 1968).

At face value, the virion survival methods developed in this early work are ideally suited to test the foundations of lethal mutagenesis theory, because they seem to provide genome survival rates that could be aligned with base substitution rates. However, there are reasons to question whether those mutagens act solely or even primarily through classical mutations. Consider the mutagen hydroxylamine, reported to induce largely C → T transitions. Using phage T4, Tessman (1968) observed log-linear declines in viability across 5–6 orders of magnitude with time of exposure. Mutations in the survivors were detected phenotypically in a diagnostic phage gene, indicating that at least some of the mutagen’s effect was an induction of standard mutations. However, base substitutions may not be the only cause of virion death. Hydroxylamine is also known to cause breaks in DNA and to cleave specific protein bonds, both of which will cause virion death (Rhaese and Freese 1968 Tessman 1968 Taylor et al. 1970 Rauko et al. 1993 Robins et al. 2013). Thus, virion decay may be due to a combination of effects, only some of which are due to classic mutations.

### Is log linearity expected from point mutations?

Another reason to question whether log-linear survival under chemical mutagenesis is due chiefly to base changes comes from recent work measuring retention of protein function for genes subjected to various base substitution rates. In these studies, mutations were generated by error-prone PCR and average base substitution rates from libraries of clones were evaluated directly by sequencing. Relationships between base substitution rate and protein survival did not obey log linearity but instead exhibited a shoulder effect, with an accelerating downward slope at higher mutation rates—as if robustness to mutation deteriorated once a few mutations were acquired in the protein (Bloom et al. 2005, 2006, 2007). This curvature implies negative epistasis on a multiplicative fitness scale, the deleterious effects of mutations together being stronger than when alone. The absence of log-linear survival for individual proteins seems incompatible with log linearity of genome survival. However, it is not intuitive how much deviation from log linearity to expect at the genome level when log linearity is violated at the gene level. We thus offer a model bridging the two processes. The model is simplified for analytical tractability.

Suppose that there are n genes in the genome. Genome survival is the product of gene survival rates across all genes. Let survival of gene i be 1 in the absence of mutation, 1 − s for a single mutation, and 0 for two or more mutations in that gene the latter assumption implies negative epistasis within genes on the multiplicative scale except for s = 1. (Lethality of two or more mutations is assumed because it greatly facilitates the calculations.) Let the mutation rate of gene i be Ui ( ), and for further mathematical necessity, all genes have the same mutation rate,: Ui = U/n, and all mutations have the same fitness effect, s.

The surviving fractions for genomes with different numbers of mutations are calculated as follows. Let Yi be the number of mutations arising in gene i at rate U/n. The probability of k single mutations in any set of k genes is times the probability that the singles fall in the first k genes (since all possible combinations have the same probability) and is A genome with k single mutations has survival (1 − s) k , so viability over all possible numbers of single mutations per genes becomes (4) When s = 1, we recover the result that survival is merely eU . If s = 0, and then as n increases without bound, the survival probability approaches e U eU = 1. This result is easily understood: with infinitely many genes and a finite number of mutations, two mutations never fall in the same gene.

As seen in Figure 2, the deviation from log-linear viability is pronounced for strong epistasis (s = 0, gray curve) but barely detectable for moderate epistasis ( , blue line). The slopes are greatly affected by s, but it is the curvature that is of interest when interpreting the published data, as we have no basis for interpreting that slope. The observation of log linearity for whole genomes is thus visually compatible with moderate epistasis at the level of individual genes. For comparison to the case, the figure also shows a curve for a mixed genome in which half the genes experience s = 1 and the other half experience s = 0 (viability follows ). The latter shows a slightly greater curvature than does (dashed green line) but is still not pronounced curvatures for s between and 1 are likewise slight (not shown). While the generality of these results remains to be demonstrated with more realistic models, the suggestion here is that log linearity is only slightly violated by moderate levels of epistasis within genes.

