Difference between revisions of "Team:Freiburg/Model"

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<h1 align="center">Modeling</h1>
 
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<p>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).</p>
 
<p>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).</p>
  
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                <img src="https://static.igem.org/mediawiki/2017/d/df/.png" alt="" height="100%" width="100%">
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                    <p><strong>Fig. 1: Schematic depiction</p>
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                        <p><strong>Fig. 1: Schematic depiction</strong></p>
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<h3>Finding the CARTEL<sup>TM</sup> AND gate</h3>
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<h2>Finding the CARTEL<sup>TM</sup> AND gate</h2>
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        The hypoxia response element (<i>HRE</i>), cAMP response element (<i>CRE</i>) and <i>CTLA4</i> promoter can be utilized for a more specific <i>CAR</i> expression. Combining these three enhancers in an AND gate to allow a specific <i>CAR</i> expression (Brophy et al., 2014) proved to be quite challenging. Using endogenous systems came with a drawback - a knockout or knockdown of either <i>HIF1</i>, <i>VEGFR-2</i> or <i>TDAG8</i> had to be generated.
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        </p>
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        <p>
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        Generating a single knockout or knockdown is challenging enough but generating three to test all possibilities seemed quite impossible in six months. So using modeling to find the best combination of enhancers and knockout was an attractive option instead of choosing a random AND gate design.
 +
        </p>
 +
       
 +
        <p>
 +
        To create such a model, the changing concentration of CAR can be described with an system of coupled ODEs. For each component of the genetic circuit - proteins and mRNAs -  rate equations describing its synthesis, degradation, association or other processes are added (Chen et al., 1999). How these ODEs can be set up in their simplest form is shown below.
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<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns="http://schemas.openxmlformats.org/officeDocument/2006/math"><msup><mi>f</mi><mi>'</mi></msup><mfenced separators="|"><mi>t</mi></mfenced><mo>=</mo><mi>y</mi><mfenced separators="|"><mi>z</mi></mfenced><mo>-</mo><mi>k</mi><mn>1</mn><mi>*</mi><mi>f</mi><mfenced separators="|"><mi>t</mi></mfenced></math>
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              <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>-</mo><mi>k</mi><mn>1</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>&#xA0;</mo></math>
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                <p>(1)</p>
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(1)
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              <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>'</mo><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>k</mi><mn>2</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>-</mo><mi>k</mi><mn>3</mn><mo>*</mo><mi>y</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>
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                <p>(2)</p>
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        The variables are functions of time t, where f(t) describes the mRNA concentration,a(z)the transcription function, k1 the mRNA degradation rate, y(t)the protein concentration, k2translation rate and k3 protein degradation rate. This kind of ODEs can be solved via numerical integration to describe changing protein and mRNA levels. To obtain the rate constants, experimental data have to be produced which is suitable for a nonlinear regression (Ingalls et al., 2012).
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        <p>
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        Equations (1) and (2) were further simplified for the AND gate comparison into equation (3) by neglecting the mRNA level, because it better describes delayed protein expression.
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              <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>'</mo><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>k</mi><mn>4</mn><mo>+</mo><mi>k</mi><mn>5</mn><mo>*</mo><mi>b</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>-</mo><mi>k</mi><mn>6</mn><mo>*</mo><mi>x</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>
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<mi>z</mi><mi>'</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>k</mi><mn>2</mn><mi>*</mi><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>-</mo><mi>k</mi><mn>3</mn><mi>*</mi><mi>z</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>
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(2)
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        The variables are functions of time t, where x(t) describes the protein concentration over time, k4the basal expression rate, k5 the maximum expression rate, b(t)the activation function and k6 the degradation rate.
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        The variables are functions of time t, where x(t) describes the protein concentration over time, k4the basal expression rate, k5 the maximum expression rate, b(t)the activation function and k6 the degradation rate.
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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.
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        The first possible system was a knockout of <i>HIF1A</i> or <i>HIF1B</i> and its reintroduction via lentiviral transduction under the control of either <i>CRE</i> or <i>CTLA4</i>. Considering the law of mass action, a knockout of HIF1B would have a kinetic disadvantage over a knockout of HIF1A because HIF1B is accumulated permanently and independently from external conditions (Pescador, et al., 2005) while HIF1A is only accumulated under hypoxia. Therefore only a knockout of <i>HIF1A</i> was considered a possible candidate for an AND gate.
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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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        The second or third possibility would be a knockout of either TDAG8 or VEGFR2. Both can be described by the same model as both receptors are activated by one input and trigger activation of the associated promoter afterwards.  
 +
        </p>
 +
       
