Tracking changes in patterns of cell growth and expression of resistance genes across the colony during an abrupt exposure to 100 μg/ml of tetracycline (which is lethal to planktonic populations), we find an initial reduction of growth among fast-growing cells near the opening of the trap and reactivation of previously dormant cells at deeper layers, presumably because of a redistribution of nutrients toward the interior of the colony (Figure 2). Tetracycline is a translation inhibitor, which binds ribosomes and reduces cell growth (Chopra and Roberts, 2001). Therefore, immediately after exposure, cells at the surface of the colony have their growth rate significantly reduced (Figures 2B, 3A), which also decreases consumption of nutrients. Following the exposure, a rearrangement of the growth profile creates a zone of intermediate growth rates that extends deeper into the colony (Figure 2) and temporarily reactivates cells beyond the original boundary, which were dormant before exposure. This observation is consistent with the reduced nutrient consumption at the colony surface, where the resulting surplus of nutrients becomes available to cells further inside the colony, blurring the boundary between growing and arrested cells and causing the reactivation.

After a transient period, growth at the colony surface is restored, and expression of resistance is resumed among growing cells at the colony surface. Unlike nutrients, active import of antibiotics is at least very rare (Delcour, 2009; Sugano et al., 2010; Housden et al., 2021; Rybenkov et al., 2021). In our case, tetracycline diffuses slowly through the cell membrane, with a half-equilibration time of approximately 45 min (Sigler et al., 2000; Reuter et al., 2020). Tetracycline is also not actively degraded intracellularly by enzymes, so cells do not act as a significant sink for the drug, as they do for nutrients. Since diffusion of tetracycline through the extracellular space of the trap is much faster than uptake by cells and removal by advection (diffusion time of ∼20 s like for nutrients, see section “Materials and Methods”), the drug can quickly diffuse from the opening of the trap into the interior. We confirm the timescale and reach of diffusion of tetracycline through the trap by measuring the diffusion of a dye of similar size (sulforhodamine, MW = 558) added to the medium containing the drug (Supplementary Figure 2). Therefore, upon exposure to antibiotics, all growing cells across the colony can sense the presence of the drug and induce drug responses. As TetA is expressed and growth at the surface of the colony resumes, so does the consumption of nutrients, which causes the boundary between growing and arrested cells to move closer to the opening of the trap once again (Figures 2E,G). Around 5 h after exposure, after expression of resistance and cell metabolism have stabilized to the new steady state, growth at the surface of the colony settles at a rate 75% of that in the absence of drug, and a sharp boundary is again delineated 20 μm further into the trap from the location of the original boundary before drug exposure (Figures 2B,E,G). Upon removal of tetracycline, the growth profile of the colony returns to the same levels as before exposure within 3 h.

The transient period following exposure to tetracycline is dominated by two processes: within the first hour, the growth profile of the colony is determined by levels of TetA already present at the time of exposure; then, in the following 4 h, the growth profile is determined by activation of resistance in growing cells throughout the colony. Slow-growing cells around the boundary generally show higher levels of TetA expression prior to exposure (Figure 2C), an effect which will be discussed in more detail in section “Slow-Growing Cells Express Higher Levels of Resistance Genes” below. Due to this growth-dependance in the expression of resistance, when fast-growing low-TetA cells at the surface of the colony are suddenly arrested by contact with tetracycline, dormant or slow-growing high-TetA cells at the boundary are reactivated and increase growth to occupy the top of the colony, displacing the arrested cells (Figures 2B,C). Although preexisting TetA levels are initially reduced in these cells as they begin to grow faster, this reduction is compensated by the strong expression of TetA induced upon exposure, reaching high levels even in fast-growing cells as the colony approaches steady state (Figure 3). Throughout this process the levels of repressor TetR change in similar fashion as TetA, reflecting their common regulation by TetR itself (Schultz et al., 2017), although fully expressed TetR does not reach the same increase in relation to basal levels as TetA does (Figure 3).

