Agent-based model for microbial populations exposed to radiation (AMMPER) simulates yeast growth for deep-space experiments

AMMPER was written in Python 3.10.2, and utilizes packages included in the Python Standard Library, along with Numpy and Matplotlib. All model runs were executed on a PC laptop running Windows 10 with a 10th generation Intel core i5-10310U processor and 16 GB of RAM. Simulations typically took approximately 30 min to run.

In the ground study referenced here, wild-type (YBS21-A) and rad51Δ (YBS29-1, RAD51 gene deletion, necessary for homologous recombination-based DSB repair) [19] diploid strains of Saccharomyces cerevisiae were exposed to 0 – 30 Gy 150 MeV protons at Loma Linda University Proton Treatment and Research Center (Loma Linda, CA). To mimic the expected conditions of the spaceflight experiment, strains were desiccated at 10,000 cells per well in 96-well Stripwell™ polystyrene microplates (Costar^®; 9102) and kept in a dry state in cold storage (4°C) for 7 weeks. The cells were rehydrated with 100 μL of Synthetic Complete (SC) growth medium [19] directly before exposure to proton radiation, resulting in an initial density of 10⁵ cells/mL. Exposures were performed using a 20-cm diameter circular unmodified beam. The dose rates were 423.6, 844.8, 1,684.2, 3,367.2, and 5,051.6 cGy/min for the 2.5, 5, 10, 20, and 30-Gy doses, respectively. Growth was measured as optical density at 690 nm, a wavelength chosen to avoid interference with the metabolic dye alamarBlue^TM which was included in the medium and tracked via absorbance at 570 nm and 630 nm. Because alamarBlue dynamics are not simulated in this version of AMMPER, those data are not discussed here. Plate optical measurements (OD₆₉₀) were initiated approximately 8 hours after exposure using a Molecular Devices VersaMax microplate reader, and measurements were performed once per hour. The same strains were included in one other 150 MeV proton exposure experiment, but only up to 10 Gy, as well as in several other radiation experiments using different radiation types (250 MeV proton, simulated solar particle event exposure, gamma irradiation); these experiments validated the greater sensitivity of the rad51Δ strain to radiation-induced cell damage, and some of the datasets may be used to refine future versions of AMMPER. Further information about experimentation with these strains is available in earlier manuscripts [19, 28].

We designed the AMMPER simulation setup to mimic the cell density of the experimental population at early log phase of an experiment, when OD₆₉₀ = 0.3, corresponding roughly to a density of 3.85×10⁶ cells/mL. Assuming all cells are equally distributed, each cell in an OD₆₉₀ = 0.3 culture would have 2.5974 × 10⁵ μm³ of space to itself. Therefore, the AMMPER simulation was set to begin with a single cell at the center of a cubic 64×64×64 μm cubic space, which is equivalent to a volume of 2.62144 × 10⁵ μm³/cell. A model simulation was conducted three times for each radiation dose. The radiation event occurred at generation 2, to approximate the experimental setup described above, in which hydrated cells were irradiated in a single short treatment followed by several generations of growth. Simulated wild-type and rad51Δ cells underwent log phase growth under exposure to 0, 2.5, 5, 10, 20, and 30 Gy of 150 MeV proton radiation. Cell populations in a typical simulation typically reached 2–3 × 10³ cells per cubic space by the end of exponential phase (Fig. S2), equivalent to a density between 7.63 × 10⁹ and 1.14 × 10¹⁰ cells/mL. This is higher than the final number typically reached in a real experiment (approximately 2–5 × 10⁷ cells/mL), because growth in AMMPER is limited only by space and not by growth substrate concentration or medium composition.

To achieve a uniform distribution of the omnidirectional tracks, a spherical coordinate system was used. The theta and phi values (angular parameters for position in a spherical coordinate system) of the beginning and end of the particle track were generated randomly via a uniform distribution. The beginning and the end of the particle track were constrained to the surface of a sphere inscribed within the cubic simulation space. Then, a coordinate system transformation was carried out on the energy depositions of a pregenerated particle track to reorient it into the new position and direction.

