Team:Slovenia/SafetyMechanisms

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Quantitative model and stability analysis

In order to be able to predict the quantitative behavior of in vivo application of the genetic switches, we set up a quantitative model of a Transcription-activator like effector (TAL) based bistable switches. We apply experimental measurements for individual parts and predict their behavior when applied into a single system. The essential characteristics of a switch are responsiveness (reaching a stable state with the introduction of the corresponding inducer), stability (not leaving the state it after inducer removal) and robustness (expressing equivalent qualitative behavior under a wide range of conditions). In the following subsections, modeling approaches for individual parts are described.

A variety of well-established models in the literature were examined, which resulted in choosing ordinary differential Hill equations model, presented in (Tigges et al., 2009). The former work presents a tunable synthetic mammalian oscillator, whose model was readjusted to present a switch structure. On top of that, the host choice of mammalian cells and pristinamycin-based inducible system corresponds to our system.

To get a better idea of the functioning of the model, an interactive web application was developed and is available here.

Model description and parameter determination

TAL:KRAB repressor constructs

For repressor constructs, the percentage of remaining transcription rate comparing to the unrepressed reporter plasmid was measured. Intuitively, the remaining rate was directly proportional to the repressor/reporter ratio, but not in a linear fashion. To approximate this relation for TAL:KRAB constructs, the following analytical function was fitted to the measurements:


where x is repressor/reporter plasmid ratio, and a, b, c are parameters subject to least square error fitting. This produced decreasing function for remaining transcription rate q, depicted in Figure 1a. The achieved percentage of remaining transcription rate q was directly employed in repressed promoter rate equation. The dynamics were modeled using Hill equations for repression and activation (Alon, 2007). For example, the effect of a repressor on transcription rate is modeled as a factor in a rate equation:


Intuitively, the unrepressed transcription rate r is inversely proportional to the concentration of TAL-A:KRAB protein with non-linearity coefficient n. The remaining rate percentage q was used to determine the s constant, which determines the concentration at which half of the unrepressed rate is reached, after the concentration threshold t is crossed.

TAL:VP16 activator constructs

Using a similar approach to that described above, we fitted the data achieved for activator constructs TAL-A:VP16 and TAL-B:VP16. As expected, the transcription rate increased proportionally with increasing activator/reporter ratio of plasmids transfected, again in a non-linear fashion. To approximate the behavior, the following increasing function was fitted:


where x is activator/reporter plasmid radio and c, b are parameters subject to least square error fitting. The plot of the function is shown in Figure 1b. The factor of activation a is again directly employed as a rate equation factor for activated promoter:


where the increasing concentration of TAL-B:VP16 protein reaches half the maximum activation rate a when crossing the concentration threshold t, with non-linearity exponent n.


Figure 1: Functions fitted to experimental data for repressor and activator constructs. (a) Data measured for TAL-A:KRAB (blue) and TAL-B:KRAB (red) constructs and averaged afterwards (black). (b) Data measured for TAL-A:VP16 (blue) and TAL-B:VP16 (red) constructs and averaged afterwards (black).

Inducible system

The inducible system in both switches is built upon two different inducer molecules. In the mutual repressor switch, we employ a pristinamycin-inducible protein (PIP) with KRAB repressor domain. After the introduction of pristinamycin, PIP:KRAB is inactivated and thus unbound from its binding site at the pCMV promoter. The concentration of active PIP:KRAB is hence inversely proportional to the pristinamycin concentration:


Consequently, the transcription rate of the corresponding promoter is proportional to the concentration of active PIP:KRAB :


where k is the maximum transcription rate, f scaling factor and alpha the fraction of inactivated transcription rate. The increasing concentration of active PIP:KRAB causes the resulting rate r to approach the basal rate, with half the maximum rate concentration determined by the threshold K. In an analogue manner, the erythromycin and E:KRAB inducer system was modeled.

Stability analysis

For the purpose of stability analysis, the simulation was run multiple times with varying pairs of parameters and producing a two dimensional parameter map. For example, with varying plasmid input dosages (other things being equal), one or the other state might become not reachable. For an illustrative example, see Figure 2.