Log survival per mutation rate for different values of s for a genome with 30 genes (n = 30) from Equation 4 all genes experience the same value of s except where indicated. The gray curve represents maximal epistasis within genes (s = 0), the red line is no epistasis (s = 1), and the blue curve represents intermediate epistasis s = 0.5 (epistatic if fitness is multiplicative within genes). The curve for s = 1 is strictly linear. The thin black line overlaid on the blue curve is also strictly linear, so the blue curve is seen to bend only slightly. The dashed green curve represents a genome with an equal mix of genes with s = 1 and s = 0 and is seen to have slightly greater curvature than the curve for . However, both the blue and green curves deviate from linearity only slightly over four logs—suggesting that a modest level of epistasis within genes might not be detectable in these plots.

### Hydroxylamine and T7

Using T7, we revisited the effect of hydroxylamine on virion survival and also measured mutation rates of DNA extracted from exposed virions over a three- to four-log drop in survival (Table 1). The viability varies fivefold across the three trials for the longest treatment time (45 hr) and twofold for the 21-hr treatments. When subtracting baseline error/mutation rates, nearly the total increase in average mutations per genome is due to C → T transitions, as expected for this mutagen. To attribute the loss in viability to the measured increase in point mutations, consider the 21-hr data. The most generous, high survival rate is 0.05, and the excess mutations per genome is 4.6. The lethal fraction (L) of those mutations under a Poisson model is found as e −4.6 L = 0.05, or L = 0.65. Considering that approximately one-third of the genome is nonessential, that the lethal rate observed in a variety of small genome viruses ranges from 0.2 to 0.4 (Sanjuán et al. 2004 Domingo-Calap et al. 2009), and that only ∼1/5 of residues of an essential T7 protein are lethal when mutated (Robins et al. 2013), it appears that the loss in viability from exposure to hydroxylamine is too high to be explained by the observed rate of point mutations (under a Poisson model).

A possible concern with virion mutagenesis is an unequal distribution of mutations across the genome. DNA density in phage heads is 500 mg/ml, approaching crystalline density (Earnshaw and Casjens 1980). If only a small fraction of the genome is exposed to mutagen, as may be plausible, the observed relationship between average mutation rate and virion survival may poorly reflect the genome-wide tolerance of mutations. A plot of C → T mutation frequency across hydroxylamine-treated genomes suggests only modest variation in exposure across different regions (Figure 3). As the sliding window method obscures site–site variation on a local scale, we also counted the incidence of sites with no mutations, singles, and so on (17586, 837, 134, 40, 11, 7, 1, 1), observing one site each with six and seven mutations. Ignoring the site–site variation in number of reads, these numbers show a strong violation of Poisson due to an excess of multiply hit sites, consistent with the much earlier results of Benzer (1961). Thus, there appears to be quantitative, nonrandom variation in exposure to the mutagen, but not strong enough that large portions of the genome completely avoid exposure.

A sliding window analysis of the number of C to T mutations in a T7Hi genome treated with hydroxylamine 45 hr exhibits a modest deviation from uniformity, suggestive of unequal exposure across the genome. The counts are 10,000 times the total number of C to T mutations observed in all reads within the window, divided by the number of reads at which a C was observed as the template base within the window. A window span of 1001 nucleotides was applied stepwise across the genome and plotted every 50 bases. Methods are as in Table 1, except that a minimum quality score of 20 was applied here.

### Measuring the relevant mutation rate in double-strand genomes

Although it is easy to model an arbitrary mutation rate, fitting the relevant empirical rate may be challenging. In a double-stranded genome, mutagenesis typically converts a base on one side of the duplex, not also its complement. If no subsequent replication occurs before the genome infects, virions will then carry different mutations on each strand. There are several ramifications of this heteroduplex asymmetry that depend on the viral life cycle, the fitness effect of the mutations, and on recombination. For tractability in everything that follows, we consider a single episode of mutation—progeny are not exposed to further mutagenesis.

