Asymmetric division sustains stem cell heterogeneity in the Drosophila testicular niche

Abstract

The stem cell niche provides a specialized microenvironment that supports stem cell self-renewal. Spatial constraints within the niche limit the number of resident stem cells, leading to competition for niche occupancy. Such competition can result in neutral drift, where one stem cell clone gradually dominates the pool. Theoretically, a high rate of asymmetric division is expected to mitigate this competition and preserve clonal heterogeneity, but its quantitative impact on clonal dynamics within an in vivo niche has not been defined. In this study, we use the Drosophila male germline stem cell (GSC) niche as a model to investigate how division modes, symmetric versus asymmetric divisions, shape dynamics of stem cell clones. Through a combination of lineage tracing and mathematical modeling, we show that stem cells compete via neutral competition, and an increased frequency of asymmetric division markedly delays clonal expansion, thereby maintaining stem cell diversity over time. We further found that under conditions of non-neutral competition, stem cells can actively change their rate of asymmetric division in response to variations in niche occupancy. These findings highlight the essential role of asymmetric division in preserving stem cell heterogeneity. This principle may extend across diverse stem cell systems.

Mathematical modeling of the Drosophila testis stem-cell niche reveals how asymmetric division of stem cells delays clonal expansion and preserves stem cell heterogeneity.

Introduction

In given tissues, stem cells reside in specialized microenvironments called niches, which support their maintenance. Throughout the lifespan of organisms, stochastic competition drives the expansion of stem cell clones (reviewed in ¹). The dynamics of stem cell clones have been investigated in multiple systems. Clonal expansion of hematopoietic stem cells (HSCs), also referred to as clonal hematopoiesis, is characterized by the overrepresentation of certain stem cell clones in aged humans. Clonal hematopoiesis has been well accepted as a potential cause of certain clinical conditions, including hematopoietic malignancy and cardiovascular diseases^2–5. The mouse intestinal epithelium is a well-studied in vivo clonal expansion model. Using multicolor lineage-labeling tools such as the Confetti system, previous studies have shown that intestinal stem cells gradually shift toward monoclonality over the course of aging^6,7. Mathematical analyses have shown how this process follows neutral drift^6–8. While studies have demonstrated the clonal dynamics and expansion of stem cells, it remains challenging to fully understand how this process is regulated. The challenge is mainly due to the complexity of niche anatomy and the lack of an experimental system, as the process of clone expansion may be affected by multiple factors, and it requires a long time to make the expanded clone detectable.

Studying the Drosophila GSC system has yielded valuable information for our understanding of many conserved stem-cell characteristics. At the tip of the Drosophila testis, 8–10 GSCs adhere to a cluster of somatic cells called the hub, a major niche component. The hub cells send signals which are vital for GSC maintenance. In this microenvironment, GSCs typically divide asymmetrically (asymmetric cell division: ACD) via a stereotypical spindle orientation. Such ACD results in only one daughter cell maintaining attachment to the hub and retaining its stem cell identity, while the second daughter cell is displaced away from the hub and becomes a gonialblast (GB) that begins to differentiate^9,10 (Fig. 1A). Although ACD can keep the same number of stem cells, gain and loss of GSCs also occur occasionally. Since ACD cannot change the number of stem cells, symmetric cell division (SCD) is necessary for maintaining stem cell pool size^11–13. The balance between these two division modes (ACD and SCD) varies across different stem cell systems¹⁴.

Fig. 1. Asymmetric cell division prevents clonal expansion.

A Schematic of the asymmetric division of a Drosophila germline stem cell. B Illustration of three potential outcomes of a stem cell division: asymmetric cell division ($p$), gain ($q$) and loss ($r$). C Standard parameters for models i through v, including stem cell number ($n$) and division probabilities (asymmetric: $p$, symmetric: $q$ and $r$, per cycle). D Model geometry reflected by the model. Stem cell clones are labeled A1 through A9. E–I For each model (i through v), a single representative system trajectory that most closely matched the median number of cycles required for a single clone to dominate the niche. J Graph shows the cumulative frequency of the clonal niche that emerged after the number of cycles. N = 500 independent stochastic simulation trials were conducted for each parameter set to generate the cumulative distribution. K The graph shows the relationship between the time taken to reach the clonal niche and the rate of asymmetric division ($p$).

Based on these distinct outcomes, ACD and SCD have been proposed to serve different biological roles across various stem cell systems. ACD is generally thought to maintain a stable stem cell pool, whereas SCD enables flexible expansion or reduction of stem cell numbers to meet tissue demands¹⁴. Beyond regulating pool size, ACD also contributes to the segregation of intrinsic factors. In Drosophila male GSCs, ACD results in the biased inheritance of mother centrosomes, midbody rings, histones, and ribosomal DNA copies^15–18. If asymmetric division is disrupted, these intrinsic factors are redistributed incorrectly. However, such missegregation often does not cause immediate defects, making the functional significance difficult to assess. In some contexts, however, the consequences of disrupted ACD are more apparent. For example, in Drosophila neuroblasts, ACD defects lead to missegregation of fate determinants and can drive tumorigenesis^9,19–24, suggesting a tumor-suppressive role for ACD. Paradoxically, ACD itself also has tumor-promoting effects in several tumor models, such that ACD can produce phenotypically heterogeneous cell populations in cancer, which helps to sustain clones that are resistant to drug treatment^25,26.

The roles of SCD also vary by context. In the intestinal stem cell system, environmental cues regulate SCD rates via changes in spindle orientation, demonstrating plasticity in division modes²⁷. Moreover, SCD plays a critical role in quality control mechanisms, including the elimination of damaged stem cells and their replacement by healthy ones^28–30.

Given the context-dependent significance of both ACD and SCD, it is crucial to understand how these division modes shape stem cell populations over time in physiological and pathological niches. In this study, we investigate how ACD and SCD influence clonal dynamics in the Drosophila testis niche model, using a combination of computational modeling and in vivo experiments. The simplicity and well-defined architecture of this model system offer a unique opportunity to quantitatively dissect how division modes impact stem cell clonal expansion.

Results

Asymmetric cell division prevents clonal expansion

We developed a computational model mimicking a Drosophila testicular niche and solved it using Virtual Cell (VCell), a set of computational tools for modeling in biology^27,28.

The processes governing the dynamics of GSCs in the niche include the division-associated ACD and SCD, as well as cell loss (differentiation without division) and dedifferentiation (reattachment of differentiating cells to the hub and regaining stem-cell characteristics)^11,12,29,30. As the asymmetric or symmetric outcomes occur every “event” cycle, we define the event cycle (like the cell cycle) as the average time between any two successive events, including those not associated with cell division. Throughout this study, we used a 12-hour event cycle, as was previously estimated in live imaging-based studies^11,12 (i.e., the duration of two event cycles is equivalent to 1 day).