For every instance of the simulation (a colored point in Figure 2), the outcome results were examined. During the course of a simulation, a steady state is defined as a point in phase space (all possible pairs of the two reporter concentrations) where concentrations of both reporter protein concentrations do not change, i.e.:



Figure 2. Parameter map of non-stimulated system (no inducer introduction) for parameters: [A]_pCMV_TAL-B:KRAB_NEPTUN dosage (x-axis) and [B]_pCMV_TAL-A:KRAB-mCitrine dosage (y-axis), on the interval 100-500 ng. Notice the red ambiguous states where both parameter values are equal.
The list of steady state points is achieved and analyzed for each instance of a simulation. A valid state A is defined when BFP concentration crosses a predefined threshold th while at the same time the mCitrine concentration is below th. Valid state B is defined analogously for mCitrine. If both stable states are reached during a simulation instance run, the system is labeled bistable.

If at any stable state points, both concentrations cross the threshold simultaneously or remain below threshold simultaneously, the state point and the system are defined ambiguous. In case no stable state points are found during the simulation, the system is labeled as not valid.

Summing up, five possible outcomes for each simulation instance were defined and placed on the parameter map (using separate colors to differentiate between them):

  • Bistable; The system reached both stable states on a given time interval.
  • Monostable A; The system reached expressed stable state A on a given time interval.
  • Monostable B; The system only reached stable state B on a given time interval.
  • Ambigous; The system expressed reached states simultaneously during a given time interval.
  • Not valid; The system did not reach any stable states during a given time interval.

Results

Summary


The two switches were tested and compared in various aspects. Based on intuition and simulations described in previous sections we predicted better behavior of the switch with a positive feedback loop in terms of stability, robustness, and responsiveness.

The addition of a positive feedback loop contributed strongly to stability, producing two orders of magnitude higher concentrations of stable state. Consequently, the minimal time an inducer had to be present to perform a successful state transition was twice as long, hence having slower responsiveness. Also, the time required to perform the transition increased by 25 %, due to higher stable concentration levels.

The second switch proved more robust and exhibited the absence of concentration fluctuations at the inducer removal. The initial state of the mutual repressor switch was heavily influenced by the initial plasmid dosage. The former also contributed to the overall stability, since the dosage of plasmid with TAL-A:KRAB constructs should not exceed that of TAL-B:KRAB constructs by more than 1.5-fold and vice versa. In the case of positive feedback loop switch, that same threshold was 2-fold.

We also tested the system properties under various non-linearity coefficients. Mutual repressor switch has been proven of being dependent on non-linearity of repressor constructs, requiring a non-linearity coefficient of at least 2, while this was not the case with positive feedback loop switch which has shown bistable behavior under all non-linearity coefficients greater of equal to 1. The last fact is in agreement with the previous mathematical predictions of a feedback loop being able to replace the non-linearity as a necessary condition for bistability.

Fold repression and fold induction inference


We have quantified the effect of TAL effector constructs by performing the luciferase reporter activity measurements with varying ratios of TAL effector and reporter constructs. To account for all input ratios, we fitted the data to a continuous function. Due to variations in the experiments, we took two representative measurement samples for activator and repressor constructs and averaged the resulting continuous functions afterwards. The particular data measurements were taken prior to further experiments with more complex constructs. The model outcome thus helped in predicting the optimal input mass ratios of the final switch constructs.

Figure 3 shows the luciferase reporter activity measurement under various ratios of TAL:KRAB repressor and reporter constructs. With increasing the input mass of repressor constructs, the resulting luciferase activity converges towards 8.5 % (TAL-A:KRAB) and 1.5 % (TAL-B:KRAB) of the unrepressed reporter activity. Thus, we can describe TAL-A:KRAB effect on the system with the following function:


while for TAL-B:KRAB we get:


where x is repressor/reporter construct ratio and q accounts for remaining transcription rate (fold repression). The function is plotted in Figure 3a.

