Team:Freiburg Bioware/Modeling/Virus Production

From 2010.igem.org

(Difference between revisions)
Line 50: Line 50:
</div>
</div>
</td>
</td>
-
<td>
+
<td> <img
-
<img
+
src="https://static.igem.org/mediawiki/2010/b/b8/Freiburg10_VirusProduction01.png"
src="https://static.igem.org/mediawiki/2010/b/b8/Freiburg10_VirusProduction01.png"
alt="Reaction scheme for the virus production" width="477"><br>
alt="Reaction scheme for the virus production" width="477"><br>
Line 88: Line 87:
<ul>
<ul>
<li> a linear degradation of <i>ssDNA</i> in the nucleus with the
<li> a linear degradation of <i>ssDNA</i> in the nucleus with the
-
rate constant <i>k<sub>14,1</sub></i>
+
rate constant <i>k<sub>14,1</sub></i> </li>
-
</li>
+
<li> replication of <i>ssDNA</i> in the nucleus with the rate
<li> replication of <i>ssDNA</i> in the nucleus with the rate
-
constant <i>k<sub>15,1</sub></i>
+
constant <i>k<sub>15,1</sub></i> </li>
-
</li>
+
</ul>
</ul>
<br>
<br>
Line 131: Line 128:
</td>
</td>
<td>
<td>
-
<p style="text-align: justify;">The image on the right shows one
+
<p style="text-align: justify;">The image on the left shows one
snapshot out of the time
snapshot out of the time
lapse recorded over a period of 1560 minutes (26 hours) after
lapse recorded over a period of 1560 minutes (26 hours) after
transfection. The bright spots
transfection. The bright spots
correspond to the fluorescence intensity of <i>mVenus</i> in the upper
correspond to the fluorescence intensity of <i>mVenus</i> in the upper
-
and of <i>mCherry</i> in the lower picture.<br>
+
and of <i>mCherry</i> in the lower picture.</p>
-
To see the whole time lapse as an animation just click on the picture!<br>
+
<p style="text-align: justify;">To see the whole time lapse as an
 +
animation just click on the picture!<br>
</p>
</p>
</td>
</td>
Line 150: Line 148:
microscopy of
microscopy of
transfected cells.&nbsp; Viral particles containing mCherry as gene of
transfected cells.&nbsp; Viral particles containing mCherry as gene of
-
interest are visible.
+
interest are visible. </div>
-
</div>
+
</td>
</td>
<td style="vertical-align: top;"><br>
<td style="vertical-align: top;"><br>
Line 180: Line 177:
<td>
<td>
<p style="text-align: justify;">The average intensity was
<p style="text-align: justify;">The average intensity was
-
extracted from the raw data through a script written in MathWorks®
+
extracted from the raw data uisng a script written in MathWorks®
-
MATLAB. </p>
+
MATLAB which sums up the intensity value of each pixel of one image. <br>
 +
</p>
<a
<a
href="https://static.igem.org/mediawiki/2010/1/19/Freiburg10_IntensityAnalysisCode.m">Download
href="https://static.igem.org/mediawiki/2010/1/19/Freiburg10_IntensityAnalysisCode.m">Download
Line 206: Line 204:
<div style="text-align: justify;"><span style="font-weight: bold;"><br>
<div style="text-align: justify;"><span style="font-weight: bold;"><br>
Table 1: </span>Rate constants for the virus production model.
Table 1: </span>Rate constants for the virus production model.
-
Generally forward reactions were assumed to be faster than reverse ones.
+
Generally forward reactions were assumed to be faster than reverse
 +
ones.
Replication of <span style="font-style: italic;">ssDNA</span> is
Replication of <span style="font-style: italic;">ssDNA</span> is
slower than its degradation.<br>
slower than its degradation.<br>
Line 225: Line 224:
<h2>Results and Discussion</h2>
<h2>Results and Discussion</h2>
<p style="text-align: justify;">
<p style="text-align: justify;">
-
Figure 5 shows the time course of the model for virus production. The initial plasmid concentrations were chosen to 20µM for the <i>helper</i>, <i>goi</i>, and <i>capsid-wt</i> plasmids and 10µM of the modified capsid plasmid.
+
Figure 5 shows the time course of the model for virus production. The
 +
initial plasmid concentrations were chosen to 20µM for the <i>helper</i>,
 +
<i>goi</i>, and <i>capsid-wt</i> plasmids and 10µM of the modified
 +
capsid plasmid. After the short peaks of the intranuclear plamid
 +
concentrations proteins are synthesized and capsids are formed. The
 +
ssDNA enters the capsid through a pore and infectious virus particles
 +
are reseased to the cytoplasm from where they are transported out of
 +
the cell.<br>
 +
The concentrations reach a steady state as a result of ssDNA
 +
degradation inside the nucleus.<br>
</p>
</p>
<center>
<center>
-
<div style="text-align: justify;"></div>
 