As expression of resistance recovers growth at the top of the colony, the boundary between growing and arrested cells moves back toward the surface. The temporary activation of dormant cells deep into the colony, which happens in the transient period following exposure, induces high levels of resistance in cells growing slowly in the presence of tetracycline (Figure 3). These cells once again stop growing when growth is restored at the surface, providing the colony with a fresh layer of dormant cells with high basal levels of resistance (Figures 2B–D). Due to their low metabolism, these cells keep high TetA levels even after the drug is removed, suggesting a mechanism where highly resistant dormant cells can be quickly activated in the event of future drug exposures (we explore this hypothesis in the next section). The reorganization of growth patterns upon drug exposure also ensures that the colony is able to keep consuming the available resources and maintain overall growth. Despite the reduction of growth at the surface of the colony, the population as a whole experiences only a mild reduction in growth during drug exposure (Figure 2G) as active growth is merely shifted from the surface to the interior of the colony upon drug exposure (Figure 3).

The complex dynamics of growth and expression of resistance following drug exposure, particularly around the boundary between growing and arresting cells, can lead neighboring cells to different phenotypes. Although it is difficult to track single cells throughout the experiment, we use the local velocities at each timepoint to estimate the spatial trajectories followed by single cells during drug exposure. We follow three “single-cell” trajectories that initiate at close locations in space, near the deepest point reached by the boundary, shortly after exposure (Figure 2E). A first cell, whose trajectory initiates slightly above the boundary, is quickly pushed toward the surface of the colony by the transient growth of deeper layers following exposure, exiting the trap before any significant expression of TetA. A second cell, whose trajectory initiates at the boundary, is only slightly dislocated by the transient growth of deeper layers, which lasts until growth at the surface of the colony is restored. This trajectory then goes through a period of slow growth when expression of TetA reaches high levels. Eventually, this cell enters the fast-growth region above the boundary layer, reducing TetA levels on its way out of the trap. A third cell, starting right below the boundary, goes through a period of transient growth itself, when expression of TetA is high, but does not have enough push from growth of deeper layers to move significantly up the trap. This cell eventually goes back to dormancy, keeping high levels of TetA. In general, from the top to the bottom of the colony, we see the same three phenotypes observed previously in single-cell studies of drug responses: fast-growing cells expressing moderate levels of efflux pump TetA close to the surface of the colony, slow-growing cells overexpressing TetA around the boundary, and dormant cells with little TetA expression in the deep interior (Schultz et al., 2017).

The temporary reorganization of growth patterns following drug exposure suggests a colony-wide mechanism of resistance by which transient growth promotes high expression of resistance in dormant cells in the interior of the colony. These resistant cells are then able to grow and repopulate the colony during subsequent drug exposures, when fast-growing cells at the surface of the colony are arrested by sudden contact with the drug. Since the rate of expression of resistance genes depends on the cell’s metabolic state, fast-growing cells close to the surface are better positioned to regulate resistance levels to optimize growth, whether in the presence or absence of drug. However, fast-growing cells are particularly affected upon sudden drug exposures when their resistance levels are low. Therefore, dormant cells in the interior of the colony, which are not able to change their protein levels and keep high levels of resistance even in the absence of drug, can quickly start growing and replace the arrested cells at the top. In this manner, the colony can collectively maintain cell growth during drastic changes in the environment.

To study the dynamics of antibiotic responses in fluctuating environments, we subjected the colony to windows of 5, 10, 20, and 60 min of tetracycline exposure, delivered every 2 h (Figure 4). Regardless of the duration of drug exposure, we observe the same colony dynamics described above. Pulses of high drug concentrations permanently arrest growth in fast-growing cells at the top of the colony, which have low TetA levels at the time of exposure, while promoting growth further into the colony (Figure 5). Over the next hour, the cells at the top of the trap are replaced by the progeny of cells located below the boundary at the time of exposure, which already have significant levels of TetA upon contact with the drug (Figures 4A,B). This process is initiated even by short pulses of drug and continues to take place in the absence of the drug. This suggests both that growing cells are permanently arrested shortly after contact with tetracycline and that initial recovery of colony growth does not depend on new expression of TetA, but on the presence of cells with preexisting high levels of resistance.