Figure 4 shows the luciferase reporter activity measurement under various ratios of TAL:VP16 activator and reporter constructs. With increasing the input mass of repressor constructs, the resulting luciferase activity converges towards 2000-fold (TAL-A:VP16) and 1800-fold (TAL-B:KRAB) increased reporter activity. Thus, we can describe TAL-A:VP16 effect on the system with the following function:


while for TAL-B:VP16 we get:


where x is activator/reporter construct ratio and a accounts for factor of increased transcription rate (fold induction). The function is plotted in Figure 3b.


Results: Mutual repressor switch


To evaluate the performance of the switch, we ran a simulation for a sufficiently long time that the system can reach both steady states (Figures 5,6). The introduction of inducer pristinamycin and erithromycin switched the system to produce reporters BFP or mCitrinee state respectively (Figure 5ab). Upon introduction of the inducer, a peak in the corresponding reporter concentration arises. After the inducer removal, the reporter and TAL:KRAB concentration (Figure 5c) decrease to some degree, the reason being the reduced activity of the corresponding inducible promoter. The resulting concentration remains sufficiently high to repress the opposing state and for the system to remain in the desired state after the inducer signal. Peak concentrations at steady states for reporters were of the order of 800 nM. Time to switch from on state to another was around 2000 min. In both states, the system stabilized well above the define threshold (Figure 5d).

Stability analysis: Mutual repressor switch


Stability analysis revealed more characteristics of the switch, (color encoding is described in detail in Methods_modeling). Without introduction of an inducer within a given time interval it is not determined by design in which state the system will end up. Various input ratios of plasmids containing TAL-A:KRAB and TAL-B:KRAB constructs were evaluated. Equal input masses for both plasmids resulted in ambiguous states as expected with even a 0.5 % difference being enough to put the system into the corresponding state (Figure 3a).

State transition properties were characterized in terms of duration and time difference in the introduction of the two inducers (Figure 3cd). The parameters were chosen so that the system exhibits one state transition in a time interval of 8000 minutes with the first inducer introduced at t1=0, for a d1=500 minutes duration. The second inducer was introduced at all points on time interval t2 = [1000, 5000] minutes, while the inducer duration was on the interval d2 = [0, 500] minutes. The results show a required delay of at least 3000 minutes before the second inducer could be introduced so that the first reporter reaches a stable state.

The minimal required duration for inducer presence to switch from BFP to mCitrine state or vice versa was 109 minutes. With the signal of that duration, 3950 minutes were required to perform a complete switch. The maximum tested inducer presence duration of 500 minutes required 3136 minutes for the state transition. The longer transition time than at the beginning of the simulation is due to the fact that the transition is performed between two active states of high concentrations, rather than from both concentrations being low.

Furthermore, to ensure the proper functionality of the switch, rapid introduction of an inducer is required, since large difference in input masses can result in the system not being able to switch between the states. In particular, to perform a successful mCitrine to BFP transition, the dosage of constructs containing TAL-A:KRAB should not exceed that of constructs containing TAL-B:KRAB by more than 192 %. On the other hand, the dosage of constructs containing TAL-B:KRAB should not exceed that of constructs containing TAL-A:KRAB by more than 241 %. In the opposite direction, to perform a successful BFP to mCitrine transition, the dosage of constructs containing TAL-A:KRAB should not exceed that of constructs containing TAL-B:KRAB by more than 162%. On the other hand, the dosage of constructs containing TAL-B:KRAB should not exceed that of constructs containing TAL-A:KRAB by more than 222.9%. Summing up, it is safe to say that the switch will perform successfully if no plasmid dosage exceeds the dosage of the opposite construct by more than 150 %. Also, to perform a complete switch, the dosage of Pristinamycin/Erithromicyn inducible constructs shall not be less that 25% of the dosage of reporter plasmids (Figure 3gh).

Various sources examined non-linearity as a condition for bistability (Chatterjee et. al 2008, Malphettes et al. 2006). The interval [1.0,5.0] of Hill coefficient for TAL-B:KRAB and TAL-A:KRAB proteins was examined (Figure 3b). Bistability was achieved for coefficients greater than 2 for both transcription factors.

