Conflict of Interest - A POPULATION-BASED TEMPORAL LOGIC GATE FOR TIMING AND RECORDING OF CHEMI

A POPULATION-BASED TEMPORAL LOGIC GATE FOR TIMING AND RECORDING OF CHEMICAL EVENTS

3.8 Conflict of Interest

The authors declare that they have no conflict of interest.

Parameters used for simulations

The parameters were chosen to be in biological orders of magnitude. Tetrameteri- zation of the integrase is represented with the expression

α_i(Int∗):=kflip∗

Int∗(Int∗−1)(Int∗−2)(Int∗−3)

K⁴_d∗+K_d∗³Int∗+K_d∗²Int∗(Int∗−1)+Kd∗Int∗(Int∗−1)(Int∗−2)+Int∗(Int∗−1)(Int∗−2)(Int∗−3)

(3.4) fori =1,2,3 and∗ = A,B(seeTetramerization of integrasein Appendix Section 12.2 for the derivation, and Fig. S1).

0 20 40 60 80 100

Number of integrase monomers, Int_* 0

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Propensity function, αi(Int*)

Figure ED-S1: Visualizing the nonlinear term for integrase tetramerization (Eq.

3.4). The propensity function, αi(Int∗), as a function of integrase monomers, Int∗, is zero until at least four monomers are present. Parameters for flipping and dissociation constant arek_flip∗ = 0.4 hr⁻¹, andK_d∗ =10 molecules.

Parameter Value Units α1 See equation (3.4)

α₂ See equation (3.4) α₃ See equation (3.4)

δA kdeg(IntA)

δB k_deg(IntB)

γA









k_prodA+k_leakA, if induceraexists k_leakA, if no inducer present γB









k_prodB+ k_leakB, if inducerbexists k_leakB, if no inducer present

kprodA,B 50 (µm³·hr)⁻¹

k_deg 0.3 hr⁻¹

k_flipA 0.4 hr⁻¹

k_flipB 0.4 hr⁻¹

k_leakA 0 (µm³·hr)⁻¹

k_leakB 0 (µm³·hr)⁻¹

KdA 10 molecules

K_dB 10 molecules

Table 3.1: Initial Markov transition rates and parameters. We define the rate of DNA state transitions as α1, α2 and α3 using the rate of DNA flipping for a unit concentration of IntA(k_flipA) and IntB(k_flipB). The notations IntA and IntB denote the copy number of each integrase, and [So] = 1([Sa] = 1) if the DNA state is So(S_a) and [S_o] =0([S_a]= 0) otherwise. The production and degradation rates of the integrases are defined byγandδ, respectively. k_prodAandk_prodB are the protein production rate constants, and k_leakAand k_leakB are the basal leaky expression rate constants. We assume the plasmid copy number is proportional to the volume of a cell. In this paper, we use 1 µm³ (1 femtoliter) as the estimated volume of a singleE. colicell. The integrase degradation/dilution rate constant k_deg = 0.3hr⁻¹ sets the protein half-life to approximately 2.3 hours. The binding constant,Kd∗ was estimated based on Bxb1 Kd binding constants 70 nM (Singh et al, 2013). When converted into molecules in 1 femtoliter volume, this translated to 7 molecules (70nM× ¹⁰²³^molecules

L ×10⁻⁹× ^1L

10¹⁵µm³ = 7 copies.)

Figure ED-S2: Example of individual cell trajectories and total summed population from stochastic simulations (∆t = 5h). A) Individual simulated cell trajectories for the possible cell states. A sample of 100 cells out of the population of 5000 has been shown here for clarity. The panels, from top to bottom, show time and duration of induction, cells in state So (blue), cells in state Sa (red), cells in state Sb (yellow), cells in stateSab(purple), copies per cell of integrase A (green), and copies per cell of integrase B (sky blue). B) Summed totals of all possible DNA and protein states for all 5000 cells.

