In silico model of gene correction in the oral epithelia

In order to simulate the impact of gene therapy in epithelial tissues we employed the HomeostaticEpidermis model, a three-dimensional lattice-based hybrid cellular automaton originally developed to model epidermal dynamics over human lifespans [40]. In this model, each epithelial cell is an independent agent whose rate of division and death are determined by a diffusible growth factor emanating from the basal layer. Dividing cells reside on a basal layer where the resultant progeny are displaced upward, undergo terminal differentiation and are eventually shed at the epithelial surface. This model robustly captures key epithelial features including structure, homeostasis with cell turnover, and realistic clonal expansion of cells that resist death or differentiation. We modified cellular turnover rates to adapt the epidermal model to better recapitulate properties of the oral mucosa (see Discussion and Materials and Methods). We further adapted the HomeostaticEpidermis model to explore FA oral gene therapy by introducing simulated gene correction to confer a potential proliferative advantage over uncorrected FA cells. In stratified squamous epithelium, clonal expansion may result from a bias in basal layer cell fate decisions that favors the production of progenitor over differentiated cell progeny [41–43]. While the mechanisms driving a potential epithelial proliferative advantage in the context of FA gene correction are unknown, evidence from FA HSC correction experiments shows that a selective advantage can be driven by resistance to apoptosis, increased survival in the presence of DNA damaging agents, and longer-term maintenance of self-renewal capacity [1,3,44–47]. All of these factors would contribute to longer-term residence of corrected cells in the basal layer, allowing them to retain proliferative capacity. We therefore modeled a proliferative advantage as a persistence coefficient, , which represents the probability that a corrected cell resists displacement out of the basal layer during neighboring cell divisions (Fig 1D). This mirrors the approach from Schenck et al. for modeling the proliferative advantage of NOTCH1 mutations in skin [40], and permitted us to explore the potential effect of gene correction in an FA background, where gene-corrected cells had anywhere from no advantage (or a neutral ) to an extremely strong advantage (). We first investigated the proliferative advantage necessary to promote reliable expansion of corrected cellular lineages in an FA mucosal background.

Gene correction requires a strong proliferative advantage to spread over clinically relevant time periods

We hypothesized that gene-corrected cells will require a proliferative advantage compared to uncorrected FA cells to spread through FA oral mucosa. To set baseline expectations for cellular competition without a proliferative advantage, we first considered the case in which a corrected cell has equivalent division behavior to the FA background: that is, when . We simulated 0.67 mm² (100 x 100 cells) FA tissue sections and delivered gene correction to 10 cells clustered in the tissue center (mirroring single microneedle delivery, Fig 2A). Because the median age at which FA patients develop solid tumors is ~30 years [5,7], we reasoned that corrected cells would need to displace FA cells in the first decade or two after gene correction to be most clinically impactful. We thus followed simulated tissue sections for up to 50 years to determine the fate of corrected cells and their descendants (Fig 2A). We considered three fates: all corrected cells could be displaced from the basal layer (i.e., “loss”); corrected cells could overtake 80% or more of the basal layer (i.e., “confluence”); or neither of these outcomes might be reached (i.e., “ongoing” dynamics). Note, our use of the word confluence parallels its standard definition as the percentage of a culture dish covered by a cellular population, as we are interested in the state of gene correction reaching widespread basal layer coverage (a metric for therapeutic success). Under neutral conditions in which corrected cells have no replicative advantage over uncorrected cells (), nearly all simulations (97%) led to the loss of corrected cells by 50 years (Fig 2B) with most corrected cell loss occurring within months of correction (Fig 2C). In the remaining 3% of simulations, neutral corrected patches remained, but were of modest size with the largest corrected clone reaching only 0.15 mm². Thus, in the absence of a proliferative advantage, gene correction will not be able to efficiently convert FA epithelium.

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Fig 2. Mucosal gene therapy depends on a strong proliferative advantage of gene-corrected cells.

