Difference between revisions of "Team:Freiburg/Model"

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<p>The variables are functions of time t where <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> describes the mRNA concentration, <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>y</mi><mo>(</mo><mi>z</mi><mo>)</mo></math> the transcription function and <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>z</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> the protein concentration. Rate constants are enlisted in the following table.
 
<p>The variables are functions of time t where <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> describes the mRNA concentration, <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>y</mi><mo>(</mo><mi>z</mi><mo>)</mo></math> the transcription function and <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>z</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> the protein concentration. Rate constants are enlisted in the following table.
 
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<p>This system of ODEs can now be solved via numerical integration, but to obtain constants like <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>k</mi><mn>1</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>k</mi><mn>2</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>k</mi><mn>3</mn></math>, experimental data has to be produced that is suitable for a nonlinear regression (Ingalls et al., 2012).</p>
  
 
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<p>This system of ODEs can now be solved via numerical integration, but to obtain constants like <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>k</mi><mn>1</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>k</mi><mn>2</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><mi>k</mi><mn>3</mn></math>, experimental data has to be produced that is suitable for a nonlinear regression (Ingalls et al., 2012).</p>
 
  
  
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Revision as of 19:38, 29 October 2017


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Modeling

Modeling

In synthetic biology, modeling can be applied to a wide range of topics, for example modeling of genetic circuits. In this subfield of mathematical and computational biology, ordinary differential equations (ODEs) are used to describe the transcriptional and translational processes over time, predict the behavior of the desired circuit and also to support their further development such as optimizing for a desired output if enough data is available (Chen et al., 1999).

Fig. 1: Schematic depiction

Finding the CARTELTM AND gate

f't=yz-k1*ft

(1)

z'(x)=k2*f(t)-k3*z(t)

(2)

The variables are functions of time t where f(t) describes the mRNA concentration, y(z) the transcription function and z(t) the protein concentration. Rate constants are enlisted in the following table.

This system of ODEs can now be solved via numerical integration, but to obtain constants like k1, k2, k3, experimental data has to be produced that is suitable for a nonlinear regression (Ingalls et al., 2012).