Shaer, Daniel_Senior Thesis 2026

Predicting Cell Fate: Analyzing p53 Dynamics in Ovarian Cancer Cells, Paving the Way for Future Therapies Daniel Shaer Senior Thesis | 2026

1 Predicting Cell Fate: Analyzing p53 Dynamics in Ovarian Cancer Cells, Paving the Way for Future Therapies Daniel Shaer Advisor: Prof. Galit Lahav, Systems Biology, Harvard Medical School

2 Introduction The tumor suppressor protein p53 has long been described as the “guardian of the genome,” a title that reflects its central role in coordinating cellular responses to stress, assisting in DNA repair, and initiating apoptosis when DNA damage becomes irreparable or dangerous to the host organism (Lane 1992).

Disruption of this regulatory system is among the most common events across human cancer, with approximately 50% of all tumors harboring a mutation in TP53, the gene that codes for p53 (Baugh et al., 2018). In certain cancers, this proportion is even higher. As seen in Figure 1, ovarian cancer, for example, generally has approximately 80% TP53 mutation rates (Su et al., 2022) (Figure 1).

Figure 1. Frequency of TP53 alterations across major cancer types. (Su et al., 2022).

Among ovarian cancer diagnoses, approximately 90% are diagnosed as serous ovarian carcinomas—the most lethal gynecologic cancer (American Cancer Society, n.d.). SKOV-3, a morphologically epithelial ovarian adenocarcinoma sample

3 isolated from the ovary of a 64-year-old white female, has a complete homozygous deletion of the TP53 gene causing the line to be considered p53-null—carrying no functional copies of the gene (Yaginuma & Westphal, 1992). The absence of p53 fundamentally undermines the signaling processes of these cells, causing such behaviors as unregulated proliferation, instability of the genome, and resistance to stress-induced arrest or apoptosis (Wallis et al., 2023). Understanding how to reestablish p53 in these situations has thus become a major priority in cancer biology and therapeutic development (Lozano, 2019).

The concept of restoring p53 has gained considerable momentum over recent years. Early gene therapy studies attempted to deliver wild type p53 back into tumors, but with mixed results.

Factors such as preliminary understandings of cross-talk between genes and a generally overly preliminary understanding of systems led to unexpectedly complex biological barriers (Zeimet & Marth, 2003). In mouse models, for instance, restoring wild-type p53 slowed tumor growth but often failed to cause regression, suggesting that restoration alone is not a universal cure and may interact with tumor environments and mutation landscapes in highly subtle ways (Wang et al., 2011). More recent work has begun to refine these approaches, utilizing methods such as targeted delivery systems like gold nanoparticle-based constructs (Kotcherlakota et al., 2019), synthetic mRNA delivery (Raab et al., 2021), and intracellular protein transport technologies (Yang et al., 2022), demonstrating that full or partial restoration of p53 function is realistically feasible in human cells. These innovations underscore both the promise and the challenge of p53 restoration therapies. The field now rests at the intersection of decades of evolving knowledge and insight, and rapidly evolving therapeutic strategies (Valente et al., 2018). Yet one area of inquiry remains largely unanswered: once p53 is restored, what it is that determines

4 a cell’s ultimate behavior, whether it continues proliferating, arrests, or apoptoses.

Answering this question has proven to be incredibly complex, far beyond the simple measurements of p53 abundance.

Rather, previous research suggests that the key lies in the examination of the temporal dynamics of p53 signaling, that is, how the protein behaves over time in both abundance and “shape.”

Foundational single cell work from the Lahav Lab revealed that p53 activation is inherently dynamic in and of itself, displaying oscillatory behaviors that correspond to distinct cellular outcomes (Lahav et al., 2004). This work reframed p53 signaling as a system with the capacity to be predicted. Cells do not simply “have” or “not have” p53; rather, the temporal patterns of p53 activity in some way lead to their ultimate fate decisions. Subsequent studies extended this framework to cells that underwent DNA damage, and found that specific dynamical motifs, such as the number or amplitude of p53 pulses, predict whether a cell repairs, arrests, or undergoes apoptosis (Purvis et al., 2012). However, these studies all share the critical factor that p53 is undergoing activation in cells where it already exists functionally.

