Dynamic modelling and evaluation of preclinical trials in acute leukaemia

Dynamic models are widely used to mathematically describe biological phenomena that evolve over time. One important area of application is leukaemia research, where leukaemia cells are genetically modified in preclinical studies to explore new therapeutic targets for reducing leukaemic burden. In advanced experiments, these studies are often conducted in mice and generate time-resolved data, the analysis of which may reveal growth-inhibiting effects of the investigated gene modifications. However, the experimental data is often times evaluated using statistical tests which compare measurements from only two different time points. This approach does not only reduce the time series to two instances but also neglects biological knowledge about cell mechanisms. Such knowledge, translated into mathematical models, expands the power to investigate and understand effects of modifications on underlying mechanisms based on experimental data. We utilise two population growth models – an exponential and a logistic growth model – to capture cell dynamics over the whole experimental time horizon and to consider all measurement times jointly. This approach enables us to derive modification effects from estimated model parameters. We demonstrate that the exponential growth model recognises simulated scenarios more reliably than the other candidate model and than a statistical test. Moreover, we apply the population growth models to evaluate the efficacy of candidate gene knockouts in patient-derived xenograft (PDX) models of acute leukaemia.

💡 Research Summary

The manuscript addresses a critical methodological gap in pre‑clinical acute leukaemia research, where the standard practice of comparing only two time‑points (typically using paired t‑tests) discards valuable temporal information and ignores mechanistic knowledge about cell proliferation and death. To overcome these limitations, the authors develop a model‑based framework that treats the dynamics of genetically modified and control cell populations as continuous processes described by ordinary differential equations (ODEs). Two classical population‑growth models are considered: (i) an exponential growth model with net per‑capita growth rates β₁ and β₂ for the modified and control populations, respectively, and (ii) a logistic growth model that adds a shared carrying capacity K and net growth rates λ₁ and λ₂. The observable in the experiments is the proportion η(t)=x₁/(x₁+x₂) of modified cells measured in the bone marrow at several post‑engraftment time points.

Parameter estimation is performed by maximum likelihood using all available measurements across the entire experimental horizon, thereby exploiting the full time‑series rather than isolated snapshots. The authors also compute profile‑likelihood confidence intervals to assess statistical uncertainty and conduct structural identifiability analyses. The exponential model’s parameters (β₁, β₂, and the initial conditions) are shown to be well‑identified even with modest data, whereas the logistic model suffers from strong correlations among λ₁, λ₂, and K, leading to unstable estimates when sample sizes are small.

A comprehensive simulation study evaluates the detection power of the two models and of the conventional paired t‑test under varying conditions: different true growth‑rate differences, sample sizes (N=5–30), and measurement schedules (early, late, and multiple time points). The exponential model consistently outperforms the logistic model and the t‑test, especially for small N and when early‑time data are included. The logistic model’s advantage of incorporating a biologically realistic saturation effect is offset by the difficulty of reliably estimating K without abundant data. The paired t‑test attains comparable power only when it is restricted to the latest measurement and the sample size is sufficiently large; it loses power dramatically when early measurements are considered.

The framework is then applied to real pre‑clinical data from patient‑derived xenograft (PDX) models of acute leukaemia. Four candidate genes were knocked out using CRISPR‑Cas9, and the relative abundance of modified versus control cells was measured at two to three time points per experiment. Both growth models and the paired t‑test identify similar qualitative conclusions regarding which knockouts exert a growth‑inhibitory effect. However, the exponential model provides quantitative estimates of the difference in net growth rates (β₁−β₂), enabling a mechanistic interpretation of the magnitude of inhibition or stimulation. In contrast, the logistic model yields wide confidence intervals for K, limiting its ability to quantify the effect size. The paired t‑test, limited to late‑time points, can detect significant differences only when the effect is large and the sample size is adequate.

In summary, the authors demonstrate that ODE‑based population‑growth modeling leverages the full temporal structure of pre‑clinical leukaemia data, offering superior statistical power and mechanistic insight compared with traditional two‑point tests. The exponential growth model, in particular, is robust to small sample sizes and sparse measurement schedules, making it a practical tool for early‑stage drug target validation in acute leukaemia. The logistic model may be useful when extensive longitudinal data are available, providing a more realistic saturation description. The study advocates the adoption of such dynamic modeling approaches in CRISPR‑Cas9 screens and other high‑throughput pre‑clinical pipelines to improve target prioritisation and deepen biological understanding.