Why?

From our work on LOV2 photoactivation we should be able to predict the percentage of LovTAP-VP16 proteins that are photoactivated depending on the irradiance applied.

• Can we then predict the occupancy of TrpO binding sites in our reporter plasmid by LovTAP-VP16 dimers?
• What concentration of LovTAP-VP16 would be optimal?
• Can we predict the difference in expression levels between an irradiated cell culture and one left in the dark?

What?

Well, things start to get complicated, since the number of unknowns is huge in this problem. The system is affected by the transient transfection process, the cell's metabolism, the interaction of plasmids with the genomic DNA, the interaction of VP16 with the transcriptional cofactors, and several other variables.

We can split this into two parts:

1. Estimate the proportion of active plasmids that will be bound by LovTAP-VP16. We will assume the same binding affinity ratio (light/dark) as Strickland et al (2008) found for LovTAP at 25ºC because, although the absolute affinity is temperature dependent, according to Jin et al (1993), this change is not important. We are not sure whether only one or two LovTAP-VP16 dimer can bind a TrpO sequence. According to Yang et al (1996) a whole TrpO sequence can be bound by a tandem of two TrpR dimers. We will model both cases.
2. Estimate the expression level of a reporter gene (dsRed in this case) depending on the proportion of bound reporter plasmids, based on the estimation from the previous part. Warning! This might give us an idea of the orders of magnitude, but can't be validated until many more experiments have been done.

How?

To model the behavior of LovTAP-VP16, we will start with the following assumptions:

• [LovTAP-VP16] >> [Plasmids] in the nucleus.
• LovTAP-VP16 is always a dimer and the number of activated LOV2 domains is equivalent to the number of active dimers.

In our model, plasmids can be either free or bound to LovTAP-VP16, with different transcription rates for each state. The resulting network can be seen in diagram 1:

Diagram 1: showing the network we use to modelise the system assuming a single binding site for LovTAP-VP16 per TrpO. D: free available reporter plasmids, LT: LovTAP-VP16 dimers in the nucleus, LTD: reporter plasmids bound to LovTAP-VP16, M: mRNA copies, P: reporter proteins, V_c: constitutive (leaky) transcription rate, V_LT: VP16 activated transcription rate, V_p: translation rate. In red: modelised statically, proportion of activated plasmids as function of photactivation level of LovTAP-VP16. In green: modelised dynamically, expression levels as function of bound plasmids

Photoactivation level

We will then assume that we know the proportion of activated LovTAP-VP16 monomers, since we have calculated it in this section. But LovTAP-VP16 has to dimerize to be able to bind DNA. To illustrate the importance of this, let's give an example: imagine a solution with LovTAP-VP16 where 50% of the monomers are activated. Assuming that all of them form part of a dimer, we expect that 25% of the dimers are inactive, 25% active and 50% half active. The average binding affinity will mostly depend on the affinity of the half active/half inactive dimers. In the section on the 3D protein structure of LovTAP-VP16 we conclude that it is reasonable to think that a half activated dimer will have a DNA activity somewhere between a fully activated dimer and a deactivated one. This means that we can take the monomer activation level to approximate the dimer activation level. Eitoku et al (2005) report that it takes 2 ms for the Jα-helix to undock. This is 3 orders of magnitude faster than the photoactivation rate we expect with our setup. Therefore, we can consider the undocking instantaneous and thus say that photoactivation equals active LovTAP-VP16. Nonetheless, we might have to add an efficiency factor, since Yao et al (2008) found that 92% of photoactive LOV2 has it's Jα-helix undocked.

Number of activated reporter plasmids

Supposing a single binding site

Let's go step by step; if we assume that only one LovTAP-VP16 dimer can bind the TrpO binding site, reporter plasmids can exist in two states; free or bound to a LovTAP-VP16 dimer, and the total number of available plasmids must be the sum of the two:

According to the law of mass-action, the proportion of each one will also depend on the number of LovTAP-VP16 dimers floating in the nucleus. This proportion is called K_d, the dissociation constant, defined as:

with [D] the concentration of free binding sites, equal to the number of read-out plasmids not bound by LovTAP-VP16, [LT] the concentration of free LovTAP-VP16 dimers and [DLT] the concentration of plasmids with LovTAP-VP16 bound to them.