Note that the net change of the GSC numbers is the same for cell loss and symmetric differentiation, where it is negative, and for self-renewal and dedifferentiation, where it is positive. Therefore, for simplicity, we formulate the model in terms of only three types of events: “asymmetric division”, “gain” (accounting for both symmetric self-renewal and dedifferentiation), and “loss” (accounting for both symmetric differentiation and simple cell loss). These events are treated as stochastic and characterized by respective probabilities per cycle, termed $p,q,r$, that throughout the study are assumed to be constant over time (Fig. 1B). Because the results obtained with this model compared well to the outputs from a more general model with explicit treatment of the two processes, for both wild-type and mutant parameter sets, we used the simplified model throughout the study (for mathematical details of the simplified model, see subsection “Mathematical modeling” of Materials and methods; for discussion of the generalized model, see Supplementary Note 1).

Note that the fluctuations of GSC numbers reported in Fig. 1C, and visible in Fig. 1E–I when clones expand to occupy the entire niche, are not due to changes in $q$ and $r$, which, as mentioned above, are kept constant. Rather, these fluctuations occur because, as in a real niche, we model the events as asynchronous, resulting in transient deviations of the GSC number from its average. However, because the niche tightly regulates its capacity, the fluctuations are kept to a minimum. The model includes a mechanism of such regulation. A detailed description of how this regulation is implemented mathematically is provided in the “Mathematical modeling” in the Materials and Methods section.

First, to estimate the impact of ACD rate on clonal expansion, we ran 3000 simulations for each parameter set shown in Fig. 1C (Models i-v). Each simulation began with nine distinct stem cell clones (A1–A9), which were assigned identical values of $p$, $q$, and $r$, and represented by unique colors in the simulation outputs (Fig. 1D). In the virtual niche, we recorded the number of each stem cell clone after every cycle. As shown in representative outcomes from single trials for Model (i) through Model (v), respectively, the niche will be occupied by a randomly selected clone via neutral competition (Fig. 1E–I). These simulations clarified the emergence of a “clonal niche”, defined as a niche fully occupied by the descendants of a single stem cell clone. Three factors are required: (1) stochastic fluctuations, because without randomness the initial clone distribution would remain fixed; (2) irreversible clone “loss”; and (3) replenishment through “gain”, which favors clones that produce more descendants and is further strengthened by the constraint on niche capacity.

We simulated the dependence between the time (cycles) and frequency of clonal niche emergence for varying rates of ACD ($p$), gain ($q$), and loss ($r$). The graph shown in Fig. 1J demonstrates how ACD ($p$) influences the time to clonal niche emergence. Higher ACD rates drastically delay clone expansion; for instance, increasing the ACD rate ($p$) from 0.4 to 0.96 extends the median time to clonal niche from ~23 cycles to ~342 cycles. This demonstrates a strong positive correlation between the rate of ACD and the time required for the emergence of a clonal niche (Fig. 1K), suggesting that ACD delays the onset of clonal expansion of stem cells, thereby maintaining a diverse stem cell population within the niche.

Lineage tracing recapitulates the neutral drift of GSC clones

Next, to understand whether such neutral competition/clone expansion we observed in the computational model is recapitulating the physiological niche, we conducted a lineage tracing experiment using the Drosophila testis. To mark the GSC clones with GFP, we induced Flippase expression under the heat-shock promoter (hs-FLP) by incubating flies at 37°C for a short time. FLP removes the stop codon flanked by two FRT sites located between the nanos promoter and Gal4, thereby initiating UAS-GFP expression (Fig. 2A)¹³. Flippase recombination permanently marks stem cell clones, and we can trace the lineage over time. If we mark half of the GSCs in the niche and they all divided only asymmetrically ($p=1$), the GFP-positive clone frequency would remain around 50%. However, in the presence of symmetric events, neutral competition occurs, and clonal expansion will cause the GFP-positive GSCs to either expand or vanish, so their frequency will become 0 or 100% (Fig. 2B).

Fig. 2. Lineage tracing recapitulates the neutral drift of GSC clones.

A Illustration of the marking system. The heat-shock driven UAS-FLP expression removes the mCherry-stop cassette and activates the expression of GFP in GSCs under the control of nosGal4. B Possible outcomes of population dynamics of GFP- positive stem cells after marking 50% of GSCs. If GSCs exclusively undergo asymmetric division ($p$=1), the frequency of GFP-positive clones would remain around 50%. Conversely, if symmetric events occur, the distribution of GFP-positive GSCs within each testis would shift towards 0 or 100%. C Representative immunofluorescence image of the testicular niche 24 h after a 40-min of heat-shock. D The graph illustrates the initial frequency of GFP-positive GSCs (n = 74 testes). The corresponding raw data were used for initialization of the model. E Representative immunofluorescence images of the testicular niche at days 7, 14, and 21 post-heat-shock treatment. The upper panel shows images where the proportion of GFP-positive GSCs reaches 100%. In contrast, the lower panel shows images where the GFP-positive GSCs decline to 0%. F The violin plot shows the frequency of GFP-positive GSCs in the testis (n = 74, 62, 65, and 65 for Days 0, 7, 14, and 21, respectively). Violin plots show kernel density estimate (KDE) and quantile lines. The width of each curve represents the frequency of data points. G The graphs show results of fitting experimental data based on 2000 simulation runs for the indicated parameter sets. The goodness of fit is characterized by root mean square deviations (RMSD), as defined in subsection “Utilizing the mathematical model for analysis of experimental data” of section Materials and methods. The “n” indicates the number of imaged testes. All scale bars correspond to 10 μm. Asterisks in the images indicate the approximate location of the hub. Normalized frequency was calculated as follows: when any testes with no marked GSCs or with all GSCs marked were present at the day 0 scoring, the frequencies were subtracted from the day 0, and subsequent time points (day 7, 14, and 21) (see “Mathematical modeling” in the Method section for details). The event cycle (12 h) was used for fitting.

We optimized the heat-shock duration to 40 min to mark ~50% of the GSCs (Fig. 2C, D and Supplementary Fig. 1). We then tracked the frequency of testes with different proportions of GFP-positive GSCs on days 7, 14, and 21 post-marking. In our imaging, we indeed observed a shift of the GFP-positive GSC towards fixation or extinction (Fig. 2E, F). To determine the rate $p$, $q$ and $r$, we have fitted our model to the experimental data, as detailed in the section Utilizing the mathematical model for analysis of experimental data. In particular, experimental initial numbers of GFP-positive GSCs, illustrated by the cumulative distribution in Fig. 2D, were used for initializing the model. We ran 2000 simulations for each of the following parameter sets: 1. $p=$0.9, $q=r=$0.05; 2. $p=$0.8, $q=r=$0.1, and 3. $p=$0.7, $q=r=$0.15 (all rate constants have units per cycle). Among them, we found that the best fit to our experimental results was obtained by $p=$0.8, $q=r=$0.1 (Fig. 2G and Supplementary Fig. 2A, B).

