Introduction

What is the disadvantage of a common biphase riboswitch? And why we want to purpose a novel design principle based on the idea of a triphase riboswitch?

Here we compared the general model of the biphase and triphase riboswitch, to demonstrate the differences.

We started with a coarse-grained description of the riboswitch function (Figure 1A, 1B) in order to construct a model to yield a detailed relationship between the ligand concentration (L) and protein levels (P). In this diagram, only the dominant conformations calculated, and the noise is neglected. In the general model, the three major mechanisms were considered: translational repression, transcriptional termination and the mRNA degradation. And to simplify the model, we only considered the thermodynamically driven regime (Chase L. Beisel, Christina D. Smolke, 2009) of the model, in which all the conformational changes are reversible.

Figure 1A. The schematic diagram of biphase riboswitch

Figure 1B. The schematic diagram of triphase riboswitch

 

Biphase riboswitch Model

In a biphase riboswitch model, the associated dose-response curve can be approximately described by a single general solution that includes the distribution constant K1 between the ligand-free conformation and ligand-binding conformation, the aptamer association constant K2, mRNA degradation rate constants (a1,a2) and regulatory activities of two conformations KA and KB (Figure 1A):

 

Parameter variation effects are unique on the dose-response curve for either ON (when KA/a1<KB/a2) or OFF (when KA/a2>KB/a1)[i] behaviors.

Here we list the function of performance descriptors based on the general solution in the condition of the ON behavior:

1.     Basal expression level

2.     Highest expression level

3.     Dynamic range (shown as ratio)

4.     EC50

Then we can make conclusions according to the above equations. Stabilizing conformation A (increasing K1) will improve the dynamic range by decreasing the basal level while holding highest level. The affinity of ligand binding affects the EC50 and working range simultaneously, but the dynamic range remains unchanged (CL Beisel, CD Smolke. 2009).

 

The highest level is a function of kf, KB, ap and a2, which is only related with the conformation B and have nothing to do with the conformation A. We can improve the dynamic range by raising K1 or a1. Generally speaking, it is difficult for us to alter a1 and easier to manipulate K1. That¡¯s why we tend to change K1 by directed point mutations. However, the problem arises when K1 approaches to infinity that the dynamic range tends to a fixed constant.

 

Triphase Riboswitch Model

Similarly, when we consider the circumstance that a riboswitch has three possible stable conformations, the dose-response curve can be described by a single equation as well, containing distribution constants K1,K2,K3, ligand association constant K4, mRNA degradation constant a1, a2, a3 and regulatory activities of three conformations KA,KB,KC (Figure 1B).

Parameter variation effects are unique on the dose-response curve for either ON (when KA/a1<KC/a3, KB/a2<KC/a3) or OFF (when KA/a1>KC/a3,KB/a2>KC/a3) behaviors.

To describe the performance of the riboswitch, we discuss the basal and highest level of expression, dynamic range and EC50 as well.

 

1.     Basal expression level

2.     Highest expression level

3.     Dynamic range (shown as ratio)

4.     EC50

Then we can make conclusions according to the above equations. Stabilizing either conformation A (increasing K1) or conformation B (increasing K2) will improves the dynamic range by decreasing the basal level while holding highest level (Figure 2). The affinity of ligand binding affects the EC50 and working range simultaneously, while the dynamic range remains unchanged.

Figure 2. K1 or K2 increasing improves the dynamic range of triphase riboswich, consistent with the modeling of biphase riboswich.

 

Comparison between triphase and biphase on four main performance descriptors

 

Usually, the triphase riboswitch we design is a fuse of a competitive sequence and biphase riboswitch we already have. As a result, approximately, the Gibbs free energy difference between the conformation A and ligand-combination conformation C is constant, which means that the K1 stays constant. And the mRNA decay of conformation A and C is also the same, indicating the same a1 and a3. Of course the changing of ligand binding association constant caused by the cis influence can be neglect as well. Therefore, the only difference between triphase riboswitch and biphase riboswitch is the influence from conformation B.

Here we will discuss the four main performance descriptors and see if there is any difference between the triphase and biphase riboswitch.

