IST Research Towards Scientific Unification

DEB theory as a Paradigm for the Integration of Thermodynamics with the

Natural and the Social Sciences

Tiago DomingosTania Sousa

Environment and Energy Section

Department of Mechanical Engineering

New Developments in DEB Theory and its Applications NTVB Symposium, Free University of Amsterdam

Amsterdam, The Netherlands, 24th January

IST Research Towards Scientific Unification

• Integrate the fields of – Thermodynamics,

– Ecology (or, more generally, the natural sciences)

– Economics (or, more generally, the social sciences)

• Formal analogy– The same mathematical description and interpretation of different

phenomena

– Consistency within the same domain

– Development of new theoretical results

• Substantive integration, “Consilience”– Different mathematical descriptions and interpretations of the same

phenomenon

– Consistency between different domains

– Development of new theoretical results

DEB Theory as a ParadigmMathematical Theory in the Sciences

• In Physics and Economics, mathematical theory is paramount and there is a quest for a unified theory within each domain – However, in Physics there is also a paramount concern with empirical

testing

• In contrast, in Biology mathematical theory has in general played a secondary role– Biology is frequently seen as a science of exception and particular cases,

with no interest in abstraction and generalisation

• A minor group in Biology has developed “Theoretical Biology” and “Mathematical Biology”– One of the major schools for this has been the Netherlands

• However, Theoretical and Mathematical Biology have frequently been carried out without a concern for empirical testing– When this concern appears, models are of narrow application, reducing

their theoretical breadth

• DEB– Builds on the Dutch tradition of Theoretical and Mathematical Biology,

but couples it with a fundamental concern with producing general theory, subjected to careful empirical testing

DEB Theory as a ParadigmThermodynamic Constraints

• Laws of thermodynamics– 1st Law: Conservation of mass and energy

– 2nd Law: Entropy increase in adiabatic systems

• Thermodynamic constraints must be obeyed, but are not enough to build theories in biological and social systems

• The major divide in Ecology:– Ecosystem and physiological ecology, based on energy and mass flows

– Population and community ecology, based on the behaviour (fitness) of individuals

• An analogous divide in Economics:– Ecological economics (clear minority), based on energy and mass flows

– Neoclassical economics (mainstream), based on the behaviour of humans (utility) and firms (profit)

• Optimisation requires trade-offs, for which thermodynamics is best

• DEB – Integrates a large number of empirical patterns and organizational

principles in biology with thermodynamic constraints

DEB Theory as a Paradigm

Fundamental vs. Applied Science

• In the 19th and 20th centuries fundamental science was pursued for its own sake, with no motivation from applications

• In the late 20th and the 21st centuries the priority is for scientific research to be eminently applicable, downgrading the status of fundamental research

• Paradigm: Scientific research is motivated from pratical concerns but builds new theory built on general principles – E.g, thermodynamics is a theory with the deepest fundamental

implications in many fields that was generated from the engineering concern with the optimisation of heat engines

• DEB– Is a general theory applicable to all organisms that was motivated by the

interpretation of standardised toxicity tests.

DEB Theory as a Paradigm Training for Interdisciplinary Science

• Interdisciplinary research is now accepted as fundamental for the development of science

• However, there are limits to how far the frontier of knowledge can be pushed through interdisciplinary research carried out through teams of experts

• Major breakthroughs require scientists trained in the fundamentals of several sciences

• These scientists will frequently be more knowledgeable in general aspects of scientific fields that experts in those fields

• Mathematics is the fundamental tool for this

• DEB – A paradigmatic tool for this type of training

Fundamental Principles of DEB

• Occam’s Razor: The explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory theory– Minimum number of state variables

– Minimum number of parameters

– Constant functions instead of linear

– Linear functions instead of non-linear

• [Metabolic Control: Organisms increased their control over metabolism during evolution]

• Cell Universality: Cells are metabolically very similar, independently of the organism or its size

Fundamental Principles of DEB (cont.)

• First Law of Thermodynamics: Mass and energy are conserved

• Second Law of Thermodynamics: Energy and mass conversion leads to dissipation

• Non-Equilibrium Thermodynamics: Mass and energy flows per unit surface depend only on intensive properties

– E.g., surface-dependent feeding and heating

The First Law of Thermodynamics

Energy Change = Heat + Work + Chemical Energy in Mass Flow

. .j

j

dNdUQ W

dt dt

Chemical potential of component j

Number of moles of component j

O2.

Q

O2

Entropy is the state variable that gives unidirectionality to time in physical processes ocurring in isolated systems.

• Hot coffee in a cold room gets colder and not hotter

• Radiating energy is received by the Earth from the sun and by outer space from the earth and not the other way around.

• If the valve of the tyre is opened, air gets out and not in

The Second Law of Thermodynamics

The Second Law of Thermodynamics

• Change in entropy = entropy flow associated with Heat + entropy production+entropy in mass flows

Increasing entropyIsolated system Isolated system

GASGAS VACUUM

..

jj

dNdS Qs

dt T dt

The Fundamental Structure of DEB

• Occam’s Razor– Constant chemical composition (strong homeostasis) and conversion

coefficients– Constant food: one state variable and one forcing flow– Variable composition: two state variables and one forcing flow (three

independent flows)

E (Reserve)

V (Structure)

X

E

V

ASSIMIL.

GROWTH DISS. PROC.

Dissipative Processes

• Somatic maintenance needs

• Maturity maintenance needs

• Maturation

• Dissipation in reproduction

• Overhead cost of growth?

