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The Contribution of Mathematical Modeling to Understanding Dynamic Aspects of Rumen Metabolism

View Article: PubMed Central - PubMed

ABSTRACT

All mechanistic rumen models cover the main drivers of variation in rumen function, which are feed intake, the differences between feedstuffs and feeds in their intrinsic rumen degradation characteristics, and fractional outflow rate of fluid and particulate matter. Dynamic modeling approaches are best suited to the prediction of more nuanced responses in rumen metabolism, and represent the dynamics of the interactions between substrates and micro-organisms and inter-microbial interactions. The concepts of dynamics are discussed for the case of rumen starch digestion as influenced by starch intake rate and frequency of feed intake, and for the case of fermentation of fiber in the large intestine. Adding representations of new functional classes of micro-organisms (i.e., with new characteristics from the perspective of whole rumen function) in rumen models only delivers new insights if complemented by the dynamics of their interactions with other functional classes. Rumen fermentation conditions have to be represented due to their profound impact on the dynamics of substrate degradation and microbial metabolism. Although the importance of rumen pH is generally acknowledged, more emphasis is needed on predicting its variation as well as variation in the processes that underlie rumen fluid dynamics. The rumen wall has an important role in adapting to rapid changes in the rumen environment, clearing of volatile fatty acids (VFA), and maintaining rumen pH within limits. Dynamics of rumen wall epithelia and their role in VFA absorption needs to be better represented in models that aim to predict rumen responses across nutritional or physiological states. For a detailed prediction of rumen N balance there is merit in a dynamic modeling approach compared to the static approaches adopted in current protein evaluation systems. Improvement is needed on previous attempts to predict rumen VFA profiles, and this should be pursued by introducing factors that relate more to microbial metabolism. For rumen model construction, data on rumen microbiomes are preferably coupled with knowledge consolidated in rumen models instead of relying on correlations with rather general aspects of treatment or animal. This helps to prevent the disregard of basic principles and underlying mechanisms of whole rumen function.

No MeSH data available.


Modeling approaches to quantify microbial activity and substrate degradation in the rumen (adapted from Bannink et al., 2006a). Boxes indicate state variables of rumen substrate (Sub) (QSub, quantity of rumen substrate, g or mol); rumen micro-organisms (Mi) (QMi, quantity of rumen micro-organisms, g) determined by inflows and outflows indicated by arrows (g/d or mol/d) which are defined by feed intake (Feed, g/d), fractional rate of substrate degradation (kd, /d) and fractional rate of rumen passage (kp, /d). (A) Representation of a dynamic model including interrelationships between substrate and micro-organisms. (B) Representation of a dynamic model without interrelationships between substrate and micro-organisms. A dynamic model that represents all in- and out-flows by mass action forms (using kd and kp) can be simplified into a static model (depicted in C). (C) Representation of a static model.
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Figure 1: Modeling approaches to quantify microbial activity and substrate degradation in the rumen (adapted from Bannink et al., 2006a). Boxes indicate state variables of rumen substrate (Sub) (QSub, quantity of rumen substrate, g or mol); rumen micro-organisms (Mi) (QMi, quantity of rumen micro-organisms, g) determined by inflows and outflows indicated by arrows (g/d or mol/d) which are defined by feed intake (Feed, g/d), fractional rate of substrate degradation (kd, /d) and fractional rate of rumen passage (kp, /d). (A) Representation of a dynamic model including interrelationships between substrate and micro-organisms. (B) Representation of a dynamic model without interrelationships between substrate and micro-organisms. A dynamic model that represents all in- and out-flows by mass action forms (using kd and kp) can be simplified into a static model (depicted in C). (C) Representation of a static model.

Mentions: Microbial fermentation in the rumen is generally simplified by assuming that the rumen is a chemostat with ideal mixing of contents and continuous inflow of feed substrate and subsequent outflow of rumen contents. Therefore, the basic approach to representing rumen microbial activity in mathematical terms corresponds to that used for chemostat cultures (Dijkstra et al., 1998). The quantity of substrate (to be utilized by micro-organisms) and the mass of micro-organisms present in the rumen are variables in more complex rumen models. In mechanistic rumen models, these quantities are calculated by the use of differential equations that describe the dynamics of interactions between the processes of inflow of feed substrate, microbial substrate degradation, microbial growth, and outflow of undigested feed and microbial matter. Some processes can be assumed to follow mass action kinetics but many are, in essence, of a non-linear nature, and this requires complex models comprising non-linear differential equations to be developed (Figure 1A).