In contrast, very little is known about the dynamic behavior of p53 following restoration in cells that were previously p53-null, such as SKOV-3 ovarian cancer cells. Restoration thus represents a fundamentally different biological scenario. Instead of activating a preexisting signaling network, the system must be rebuilt in order to function, with transcriptional targets reestablished, feedback loops reengaged, and the cell interpreting incoming signals through a means foreign to it. This unique biological state remains poorly understood. Given the accelerating therapeutic interest in p53 restoration technologies, this gap in understanding must be addressed.

If p53 restoration is to become an effective and realistic means of therapeutic treatment, clinicians and researchers must

5 first understand the p53 dynamical behavior that leads to regression and senescence. This knowledge would potentially enable successful therapies through optimized dosing strategies, for example.

To investigate these questions, the project analyzes a large-scale, single-cell time series dataset generated in the Lahav Lab at Harvard Medical School, in which p53-null SKOV-3 ovarian cancer cells were engineered with a doxycycline-inducible p53-Venus construct to enable controlled restoration of p53 expression. By capturing the Venus fluorescence and therefore the p53 expression levels over an extended time period, this dataset makes it possible to quantify the signaling patterns that emerge upon restoration. When paired with ultimate cell fate outcome labels, these trajectories form an ideal system for applying computational methods to uncover relationships between restored-p53 dynamics and long term cellular fate that may not be visually apparent.

The central aim of this study is therefore to determine whether temporal features and dynamics of restored-p53 signaling can predict eventual cell fate, and to identify which aspects of these dynamics are most highly correlated with cellular fates.

Addressing this question requires an approach capable of detecting subtle, multivariate temporal patterns that are difficult or impossible to capture through non-computationally-assisted measures. To this end, the study employs interpretable machine learning techniques, chosen deliberately to avoid “black box” models—models with unclear or hidden decision making processes— in order to extract biologically meaningful features from single cell p53 time series and evaluate their predictive performance. By utilizing insights from years of p53 dynamical research with modern computational analysis, this work seeks to uncover the decision making processes governing how cells interpret restored p53 signaling and make fate decisions. This

6 study thus aims to provide a framework for identifying mechanistically informative biomarkers that could ultimately guide the design, timing, and optimization of future p53-based cancer therapies.

Materials and Methods This project followed a multi-phase methodology beginning with the acquisition and preprocessing of single-cell Yellow Fluorescent Protein (YFP) time-series data derived from live-cell imaging and automated cell tracking algorithms. After fate labels were assigned, each cell’s YFP trajectory was organized into a two dimensional time series format suitable for computational analysis. A collection of quantitative features was then engineered, both manually defined and algorithmically extracted, from these YFP trajectories in order to represent distinct aspects of p53-related dynamics. Finally, using the labeled dataset, a variety of classifiers, namely decision trees and random forests, were trained and evaluated to identify which engineered features most strongly contributed to accurate fate prediction. The subsequent subsections describe each phase in detail.

Data Acquisition and Preprocessing The first phase of this project involved generating and collecting single cell p53 time series data from a controlled live cell imaging experimental setup. All experiments were performed using a SKOV-3 ovarian cancer cell line, specifically a p53 null serous cystadenocarcinoma line that provides a clean background with which to study p53 dynamics in near complete isolation. To reintroduce p53 back into the cells and track them, cells were engineered with a doxycycline inducible p53 Venus construct, allowing the tracking of p53 levels and dynamics through a fluorescent medium, and also allowing tight temporal management

7 of p53 expression. In this system, the addition of doxycycline (dox) initiates transcription of p53 bonded with the Venus fluorescent protein, thus permitting real time visualization of p53 levels through a YFP imaging channel.

At the beginning of the experiment (0 hours), cells were treated with 62.5 ng/ml of doxycycline, thus activating p53-venus expression. Cells were maintained through continuous doxycycline additions for 48 hours, allowing the cells to reach strong p53 expression levels. After 48 hours, the doxycycline was washed out to the best of possible ability, terminating further transcription of p53 or venus. Following the removal of dox, cells continued to be imaged for an additional 48 hours, resulting in a 96 hour time lapse movie, as seen in Figure 2, with images taken every 20 minutes, leading to a 289 frame movie, during which the full rise and subsequent decay or stabilization of p53 levels across hundreds of individual cells was captured (Figure 2).