(A) 10 gene-corrected cells (green) were tracked over 50 years in a 0.67 mm² FA mucosal tissue section (100 replicate simulations per condition). The gene correction fates were tracked to identify simulations reaching confluence (80% of basal layer cells corrected, red box) or loss (no remaining gene-corrected cells, blue box). (B) Number of simulations achieving confluence (red), loss (blue), or ongoing expansion (orange) at 50 years as a function of persistence coefficient ( = 0, 0.001, 0.01, 0.2, 0.5, 1). (C) Time at which simulations reached confluence or loss as a function of persistence coefficient, with mean times for each indicated in black (+) and outcome of individual simulations as points. Gene-corrected patches not reaching confluence or loss by 50 years are not plotted. (D) Number and size of gene-corrected patches at 1 year as a function of persistence coefficient . (E) Average area of confluent gene-corrected patches as a function of time and persistence coefficient . Bars indicate interquartile ranges.

https://doi.org/10.1371/journal.pcbi.1012915.g002

We next investigated how increasing the proliferative advantage might enable more efficient spread of corrected cells through epithelium on clinically-relevant timelines. While we have strong evidence that FANC gene reversions possess a proliferative advantage in non-epithelial contexts (e.g., HSCs), we have little direct knowledge about the degree of proliferative advantage conferred by FANC gene correction in epithelial tissues. We therefore investigated a wide range of persistence coefficients ranging from unlikely to guaranteed persistence () to identify how strong a proliferative advantage must be to ensure durable spread. More biological context for the strength of these persistence coefficients is given in S1 Table. In all experiments, FA cells did not resist displacement (i.e., had a persistence coefficient of 0).

As expected, larger persistence coefficients decreased the probability of corrected cell loss (Fig 2B), with a ≥ 0.1 required to avoid most loss events. When loss did occur at large persistence coefficients, it occurred early with 88% of losses within the first year after gene correction (Fig 2C). This is analogous to the establishment frequency in population genetics, where once beneficial mutations reach a certain frequency, loss becomes increasingly unlikely. In contrast, gene correction with persistence coefficients closer to neutrality can persist for years or decades before loss though rarely expand to any significant degree. Full clone size distributions one year after correction are shown in Fig 2D as a function of .

For gene-corrected cells that escape loss, larger persistence coefficients also increased the speed of corrected cell spread. Corrected cells with smaller persistence coefficients () that escaped loss almost never reached confluence in the tissue sections by 50 years. In contrast, gene correction with that avoided early loss always reached confluence by 50 years (Fig 2B). As the persistence coefficient increased, corrected cell confluence was achieved at progressively earlier times (Fig 2C), with growing at approximately five times the speed of (0.25 ± 0.027 SE mm²/year versus 0.048 mm²/year, Fig 2E). These results indicate that effective oral mucosal gene correction must confer a substantial proliferative advantage () to ensure persistence and spread on clinically-relevant timescales.

Optimizing transgene delivery for maximal corrected tissue coverage

Having demonstrated above that individual gene-corrected patches with a strong proliferative advantage could spread locally, we next considered how patch spread was determined by transgene dose and the spatial distribution of corrected cells, where microneedle delivery allows gene dose, spacing, and in-tissue diffusibility to be modified as part of microneedle design and fabrication.

We first investigated how a greater number of corrected cells, equated here to transgene dose, affected the probability of corrected cell loss and time to confluence when delivered in a single compact patch (Fig 3A). As expected, correcting more cells decreased the probability of loss across persistence coefficients (Fig 3B), where 30 as opposed to 10 corrected cells decreased the probability of loss for from 50% to 10%, but not the time to confluence under favorable conditions (Fig 3C). This reflects that the time needed to grow from 3 cells to 30 is short, compared to the longer period needed to replace a majority of cells in a target tissue of size 0.67 mm² (circa 10 years for ). Avoiding early corrected cell loss is the primary advantage conferred by a larger dose at a single injection site.

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Fig 3. Higher corrected cell numbers and optimal spacing can increase the likelihood of tissue replacement despite clonal interference.

Gene-corrected patch loss probability and time to confluence as a function of corrected cell number (A-C) and spatial delivery distribution (D-F). 100 simulations/condition were run for each persistence coefficient , with error bars indicating binomial errors (B,E) or interquartile ranges (C, F). (A) Initial spatial distribution of gene-corrected cells ( cells, in green) with a constant diffusion coefficient (). Probability of gene-corrected patch loss (B) and time to confluence (C) as a function of persistence coefficient () and initial corrected cell number (). (D) Initial spatial distribution of ten gene-corrected cells (green) as a function of diffusion coefficient (, corresponding to low, medium and high diffusion). Probability of gene-corrected patch loss (E) and time to confluence (F) as a function of persistence coefficient () and diffusion coefficient (). Visualizations of gene-corrected cell patches ten years after correction as a function of microneedle spacing (G) or density (H) on 10.67 mm² tissue sections. Initial arrayed delivery shown in panel insets, and each color represents the descendants of a single microneedle that corrects cells with . Areas of corrected cell patches at ten years are quantified in the lower right corner of each tissue section.