The Contribution of Mathematical Modeling to Understanding Dynamic Aspects of Rumen Metabolism
Modeling approaches to quantify microbial activity and substrate degradation in the rumen (adapted from Bannink et al., 2006a). Boxes indicate state variables of rumen substrate (Sub) (QSub, quantity of rumen substrate, g or mol); rumen micro-organisms (Mi) (QMi, quantity of rumen micro-organisms, g) determined by inflows and outflows indicated by arrows (g/d or mol/d) which are defined by feed intake (Feed, g/d), fractional rate of substrate degradation (kd, /d) and fractional rate of rumen passage (kp, /d). (A) Representation of a dynamic model including interrelationships between substrate and micro-organisms. (B) Representation of a dynamic model without interrelationships between substrate and micro-organisms. A dynamic model that represents all in- and out-flows by mass action forms (using kd and kp) can be simplified into a static model (depicted in C). (C) Representation of a static model.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC5120094&req=5

Figure 1: Modeling approaches to quantify microbial activity and substrate degradation in the rumen (adapted from Bannink et al., 2006a). Boxes indicate state variables of rumen substrate (Sub) (QSub, quantity of rumen substrate, g or mol); rumen micro-organisms (Mi) (QMi, quantity of rumen micro-organisms, g) determined by inflows and outflows indicated by arrows (g/d or mol/d) which are defined by feed intake (Feed, g/d), fractional rate of substrate degradation (kd, /d) and fractional rate of rumen passage (kp, /d). (A) Representation of a dynamic model including interrelationships between substrate and micro-organisms. (B) Representation of a dynamic model without interrelationships between substrate and micro-organisms. A dynamic model that represents all in- and out-flows by mass action forms (using kd and kp) can be simplified into a static model (depicted in C). (C) Representation of a static model.
Mentions: Microbial fermentation in the rumen is generally simplified by assuming that the rumen is a chemostat with ideal mixing of contents and continuous inflow of feed substrate and subsequent outflow of rumen contents. Therefore, the basic approach to representing rumen microbial activity in mathematical terms corresponds to that used for chemostat cultures (Dijkstra et al., 1998). The quantity of substrate (to be utilized by micro-organisms) and the mass of micro-organisms present in the rumen are variables in more complex rumen models. In mechanistic rumen models, these quantities are calculated by the use of differential equations that describe the dynamics of interactions between the processes of inflow of feed substrate, microbial substrate degradation, microbial growth, and outflow of undigested feed and microbial matter. Some processes can be assumed to follow mass action kinetics but many are, in essence, of a non-linear nature, and this requires complex models comprising non-linear differential equations to be developed (Figure 1A).

View Article: PubMed Central - PubMed

ABSTRACT

All mechanistic rumen models cover the main drivers of variation in rumen function, which are feed intake, the differences between feedstuffs and feeds in their intrinsic rumen degradation characteristics, and fractional outflow rate of fluid and particulate matter. Dynamic modeling approaches are best suited to the prediction of more nuanced responses in rumen metabolism, and represent the dynamics of the interactions between substrates and micro-organisms and inter-microbial interactions. The concepts of dynamics are discussed for the case of rumen starch digestion as influenced by starch intake rate and frequency of feed intake, and for the case of fermentation of fiber in the large intestine. Adding representations of new functional classes of micro-organisms (i.e., with new characteristics from the perspective of whole rumen function) in rumen models only delivers new insights if complemented by the dynamics of their interactions with other functional classes. Rumen fermentation conditions have to be represented due to their profound impact on the dynamics of substrate degradation and microbial metabolism. Although the importance of rumen pH is generally acknowledged, more emphasis is needed on predicting its variation as well as variation in the processes that underlie rumen fluid dynamics. The rumen wall has an important role in adapting to rapid changes in the rumen environment, clearing of volatile fatty acids (VFA), and maintaining rumen pH within limits. Dynamics of rumen wall epithelia and their role in VFA absorption needs to be better represented in models that aim to predict rumen responses across nutritional or physiological states. For a detailed prediction of rumen N balance there is merit in a dynamic modeling approach compared to the static approaches adopted in current protein evaluation systems. Improvement is needed on previous attempts to predict rumen VFA profiles, and this should be pursued by introducing factors that relate more to microbial metabolism. For rumen model construction, data on rumen microbiomes are preferably coupled with knowledge consolidated in rumen models instead of relying on correlations with rather general aspects of treatment or animal. This helps to prevent the disregard of basic principles and underlying mechanisms of whole rumen function.

No MeSH data available.