Results:Positive feedback loop switch


The addition of a positive feedback loop to the circuit proved beneficial to the overall performance of the system (Figure 4). The most notable are the absence of fluctuations on the inducer removal and two orders of magnitude higher stable state concentration of the active reporters (Figure 4a), due to the presence of the positive feedback loop. Consequently, repression of the currently inactive constructs is much more effective, which is proven by not noticeable activity of repressed promoters. The concentration of inactive (repressed) reporter decreased by four to five orders of magnitude (Figure 4d). Fluctuations remain in the concentrations of TAL-KRAB and TAL-VP16 constructs, but do not affect the state of the system (Figure 4d). The state transitions are successful in both directions, with effectively the same active concentrations.

Stability analysis:Positive feedback loop switch


Stability analysis confirms the improvement gained from the positive feedback loop (Figure 6). In the absence of inducers the system can randomly move into one state. Larger ratios of the two pairs of switch plasmids introduce a bias, but at ratios above 5:1 the switch cannot perform the state transition.

State transition properties were characterized in terms of the duration and time difference in the introduction of the inducers (Figure 6ab). The parameters were chosen so that the system exhibits one state transition in a time interval of 8000 minutes with the first inducer introduced at t1=0, for a d1=500 minutes duration. The second inducer was introduced at all points in time interval t2 = [1000, 5000] minutes, while the inducer duration was on the interval d2 = [0, 500] minutes. The results show that the required delay must be at least 2169 minutes before the second inducer could be introduced so that the first reporter reaches a stable state, which is 72 % of the time compared to mutual repressor switch.

The minimal required duration for an inducer to switch from BFP to mCitrine state or vice versa was 220 minutes. With the signal of that duration, 4814 minutes were required to perform a complete switch. The maximal tested duration of 500 minutes required 4255 minutes for the state transition. The longer transition times than at the beginning of the simulation are again due to the fact that the transition is performed between the two active states of high concentrations, rather than from both concentrations being low. Switching from an already active state takes longer time than in the case of mutual repressor switch, since significantly higher concentrations of proteins representing an active state. Also, an interesting duration parameter range of 109-200 minutes appears where the system could reach the undesired ambiguous state.

Furthermore, to ensure the proper functionality of the switch, a very rapid introduction of an inducer is required (Figure 6cd). In particular, to perform a successful mCitrine to BFP transition, the dosage of constructs containing TAL-A:KRAB should not exceed that of constructs containing TAL-B:KRAB by more than 208 %. On the other hand, the dosage of constructs containing TAL-B:KRAB should not exceed that of constructs containing TAL-A:KRAB by more than 204 %. In the opposite direction, to perform a successful BFP to mCitrine transition, the dosage of constructs containing TAL-A:KRAB should not exceed that of constructs containing TAL-B:KRAB by more than 202 %. On the other hand, the dosage of constructs containing TAL-B:KRAB should not exceed that of constructs containing TAL-A:KRAB by more than 202 %. Summing up, it is safe to say that the switch will perform sucessfully if no plasmid dosage exceeds the dosage with opposite construct by more than 200 %, which is a realistically achievable assumption. Due to the addition of positive feedback the threshold ratios have a significantly smaller variation than in the mutual repressor switch case, hence improving the robustness. Also, to perform a complete switch of state, the dosage of Pristinamycin/Erithromicyn inducible constructs shall not be less than 12.5% the dosage of the reporter plasmids, which is half the value of the mutual repressor switch (Figure 6ef).

Furthermore, the system proved stable over the whole interval [1.0, 10.0] for transcription factor non-linearity coefficients, confirming that the positive feedback is able to introduce a form of non-linearity. Hence, positive feedback can compensate for explicit non-linearity of transcription factors in the case of our design of the switch.

