Team:Peking/Modeling/Luminesensor

Network System with ODE Model

Firstly we established a reaction network for the DNA binding process of Luminesensor. In order to quantify this system, we used ODE (Oridinary Differential Equations) model at the beginning. Previous works by other scientists indicate that the Vivid (VVD) protein, a sensing domain of Luminesensor, dimerizes in the presence of light,^[1] and the LexA protein, a binding domain of Luminesensor, binds at specific sequences on DNA predominantly when coupled^[2] and subsequently represses the interest gene. By combining with the mechanisms of the two functional domains of Luminesensor, we concluded with the following network:

where

• L denotes Luminesensor,
• L_G denotes the ground state --- with its VVD N-cap locked,
• L_A denotes the active state --- with its VVD N-cap released,
• D_L denotes the specific DNA binding site to Luminesensor.

Since no multi-intermediate reactions are hidden in the network above, all reactions can be regarded as elementary reactions. We list all the differential equations as following:

with parameters listed following:

and then simulated the dynamic behavior of the components with our result shown below:

Stochastic Simulation

In order to check the working stability of Luminesensor, we simulated this reaction network with a stochastic model. By estimating the volume of a cell, we converted the concentration of a component into the number of molecules by 1 n mol/L : 1. The result are shown below:

According to the figure above, the noise did not influence this system. Thus, the Luminesensor is expected to work theoretically. Besides, the average value of stochastic simulation is coupled with the result of ODE model, which in turn proves the self-consistency of our ODE model.

Parameter Analysis & Optimization

After modeling the origin system, we attempted to optimize it in a rational way. We have tuned the parameters both up and down, one by one, and finally discovered four parameters which predominantly influence this system.

• k1 (Vivid decay rate constant)
• k3 (rate constant of monomer LexA releasing from specific binding site)

determines the time scale.

• K2 (Vivid association equilibrium constant)
• K5 (dimered LexA binding equilibrium constant)

determine the contrast between dark and light. Here shows the simulation data:

As for contrast optimizing, we define an expression

completely-repressing rate = completely-repressing time / total sample time

as the interest, where completely-repressing means that all specific binding sites are occupied by Luminesensor. The higher completely-repressing rate is, the better the Luminesensor represses. The completely-repressing rate of each simulation is shown at the right of Figure 5. Within the two chosen parameters, K2 (vivid association equilibrium constant) is related to the association mechanism of Vivid protein and K5 (dimered LexA binding equilibrium constant) is related to the cooperative binding mechanism.

As for speed optimizing, k1 (vivid decay rate constant) is related to the activation mechanism of Vivid protein and k3 (monomer LexA releasing rate constant from specific binding site) is related to the binding mechanism, thus also to the LexA and sequencing. If we change the binding affinity of the sequence, then it is difficult to make constant K3 (monomer LexA binding equilibrium constant with specific binding site), whose variance is predicted to ruin the contrast of this system from simulation. Therefore, we chose to apply a mutation on the Vivid protein in order to attain a faster Luminesensor, which has high levels of k1 (vivid decay rate constant).

By searching the data of mutant in vivid protein among recent papers, we focus on these mutants: M135I in vivid dimerization domain to enhance K2 (vivid association equilibrium constant)^[?] and I74V of amino acids surrounding Cys108 to enhance k1 (vivid decay rate constant)^[3]. As for K5 (dimered LexA binding equilibrium constant), we chose LexA408, the mutant of LexA.^[5] However, our main reason for choosing LexA408 over the wild-type LexA is due to the bio-orthogonality between them.

Orthogonal Test in silico

To modularize the genetic system, our Luminesensor is expected to be bio-orthogonal with the origin system in bacteria. LexA, a natural element from the lactin-SOS system in bacteria may cause unexpected crosstalk. In order to remove this obstacle on the application prospects of our Luminesensor, we use LexA408 instead of the wild-type LexA. LexA408 and LexA are bio-orthogonal with each other since the sequence of the binding sites have variations.

By adding several nodes into the network, we constructed modeling for orthogonality test:

where

• L denotes Luminesensor
• I denotes the inner wild LexA
• D_L denotes the specific DNA binding site to Luminesensor
• D_I denotes the specific DNA binding site to wild LexA

The parameters are estimated as following:

The result shows that the endurance of K6/K5 is up to around 1%. Our Luminesensor can be used in bacteria with wild-type LexA.

Conclusion

The modeling above points out a way to optimize our Luminesensor -- the two critical mutation. It also shows the system still works well even if considering noise and inner competition.

Referrence

• [1] Light Activation of the LOV Protein Vivid Generates a Rapidly Exchanging Dimer. B. D. Zoltowski etc. Biochemistry
• [2] LexA Repressor Forms Stable Dimers in Solution. R. Mohana-Borges etc. THE JOURNAL OF BIOLOGICAL CHEMISTRY
• [3] Mechanism-based tuning of a LOV domain photoreceptor, Brian D. Zoltowski, etc. NATURE CHEMICAL BIOLOGY
• [4] Protein Vivid Generates a Rapidly Exchanging Dimer, Brian D. Zoltowski, etc. BIOCHEMISTRY
• [5] A new LexA-based genetic system for monitoring and analyzing protein heterodimerization in Escherichia coli, M. Dmitrova. etc. Springer-Verlag Mol Gen Genet