Since the volume we are interested in is a CHO cell's nucleus, we can suppose it approximately constant and get rid of the concentration units:

If we reorder, we get

what can be substituted in the first expression to get

Supposing a double binding site

In E. coli, TrpR can bind the TrpO sequence as a tandem of 2 dimers (Yang et al, 1996) What if there is place for 2 LovTAP-VP16 dimers in our TrpO binding site?

Diagram 2: showing the network we use to modelise the system assuming a single binding site for LovTAP-VP16 per TrpO. D: free available reporter plasmids, LT: LovTAP-VP16 dimers in the nucleus, LTD1: reporter plasmids bound to one LovTAP-VP16 dimer,LTD2: reporter plasmids bound to two LovTAP-VP16 dimer, M: mRNA copies, P: reporter proteins, V_c: constitutive (leaky) transcription rate, V_LT: VP16 activated transcription rate, V_p: translation rate.

In this case, a binding site can be in 3 different states: free, bound to one dimer or bound to two dimers. Now the following expression should hold:

We have now two dissociation constants:

Performing the same operations as before:

Combining them:

Substituting DLT1 into DLT2:

And substituting DLT1 and DLT2 in the first expression:

Some steps of reordering:

If we substitute this in the following:

We get:

And finally:

Parameters

Fig. 1: Percentage gain in site occupancy from dark to light (saturation) for different LovTAP-VP16 dimer concentrations and 4 model assumptions.

If we just want to know the light/dark ratio of binding site occupancy, the concentration of reporter plasmids has no effect, so one parameter less. The K_d(light) = 142 ± 61 and K_d(dark) = 788 ± 94 nM have been set by Strickland et al (2008) for nano molar concentrations, up to 690 nM. Both K_d seem to depend on the concentration, with a maximum K_d(dark)/K_d(light) around 400 nM. This means that in fig. 1 only the areas of the curves around the maximum are reliable and the rest has a higher value than it would in reality.

Conclusion

As we see in fig. 1, the curve which maximum is nearer to 400 nM is the one assuming double binding site and 30% activity of LTD1. If as activity we refer to the one corresponding to Strickland's experiment, protection of a RsaI restriction site from digestion, we can conclude that the tandem binding site model fits better with the real data.

400 nM, the optimal concentration according to the model (and to Strickland et al) would mean some 50000 dimers floating around in a nucleus of 4 µm in radius.

Expression levels

Single binding site

We now know, more or less, the number of reporter gene copies that will be activated by LovTAP-VP16 and those that will be expressing only at constitutive levels.

The number of reporter mRNA copies in the cell will vary according to both transcription rates and the mRNA degradation rate:

And the number of reporter proteins in the cell will change depending on the number of mRNA copies and the protein degradation rate:

Double binding site

We have the same sort of expression as before, but we might have two different transcription activation rates with one or with two LovTAP-VP16 dimers binding a site:

Parameters

So far, we have been transfecting our CHO cells transiently using [http://en.wikipedia.org/wiki/Polyethylenimine PEI]. Following our protocol, we add 1.5 µg of DNA per million cells; that is 1.5x10⁻⁶ µg per cell. Our plasmids are about 6000 bp, or around 10⁻¹¹ µg per plasmid. This means we dose some 1.5x10⁵ plasmids per cell. How many can we expect, on average, to reach the nucleus? Well, experience in the lab shows that only some 15% to 30% of the cells show expression. According to Cohen et al, 2009, we could expect somewhere between 100 and 1000 plasmids to reach the nucleus on average. We don't know how many of those will be transcribed, and we don't know how the conditions in the nucleus will affect the way LovTAP-VP16 binds DNA.

From now on we can't expect to produce more than qualitative information due to the lack of data.

We have started building a stochastic model, based on typical parameter distributions for mammalian cells (Schwanhausser et al, 2011).

The code

File:Team-EPF-Lausanne expression.zip contains all the MATLAB code we have used.