https://doi.org/10.1371/journal.pcbi.1012915.g003

We next investigated how transgene diffusion from a microneedle injection site might improve corrected cell spread by distributing a fixed number of corrected cells over a larger tissue area. We reasoned that more spatially distributed delivery might allow corrected cells to more effectively compete for space and replace FA cells. We modeled transgene diffusion from a point of delivery with an approximation to Brownian diffusion. The diffusion constant (see Materials and Methods) was examined for to capture low, intermediate and high degrees of spatial diffusion from 10 initial corrected cells (Fig 3D). Surprisingly, increased diffusibility did not affect the probability of corrected patch loss or its rate of spread (Fig 3E and 3F). One explanation is that early stochastic loss of individual corrected cells is more likely driven by being displaced by neighboring cells (regardless of correction status), rather than a failure to displace corrected neighboring cells when dividing. These results indicate that efforts to enable wider transgene diffusion from single microneedles is unlikely to improve the spread of corrected cell patches.

A key advantage of microneedles is their ability to be arrayed in different configurations to optimize transgene delivery. In light of finding that transgene diffusibility minimally affected the rate of spread from single needles, we investigated how microneedle arrays could be used to optimize transgene delivery and tissue correction over a 10 year period.

We first asked how needle spacing might be configured to avoid competition and promote spread within a tissue section. We reasoned that individual microneedles could be designed to minimize loss, with interference between microneedle sites a potentially more important determinant of the spread of corrected cells as illustrated in Fig 3D-3F. We investigated the impact of needle spacing on transgene delivery, corrected cell persistence and rate of spread using a 4x4 array of 16 low diffusibility () microneedles in which each needle corrected 30 cells to confer a strong proliferative advantage (). The needle spacings we explored, of 175 µm, 350 µm, and 700 µm, reflect commonly engineered interneedle distances, where our target for gene correction and spread was a 10.67 mm² tissue section (Fig 3G). We found that the most widely spaced microneedle arrays corrected more than five times as much tissue area in a 10 year period than the most tightly spaced arrays for a given number of microneedles. In tightly spaced arrays, corrected cells at the perimeter expanded more than those in the interior; this apparent competition among corrected cells was not observed in the most widely spaced arrays. Thus appropriate transgene delivery spacing has the potential to minimize interference or competition of corrected cells and maximize the area of corrected tissue.

Microneedle arrays can be engineered with substantially higher densities than the ones we examined above. Although tightly spaced arrays led to a slower rate of confluence, they achieved greater localized tissue coverage than did widely spaced arrays (Fig 3G). We found that further increasing needle densities led to more complete conversion of a given tissue area, but did not limit the approach to confluence (Fig 3H). For example, increasing microneedle density to 8x8 on a fixed backing size of 4.43 mm² increased tissue correction by ~25%, whereas decreasing microneedle density to 2x2 on the same backing patch size decreased the tissue correction by ~70%. These results indicate that dense microneedle array transgene delivery in conjunction with a strong proliferative advantage can provide widespread tissue level correction even when promoting potential spatial competition among corrected cells and clones. Thus our model should be useful for testing a broad array of potential gene correction arrays to optimize gene delivery under different clinical constraints (see Discussion).

Gene correction reduces TP53^– clonal expansion in genomically unstable FA epithelium

