Dijkstra Jan, Mills Jonathan A N, France James
Animal Nutrition Group, Wageningen Institute of Animal Sciences, Wageningen University, Marijkeweg 40, 6709 PG Wageningen, The Netherlands.
Nutr Res Rev. 2002 Jun;15(1):67-90. doi: 10.1079/NRR200237.
Mechanistic models of microbial metabolism in the rumen aim at an improved understanding and integration for research purposes or at an improved prediction for practical purposes. The standard way of representing such models is the rate : state formalism. The system is defined by a number of state variables and a set of differential equations describe the change of the state variables with time. Three different types of solution to these dynamic models are distinguished, and examples of these solutions are described to illustrate the applications and contributions of dynamic modelling in the study of the rumen microbial ecosystem. Type I solutions are obtained when the system is in steady state and the differential equations are solved by setting the differentials to zero. An application of the type I solution is the indirect approach to quantifying the fibrolytic anaerobic fungi in the rumen. The solutions of the model describing the alternate life cycle of rumen fungi, with its free-swimming dispersal and particle-attached stages, appear to be consistent with ruminal and faecal observations. Type II solutions are obtained when the system is not in steady state but the differential equations can be integrated analytically. An application of this type of solution is the quantification of the growth and growth yield in batch cultures. Such models help to quantify the degradation of substrates in the rumen and to elucidate the interactions between groups of rumen micro-organisms. Type III solutions are obtained when the system is not in steady state and when the differential equations have to be solved numerically. Applications of the type III solutions are the rumen simulation models that describe substrate degradation, endproduct formation and microbial metabolism in an integrated manner. To illustrate this type III solution, a model of lactic acid metabolism in the rumen is defined, and its contribution to understanding of the paths and rates of lactic acid disappearance described. It is essential that the models are based on sound mathematical and biological principles. However, the various applications described in the paper show that models need not necessarily be complex and very detailed to contribute to better understanding.
瘤胃微生物代谢的机理模型旨在为研究目的而增进理解与整合，或为实际应用目的而改进预测。表示此类模型的标准方法是速率：状态形式主义。该系统由若干状态变量定义，一组微分方程描述状态变量随时间的变化。区分了这些动态模型的三种不同类型的解，并描述了这些解的示例，以说明动态建模在瘤胃微生物生态系统研究中的应用和贡献。当系统处于稳态且通过将微分项设为零来求解微分方程时，可得到I型解。I型解的一个应用是瘤胃中纤维分解厌氧真菌的间接定量方法。描述瘤胃真菌交替生命周期（包括其自由游动传播和附着于颗粒阶段）的模型解似乎与瘤胃和粪便观察结果一致。当系统不处于稳态但微分方程可进行解析积分时，可得到II型解。此类解的一个应用是分批培养中生长和生长产量的定量。这些模型有助于量化瘤胃中底物的降解，并阐明瘤胃微生物群体之间的相互作用。当系统不处于稳态且微分方程必须进行数值求解时，可得到III型解。III型解的应用是瘤胃模拟模型，该模型以综合方式描述底物降解、终产物形成和微生物代谢。为说明这种III型解，定义了瘤胃中乳酸代谢的模型，并描述了其对理解乳酸消失途径和速率的贡献。至关重要的是，这些模型要基于可靠的数学和生物学原理。然而，本文所述的各种应用表明，模型不一定必须复杂且非常详细才能有助于更好地理解。