Characterization of inducer separation time

A B C

D E F

0 10 Time20 30 40

Number of cells in Sa state(N) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

A then B scenario:

Cells in state S_a (A only)

Delta t =0 Delta t =1 Delta t =2 Delta t =3 Delta t =4 Delta t =5 Delta t =6 Delta t =7 Delta t =8 Delta t =9 Delta t =10 Delta t =A only

0 10 Time20 30 40

Number of cells in Sa state(N) 0 200 400 600 800 1000 1200 1400

B then A scenario:

Cells in state S_a (A only)

Delta t =0 Delta t =1 Delta t =2 Delta t =3 Delta t =4 Delta t =5 Delta t =6 Delta t =7 Delta t =8 Delta t =9 Delta t =10 Delta t =Bonly

0 10 Time20 30 40

Number of cells in Sb state(N) 0 500 1000 1500 2000 2500 3000

A then B scenario Cells in S_b state (B first)

Delta t =0 Delta t =1 Delta t =2 Delta t =3 Delta t =4 Delta t =5 Delta t =6 Delta t =7 Delta t =8 Delta t =9 Delta t =10 Delta t =Aonly

0 10 Time20 30 40

Number of cells in Sb state(N) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

B then A scenario Cells in S_b state (B first)

Delta t =0 Delta t =1 Delta t =2 Delta t =3 Delta t =4 Delta t =5 Delta t =6 Delta t =7 Delta t =8 Delta t =9 Delta t =10 Delta t =Bonly

0 10 Time20 30 40

Number of cells in So state (N) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

A then B scenario Cells in S_o (Initial state)

Delta t =0 Delta t =1 Delta t =2 Delta t =3 Delta t =4 Delta t =5 Delta t =6 Delta t =7 Delta t =8 Delta t =9 Delta t =10 Delta t =Aonly

0 10 Time20 30 40

Number of cells in So state (N) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

B then A scenario Cells in S_o (Initial state)

Delta t =0 Delta t =1 Delta t =2 Delta t =3 Delta t =4 Delta t =5 Delta t =6 Delta t =7 Delta t =8 Delta t =9 Delta t =10 Delta t =Bonly

Figure ED-S3: Effect of varying ∆t on number of Sa, Sb, and So state cells in simulation (Supplementary to Figure 3 in the main text). For each value of ∆t, a population of 5000 individual cell trajectories was generated and summed. A) Sa

cell counts for Eabevent. In the case of a only, 100% of the cells become Sa. For the other states, the cell count drops off at time ∆t as Satransition into Sab. B) Sb

state cells forEab. The number ofSbcells that transition is a function of available So cells left at time∆t. With high∆t, the most cells are already inSa. C)Sostate cells for Eab decrease exponentially with time as they convert into either Sa orSo. D)Sastate cell count with anEbaevent are inversely proportional to∆t. E)Sbstate cells gain fractional dominance with increasing∆tduring with anEba event. In the case ofb only, 100% of the cells becomeSb. F)Sostate cells decrease exponentially withEba event as well.

Time (h)

0 10 20 30

RFP/OD

x10

0 0.5 1 1.5 2 2.5

Time (h)

0 10 20 30

RFP/OD

x 10

0 0.5 1 1.5 2 2.5

Fraction of max RFP

0 0.2 0.4 0.6 0.8 1

RFP Population (%)

0 10 20 30 40 50 60 70

0 2 4 6 8 10

Inducer separation time, ∆t (h) 0 2 4 6 8 10

Inducer separation time, ∆t (h) E_ab

E_ba E_ab

E_ba

a only

b only

a only

b only

No inducer a only

∆t = 0h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h

∆t = 7h

∆t = 1h

∆t = 8h

No inducer

∆t = 0h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h

∆t = 7h

∆t = 1h

∆t = 8h b only

C D

Figure ED-S4: RFP expression forin vivoexperiments with increasing∆t(Supple- mentary to Figure 4 in the main text). A) RFP expression as a proxy forSastate cells when population is exposed toEab. B) RFP expression when the inverseEba event occurs. C) Endpoint RFP bulk fluorescence measurement of cultures as a function of∆t. In an infinite step induction experiment, we expect no cells to be expressing RFP since all Sa cells become Sab. However, cultures with later ∆t values spend up to 8 hours in Sa and build up a lot of RFP that does not completely dilute even upon switching to Sab. D) Flow cytometry counts of RFP population. The flow cytometry shows that a high percentage of cells are expressing a low amount of RFP.