...

1

1

E VE V

V E VE

V E E VE E V V E EV GV

G E EV GV

M y M

M M y

M M y M d y pd

dV dVp y E

dt d dt

The Thermodynamics of Klebsiella Aerogenes

ASSUMPTIONS

In aerobic organisms, reaction entropy change is negligible

Organism temperature is constant

IMPLICATIONS

All entropy production is reflected in the heat release, which MUST be positive

Entropy production is proportional to heat release

ENTROPY PROD.

1.70 kJ/K

1.64 kJ/K

0.3 kJ/K

ASSIMILATION

DISSIPATION

GROWTH

HEAT

522 kJ

504 kJ

49 kJ320.200.381.64

220.310.421.66

NH0.13CO0.10NOCH0.90

OH0.089O0.013NOCH

3 8 3 2 3

1.66 0.42 0.31 2 2

C H O +1.32O +0.69 NH

2.22CH O N +0.78CO +3.18H O

OH0.36CONH0.31

O0.97NOCH

223

20.310.421.66

Dioxygen Flow in the Organism

• Dioxygen flow– Plays a fundamental role – respiration, Kleiber, etc…

• Indirect Calorimetry– Heat is a weighted average of CO2, nitrogenous waste and O2

– DEB: Any flow produced or consumed in the organism is a linear combination of any three other flows.

• Thornton’s Rule– Heat release is proportional to dioxygen consumption:

444 kJ/mol O2

– DEB:This coefficient is the mean of the heats released per each mol of O2 that would be consumed in the complete combustion of food, reserve and structure weighted by its net flows.

How to measure Metabolic Rate?The Problem

• The metabolic rate is measured using:– Respiration: consumption of dioxygen

– Respiration: production of carbon dioxide

– Dissipating heat

• Does metabolic rate depend on the way it is measured?– The heat dissipated, the dioxygen consumption and the

production of carbon dioxide are independent although they are correlated (Indirect Calorimetry)

or

– The heat dissipated and the dioxygen consumed are not independent (Thornton’s rule)

How to measure Metabolic Rate?an answer...

• Complete combustion of X in Klebsiella aerogenes

– The amount of heat released is 1646 kJ, i.e., 470 kJ/mol O2

• Complete combustion of E in Klebsiella aerogenes


• Complete combustion of V in Klebsiella aerogenes


• Thornton’s Rule:

1.66 0.42 0.31 2 2 2 30.9725 0.365 0.31 +HeatCH O N O CO H O NH

3 8 2 2 2 23.5 3 4 HeatC H O O CO H O


2Heat kJ = 444 mol O


• Metabolic rate depends on:– Assimilation (combustion of X – 2.22 combustion of E)

• The amount of heat released is 391 kJ /mol O2 consumed

– Dissipation (combustion of E)

• The amount of heat released is 520 kJ/mol O2 consumed

– Growth (combustion of E – 0.904 combustion of V)

• The amount of heat released is 3752 kJ/mol O2 consumed


3 8 2 2 2 23.5 3 4 HeatC H O O CO H O





• DEB’ Rule (Kleb): Heat (kJ)

– A growing organism should dissipate less heat per mol of O2 consumed

• Thornton’s Rule:

2 2 2Heat kJ = 391 mol O + 520 mol O - 3091 mol OA D A

2Heat kJ = 444 mol O

Thornton’s coefficient

kJ/mol O2

D(h-1)

G

DEB in Social Systems

• Homeostasis– Again, control and simplicity...and compatibility with

thermodynamics (economic goods are not thermodynamically free)

• Reserves– Stocks in economics, with a well known role in economic

dynamics

• Growth patterns– In general, exponential for economies, but... who knows about

the future?

– V1-morphs? (constant returns to scale)

Scaling Exponents for Urban Indicators vs. City Size

Scaling in Cities

• Allometric patterns, e.g. Cities– Sub-linear (isomorphs?)

– Linear (V1-morphs?)

– Super-linear (?)

– ...but not really possible, because it is all in the same city...

Conclusions

• DEB theory is built on a set of fundamental epistemological, physical and biological principles and on compatibility

• DEB theory is successful in integrating thermodynamics with biology

• It seems possible to transpose the fundamental principles of DEB to social systems, ensuring the integration of thermodynamics with the social sciences

DEB theory as a Paradigm for the Integration of Thermodynamics with the

Natural and the Social Sciences

Tiago Domingos

Environment and Energy Section

Department of Mechanical Engineering

New Developments in DEB Theory and its Applications NTVB Symposium, Free University of Amsterdam

Amsterdam, The Netherlands, 24th January

Entropy and Enthalpy in Klebsiella Aerogenes

• The entropies are:

(structure)

(reserve)

• The entropy of biomass varies from: 52.4 J.C-mol to 61.4 J C-mol

• The enthalpies are:

(structure)

(reserve)

• The enthalpy of biomass varies from: -76 kJ.C-mol to –105 kJ C-mol


• Complete combustion of organic compounds

– The heat released per mol of O2 is constant if the chemical composition and the entalphy are constant

H(kcal/mol) 0 -94.05 -68.32

2 2 2

1 1Heat

1 0.25 0.5 1 0.25 0.5 2 0.5n m

nCH O O CO H O

n m n m n m

194.5 68.32 Heat

1 0.25 0.5 2 Biomass

nH h

n m

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IST Research Towards Scientific Unification