Consider first that all mutations have no fitness effect (are neutral): all infections are equally viable regardless of mutation content on either strand. Upon infection by a heteroduplex genome, and in the absence of DNA repair, semiconservative replication of the parent genome will distribute mutations on each strand to half the genomes destined for progeny, but now as homoduplexes. In T7 at least, recombination among the homoduplexes will create progeny genomes with a mix of mutations from the two parental strands for convenience the mix may be assumed to obey linkage equilibrium, each mutation at a frequency of 0.5. If the mutation rate per parental strand is U, progeny carry an average total of 2U mutations in their double-strand genomes. With free recombination, individual progeny inherit half the total, an average of U. The distribution (Poisson) will be the same as in single strands of the parent genomes. The same result would apply if there was no recombination during the process.

The situation changes when mutations have deleterious effects. Consider the extreme case that all mutations are lethal and furthermore that they are lethal regardless of strand. If the lethal rate per strand is UL, parent genomes are now subject to a lethal rate of 2UL, twice the per-strand rate. In the absence of other types of mutations, sequencing would observe a mutation rate UL, whereas the survival rate would be observed to decline at 2UL, an apparent impossibility under the standard Poisson model. As no real system experiences only lethal mutations, the ramifications of this process would merely be an overestimate of the fraction of mutations that are lethal. Recombination makes no difference in this case.

A less extreme case is one that applies to T7: all genes are transcribed from the same strand, and mutations on that strand will largely determine viability of the infection (Molineux 2005). Again assume that only lethal mutations occur, albeit a lethal mutation on the non-transcribed strand (NTS) does not manifest an effect until its complement is generated by replication using products made from the transcribed strand of the infecting genome. Lethals arise at rate UL on each genomic strand, independently of the opposing strand. The transcribed strand escapes lethals with probability , which is thus the fraction of virions that produce viable progeny. Of interest, then is the fraction of progeny in those viable infections that inherit lethal mutations from the NTS.

Within viable infections and with complete recombination, the surviving progeny for different numbers of mutations on the NTS are enumerated in Table 2. The fraction of all progeny in viable infections escaping inheritance of lethals from the NTS sums as (5) and is thus . A plot of surviving infectious particles (parent genomes producing at least some viable progeny) would be log-linear with slope −U, but the number of viable progeny from mutagenized parents would have slope −1.5U. As before, therefore, mutations arising independently on each strand will have a greater lethal effect than expected from the mutation rate observed using sequence methods (which is per strand).

Abolishing recombination among progeny genomes raises fitness in this case. In the absence of recombination, minimally half the progeny of a viable infection are themselves viable because their genome is descended from the mutation-free transcribed strand of the parent progeny survival follows eU (1 + eU )/2. Progeny survival without recombination is invariably larger than with recombination, markedly so at high mutation rates. Without recombination, survival is approximately and would not necessarily be empirically distinguishable from eU .

## Discussion

This report presents the first forward and reverse genetic screens for chemically induced mutations in X. tropicalis. We have isolated a diverse set of heritable phenotypic abnormalities in organogenesis and differentiation, and also successfully identified frogs carrying mutations in known genes for use in future studies of specific gene functions. Some of the phenotypes isolated in our forward screen resemble those already uncovered in other model systems, validating our screen design. Others, such as the cyd vicious phenotype, do not appear to resemble known mutations, and confirm that X. tropicalis forward genetics can be a highly effective tool for discovery of novel gene functions. While this pilot screen clearly demonstrates the feasibility of the approaches we have taken, there are a number of factors to consider for future screens.