Quadrant analysis of RFP vs GFP populations shows that these RFP-expressing cells are all in Q2, the transitory quadrant in which cells have switched to Sab but still have undiluted RFP molecules (Figure EV1). See also Appendix Figure ED-S12 for conversion between flow populations and bulk intensity measurements.

Time (h)

-10 0 10 20 30

GFP/OD

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Time (h)

0 5 10 15

GFP/OD

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 No inducer

a only

∆t = 0h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h

∆t = 7h

∆t = 1h

∆t = 8h

Aligned by inducer b induction time Aligned by inducer b induction time

A B

∆t = 0h

∆t = 1h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5-8h

Figure ED-S5: In vivo GFP expression curves aligned by ∆t (Supplementary to Figure 4 in the main text). A) Curves have been aligned by ∆t such that cell switching toSaband GFP expression all starts at time 0. B) Zoomed in panel shows different slopes of the various∆tcurves.

Time (h)

0 5 10 15 20 25 30

GFP/OD

0 1000 2000 3000 4000 5000 6000 7000

8000 Delta t = 2h

Delta t = 3h Delta t = 4h Delta t = 5h Delta t = 6h Delta t = 7h Delta t = 8h

Time (h)

0 5 10 15 20 25 30

GFP/OD

0 1000 2000 3000 4000 5000 6000 7000

8000 Delta t = 2h

Delta t = 3h Delta t = 4h Delta t = 5h Delta t = 6h Delta t = 7h Delta t = 8h

Time (h)

0 5 10 15 20 25 30

RFP/OD

#10⁴

0 0.5 1 1.5 2 2.5

3 _{No inducer}

A only Delta t = 0h Delta t = 1h Delta t = 2h Delta t = 3h Delta t = 4h Delta t = 5h Delta t = 6h Delta t = 7h Delta t = 8h

Time (h)

0 5 10 15 20 25 30

RFP/OD

#10⁴

0 0.5 1 1.5 2 2.5

3 _{No inducer}

B only Delta t = 0h Delta t = 1h Delta t = 2h Delta t = 3h Delta t = 4h Delta t = 5h Delta t = 6h Delta t = 7h Delta T = 8h

C D

Figure ED-S6: Time-course data for Figure 4 with more separated color scheme.

The color gradient used in Figure 4 can make it difficult to distinguish individual curves, and so here we have more color-separated plots. A) GFP fluorescence with eventEab. B) GFP fluorescence with eventEba. C) RFP fluorescence withEab. D) RFP fluorescence with Eba.

Time (h)

0 5 10 15 20 25 30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1 _{No inducer}

A only Delta t = 0h Delta t = 1h Delta t = 2h Delta t = 3h Delta t = 4h Delta t = 5h Delta t = 6h Delta t = 7h Delta t = 8h

Time (h)

0 5 10 15 20 25 30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1 _{No inducer}

A only Delta t = 0h Delta t = 1h Delta t = 2h Delta t = 3h Delta t = 4h Delta t = 5h Delta t = 6h Delta t = 7h Delta t = 8h

Figure ED-S7: OD growth curves forin vivoexperiments with increasing∆t(Sup- plementary to Figure 4 in the main text). Growth curves are fairly linear due to growth in M9CA minimal media at 37C. A) OD growth curves for cells subjected toEabevent. B) OD growth curves for cells subjected toEba event

