Henriksson Oskar, Améndola Carlos, Rodriguez Jose Israel, Yu Polly Y
Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.
Institute of Mathematics, Technical University of Berlin, Berlin, Germany.
J Math Biol. 2025 Sep 10;91(4):34. doi: 10.1007/s00285-025-02262-5.
A fundamental question in the field of molecular computation is what computational tasks a biochemical system can carry out. In this work, we focus on the problem of finding the maximum likelihood estimate (MLE) for log-affine models. We revisit a construction due to Gopalkrishnan of a mass-action system with the MLE as its unique positive steady state, which is based on choosing a basis for the kernel of the design matrix of the model. We extend this construction to allow for any finite spanning set of the kernel, and explore how the choice of spanning set influences the dynamics of the resulting network, including the existence of boundary steady states, the deficiency of the network, and the rate of convergence. In particular, we prove that using a Markov basis as the spanning set guarantees global stability of the MLE steady state.
分子计算领域的一个基本问题是生化系统能够执行哪些计算任务。在这项工作中，我们专注于寻找对数仿射模型的最大似然估计（MLE）的问题。我们重新审视了戈帕尔克里什南构建的一个质量作用系统，该系统以MLE作为其唯一的正稳态，这是基于为模型的设计矩阵的核选择一个基。我们扩展了这个构建，以允许核的任何有限生成集，并探讨生成集的选择如何影响所得网络的动态，包括边界稳态的存在、网络的亏度以及收敛速率。特别地，我们证明使用马尔可夫基作为生成集可保证MLE稳态的全局稳定性。
