Difference between revisions of "Team:Waterloo/Modeling/Antiviral Application"
m (Added parameter table) |
m (Added the remaining parameters to the table) |
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| Line 65: | Line 65: | ||
<tbody> | <tbody> | ||
<tr> | <tr> | ||
| − | <td>k_v</td> | + | <td>$k_v$</td> |
<td>0.1</td> | <td>0.1</td> | ||
| − | <td>min^-1</td> | + | <td>min$^{-1}$</td> |
<td>Rate at which virions produced by the cell reinfect the nucleus.</td> | <td>Rate at which virions produced by the cell reinfect the nucleus.</td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td>d_{max}</td> | + | <td>$d_{max}$</td> |
<td>100/vol</td> | <td>100/vol</td> | ||
<td>molecules/volume</td> | <td>molecules/volume</td> | ||
| Line 77: | Line 77: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td></td> | + | <td>$\alpha_c$</td> |
| − | <td></td> | + | <td>0.1</td> |
| − | <td></td> | + | <td>min$^{-1}$</td> |
| − | <td></td> | + | <td>Rate at which gaps are repaired in gapped DNA to form cccDNA.</td> |
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$k_g$</td> | ||
| + | <td>0.01</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Rate at which the P6 gene on the gapped DNA is modified.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$k_c$</td> | ||
| + | <td>0.01</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Rate at which the P6 gene on cccDNA is modified.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\gamma_d$</td> | ||
| + | <td>0.001</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>DNA Degradation rate.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\alpha_{19S}$</td> | ||
| + | <td>0.01</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Transcription rate of 19S RNA.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\alpha_{35S}$</td> | ||
| + | <td>0.05</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Transcription rate of 35S RNA.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\gamma_{19S}$</td> | ||
| + | <td>0.001</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Degradation rate of 19S RNA.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\gamma_{35S}$</td> | ||
| + | <td>0.001</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Degradation rate of 35S RNA.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$f_u$</td> | ||
| + | <td>0.3</td> | ||
| + | <td>unitless</td> | ||
| + | <td>Fraction of unspliced 35S RNA in the cell (assumed at equilibrium).</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\beta_3$</td> | ||
| + | <td>0.1</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Translation rate of P3.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\beta_4$</td> | ||
| + | <td>0.1</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Translation rate of P4.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\beta_5$</td> | ||
| + | <td>0.1</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Translation rate of P5.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\beta_6$</td> | ||
| + | <td>0.1</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Translation rate of P6.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$K_6$</td> | ||
| + | <td>1000</td> | ||
| + | <td>molecules/volume</td> | ||
| + | <td>Half-saturation constant for transactivation of P1-P5 production.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\delta_3$</td> | ||
| + | <td>0.001</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Degradation rate of P3.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\delta_4$</td> | ||
| + | <td>0.001</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Degradation rate of P4.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\delta_5$</td> | ||
| + | <td>0.001</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Degradation rate of P5.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\delta_6$</td> | ||
| + | <td>0.001</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Degradation rate of P6.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$k_p$</td> | ||
| + | <td>0.1</td> | ||
| + | <td>???</td> | ||
| + | <td>Packaging rate.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$k_a$</td> | ||
| + | <td>0.1</td> | ||
| + | <td>???</td> | ||
| + | <td>Rate of P3 anchoring to virions.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$v_e$</td> | ||
