Radulescu Ovidiu, Grigoriev Dima, Seiss Matthias, Douaihy Maria, Lagha Mounia, Bertrand Edouard
LPHI, University of Montpellier and CNRS, Place Eugène Bataillon, 34095, Montpellier, France.
Mathématiques, CNRS, Université de Lille, 59655, Villeneuve d'Ascq, France.
Bull Math Biol. 2024 Dec 3;87(1):11. doi: 10.1007/s11538-024-01385-y.
Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type distribution, can we identify the transition rate parameters of the underlying Markov chain? For a specific class of solvable Markov models, we show this problem has a unique solution up to finite symmetry transformations, and we outline a recursive method for computing symbolic solutions for these models across any number of states. Using the Thomas decomposition technique from computer algebra, we further provide symbolic solutions for any model. Interestingly, different models with the same state count but distinct transition graphs can yield identical phase-type distributions. To distinguish among these, we propose additional properties beyond just the time to the next event. We demonstrate the method's applicability by inferring transcriptional regulation models from single-cell transcription imaging data.
许多生物学和医学问题可以用有限状态马尔可夫链中的事件发生时间数据来建模，其中相位类型分布描述了事件之间的间隔。我们解决逆问题：给定一个相位类型分布，我们能否识别基础马尔可夫链的转移速率参数？对于一类特定的可解马尔可夫模型，我们表明这个问题在有限对称变换下有唯一解，并且我们概述了一种递归方法，用于计算这些模型在任意数量状态下的符号解。使用计算机代数中的托马斯分解技术，我们进一步为任何模型提供符号解。有趣的是，具有相同状态数但不同转移图的不同模型可以产生相同的相位类型分布。为了区分这些，我们提出了除了到下一个事件的时间之外的其他属性。我们通过从单细胞转录成像数据推断转录调控模型来证明该方法的适用性。