It should be noted that our estimation differs from a previous report, in which the rate of ACD was estimated as $p$ ~0.94–0.98 per cycle by ref. ¹³. They used short heat shocks to generate a small number of GFP-positive cells per niche and classified them as singlets, doublets, etc., depending on their mutual positions in the niche (Fig. 2 in ref. ¹³ and the diagram in Supplementary Fig. 3A; note that the images in the lower panel of Supplementary Fig. 3A are from our own experiment as described later in this section). The authors obtained their estimate by interpreting multiplets as outputs of symmetric self-renewal and analyzing how the fractions of singlets were changing over several cell cycles. This approach, however, is prone to underestimating the net decrease in the number of singlets. At later times, an output of symmetric self-renewal, which in Drosophila testes occurs also by way of dedifferentiation¹¹, might be mistaken for two individual singlets, since the reattachment of a dedifferentiated cell to the hub can occur at any position; together, these errors would cause the underestimation of the net drop in the number of singlets.

We confirmed the underestimation by repeating the experiments with 30-min heat shocks and first analyzed the experimental data using the method of ref. ¹³, i.e., by identifying the singlets and multiplets of the GFP-positive cells, as exemplified in Supplementary Fig. 3A. The singlet-multiplet identification (Supplementary Fig. 3B) yielded a decrease in the fraction of singlets of ~6% over two cycles, resulting in $p\approx$0.94 per cycle, close to the estimates by Salzmann et al., thus reproducing their results.

We then used the same experimental data to determine the time dependence of the number of all GFP-positive cells in the niche, no matter whether they are separated from, or adjacent to, other activated cells, thus avoiding the potential pitfalls of discriminating singlets from multiplets. The decline of the GFP-positive fraction (Supplementary Fig. 3C) is due to the smallness of the number of initially activated cells by short heat shocks. Indeed, with only a few GFP-positive cells in the niche, their loss is most likely compensated by the gain of GFP-negative cells, and an increase in the number of GFP-positive cells is much less likely than that of GFP-negative cells. Thus, the rate of the observed decline largely reflects the rate of loss of the GFP-positive cells, $-r{f}_{GFP+}\left(t\right)$, where $f_{GFP+}\left(t\right)$ stands for the GFP-positive fraction at time $t$; thus, $f_{GFP+}\left(t\right)\approx f_{GFP+}\left(0\right)e^{-rt}$.

We therefore used a single exponential, $A{e}^{-kt}$, to fit the experimental time dependence by varying $A$ and $k$, $k$ being an estimate of $r$ (Supplementary Fig. 3C). This yielded the estimate $p\approx$ 0.83 per cycle, which is much closer to the findings obtained with our model.

Taken together, our data fitting suggests that the ACD rate in the physiological GSC niche is roughly $p\approx$0.8 per cycle, thus a large proportion of niches indeed become clonal in aged flies (~50-day age, equivalent to 100 cycles, Fig. 1J).

Estimation of the effect of altered division mode on the time to clone expansion

Next, we sought to estimate the effect of altered p, q, and r rates on clone dynamics. E-cadherin (shotgun or shg) is a key regulator of ACD through its role in centrosome and spindle orientation³¹, and it also mediates adhesion between GSCs and hub cells³². We therefore choose to perturb shg expression to maximize the rates of q, and r. Based on the previously reported roles of Shg in the Drosophila testicular niche, we expected that removal of Shg may alter p, q, and r rates through two distinct mechanisms.

First, disruption of homotypic Shg interactions between GSCs and hub cells was expected to increase the stem cell “loss” rate due to weakened adhesion³². However, shg knockdown in the entire GSC population (nosGal4 >shg RNAi) does not lead to GSC depletion (Supplementary Fig. 3A). This is likely because shg expression was only partially reduced, and the increased rate of “loss” was compensated by a corresponding rise in the “gain” rate. Therefore, we expected a rise in both q and r.

Second, Shg is an essential component of the centrosome orientation checkpoint in concert with its downstream modulator, Bazooka³³, Par-1³⁴, and Cyclin A^34,35. This checkpoint monitors the interaction of centrosomes and apical Shg during GSC interphase^31,33. When centrosomes fail to orient correctly, the checkpoint delays mitotic entry^36,37. Because loss of Shg will allow cells to bypass the checkpoint and proceed with symmetric divisions^31,33, we expected that shg RNAi would elevate the rate of SCD without affecting mitotic activity.

To determine the p, q, and r rates of shg RNAi GSCs, we performed long-term live imaging (~16 h). We observed substantially higher rates of non-asymmetric events, both gain and loss (q and r) (Fig. 3A–F, wild-type data are shown in ref. ¹¹). The observed frequency of non-asymmetric events (q plus r) was 10.70 + 3.74 + 6.42 + 4.28 = 25.14% per cycle in wild-type GSCs, while it was 10.81 + 16.22 + 10.81 + 9.46 = 47.3% in shg RNAi GSCs (Fig. 3F), indicating that shg RNAi has roughly twice as many non-asymmetric events as wild-type GSCs (Fig. 3F). Therefore, we roughly determined the parameter for shg RNAi modeling as $p=$0.6/cycle, $q=r=$0.2/cycle, compared to the wild-type rate constants,$p=$0.8/cycle, $q=r=$0.1/cycle.

Fig. 3. Estimation of the effect of altered division mode on the time to clone expansion.

A–E Diagrams on the left illustrate the distinct events observed during long-term live imaging shg RNAi testis. To visualize GSCs, GFP-αTubulin was expressed together with shg RNAi under the nosGal4 germline-specific driver (see Method for more details). Selected frames from time-lapse imaging highlight each event, with germline cells outlined by yellow dotted lines. The interface between the indicated cell and the hub is marked with red solid lines. Asterisks denote the approximate location of the hub. Observed events include asymmetric division (A), symmetric self-renewal with misoriented spindles (left) or without (right) (B), symmetric differentiation (C), loss of a GSC (D), and dedifferentiation from a single gonialblast (E). All scale bars represent 10 μm. Asterisks indicate the location of the hub. The number of observed events for each category is indicated in parentheses. Corresponding movies are provided in supplementary materials (Movies S1–S6). F Pie charts show the average frequency of the event observed in a given time (12 h/cycle) in control: nosGal4>GFP-αTubulin (left, n = 31) and nosGal4>GFP-αTubulin plus shg RNAi (right, n = 11) testes. Details are provided in Supplementary Data. 2. G The graph shows the cumulative frequency of the clonal niche as a function of the number of cycles, based on 2000 simulations with the indicated parameters.