If FA gene-corrected cells can spread through an FA oral epithelium, how might this counter HNSCC risk or progression? An early stage in the development of FA-associated and sporadic HNSCCs is the clonal expansion of pathogenic mucosal TP53 mutations [9–11]. We thus asked if FA gene correction could counter the spread of TP53 mutations in oral epithelium. In our model, mutations in a single copy of TP53 can occur in either corrected (here denoted FANC⁺) or FA (here denoted FANC^–) cells according to mutation rates and (Fig 4A), with TP53 mutations conferring persistence coefficient advantages of and , respectively. As before, corrected FANC⁺ cells without TP53 mutations have a persistence coefficient of , so corrected FANC⁺ cells with a TP53 mutation have a total persistence coefficient of (Fig 4B). We estimated a mutation rate () and persistence coefficient () of TP53 mutations in a FANC⁺ background based on the rate of occurrence and size of TP53 clones in healthy human esophageal tissue (see Materials and Methods). In the absence of direct measures, we initially assumed that the rates of occurrence and clonal expansion of TP53 mutations were similar in FANC⁺ and FANC^– tissues (i.e., and ). We reasoned that even if FA gene-corrected and uncorrected cells produced the same number of TP53 mutations with comparable proliferative advantages, gene correction might make TP53 mutant cells less able to displace FANC⁺ as opposed to FANC^– cells, thus restricting their expansion potential.

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Fig 4. Gene correction reduces spread of TP53 mutations through FA tissue.

(A) Model of four cellular genotypes at two loci: FA cells (FANC^–/TP53⁺) in grey; FA cells with TP53 mutations (FANC^–/TP53^–) in magenta; gene-corrected cells (FANC⁺/TP53⁺) in green; gene-corrected cells with TP53 mutations (FANC⁺/TP53^–) in cyan. Arrows indicate transitions that can occur via mutation or gene correction. (B) Genotype-specific persistence coefficients for (A). (C-H) TP53^– tissue coverage as a function of gene correction at 46 years in 0.33 mm² simulated tissue sections, comparing no correction (Ø) to correction with or . Panels used 100 simulations at a given persistence coefficient except in panels C,F where 300 simulations were performed. C-E show the proportion of tissue coverage at 46 years with (C) comparable TP53 mutation rates and persistence coefficients regardless of FA genotype, (D) an elevated TP53 mutation rate in FANC^– cells (, ) and equivalent TP53 persistence coefficients or (E) equal TP53 mutation rates in FANC^– and FANC⁺ cells with elevated TP53 persistence coefficients in FANC^– cells (). Error bars represent standard errors. Yellow bars represent TP53 tissue coverage range from Martincorena et al. [48] for normal esophagus. (F-H): six representative tissue sections at 46 years from C-E, with colors corresponding to genotypes shown in (A). (G) Consequence of an 8-fold increase in , and (H) a 4-fold increase in .

https://doi.org/10.1371/journal.pcbi.1012915.g004

To test this idea, we asked if gene correction could limit TP53 mutational prevalence in FA tissue when TP53 mutation rates and proliferative advantages were comparable for FANC^– and FANC⁺ cells (Fig 4C and 4F). We simulated 0.33 mm² (70x70 cells) tissue sections in which a single microneedle gene corrected 30 cells () with persistence coefficients of or at the tissue center, then followed these sections up to 50 years. We compared these corrected tissue sections to uncorrected tissue section controls, and also plotted TP53^– expansion in healthy esophageal tissue as a reference [48]. We found that TP53 mutations reached similar tissue frequencies over 46 years regardless of gene correction status (Fig 4C and 4F), as might be expected under an additive fitness model. Gene correction restricted TP53^– spread in FANC^– cells, while mutations still arose and expanded within corrected FANC⁺ cells leading to similar overall tissue frequencies (compare cyan FANC⁺/TP53^– cells with in Fig 4F tissue sections to uncorrected magenta FANC^–/TP53^– cells). Gene correction might be beneficial if FANC^–/TP53^– double mutants are more likely to progress to cancer than FANC⁺/TP53^– mutants. However, this is unlikely to lower the overall TP53^– burden if TP53 mutation rates and proliferative advantages are comparable between corrected and uncorrected tissue. Full 46-year tissue coverage trajectories from these simulations are shown in S1A-S1C Fig, and demonstrate that TP53^– tissue coverage over time is similar for each value of

The above results assumed that the TP53 mutation rate and mutant proliferative advantage are identical regardless of FANC genotype. However, the dramatically increased risk of HNSCC in FA individuals likely reflects genomic instability in FA that could generate and promote the spread of pathogenic mutations through FA epithelia. We therefore investigated how FA genotype affects the rate of TP53 mutation generation and spread, and thus could determine the outcome of FA gene correction.