Live cell imaging was conducted on an automated microscope using both phase contrast microscopy (PCM) and a YFP fluorescence channel. Further, a digital cell tracking algorithm developed in the lab in a previous experiment was used to identify and follow individual cells so as to maintain consistent cell IDs throughout the duration of the movie and quantify each cell's YFP fluorescence intensity at every timepoint. This interface was also utilized to mark any time at which there was a cellular division or a cell death event. This pipeline led to the production of a raw fluorescence time series for each tracked cell in arbitrary units, representing dynamic changes in p53 expression over the 96 hour experimental period, as well as a one-hot dataset—a dataset filled with 0s except for 1s at event points—for cell death and cell divisions.

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Figure 2. Experimental design for p53 restoration in SKOV-3 cells using a doxycycline-inducible p53-Venus construct.

To generate a fate classified dataset suitable for later machine learning analyses, each tracked cell was labeled according to its proliferatory and apoptotic behavior. Because the experimental objective at 62.5 ng/ml of doxycycline was to distinguish between cells the differences in p53 dynamic behavior between cells that continued proliferating and those that entered arrest, and because only a small number of cells underwent death, all cells that apoptosed were excluded from the final dataset. In addition, only cells that remained continuously trackable throughout the full duration of the 96 hour movie were retained to avoid artifacts from partial cell trackings (traces).

Accurately labeling the proliferating versus arrested cells required first establishing the distribution of SKOV-3 division cycle lengths amongst the 62.5ng/ml doxycycline group. For each cell, all time intervals between successive divisions—for example between the first and second division of a cell, and the second and third, etc—were collected and plotted, leading to the formation of a skewed distributed array of interdivision times, favorable for the minimal loss of data in later steps. Importantly, intervals between the start of the movie and the first division, and between the last

9 observed division and the end of the movie were excluded, as these truncated intervals would bias the distribution due to their potential inaccuracy.

Figure 3. Distribution of time intervals in hours between consecutive cell divisions, excluding the first division event per cell. 10th and 90th percentile values marked with vertical dotted green and red lines, respectively.

Using this distribution, fate labels were assigned through the utilization of percentile thresholds of the cell cycle distribution, to ensure maximum confidence in cell trace fate labeling. Cells that underwent a division within the 10th percentile cutoff for interdivision length (25 hours) prior the end of imaging were labeled as proliferating, since fewer than 10% of cells were overserved to divide more quickly than this threshold. Therefore, the probability of one of these proliferating labeled cells in reality being arrested would be highly unlikely. On the other hand, cells that did not divide within the 90th percentile value of interdivision

10 times (52 hours) from the end of the movie were labeled as arrested, since fewer than 10% of cells were observed to have divided faster than this threshold (Figure 3). Therefore, incorrectly labeling one of these cells as arrested when in reality it was simply dividing at an incredibly low rate would be highly unlikely. Cells whose last observed division fell in between these bounds, approximately 25% of the population, were considered ambiguous and removed from the final dataset to ensure that only confidently labeled traces were used for machine learning model training and evaluation.

Figure 4. Heatmap of multiple single-cell p53 dynamics over time (thin horizontal strips), with cells sorted by time of last division.

11 In Figure 4, Red dots denote division events, blue dots denote death events. Blue denotes low p53 intensity, yellow denotes high p53 intensity. Upper horizontal dotted lines denote the 90th percentile value from Figure 3 (52.2 hours) before the movie ends. All traces above this line are labeled as arrested. The bottom horizontal line denotes the 10th percentile value from Figure 3 (25.3 hours) before the movie ends. All traces below this line are labeled as proliferating. All traces in between two lines are labeled as ambiguous.

Feature Engineering Following the creation of a confidently labeled dataset of p53-level traces and their corresponding fates, the next stage in the methodology involved converting each raw YFP time-series trace into a series of numerical representations that could be passed into and interpreted by machine learning algorithms. This transformation process, known as feature engineering, is essential in time-series classification problems because machine learning models cannot meaningfully directly interpret the raw YFP trajectories, since the means by which those models of interest in this experiment operate, namely decision tree classifiers (DTCs) and Random Forest classifiers (RFCs) use boolean cutoffs, and having continuous data of two dimensions is not easily passable.