 +
        <p>
 +
        Unfortunately, experimental data only exist for HEK cells which are not representative for T cells (Ausländer <i>et al.</i>, 2014; Nguyen <i>et al.</i>, 2012). Therefore, the different AND gate designs were modeled with the same rate constants to compare their performances.
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Revision as of 21:29, 29 October 2017


Logo
Overview Motivation CAR T Cells Tumor Microenvironment AND Gate Outlook Achievements References
Members Attributions Partners Contact
Main Project Modeling Applied Design Proof of Concept BioBricks Basic Part BioBrick Improvement Interlab Study
Safety Cloning HIF1A Knockdown Cell Culture Lab Book
Human Practice Integrated Human Practice Collaborations

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

The hypoxia response element (HRE), cAMP response element (CRE) and CTLA4 promoter can be utilized for a more specific CAR expression. Combining these three enhancers in an AND gate to allow a specific CAR expression (Brophy et al., 2014) proved to be quite challenging. Using endogenous systems came with a drawback - a knockout or knockdown of either HIF1, VEGFR-2 or TDAG8 had to be generated.

Generating a single knockout or knockdown is challenging enough but generating three to test all possibilities seemed quite impossible in six months. So using modeling to find the best combination of enhancers and knockout was an attractive option instead of choosing a random AND gate design.

To create such a model, the changing concentration of CAR can be described with an system of coupled ODEs. For each component of the genetic circuit - proteins and mRNAs - rate equations describing its synthesis, degradation, association or other processes are added (Chen et al., 1999). How these ODEs can be set up in their simplest form is shown below.

f'(t)=a(z)-k1*f(t) 

(1)

y'(t)=k2*f(t)-k3*y(t)

(2)

The variables are functions of time t, where f(t) describes the mRNA concentration,a(z)the transcription function, k1 the mRNA degradation rate, y(t)the protein concentration, k2translation rate and k3 protein degradation rate. This kind of ODEs can be solved via numerical integration to describe changing protein and mRNA levels. To obtain the rate constants, experimental data have to be produced which is suitable for a nonlinear regression (Ingalls et al., 2012).

Equations (1) and (2) were further simplified for the AND gate comparison into equation (3) by neglecting the mRNA level, because it better describes delayed protein expression.

x'(t)=k4+k5*b(t)-k6*x(t)

The variables are functions of time t, where x(t) describes the protein concentration over time, k4the basal expression rate, k5 the maximum expression rate, b(t)the activation function and k6 the degradation rate.

The variables are functions of time t, where x(t) describes the protein concentration over time, k4the basal expression rate, k5 the maximum expression rate, b(t)the activation function and k6 the degradation rate.

The first possible system was a knockout of HIF1A or HIF1B and its reintroduction via lentiviral transduction under the control of either CRE or CTLA4. Considering the law of mass action, a knockout of HIF1B would have a kinetic disadvantage over a knockout of HIF1A because HIF1B is accumulated permanently and independently from external conditions (Pescador, et al., 2005) while HIF1A is only accumulated under hypoxia. Therefore only a knockout of HIF1A was considered a possible candidate for an AND gate.

The second or third possibility would be a knockout of either TDAG8 or VEGFR2. Both can be described by the same model as both receptors are activated by one input and trigger activation of the associated promoter afterwards.

Unfortunately, experimental data only exist for HEK cells which are not representative for T cells (Ausländer et al., 2014; Nguyen et al., 2012). Therefore, the different AND gate designs were modeled with the same rate constants to compare their performances.