Hereafter, we will discuss the modeling with ON behavior riboswitch under three different conditions

;

And it will be also always true that:

1.     Basal level expression

;

;

It is obvious that Ptriphase will always have a lower basal level under limited conditions of ON behaviors, Bd pattern (Figure 3A), bal pattern and some of Ad pattern (Figure 3B).

Figure 3A. With the dominant conformation B, triphase riboswitch always have a lower basal level than the biphase riboswitch, with the changing K2. And the lowerlimit of triphase riboswitch is lower as well.

Figure 3B. The dominant conformation B in triphase riboswich is sufficient but not necessary; even under some condition of Ad, triphase still have a lower basal expression level.

2.     Highest level expression

;

;

Therefore the highest level expression of both triphase and biphase riboswitch are the same. And the highest-level expression is only related to the regulatory activity and decay rate of the ligand-binding conformation C and the input (kf) and output (ap) of the whole riboswitch system.

3.     Dynamic range (shown with ratio)

;

;

It is obvious that triphase riboswitch will always have the higher dynamic range under limited conditions of ON behaviors, B dominant.

4.     EC50

=;

;

It is obvious that EC50triphase is always larger than EC50biphase (Figure 3C). If a biphase riboswitch with a constant K2¡¯ has the identical EC50 with the triphase one, then:

And then the ratio between the dynamic range of triphase riboswitch and the new biphase riboswitch will be: (Figure 3D)

 

Figure 3C. The triphase riboswich always have a higher EC50 value.

Figure 3D. However, the loss on EC50 can be compensated by much higher dynamic range in a B dominant pattern, therefore resulting in a higher profit and loss ratio. The product by multiplying Dynamic range and EC50 is almost constant in a biphase riboswitch but sensitive to K2 in a triphase riboswitch. And that product in a biphase riboswitch is always lower than that in a triphase riboswitch.

 

The triphase design is more feasible than mutgenesis

 

Heretofore, we have discussed the difference between triphase and biphase riboswitch on the four main performance descriptors. Nevertheless, though the advantages of triphase riboswitches have been shown, there is no evidence to support that it is necessary to apply the triphase riboswitch. In other word, if there is any alternative method?

What about the traditional way?

Since usually it is hard and hazardous to change KA and KC, changing mRNA degradation need to add conformation-controled ribozyme cleavage sites which is difficult, and the ¦Çbiphase is also the function of K2, therefore it seems to be a good strategy to increase K2 by probable site-directed mutagenesis, which is what we used to do.

However, it only allows few options (in the case of ALeader, only 2^4 =16 options), and most of mutations are not useful, resulting in the failure of function; consequently, we prefer to the triphase switch, which provides millions of choices for engineering, (because we are adding not changing the sequence)

In brief compared with mutagenesis, the triphase design is much more easily programming, with more options and more success rate.

 

The triphase design can change the upperlimit of dynamic range

 

However, for fastidious conservative, it may still not sufficient to say triphase riboswitch is not alternative.

So, what kind of breakthrough can triphase riboswitch make but other methods cannot?

The answer is about the limitation of dynamic range.

It is known that there is an upperlimit of biphase riboswitch, and the triphase-switch derived from biphase riboswitch can break that barrier of limitation.

Here is the riboswitch of

;

And in triphase design, that value can be achieved by increasing the K1 and K2 at the same time. Under this condition, the triphase switch degenerate into a biphase switch in fact:

;

If only trying to change the K2 in a triphase switch, we found that:

;

Therefore we can break the inherent barrier of dynamic range upperlimit by adding the probable competitive sequence.

That is why we need to purpose this novel strategy.

Actually, the ¦Çtriphase can be higher than the limitation of ¦Çbiphase, in this situation that:

; (Figure 4)

Then we can break the limitation of ¦Çbiphase by improve the stability of conformation B (increasing K3).

