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Dynamic energy budget theory

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Dynamic Energy Budget (DEB) theory aims to identify simple quantitative rules for metabilism organisation of individual organisms that can be understood from basic physical chemical principles, such as conservation of mass, energy and time, relationships between surface area and volume, and stoichiometric constraints on production. The word "Dynamic" refers to the life cycle perspective of the theory, where the budget changes dynamically over time.

Strong and weak homeostasis and the partionability of reserve kinetics are cornerstones of the theory and essential to understand the evolution of metabolic organisation. Organisational uncoupling of metabolic modules characterise the organisational structure of DEB theory. Such modules are assimilation, reserve mobilisation, allocation, growth plus somatic maintenance versus maturation plus maturity maintenance (or reproduction).

DEB theory delineates reserves, as separate from structure.Reserves are not meant to be compounds that are set apart for later use, but as a pool of compounds that are synthesised from environmental substrates for use by the metabolism for the purpose of somatic maintenance (including protein turnover, maintenance of concentration gradients across membranes, activity and other types of work), growth (increase of structural mass), maturity maintenance (installation of regulation systems, preparation for reproduction, maintenance of defence systems, such as the immune system), maturation (increase of the state of maturity) and reproduction. This creates a rather constant internal chemical environment, with only an indirect coupling with the extra-organismal environment. Reserves as well as structure are taken to be generalised compounds, i.e. mixtures of a large number of compounds, which do not change in composition. The latter requirement is called the strong homeostasis assumption. Polymers (carbohydrates, proteins, and sometimes ribosomal RNA) and lipids form the main bulk of reserves and of structure. Some reasons for including reserves in even the simplest characterisations are:

  1. Reserves account for metabolic memory, which is important during transient states (shifts up and down in substrate availability). Production (growth or reproduction) reacts slowly to changes in feeding condition. Growth continues for some time during starvation; embryo development is fuelled by reserves
  2. Reserve explain observed respiration patterns, which have a close link with the use of energy. Freshly laid eggs hardly respire; the developing embryo respires at an increasing rate, while the total egg-mass decreases. The DEB theory explains this (and other observations) by assuming that structure requires maintenance, while reserves do not. Part of maintenance relates to protein turnover of the structure; turnover is already implied in reserves as a result of assimilation and catabolism.
  3. The composition of biomass depends on growth rate. With two components (reserves and structure) particular changes in composition can be captured. More complex changes require several reserves, as is required for autotrophs.
  4. All mass fluxes turn out to be linear combinations of assimilation, dissipation and growth. If reserves are omitted, these three processes are mutually dependent and actually provide two degrees of freedom, rather than three. This does not provide enough flexibility to capture product formation and explain indirect calorimetry.
  5. They allow body size scaling of life history parameters. The specific respiration rate decreases with (maximum) body size between species because large bodied species have relatively more reserve. Many other life history parameters directly or indirectly relate to respiration.

The standard model quantifies the metabolism of isomorphs with 1 reserve and 1 structure that feeds on one type of food with a constant composition. The rules for the standard model for reproducing multicellulars, and modified for dividing unicellulars, are:

General assumptions, for the specification of mass--energy relationships

  1. Structural body mass and reserves are the state variables of the individual; they have a constant composition (strong homeostasis).
  2. Food is converted into faeces, and assimilates derived from food are added to reserves. Reserves fuel all other metabolic processes, which can be classified into three categories: synthesis of structural body mass, synthesis of gametes, and processes that are not associated with synthesis of biomass. Products that leave the organism may be formed in direct association with these three categories of processes, and with the assimilation process.
  3. If the individual propagates via reproduction (rather than via division), it starts in the embryonic stage, and initially has a negligibly small structural mass (but a substantial amount of reserves).

Specific assumptions, for the specification of the powers

  1. The reserve density of the hatchling equals that of the mother at egg formation. Foetuses develop in the same way as embryos in eggs, but at a rate unrestricted by energy reserves.
  2. The transition from embryo to juvenile initiates feeding, that from juvenile to adult initiates reproduction, which is coupled to the cessation of maturation. The transitions occur when the cumulated energy invested in maturation exceeds certain threshold values. Unicellulars divide when the cumulated energy invested in maturation exceeds a threshold value.
  3. Somatic and maturity maintenance are proportional to structural body volume, but maturity maintenance does not increase after a given cumulated investment in maturation. Heating costs for endotherms are proportional to surface area.
  5. The feeding rate is proportional to the surface area of the organism and the food handling time and the digestion efficiency are independent of food density.
  6. The reserves must be partitionable, such that the dynamics is not affected; the reserve density at steady state does not depend on structural body mass (weak homeostasis).
  7. A fixed fraction of energy, utilised from the reserves, is spent on somatic maintenance plus growth, the rest on maturity maintenance plus maturation or reproduction (the kappa-rule).
  8. Under starvation conditions, individuals always give priority to somatic maintenance and follow one of two possible strategies: they do not change the reserve dynamics (so continue to invest in development or reproduction), or cease energy investment in development and reproduction (thus changing reserves dynamics).

These assumptions quantify all energy and mass fluxes in an organism (including heat, dioxygen, carbon dioxide, nitrogen waste) and imply rules for the covariation of parameter values across species (body size scaling relationships).

extensions

DEB theory has been extended into many directions, such as

  • effects of changes is shape during growth (e.g. V1-morphs and V0-morphs)
  • inclusion of more types of food (substrate), which requires Synthesizing Units to model
  • inclusion of more reserves (which is necessary for organisms that do not feed on other organisms) and more structures (which is necessary to deal with plants)
  • the formation and excretion of metabolic products (which is a basis for syntrophic relationships, and useful in biotechnology)
  • the production of free radicals (linked to size and nutritional status) and their effect on survival (aging)
  • the growth of body parts (including tumours)
  • effects of chemical compounds (toxicants) on parameter values and the hazard rate (which is useful to establish no effect concentrations for environmental risk assessment): the DEBtox method
  • processes of adaptation (gene expression) to the availability of substrates (important in biodegradation)

DEB theory provides constraints on the metabolic organisation of sub-cellular processes. Together with rules for interaction between individuals (competition, syntrophy, prey-predator relationships), it also provides a basis to understand population and ecosystem dynamics. The theory, therefore, links various levels of biological organisation (cells, organisms and populations). A considerable number of popular empirical models turn out to be special cases of the DEB model, or very close numerical approximations.


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