Dynamic Energy Budget Theory - I

Tânia Sousa with contributions from : Bas Kooijman

Energy flows vs. Mass flows

Fluxes Parameters�̇�𝑋= �̇� 𝑋 𝐴𝑋= 𝑓 (𝑋 ) {�̇�𝑋𝑚 }𝑉 2/3

�̇�𝐴= �̇� 𝐸𝐴𝐸= 𝑓 (𝑋 ) {�̇�𝐴𝑚 }𝑉 2 /3

�̇�𝑆= �̇� 𝐸𝑆𝐸= [�̇�𝑀 ]𝑉 + {�̇�𝑇 }𝑉 2/3

=

�̇�𝑅= �̇� 𝐸𝑅𝐸

{�̇�𝑋𝑚 }=𝑋 { �̇� 𝑋𝑚}{�̇�𝐴𝑚 }=𝐸 { �̇� 𝐴𝑚}

State Variables

[�̇�𝑀 ]=𝐸 [ �̇� 𝐸𝑀 ]�̇�𝐶= �̇�𝐸𝐶𝐸=𝐸( �̇�𝐿 − �̇� ) {�̇�𝑇 }=𝐸 { �̇�𝐸𝑇 }

�̇�𝐺= �̇� 𝐸𝐺𝐸=[𝐸𝐺 ] 𝑑𝑉𝑑𝑡

[𝐸𝐺 ]=𝑦𝐸𝑉 𝐸 [𝑀𝑉 ]

What would be the expression for a parameter

that is the equivalent of for the somatic maintenance associated with volume?

Suggestions: Write as a function of

Exercises

- energy spent in the maintenance of structure built with 1 unit of reserve energy per unit time - energy spent in the maintenance of maturity built with 1 unit of reserve energy per unit time

Metabolism in a DEB

individual. Rectangles are state

variables Arrows are flows of food

JXA, reserve JEA, JEC, JEM, JET , JEG, JER, JEJ or structure JVG.

Circles are processes The full square is a fixed

allocation rule (the kappa rule)

The full circles are the priority maintenance rule.

A DEB organism Assimilation, dissipation and growth

MV - Structure

Feeding

MH - Maturity

XAJ EAJ

Assimilation

ME - ReserveMobilisation

ECJ

Offspring MER

Somatic Maintenance

Growth

Maturity Maintenance

Reproduction

Maturation

ESJ

EGJEJJ

ERJ

VGJ

Assimilation: X(substrate)+M E(reserve) +

M linked to surface area

Dissipation: E(reserve) +M M

somatic maintenance: linked to surface area & structural volume

maturity maintenance: linked to maturity maturation or reproduction overheads

Growth: E(reserve)+M V(structure) + M Compounds:

Organic compounds: V, E, X and P Mineral compounds: CO2, H2O, O2 and Nwaste

3 types of aggregated chemical transformations

�̇�𝐷=�̇�𝑆+�̇� 𝐽+(1−κ𝑅 ) �̇�𝑅

Obtain the aggregated chemical reactions for

assimilation, dissipation and growth

considering that the chemical compositions

are: food CH1.8O0.5N0.2, reserve CH2O0.5N0.15,

faeces CH1.8O0.5N0.15, structure CH1.8O0.5N0.15 and

NH3.

Identify in these equations yXE, yPE and yEV.

Constraints on the yield coeficients Degrees of freedom

Exercises

What is the relationship between these

equations and , , , , , and .

Compute the total consumption of O2.

Write it as a function of , and .

Compute the aggregate chemical

transformation

Exercises

The stoichiometry of the aggregate chemical transformation that describes the organism has 3 degrees of freedom: any flow produced or consumed in the organism is a weighted average of any three other flows

Write the energy balance for each chemical

reactor (assimilation, dissipation and growth)

Compute the total metabolic heat production

as a function of , and .

If the organism temperature is constant then the

metabolic heat must be equal to the heat released

Exercises

Indirect calorimetry (estimating heat production without mesuring it) : Dissipating heat is weighted sum of three mass flows: CO2, O2 and nitrogeneous waste (Lavoisier in the XVIII century).

T EA T A EG T G ED T Dp J p J p J p

Dissipating heat

Steam from a heap of moist Prunus serotina litter illustrates metabolic heat production by fungi

Definition:

O2 consumption that is associated with assimilation per unit of ingested food

Strange name relates to common practice to take pT+ JO which generally does not hold true

Exercise: What is the relationship between O2 consumption and heat production

Heat increment of feeding

Metabolic rates: the effect of temperature

The Arrhenius relationship has good empirical support The Arrhenius temperature is given by minus the slope: the higher the

Arrhenius temperature the more sensitive organisms are to changes in temperature

ln r

ate

104 T-1, K-1

reproductionyoung/d

ingestion106 cells/h

growth, d-1

aging, d-1

K 293K; 6400

}exp{)(

1

11

TTT

T

T

TkTk

A

AA

Daphnia magna

All metabolic rates depend on temperature and all depend on the same way (evolutionary principle)