0.002 0.005

0.61 99.4

0.43 2.55

58.2 38.8

23.4 2.07

1.21 73.3

29.4 2.88

1.17 66.5

35.6 4.65

1.05 58.7

38.0 7.80

1.07 53.1

40.9 13.7

1.27 44.1

30.7 23.6

1.38 44.4

19.7 32.0

1.45 46.8

9.49 43.0

1.81 45.7

4.54 50.5

2.07 42.9

0.002 0.004

0.83 99.2

0.093 0.024

1.68 98.2

23.8 2.20

1.35 72.6

22.8 2.04

1.33 73.9

20.9 1.79

1.36 75.9

18.9 1.73

1.54 77.8

9.44 0.77

1.87 87.9

1.55 0.19

2.44 95.8

0.49 0.063

2.63 96.8

0.64 0.10

2.70 96.6

0.61 0.081

2.76 96.5

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

Q1 Q2

Q4 Q3

10⁵ 10⁴ 10³ 10² 10¹ 0

GFP

10⁵ 10⁴ 10³ 10² 10¹

0 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴

GFP

RFP RFP RFP RFP RFP RFP RFP RFP RFP RFP RFP

∆t = 0h ∆t = 1h ∆t = 2h ∆t = 3h ∆t = 4h ∆t = 5h ∆t = 6h ∆t = 7h ∆t = 8h

a then b

b then a

No inducers

b only a only

Figure ED-S8: Flow cytometry populations, RFP vs GFP (Fig. 4). Populations are split into quadrants Q1 (GFP only, Sab), Q2 (GFP + RFP, Sab), Q3 (RFP only, Sa), and Q4 (non-fluorescent, So+ Sb.) ∼ 100,000 cells were analyzed for each population.

0.008 100.0

3.17

96.8 74.4 25.6 67.6 32.4 59.6 40.4 54.0 46.0 45.3 54.7 45.6 54.4 48.2 51.8 47.4 52.6 44.9 55.1

0.010 100.0

0.13

99.9 73.9 26.1 75.1 24.9 77.2 22.8 79.2 20.8 89.7 10.3 98.2 1.77 99.4 0.57 99.2 0.76 99.3 0.71

GFP- GFP+

Cell Count

10⁴ 10³ 10²

10¹ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴

Cell Count

GFP GFP GFP GFP GFP GFP GFP GFP GFP GFP GFP

0 5.0K 10K 15K

GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+

GFP- GFP+

GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+GFP- GFP+

∆t = 0h ∆t = 1h ∆t = 2h ∆t = 3h ∆t = 4h ∆t = 5h ∆t = 6h ∆t = 7h ∆t = 8h

a then b

b then a

No inducers

b only a only

Figure ED-S9: Flow cytometry GFP histograms (Fig. 4). ∼ 100,000 cells were analyzed for each population.

1.13 98.9

61.2

38.8 94.5 5.47 93.6 6.42 91.4 8.61 87.5 12.5 80.2 19.8 70.0 30.0 62.4 37.6 52.6 47.4 45.9 54.1

1.44

98.6 97.0 3.04 94.3 5.71 94.4 5.55 94.6 5.40 94.6 5.45 95.4 4.59 95.5 4.49 95.3 4.71 95.1 4.86 95.0 5.01

RFP- RFP+

Cell Count

10⁴ 10³ 10²

10¹ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴ 10¹10²10³10⁴

Cell Count

RFP RFP RFP RFP RFP RFP RFP RFP RFP RFP RFP

0 2.0K 4.0K 6.0K 8.0K

RFP- RFP+RFP- RFP+ RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+

RFP- RFP+

RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+RFP- RFP+

∆t = 0h ∆t = 1h ∆t = 2h ∆t = 3h ∆t = 4h ∆t = 5h ∆t = 6h ∆t = 7h ∆t = 8h

a then b

b then a

No inducers

b only a only

Figure ED-S10: Flow cytometry RFP histograms (Fig. 4). ∼ 100,000 cells were analyzed for each population.

b only b then a

Δt = 0h b then a

Δt = 8h

No inducer a only a then b

Δt = 0h a then b

Δt = 8h

b only b then a

Δt = 0h b then a

Δt = 8h

No inducer A only atb dt0 atb dt8 B only bta dt0 bta dt8

None 100.0 41.7 83.0 45.8 100.0 77.1 98.0

GFP 0.0 4.2 17.0 54.2 0.0 22.9 2.0

RFP 0.0 54.2 0.0 0.0 0.0 0.0 0.0

0 10 20 30 40 50 60 70 80 90 100

Colonies (%)