As expected, we did not observe a notable change in cell division rate in shg RNAi GSCs. The estimated average cell cycle time for control was 14.40 h (159 mitoses; 2290 total hours derived from 458 recording hours ~5 GSCs/niche). Similarly, the shg RNAi group showed an average cycle of 13.98 h (59 mitoses; 825 total hours derived from 165 recording hours ~5 GSCs/niche). Therefore, we concluded that shg RNAi is suitable for testing the effects of $p,q,r$ rate changes.

To assess computationally the impact of reduced ACD rates on clonal expansion, we performed simulations mimicking the shg RNAi conditions. For this, we used the experiment-based parameters, $p=$0.6/cycle, $q=r=$0.2/cycle, for which the clone expansion closely matches predictions of the detailed model (Supplementary Note 1 and Supplementary Fig. 5). Under these conditions, the median time to reach a clonal niche was 34 cycles, ~17 days. This was notably shorter than the 68 cycles (~34 days) observed in wild-type testes, where parameters were $p=$0.8/cycle, $q=r=$0.1/cycle (Fig. 1J).

It should be noted that the shg RNAi testes have a shorter event cycle (~10 h, compared to ~12 h for wild type, Fig. 3G), because of the increased frequency of “simple loss” and “dedifferentiation” events occurring independently of cell division. When the observed event cycle time in shg RNAi was used, the median time for reaching a clonal niche was even shorter, equivalent to ~14 days.

These results indicate that decreased ACD substantially shortens the time to clonal expansion of stem cells, consistent with our model showing ACD’s effect on extending the time to clone expansion.

GSC dynamics in conditions of non-neutral competition

The size of a stem cell pool is typically constrained by niche capacity. Within this constrained environment, stem cells compete through either “neutral” competition, where all cells have same p, q, r rates, or “non-neutral” competition, where a single, or a certain fraction of cells has different p, q, r rates³⁸. Indeed, studies have shown that oncogenic mutations in intestinal and hematopoietic stem cells can drive non-neutral, selective clonal expansion^7,39–41.

To generate a population of cells with differential p, q, r rates within the niche environment, we knocked down shg in a subset of GSCs. Heat-shock-induced flipping of stop codons located between the nanos promoter and Gal4 allows expression of GFP while simultaneously driving shg RNAi under the control of nosGal4 (Fig. 4A). Unflipped cells, which remain GFP-negative, do not express shg RNAi. This strategy generates a mixed population of GFP-positive (with RNAi) and GFP-negative (wild-type) GSCs within the same niche and allows us to investigate how a mixture of GSC clones with different p, q, r rates affect stem cell competition and dynamics (Fig. 4A).

Fig. 4. GSC dynamics in conditions of non-neutral competition.

A Schematic of the marking system used for the selection experiment. The heat-shock induced UAS-FLP expression removes the stop codon and starts expression of Gal4, which activates the expression of GFP in GSCs. GFP-positive GSCs also express shg RNAi driven by nosGal4, whereas GFP-negative GSCs remain wild-type. B Frequency of testes with different proportions of GFP-positive GSCs at 24 h post-heat-shock treatment (n = 50 testes). C The violin plot shows the frequency of GFP-positive GSCs in the testis (n = 50, 35, 50, and 45 for Days 0, 7, 14, and 21, respectively). n indicates the number of scored testes for each time point. D The violin plot shows the frequency of GFP-positive GSCs in the testis (n = 50, 49, 64, and 55 for Days 0, 7, 14, and 21, respectively). n indicates the number of scored testes for each time point. GFP-positive GSCs but not GFP-negative GSCs were expressing shg RNAi under the nosGal4 driver. Violin plots show kernel density estimate (KDE) and quantile lines. The width of each curve represents the frequency of data points. E, F Graphs show 2000 simulation results and experimental data. Indicated parameters were used for simulations. G Model for the global regulation of GSC number and niche compensation. When shg RNAi clones are frequently lost, wild-type clones contribute to compensation via increasing their gain rate. Root mean square deviations (RMSD) (in E, F) were calculated for fitting between the model and the experimental data, from the three time points. The “n” indicates the number of imaged testes. Normalized frequencies (in B) were calculated as follows: when any testes with no marked GSCs or with all GSCs marked were present at the day 0 scoring, the frequencies were subtracted from the day 0, and subsequent time points (days 7, 14, and 21) (see “Mathematical modeling” in the Method section for details). For fitting, event cycle = 10 h was used mimicking shg RNAi testes in which loss and gain increase independent of cell division during the selection process.

A single 40-min heat-shock treatment successfully marked ~50% of the GSCs (Fig. 4B). In control testes, where both GFP-positive and GFP-negative GSCs were wild-type, the GFP-positive and negative cells were often found co-existing in the same niche throughout the examined time points (Fig. 4C). Over time, either GFP-positive, or GFP-negative cells expanded towards 100% or were entirely lost (0%), representing the expected outcomes of a neutral drift (Fig. 4C). However, GFP-positive cells with shg RNAi were rapidly lost, indicating the competitive disadvantage of shg RNAi GSCs against the GFP-negative (wild-type) GSCs (Fig. 4D).

To see whether our model can reproduce the experimentally observed dynamics, we first assumed that the two subgroups of GSCs sharing the niche are regulated independently—a scenario in which the expansion of wild- type GSCs passively takes spaces freed by the shg RNAi GSCs that have left the niche. Correspondingly, the parameters of these two types of GSC clones were assigned the estimates from the previous section, which were based on our live imaging data: for the shg RNAi GSCs (GFP-positive), the ACD rate (p) was set at 0.6/cycle, with $q=r=$ 0.2/cycle, while for wild-type (GFP-negative) GSCs, the rates were $p=$ 0.8/cycle with $q=r=$0.1/cycle. The simulation outcomes obtained with this combination of parameters (red solid lines in Fig. 4E) were in qualitative agreement with the experimental data (blue dots in Fig. 4E), but the fit was not entirely accurate. In particular, the simple mixture of the clones predicted that a small fraction of testes would become 100% GFP-positive by days 14 and 21 (see blue-highlighted areas in Fig. 4E and Supplementary Fig. 6A in the middle and right panels), which was inconsistent with the experimentally observed rapid loss of GFP-positive GSCs with shg RNAi (Fig. 4D, E and Supplementary Fig. 6A).

We were able to obtain a substantially better fit to the experimental data, particularly for the probabilities of GFP-positive fractions of zero and unity, by decreasing the value of $p$ for the wild-type GSC in the mixture to $0.6$ per cycle (the full parameter sets used were $\left(p,q,r\right)=\left(0.6,0.1,0.3\right)$ (per cycle), for shg RNAi GSCs, and $\left(p,q,r\right)=\left(0.6,0.3,0.1\right),$ for the wild-type subgroup) (Fig. 4F and Supplementary Fig. 6B, compare with Fig. 4E and Supplementary Fig. 6A). These simulations describe a scenario in which the outcompeting GFP-negative GSCs actively respond to the decreases in niche occupancy by reducing their ACD frequency (Fig. 4G).