We first considered that FANC^– cells have a higher mutation rate than FANC⁺ cells [49–51]. As there have been a range of values reported for this increase (up to 8-30x), we reran the experiments above to determine outcomes with TP53 mutation rates in uncorrected FANC^– cells () of 1.5-, 2-, 4-, or 8-fold higher than in corrected FANC⁺ cells (, Fig 4D and 4G). In the absence of FA gene correction, increased by a factor of eight led to a corresponding increase in the tissue burden of TP53^– cells to cover 23% of tissue sections at 46 years, or nearly 10-fold higher than the coverage estimate of 2.7% under the background mutation rate (Fig 4D). While elevated mutation rates produced more TP53^– clones, individual clone sizes remained similar to those under baseline mutation rates (S2A and S2B Fig). We found that by introducing gene correction with a small persistence coefficient ( Fig 4D), TP53^– tissue coverage was modestly reduced compared to uncorrected tissue (a reduction of 42% in simulations where FANC^– cells had a 8x elevated mutation rate). In contrast, gene correction with a larger persistence coefficient (, Fig 4D) resulted in tissue sections with almost no additional TP53 mutations above baseline simulations that used background mutation rates. This effect depended on gene-corrected FANC⁺ cells replacing more mutable FANC^– cells: in the 2% of simulations in which gene corrected cells were stochastically lost, FANC^–/TP53^– cells expanded as if they were in uncorrected tissue (see panel inset in Fig 4G). Full 46-year tissue coverage trajectories from these simulations are shown in S1D-S1F Fig.

We next considered that TP53 mutations might confer a stronger proliferative advantage in FA cells than in gene-corrected cells (i.e., ). The basis of this assumption is observed non-additive effects on the rate of cell turnover and tumor formation in cells harboring both TP53 mutations and FA mutations (see Discussion, [52–55]). We parameterized possible fitness advantages using human lymphoblastoid and mouse HSC experimental data (see Materials and Methods). To test the impact of this effect, we reran the experiments above with identical FANC^– and FANC⁺ mutation rates, but with increased by a factor of 1.5-, 2-, or 4-fold compared to (Fig 4E and 4H). In the absence of gene correction, when was increased by a factor of 4, there was a corresponding increase in the tissue burden of TP53^– cells to cover 33% of tissue sections at 46 years, compared with 2.7% under the background proliferative advantage. In contrast to the mutation rate experiments, increased TP53^– coverage was driven primarily by larger clones in conjunction with a more modest increase in clone number (S2C and S2D Fig). As was the case for gene correction affecting mutation rates, gene correction with a small persistence coefficient (, Fig 4E) modestly reduced the TP53^– tissue burden by ~31% among cells with a 4x elevated proliferative advantage compared to uncorrected tissue. Gene correction with a large persistence coefficient (, Fig 4E) resulted in tissue sections with almost no excess TP53^– mutational coverage beyond baseline simulations in which FANC^– and FANC⁺ cells have identical persistence coefficients associated with TP53 loss. Again, the rapid spread of gene-corrected cells largely abrogated the proliferative advantage of TP53 mutations in a FANC^– background. Full 46-year tissue coverage trajectories are shown in S1G-S1I. These results collectively indicate that FA-directed mucosal gene therapy has the potential to reduce TP53-associated HNSCCs in FA, and that likely mechanisms include a suppression of FA-associated genomic instability and the strong selective pressure for loss of TP53 function.

Overview of the model

Adaptation of epidermal model for the oral epithelium

We sought to preserve homeostatic behavior of the HE model while accounting for the increased turnover rate of oral epithelial cells compared to epidermal cells. Under the default parameters in the HE model, basal cells divide on average 0.4 times per week (S3 Fig). However, basal cells in the oral epithelium and esophagus divide approximately twice per week [27,41,62]. We therefore rescaled time in our model such that each reported year of simulation time in the oral epithelium corresponds to 4.5 years of simulation time in the HE model.

To reflect the higher density of cells in the oral epithelium versus epidermal tissue, tissue section sizes are determined using a density of 15,000 basal layer cells/mm² [23,41], instead of 10,000 basal layer cells/mm² in the HE model [40,87].

