论文标题
自催化反应网络上的生物质转移：延迟微分方程公式
Biomass transfer on autocatalytic reaction network: a delay differential equation formulation
论文作者
论文摘要
为了使生物系统生长和扩展，必须将质量从环境转移到系统中，并将其吸收到其反应网络中。在这里，我表征了生长自催化系统的生物量转移过程。通过沿反应途径的轨道生物量，可以将反应网络的N维常规微分方程（ODE）重新构成其长期动力学的一维延迟微分方程（DDE）。 DDE的内核函数总结了系统的总体扩增和转移延迟，并用作自催化动力学的签名。 DDE公式允许比较各种拓扑和复杂性的反应网络，并在反应网络降低时为生长速率提供了严格的估计方案。
For a biological system to grow and expand, mass must be transferred from the environment to the system and be assimilated into its reaction network. Here, I characterize the biomass transfer process for growing autocatalytic systems. By track biomass along reaction pathways, an n-dimensional ordinary differential equation (ODE) of the reaction network can be reformulated into a one-dimensional delay differential equation (DDE) for its long-term dynamics. The kernel function of the DDE summarizes the overall amplification and transfer delay of the system and serves as a signature for autocatalysis dynamics. The DDE formulation allows reaction networks of various topologies and complexities to be compared and provides rigorous estimation scheme for growth rate upon dimensional reduction of reaction networks.
