Dynamic Energy Budget Theory - I

Tânia Sousa with contributions from : Bas Kooijman

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 + P 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

Identify in these equations yXE, yPE and yEV.

Constraints on the yield coeficients Degrees of freedom

Exercises

Identify in these equations yXE, yPE and yEV.

Constraints on the yield coeficients Degrees of freedom

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.

Exercises

Identify in these equations yXE, yPE and yEV.

Constraints on the yield coeficients Degrees of freedom

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.

How would you obtain the aggregate chemical

transformation?

Exercises

What is the relationship between these

equations and , , ,, ,

and .

Considering for the juvenile

Exercises

What is the relationship between these

equations and , , ,, ,

and .

Compute the total consumption of O2.

Write it as a function of , and .

Exercises

What is the relationship between these

equations and , , , , , and .

Compute the total consumption of O2.

Write it as a function of , and .

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)

Exercises

Write the energy balance for each chemical

reactor (assimilation, dissipation and growth)

Compute the total metabolic heat production

as a function of , and .

Exercises

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 measuring 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

Obtain an expression for the dynamics of the

reserve density mE using the equations for the dynamics of ME and MV and the following equations:

Exercises

Obtain an expression for the dynamics of the

reserve density mE

Set dmE/dt=0 (weak homeostasis). What is the maximum value of mE?

Exercises

EAmEE

V

f x Jdm vm

dt L v M

Obtain an expression for the dynamics of the

reserve density mE

Set dmE/dt=0 (weak homeostasis). What is the maximum value of mE?

Can you understand the meaning? What is the value for mE in weak homeostasis?

Exercises

- maximum reserve density

EAmEE

V

f x Jdm vm

dt L v M

Obtain an expression for the dynamics of the

reserve density mE

Set dmE/dt=0 (weak homeostasis). What is the maximum value of mE?

Can you understand the meaning? What is the value for mE in weak homeostasis?

Exercises

- maximum reserve density

EAmEE

V

f x Jdm vm

dt L v M

E Emm f x m

Obtain an expression for the dynamics of the

reserve density mE

Set dmE/dt=0 (weak homeostasis). What is the maximum value of mE?

Can you understand the meaning? Rewrite using mEm.

Exercises

- maximum reserve density

EAmEE

V

f x Jdm vm

dt L v M

Obtain an expression for the dynamics of the

reserve density mE

Set dmE/dt=0 (weak homeostasis). What is the maximum value of mE?

Can you understand the meaning? Rewrite using mEm. What is the meaning of ?

Exercises

- maximum reserve density

E EAm

T

Em Em

m JL L

m J

EAmEE

V

f x Jdm vm

dt L v M

EAm

Em

J

J

Obtain an expression for the dynamics of the

reserve density mE

Set dmE/dt=0 (weak homeostasis). What is the maximum value of mE?

Can you understand the meaning? Rewrite using mEm. What is the meaning of ?

Exercises

- maximum reserve density

E EAm

T

Em Em

m JL L

m J

EAmEE

V

f x Jdm vm

dt L v M

- maximum length- maximum reserve density