### Gynogenetic Forward Screen Limitations

In our screen strategy, in vitro mutagenesis followed by gynogenesis and morphological inspection was employed to perform rapid surveillance of postneurulation phenotypes. While this approach permits screening only one life cycle after mutagenesis and greatly reduces colony requirements, several types of bias are introduced. First, highly penetrant phenotypes in early development will not be isolated in this pilot screen. Embryos with these types of defects can be difficult to identify on the complex background of nonspecific gastrulation defects associated with early pressure gynogenesis and incomplete rescue from the haploid state. The overlooked gene functions may include many housekeeping genes required for cell survival, as well as a number of tissue-specific zygotic genes involved in early tissue movements and embryogenesis. Replacement of early pressure with early cold shock to effect gynogenesis reduces this background noise to a degree, and may permit isolation of earlier phenotypes. Second, gynogenesis by suppression of polar body formation is biased towards recovery of centromerically linked loci due to meiotic recombination [5,20,27,28], so effectively only this subset of the genome is being screened. This bias comes with the significant advantage that mapping studies can focus on these centromeric regions. In some cases, we have observed additional phenotypes segregating in Mendelian ratios in the F3 progeny of sibling crosses, which were not observed in gynogenetic embryos, consistent with recovery of more distal alleles. Third, in vitro mutagenesis of mature sperm results in a mosaic F1 generation, further reducing the frequency with which recessive gynogenetic phenotypes may be observed. We chose an arbitrary number of 20 viable gynogenetic F2 neurulae as a practical threshold at which to consider an F1 genome screened examination of larger numbers of embryos is likely to result in the identification of additional phenotypes. Likewise, germline mosaicism can also interfere with recovery of detected phenotypes, so we have designated as “provisional” (color-coded green in Tables 2 and 3, and Figure 2) alleles that have not yet been shown to be heritable. However, it should be noted that 100% (29/29) of those phenotypes which have been observed twice in the gynogenetic progeny of F1 founders have been shown to be heritable thus far. As a practical point, this suggests that it should be feasible to perform preliminary characterization of a large number of provisional alleles, which can be maintained long-term as individual F1 founder frogs. Limited colony resources can then be dedicated to breeding specific phenotypes of interest, without undue risk that many will not be heritable. Replacing gynogenetic screens with a conventional three-generation screen design is unwieldy in combination with in vitro mutagenesis, as mosaicism in the F1 animals greatly reduced the frequency with which nonmosaic F2 carriers will be randomly paired in matings to produce F3 embryos to screen. Finally, morphological inspection is a relatively superficial approach, and additional phenotypes might be recovered by use of in situ hybridization or mutagenesis of transgenic multireporter strains [13] to detect more subtle variations in gene expression.

### Structure of Induced Mutations

We initially chose to pursue in vitro chemical mutagenesis of postmeiotic sperm, rather than in vivo spermatogonial treatment, for speed of analysis and efficiency of mutation induction. One drawback to this approach is that the F1 animals generated by in vitro fertilization with mutagenized sperm are mosaic, and hence phenotypes in their progeny may not appear in Mendelian ratios. As our forward genetic screen was based on gynogenesis, which precludes the production of Mendelian ratios, this was not a significant problem. In addition, mutations induced by postmeiotic sperm mutagenesis in other vertebrates include not only point mutations [39,40] but also deletions and chromosomal rearrangements [41–43]. Deletions can be highly useful genetic resources for functional and mapping studies, but as yet neither deletions nor translocations have been identified among our induced mutations. The majority of mutations that have been subjected to F2 sibling intercrosses in our study have produced Mendelian phenotypic ratios in F3 progeny, which are not indicative of gross chromosomal defects [28]. While it is possible that multigene deletions are induced in our protocol, these may result in a higher frequency of early lethal phenotypes, which we have discarded. It has also been proposed that subtle differences in mutagenesis conditions may result in significant differences in the kinds of lesions produced [41]. What is clear is that the sequence of a large number of specific amplicons in our mutagenized population indicates a high frequency of induced point mutations. While direct sequencing will not detect deletions or rearrangements, we conclude that single base changes are induced highly efficiently in our protocol. Mapping and cloning studies will ultimately be required to confirm whether point mutations or deletions are responsible for the majority of the phenotypes observed in the forward screen.

