This document presents a methodology for vertically translating between molecular and organismal levels in biological feedback loops. It discusses modeling techniques like Michaelis-Menten kinetics and non-competitive inhibition that can be used as "building blocks" for models. Computer simulations demonstrate how molecular interactions modeled with these techniques can translate to global behavior at the organismal level. The goal is to develop a standardized approach to link molecular mechanisms to physiological processes through mathematical modeling of feedback loops.

1. Physical Chemistry 2021:
A Methodology for Vertical Translation between Molecular
and Organismal Level in Biological Feedback Loops.
J. W. DIETRICH

3. Tous les mécanismes
vitaux, aussi différents
qu’ils soient, ont pour
unique but de maintenir
constantes les conditions
de la vie dans le milieu
intérieur.
Claude Bernard 1859
La fixité du milieu intérieur
est la condition de la vie
libre, indépendante.
Claude Bernard 1878
Claude Bernard and his pupils. Oil painting after Léon-Augustin Lhermitte. wellcome collection

4. The coordinated physiological processes which
maintain most of the steady states in the
organism are so complex and so peculiar to
living beings – involving, as they may, the
brain and nerves, the heart, lungs, kidneys and
spleen, all working cooperatively – that I have
suggested a special designation for these
states, homeostasis.
Walter B. Cannon 1932

5. Peter Sterling
(1988)
Bruce McEwen
(2003)
So, we coined a new word, allostasis, to
emphasize two key points about
regulation: parameters vary, and
variation anticipates demand.
Peter Sterling 2004
Stability through change

6. Biological feedback loops
VERTICAL TRANSLATION IN BIOLOGICAL FEEDBACK | 20210920 6
Zavala E, Wedgwood KCA, Voliotis M, Tabak J, Spiga F, Lightman SL, Tsaneva-Atanasova K. Mathematical Modelling of
Endocrine Systems. Trends Endocrinol Metab. 2019 Apr;30(4):244-257. doi: 10.1016/j.tem.2019.01.008. PMID 30799185.

7. Biological feedback loops
VERTICAL TRANSLATION IN BIOLOGICAL FEEDBACK | 20210920 7

8. Biological feedback loops
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Hoermann R, Midgley JE, Larisch R and Dietrich JW (2015). Homeostatic Control of the Thyroid Pituitary Axis:
Perspectives for Diagnosis and Treatment. Front. Endocrinol. 6:177. doi: 10.3389/fendo.2015.00177

9. Pathophysiology of COVID-19
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Tretter F, Wolkenhauer O, Meyer-Hermann M, Dietrich JW, Green S, Marcum J, Weckwerth W. The Quest for System-Theoretical Medicine in the
COVID-19 Era. Front Med (Lausanne). 2021 Mar 29;8:640974. doi: 10.3389/fmed.2021.640974. PMID: 33855036; PMCID: PMC8039135.

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LTI Systems

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Bolie 1960, 1961
A. de Gaetano (2005) Models for the Glucose/Insulin system. Summer school “Control Theory
with Modelling Applications to Physiology and Medicine. Schloss Seggau, Austria

12. Clinical Applications: HOMA
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D. R. Matthews, J. P. Hosker, A. S. Rudenski, B. A. Naylor, D. F. Treacher and R. C. Turner (1985) Homesostasis model
assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man.
Diabetologia 28: 412–9

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commons.wikimedia.org/wiki/File:Mind-The-Gap-Bank.jpg

14. The Problem of Vertical Translation
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Tretter F, Wolkenhauer O, Meyer-Hermann M, Dietrich JW, Green S, Marcum J, Weckwerth W. The Quest for System-Theoretical Medicine in the
COVID-19 Era. Front Med (Lausanne). 2021 Mar 29;8:640974. doi: 10.3389/fmed.2021.640974. PMID: 33855036; PMCID: PMC8039135.