Effect of shg RNAi clone induction on wild-type GSCs sharing the same niche

To directly investigate the spatiotemporal nature of this compensatory behavior, we attempted long-term live imaging. However, due to the difficulty to maintain GFP signal over the long-term time-lapse imaging, we could not follow the behavior of GFP positive vs. negative clones. Therefore, to test experimentally whether the induced shg RNAi clones have an effect on wild-type GSCs sharing the same niche, we examined mitotic spindle orientation in fixed samples.

Spindle orientation is a strong indicator of the ability of the cells to divide asymmetrically⁹. After we knocked down shg in approximately half of GSCs with 40-min heat-shock treatment, we cultured flies for 4 days and dissected before the GFP-positive cells with shg RNAi were completely lost (Fig. 4D). Consistent with the rapid loss of shg RNAi GSCs, testes with induced shg RNAi clones tended to contain slightly lower GSC numbers at the day 4 time point compared with control testes (Control:8.37 ± 2.31, shg RNAi:5.79 ± 1.58, p value:0.00029, n = 19 each). Moreover, shg RNAi SGs are often found in the testis where remaining GFP-positive GSCs are no longer present (16 cases out of 20), while in control testes, GFP-marked spermatogonia are always found when GFP-positive, ancestor GSCs are present (in all 26 cases out of 26 (Fig. 5A, B). This indicates that shg RNAi GSCs are mainly lost by differentiation as observed in the live imaging experiments (Fig. 3F).

Fig. 5. Effect of shg RNAi clone induction on wild-type GSCs sharing the same niche.

A, B Representative images of the testis tip of 4 days post-marking, approximately half GSCs per testis on average (40 min heat shock was used). C, D Representative images of mitotic GSCs in a GFP-negative neighbor in control (oriented, C or shg RNAi (misoriented, D) samples. Mitotic cells were determined by the absence of a nuclear envelope, with uniform Vasa distribution throughout the cell (blue). E Frequency of spindle orientation scored in control clones, neighbors, and shg RNAi clones and neighbors. Note that the apparent 100% in our control samples is likely due to the small sample size. Testes were dissected at the 4-day point after clone induction. “n” indicates the number of scored mitotic GSCs. Šídák’s multiple tests calculated p values. All scale bars correspond to 10 μm. Asterisks in the images indicate the approximate location of the hub. All data were shown as means ±  s.d.

We then examined mitotic spindle orientation, a parameter often controlled by regulatory pathways that influence stem cell division mode^42,43. In most wild-type GSCs, mitotic spindles are perpendicularly oriented towards the hub-GSC interface, where one of the two centrosome is located close to the hub-GSC interface, while the other is at the opposite side of the GSC (Fig. 5C). It must be noted that GSCs typically exhibit a higher spindle orientation rate (i.e., ~95%)³⁷ than the frequency of asymmetric outcomes (i.e., 70–80%, Fig. 3F). This discrepancy reflects the frequency of dedifferentiation and loss occurring independent of cell division, and that spindle orientation is necessary but not sufficient to ensure asymmetric fate in GSCs.

Strikingly, misoriented spindles were frequently observed in both remaining shg RNAi GSC clones and in GFP-negative wild-type GSCs (Fig. 5D, E), indicating that the wild-type GSCs indeed actively decrease the frequency of ACD when compensating for the loss of the shg RNAi GSCs. Since we often observed misoriented GSCs in testes without any remaining GFP-positive shg RNAi clones (Fig. 5D), this compensatory behavior is likely caused by global loss of GSCs, rather than directly activated by neighboring cells.

Collectively, these data support a model where wild-type GSCs sense niche occupancy and actively adjust their division mode to maintain homeostasis. Future studies will be required to identify the global signals that sense niche occupancy and modulate the behavior of resident GSCs. Moreover, while this method provides high-resolution snapshots of spindle orientation, the reliance on fixed cells remains a potential limitation that precludes the direct, real-time assessment of cell behavior. Future studies will be needed to develop more robust markers compatible with live cell imaging.

Discussion

Tissue stem cells reside in a specialized microenvironment called the niche. Traditionally, ACD has been suggested to be the primary mechanism of stem cell maintenance by balancing self-renewal and differentiation. However, stem cells can also be maintained through SCD without expansion or reduction. When stem-cell fate determination relies on niche environment signals, the stem cell pool size is maintained via niche-capacity restriction. In fact, both ACD and SCD contribute to the long-term tissue homeostasis in most tissues.

In this study, we found that a niche with a higher probability of ACD shows later emergence of a clonal niche (the condition in which a niche is occupied by a single clone). When the ACD rate is high ($p>$ 0.9), a clonal niche will not emerge within the average fly lifetime (~120 divisions, equivalent to ~60 days, Fig. 1J, K). In contrast, a low probability of ACD ($p<$0.4) results in a niche that quickly becomes clonal (Fig. 1J, K), supporting our hypothesis that ACD is an essential factor for delaying clone expansion.

In recent years, clonal expansion of stem cells has emerged as a crucial factor in the development of multiple pathological conditions. Clonal hematopoiesis (CH) is a condition characterized by the presence of clonally expanded hematopoietic stem cells (HSCs) and has emerged as a risk factor for hematopoietic malignancy and cardiovascular diseases^2,5. Human and mouse HSC clones can be detected using multiple tools, such as CRISPR-based barcoding and mitochondrial DNA mutation tracking, combined with single-cell sequencing technologies^4,5,44,45. Moreover, extensive clinical studies have identified commonly mutated genes within these expanding HSC clones and explored the mechanisms by which these mutations contribute to disease progression^4,5. Removal of mutant clones by manipulating competition between mutant and normal cells has been suggested as a novel strategy for definitive treatment^46–53, but much of the mechanistic knowledge required for implementation of such treatment is still lacking.

Our mathematical model of clonal expansion, used in this study to obtain accurate estimates of the effect of ACD and SCD in Drosophila testes, could also be adapted to predict stem cell behavior in mammalian stem cell niches, both in normal and various pathological conditions. The degree of the effect of division mode on clonal expansion likely varies among systems. We further tested the effect of stem cell pool size, which indicates that the rate of neutral drift is inversely correlated with stem cell pool size (Supplementary Fig. 7). Along with slower division rates and limited stem cell mobility, larger pool size is characteristic of many mammalian stem cell systems. These factors explain why mammalian stem cells, such as HSCs, generally take longer to develop a detectable clone size.

