A conceptual approach to the mathematical modelling of microbial functionality in the rumen

Introduction

The rumen as a digestive organ plays a very important role in feed digestion in ruminants because it hosts a vast microbial population that enables the host to ferment fibrous (as well as non-fibrous) feed and benefit from the end-products produced. Because of this, ruminants can thrive on feeds of low nutritional value or even on those feeds deemed inedible by many other animals. The digestive role of the rumen is mainly fermentative and is attributed to the activity of the microbial population it harbours. This population includes bacteria, protozoa and fungi, but due to the rather anoxic intra-ruminal conditions it also includes Archaea (methanogens). Although there is enormous complexity and functional diversity of this microbial population across species, a core microbiome always appears to be present across ruminant species and across regions and management types (Henderson et al., 2015). Variation around this core microbiome was established to be related most to diet, which is an outcome fully comprehensible as the diet determines the amount, the type and the matrix in which substrates become available for the rumen microbiota. Furthermore, in interaction with the ruminant host (rumination and particle size reduction, rumen contractions and movement of rumen contents, rumen outflow) the diet strongly impacts on the dynamics of intra-ruminal flow of digesta and on the physical and chemical conditions in

http://dx.doi.org/10.19103/AS.2020.0067.27 © Burleigh Dodds Science Publishing Limited. 2020. All rights reserved.

rumen digesta, both being main drivers of rumen microbial activity (Zebeli et al., 2012; Bannink et al., 2016). Relevant physical and chemical conditional factors are particle size distribution of rumen contents, the different physical phases in the rumen including a fibrous mat, fluid volume, water and particle flow rate, fluid osmolality, acidity and redox potential, and the gas pressures of carbon dioxide, methane and hydrogen. Most of these factors have received attention from researchers for more than half a century now in modelling efforts, with rumen redox potential (Dijkstra et al., 2020), the effect of rumen gas pressures (Van Lingen et al., 2017) and effects of osmolality (Lopez et al., 2003) having received least attention. The current technological advancement made in molecular biology and biotechnology enables researchers to study the rumen environment with increasing detail. The recent e-book of Ungerfeld and Newbold (2018) contains various excellent reviews demonstrating the recent developments in this field of research. In their editorial, they foresee future developments resulting from the integration of microbial ecology 'multi-omics' techniques, in particular regarding the expression of functional genes as well as the application of physical-chemical principles and the refinement of thermodynamic and kinetic measurements in the rumen environment.

To benefit from all the data gathered, with new techniques and new data types being introduced continuously, mathematical models need to be constructed that attempt to capture the biological evidence gathered and predict functionality at the level of the whole rumen. There have been many modelling efforts at the level of the whole rumen already; however, they vary substantially in the levels of organization represented and in modelling concepts adopted. Figure 1 lists the various levelsof organization involved with extantand most complex dynamic, mechanistic approaches available to date. The most detailed approaches so far are the dynamic models which are successors of the models developed by Baldwin et al. (1987) and Dijkstra et al. (1992), and many descendants from these two early models have been published meanwhile by various groups. Other model approaches, as reviewed by Tedeschi et al. (2014), followed a more simple approach (which may be for very good reasons, depending on the actual aim of the modelling effort) adopting either static or more empirically based, less mechanistic representations (reviewed by Bannink et al., 2016). Recently, the effect of thermodynamic driving forces on rumen microbiota (Van Lingen et al., 2016) and the effect of rumen hydrogen dynamics on rumen microbial activity (Wang etal., 2016; Van Lingen et al., 2019) were implemented to represent thermodynamic control of rumen hydrogen pressure on the formation of end products of fermentation. However, none of these rumen modelling efforts involves the aforementioned integration with results from multi-omics techniques. Quantification of microbial functionality by models that aim to predict whole rumen function still seems to go parallel instead of being integrated with quantification from multi-omics approaches.

Figure 1 Schematic representation of the various levels of organization related to rumen function, ranging from the whole rumen level to that of multi-omics data collection.