Gene correction

To mimic in vivo microneedle gene delivery that corrects FA oral epithelial cells, we allowed FA cells to be transformed into corrected cells by exposure to a simulated transgene at a pre-specified treatment time. We apply the in silico transgene delivery to the center of simulated tissue sections except when otherwise noted at the start of the simulation. Transgene spread through the tissue is governed by an approximation to Brownian diffusion away from the injection site. Specifically, for each cellular position on the tissue basal layer, we determine the relative probability of correction by integrating the PDF of a bivariate Gaussian distribution over the cell’s x and y coordinate boundaries on the lattice. We then sample k cell coordinates for correction from this probability distribution without replacement. To simulate a transgene injection with greater or lesser diffusion, we examine Gaussian distributions with different variances (D) centered on the injection site coordinates () as follows:

Corrected cells can have altered dynamics in the basal layer that may allow them to spread, in analog to the ability of gene-corrected cells to spread in the hematopoietic compartment. In stratified squamous epithelium, clonal expansion occurs due to an imbalance in the fate of progenitor cells in the basal layer [23,41,43]. We model this mechanism via a persistence coefficient (), which prevents a cell from being displaced by its neighbor cell’s division. Specifically, when a cell divides and randomly chooses to displace a neighboring cell possessing a persistence coefficient , the neighboring cell will not be displaced vertically with probability , and will be displaced vertically with probability 1 - . If the neighboring cell is not displaced, the dividing cell instead places its daughter cell vertically and does not displace any neighboring cells. This mirrors the implementation of NOTCH1 mutations in Schenck et al. ([40]. FA cells are assumed to have throughout.

Interrogating clonal expansion of corrected cells in an FA background

To investigate the spread of gene correction through the oral epithelium, we simulated FA tissue sections of size 0.67 mm² (100 cells x 100 cells). We introduced a single corrected patch of k cells with persistence coefficient in the center of the basal layer of the tissue as described above and recorded tissue states longitudinally for up to 50 years at six month intervals. Unless otherwise noted, k = 10 and , reflecting a tightly clustered patch of few corrected cells. Simulations were stopped if no corrected cells remained in the basal layer (‘loss’) or if the corrected patch of cells occupied 80% of the basal layer (‘confluence’). Simulations reaching neither endpoint in 50 years were designated as ‘ongoing’. We ran 100 correction replicates for and recorded the proportion of simulations in which correction was lost or reached confluence and the time at which that event occurred. We repeated these analyses examining different numbers of corrected cells () and different degrees of transgene diffusion (). Clone size distributions were determined by computing the number of cells associated with each of the corrected patches for each persistence coefficient after one year. To determine the expansion rates of corrected patches, we examined only simulation replicates reaching confluence and converted the number of corrected cells at each timepoint (six-month intervals) into area assuming each cell was 66.7 µm² [23,41].

Lineage competition between gene-corrected cells and TP53 mutants

We investigated how gene correction might decrease the prevalence of TP53 mutant cells in the oral epithelium of people with FA. To run these analyses, we expanded our model to permit cells to acquire TP53 inactivating mutations at cell division in both FANC^– (FA) and FANC⁺ (corrected) cells. Each cell division, each FANC^– and FANC⁺ cell acquires an expected number of TP53 inactivating mutations, and , respectively. We determined the probability of TP53 inactivation to be as the product of the normalized genewide TP53 mutation rate [40,88] and the probability of gene inactivation conditional on mutation as determined from deep mutational scanning data (~0.25, [89]). More information on this calculation is available in ‘Parametrizing the proliferative advantage and mutation rate of TP53^– mutations’. A Poisson number of inactivating mutations with or is drawn for each cell division and cells gain a fitness advantage if an inactivating mutation occurs. Acquiring multiple mutations in TP53 did not alter clonal fitness beyond a single hit (see Discussion). FANC^– and FANC⁺ cells containing a TP53 inactivating mutation had an additional increase in their persistence coefficient of and , respectively. Initially, we assumed that , based on model fitting to the prevalence of TP53 mutations in noncancerous tissue (see section ‘Parametrizing the proliferative advantage and mutation rate of TP53^– mutations’ for full details).

We considered three experimental conditions in which gene correction could slow the rate at which TP53 mutations accumulated in tissue:

1. If FANC⁺ cells were more difficult to displace than FANC^– cells, but were otherwise identical in terms of the TP53 mutation rate and clonal expansion speed. In this case, we examined simulation runs in which and .
2. If FANC⁺ cells were more genetically stable than FANC^– cells and thus acquired fewer TP53 mutations. In this case, we examined simulations in which and , where .
3. If FANC^– cells permitted a faster rate of clonal expansion of TP53 inactivating mutations than FANC⁺ cells. In this case, we examined simulations in which and , where .