Moreover, various types of systemic factors, such as a large-scale cell loss, chemotherapy, irradiation, or changes in metabolism or hormones, can accelerate drift by altering the competitive landscape. Factors that affect clone dynamics would vary in different systems. The impact of these factors may depend on the proportion of steady-state division modes, cell proliferation rates, and sizes of stem cell pools. Nevertheless, we propose that our simplified model with experimental verification can be easily modified to apply to different systems and will provide fundamental knowledge on how stem cells may contribute to disease development.

In addition to systemic influences, intrinsic alterations in the stem cell itself can contribute to clonal expansion. These “non-neutral” competitions, such as those caused by mutations, can override neutral drift and promote selective clonal expansion. Multiple intrinsic mutations have been identified in dominant clones associated with human clonal hematopoiesis⁴. The extent to which these diverse factors influence the rate of clonal expansion likely varies depending on the specific context and nature of the mutation. In some reported cases, stem cell competition occurs in a more aggressive manner, a phenomenon referred to as “supercompetition”. Such behavior has been documented in mammalian intestinal stem cells^47,48, where Apc (Adenomatous polyposis coli)-mutant clones actively suppress the proliferation of neighboring wild-type crypt cells by secreting signaling antagonists that induce their differentiation, thereby displacing wild-type cells from the niche^47,48. In our experiment, induction of shg RNAi clones in the testis caused the RNAi clones to be lost from the niche, which in turn prompted the remaining stem cells to undergo more symmetric divisions (Figs. 4G and 5). Notably, these symmetrically dividing stem cells were not necessarily located adjacent to shg RNAi stem cells (Fig. 5), suggesting that the compensatory response occurs through a global regulation to promote “gain” events in response to the “loss”. The effect is unlikely to be mediated through direct competition among neighboring cells.

Overall, our work provides a simple model for understanding the clonal dynamics of stem cells. Our data indicate that the Drosophila male GSC niche exerts population-level control over GSC pool size as proposed in many stem cell systems, in which GSCs compete through both neutral and non-neutral mechanisms. Our study demonstrates that the interplay between these modes of competition governs clonal dynamics, providing a useful framework for understanding how stem cell clones expand across an organism’s lifetime.

Materials and methods

Fly husbandry and strains

All fly crosses were performed on standard Bloomington medium at 22 °C to avoid hs-flp expression, and the indicated age (days after clone marking) of flies were used for all experiments. The following fly stocks were obtained from Bloomington stock center (BDSC); hs-flp (BDSC1929), shg RNAi (BDSC38207), nosGal4 (BDSC64277)⁵⁴ and nos-FRT-mCherry-stop-FRT-Gal4, UAS-GFP¹³ was from Inaba lab stock. UAS-GFP-αTub⁵⁵ is a kind gift from Yukiko Yamashita.

GFP labeling of germline stem cells

Flies carrying the heat-shock-FLP allele were crossed with nos-FRT-mCherry-stop-FRT-Gal4, UAS-GFP flies and maintained at 22 °C. About 0–3 days old progenies were heat-shocked in a 37 °C water bath once for 40 min (optimized for 50% marking, Supplementary Fig. 1) in vials with fly food. Vials were placed back at 22 °C and testes were dissected at desired time points (24 h, days 7, 14, and 21 post-heat shock). For single GSC marking (Supplementary Fig. 2), we used 30-min heat shock.

Immunofluorescence staining

Testes were dissected in phosphate-buffered saline (PBS) and fixed in 4% formaldehyde in PBS for 30–60 min. Next, testes were washed in PBST (PBS + 0.2% Triton X-100, Thermo Fisher) for at least 60 min, followed by incubation with primary antibody in 3% bovine serum albumin (BSA) in PBST at 4 °C overnight. Samples were washed for 60 min (three times for 20 min each) in PBST, incubated with secondary antibody in 3% BSA in PBST at room temperature for 2 h and then washed for 60 min (three times for 20 min each) in PBST. Samples were then mounted using VECTASHIELD with 4’,6-diamidino-2-phenylindole (DAPI) (Vector Lab).

The primary antibodies used were as follows: rat anti-Vasa (1:20; developed by A. Spradling and D. Williams, obtained from Developmental Studies Hybridoma Bank (DSHB); mouse-anti-Hts (1B1, 1:20; DSHB) mouse-anti-FasIII (1:20, 7G10; DSHB); mouse-anti-γ-Tubulin (GTU-88, 1:200, Sigma). AlexaFluor-conjugated secondary antibodies (Abcam) were used at a dilution of 1:400.

Long-term live imaging

Live imaging was conducted based on an established protocol⁵⁶. Testes were dissected into 1X Becker’s Ringer’s solution⁵⁶ and mounted on 35 mm glass-bottom dishes (Nunc). About 500 µL of 1 mg/mL poly-L-lysine solution (Sigma) was applied to the coverslip portion of the dish and left to incubate at room temperature for 5–7 h. After incubation, the poly-L-lysine was replaced with Becker’s Ringer’s solution. Testes were placed on the poly-L-lysine-coated surface, with their tips oriented downward. The Becker’s Ringer’s solution was then carefully removed and replaced with prewarmed Schneider’s Drosophila medium supplemented with 10% fetal bovine serum and glutamine–penicillin–streptomycin (Sigma).

Time-lapse Z-stack images (2 µm intervals over 10–15 stacks) were captured every 10 min for up to 16 h using a Zeiss LSM800 Airyscan confocal microscope equipped with a 63× oil immersion objective (NA = 1.4). Automated acquisition was performed using the preset tiling function.

Image analysis

Airyscan time-lapse images were processed using Zen software (Zeiss) using 2D processing mode, and each event in Fig. 3 was manually tracked across z-stacks. Testes from 0–3-day-old flies were used. The hub area was identified as a circular region with autofluorescence at the testis tip, surrounded by fluorescently labeled germline stem cells. Dedifferentiation was identified when germline cells from more than one cell layer outside the hub edge reattached to the hub and remained in position for at least ten frames (equivalent to 100 min). Movies were annotated using Veed.io.

Quantification of spindle orientation

Spindle orientation was quantified based on the positioning of the proximal spindle pole relative to the hub interface. In accordance with the established criteria³⁷, a spindle was classified as “oriented” if the proximal spindle pole was closely located near the hub-GSC interface (within 90 degree angle)³⁷. The position of the spindle pole is identified by visualizing the spindle itself using the marker UAS-GFP-αTub⁵⁵, under the germline-specific nosGal4 driver.

Mathematical modeling

To study the dynamics of unsynchronized clones, we formulated a continuous-time stochastic model. We first assume that all clones are described by the same probability rates of outcomes of randomly occurring asymmetric and symmetric divisions; thus, there are three model parameters: the rate constant of asymmetric division $p$, and the rate constants of gain $q$ and loss $r$.