Each pulse of tetracycline was followed by temporary expression of resistance genes at the top of the colony, which had mostly subsided by the time of the next pulse (Figures 4B,C). While TetR was expressed quickly and strongly regardless of pulse length, TetA concentration was higher after longer drug exposures, but concentration of either resistance gene was quickly reduced in growing cells in the absence of drug. On the other hand, each pulse of tetracycline permanently increased expression of resistance in slow-growing cells below the boundary (Figure 5D). Periods of transient growth following each exposure build up resistance in the slow-growing layer of cells below the boundary, which is not diluted in the absence of drug when these cells return to dormancy. This effect is strengthened during exposures to higher drug concentrations, which induce longer periods of transient growth following exposure, and reach dormant cells deeper into the colony (Figure 4D). Similar transient growth dynamics were observed for short drug pulses of any length, which were sufficient to permanently arrest fast-growing cells at the surface of the colony.

We follow a single-cell trajectory initiating below the boundary at the beginning of the experiment. Slow-growing cells deep into the colony already show higher expression of resistance genes than fast-growing cells even before first contact with the drug. With each pulse of tetracycline, transient growth at the bottom of the colony moves this cell toward the surface, while increasing TetA levels (Figures 4D,E). Immediately before the last exposure, this trajectory is right below the boundary, with high TetA levels. The cell following this trajectory then resists the exposure, keeps growing, and quickly moves to occupy the top of the colony. This trajectory shows the buildup of resistance by slow-growing cells in the interior of a colony subjected to frequent exposures to the drug, which allows a quick transition into fast growth when an exposure causes nutrients to become available to them.

The collective dynamics of the drug response in the microcolony is characterized by markedly different gene expression levels between fast- and slow-growing cells. To determine the functional relationship between cell growth and expression of TetA and TetR, we correlated gene expression with cell growth across the trap during steady states, both in the absence and presence of tetracycline. In the absence of drug, we find that TetA and TetR expression decreases linearly with the cell growth rate (Figure 6A). This linear relationship is predicted by the theory of proteome partition, whereby for a cell to grow faster, it needs to dedicate a larger portion of its protein synthesis capacity for ribosome production (up to 50%), leaving less resources for the remaining portion of its proteome (Scott et al., 2010).

Higher expression of TetA and TetR among slow-growing cells is also found in the presence of drug. A further increase of TetA expression in slow-growing cells, in comparison to TetR, might reflect the different steady states reached in the interplay between drug import, TetA expression and TetR repression at different growth rates (Møller et al., 2016). At lower growth rates, a decrease in dilution of intracellular drug could be compensated by increased export by TetA. However, it should be noted that high-TetA slow-growing cells around the boundary only go through a few division cycles (∼6) on their way out of the trap, and therefore gene expression is not likely to reach equilibrium at any given growth rate during this process. At extremely low cell growth in the back of the trap, both TetA and TetR expression are low even in the presence of drug, since these cells do not experience any growth and largely keep the same protein levels as before drug exposure.

Both the dynamics of antibiotic responses and the resulting changes in the phenotypic structure of the colony are ultimately controlled by gene regulatory circuits (Schultz et al., 2009). However, upon environmental shifts, the progression of cellular responses does not only depend on the direct regulation provided by transcription factors but also on global effects on protein expression linked to the metabolic state of the cell (Klumpp et al., 2009; Scott et al., 2010). Failure to quickly deploy resistance genes results in higher concentrations of intracellular drug and further reduction in expression of resistance genes and drug accumulation, a positive feedback known to result in the coexistence of growing and arrested cells in the presence of antibiotics (Deris et al., 2013). Therefore, gene regulatory mechanisms control expression of resistance across the colony both directly by regulation and indirectly by the reorganization of growth patterns across the colony resulting from the expression of resistance and nutrient redistribution (Stewart et al., 2019).