<table
<table
style="text-align: left; width: 642px; height: 504px; margin-left: 0px; margin-right: 0px;"
style="text-align: left; width: 642px; height: 504px; margin-left: 0px; margin-right: 0px;"
Line 238: Line 245:
alt="" width="800"><br>
alt="" width="800"><br>
<div style="text-align: justify;"><span style="font-weight: bold;">Figure
<div style="text-align: justify;"><span style="font-weight: bold;">Figure
-
5:</span><br>
+
5:</span> <br>
</div>
</div>
</td>
</td>
Line 245: Line 252:
</table>
</table>
<br>
<br>
 +
<p style="text-align: justify;">A model extension was made taking into
 +
account the production efficiency dependend on the level of
 +
modfication. The resulting curves are plotted in figure 6. <br>
 +
</p>
</center>
</center>
<br>
<br>
-
<table
 
-
style="text-align: left; width: 693px; height: 516px; margin-left: auto; margin-right: auto;"
 
-
border="0" cellpadding="2" cellspacing="2">
 
-
<tbody>
 
-
<tr>
 
-
<td style="vertical-align: top;">
 
-
<center>
 
-
<div style="text-align: center;"><img
 
-
src="https://static.igem.org/mediawiki/2010/a/ac/Freiburg10_VirusProductionPlot02.png"
 
-
alt="" width="800"><br>
 
-
</div>
 
-
<div style="text-align: justify;"><span style="font-weight: bold;">Figure
 
-
6:</span><br>
 
-
</div>
 
-
</center>
 
-
</td>
 
-
</tr>
 
-
</tbody>
 
-
</table>
 
<br>
<br>
<table
<table
Line 277: Line 269:
width="800"><br>
width="800"><br>
</div>
</div>
-
<div style="text-align: justify;"><span style="font-weight: bold;">Figure
+
<div style="text-align: justify;"> <span
-
7:</span> <br>
+
style="font-weight: bold;">Figure
 +
6: A:</span> Enzyme concentration depending on different degrees of
 +
modification. <span style="font-weight: bold;">B:</span> production
 +
efficiency as a function of modification degree <span
 +
style="font-style: italic;">m</span>.<br>
</div>
</div>
</td>
</td>
Line 285: Line 281:
</table>
</table>
<br>
<br>
 +
<p style="text-align: justify;">
 +
Fitting the model to the data obtained from the fluorescence experiment
 +
was performed by the method of least squares in logarrithmic parameter
 +
space. Unfortunately only one data set quantifying the single protein,
 +
capsid and virus concentration was availible so that the optimization
 +
problem was clearly under-determined and no explicit ideal parameter
 +
set could be found with out loosing the biological signification. More
 +
precisely, the data was fitted by an exponential increase while the
 +
biological system is expected to saturate for large time values because
 +
no more virus is poduced if its plasmid are completely degraded. Figure
 +
7 shows more realistic model characteristics where the blue line
 +
represents the sum of all concentrations containing mVenus and the red
 +
dots describe the mVenus intensity data set. Thereby the desired
 +
simoidal shape was achieved though the chi-square value and
 +
consequently the quality of the fit is not optimal. <br>
 +
In order to improve the predictive capability of this mathematical
 +
model one has to perform further adjustments and more experimental data
 +
is needed accordingly.<br>
 +
</p>
<br>
<br>
<table
<table
Line 296: Line 311:
</span>
</span>
<div style="text-align: justify;"><span style="font-weight: bold;">Figure
<div style="text-align: justify;"><span style="font-weight: bold;">Figure
-
9:</span> Data fitting approach. The model can be fitted perfectly to
+
7:</span> Data fitting approach. The model can be fitted perfectly to
the data (not shown) but is not meaningful in a biological sense
the data (not shown) but is not meaningful in a biological sense
because exponential increase does not occur in this system. Considering
because exponential increase does not occur in this system. Considering

Revision as of 23:56, 27 October 2010

Model for Virus Production


Reaction Scheme

Reducing the complexity of virus production we divide the cell into three compartments: the extracellular matrix (all quantities with the index ext), the cytoplasm (cyt) and the nucleus (nuc). Four plasmids are transfected - the plasmid coding for the helper proteins (helper), the gene of interest (goi) and two types of plasmids coding for the capsid proteins (capwt [wild type], capmod [modified]).
The plasmids are transported into the nucleus where gene expression is initiated. Processed mRNA is transported into the cytoplasm and proteins (phelper, pcapwt, pcapmod) are produced. Containing a nuclear localization sequence proteins are relocated into the nucleus where capsid assembly occurs. The viral capsid is compose of 60 subunits of viral coat proteins. Titration of the two plasmids coding for the capsid proteins leads to virus surfaces with different ratios of wild type and modified capsid proteins.
The gene of interest is replicated by cellular polymerases and single stranded DNA (ssDNA) is encapsidated into the preformed capsids (capsid) forming infectious viral particles (V).
Finally the recombinant viruses are released into the extracellular matrix and can be harvested for transduction.