Let $\nu$ be the average event frequency, then $p+q+r=\nu .$ Because the model time scale is set by the average time between subsequent events, which we will term “event cycle”, it is convenient to use it as a time unit, then $\nu =1\left(\frac{1}{\mathrm{cycle}}\right)$ and $p+q+r=1\left(\frac{1}{\mathrm{cycle}}\right)$. Since the average number of cells in the niche is constant, then $q$ must equal $r$, so the system has only one independent parameter. Note that even with $q=r$, fluctuations of the niche population around its average size would grow with time, unless additional regulation is exercised, as described below.

Our model is formulated in terms of the number of descendants of individual clones $\left\{n_i\right\}$, where index $i$ enumerates original clones (and their descendants): $i=1,\dots ,N$, where $N$ is the niche capacity. The dynamics of $n_i$ are governed by the randomly occurring events of asymmetric and symmetric divisions.

To restrict fluctuations of the population size, the niche must ensure that the total number of cells, $n_{\mathrm{tot}}$ = ${\sum }_1^N{n}_i$, at any time remains close to $N$: $∣n_{\mathrm{tot}}-N∣<\epsilon ,$ where $\epsilon$ is a small positive integer. Care must be taken to interpret such control in a biologically consistent manner (see detailed discussion later in this section). Our implementation of tight control over $n_{\mathrm{tot}}$ by the niche assumes a strong correlation between gain and loss occurrences. Specifically, the system is governed by the following transition probabilities:

$$P\left(n_i,t+dt\mid n_i,t\right)=p{n}_{i}dt\left(\mathrm{clone\; maintenance}\right),P\left(n_i+1,t+dt\mid n_i,t\right)=n_{i}dt\cdot \left\{\begin{array}{c}\hfill {q,\mathrm{if}N-\epsilon <n}_{\mathrm{tot}}<N+\epsilon \hfill \\ \hfill q+r,\mathrm{if}{n}_{\mathrm{tot}}=N-\epsilon \hfill \end{array}\right)\left(\mathrm{gain}\right),P\left(n_i-1,t+dt\mid n_i,t\right)=n_{i}dt\cdot \left\{\begin{array}{c}\hfill {r,\mathrm{if}N-\epsilon <n}_{\mathrm{tot}}<N+\epsilon \hfill \\ \hfill q+r,\mathrm{if}{n}_{\mathrm{tot}}=N+\epsilon \hfill \end{array}\right)\left(\mathrm{loss}\right).$$ 1

The model was solved by generating stochastic trajectories of the system in VCell²⁷ with a nonspatial Monte Carlo solver based on the Gibson–Bruck method⁵⁷. The clonal expansion was analyzed for the uniform initial conditions, ${n_i\mid }_{t=0}=1$ for all $i=1,\dots ,N.$ Results indicate that our model retains features of discrete-time Moran-type stochastic processes^58,59, with all $n_i$ being interdependent.

Note that the inequality $∣n_{\mathrm{tot}}-N∣<\epsilon$ can also be enforced by lowering transition probabilities of the symmetric outcomes that violate this inequality or setting such probabilities to zero. Below is an example of postulating low probabilities of unwanted symmetric outcomes⁵⁹:

$$\begin{array}{c}\hfill \begin{array}{c}\hfill P\left(n_i+1,t+dt\mid n_i,t\right)=n_{i}dt\cdot f\left(n_{\mathrm{tot}}\right)\left(\mathrm{gain}\right),\hfill \\ \hfill P\left(n_i-1,t+dt\mid n_i,t\right)=n_{i}dt\cdot \left(1-f\left(n_{\mathrm{tot}}\right)\right)\left(\mathrm{loss}\right),\hfill \\ \hfill \mathrm{with}f\left(n_{\mathrm{tot}}\right)={\left(1+{\left(n_{\mathrm{tot}}/N\right)}^{10}\right)}^{-1}\hfill \end{array}\hfill \end{array}$$ 2

Alternatively, the probabilities of the outcomes violating the limits for $n_{\mathrm{tot}}$ could be set to zero:

$$P\left(n_i+1,t+dt\mid n_i,t\right)=n_{i}dt\cdot \left\{\begin{array}{c}\hfill 1,{\mathrm{if}n}_{\mathrm{tot}}\le N+\epsilon -1\hfill \\ \hfill 0,\mathrm{otherwise}\hfill \end{array}\right)\left(\mathrm{gain}\right),P\left(n_i+1,t+dt\mid n_i,t\right)=n_{i}dt\cdot \left\{\begin{array}{c}\hfill 1,{\mathrm{if}n}_{\mathrm{tot}}\ge N-\epsilon +1\hfill \\ \hfill 0,\mathrm{otherwise}\hfill \end{array}\right)\left(\mathrm{loss}\right).$$ 3

The transition probability of asymmetric divisions in these approaches is the same as in Eqs. (1).

Equations (2) and (3), however, result in an artificial dependence of a cycle period on the type of division the stem cell decides to undergo. Indeed, because these methods effectively rule out certain symmetric outcomes, there are, on average, fewer symmetric divisions per unit time than asymmetric ones. As a result, the average period of a symmetric division is longer than that of an asymmetric one.

Such artefacts do not arise in the model defined by Eqs. (1). The VCell implementation of this model can be found in VCell database of public MathModels under username “boris”; the model name is “Inaba_population_model_5_1(stoch)_As_only_automated”.

Utilizing the mathematical model for the analysis of experimental data

In this section, the mathematical modeling is used for analyzing the data obtained in experiments with transgenic male flies that enable the induction of GFP-labeled stem cell clones. The experiments were aimed at determining values of $p$, $q$ and $r$ characteristic of the population dynamics of GSCs in Drosophila testes.

Frequencies of symmetric divisions in Drosophila testes were estimated in an earlier study¹³, where observed population dynamics of GFP-marked cells were also compared against predictions from a mathematical model. The model used in¹³ was applicable only to experiments with few GFP-positive cells per niche at any time, because it ignored the dynamics of unmarked cells. However, amassing statistically significant data from experiments with a small number of GFP-positive cells per niche requires examining large pools of flies, which makes these experiments inefficient.

In our experiments, the flies were induced to have an initial number of marked stem cells of about half the niche capacity. As in ref. ¹³, we tracked over time the fractions of GFP-positive cells in the niches, $\frac{n_{GFP+}}{N}$. Specifically, four portions of a large pool of inducted flies were sacrificed at times separated by 7 days, with time zero being the closest to the time of induction. For each time point, testes were dissected, the total number of stem cells and the number GFP-positive cells were counted, and their ratio $\frac{n_{GFP+}}{N}$ was computed for each testis. The value of $p$ was determined by comparing experimental distributions of $\frac{n_{GFP+}}{N}$ at the specific times $t$, $P_{\exp }\left(\frac{n_{GFP+}}{N}\mid t\right)$, to corresponding theoretical distributions $P_{\mathrm{theor}}\left(\frac{n_{GFP+}}{N}\mid t\right)$ predicted for varying $p$ by our model whose applicability was not limited to small $n_{GFP+}$ .