To test whether coupling between direct resistance regulation, metabolism and environmental interactions is indeed sufficient to explain the complex spatiotemporal dynamics described above, we set up an agent-based computational model of growing rod-shaped bacteria incorporating these three ingredients. Each cell in the simulation is equipped with a gene regulatory circuit for the expression of resistance genes, where growth and expression are sensitive to both drug concentration and nutrient availability, and nutrient concentration in the environment is tracked separately by a continuous field throughout the trap (see section “Materials and Methods” and Supplementary Figure 7 for details). The regulatory part of the mathematical model closely follows the previously established resistance mechanism (Schultz et al., 2017) and includes the proteome allocation mechanism (Scott et al., 2010) necessary for growth-dependent expression as described in the previous section (cf. Figure 6 and Supplementary Figure 8; also see section “Discussion”).

In the absence of the drug, the colony reaches a steady state similar to our experimental system (Figure 7A; first snapshot), where cells close to the outlet at the top grow (blue cells) while the cells deep in the trap are deprived of nutrients and stop growing (white cells). We then subjected our virtual colony to two pulses of drug: A short 30 min pulse and a long 500 min pulse. These pulses triggered changes in the growth pattern and nutrient distribution (Figures 7A,B,G) as well as expression of the resistance genes TetA and TetR (Figures 7C,D).

Upon exposure of the colony to the shorter first pulse, we see two main effects: First, growth is suppressed in the growing part of the population, which leads to diminished nutrient consumption and a redistribution of nutrients deeper into the trap (Figure 7G). This causes dormant cells deeper in the trap to resume growth, albeit at a reduced rate (Figure 7A, t = 5.3 h; Figure 7B). When the pulse is over, the growth pattern returns to its original state (Figure 7A, t = 8.5 h). However, the expression of resistance genes triggered by the drug induces a lasting change: When cells in the lower part of the trap return to their dormant state, their TetA and TetR concentrations are still elevated, leading to a reservoir of dormant cells with active resistance. Consequently, these cells are able to tolerate the next pulse with a higher growth rate, while growth of cells at the top is suppressed to the same extent as in the naive colony (wedge-shaped region outlined in red in Figures 7B–D).

During the longer pulse, we can see the adaptation process more clearly: The growth boundary initially deepens (albeit slightly less than during the first pulse due to the reservoir of resistant cells), but eventually settles at an intermediate position, when expression of resistance in the growing cells has reached its steady state (Figure 7A, t = 11.9 h; Figure 7B). Expression is enhanced in cells that grow slowly due to nutrient deprivation, leading to the creation of a reservoir of cells with very high levels of resistance after the steady state under drug exposure is reached (Figures 7C–E). Again, this reservoir is maintained even when the colony returns to its original growth pattern upon drug removal. The full spatiotemporal dynamics can also be observed in Supplementary Movie 2.

In contrast to the experiment, we had the ability to track individual cells throughout the simulation, since they are represented by discrete units. We chose three initial cells and extracted their growth rate, TetA concentrations as well as the nutrient availability at their respective positions (squares in Figure 7A and Supplementary Movie 2; corresponding trajectories in Figures 7E–G). The initial positions were chosen similarly to the experiment, such that the deepest cell, despite moving toward the top during transient growth, stays in the dormant part of the population, while the middle cell is expelled from the colony after drug removal, and the top cell leaves the colony even earlier, shortly after drug exposure during the long pulse. The time traces clearly show transient growth for the bottom cell and permanent reactivation of growth for the top cell upon exposure (Figure 7F). In contrast, the middle cell experiences a complex sequence of environments during the long pulse: First, growth is triggered by increased nutrient availability. While the cells in the upper growing part of the population recover, the cell is again deprived of nutrients, leading to reduced, but non-zero growth. Simultaneously, resistance expression is markedly increased (Figures 7F,G). Finally, the residual growth allows the cell to reach the region of the trap with high nutrient availability, which both increases its growth rate and leads to a decline in resistance levels until the cell leaves the trap.