Additionally, having only one feature would lead to significantly lower accuracies as the data is far more complex than single-dimensional classification. These models instead require distinct and quantitative descriptors, or features, that convey potentially meaningful aspects of the underlying signal. A feature, in this context, is a single measurable property extracted from a cell's p53 trace that captures a biological or mathematical characteristic of its behavior. The remainder of this section

12 elaborates on the reasoning and methodology of how the accurately labeled p53 dataset was converted into a matrix with the first column remaining the cellular identifiers, but the following many hundred columns being single value calculated features for each given trace, the same features across all traces but distinct values.

Feature engineering is processed along two simultaneous and complementary paths: one based on manual, biologically informed decision making and design for each feature, and the other based on automated, large scale, algorithmic extraction of features through the utilization of a preexisting algorithmic software imported into the codespace. The manually derived features, numbering approximately 50, were informed by prior studies and by analyses performed earlier in the project. These features quantified properties such as the overall direction and shape of the trajectory, through linear regression slopes, maximum slope values, and acceleration metrics, local variability (for example rolling standard deviations capturing fluctuations in the trace), and timing-related characteristics such as the rise time or area under the curve above specified thresholds. Each of these features was informed by previous research conducted in the lab and to an extent also corresponded to a biologically interpretable hypothesis in the situation that downstream in the research, a given feature was shown to have a strong correlation with cell fate.

In parallel with this biologically informed approach of feature engineering, automated feature extraction was performed using computational algorithms, specifically tsfresh, a python importable package that calculates hundreds of features based on the provided time series data. These features include many arbitrary mathematical transformations and calculations, including distributional, autocorrelation coefficients, and other mathematically defined quantities that do not rely on prior biological intuition or necessarily correspond with a biological

13 interpretation. Although many of these features lack immediate interpretability, their inclusion allowed the classifiers to potentially reveal the significance of subtle or unexpected relationships embedded in the time-series data.

Features were computed from the complete 96 hour traces for each cell. This is due to the fact that approximately 1% of cells apoptosed prior the end of the movie and those that did were removed from the dataset, as well as those that went out of frame during the tracking process. Thus all the cells in the dataset had complete traces to utilize in the feature calculations. However, many features were nonetheless designed to emphasize or take note of early behavior, for example, statistics over lower percentiles of the trace, which occurred at the beginning of the movie, or measures of initial slopes. This approach allowed the analysis to focus both on overall trace behaviors and potential giveaways as well as on specifically early-timeframe patterns that could be more likely to contain the “decision point” for a cell’s fate. The final output of this feature-engineering process was a comprehensive feature matrix, in which each row represented a single cell and each column represented an engineered feature, each box containing the feature’s calculated value for that cell.

This matrix served as the input to the classification models described in the following section.

Model Training and Evaluation Once the feature matrix was constructed, the next phase of the methodology involved training machine learning models to determine which quantitative aspects of p53 dynamics most accurately predicted cellular fate. Because the central objective of the analysis was not solely to achieve high predictive accuracy but to identify specific properties and behaviors of p53 dynamics that distinguish proliferating from arrested cells, it was essential that

14 the machine learning models utilized were both interpretable in their decision making processes and suited for a range of biological data. For this reason, two supervised learning algorithms were selected: the Decision Tree Classifier (DTC) and the Random Forest Classifier (RFC).

Before the classifiers were created, the full dataset was divided into two non-overlapping subsets: a training set, used to construct the classifiers and a test set, used only to evaluate the ability of the model to predict previously unseen data. A 70/30 split was employed to create a training set and test set, respectively. Because the number of arrested cells exceeded the number of proliferating cells in the original dataset, the training set was balanced by oversampling the proliferating class until the two fates were represented in equal or near-equal proportion. This ensured that the classifiers did not become biased toward the more abundant fate and that both classes were weighed equally during model construction.

A decision tree classifies data by recursively dividing the dataset according to threshold based Boolean logic applied to individual features. At each potential split (node), the algorithm evaluates all possible thresholds across all available features and selects the one that most effectively separates the two fate classes.

The metric used to quantify the quality of a split is Gini Impurity, a measure of how mixed classes are within a given node. A node containing an equal mixture of both classes has the maximum impurity of 0.5, while a node containing only one class has a minimum impurity of 0. The Gini impurity at a node is represented in (1): 𝐶

2

𝐺 = 1 − ∑ 𝑝𝑖 , 𝑖=1

(1)

15 Where 𝑝𝑖 represents the proportion of samples belonging to class 𝑖 within that node, and 𝐶 is the number of classes. During the training stage, the decision tree evaluates all candidate splits and selects the one that causes the lowest overall gini impurity, thus iteratively creating a structure of decision rules that map the features into distinct fate outcomes.