Controls SabSa

No inducer a only a then b

Δt = 0h a then b

Δt = 8h

b only b then a

Δt = 0h b then a

Δt = 8h Non-fluorescent colonies + 0.01% arabinose

B C

D E

inducerNo a only atb dt0 atb dt8 b only bta dt0 bta dt8

So 100.0 41.7 0.0 0.0 0.0 0.0 0.0

Sb 0.0 0.0 83.0 43.8 100.0 77.1 98.0

Sab 0.0 4.2 17.0 56.3 0.0 22.9 2.0

Sa 0.0 54.2 0.0 0.0 0.0 0.0 0.0

0 10 20 30 40 50 60 70 80 90 100

Colonies (%)

Figure ED-S11: Single colony analysis of non-fluorescent colonies in∆texperiment (Fig. 4) was done to determine genetic state (So or Sb). A) Experimental cultures were diluted 1:10,000 after experiment and plated on LB agar plates with no inducer.

B) 48±2 single colonies were randomly picked from each plate and re-streaked on a new agar plate. C) Single colonies were counted based on fluorescence and the resulting distributions are similar to those measured via flow cytometry. D) The non-fluorescent colonies from each condition were then re-streaked again onto plates with 0.01% arabinose. OnlySocells would turn red (Sa), whileSbcells would remain non-fluorescent. We determined that 100% of the no inducer and a only non-fluorescent colonies were So, while the 100% of the non-fluorescent colonies in the other experimental conditions wereSb. E) Revised genetic state distributions based on single colony analysis of non-fluorescent colonies.

Comparing plate reader fluorescence readings with flow cytometry

We were interested to know how bulk culture florescence compared with actual single cell expression profiles. With bulk fluorescence, it is possible that bimodal expression of fluorescent molecules result in a few bright cells dominating the overall fluorescence measurement, and so we wanted to ensure that this was not the case with our time-course measurements. Endpoint bulk fluorescence was measured via BioTek Synergy H1F plate reader (BioTek Instruments, Inc, VT, USA) and normalized by the maximum fluorescence. Flow cytometry was done with a MACSQuant VYB flow cytometer (Miltenyi Biotec, Germany), and for both RFP and GFP, cells were counted and their relative fluorescence intensity was measured. Flow cytometry data was gated using FlowJo Version 10.0.8r1 (Flowjo, LLC, Ashland, OR).

In Figure ED-S12, we compare bulk fluorescence (Fig. ED-S12A) with flow cytometry populations (Fig. ED-S12B), then reconstruct the bulk fluorescence measurements by multiplying the cell counts with average measured intensity (Fig.

ED-S12C). We find that GFP fluorescence is not disproportionately skewed by bulk fluorescence, indicating that cells that are “on” in state Sab have a relatively tight distribution and are not overly dominated by a minority of bright cells. This can also be seen in the GFP histograms (Fig. ED-S9). For this experiment, in which both inducers are present long after∆t induction, we would expect no cells to remain in state Sa. However, we still measure RFP at the endpoint. We find that this RFP is leftover RFP from cultures that spent more time in Sa prior to transitioning to Sab (Fig. EV1). These cells have stopped production of RFP, but existing RFP concentrations have not yet diluted completely. Flow cytometry analysis of cell counts find a high number of cells with low RFP fluorescence. This can also be seen in the RFP histograms (Fig. ED-S10).

Fraction of max RFP 0 0.2 0.4 0.6 0.8 1

0 2 4 6 8 10

Fraction of max GFP

0 0.2 0.4 0.6 0.8 1

GFP population (%)

0 10 20 30 40 50 60 70

RFP Population (%)

0 10 20 30 40 50 60 70

GFP intensity (arbitrary units) 0 0.5 1 1.5 2 2.5

3 x10⁸

RFP intensity (arbitrary units)

x10⁸

0 2 4 6 8 10

Inducer separation time, ∆t (h) 0 2 4 6 8 10

Inducer separation time, ∆t (h)

0 2 4 6 8 10

Inducer separation time, ∆t (h) 0 2 4 6 8 10

Inducer separation time, ∆t (h) Plate reader bulk fluorescence Flow cytometry cell count

Re-creating bulk fluorescence from flow data Number of cells x avg. intensity per cell

E_ab

E_ba

E_ab

E_ba

E_ab

E_ba

E_ab E_ba E_ab

E_ba E_ab

E_ba a only

b only

a only

a only a only a only

a only

b only b only b only

b only b only

A B C

Figure ED-S12: Comparison of plate reader bulk fluorescence readings with flow cytometry cell counts. A) Bulk fluorescence GFP and RFP readings normalized by max GFP and max RFP. B) Flow cytometry counts of cell percentages about GFP and RFP gated thresholds. C) Re-creating bulk fluorescence data from average intensity per cell multiplied by number of cells.