This chapter discusses the concepts and the approaches taken with the quantification or mathematical modelling of rumen microbiota. The consequences from the perspective of mathematical modelling of microbial functionality at the whole rumen level are discussed as it is thought that models need to cover this level to predict fermentative and digestive aspects of the rumen as an organ.

Conceptual approaches in modelling whole rumen function

Interactions between ruminant host and rumen content

There are extensive interactions between rumen content and the host ruminant (Fig. 1). Genetic as well as environmental factors underlie the variation among individuals in feeding and rumination behaviour, in the morphological and physiological aspects of the rumen wall, and in the regulation of rumen contractions and passage through the reticulum towards the omasum and abomasum. The regulatory mechanisms in place for the host to control retention time of fluid and particles are of high importance for the adaptive capacity of the host to a wide range of diet qualities. By these mechanisms, more slowly degradable particles may reside longer in the rumen, leading to a larger rumen volume with increased content of slowly degradable particles, enhancing the available time for micro-organisms to degrade them before they flow out of the rumen. Another important determinant of rumen microbial activity is the buffer mechanisms of saliva production and absorption of volatile fatty acids (VFA) as end products of that microbial activity. The rumen wall appears to be highly adaptive to the acid load it receives from the rumen environment, demonstrating the regulatory role the rumen wall tissue has in ensuring rumen fermentation. Without these buffer mechanisms the rumen would become acidic and diminish the activity of micro-organisms that ferment the feed ingested by the ruminant and reduce faecal digestibility and nutritive value of the feed. A further important interaction between host and the rumen environment is the process of nitrogen (N) and phosphorus recycling from blood to the rumen through the rumen wall and through the saliva produced.

Most of the aforementioned interactions between ruminant host and rumen microbial activity are standard elements of the more complex rumen models that are available (Bannink et al., 2016). These models aim to quantify whole rumen function and to predict feed degradation and the formation of end products of fermentation (microbial protein synthesis, formation of VFA, ammonia and methane). Whereas the more detailed rumen models adopt a highly mechanistic representation, more applied models such as the protein evaluation systems applied in current practice, are far less complex. These applied models take general assumptions on, for example, fractional rumen outflow rates and intra-ruminal conditions (reviewed by Tedeschi et al., 2014). They also consider the concept of calculated rumen N balance which should not become below a threshold in orderto prevent a potential N shortage in the rumen. In contrast, more mechanistic models attempt to describe the process of N recycling in itself, and as a result have predicted rumen fermentation also as a function of modelled N recycling. Many of the interactions between the ruminant host and rumen content (Fig. 1) are basically ignored in applied rumen models. Although these interactions may have been represented in the more complex and mechanistic rumen models, these still describe the average ruminant host because for many of the model parameters no phenotypic data are available which hampers the parameterization of individuals. For a further discussion of interactions and how these are adopted in rumen models, the reader is referred to a review by Bannink et al. (2016). Many rumen models have a position in between the extremes discussed above, and for an overview the reader is referred to the review by Tedeschi et al. (2014).

Intra-ruminal conditions

Also at the intra-ruminal level various physical-chemical parameters that affect microbial activity have been the subject of modelling. These include, among others, the effect of rumen hydrogen as a thermodynamic driving force for microbial metabolism and on activity of methanogens (Wang et al., 2016; Van Lingen et al., 2016, 2019), regulation of rumen acidity by the host, including the activity of epithelial tissue in the rumen wall (Bannink et al„ 2012) and the dynamics of particle distribution, particle size reduction and rumen fluid outflow (Gregorini et al., 2015). Through their direct effect on microbial metabolism, quantification of these parameters is important for accurate prediction of the consequences of nutritional strategies on rumen function, or of any host- specificity of rumen function. Despite their importance, intra-ruminal conditions as driving factors will not be discussed in-depth in this chapter, rather we focus on the diversity in composition and functionality of rumen microbiota along with its consequences for rumen function in terms of the microbial fermentation process in the entire rumen digesta volume.