While decision trees are highly interpretable, they may also overfit by finding non-generalizable patterns in the data, particularly when the number of features is large or when the dataset contains some noise, as is often the case in tracking biological systems. To address this potential overfitting, all decision tree models were given a max depth of 3, meaning that they could only make three levels of decisions before assigning a fate, and additionally is why a Random Forest Classifier was also employed. A random forest constructs a “forest,” or a large collection, of decision trees, each trained on a different subset of the dataset. This variability in the data leads to a wide variety of decision tree structures, which in turn improves generalization and yields a more stable model at lower risk of overfitting. Each individual tree outputs a class prediction for a given trace, and the classifier’s overall final prediction is determined by a majority vote of all the trees.

To quantify model performance, predictions on the held-out test set were evaluated using accuracy, precision, recall, and F1 scores, computed from the confusion matrix of true positives (TPs), true negatives (TNs), false positives (FPs), and false negatives (FNs).

The accuracy score measured the proportion of all predictions that were correct, represented in (2):

16 𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 =

𝑇𝑃 +𝑇𝑁 𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁

(2)

Precision quantified the fraction of predicted positive cases that were actually positive, represented in (3): 𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 =

𝑇𝑃 𝑇𝑃 + 𝐹𝑃

(3)

Recall on the other hand measured the fraction of total actual positive cases that the model successfully identified, represented in (4): 𝑅𝑒𝑐𝑎𝑙𝑙 =

𝑇𝑃 𝑇𝑃 + 𝐹𝑁

(4)

Finally, the F1 score, defined as the harmonic mean of precision and recall, represented in (5): 𝐹1 = 2 ·

𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 ·𝑅𝑒𝑐𝑎𝑙𝑙 𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛+𝑅𝑒𝑐𝑎𝑙𝑙

(5)

provided a single summary metric balancing both types of classification performance.

A key element of both DTCs and RFCs is their ability to generate feature-importance scores. These scores quantify the contribution of each inputted feature to the total reduction in gini impurity across the model. For decision trees, importance is based on how frequently and how effectively a feature contributes to impurity reduction within the overall construct of splits. For random forests, importance scores are averaged across all trees, producing an average estimate of a feature's importance. These importance values functioned as the core analytical output of this research due to the fact that they allowed for the identification of specific p53

17 dynamical behaviors that differentiated proliferating cells from arrested cells.

Results Initial exploratory analysis revealed a strong inverse relationship between overall p53 abundance and division count following p53 restoration. Visualization of single-cell p53 traces, sorted by total number of divisions appeared to show some level of correlation between the amount of times a cell has divided, and its overall levels of p53 expression, with a cell dividing fewer times, and thus more likely to be labeled as arrested, tending to have higher p53 levels (Figure 5). On the other hand, cells with lower p53 levels tended to continue proliferating and have higher division counts.

Figure 5. Heatmap of multiple single-cell p53 dynamics over time (thin horizontal strips), with cells sorted by division count and then

18 by time of last division. Red dots denote division event, blue dots denote death event, blue denotes low p53 intensity, yellow denotes high p53 intensity. Horizontal dotted lines separated division count.

To quantify this trend, the mean p53 level of each cell trace was calculated and then grouped by the total number of divisions observed in that trace during the 96-hour imaging window. These groupings, separated by division count, were then each averaged for an all-encompassing average p53 level for cells that divided a given number of times (Figure 6).

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Figure 6. Bar graph of mean p53 level of traces sorted by division count, increasing from left to right. Sample quantity included above mean p53 value.

The hypothesis proposed from initial observation that there appeared to be a relationship between division count and p53 levels was shown to be true, with mean p53 levels shown to decrease consistently as the amount of divisions increased, with non-dividing cells exhibiting the highest average p53 levels, and cells undergoing four divisions—the most observed— exhibiting the lowest. To determine the statistical significance of these findings and the extent to which this relationship held truth, a one-way ANOVA test was run. It confirmed that mean p53 levels differed significantly across divisions groups (F = 24.13, p = 1.8 · 10-18), indicating that the observed trend was statistically significant. These results establish a clear association between elevated p53 levels and reduced proliferative capabilities following restoration.