Varying model parameters for integrase activity and leaky basal expression Parameter Value Units

k_prodA 50 (µm³·hr)⁻¹

k_prodB 50 (µm³·hr)⁻¹

k_deg 0.3 hr⁻¹

k_flipA 0.2 hr⁻¹

k_flipB 0.3 hr⁻¹

k_leakA 0.01*k_prodA (µm³·hr)⁻¹ kleakB 0.02*k_prodB (µm³·hr)⁻¹

Table 3.2: Table of revised parameters for uneven flipping to better match experimental data. IntA was set to be less efficient in flipping, and leakiness was added.

0 2 4 6 8 10

Inducer separation time, ∆t 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sab fraction

kflipA = 0.1, MSE = 0.044

kflipA = 0.2, MSE = 0.004

kflipA = 0.3, MSE = 0.020

kflipA = 0.4, MSE = 0.038

kflipA = 0.5, MSE = 0.052

kflipA = 0.6, MSE = 0.067

Experimental data

0.0096 0.0228 0.0431 0.0567 0.0689 0.0824

0.0211 0.0098 0.0040 0.0041 0.0071 0.0088

0.0442 0.0320 0.0196 0.0120 0.0098 0.0094

0.0605 0.0508 0.0381 0.0301 0.0251 0.0220

0.0762 0.0675 0.0560 0.0465 0.0370 0.0354

0.0840 0.0810 0.0710 0.0611 0.0508

0.0452

0.1 0.2 0.3 0.4 0.5 0.6

k_flipA kflipB

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.1 0.08

0.2 0.3 0.4 0.5 0.6

0.60 0.02 0.04

0.5

Mean squared error

0.06

0.4 0.5 0.08

0.3 0.4 0.1

0.20.3

0.20.1 0.1

0.08

0.01 0.02 0.03 0.04 0.05 0.06 0.07

0.6

k_flipA k_flipB

k_flipB = 0.3 Mean squared error

A B C

Figure ED-S13: Fitting model parameters for Figure 5C. In stochastic simulations, the flipping efficiency parameters for both integrases,kflipA,B, were varied from 0.1 to 0.6 hr⁻¹forEab(N = 500 cell trajectories). Leaky basal expression of the integrases were held constant based on experimentally measured values (k_leak_a= 1% ofk_prodA, kleak_b= 2% ofkprodB). A) Simulation results for each set ofkflipA,Bparameters were fit to a one-term Gaussian function (MATLAB,fit(x,y,’gauss1’)). Mean squared error (MSE) was calculated by comparing the fitted curves to experimental data from Figure 4C (MATLAB,goodnessoffit(reference,model)). This graph shows fits from varying k_flipA for constant k_flipB = 0.3hr⁻¹. Experimental data is shown in black.

B) Heatmap showing MSE values for combinations of kflipA,B parameters. Lower MSE values indicate a better fit. Best fit is forkflipB =0.3hr⁻¹,kflipA= 0.2hr⁻¹. C) Surface plot showing MSE values for combinations of k_flipA,B. Lower MSE values indicate a better fit.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

k_prodA,B = 5 k_prodA,B = 10 k_prodA,B = 50 k_prodA,B = 100 Fraction of Sab cells

Separation time, ∆t (h) Δt90

Δt90

GFP population fraction

Separation time, ∆t (h)

0 1 2 3 4 5 6 7 8 9 10

0 0.1 0.2 0.3 0.4 0.5

Half induction Full induction

E_ba

Figure ED-S14: Varying protein production rates to tune the∆t90limit. A) Simula- tion results for varyingk_{pr odA,B}from 5 to 100 (µm³·hr)⁻¹(N = 2500 per population).