Reaction scheme for the virus production



Figure 1: Schematic overview of virus production: A production cell line is  transfected with 4 plasmid types. DNA is replicated, transcribed (1) and proteins are synthesized (2). Capsid assembly occurs (3) and single-stranded DNA is packaged into the viral particle (4).
Reaction scheme for the virus production



Reduced Reaction Scheme

Even the coarse model for virus production described in the previous paragraph would still consist of 24 ODEs containing 39 parameters (35 rate constants and 4 initial plasmid concentrations). Taking into account the linearity of the law of mass action (LMA) for simple transport processes we can neglect these fast reactions and for this reason reduce the model to the rate limiting steps like protein synthetization, capsid formation and virus packaging.



reduced reaction scheme for the virus production


Differential Equations

The 13 reactions for the virus production are represented in a system of 17 coupled ODEs.
In addition to the terms provided by the law of mass action we considered the following terms:

  • a linear degradation of ssDNA in the nucleus with the rate constant k14,1
  • replication of ssDNA in the nucleus with the rate constant k15,1


Reaction scheme for the virus production


Methods and Simulation

The ODE model was implemented in MathWorks® MATLAB R2010b. Integration of the differential equations was achieved using the stiff integrator ode15s with automatic integration step size management.
In order to adjust the dynamical model to biological data we extracted the average intensity out of the time lapse recordings of fluorescence experiments as well as published values for the rate constants. For initial conditions we took the plasmid concentrations we used in experiments.


Figure 2: Fluorescence microscopy of transfected cells.  mVenus is included to the modified capsid plasmid i.e. fluorescence intensity reflects capsid protein concentration.

The image on the left shows one snapshot out of the time lapse recorded over a period of 1560 minutes (26 hours) after transfection. The bright spots correspond to the fluorescence intensity of mVenus in the upper and of mCherry in the lower picture.

To see the whole time lapse as an animation just click on the picture!


Figure 3: Fluorescence microscopy of transfected cells.  Viral particles containing mCherry as gene of interest are visible.


Data
Figure 4: A shows the average intensity of mCherry recorded using fluorescence microscopy. The curve corresponds to the rising phase of protein concentration and is expected to saturate for longer times as the harvest of viral particles is done after 3 days (4320min). B: time course of the intensity of mCherry. Due to the weak expression of mCherry the signal to noise ratio is quiet low and the functional dependency is not clearly determinable.

The average intensity was extracted from the raw data uisng a script written in MathWorks® MATLAB which sums up the intensity value of each pixel of one image.

Download the m-File (MATLAB source code).

The used model parameters are given in the table below.



Table 1:
Rate constants for the virus production model. Generally forward reactions were assumed to be faster than reverse ones. Replication of ssDNA is slower than its degradation.


 
Download the m-File (MATLAB source code).


Results and Discussion

Figure 5 shows the time course of the model for virus production. The initial plasmid concentrations were chosen to 20µM for the helper, goi, and capsid-wt plasmids and 10µM of the modified capsid plasmid. After the short peaks of the intranuclear plamid concentrations proteins are synthesized and capsids are formed. The ssDNA enters the capsid through a pore and infectious virus particles are reseased to the cytoplasm from where they are transported out of the cell.
The concentrations reach a steady state as a result of ssDNA degradation inside the nucleus.


Figure 5:

A model extension was made taking into account the production efficiency dependend on the level of modfication. The resulting curves are plotted in figure 6.




Figure 6: A: Enzyme concentration depending on different degrees of modification. B: production efficiency as a function of modification degree m.

Fitting the model to the data obtained from the fluorescence experiment was performed by the method of least squares in logarrithmic parameter space. Unfortunately only one data set quantifying the single protein, capsid and virus concentration was availible so that the optimization problem was clearly under-determined and no explicit ideal parameter set could be found with out loosing the biological signification. More precisely, the data was fitted by an exponential increase while the biological system is expected to saturate for large time values because no more virus is poduced if its plasmid are completely degraded. Figure 7 shows more realistic model characteristics where the blue line represents the sum of all concentrations containing mVenus and the red dots describe the mVenus intensity data set. Thereby the desired simoidal shape was achieved though the chi-square value and consequently the quality of the fit is not optimal.
In order to improve the predictive capability of this mathematical model one has to perform further adjustments and more experimental data is needed accordingly.



Figure 7: Data fitting approach. The model can be fitted perfectly to the data (not shown) but is not meaningful in a biological sense because exponential increase does not occur in this system. Considering the fact that virus concentration should saturate a sigmoidal shape is expected. Such a fit was not achieved because to many unknown parameters for one single data set.