Mutual repressor switch model formalization

Indexing of the constructs is described in List~1. The observed chemical species in the system are listed in Table~1, while the parameter values are found in Table~1. Ordinary diferential equations for the mutual repressor switch model are Eq. 1-22.
Number Used construct
1 [A]_pCMV_TAL-B:KRAB_BFP
2 [B]_pCMV_TAL-A:KRAB_mCitrine
3 pCMV_[PIR]_TAL-B:KRAB
4 pCMV_[ETR]_TAL-B:KRAB
5 pCMV_PIP:KRAB
6 pCMV_E:KRAB
Symbol Chemical species
[E:KRABm] Erythromycin binding protein (mRNA)
[E:KRABp] Erythromycin binding protein
[E:KRABa] Erythromycin - E:KRAB complex
[PIP:KRABm] Pristinamicyn binding protein (mRNA)
[PIP:KRABp] Pristinamicyn binding protein
[PIP:KRABa] Pristinamicyn - PIP:KRAB complex
[Pc] Pristinamycin inducer
[Rg] Rapamicyn inducer
[TAL-B:KRABm] TAL-B:KRAB repressor protein (mRNA)
[TAL-B:KRABp] TAL-B:KRAB repressor protein
[TAL-A:KRABm] TAL-A:KRAB repressor protein (mRNA)
[TAL-A:KRABp] TAL-A:KRAB repressor protein
[BFPm] BFP reporter protein (mRNA)
[BFPp] BFP reporter protein
[MCTm] mCITRIN reporter protein (mRNA)
[MCTp] mCITRIN reporter protein
Symbol Parameter Initial value Units Source/reference
G1 Plasmid 1 dosage 190.0 ng Literature data (Tigges et. al, 2006)
G2 Plasmid 2 dosage 180.0 ng Literature data (Tigges et. al, 2006)
G3 Plasmid 3 dosage 180.0 ng Literature data (Tigges et. al, 2006)
G4 Plasmid 4 dosage 180.0 ng Literature data (Tigges et. al, 2006)
G5 Plasmid 5 dosage 180.0 ng Literature data (Tigges et. al, 2006)
G6 Plasmid 6 dosage 180.0 ng Literature data (Tigges et. al, 2006)
k1 Plasmid 1 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k2 Plasmid 2 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k3 Plasmid 3 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k4 Plasmid 4 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k5 Plasmid 5 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k6 Plasmid 6 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
sB TAL-B:KRAB scaling constant - - Calculated from experimental data
sA TAL-A:KRAB scaling constant - - Calculated from experimental data
nB TAL-B:KRAB Hill coefficient 3.0 - Literature data [3]
nA TAL-A:KRAB Hill coefficient 3.0 - Literature data [3]
tB TAL-B threshold concentration 100.0 nM Adjusted by user defined state threshold
tA TAL-A threshold concentration 100.0 nM Adjusted by user defined state threshold
dm mRNA degradation rate 0.0173 mRNA/min Literature data (Tigges et. al, 2006)
dp Protein degradation rate 0.0058 nM Literature data (Tigges et. al, 2006)
tp Translation rate 0.2 nM Literature data (Tigges et. al, 2006)
Apc Pristinamicyn-PIP:KRAB binding affinity 1.0 - Literature data (Tigges et. al, 2006)
Aec Erythromycin-E:KRAB binding affinity 1.0 - Indentical to Apc
Kpc Promoter-PIP:KRAB binding affinity 1.0 - Literature data (Tigges et. al, 2006)
Krc Promoter-E:KRAB binding affinity 1.0 - Identical to Kpc
Alphapc Basal activity of PIP:KRAB inducible promoter 0.085 nM Literature data (Tigges et. al, 2006)
Alphaec Basal activity of E:KRAB inducible promoter 0.025 nM Calculated from experimental data
npc PIP:KRAB Cooperativity coefficient 2.0 - Literature data (Tigges et. al, 2006)
nec E:KRAB Cooperativity coefficient 2.0 - Identical to npc
fv Concentration scaling factor 92500 - Literature data (Tigges et. al, 2006)
tau Active state concentration threshold 100.0 nM Adjustable user defined state threshold