To evaluate AMMPER simulation outputs, we compared log phase cell growth rates and lag times between simulated and empirical datasets. First, we manually selected the log phase of the empirical data for both the wild-type and rad51Δ S. cerevisiae populations. For the wild-type (WT) samples, we determined that the log phase occurred at 0.2–0.7 OD₆₉₀ (Fig. S1a). For the rad51Δ samples, growth appeared to be biphasic, it continued for a longer duration than for WT, and in many cases reached a higher final OD (optical density) than in WT (Fig. S1b). For the purposes of comparison with AMMPER, log phase was determined as the growth between 0.2–0.6 OD₆₉₀. We used the 0 Gy empirical data to calculate the doubling time of the population, which we then used to convert the simulation’s generational time to hours, facilitating comparison between the simulated and empirical data. For the simulation, growth rate was based on total cell count (rather than live cells only) for comparison with empirical OD data, which does not distinguish between live and dead cells. Lag time was defined as the time elapsed between the start of the experiment and when the growth curves reached OD = 0.2 (for experiments), or between the start of the simulation and when the cell population reached 1000 cells (for AMMPER simulations). For the empirical data, “lag time” therefore includes contributions from both physiological lag (delay in growth due to cells’ transition out of stasis or recovery from damage) and differences in growth rate.

All statistical analysis was performed using Microsoft Excel. The growth rate for each simulated replicate was calculated using a least-squares linear regression (LINEST, Microsoft Excel) for the number of cells at each timestep in hours. Each replicate was individually analyzed. The variance calculations for an assessment of the accuracy of the simulated dataset stochasticity was done using a sample variance function (VAR.S, Microsoft Excel). The comparison between the no-radiation control group, rad51Δ, and the wild-type strains for the NSRL GCRSim simulation and the deep space proton simulation was done using Tukey’s HSD in Microsoft Excel. The “Anova: Single Factor” analysis tool from the Excel Data Analysis ToolPak was used to determine whether the growth rates from the three groups differed significantly.

The code for AMMPER developed in this study is freely available on the NASA GitHub Repository (https://github.com/nasa/AMMPER) [37]. The data generated by AMMPER in this study and the empirical yeast growth data used in comparisons are available in an online repository on Zenodo, DOI: 10.5281/zenodo.7379875, web link: https://zenodo.org/records/7379875.

AMMPER integrates an existing model of energy deposition from particle radiation with novel algorithms for exponential population growth, DNA damage, DNA repair, and cell death in a single Python package (Fig. 2). AMMPER is built from a simplified understanding of the fundamental processes involved in microbial radiation response, with most values taken from the literature, and experimental data used to refine only two parameter values. A summary of parameter values and assumptions is provided in Table 1. By modeling the dynamics of a microbial population, AMMPER aims to generate testable predictions on the survivability of yeast in the deep space radiation environment.

Figure 2.

Block diagram of AMMPER. AMMPER integrates a model of radiation energy deposition with algorithms for population growth, cell damage, and DNA repair, and is parameterized with experimental data.

The AMMPER simulation space consists of a 64×64×64 μm cubic volume, analogous to an aqueous culture medium with nonlimiting nutrient and pH buffering, in a typical laboratory microwell plate or a microfluidic culture card of the type used in BioSentinel [26]. The space initially contains a single model cell at the center that may then replicate to form a population. During population growth (for this study, we chose generation 2 as the exposure timepoint), a radiation environment is applied to the simulation space, consisting of an energy deposition map of both proton-based energy depositions and delta ray energy depositions. This energy map is used to calculate DNA damage in each of the cells and to create reactive oxygen species (ROS) molecules that persist and continue to cause DNA damage and concentration-dependent apoptotic cell death in ensuing generations. Based on parameters such as space availability and cell health, the model cells diffuse, replicate, and repair damage.

AMMPER is intended to be a user-friendly tool to aid biological researchers with experimental design and data interpretation and to assist in outreach and education on the effects of deep-space radiation. We therefore aimed to create the simplest model possible that could still recapitulate scientifically relevant features of experimental data and designed it to be able to run on a standard laptop computer. In this initial release of AMMPER, the scientifically relevant features we targeted include the dose-dependent effects of proton radiation on population growth, and the variability observed among biological replicates of yeast growth experiments. Future versions of AMMPER may target different features to recapitulate.