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Ways of improvement

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16
Modelling Techniques
Building Bricks for “Parametrically Isomorphic” Models
Elimination and Distribution
Michaelis-Menten Kinetics
Non-competitive Inhibition
Plasma Protein Binding
ASIA NoCoDI

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17
Modelling Techniques
Building Bricks for “Parametrically Isomorphic” Models
Elimination and Distribution
Michaelis-Menten Kinetics
Non-competitive Inhibition
Plasma Protein Binding
NoCoDI

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18
Modelling Techniques
Building Bricks for “Parametrically Isomorphic” Models
Elimination and Distribution
Michaelis-Menten Kinetics
Non-competitive Inhibition
Plasma Protein Binding
ASIA NoCoDI

19. VERTICAL TRANSLATION IN BIOLOGICAL FEEDBACK | 20210920 19
19
Modelling Techniques
Building Bricks for “Parametrically Isomorphic” Models
Elimination and Distribution
Michaelis-Menten Kinetics
Non-competitive Inhibition
Plasma Protein Binding
ASIA NoCoDI

20. VERTICAL TRANSLATION IN BIOLOGICAL FEEDBACK | 20210920 20
20
Modelling Techniques
Building Bricks for “Parametrically Isomorphic” Models
Elimination and Distribution
Michaelis-Menten Kinetics
Non-competitive Inhibition
Plasma Protein Binding
ASIA NoCoDI

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21
Modelling Techniques
Building Bricks for “Parametrically Isomorphic” Models
Elimination and Distribution
Michaelis-Menten Kinetics
Non-competitive Inhibition
Plasma Protein Binding
ASIA NoCoDI

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Michaelis-Menten Function (MiMe)

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Receptor Binding

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MiMe Element for Feedback Loops

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25
Modelling Techniques
Building Bricks for “Parametrically Isomorphic” Models
Elimination and Distribution
Michaelis-Menten Kinetics
Non-competitive Inhibition
Plasma Protein Binding
ASIA NoCoDI

26. VERTICAL TRANSLATION IN BIOLOGICAL FEEDBACK | 20210920 26
26
Modelling Techniques
Building Bricks for “Parametrically Isomorphic” Models
Elimination and Distribution
Michaelis-Menten Kinetics
Non-competitive Inhibition
Plasma Protein Binding
ASIA

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Non-Competitive Inhibition (NoCoDI)

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MiMe-NoCoDI Element
x2
–x1
y

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MiMe-NoCoDI Element

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MiMe-NoCoDI Element
x2
x1
y

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31
MiMe-NoCoDI Platform
Equifinal solution:

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32
MiMe-NoCoDI Platform

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33
MiMe-NoCoDI Platform

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34
MiMe-NoCoDI Platform

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35
MiMe-NoCoDI Platform
Dietrich JW, Boehm, BO (2006) Equilibrium behaviour of feedback-coupled physiological
saturation kinetics. Cybernetics and Systems 2006. 269-74. DOI: 10.13140/2.1.2400.2568
Dietrich, Johannes W. & O Böhm, Bernhard. (2015). Die MiMe-NoCoDI-Plattform: Ein Ansatz für die
Modellierung biologischer Regelkreise. DOI: 10.3205/15gmds058.
Equifinal solution:
Recursive equation:
Equifinal equation:

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36
Computer Simulations

37. Serial Michaelis-Menten Kinetics
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Parallel Michaelis-Menten Kinetics
For k parallel loops:
Dietrich JW, Boehm, BO (2006) Equilibrium behaviour of feedback-coupled physiological saturation
kinetics. Cybernetics and Systems 2006. 269-74. DOI: 10.13140/2.1.2400.2568
Equifinal solution:
Iterative equation:

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40. Example: MiMe element
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41. Molecular and Global Behaviour
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42. Molecular and Global Behaviour
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u(t)

43. Molecular and Global Behaviour
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x 1000
Slope ≈ 5080 / sec
/ 1000

44. Example: MiMe element
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45. Molecular and Global Behaviour
VERTICAL TRANSLATION IN BIOLOGICAL FEEDBACK | 20210920 45

46. BIOKYBERNETIKA 2017 ALLOSTASIS | 03.07.2022 46
Physical Chemistry 2021:
A Methodology for Vertical Translation between Molecular
and Organismal Level in Biological Feedback Loops.
J. W. DIETRICH
20210920
Thanks to:
Ljiljana Kolar-Anić
Željko D Čupić
Bernhard Boehm
Jochen Mau
Felix Tretter
and the team of the lab XU44