Direct sequencing of genomic PCR products also confirms a varying degree of mosaicism in the F1 generation, as demonstrated by the observation of one mutation at a frequency of

1/5 and others at 1/24 or less. In the first case, the observed ratio is in line with the expected result of in vitro ENU mutagenesis of mature sperm. If a DNA adduct forms on one strand of sperm DNA, that lesioned strand might be expected to be distributed to one of two cells at first cleavage, resulting in a 50% mosaic heterozygous embryo, such that on average 25% of the germline might carry a specific lesion. The majority of the phenotypes obtained in the forward screen are likely to be of this less-mosaic category. Two explanations are likely for the higher observed level of mosaicism in some of the other families. One is that there may be a degree of selection in the F1 spermatogonia against individual germ cells carrying particular combinations of mutations. The second possibility is that repair of modified bases carried by the mutagenized sperm may be delayed for a number of cell divisions, resulting in a significantly higher degree of mosaicism, and a lower frequency of specific F1 carriers. Consistent with this notion, it is not until later stages of development that cells carrying damaged DNA are recognized and eliminated by apoptosis [44,45].

Several observations suggest that the majority of these mutations are induced, rather than already present in the strain of frogs used. Naturally occurring recessive alleles have been found in an inbred N (Nigerian) strain [46], and a number have been recovered from outbred wild-caught X. tropicalis [21]. One of these naturally occurring mutations, grinch, has been identified in our N strain stock and confirmed in complementation tests (Tim Grammer and Richard Harland, personal communication). Since the stocks used for mutagenesis are the grandchildren of a single pair of animals, a maximum of four alleles preexisted at each locus in the population. We would therefore expect background mutations to be recovered several times in a pilot of this size, as indeed we have seen with grinch. While we have only shown complementation among a limited number of mutations, the majority of the remainder are phenotypically distinct, consistent with induced mutations in a number of different genes. In addition, gynogenesis of nonmosaic F2 animals can also provide an indication of whether loci are distinct, since the frequency with which recessive phenotypes are uncovered is inversely dependent on meiotic recombination rate, a function of the gene–centromere distance [47]. Mutations that are recovered with different frequencies in the gynogenetic progeny of nonmosaic females are likely to be distinct loci. Finally, the appearance of mosaicism in the F1 generation, which is expected in the products of in vitro mutagenesis of mature sperm, also supports the induced nature of the mutations. This mosaicism is evident in Table 3, in which the preponderance of mutant phenotypes are observed at a lower frequency in the gynogenetic progeny of F1 females compared with those of (nonmosaic) F2 females. Background recessive mutations would be expected to be nonmosaic in both the F1 and F2 generations, and the ratio recovered in the gynogenetic progeny of carrier females would not be expected to change.

### Reverse Screen

This TILLING screen demonstrates the feasibility of identifying and recovering carriers of mutations in known genes. Our pilot scheme, designed for speed, was somewhat hampered by dependence on recovering carriers among the progeny of variably mosaic F1 animals. Efficiency in future screens can be increased by sequencing exons from an adult nonmosaic F2 mutagenized population, among whose progeny carriers can be expected to be recovered in predictable Mendelian ratios. Accordingly, we are in the process of generating a library of F2 DNA and germline stocks (maintained both as frozen sperm and living frogs), which will greatly enhance recovery of identified mutations. While maintaining a living library is more space- and labor-intensive, fertilization yield from an individual X. tropicalis ' frozen testes is typically limited to about 500 embryos, and sperm viability after freezing can vary. X. tropicalis females are fecund (producing up to 9,000 eggs per ovulation and capable of breeding six times per year [14]), long-lived, and are likely to be fertile for more than 10 y (in contrast to zebrafish or mice, with a typical fertility span of less than 2 y). As each individual X. tropicalis may harbor a number of different mutations, it may be very useful to be able to perform multiple screens over a decade. Resequencing a large number of X. tropicalis exons validates the quality of the genome assembly as well as the annotation used to identify intron/exon boundaries for primer design. These data also provide a useful estimation of the induced mutation rate, which was found to be about double that calculated in zebrafish and rat TILLING screens following spermatogonial mutagenesis [10,48].