We conducted 300 replicates of experimental condition 1 and 100 replicates of experimental conditions 2 and 3, both with and without gene correction. Among simulations with gene correction, we examined small and large persistence coefficients for corrected cells ( and , respectively). We ran simulations on 0.33 mm² (70 x 70 cells) tissue sections for up to 50 years with initially corrected cells distributed with . Simulations without correction ran uninterrupted for the full 50 years. Simulations with correction were run for up to 50 years, but were stopped if all corrected cells were lost from the basal layer. This stoppage criterion reflects our assumption that once all corrected cells are lost from the basal layer, the tissue behaves similarly to one never having undergone correction. To address variation in replicate numbers caused by early stoppage, mutational characteristics for samples in which gene correction was lost were sampled from a random replicate that did not undergo correction at each timepoint. We then quantified the proportion of the tissue with at least one TP53 mutation at six month intervals for up to 46 years.

Parametrizing the proliferative advantage and mutation rate of TP53^– mutations

To quantify how gene correction could disrupt TP53 mutation clonal expansions in FA oral epithelium, we first parameterized TP53^– mutation rates () and proliferative advantages () in the context of our model. We estimated these parameters via comparison to a published study of TP53 mutational expansion in healthy (i.e., non-FA) esophagus [48], another non-keratinized stratified squamous epithelium that is spatially-contiguous with the oral mucosa.

Martincorena et al. [48] collected 2 mm² sections of esophageal tissue from study participants of different ages and deep sequenced each section to measure the number of unique TP53 mutations and their corresponding variant allele frequencies (VAFs). Because 2 mm² tissue sections are computationally expensive to simulate under the HE model, we simulated smaller tissue sections (70 x 70 cells or ~0.33 mm²) and compared them to a spatially downsampled version of [48], intended to mimic results from Martincorena et al. if smaller sections were sequenced.

To approximate downsampling of the clinically-derived 2 mm² samples, we first spatially reconstructed possible tissue sections that reflect the mutation data observed in each full 2 mm² sample (i.e., each tissue section at a given age has distinct TP53 mutations indexed , at frequencies ). With our expected cellular density, each 2 mm² tissue section is represented by a 173 x 173 cellular grid. We then place mutations in cells on the grid such that each mutation is spatially contiguous and at its observed frequency, . Specifically, starting with the most frequent mutation, we choose a random starting point on the grid to assign the mutation and then mutate a random neighboring cell of the currently mutated cells to extend the spatially contiguous mutational patch until the mutation reaches its observed frequency . This process is repeated serially for each additional mutation observed in a tissue section, with the additional constraint that if the frequency of total mutations reaches 0.5 or more, the mutation that would exceed this threshold is instead assigned to an existing mutant clone background of higher frequency. After reconstructing potential tissue sections that could produce the correct number of TP53 mutations and their VAFs in the 2 mm² sections, we randomly sampled a 0.33 mm² (70 x 70 cell) square subsection from each larger reconstructed sample and counted the number of mutations and their VAFs in this subsection. To align with Martincorena et al. [48], who excluded mutations sampled at frequencies below 0.0018 (108 genomic copies/(29929 cells * 2 genomic copies/cell)) in 2 mm² tissue sections, we applied the equivalent threshold in our 0.33 mm² sections, corresponding to a frequency 0.011 (i.e., 108 genomic copies/(4900 cells * 2 genomic copies/cell)).

To identify the TP53 persistence coefficient value that most accurately reflects the mutation patterns observed in empirical data, we simulated 70x70 tissue sections across a range of values and compared the simulated data with the downsampled empirical observations. Martincorena et al. [48] collected 844 samples from nine donors of varying ages. We examined the 560 samples from the six donors aged 20 to 55 to match the correction timescales profiled in this study. 177 samples contained detectable TP53 mutations, which were spatially reconstructed and then downsampled as described above. Only TP53 nonsense, missense and synonymous SNV mutations were included, with non-SNV and splice mutations excluded. Total empirical mutational prevalences (i.e., the number of unique TP53 mutations per tissue) were computed by combining the downsampled tissue sections and the tissue sections containing no TP53 mutations.