AMMPER simulates a complex system consisting of physical, chemical, and biological processes. We began with information from subject matter experts and from the scientific literature to build an initial model capturing only what we hypothesized to be the salient features of these processes: those that would contribute to the features we wanted to recapitulate. The sources of the assumptions made for the cell growth, DNA damage, and DNA repair algorithms are described below. We then carried out only two refinement steps: to determine the values of the doubling time parameter and the ROS longevity parameter. Finally, we tested our hypothesis that this very simple model could generate similar effects to those observed in experimental data.

AMMPER is open-source software and publicly available through NASA GitHub [37] The version presented here may be seen as an initial framework whose parameters and modules may be modified and improved upon in the future to accommodate other organisms and data types and to simulate chemical and biological processes with better fidelity.

In AMMPER, each yeast cell is simulated as a sphere inscribed inside a 4×4×4 μm volume, resulting in a 33.51 μm³ cellular volume (Fig. 3) like that of a typical S. cerevisiae cell, with the nucleus sized to span 7% of the spherical volume [38] (DNA is not modeled specifically). A cell agent has the following properties: UUID (universally unique identifier), position of center, health status, generation at “birth,” generation at death, number of DNA single strand breaks (SSBs), and number of DNA double strand breaks (DSBs). The health status property has three options: 1 indicates a completely healthy (no DNA damage) cell, 2 indicates a damaged (nonzero amount of DSBs or SSBs) cell, and 3 indicates a dead cell [39]. Damaged cells are defined as cells that have halted replication until repair is complete, and dead cells are defined by their inability to repair damage or reproduce [4].

Figure 3.

Model cell spatial definition. A cell is represented by the red sphere with a diameter of 4 μm, inscribed inside a 4×4×4 μm cubic space (shown on the left, with each blue cube having dimensions of 1×1×1 μm). Each cell exists in a neighborhood (shown on the right, with each larger blue cube having dimensions of the 4×4×4 μm volume that holds a single cell), which consists of all 26 cell spaces bordering the cell’s cubic space.

AMMPER is implemented in generational time, with a single time step representing the amount of time it takes for a cell to replicate. We calculated the real-time value of one generation using empirical data from nonirradiated wild-type cells (see Materials and Methods); we found that the cell populations doubled in roughly 5 hours.

The cells exist in a three-dimensional neighborhood, defined by the 26 4×4×4 μm spaces surrounding it (Fig. 3). During replication, the cell object evaluates its neighborhood for empty spaces. Then, a random empty space is chosen for the cell to replicate into, at a rate of one new cell per generation. This form of replication results in exponential growth until saturation occurs, in which all 26 spaces around a cell are occupied and a cell can no longer replicate. To reduce the dependence of the growth curve on available space, a simplified Brownian motion algorithm is implemented that allows cells to spread out in space [41]. Like the replication algorithm, the cell object first evaluates its neighborhood for empty spaces. If no empty spaces are found, no movement occurs; otherwise, the cell moves into a random empty space. This algorithm increases the space between cells; the result is that saturation is delayed, and the population can maintain exponential growth for longer.

AMMPER has the capacity to simulate multiple GCR-analogous radiation environments: deep space proton, NSRL GCRSim (NASA Space Radiation Laboratory Galactic Cosmic Ray Simulation) proton [42], and 150 MeV proton. We chose to simulate 150 MeV proton exposure to correspond to the available empirical data. For deep space and GCRSim, this version of AMMPER simulates only the proton component for simplicity, because protons are the most abundant component of GCR: Hydrogen ions account for 87% of the total flux of GCR, with helium ions accounting for 12% and other heavier elements (HZE) accounting for <1% [42] (see Supplementary Background). While ions of higher Z may pose different health risks to multicellular organisms (an effect known as relative biological effectiveness) [30], very little data are available on the relative risks for single-celled organisms, so our initial focus is on ions with the highest chance of encountering cells. Future versions of AMMPER may include HZE as well as other low-LET radiation types, such as gamma radiation.