∆t₉₀ is the limit with whichSabpopulation fractions can be used to resolve unique

∆t values, and therefore determines overall system sensitivity to inputs. Based on simulation results,∆t₉₀ is inversely proportional to protein production rate. Curve fits were generated for each set of simulated populations (MATLAB, 2-term exponential fit) in order to find ∆t90. B) Experimental results show lower ∆t90 at half induction of integrases. Protein production rate was modulated by reducing the concentrations of the inducers. We compared population-level responses with full inducer concentrations (ara: 0.01%/vol, aTc: 200ng/ml) and half inducer concentrations (ara: 0.005%/vol, aTc: 100ng/ml). The data was fit to a 2-term exponential function (MATLAB, 2-term exponential fit) and the∆t₉₀limit was estimated based on the fitted curve. The∆tvalues are consistent with being in the saturation regime of integrase production.

Simulation results suggest that the∆t₉₀detection limit can be tuned by increasing or decreasing the overall production ratek_{pr od∗}(∗= A or B) (Appendix Fig. ED-S14).

In Figure 4C, the ∆t90 limit was ∼ 4 hours, meaning that within the 0 – 4 hour window, Sab population fraction can be used to uniquely determine ∆t. Outside of this window, the only assertion that can be made is that ∆t > 5 hours. In silico, we see that the rate of protein production is inversely proportional to the

∆t₉₀ detection limit (Appendix Fig. ED-S14A). When kprodA,B is high, integrase molecules accumulate faster, increasing the probability of DNA flipping, and thus causing the Sab population fraction to saturate at lower∆tvalues. However, within that smaller time window,Sabfractions would also be measurably different at much smaller intervals, and so∆t could be resolved with much higher resolution. When protein production is slow, the stochastic DNA recombination events happen less

frequently, resulting in a population that is more sensitive to inputs for a longer period of time (high ∆t90), but has lower resolution overall since the population fractions are not changing as quickly. These simulation results were compared to some preliminary experimental data in which lower production rates for intA and intB were approximated by halving the inducer concentrations for both a and b (Appendix Fig. ED-S14B, ED-S15). ∆t₉₀ was estimated by fitting curves to the experimental data to determine maximumSab (MATLAB, 2-term exponential fit).

When inducer concentrations were halved (ara: 0.005%/vol, aTc: 100ng/ml), we see that the∆t₉₀ is the same as before, so even with half induction, we are still in the saturation regime of integrase production.

Varying protein production rates more accurately is something we would like to pursue further. We limited the scope of this study to a single concentration of inducer and∆t₉₀ such that we could fully understand the information that can be gained from other states in the system.

NoA onlydt0 dt1 dt2 dt3 dt4 dt5 dt6 dt7 dt8

Population fraction (%)

0 20 40 60 80 100

a then b

q1:GFP only q2:RFP+GFP q3:RFP only q4:none

NoB onlydt0 dt1 dt2 dt3 dt4 dt5 dt6 dt7 dt8

Population fraction (%)

0 20 40 60 80 100

b then a

q1:GFP only q2:RFP+GFP q3:RFP only q4:none Time (h)

0 10 20 30

RFP/OD

x10⁴

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (h)

0 10 20 30

RFP/OD

x10⁴

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 5 10

RFP Population (%)

0 10 20 30 40 50 60 70

Separation time, ∆t (h)

Time (h)

0 10 20 30

GFP/OD

0 1000 2000 3000 4000 5000 6000 7000 8000

Time (h)

0 10 20 30

GFP/OD

0 1000 2000 3000 4000 5000 6000 7000 8000

0 5 10

GFP population (%)

0 10 20 30 40 50 60 70

Separation time, ∆t (h)

E_ab

E_ba E_ab E_ba

a only

b only

b only a only No inducer

a only

∆t = 0h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h

∆t = 7h

∆t = 1h

∆t = 8h

No inducer

∆t = 0h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h

∆t = 7h

∆t = 1h

∆t = 8h b only No inducer

a only

∆t = 0h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h

∆t = 7h

∆t = 1h

∆t = 8h

No inducer

∆t = 0h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h

∆t = 7h

∆t = 1h

∆t = 8h b only

Figure ED-S15: Varying protein production rates, timecourse. Here, we have used half the normal inducer concentrations to test the effects of lower protein production rates. Concentrations of aandbare 0.005%/vol arabinose and 100ng/ml aTc.