All strains were derived from E. coli K-12 strain MG1655 rph+ ΔlacIZYA. The native tet resistance mechanism from the Tn10 transposon was ordered from Genewiz in a pIT3-CH integrating plasmid and integrated in the chromosome at site HKO22. Matching fluorescent reporters for TetR and TetA (GFPmut3 and mCherry, respectively), were also ordered from Genewiz in a pZS1 plasmid and transformed using TSS (Schultz et al., 2017). The pZS1 vector has a pSC101 origin of replication with stringent control, which provides good accuracy in fluorescence measurements due to low copy number variation [10 to 12 copies per cell, Lutz and Bujard (1997)]. All experiments were performed in EZ-rich defined medium (Teknova) prepared according to the manufacturer’s instructions with 0.2% glucose as the carbon source. To prevent cell adhesion to microfluidic channels, all media were supplemented with 0.075% (w:v) Tween 20. Tetracycline solutions were freshly made from powder stocks (Sigma) and filter-sterilized before each experiment. All media containing tetracycline also had 0.008% (v:v) sulforhodamine dye added, so drug concentration inside the chip could be calculated from microscopy images.

To image spatially extended micro-colonies of tetracycline-resistant E. coli, we used a microfluidic device that consists of multiple 100 by 170 μm traps (Bittihn et al., 2020). The night before the experiment, a culture was inoculated from a -80°C glycerol stock into lysogeny broth (Difco) supplemented with the appropriate selection antibiotics and grown overnight in a shaking incubator at 37°C. On the day of the experiment, the saturated overnight culture was diluted 1:1,000 into 5 ml of the same medium supplemented with 0.075% (w:v) Tween 20 and incubated until an OD600 of 0.1 was reached. Then, 1 ml of this culture was spun down at 3,000 g in a standard tabletop microcentrifuge for 3 min, and the cells were resuspended in 5 μl of the base medium used for the microfluidic experiment. The cell suspension was then immediately loaded into the waste port of the microfluidic device, which had been degassed in a vacuum chamber for at least 30 min, and base medium was loaded into all other ports. The experiment was performed at 37°C. After the traps had been seeded, media and waste ports were connected to the corresponding reservoirs and media channels were flushed with base medium at a high flow rate (>2,000 μm s^–1) before calibrating the flow rate to 100 μm s^–1 in the media channels. A linear on-chip mixer was used to mix growth media from two inputs in 8 different proportions to achieve different drug concentrations. One of the inputs can be switched in real-time between growth media containing no tetracycline and growth media containing tetracycline to expose colonies to abrupt shifts in drug concentration. Supplementary Movie 1 shows a microcolony subjected to the tetracycline exposure regimens described in Figures 2, 3.

A Nikon Eclipse Ti2 inverted microscope was used with a Photometrics CoolSNAP HQ2 CCD camera to capture images and a Lumencor SOLA SE LED Light Engine for fluorescent excitation. The stage holding the microfluidic device was enclosed in a plexiglass incubation chamber, maintaining a constant 37°C environment. The acquisition software was NIS-Elements. High-resolution data was acquired at × 30 magnification, with exposure times of 20 ms for phase contrast, 100 ms for GFP (25% LED intensity) and 500 ms for mCherry (20% LED intensity). With one image for each trap size and medium composition (16 images), each containing two traps, an imaging interval of 2 min was possible.

GFP and mCherry fluorescence was extracted from microscopy images using custom-written MATLAB scripts. Drug concentration at each time point was calculated by extracting the fluorescence of the medium flowing through the medium channel above the traps, as media containing tetracycline also contained a fluorescent dye. Phase contrast images were stabilized using the Image Stabilizer plugin in ImageJ. The velocity of cells was estimated from the stabilized images using the PIVlab tool in MATLAB (Thielicke and Sonntag, 2021). All images were pre-processed, regions of interest (ROIs) encompassing the full traps were selected manually, and three interrogation areas were used to calculate velocity vectors. Estimates of velocity vectors were calibrated using reference distances in the microfluidic device, and the estimated vectors were validated in post-processing by restricting velocity limits. The local cell growth rate at different depths of the trap was estimated from the vertical components of velocity vectors. Assuming that cells in the microfluidic trap are densely packed and incompressible, the velocity v(x,t) at a depth x is determined by the instantaneous, cumulative cell growth rate in the trap v(x,t)=∫Lxg(x,t)dx. Therefore, we calculate the local growth rate by differentiating the velocity g(x,t)=-dv(x,t)dx.