Model ordinary differential equations

Inducible system


The Switch


Reporters


The positive feedback loop switch model formalization

Indexing of the constructs is described in List~2. The observed chemical species in the system are listed in Table~1, while the parameter values are found in Table~2. Ordinary diferential equations for the mutual repressor switch model are Eq. 23-47.
Number Used construct
1 [A]_pCMV_TAL-B:KRAB_TAL-A:VP16_BFP
2 [B]_pCMV_TAL-A:KRAB_TAL-B:VP16_mCitrine
3 pCMV_[PIR]_TAL-B:KRAB_TAL-A:VP16
4 pCMV_[ETR]_TAL-A:KRAB_TAL-B:VP16
5 pCMV_PIP:KRAB_E:KRAB
Symbol Chemical species
[E:KRABm] Erythromycin binding protein (mRNA)
[E:KRABp] Erythromycin binding protein
[E:KRABa] Erythromycin - E:KRAB complex
[PIP:KRABm] Pristinamicyn binding protein (mRNA)
[PIP:KRABp] Pristinamicyn binding protein
[PIP:KRABa] Pristinamicyn - PIP:KRAB complex
[Pc] Pristinamycin inducer
[Rg] Rapamicyn inducer
[TAL-B:KRABm] Tal-BKrab repressor protein (mRNA)
[TAL-B:KRABp] Tal-BKrab repressor protein
[TAL-A:KRABm] Tal-AKrab repressor protein (mRNA)
[TAL-A:KRABp] Tal-AKrab repressor protein
[TAL-B:VP16m] Tal-B:Vp16 activator protein (mRNA)
[TAL-B:VP16p] Tal-B:Vp16 activator protein
[TAL-A:VP16m] Tal-AVp16 activator protein (mRNA)
[TAL-A:VP16p] Tal-AVp16 activator protein
[BFPm] BFP reporter protein (mRNA)
[BFPp] BFP reporter protein
[MCTm] mCITRIN reporter protein (mRNA)
[MCTp] mCITRIN reporter protein
Symbol Parameter Initial value Units Source/reference
G1 Plasmid 1 dosage 190.0 ng Literature data (Tigges et. al, 2006)
G2 Plasmid 2 dosage 180.0 ng Literature data (Tigges et. al, 2006)
G3 Plasmid 3 dosage 180.0 ng Literature data (Tigges et. al, 2006)
G4 Plasmid 4 dosage 180.0 ng Literature data (Tigges et. al, 2006)
G5 Plasmid 5 dosage 180.0 ng Literature data (Tigges et. al, 2006)
G6 Plasmid 6 dosage 180.0 ng Literature data (Tigges et. al, 2006)
k1 Plasmid 1 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k2 Plasmid 2 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k3 Plasmid 3 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k4 Plasmid 4 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k5 Plasmid 5 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k6 Plasmid 6 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
sB TAL-B:KRAB scaling constant - - Calculated from experimental data
sA TAL-A:KRAB scaling constant - - Calculated from experimental data
nB TAL-B:KRAB Hill coefficient 3.0 - Literature data [3]
nA TAL-A:KRAB Hill coefficient 3.0 - Literature data [3]
tB TAL-B threshold concentration 100.0 nM Adjusted by user defined state threshold
tA TAL-A threshold concentration 100.0 nM Adjusted by user defined state threshold
dm mRNA degradation rate 0.0173 mRNA/min Literature data (Tigges et. al, 2006)
dp Protein degradation rate 0.0058 nM Literature data (Tigges et. al, 2006)
tp Translation rate 0.2 nM Literature data (Tigges et. al, 2006)
Apc Pristinamicyn-PIP:KRAB binding affinity 1.0 - Literature data (Tigges et. al, 2006)
Aec Erythromycin-E:KRAB binding affinity 1.0 - Indentical to Apc
Kpc Promoter-PIP:KRAB binding affinity 1.0 - Literature data (Tigges et. al, 2006)
Krc Promoter-E:KRAB binding affinity 1.0 - Identical to Kpc
Alphapc Basal activity of PIP:KRAB inducible promoter 0.085 nM Literature data (Tigges et. al, 2006)
Alphaec Basal activity of E:KRAB inducible promoter 0.025 nM Calculated from experimental data
npc PIP:KRAB Cooperativity coefficient 2.0 - Literature data (Tigges et. al, 2006)
nec E:KRAB Cooperativity coefficient 2.0 - Identical to npc
fv Concentration scaling factor 92500 - Literature data (Tigges et. al, 2006)
