Template:ETH Modeling Formulas

From 2006.igem.org

(Difference between revisions)
Jump to: navigation, search
m (-'s == genitive, -s == plural)
m
Line 52: Line 52:
  [P]<sub>  </sub>: product (protein) concentration
  [P]<sub>  </sub>: product (protein) concentration
  [M]<sub>  </sub>: mRNA concentration
  [M]<sub>  </sub>: mRNA concentration
-
  k<sub>tl</sub>  : kinetic konstant (translation)
+
  k<sub>tl</sub>  : kinetic constant (translation)
-
  d<sub>P </sub>  : degradation konstant for protein P
+
  d<sub>P </sub>  : degradation constant for protein P
References:
References:
* ''Modeling Molecular Interaction Networks with Nonlinear Ordinary Differential Equations''. Emery D. Conrad and John J. Tyson<br/>in ''System Modeling in Cellular Biology. From Concepts to Nuts and Bolts.''<br/>Editors: Zoltan Szallasi, Jorg Stelling and Vipul Periwal, [http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10923 MIT Press].
* ''Modeling Molecular Interaction Networks with Nonlinear Ordinary Differential Equations''. Emery D. Conrad and John J. Tyson<br/>in ''System Modeling in Cellular Biology. From Concepts to Nuts and Bolts.''<br/>Editors: Zoltan Szallasi, Jorg Stelling and Vipul Periwal, [http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10923 MIT Press].
* ''Synthetic Gene Regulatory Systems''. Mads Kaern and Ron Weiss<br/>in ''System Modeling in Cellular Biology. From Concepts to Nuts and Bolts.''<br/>Editors: Zoltan Szallasi, Jorg Stelling and Vipul Periwal, [http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10923 MIT Press].
* ''Synthetic Gene Regulatory Systems''. Mads Kaern and Ron Weiss<br/>in ''System Modeling in Cellular Biology. From Concepts to Nuts and Bolts.''<br/>Editors: Zoltan Szallasi, Jorg Stelling and Vipul Periwal, [http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10923 MIT Press].

Revision as of 11:21, 20 November 2006

To get our models into a form which can be simulated, we needed to transform the wiring diagrams into a set of ODEs (ordinary differential equations), which in our case will be non-linear.

For every concerned species X, we write

d[X]/dt = production - consumption

For enzymatic transformation of substrate S into product P (catalyzed by enzyme E), we write

       k+1      k2
S + E <==> E•S --> P + E
       k−1

d[S]/dt = −k+1[S][E] + k−1[E•S]           − dS[S]
d[E]/dt = −k+1[S][E] + k−1[E•S] + k2[S•E] − dE[E]
d[P]/dt =                       + k2[E•S] − dP[P]

[S]   : substrate concentration
[E]   : enzyme conc.
[E•S] : concentration of enzyme-substrate complex
[P]   : product concentration

kinetic constants:
  kk+1 : building enzyme-substrate complex (forward)
  kk−1 : resolving enzyme-substrate complex (backward)
  k2   : product formation
  dXXX : degradation constants

For constitutive transcription, we have constant production rate and simply write

d[M]/dt = ktr•u − dM[M]

[M]  : mRNA concentration
ktr  : kinetic konstant (transcription)
u    : system input, e.g. transcription rate (≅PoPS)
dM   : degradation konstant for mRNA

A transcriptional regulatory module can be described by and ODE of the following form:

                       1
d[M]/dt = ktr ( a + −−−−−−−−−−−−−− ) − dM[M]
                    1 + (K/[S])α•n

[M]  : mRNA concentration
ktr  : kinetic konstant (transcription)
a    : constitutive portion, 0 ≤ a < 1
[S]  : inducer (α=+1) / repressor (α=−1) concentration
K    : hill constant
n    : hill coefficient
α    : α=+1 for induction, α=−1 for repression
dM   : degradation konstant for mRNA

Finally, translation is usually modeled like this:

d[P]/dt = ktl[M] − dP[P]

[P]  : product (protein) concentration
[M]  : mRNA concentration
ktl  : kinetic constant (translation)
dP   : degradation constant for protein P

References:

  • Modeling Molecular Interaction Networks with Nonlinear Ordinary Differential Equations. Emery D. Conrad and John J. Tyson
    in System Modeling in Cellular Biology. From Concepts to Nuts and Bolts.
    Editors: Zoltan Szallasi, Jorg Stelling and Vipul Periwal, [http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10923 MIT Press].
  • Synthetic Gene Regulatory Systems. Mads Kaern and Ron Weiss
    in System Modeling in Cellular Biology. From Concepts to Nuts and Bolts.
    Editors: Zoltan Szallasi, Jorg Stelling and Vipul Periwal, [http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10923 MIT Press].
Personal tools
Past/present/future years