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.

翻译：动态模型被广泛用于数学描述随时间演变的生物现象。白血病研究是该模型的一个重要应用领域，在临床前研究中通过对白血病细胞进行基因修饰，以探索减轻白血病负荷的新治疗靶点。在高级实验中，这些研究通常在小鼠中进行，并生成时间分辨数据，对其分析可能揭示所研究基因修饰的生长抑制效应。然而，实验数据通常仅通过比较两个不同时间点测量值的统计检验进行评估。这种方法不仅将时间序列简化为两个时间点，而且忽略了关于细胞机制的生物学知识。将这些知识转化为数学模型，能够增强基于实验数据研究和理解修饰对潜在机制影响的能力。我们采用两个种群增长模型——指数增长模型和逻辑增长模型——来捕捉整个实验时间范围内的细胞动态，并联合考虑所有测量时间点。这种方法使我们能够从估计的模型参数中推导出修饰效应。我们证明，指数增长模型比另一个候选模型及统计检验能更可靠地识别模拟场景。此外，我们应用种群增长模型评估了急性白血病患者来源异种移植（PDX）模型中候选基因敲除的疗效。