Fluorescence recovery after photobleaching (FRAP) is a common experimental method for investigating rates of molecular redistribution in biological systems. Many mathematical models of FRAP have been developed, the purpose of which is usually the estimation of certain biological parameters such as the diffusivity and chemical reaction rates of a protein, this being accomplished by fitting the model to experimental data. In this article, we consider a two species reaction–diffusion FRAP model. Using asymptotic analysis, we derive new FRAP recovery curve approximation formulae, and formally re-derive existing ones. On the basis of these formulae, invoking the concept of Fisher information, we predict, in terms of biological and experimental parameters, sufficient conditions to ensure that the values all model parameters can be estimated from data. We verify our predictions with extensive computational simulations. We also use computational methods to investigate cases in which some or all biological parameters are theoretically inestimable. In these cases, we propose methods which can be used to extract the maximum possible amount of information from the FRAP data.

光漂白后的荧光恢复 (FRAP) 是研究生物系统中分子再分布率的常用实验方法。已经开发了许多 FRAP 数学模型，其目的通常是估计某些生物参数，例如蛋白质的扩散率和化学反应速率，这是通过将模型与实验数据拟合来实现的。在本文中，我们考虑两种反应扩散 FRAP 模型。使用渐近分析，我们推导出新的 FRAP 恢复曲线近似公式，并正式重新推导现有的公式。在这些公式的基础上，调用Fisher信息的概念，我们在生物学和实验参数方面预测了充分条件，以确保所有模型参数的值都可以从数据中估计出来。我们通过广泛的计算模拟来验证我们的预测。我们还使用计算方法来研究某些或所有生物参数在理论上不可估计的情况。在这些情况下，我们提出了可用于从 FRAP 数据中提取最大可能信息量的方法。