The deep space proton model consists of the flux of the proton component of GCR, across the 90,000 μm² cross-sectional area of the 300×300×300 μm simulation volume, over three days in space beyond LEO [42]. The omnidirectional nature of space radiation is simulated by randomly generating traversal directions and positions over the simulation space [43], and the dose rate of the deep space proton model (4.49 mGy/3 days) is intended to approximate the dose rate of protons present in the deep space environment. This is a unique feature of this computational model that is very difficult to reproduce in experiments. The NSRL GCRSim proton model simulates the protons delivered during exposure to the NSRL GCRSim [42,44], which provides exposure to a succession of energetic particles designed to simulate the major components of GCR. In AMMPER, GCRSim radiation is delivered during a short period of time, and the traversals are oriented unidirectionally. Because one proton of each energy level is provided (for a total of 1940 MeV), the total dose delivered to the 64×64×64 μm simulation space is ~1.19 Gy. The 150 MeV proton model also contains unidirectional traversals but enables the user to vary the radiation dose delivered by 150 MeV protons to enable comparison to empirical data (Fig. 4). Detailed descriptions of the fluences for each simulation are included in Tables S1–S3 in the Supplementary Information.

Figure 4.

PNG images generated by AMMPER code as a product of the simulation run, showing three different radiation environments. Each simulation produces one PNG image file per generation; generation number is noted at the top as “g=”. Yellow dots represent energy depositions from protons and electrons, green dots represent ROS produced in the ionization of water molecules, and blue dots represent the cells in the simulation space. For all simulations, a cell is placed in the center of the cubic simulation space and undergoes exponential growth. (a) Deep Space Proton: The proton traversals are omnidirectional, and the timing of each proton is staggered to produce an environment that simulates the constant radiation exposure of deep space. Generation 11 shown here. Total dose delivered is 4.49 mGy in a 3-day simulation. (b) NSRL GCRSim Proton: All radiation is delivered at Generation 2, shown here. Proton traversals are parallel, and the total dose simulates the dose of a year of deep space radiation (1.19 Gy). (c) 150 MeV Proton, 10 Gy: All radiation is delivered at Generation 2, shown here. Total dose delivered is 10 Gy.

To reduce simulation time, we precalculated the track structures resulting from individual proton traversals using RITRACKS [33]. We generated the energy deposition map for both ion and delta ray energy depositions at a resolution of 20 nm voxels. For each proton energy, we generated eight possible track options and unique energy deposition maps; the data for these are included with the AMMPER package. The absorbed dose from each track was calculated by summing all the energy deposition events associated with the track and dividing by the total mass of water in the simulation space, generating an estimate of the spatially averaged absorbed dose from that track. To simulate a particular treatment, AMMPER code randomly selects tracks and combines the appropriate number of them to achieve the desired dose (Tables S1–S3). For the NSRL GCRSim proton and the deep space proton simulations, each track is also assigned a random position in space. Tracks for NSRL GCRSim are parallel to simulate the beamline source, whereas tracks for deep space proton are randomly reoriented to simulate omnidirectional radiation.

As a confidence check, we compared energy depositions for proton energies between 0.5 to 1000 MeV in AMMPER to theoretical calculations for energy deposition as a function of radial distance from the particle track based on microdosimetry [45] (Fig. 5a). We found that the microdosimetry calculation is consistent with AMMPER’s RITRACKS-generated data across the spectrum of 0.5 to 500 MeV protons. Additionally, the dose from delta ray energy depositions decreases as a function of radial distance from the core of the particle track (Fig. 5b), which is consistent with the findings of Wingate and Baum, who experimentally measured the radial distribution of dose from protons of energies between 1 and 3 MeV. [46].

Figure 5.

Distribution of RITRACKS ion and electron energy depositions. (a) Energy deposition in a single cell volume for radiation due to proton traversals of various energies. The RITRACKS data are depicted in yellow, and the microdosimetry-based calculations depicted in green. (b) Energy depositions by a 1 MeV proton. Light blue dots and line show energy depositions from delta rays, generated by RITRACKS, as a function of radial distance. Dark blue dots show Wingate and Baum experimental data on energy deposited by a 1 MeV proton in tissue-equivalent gas as a function of radial distance [46]. As distance from the proton track increases, the amount of energy deposited decreases.

We modeled the generation of ROS as a constant rate of OH^· and H₂O₂ production, equivalent to the primary radioloytic yield of ROS from a 100 eV energy deposition in water (G_OH = 2.5, G_H2O2 = 0.7 molecules/100 eV. AMMPER’s native ROS generation algorithm calculates the amount of energy deposited in a 20-nm voxel, and, using the primary radiolytic yield of molecules/100eV, calculates the number of molecules of OH^· and H₂O₂ in that voxel (Fig. 6). For simplicity and speed of implementation in this initial version of AMMPER, we used the primary radiolytic yield of ROS in pure water as a simplified approximation for ROS generation rate. However, it is worth noting that the cell environment differs from pure water. Various elements (i.e., concentration of pH buffering, scavenging capacity of the cellular environment) affect these values [47], and the model may be modified in future versions to take these elements into account, or, alternatively, to utilize the more detailed but computationally intensive chemical reaction calculations available in RITRACKS.