20 Based on the previous findings, it seemed that there might be some relationship between cell-fates and p53 levels. To further investigate how p53 dynamics relate to long-term cell fate, p53 traces were first grouped by their cell fate labels (arrested vs. proliferating) and then plotted by their average p53 levels at each timepoint. Arrested cells exhibited noticeably higher p53 expression levels across the duration of the experiment compared to proliferating cells, particularly as the movie lengthened in duration, with the second half having near non-existent overlap in interquartile ranges (IQRs) (Figure 7). However, even in the first 48 hours, there was evident separation between the two fate categories, with, at the arrested category’s signature peak at approximately 20 hours, a separation in the average p53 expression levels of over threefold.

Figure 7. Median single-cell p53 trajectories over time for arrested and proliferating cells, with shaded regions indicating the interquartile range (25-75%).

21 To assess whether differences in p53 dynamics and shape drive fate decisions, p53 trajectories were normalized by each cell’s maximum observed p53 level. This means that a new dataset was created in which every trace was recalculated to have values between 0 and 1, with 1 representing the maximum observed p53 level in that trace. This normalization enabled the comparison of different traces simply by their “shape,” and removing the variable of p53 levels. After normalization, the distinction between arrested and proliferating cells largely disappeared (Figure 8). Median trajectories and IQR ranges overlapped substantially across the two fate groups, suggesting that normalized macro-temporal patterns do not robustly separate fate outcomes. However, it should be noted that there is the possibility of macro-temporal patterns losing some separative capabilities due to the potential loss of behaviors observable in the data when it was averaged.

Figure 8. Normalized (out of 1) single-cell p53 trajectories over time for arrested and proliferating cells, with shaded regions indicating the interquartile range (25-75%).

22 Machine Learning Findings Application of supervised machine learning models to the engineered feature set identified a small subset of features that exhibited high importance and strong discriminatory power between arrested and proliferating cells. Particularly, three features emerged as dominant contributors to fate classification, together accounting for the majority of impurity reduction within the trained models. ​

40th Percentile p53 Feature

The first of these most influential features, derived from automated feature extraction using tsfresh, was the 40th percentile p53 value of each single-cell trace (Figure 9). This feature alone accounted for 61.5% of the total feature importance in the decision tree classifier trained on a dataset in which the smaller proliferating category was overrepresented such that there was a 1:1 ratio of arrested and proliferating data points that the model trained on.

When distributions were compared across fate groups, arrested cells exhibited substantially higher 40th percentile p53 levels than proliferation cells, with the IQRs entirely separated from one another, and arrested cells, as observed earlier, exhibited significantly higher values than proliferating cells. This separation translated into strong classification performance, contributing to an overall model accuracy of 0.82 and an F1 score of 0.87 for arrested cells.

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Figure 9. Feature value distribution separated by class of 40th percentile p53 value, including median value, denoted by red line, and IQR.

​

Δp53 in lower 20th Percentile Feature

The second most important feature, also originating from the utilization of tsfresh engineering, was derived through the tweaking of the sampling ratios of the two fate groups, such that the proliferating training group was oversampled with a 4:3 ratio.

This was done in an attempt to maximize predictive accuracy, since altering sample sizes could emphasize certain patterns over others which in turn could lead to less or more overall predictive accuracy. With a feature importance of 54.2%, the feature quantified the average rate of change of p53 in the lowest twenty percent of a trace (Figure 10).

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Figure 10. Feature value distribution separated by class of 20th percentile p53 value, including median value, denoted by red line, and IQR. In other words, since both proliferating and arrested cells began the movie with 0 arbitrary units of p53 expression, and at the 96-hour point were both generally significantly above their 20th percentile values, what this feature signals is how quickly a trace shot upwards in magnitude towards the beginning of the movie relative to its normalized values, with proliferating cells generally leaving their low values over a longer period of time than their arrested counterparts. Again, the IQRs of the feature between the two distinct fates were entirely separated (Figure 10). This feature achieved an overall accuracy of 87% and a F1-arrest score of 0.90. ​

20th Percentile p53 Feature

25 The third key feature identified was derived through manual feature engineering, and when there was no oversampling procedure to create an equal sampling quantity between the two fates for the training dataset. This meant that there were approximately three times more arrested cell traces for the decision tree to train on than proliferating cells. This feature was similar in some ways to the first identified significant feature, in that it measured the 20th percentile average value for each trace, with 65.3% feature importance (Figure 11). Yet again, the IQRs between the two fate categories were completely separated, signaling a strong degree of predictive capability. Indeed this was found to be the case, with an overall accuracy of 83%, as well as an F1 arrest score of 0.87.