tau Active state concentration threshold 100.0 nM Adjustable user defined state threshold
Symbol Parameter Initial value Units Source/reference
G1 Plasmid 1 dosage 190.0 ng Literature data (Tigges et. al, 2006)
G2 Plasmid 2 dosage 180.0 ng Literature data (Tigges et. al, 2006)
G3 Plasmid 3 dosage 180.0 ng Literature data (Tigges et. al, 2006)
G4 Plasmid 4 dosage 180.0 ng Literature data (Tigges et. al, 2006)
G5 Plasmid 5 dosage 180.0 ng Literature data (Tigges et. al, 2006)
k1 Plasmid 1 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k2 Plasmid 2 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k3 Plasmid 3 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k4 Plasmid 4 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
k5 Plasmid 5 basal transcritiption rate 30.0 mRNA/min Literature data (Tigges et. al, 2006)
aB TAL-B:Vp16 activation rate - - Calculated from experimental data
aA TAL-A:VP16 activation rate - - Calculated from experimental data
sB TAL-B:KRAB scaling constant - - Calculated from experimental data
sA TAL-A:KRAB scaling constant - - Calculated from experimental data
nB TAL-B:KRAB Hill coefficient 3.0 - Literature data [3]
nA TAL-A:KRAB Hill coefficient 3.0 - Literature data [3]
tB TAL-B threshold concentration 100.0 nM Adjusted by user defined state threshold
tA TAL-A threshold concentration 100.0 nM Adjusted by user defined state threshold
dm mRNA degradation rate 0.0173 mRNA/min Literature data (Tigges et. al, 2006)
dp Protein degradation rate 0.0058 nM Literature data (Tigges et. al, 2006)
tp Translation rate 0.2 nM Literature data (Tigges et. al, 2006)
Apc Pristinamicyn-PIP:KRAB binding affinity 1.0 - Literature data (Tigges et. al, 2006)
Aec Erythromycin-E:KRAB binding affinity 1.0 - Indentical to Apc
Kpc Promoter-PIP:KRAB binding affinity 1.0 - Literature data (Tigges et. al, 2006)
Krc Promoter-E:KRAB binding affinity 1.0 - Identical to Kpc
Alphapc Basal activity of PIP:KRAB inducible promoter 0.085 nM Literature data (Tigges et. al, 2006)
Alphaec Basal activity of E:KRAB inducible promoter 0.025 nM Calculated from experimental data
npc PIP:KRAB Cooperativity coefficient 2.0 - Literature data (Tigges et. al, 2006)
nec E:KRAB Cooperativity coefficient 2.0 - Identical to npc
fv Concentration scaling factor 92500 - Literature data (Tigges et. al, 2006)
tau Active state concentration threshold 100.0 nM Adjustable user defined state threshold

Model ordinary differential equations

Inducible system


The Switch


Reporters


References

Alon U. (2007), An introduction to systems biology: design principles of biological circuits. Chapman & Hall/CRC.

Chatterjee A., Kaznessis Y., and Hu W. (2006) Tweaking biological switches through a better understanding of bistability behavior. Current opinion in biotechnology, 19(5):475-81.

Gardner T., Cantor C., and Collins J. (2000) Construction of a genetic toggle switch in Escherichia coli. Nature, 403(6767):339-42.

Batard P., and Wurm F. (2001) Transfer of high copy number plasmid into mammalian cells by calcium phosphate transfection. Gene: An international Journal on Genes and Genomes, 270:61-68.

Malphettes L., and Fussenegger M. (2006) Impact of RNA interference on gene networks. Metabolic engineering, 8(6):672-83.

Tigges M., Marquez-Lago T., Stelling J., and Fussenegger M. (2009) A tunable synthetic mammalian oscillator. Nature, 457(7227):309-12.

Zakharova A., Kurths J., Vadivasova T., and Koseska A. (2011) Analysing dynamical behavior of cellular networks via stochastic bifurcations. PloS one, 6(5):e19696.

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