Figure 6.

One of the PNG images generated by AMMPER code as a product of the simulation run, showing ROS species generation for the NSRL GCRSim proton simulation in AMMPER. ROS species are shown as green dots; each point corresponds to a single molecule of either OH^· or H₂O₂. ROS species are generated due to the ionization of water molecules by the energy depositions from the ions of the radiation tracks.

The longevity of ROS is complicated by ongoing chemical reactions and metabolic processes that result in the production of more ROS [48,49,50,51]. Because we were unable to find suitable experimental data on ROS lifetime inside yeast cells, we modeled ROS lifetime in AMMPER using a deterministic lifetime for each molecule, called the longevity parameter. For the initial implementation of the model, we chose a longevity parameter by assessing the effect of ROS longevity on yeast death in the model (Fig. 7).

Figure 7.

Comparison between cell survival for long and short ROS models. Simulations were initiated with 1 cell per 64×64×64 μm cubic volume. Total radiation dose in Gy is depicted along the x axis. The circles represent the number of dead cells in the long ROS model, whereas the diamonds represent those in the short ROS model. Note that damaged cells are not included. Each symbol represents one model replicate. (a) Wild-type simulated data. Circles and diamonds lie on top of each other; no cell death was observed in either ROS model. (b) rad51Δ simulated data.

We simulated two different yeast strains: wild type and rad51Δ, a DNA-repair mutant (see Materials and Methods). We compared the results of two ROS longevity parameters at the extreme ends of the range of potential values: “short” (one generation, as short as possible) and “long” (>14 generations, or longer than remaining simulation time). In the simulated wild-type population, the long ROS model resulted in cell damage (not shown), but neither model resulted in any cell death. In the simulated rad51Δ population, the long ROS model, but not the short ROS model, resulted in increased cell death as the radiation dose increased. The long ROS model is therefore necessary to generate cell damage or death. This long duration of ROS presence, which creates a toxic environment that persists in the space even after initial radiation exposure, may be interpreted as mimicking the complex chain of reactions that begin with the ionization of water molecules and result in long duration, nontargeted effects of ionizing radiation on cell populations [52].

We implemented a simplified model of DNA damage and repair in AMMPER with the main goal of providing a quantitative structure to express a relationship between damage-causing elements (energy deposition and ROS contact) and effects on growth. A detailed consideration of the numerous forms of radiation-induced DNA damage and repair is beyond the scope of AMMPER (see Supplementary Background); for the model, we chose to focus on SSBs and DSBs and to make a number of simplifying assumptions in order to keep the model tractable. We assumed that SSBs result primarily from electrons (delta rays), and DSBs only result from the actual proton traversal, as the energy required to generate a DSB is often higher than that contained in the delta rays [53].

DNA is not explicitly modeled as a molecule in AMMPER; damage occurs as a result of energy deposition anywhere within the nucleus region. For each electron energy deposition at a nucleus, AMMPER generates an SSB, consistent with assumptions by Cucinotta et al. [53] and Nikjoo et al. [54] that SSB formation occurs when the energy deposition is above 17.5 eV. AMMPER then calculates the radiation dose from proton energy depositions at the nucleus and determines the number of DSBs using an estimate of 35 DSBs/cell/Gy, assuming that there is a linear relationship between radiation dose and number of DSBs for S. cerevisiae [55, 56].. Future versions of AMMPER may include more detailed models of DNA damage and repair (including types other than SSB or DSBs, like abasic sites, DNA cross-links, alkylation or oxidation of DNA bases) and/or simulations of different model organisms.

Under exposure to the simulated ROS environment, a cell may undergo additional damage. We assumed that each OH^· molecule at the nucleus will cause an SSB. AMMPER also calculates the concentration of H₂O₂ in each cell to determine the probability of apoptosis, using the relationship between apoptosis and H₂O₂ concentration reported by Madeo et al. [57] This relationship is described in the Supplementary Background; briefly, probability increases from 20% (at an intracellular concentration of 0.3 mM H₂O₂) to 70% (at 5 mM H₂O₂).