### Microarray Analysis

Microarrays are the most efficient means to quickly obtain expression information for thousands of genes. We have utilized the exceptional sequence resources now available for X. tropicalis to construct custom microarrays for a first-pass analysis of phenotypes identified in forward and reverse screens. By choosing well-described genes with known expression patterns and functions, our array design seeks to provide a snapshot description of phenotypes in order to suggest further strategies for characterization. Comparison of gene expression patterns in the wha mutation relative to wild-type embryos confirms that we can observe specific changes consistent with the observed morphological phenotype, as well as obtain new information suggesting fresh avenues for investigation. The combination of these molecular phenotyping tools with the mutagenesis procedures and genetic screens described here helps to establish an infrastructure for obtaining and analyzing chemically induced phenotypes in the emerging model vertebrate Xenopus tropicalis .

## Isoform-specific Functions of Kras in Lung Carcinogenesis

As a result of alternative splicing, the human and mouse Kras loci encode two highly similar proteins, Kras4A and Kras4B, that are jointly affected by activating mutations commonly found in cancer ( Figure 1 ). While Kras4B is ubiquitously expressed, albeit at varying levels across tissues, Kras4A expression is tissue-specific and not essential for embryonic development, suggesting that Kras4A has a minor role in Kras biology. However, we have shown that mice lacking Kras4A are highly resistant to carcinogen-induced lung tumor development [33] . Similar findings have been reported using a different mouse model that also lacks Kras4A [52] . These studies suggest that Kras4A is essential for lung Carcinogenesis. The requirement for Kras4A in Carcinogenesis is compatible with the observation that Kras4A is expressed in the lung and a number of other tissues from which arising tumors frequently harbor Kras mutations, namely the colon and the pancreas [53] , [54] . In the lung, Kras4A is highly expressed in a subset of epithelial cells, which could potentially be the originating cells of NSCLC [33] . Studies of the cellular origin of NSCLC in the mouse have identified a number of candidates [55] , [56] , but their relationship to Kras4A remains to be determined. Nevertheless, the identification of Kras4A as an essential component of mutant Kras-driven lung tumors may have important implications for the design and development of KRAS-targeted therapeutics.

## Appendix: Mean Fitness per Generation Under Mutagenic Exposure

We consider the fitness of a genotype G in generation k + 1 based on its mutational and selective history through the previous generations. Let P(Mj) represent the Poisson probability of the set of M mutations that were acquired by genotype G in generation j: mj,1 mutations acquired in class 1 at rate U1, mj,2 in class 2 at rate U2, and so on for j = 1 though k. Mean fitness in generation j is W ¯ j . The fitness of a genotype G in generation k + 1 is

## LD50 determination and phenotypic evaluation of three Echeveria varieties induced by chemical mutagens

The study aims to determine the Lethal Dose 50 (LD50) of Echeveria varieties as induced by chemical mutagens.

### Methods

Three cultivated varieties from Echeveria species, namely ‘Brave,’ ‘Viyant,’ and ‘Snow bunny,’ were induced with chemical mutagens: colchicine, ethyl methanesulfonate (EMS), methyl methanesulfonate (MMS), and sodium azide (NaN3). Each mutagen was diluted to different concentrations: colchicine (0.2%, 0.4%, 0.6%, 0.8%, 1.0%), NaN3 (0.02%, 0.04%, 0.06%, 0.08%, 0.1%), EMS, and MMS (0.1%, 0.2%, 0.3%, 0.4%, 0.5%). Soaking durations for each concentration level were 3, 6, 9, and 12 h. The survival rate and phenotypic data for mutated plants per variety in response to chemical mutagens were collected.

### Results

The LD50 evaluation revealed maximum concentration and treatment duration vary per varieties. Regardless of varieties, EMS-treated leaf cuttings had the highest survival rate. However, upon phenotypic evaluation, the results revealed that mutagenic plants were only taken from those treated with colchicine.

### Conclusion

The use of colchicine to produce mutated succulents should be further investigated at the molecular level. The results of the study are highly beneficial for mutation breeding programs for other succulent varieties or other related crops.