The direct use of the model described by Eqs. (1) for deriving predicted distributions involves significant postprocessing. A more efficient version of the model is formulated in terms of only two variables $\left\{n_{1,}{n}_2\right\}$ denoting the numbers of the GFP-negative and GFP-positive cells in the niche, respectively. This model reduction also applies to modeling clone selection and mutant dynamics, where the two subsets are characterized by different parameters $\left(p_1,q_1,r_1\right)$ and $\left(p_2,q_2,r_2\right)$. Therefore, $n_1$ and $n_2$ are governed by the following transition probabilities:

$$P\left(n_1,t+dt\mid n_i,t\right)=p_1{n}_{1}dtP\left(n_2,t+dt\mid n,t\right)=p_2{n}_{2}dt\left(\mathrm{clone\; maintenance}\right);P\left(n_1+1,t+dt\mid n_1,t\right)=n_{1}dt\cdot \left\{\begin{array}{c}\hfill {q_1,\mathrm{if}N-\epsilon <n}_{\mathrm{tot}}<N+\epsilon \hfill \\ \hfill q_1+r_1,\mathrm{if}{n}_{\mathrm{tot}}=N-\epsilon \hfill \end{array},\right)P\left(n_2+1,t+dt\mid n,t\right)=n_{2}dt\cdot \left\{\begin{array}{c}\hfill {q_2,\mathrm{if}N-\epsilon <n}_{\mathrm{tot}}<N+\epsilon \hfill \\ \hfill q_2+r_2,\mathrm{if}{n}_{\mathrm{tot}}=N-\epsilon \hfill \end{array},\right)\left(\mathrm{gain}\right);P\left(n_1-1,t+dt\mid n_1,t\right)=n_{1}dt\cdot \left\{\begin{array}{c}\hfill {r_1,\mathrm{if}N-\epsilon <n}_{\mathrm{tot}}<N+\epsilon \hfill \\ \hfill q_1+r_1,\mathrm{if}{n}_{\mathrm{tot}}=N+\epsilon \hfill \end{array},\right)P\left(n_1-1,t+dt\mid n_1,t\right)=n_{1}dt\cdot \left\{\begin{array}{c}\hfill {r_1,\mathrm{if}N-\epsilon <n}_{\mathrm{tot}}<N+\epsilon \hfill \\ \hfill q_1+r_1,\mathrm{if}{n}_{\mathrm{tot}}=N+\epsilon \hfill \end{array},\left(\mathrm{loss}\right).\right)$$ 4

where $n_{\mathrm{tot}}=n_1+n_2$.

In a single run, the solver returns an instance of $n_{GFP+}$ at time $t$ for a given $N$ and an initial value of $n_{GFP+}$ (in all calculations, we used $\epsilon =1$ and assumed that $N$ does not change with time). Because in the experiments $N$ varied from subject to subject, the predicted distribution $P_{\mathrm{theor}}\left(\frac{n_{GFP+}}{N}\mid t\right)$ is a weighted average of the distributions obtained for each $N$, experimentally observed at time $t$, and each $n_{GFP+}$ observed at $t=0$, which did not exceed the given $N$.

Accordingly, we first determined, by statistically processing the experimental results for each time point $t$, the frequencies, or “weights”, of all values of $N$ observed at time $t$, $w_{\exp }\left(N,t\right)$. Similarly, we determined the frequencies of all initial $n_{GFP+}$ for each $N$ observed at time $t$, $w_{\exp }\left(n_{GFP+},0\mid N,t\right)$. Both weights were normalized to unity. Secondly, for each pair of $N$ and initial $n_{GFP+}$, we determined the probability distribution of$\frac{n_{GFP+}}{N}$ at a time point $t$, $P\left(\frac{n_{GFP+}}{N},t\mid \left(N,t\right),\left(n_{GFP+},0\right)\right)$. For this, we simulated large amounts of predicted $n_{GFP+}$ by running the Monte Carlo solver with the transition probabilities defined by Eqs (4), assuming that the GFP-positive and GFP-negative cells are characterized by the same parameter set. The predicted distribution was then computed as ${\mathrm{P}}_{\mathrm{theor}}\left(\frac{n_{GFP+}}{N},t\right)={\sum }_{\left(N,t\right)}\left\{w_{\exp }\left(N,t\right)\left[{\sum }_{\left(n_{GFP+},0\right)}{w}_{\exp }\left(n_{GFP+},0\mid N,t\right)P\left(\frac{n_{GFP+}}{N},t\left(N,t\right),\left(n_{GFP+},0\right)\right)\right]\right\}.$

For each time point and for each tested value of parameter $p$, we compared $P_{\exp }\left(\frac{n_{GFP+}}{N}\mid t\right)$ and $P_{\mathrm{theor}}\left(\frac{n_{GFP+}}{N}\mid t\right)$ by computing the root mean squared deviations,

$$\delta ={\left(\frac{1}{M}{\sum }_{\left(n_{GFP+,t}\right)}{\left(P_{\exp }\left(\frac{n_{GFP+}}{N}\left.∣\right)t\right)-P_{\mathrm{theor}}\left(\frac{n_{GFP+}}{N}\left.∣\right)t\right)\right)}^2\right)}^{1/2},$$

where $M$ is the number of values of $\left(\frac{n_{GFP+}}{N}\mid t\right)$ for which the probabilities were computed.

The VCell implementation of the reduced model defined by Eqs (4) can be found in the VCell database of public MathModels under username “boris”; the model name is “Inaba_population_model_10_(stoch)_selection_reduced”.

Statistics and reproducibility

No statistical methods were used to predetermine sample size. The experiment values were not randomized. The investigators were not blinded to allocation during experiments and outcome assessment. Statistical analysis and graphing were performed using GraphPad Prism 9. The illustrations were generated using BioRender.com or Adobe Illustrator. All data were shown as means ± s.d.

Author contributions

All authors contributed equally to conception and design, interpretation of data, wrote, and edited the manuscript. B.M.S. and M.B.B. performed mathematical modeling and data fitting using VCell. M.B.B. and M.I. performed acquisition and analysis of experimental data.

Peer review

Peer review information

Communications Biology thanks Hwei-Jan Hsu, who co-reviewed with Kreeti Kajal and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Ophelia Bu. A peer review file is available.

Data availability

The data that support all experimental findings of this study are available within the paper and its Supplementary Information files. Numerical values for all graphs are provided in Supplementary Data. 1 and 2. The VCell implementation of all models used in this study can be found in the VCell database of public MathModels under model names shown in the Materials and methods section. Live imaging files are available from BioStudies website (https://www.ebi.ac.uk/biostudies) under the accession number S-BSST2892. Simulation details for each figure are found in Figshare: 10.6084/m9.figshare.31909696.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s42003-026-10079-1.