Just like all the hill functions, the curve of triphase riboswitch also has an upperlimit. To demonstrate this point, we have to rewrite the equation of dynamic range with K1 and K3:

;

Then the limitation of triphase riboswitch will be

;

Figure 4. Triphase riboswitch can break through the upperlimit of a biphase riboswitch when the conformation B is dominant to conformation A

 

Response to the ligand concentration upper limit

In our analysis thus far, we presume that the maximum ligand concentration can always saturates the dose-response function. Nevertheless, many of riboswitches may not be saturated by the accessible upper limit in ligand concentration due to permeability of the ligand across the cell membrane, cytotoxicity of the ligand and so on. For example in our case, the ligand aminoglycosides antibiotics will do harm to the bacterium without resistance genes. Here we set the accessible upperlimit of ligand concentration as L¡¯ (Figure 5A).

The modeling revealed that the limit affects the dynamic range on the conformational partitioning constant K2, consistent with the previous study. Moreover, the triphase riboswitch is influenced more significantly by limit of ligand concentration, because of a higher EC50 value (Figure 5B).

Figure 5B. Both triphase and biphase riboswitch are impacted by the limitation of ligand concentration. Triphase riboswitch is more sensitive to that effect because it always has a higher EC50 value. Higher K2L¡¯ level will reduce the influence, in both of them.

 

ODE model of Dynamic Process

In the former discussion, we studied the steady state solution of biphase riboswitch and triphase riboswitch. However, in spite of the upperlimit of ligand concentration, steady state solution is impossible to achieve and the assumption of thermodynamic-driven regime is not always true. To more precisely quantify the dose-response of riboswitch, we used an ODE (ordinary differential equations) model to describe the dynamic process with limitation of both ligand concentration and incubation time.

In a biphase riboswitch:

∂[A]/∂t =kfA-k2[A]-a1[A]+k-2[C]

∂[C]/∂t =kfC-k-2[C]-k4[C][L]-a3[C]+k2[A]+k-4[CL]

∂[CL]/∂t=-k-4[CL]-a3[CL]+k4[C][L]

∂P/∂t = KA[A]+KC[C]+KC[CL]-ap[P]

In a triphase riboswitch:

∂[A]/∂t =kfA-k1[A]-k2[A]-a1[A]+k-1[B]+k-2[C]

∂[B]/∂t =kfB-k-1[B]-k3[B]-a2[B]+k1[A]+k-3[B]

∂[C]/∂t =kfC-k-2[C]-k-3[C]-k4[C][L]-a3[C]+k2[A]+k3[B]+k-4[CL]

∂[CL]/∂t=-k-4[CL]-a3[CL]+k4[C][L]

∂P/∂t = KA[A]+KB[B]+KC[C]+KC[CL]-ap[P]

With following limitation:

K1 = k-1/k1, K2 = k-2/k2, K3 = k-3/k3, K4 = k4/k-4£»

And £»

In the ODE model that is closer to reality than the steady-state solution, triphase riboswitch performs better in the perspective of dynamic range and other descriptors.

Qualitatively speaking, the EC50 value and dynamic range of triphase riboswitch is higher than that biphase riboswitch (Figure 6A), consistent with former solution. The effect of ligand concentration limit is also similar (Figure 6B).

Some of conclusion should be revised in the ODE model. For example, the highest level of triphase riboswitch in the limited time is not equal to that of biphase riboswitch (Figure 6C). And the dynamic range difference between two patterns is so significant that that even with a1 increasing, the triphase one is always better (Figure 6D)

Figure 6B. The Limitation of ligand concentration affects the dynamic range – K2 curve. The triphase riboswitch is more sensitive, similar to former modeling.

 

Figure 6D. Triphase riboswitch always has a higher dynamic range, even with the faster mRNA decay of conformation A.

Figure 6C. The highest levels of triphase and biphase riboswitch are not equal. The difference of highest level between triphase and biphase riboswitch is related to the irreversible processs, measured by K2/(K1*K3).

Figure 6A. In the ODE model, the triphase riboswitch shows a significant high dynamic range and a higher EC50 value.

 

 

Reference:

Beisel C L, Smolke C D. Design principles for riboswitch function[J]. PLoS Computational Biology, 2009, 5(4): e1000363.