A birth-death-move process with mutations is a Markov model for a system of marked particles in interaction, that move over time, with births and deaths. In addition the mark of each particle may also change, which constitutes a mutation. Assuming a parametric form for this model, we derive its likelihood expression and prove its local asymptotic normality. The efficiency and asymptotic distribution of the maximum likelihood estimator, with an explicit expression of its covariance matrix, is deduced. The underlying technical assumptions are showed to be satisfied by several natural parametric specifications. As an application, we leverage this model to analyse the joint dynamics of two types of proteins in a living cell, that are involved in the exocytosis process. Our approach enables to quantify the so-called colocalization phenomenon, answering an important question in microbiology.

翻译：生灭移动过程是一种带标记粒子相互作用系统的马尔可夫模型，粒子随时间移动并经历出生与死亡事件。此外，每个粒子的标记也可能发生变化，这构成了突变过程。假设该模型具有参数化形式，我们推导了其似然函数表达式，并证明了其局部渐近正态性。由此推导出最大似然估计量的渐近分布、效率及其协方差矩阵的显式表达式。研究表明，多种自然参数设定均满足所涉及的技术假设。作为应用，我们利用该模型分析了参与胞吐过程的活细胞中两种蛋白质的联合动态。该方法能够量化所谓的共定位现象，从而回答了微生物学中的一个重要问题。