If the number of DSBs or SSBs present in a cell is nonzero, the health status parameter increases to 2, indicating that the cell must halt the replication process until all damage is repaired. If apoptosis occurs, however, the health status parameter increases to 3, indicating that the cell is dead. Dead cells remain in the simulation space, but do not undergo the replication or repair algorithms [40].

In AMMPER, cells repair the different forms of DNA damage through two simulated mechanisms: “simple repair” and “complex repair,” which are distinguished by the time required for repair and probability of success [58,59,60].

Simple repair is used on SSBs. In AMMPER, a cell repairs 3 SSBs per generation with a 100% probability of success. Complex repair is used on DSBs, and in AMMPER, a cell attempts repair on only 1 DSB per generation. Success is stochastic, with a 50% probability of success at each timestep, to account for the various probabilities of repair associated with the different DSB repair pathways, as reported by Lettier et al. [61]. When repair of a particular DSB is unsuccessful, the cell continues attempting to repair that DSB until successful before attempting repair on another DSB. Because genomes are not represented in this simulation, the cells do not have the capability to accumulate genome mutations. The values implemented in AMMPER for repair time and probability of success for the simple repair method are placeholders that we developed from the theory that base excision repair has a relatively high accuracy and low risk (see Supplementary Background) and were not refined or fit using experimental data. Additional research is required to determine the length of time it takes for a yeast cell to repair damage of various complexities.

After the simulation has finished running, AMMPER outputs data in a comma-delimited text file listing information from each timepoint on each cell present in the simulation space and in a folder of figures depicting the simulation environment, radiation traversals/timing, ROS generation, cell position, and cell health status at each generation of simulation time (examples of these images are included in Figures 4 and 6). These may be aggregated and processed by the user to generate data products as desired. For this study, growth curves were calculated from the number of dead, damaged, and healthy cells at each generation.

As an initial evaluation of the ability of AMMPER to simulate the effects of radiation on microbial populations, we compared the data generated from AMMPER to those from a ground study done on yeast survival in response to ionizing radiation exposure that was carried out to support NASA’s BioSentinel mission [17,18, 26]. As described above, the only components of the model that were refined using empirical data were the cell doubling time parameter and the ROS longevity parameter. This comparison allowed us to test the hypothesis that the processes simulated in AMMPER are sufficient to recapitulate the dose–response relationship of two yeast strains to proton irradiation and to generate variability among replicate simulations comparable to that observed among replicate experiments.

Two strains of S. cerevisiae, a wild type and a DNA repair mutant (rad51Δ; see Methods for details), were exposed to proton radiation at dose levels between 0 and 30 Gy. The cells were then allowed to grow, and optical density (OD₆₉₀) measurements were taken for 83 hours. In AMMPER, rad51Δ cells were simplified to lack DNA repair capabilities entirely. Therefore, any DNA damage to the model rad51Δ cell type results in cell death, but in the absence of radiation their growth is identical to that of wild type. Our goal was to evaluate whether the model recapitulated two metrics from the empirical data: the relationship between growth rate and dose, and the variance among experimental replicates.

Growth rate

We found that there was no statistically significant dependence of growth rate on radiation dose in either strain in the empirical dataset, and AMMPER recapitulated this (Fig. 8; full growth curves in Fig. S2). In the rad51Δ strain, there did appear to be a decrease in growth rate as a function of the radiation dose at the lower dose levels (0–10 Gy), and an increase in growth rate at the higher dose levels (20–30 Gy), which were partially recapitulated in model results, but these trends were not statistically significant. To assess the effect that the choice of ROS longevity made, we also ran one replicate of each simulation in which ROS species disappeared after only one generation; the results were qualitatively similar (Fig. S3).

Figure 8.

Comparison between empirical and simulated log phase growth rates. Radiation dose in Gy is depicted along the x axis. The open triangles represent the data from AMMPER, and the filled squares represent the empirical data. Each symbol represents one replicate (3 replicates/dose level for empirical and model data), and the error bars represent the linear regression fit error. Colors match the color codes in Figure S2. (a) wild-type empirical data; (b) wild-type simulated data; (c) rad51Δ empirical data; (d) rad51Δ simulated data.