Figure 11. Feature value distribution separated by class of 20th percentile p53 value, including median value, denoted by red line, and IQR. Together, these results demonstrate that fate classification following p53 restoration is driven significantly by quantitative

26 properties of low-to-near average p53 dynamics, particularly with some suggestions regarding early-stage behavior. The convergence of importance across independently derived features underscores the significance of these findings and motivated further biological interpretation, addressed in the Discussion Section.

Discussion This study set out to investigate whether the temporal dynamics of p53 signaling following restoration in a p53-null cancer cell line, SKOV-3, could predict long term cellular fate, and to identify which aspects of those dynamics are most strongly associated with arrest versus continued proliferation. By combining single cell live-imaging data with interpretable machine learning approaches, the analysis reveals that fate decisions following p53 restoration have a strong correlative relationship with both certain dynamical features and magnitude oriented features of the traces. It was also determined that general normalized dynamics do not have an apparent correlation with cell fate. The three most significant features determined could generally be classified as quantitative properties of p53 abundance at low to near average levels and early dynamic behavior. Together, these findings provide insight into how restored p53 signaling dynamics relate to cell fate and form the fundamental insight into what constitutes an “effective” p53 response for eventual therapies.

Biological Interpretation of Key Features Across multiple independent feature-engineering strategies and model configurations, features capturing behaviors related to low-percentile p53 levels consistently emerged as the strongest predictors of fate (Figures 9, 10, 11) Cells that continued

27 proliferating were characterized by persistently lower p53 values throughout the trace, while cells that entered arrest exhibited elevated p53 levels even at relatively early timepoints, finally stabilizing at average levels significantly above proliferating cells (Figure 7). Importantly, these results suggest that it might be the ability of the cell to sustain average p53 expression above a minimum effective threshold in the long-term that appears to be decisive.

This interpretation is well supported by the dominance of the 20th and 40th percentile p53 features. Unlike measures of peak intensity or high percentile features, these two features quantify the lower bound of a cell's p53 signal across the full trajectory. In arrested cells, these lower-percentile values are consistently elevated—particularly once they stabilize and flatten at a relatively high magnitude after the first peak—indicating that even the lower sustained p53 levels remain above those observed in proliferation cells. In contrast, proliferating cells exhibit low percentile values that remain near baseline, even when occasional increases in p53 may occur. As a result, the lower end of the arrested cell distribution rarely overlaps with even the upper end of the proliferating cell distribution once the p53 levels in each category stabilize approximately 48 hours into the movie, producing the near-complete separation observed from these features.

Biologically, this pattern supports a threshold-based interpretation of restored p53 signaling. Rather than responding to a brief increase in p53, cells appear to commit to arrest only once p53 is maintained above a critical quantitative level for an undetermined sufficient duration (Figure 7). This idea is supported by the fact that there is significant IQR overlap of raw p53 values between the proliferating and arrested groups toward the beginning of the movie when the peak is observed, but only later a stabilized separation is observed. Cells that fail to reach or sustain this threshold, despite expressing p53, remain vulnerable to continued

28 cell-cycle progression. The stabilization of p53 at distinct plateau levels further reinforces this view: once trajectories settle, arrest and proliferating cells occupy clearly separated quantitative areas, suggesting that fate commitment reflects long-term signal maintenance.

The normalization analysis reinforces this conclusion.

When p53 trajectories were normalized by their respective maxima, thereby isolating temporal dynamics independent of any absolute magnitude, the distinction between arrested and proliferating cells largely disappeared (Figure 8). This convergence occurs because both fate groups stabilize at similar relative proportions of their maximum p53 levels, even though their absolute plateau values differ significantly. This indicated that normalized macro-dynamics obscure the quantitative differences that appear to be biologically decisive.