Both nutrients and drug penetrate the trap by two processes: diffusion through the medium and advection, where inflow of medium into the trap counters the outflow of cells. Here, we estimate the relative importance of these phenomena in determining nutrient and drug concentrations in the medium along the trap. Assuming a fast cell growth rate of 3 doublings per hour (an overestimation) and a depth of the growing layer of 100 μm (as seen experimentally), the maximum advection velocity at the top of the trap is 300 μm h^–1. Therefore, the transfer time of cell mass from the growth boundary to the top of the trap is on the order of 20 min, and similarly for nutrients for the counter-flow inward for a volume fraction on the order of 0.5. The value for the diffusion constant of nutrients found to be consistent with our experimental observations for this system is D = 500 μm² s^–1 (Bittihn et al., 2020), which is in line with known diffusion constants (Stein and Litman, 1990; Ma et al., 2005), a recent study on biofilm front propagation (Wang et al., 2017) and the general order of magnitude for small molecules in water. Therefore, the typical time for nutrients to travel 100 μm from the top edge to the growth boundary simply by diffusion is (100 μm)²/D = 20 s. Thus, an upper bound for the Péclet number in this system is Pe = 20 s/20 min = 1/60, which leads us to conclude that this system is diffusion-dominated and we can neglect mass transfer by advection in the growth medium. In addition, the advection velocities decrease toward zero at the growth boundary, below which only the (very fast) diffusion acts. Since diffusion constants for antibiotics are typically on the same order or even larger (tetracycline has a molecular weight of 444), this applies to all the relevant substances (nutrients and antibiotics) in our system. We also confirm the timescale of diffusion experimentally by measuring the penetration of a dye of similar size (sulforhodamine, MW = 558) added to the medium containing the drug (Supplementary Figure 2).

We model the main biochemical interactions involved in the response as a set of differential equations that describe changes in the concentrations of the intracellular drug (d), the efflux pump TetA (a), and the repressor protein TetR (r):

where K_i stands for the import rate, D for extracellular drug concentration, d_f for free intracellular drug, K_a for the catalytic rate constant of TetA, k_a the Michaelis constant, respectively, r_f free repressor, and H_a(r_f) and H_r(r_f) the synthesis rates for TetA and TetR that depend on free TetR. Since the biochemical binding and unbinding of the substrate to the transcription factor typically happens at a much faster rate than the aforementioned processes, we consider their unbound (free) forms (d_f, r_f) to be in chemical equilibrium with the bound form [rd] with a dissociation constant K_d, such that r_fd_f = K_d[rd]. The term K_i(D(t)−d_f) represents the diffusion of drug across the membrane into the cell, Kaadf(ka+df) the export of drug out of the cell by the efflux pump. The terms λd, λa and λr represent the dilution due to cell growth of drug, TetA and TetR, respectively, where λ is the current growth rate. Both f, which allows us to modulate the strength of gene expression, and the growth rate λ depend on the nutrient level and the intracellular drug concentration.

To model these dependencies, we used the framework introduced by Scott et al. (2010). In this framework κ_n and κ_t are the nutritional and translational capacity of the cell, respectively. Here, we refer to their base values (full nutrients, no drug) as κn0 and κt0, respectively.

For the nutritional capacity, we assume a Monod dependency on the limiting nutrient concentration c with κn=κn0cc0+c, where c₀ is the half-maximum concentration, which we assume to be much smaller than the nutrient concentration at the top boundary of the trap in order to obtain the sharp growth boundary. For the translational capacity, we assume inhibition by tetracycline according to κt=κt0KriboKribo+df, where the fraction represents the fraction of free ribosomes in the cell, and K_ribo is the dissociation constant for tetracycline and the ribosome. Lower K_ribo values correspond to stronger inhibition, and vice versa. According to Scott et al. (2010), the growth rate can then be calculated as λ=ϕcρ⋅κtκnκt+κn, where ϕ_c = 0.48 and ρ = 0.76 are universal constants.

κt0 has a universal value of 4.5 h⁻¹ for E. coli. κn0 varies according to nutrient quality. We chose κn0=7.176h-1 such that λ0=ϕcρ⋅κt0κn0κt0+κn0 (corresponding to a state without tetracycline, at full nutrients) yields a maximum growth rate of λ₀ = 0.029min⁻¹ as observed in the experiment (the full range of growth rates during the experiment is shown in Supplementary Figure 1).