| + | <td>0.1</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Rate at which virions exit the cell.</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>$\delta_v$</td> | ||
| + | <td>0.001</td> | ||
| + | <td>min$^{-1}$</td> | ||
| + | <td>Rate of virion degradation.</td> | ||
</tr> | </tr> | ||
</tbody> | </tbody> | ||
Revision as of 02:22, 13 September 2015
Contents
Antriviral Application
Copy and past code from this page as a template for the res
<section id="CRISPR Targeting" title="CRISPR Targeting">
Headers
Headers
Headers
</section>
<section id="CaMV Replication" title="CaMV Replication">
ODE System
DNA
$$\frac{d d_g}{dt} = k_v V (d_{max} - d_{total}) - \alpha_c d_g - k_g d_g - \gamma_d d_g$$ $$\frac{d d_c}{dt} = \alpha_c d_g - k_c d_c - \gamma_d d_c$$ $$\frac{d d_{gm}}{dt} = k_v V_m (d_{max} - d_{total}) - \alpha_c d_{gm} + k_g d_g - \gamma_d d_{gm}$$ $$\frac{d d_{cm}}{dt} = \alpha_c d_{gm} + k_c d_c - \gamma_d d_{cm}$$
RNA
$$\frac{d r_{19S}}{dt} = \alpha_{19S} d_c - (\gamma_{19S}+\gamma_{r}) r_{19S}$$ $$\frac{d r_{35S}}{dt} = \alpha_{35S} d_c - k_p p_4 p_5 f_u r_{35S} - (\gamma_{35S}+\gamma_{r}) r_{35S}$$ $$\frac{d r_{35Sm}}{dt} = \alpha_{35S} d_{cm} - k_p p_4 p_5 f_u r_{35Sm} - (\gamma_{35S}+\gamma_{r}) r_{35Sm}$$
Protein
$$\frac{d p_3}{dt} = \beta_3 \left( \frac{p_6}{p_6+K_6} \right) (r_{35S} + r_{35Sm}) - k_a p_3 (V_i+V_{im}) - \delta_3 p_3$$ $$\frac{d p_4}{dt} = \beta_4 \left( \frac{p_6}{p_6+K_6} \right) (r_{35S} + r_{35Sm}) - k_p p_4 p_5 f_u (r_{35S} + r_{35Sm}) - \delta_4 p_4$$ $$\frac{d p_5}{dt} = \beta_5 \left( \frac{p_6}{p_6+K_6} \right) (r_{35S} + r_{35Sm}) - k_p p_4 p_5 f_u (r_{35S} + r_{35Sm}) - \delta_5 p_5$$ $$\frac{d p_6}{dt} = \beta_6 r_{19S} - \delta_6 p_6$$
Virions
$$\frac{d V_i}{dt} = k_p p_4 p_5 f_u r_{35S} - k_a p_3 V_i$$ $$\frac{d V}{dt} = k_a p_3 V_i - k_v V (d_{max} - d_{total}) - v_e V - \delta_v V$$ $$\frac{d V_{im}}{dt} = k_p p_4 p_5 f_u r_{35Sm} - k_a p_3 V_{im}$$ $$\frac{d V_m}{dt} = k_a p_3 V_{im} - k_v V_m (d_{max} - d_{total}) - v_e V_m - \delta_v V_m$$
Algebraic Equations
$$d_{total} = d_g + d_c + d_{gm} + d_{cm}$$ $$\gamma_r = \frac{L}{1+e^{k (p_6-x_0)}}$$ $$x_0 = \frac{1}{2} p_6 ^{ss}$$ $$p_6 ^{ss} = \frac{\beta_6}{\delta_6} \frac{\alpha_{19}}{\gamma_{19}} d_{max}$$
Parameters
<section id="table" title="Table">
Parameter Table
Here are the parameters for the model
| Symbol | Value | Units | Description |
|---|---|---|---|
| $k_v$ | 0.1 | min$^{-1}$ | Rate at which virions produced by the cell reinfect the nucleus. |
| $d_{max}$ | 100/vol | molecules/volume | Maximum concentration of viral genomes in the nucleus. |
| $\alpha_c$ | 0.1 | min$^{-1}$ | Rate at which gaps are repaired in gapped DNA to form cccDNA. |
| $k_g$ | 0.01 | min$^{-1}$ | Rate at which the P6 gene on the gapped DNA is modified. |
| $k_c$ | 0.01 | min$^{-1}$ | Rate at which the P6 gene on cccDNA is modified. |
| $\gamma_d$ | 0.001 | min$^{-1}$ | DNA Degradation rate. |
| $\alpha_{19S}$ | 0.01 | min$^{-1}$ | Transcription rate of 19S RNA. |
| $\alpha_{35S}$ | 0.05 | min$^{-1}$ | Transcription rate of 35S RNA. |
| $\gamma_{19S}$ | 0.001 | min$^{-1}$ | Degradation rate of 19S RNA. |
| $\gamma_{35S}$ | 0.001 | min$^{-1}$ | Degradation rate of 35S RNA. |
| $f_u$ | 0.3 | unitless | Fraction of unspliced 35S RNA in the cell (assumed at equilibrium). |
| $\beta_3$ | 0.1 | min$^{-1}$ | Translation rate of P3. |
| $\beta_4$ | 0.1 | min$^{-1}$ | Translation rate of P4. |
| $\beta_5$ | 0.1 | min$^{-1}$ | Translation rate of P5. |
| $\beta_6$ | 0.1 | min$^{-1}$ | Translation rate of P6. |
| $K_6$ | 1000 | molecules/volume | Half-saturation constant for transactivation of P1-P5 production. |
| $\delta_3$ | 0.001 | min$^{-1}$ | Degradation rate of P3. |
| $\delta_4$ | 0.001 | min$^{-1}$ | Degradation rate of P4. |
| $\delta_5$ | 0.001 | min$^{-1}$ | Degradation rate of P5. |
| $\delta_6$ | 0.001 | min$^{-1}$ | Degradation rate of P6. |
| $k_p$ | 0.1 | ??? | Packaging rate. |
| $k_a$ | 0.1 | ??? | Rate of P3 anchoring to virions. |
| $v_e$ | 0.1 | min$^{-1}$ | Rate at which virions exit the cell. |
| $\delta_v$ | 0.001 | min$^{-1}$ | Rate of virion degradation. |
</section>
Assumptions
Headers
</section>
<section id="Intercellular Spread" title="Intercellular Spread">
Headers
Headers
Headers
</section>Top