We conducted 100 simulation replicates for each and matched two metrics between the simulated and observed data: the number of unique TP53 mutations in the tissue and the average mutational VAF of an observed TP53 mutation. Using the default mutation rate of the HE model resulted in an excess number of TP53 mutations compared to empirical data, even when these mutations conferred no proliferative advantage (S4A Fig). To better align the number of mutations in a tissue sample with observed data, we reasoned that the mutation rate producing mutations capable of expanding was likely lower than expected from the gene length and average mutation rate alone. To compute an adjusted mutation rate, we referenced deep mutational scanning data of TP53 and found that approximately 25% of TP53 mutations were expected to confer a selective benefit [89]. We therefore reduced the model’s default expected number of TP53 mutations by a factor of four, and found that this reduced mutation rate () was capable of producing mutation counts and sizes that roughly matched Martincorena et al. [48], as shown in S4 and S4B Fig.

To compare the number of distinct mutations arising, we calculated the squared differences between the mean number of mutations in the downsampled empirical data and the mean number of mutations in the simulated data for each timepoint and for each value. We then averaged these squared differences across all timepoints and identified which value minimized the mean squared error (S4 and S4D Fig).

To find the value best able to produce empirical TP53 mutational size distributions (i.e. VAFs), we took a two step approach. First, we fit exponential distributions that described the simulated VAFs for each value separately at each timepoint. We fit these distributions using the R fitdist function within the fitdistrplus package [90]. Before fitting, we recentered the simulated VAFs by subtracting off the lower limit of detection frequency (0.011) to better conform to the shape of the exponential distribution (i.e., bounded below at 0). Second, we then used the best fit at each time point and for each simulated to compute the probability that an interval encompassing each empirical downsampled VAF measurement was drawn from each of the best fit distributions. Specifically, for an observed VAF measurement and best fit parameter for a given age group and , we computed the probability of the observed data as:

We used although we found that results were robust to our choice of small . As when fitting the distributions initially to find the best fit s, we recentered the observed VAFs by subtracting off the lower limit of detection before evaluating the probability expressions above. We then summed the log probabilities for a given across all age groups to find the that generates simulated data that best conforms to the empirical data through time (S2 Table and S4C- S4E Fig). We did not perform exponential best fit calculations to as there was only one observed mutation for the age ranges 20-23 and 24-27. Two outlier measurements diverging substantially from the overall temporal signal were excluded when determining the best fit parameters: the number of mutations in a heavy smoker aged 44-47 and the variant allele frequencies among ages 20-23 (S4B-S4C Fig).

We found that = 0.01 both minimized the squared error for the number of mutations and minimized the negative log-likelihood fit to the mutational VAFs, so we proceeded with = 0.01 as our proliferative advantage of TP53 mutations in healthy tissue.

Due to interactions between the FA and TP53 pathways, loss of TP53 function in cells already carrying FANC mutations is likely to confer a more extreme growth phenotype (i.e., , see Discussion). To parameterize , we drew on both in vitro and in vivo data from human lymphoblastoid and mouse HSC experiments [52,53] which provide consistent, quantitative evidence that TP53 inactivation enhances proliferation to a greater degree in FA cells than non-FA cells:

1. 1). FA and non-FA lymphoblastoid cell lines, both with and without TP53 knockdown, were exposed to a pulse of interstrand crosslinking agents then grown in culture for 72 hours [52]. In non-FA cells, TP53 knockdown increased growth by 17%, but in FA cells, TP53 knockdown increased growth by 40%. These values were extracted from time point H72 in Fig 3C of the original publication [52] using WebPlotDigitizer [91]. This suggests .
2. 2). HSCs from mice constructed with all combinations of Fanca^+/+ or Fanca^–/– and Tp53^–/– or Tp53^+/+ were tracked for 20 weeks [53]. The depletion of HSCs was measured to track proliferative exhaustion due to more rapid cycling. Addition of Tp53^–/– to a Fanca^+/+ background resulted in a decrease in abundance of 35% between weeks 8 and 20, while addition of Tp53^–/– to a Fanca^-/- background resulted in a decrease in abundance of 86% between weeks 8 and 20. These values were extracted from Fig 1D of the original publication [53] using WebPlotDigitizer [91]. This suggests , although provides less direct evidence than the growth experiments described above.

The consistency between these two studies, in different cell types from different organisms, prompted our use of an increased proliferative advantage (i.e., ) in the range of ~2.4. Specifically, we tested to explore potential increases or decreases in proliferative advantage that may accompany an epithelial context.