We assume that TetA and TetR are part of the P sector of the proteome, which scales as ϕP=ϕc⋅κtκt+κn. Without regulation of the synthesis rates H_a(r_f) and H_r(r_f), we would expect the concentrations of TetA and TetR to scale in the same way. Hence, we define f=λλ0⋅κtκt+κn/κt0κt0+κn0, which leads to steady states proportional to ∼κtκt+κn and simplifies to f=1 at full nutrients and no drug. Example dynamics of these biochemical equations are shown in Supplementary Figure 7.

We combined the above biochemical equations with an agent-based model of growing and dividing cells. In this physical model, cells are represented by rod-shaped particles (a rectangle of varying length and width 2R with semi-circular caps of radius R) with diameter 2R = 1μm. Volume exclusion is implemented by Hertzian repulsion forces ∼(2R−d)^3/2 for d≤2R, where d is the distance between the centerlines (from cap center to cap center) of two cells. We consider the incompressible limit where repulsion is so strong that the overlap between cells is minimal at all times. Consequently, the resulting dynamics are insensitive to the exact force law for repulsion and mechanical parameters of the cells. Cells grow from a total length of 2 μm to 4 μm before they divide, with an elongation rate that leads to a doubling time of ln(2)/λ with λ from above. At birth, the nominal growth rate λ₀ is chosen randomly within a window of 25% for each cell in order to avoid synchronization of division, by multiplying the above-mentioned base values κn0 and κt0 by a factor [0.75,1.25]. Cells are removed from the system when they reach the top of the domain. The left, right and bottom wall of the domain are modeled with Hertzian repulsion forces as well.

Each cell is equipped with the biochemical reaction scheme introduced above. Nutrients are tracked throughout the domain by a continuous field c(x,y,t) which follows the diffusion equation ∂t⁡c=Dn∂x2⁡c-γ with a boundary condition c=1 (full normalized nutrient concentration) at the top boundary of the domain. The local consumption rate γ(x,y,t) is determined by the state of the corresponding cells: Each cell consumes nutrients at a rate γ₀⋅A⋅λ/λ₀, where γ₀ is the nominal nutrient consumption rate at full nutrients and no drug (per unit time and unit area), and A and λ are the current area and growth rate of the cell, respectively.

An Euler method with adaptive time stepping was used for the evolution of the physical equations of motion of the cells and the biochemical reactions. The size of the time step was capped at a maximum of 10⁻⁴ min, and the maximum displacement of the cells was kept below 0.02 μm by decreasing the time step as necessary. The diffusion equation for the continuous nutrient field was solved using a forward-time centered-space finite-difference scheme on a grid with a spatial discretization step size of 1 μm in both directions and the same time step as for the equations of motion of the cells, using a standard 5-point stencil in two dimensions. The model was implemented in Julia (Bezanson et al., 2017). Note that, to allow for a larger time step when solving the diffusion equation numerically, we use a diffusion constant D_n in the simulation that is smaller than the real diffusion constant for small molecules in this system (which is on the order of 500 m²/s, see timescale discussion above and Bittihn et al., 2020), but which still ensures sufficiently fast diffusion across the trap. This does not alter the results if γ is scaled appropriately and other time scales in the system are larger than the typical equilibration time.

Remaining model parameters, from Schultz et al. (2017) where applicable: K_i = 0.015min⁻¹, K_a = 50min⁻¹, k_a = 10μM, K_d = 0.001μM, K_ribo = 1μM, Ha(rf)=Ar0,a5r0,a5+rf5, A = 0.008μMmin⁻¹, r_0,a = 0.0001μM, Hr(rf)=Rr0,r3r0,r3+rf3, R = 0.0003μMmin⁻¹,  r_0,r = 0.000075μM, D(t) = 0or 50μM, D_n = 1200μm²min⁻¹, γ₀ = 0.4a.u.μm⁻²min⁻¹, c₀ = 0.01a.u.μm⁻².