Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Budapest, Hungary.
Systems and Control Laboratory, Institute for Computer Science and Control (SZTAKI), Budapest, Hungary.
PLoS One. 2023 Jul 7;18(7):e0288148. doi: 10.1371/journal.pone.0288148. eCollection 2023.
In this paper some important qualitative dynamical properties of generalized ribosome flow models are studied. Ribosome flow models known from the literature are generalized by allowing an arbitrary directed network structure between compartments, and by assuming general time-varying rate functions corresponding to the transitions. Persistence of the dynamics is shown using the chemical reaction network (CRN) representation of the system where the state variables correspond to ribosome density and the amount of free space in the compartments. The L1 contractivity of solutions is also proved in the case of periodic reaction rates having the same period. Further we prove the stability of different compartmental structures including strongly connected ones with entropy-like logarithmic Lyapunov functions through embedding the model into a weakly reversible CRN with time-varying reaction rates in a reduced state space. Moreover, it is shown that different Lyapunov functions may be assigned to the same model depending on the non-unique factorization of the reaction rates. The results are illustrated through several examples with biological meaning including the classical ribosome flow model on a ring.
本文研究了广义核糖体流动模型的一些重要定性动力学性质。通过允许隔室之间的任意有向网络结构，并假设与跃迁相对应的一般时变速率函数，对文献中已知的核糖体流动模型进行了推广。利用系统的化学反应网络 (CRN) 表示来证明动力学的持久性，其中状态变量对应于核糖体密度和隔室中自由空间的量。在具有相同周期的周期反应速率的情况下，还证明了解的 L1 收缩性。此外，通过将模型嵌入具有时变反应速率的弱可逆 CRN 中，并在简化状态空间中，对包括具有熵似对数李雅普诺夫函数的强连通隔室结构的稳定性进行了证明。此外，还表明根据反应速率的非唯一分解，可以为同一模型分配不同的李雅普诺夫函数。通过包括环上经典核糖体流动模型在内的几个具有生物学意义的例子来说明结果。