Lag time

In addition to growth rate, lag time is a commonly measured parameter of microbial growth. Comparing the model and empirical results in lag time was not a primary focus of this study because (1) AMMPER does not explicitly model a physiological lag phase, so any apparent lag time would actually be a product of slow growth rate; and (2) the threshold for defining lag is different between simulation and empirical cases (simulation: number of cells; empirical: OD₆₉₀), so the two lag times cannot be directly compared in absolute values. Nonetheless, we determined the relationship between lag time and radiation dose and compared between the empirical and simulated populations. The empirical wild-type lag time did not exhibit a dependence on radiation dose; however, the empirical rad51Δ data displayed a statistically significant increase in lag time as the radiation dose increased, at levels below 30 Gy (slope: 0.5137; R²: 0.93, p: 0.0019; p < 0.05) (Fig. 9). Between 20 and 30 Gy, we observed a decrease in lag time, which may be related to the same complicating factors that also increased the growth rate in those samples. In contrast, the simulated data for both the wild type and rad51Δ strains did not exhibit a statistically significant dependence of lag time on radiation dose (Fig. 9).

Figure 9.

Comparison between empirical and simulated lag time. Radiation dose in Gy is depicted along the x axis. The open triangles represent the data from AMMPER, and the filled squares represent the empirical data. Each symbol represents one replicate (3 replicates per dose for both empirical and model data), and the error bars represent the error in the linear regression fit. Colors match the color codes in Figure S2. (a) wild type empirical data; (b) wild type simulated data; (c) rad51Δ empirical data; (d) rad51Δ simulated data.

Deep space proton/NSRL GCRSim proton simulations

One goal for the creation of AMMPER was to enable experimental design and hypothesis generation. To this end, we used the deep space proton and NSRL GCRSim proton models to predict results we might expect to see in future experiments (Fig. 10).

Figure 10.

Log phase growth rate for deep space proton and NSRL GCRSim proton simulations. Error bars represent the error in the linear regression fit. Dark blue, gray, and light blue represent the three replicates. noRad = control simulation without radiation, both strains (6 points). wt = wild type S. cerevisiae. rad51 = rad51Δ mutant. (a) Deep space proton simulation. There is minimal difference among the growth rates, regardless of modeled cell strain and radiation level. (b) NSRL GCRSim proton simulation. Growth rate is higher in wild-type cells exposed to radiation, and lower in rad51Δ cells exposed to radiation.

In the deep space simulation, cells experienced a fluence rate equivalent to what they would experience in deep space (see Table S1 for dose delivery), and the simulated three-dimensional space was 300×300×300 μm rather than 64×64×64 μm. This ability to simulate the very low dose rates of deep space is one of the major advantages of AMMPER, as it is currently not feasible to simulate deep-space radiation on Earth for experiments at realistic dose rates. The larger simulation size enabled us to observe more particle traversals for the same amount of simulation time, which is important given that the fluence rate in deep space is very low, although most traversals in the large simulation size do not interact directly with cells. Due to computational constraints, we were only able to simulate 3 days of growth for this project; future applications may include longer simulations. During this time, fewer than 200 cells experienced DNA damage due to radiation or ROS interaction in each simulation (in one of the six simulations, only 15 cells were damaged; in others, the numbers were 38, 50, 170, 175, and 197). Overall growth rates were thus unaffected by exposure to the deep space environment: we found no statistically significant differences among the control, wild type exposed to radiation, and rad51Δ cells exposed to radiation (ANOVA: df = 2, F = 2.41, p = 0.170) (Fig. 10). In contrast, the radiation delivered in the NSRL GCRSim simulation is equivalent to the dose and spectrum of particles that an astronaut would be exposed to over the course of a Mars mission, but delivered in the course of 1 hour [42]. We found that in this simulation, because the number of cells damaged was much higher (223, 238, 296, 470, 516, and 546 in the six simulations) and damage occurred earlier than in the deep space simulation, there was a growth effect. Growth rates of irradiated rad51Δ cells were significantly lower than those of the irradiated wild-type cells (ANOVA: df = 2, F = 8.87, p = 0.016; Tukey HSD for wt v. rad51Δ: q = 5.85 > q_crit = 4.34) (Fig. 10). Irradiated wild-type cells appeared to show an increase in growth rate relative to untreated cells, which may be related to the fact that cell death in the model can result in increased space for growth; however, the difference was not statistically significant.