A) RFP fluorescence over time for Eab(left), Eba(center), and endpoint population fractions as measured by flow cytometry (right). B) GFP fluorescence over time for Eab(left), Eba(center), and endpoint population fractions as measured by flow cytometry (right). C) Population distributions gated by quadrants. Overall population behavior was the same as full inducers, but response was more graded with increasing∆t.

Deducing inducer pulse width: simulations

Pulse Width(h)

0 2 4 6

Sa cells

0 500 1000 1500 2000 2500 3000

Pulse Width(h)

0 2 4 6

Sab cells 0 500 1000 1500 2000 2500

3000 ⁰ Pulse Width(h)² ⁴ ⁶

Sa + Sab cells 0 500 1000 1500 2000 2500 3000

Pulse Width(h)

0 2 4 6

Sb cells 0 500 1000 1500 2000 2500 3000

∆t = 0h

∆t = 1h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h

∆t = 0h

∆t = 1h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h

∆t = 0h

∆t = 1h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h

∆t = 0h

∆t = 1h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h

A B

C D

Figure ED-S16: Deducing pulse width, additional states with varying∆t,PWb, N = 3000 cells. A)Sa cells decrease as function ofPWb. Sa fraction is independent of

∆t. B) The sum ofSa+Sabis the fraction of cells that seeafirst, and this increases with∆t andPWb. C) The number ofSabcells increases with∆t andPWb. D) The number ofSbcells decreases with∆t but increases withPWb.

A B

A only cells

0 500 1000 1500 2000 2500 3000

A then B cells

0 500 1000 1500 2000 2500

3000 DeltaT:0h

DeltaT:0.5h DeltaT:1h DeltaT:1.5h DeltaT:2h DeltaT:2.5h DeltaT:3h DeltaT:3.5h DeltaT:4h DeltaT:4.5h DeltaT:5h DeltaT:5.5h DeltaT:6h

A only cells

0 500 1000 1500 2000 2500 3000

A then B cells

0 500 1000 1500 2000 2500

3000 PulseWidth:0h

PulseWidth:0.5h PulseWidth:1h PulseWidth:1.5h PulseWidth:2h PulseWidth:2.5h PulseWidth:3h PulseWidth:3.5h PulseWidth:4h PulseWidth:4.5h PulseWidth:5h PulseWidth:5.5h PulseWidth:6h

Figure ED-S17: Unique populations for different combinations of ∆t and PWb

(Fig.7). Each point represents a simulation with 3000 cells. A) Lines represent increasing∆t values. B) Lines represent increasingPWbvalues.

Deducing inducer pulse width: experimental

A B

RFP population fraction (%) 0 10 20 30 40 50 60 70

GFP population fraction (%)

0 10 20 30 40 50 60 70

∆t = 0h

∆t = 1h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h 0 1

2 3

6 45 PW_b (h)

RFP/OD

0 5000 10000 15000

GFP/OD

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

∆t = 0h

∆t = 1h

∆t = 2h

∆t = 3h

∆t = 4h

∆t = 5h

∆t = 6h 0 1

2 3

65 4 PW_b (h)

Figure ED-S18: Fluorescence measurements vs flow cytometry for Figure 7C.

Experimental pulse modulated populations were sampled and grown in triplicate in 96-well microplates. ∆tandPWbwere varied from 0 – 6 hours. Dotted circle shows control populations with no inducer exposure. A) Fluorescence measurements show standard error between triplicates for RFP and GFP fluorescence. Differences in single cell fluorescence expression results in skewing of population coordinates. B) Triplicates were pooled for flow cytometry measurements (Same data as Figure 7C).

Dalam dokumen Synthetic Circuits for Feedback and Detection in Bacteria (Halaman 84-123)