Taken together, the conceptual convergence of all three high-importance features reinforces a unified interpretation of restored p53 signaling as a threshold-regulated process. The 20th and 40th percentile p53 features appear to capture the ability of a cell to maintain its lower bound of p53 expression above some critical level once trajectories stabilize, while the early low percentile slope feature captures how rapidly a cell escapes its lowest quintile of p53 levels following restoration. These features all describe complementary aspects of the same proposed regulatory behavior: whether a cell can both establish and sustain p53 above a functional threshold within an undetermined temporal window. Cells that fail either component, by remaining near baseline for too long early on, denoted by the early slope feature, or by stabilizing at insufficient p53 levels later, denoted by the 20th and 40th percentile features, tend to continue proliferating. Cells that rapidly exit low-p53 states and maintain elevated baseline levels committee to arrest on the other hand. In this framework, fate determination reflected not just the presence of p53, but the

29 cell’s capacity to regulate restored p53 signaling to quantitatively stable and functionally effective levels.

Implications for Therapeutic Design The threshold-regulated interpretation of restored p53 signaling has direct implications for the development and evaluation of p53-restoring therapies. These findings suggest that therapeutic success should not be assessed solely by the presence of restored p53 or by peak expression levels, but rather by whether p53 signaling is regulated in a manner consistent with that of stabilized, self-maintaining cells. Cells that express p53 but fail to establish or maintain sufficient baseline levels may remain vulnerable to proliferation, offering a potential explanation for the heterogeneous responses observed in p53 restoration.

Methodological Contributions In addition to its biological implications, this study demonstrates the value of integrating interpretable machine learning with single-cell time-series analysis to analyze dynamic signaling systems. Rather than rely on basic statistics or qualitative inspection of traces, this approach enabled the systematic identification of specific quantitative features that correlate with fate outcomes. The deliberate use of interpretable classifiers ensured that predictive features could be directly linked back to biologically meaningful aspects of p53 and cellular behavior.

The dual feature engineering strategy employed here proved particularly effective. By combining biologically informed, manually designed features with automated engineering methods, the analysis captured both intuitive and non-obvious properties of p53 dynamics. The convergence of importance across independently derived features strongly suggests that the identified

30 predictors reflect genuine structure in the data rather than the results of a certain modeling choice. This framework is broadly applicable to other signaling pathways in which fate decisions emerge from complex temporal dynamics and where interpretability is essential for biological insight.

Limitations and Future Directions Several limitations should be considered when interpreting these results. First and most significantly, the analysis focused exclusively on arrest versus proliferation, excluding apoptotic cells due to their low representation in the dataset. While this ensured confident labeling and simplified model complexity, inclusion of cell death as a third fate class in other experimental setups in which it’s more abundant is essential, since in providing a more complete understanding of how p53 dynamics lead to death, therapies can aim to cause cancer regression as opposed to senescence.

Secondly, this study examined a single p53-null ovarian cancer cell line and a specific restoration strategy. Although SKOV-3 cells provide a clean system for isolating restored p53 behavior, it remains unclear how generalizable these dynamics are across other cancer types, genetic backgrounds, or p53 restoration methods. Extending this analysis to additional systems will be necessary to determine whether the proposed threshold regulation model represents a general principle of p53 restoration or is a context-dependent occurrence.

Finally, while the computational findings strongly support a threshold-based interpretation, experimental validation will be essential to establish causality. Experiments that systematically alter the timing, rate, or magnitude of restored p53 expression could directly test whether threshold establishment and sustained baseline regulation are required for fate commitment.

31

Conclusion This study demonstrates that p53 restoration dynamics can be quantitatively linked to long-term cell fate decisions in a p53-null ovarian cancer cell line, SKOV-3. By combining single-cell live imaging with interpretable machine learning, the analysis shows that fate determination following p53 restoration is driven by quantitative properties of p53 abundance and early— likely regulatory—behavior. Together these findings support a threshold-based model of restored p53 signaling. Cells that rapidly establish p53 above a critical threshold and maintain that baseline appear to commit to arrest, whereas cells that fail to do so remain vulnerable to continued proliferation.

By extending p53 dynamic analysis into a restoration context, this work helps explain the heterogeneous outcomes observed in p53-targeted efforts and provides a computational foundation for identifying predictive biomarkers. Understanding how restored p53 could be regulated over time in these p53-restored cells may be essential for translating restoration strategies into effective and reliable cancer therapies.

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