System biology
Simple metabolic model of rumen organism

Background

Diagram 1: Selected catabolic abilities of some bacteria and archaea of the rumen microbiota

Catabolic Activities of some Bacteria

 

Diagram 2: Metabolism of Ruminococcus flavefaciens in single culture

Metabolism of Ruminicoccus flavefaciens

Cellulose Q1: dQ1/dt = -k1*Q1
Glucose Q2: dQ2/dt = s1*k1*Q1 – k2*Q2 = 100*k1*Q1 – k2*Q2 (s1=100 ist willkürlich von mir gesetzt)
Pyruvat Q3: dQ3/dt = s2 *k2*Q2 – k3*Q3 = 2*k2*Q2 – k3*Q3

Formiat dQ4/dt = a* dQ3/dt; a= s3/200
Acetat dQ5/dt = a* dQ3/dt + b* dQ3/dt; b= s4/200
Succinat dQ6/dt = c*dQ3/dt = dQ3/dt – dQ4/dt – dQ5/dt = dQ3/dt – a* dQ3/dt – b* dQ3/dt;
c=1-a-b

dATP/dt: dQ7/dt = 2 * k2*Q2 + b * dQ3/dt  
dH2/ dt : dQ8/dt = b* dQ3/dt + (k3*Q3 - 2* dQ6/dt)
dNADH/dt: dQ9/dt = 2*k2*Q2 - 2(dQ3/dt – a* dQ3/dt – b* dQ3/dt) 

 

Subroutine

Bacteria growth:
dN/dt = μ * N
Growth rate: μ ~ qs, YATP
μ = qs *YATP
Substrate dependant metabolic rate:
qs = qmax S/(Ks + S);


Diagram 3: Syntrophism: Ruminococcus flavefaciens & Methanobrevibacter ruminantium

Syntrophism: Ruminococcus flavefaciens & Methanobrevibacter ruminantium

 

Formiat dQ4/dt = a* dQ3/dt; a= s3/200; s3= 0 
Acetat dQ5/dt = b* dQ3/dt; b= s4/200 s3= 0.945 
Succinat dQ6/dt = c*dQ3/dt = dQ3/dt – b* dQ3/dt;
c=1- b

Methan Q9: dQ9/dt = s5* dQ8/dt; s5= 0.89
= 0.89*s5*k3*Q3

2. Assignment

Part one: basic processes and products

Aim: Learn how to use the model. Understand the basic metabolic processes.

  1. Vary the metabolic rates and observe the consequences to the fatty acids.
  2. Vary the cellulose pool and observe the consequences to the fatty acids.
  3. Try to understand how the equations have been computed with simulink.

Part two: By-products

Aim: Understand the computation of the metabolic by-products of Ruminococcus flavefaciens based on the model.
Vary the metabolic rates and cellulose pool.

  1. Observe the consequences to the NADH.
  2. Observe the consequences to H2.
  3. Observe the consequences to ATP.
  4. Try to comprehend the computation of the by-products

Part three: Subroutine with bacteria growth

Aim: Coherences of important pools, constants and variables. Discussion of the model.

  1. Vary the metabolic rates and cellulose pool and observe the consequences to the different outputs
  2. What is the connection between YATP and the bacteria population?
  3. What kind of processes are missing in the model in a biological view?
  4. What are mathematical limits/ weak points of the model?
  5.  Try to insert a periodic feeding.

Part four: Syntrophism

  1.  Try to insert the second organism, the archaea Methanobrevibacter ruminantium. Apply the diagram 3.

àWhat has to be changed in the model?/ What has to be inserted in the model?

  1.  Observe in the new model the YATP. What has changed? What ist the explantation?
  2.  Sample ideas for an expantation of the model. Try to realise them.