DESIGN OF ENGINEERED BACTERIA FOR REGULATED PHAGE RELEASE: PROGRESS TOWARDS TARGETED

ELIMINATION OF PATHOGENS

by

A thesis submitted in conformity with the requirements for the degree of Master of Science

Graduate Department of Cell and Systems Biology University of Toronto

Ursula Alexandra Florjanczyk

© Copyright by Ursula Alexandra Florjanczyk (2014)

ii

Abstract

Thesis Title: Design of engineered bacteria for regulated phage release: Progress towards targeted elimination of pathogens

Degree: Masters of Science

Year of Convocation: 2014

Author: Ursula Florjanczyk

Graduate Department: Cell and Systems Biology

University: University of Toronto

Cholera outbreaks, caused by surges in pathogenic Vibrio cholerae, recur frequently in

areas with water reservoirs around unsanitary living conditions. Phage therapy is being pursued

as a possible alternative treatment to antibiotics. A seek-and-destroy circuit was designed for

implementation in probiotic E.coli so that they could be used as a controlled delivery system for

the phages. These engineered bacteria (EB) were designed to fulfill two functions: to regulate

their own population growth and to respond to V.cholerae by lysing to release phages. In this

study, it was confirmed that the lysogenic E.coli strain K-12 could represent EB, since it could

be induced to produce lambda phage virions. Construction of the seek-and-destroy circuit was

begun by characterizing a lytic cassette, which showed promise as a population growth regulator

and a prophage inducer. Finally, numerical simulations of a mathematical model representing the

circuit implied that EB can successfully eradicate a V.cholerae population.

iii

Acknowledgments

I express my warm thanks to my supervisor Dr. David McMillen for his support and

guidance, without which this work could not have come together. I would also like to thank

current and past members of the McMillen lab for their encouragement and patience. To Grand

Challenges Canada for giving us the opportunity to explore this exciting project. To Dr. Sergio

Peisajovich and Dr. George Espie for their invaluable insights. Finally, I am sincerely grateful to

my friends and family whose unwavering support has buoyed me through this degree.

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Table of Contents Introduction 1

Methods and Materials 10

Results 20

Discussion 34

Conclusion 43

References 45

Supplementary Material 49

Reagents and Buffers 10

Induction of E.coli K-12 lysis with exposure to ultraviolet light 10

Infectivity Assay 11

Phage Plaque Assay 11

Transformations and other plasmid making techniques 11

Making the pZe12-K112808 plasmid 12

Mathematical Model 14

Inducible lambda phage production in E.coli K-12 20

BioBrick Lytic Cassette 24

Mathematical Model 29

List of Supplementary Figures 48

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List of Figures

Figure 1: V.cholerae quorum-sensing architecture 4

Figure 2: Population growth controller 4

Figure 3: Seek-and-destroy circuit 8

Figure 7. UV induction of lambda prophage 21

Figure 8. Phage Plaque Assay for UV induced K-12 23

Figure 9. Fitting infection model to infectivity assay data 23

Figure 10. Expressing the lytic cassette 26

Figure 11. Phage Plaque Assay for the lytic cassette constructs 28

Figure 12. Numerical simulations of full mathematical model 30

Figure 13. Numerical simulations of reduced mathematical model 32

Figure 14. Numerical simulations of 3-ODE model 33

Figure 4. Diagram of plasmid pZe12-luc 12

Figure 5. Diagram of Long and Short constructs 13

Figure 6.Diagram of seek-and-destroy mathematical model 15

Figure 15. Lysis/Lysogeny switch in lambda phage 38

1

Introduction

Cholera outbreaks continue to plague areas with high human population density and poor

water treatment systems, and are among the leading global causes of death for children under the

age of 5 [1,2]. The etiological agents responsible are Vibrio cholerae, gram-negative bacteria

which propagate in environmental aquatic reservoirs. V.cholerae persist in a predator-prey

equilibrium with lytic phages, called vibriophages, which specifically target the pathogens.

Cholera outbreaks can be instigated through external or internal factors that result in a sudden

surge of bacterial population or a decrease in predation by the vibriophages. Once the V.cholerae

acquire pathogenicity via gene transfer from certain vibriophages, and begin colonizing human

hosts, progress through the outbreak cycle is hastened via the shedding of pathogenic bacteria

into aquatic reservoirs where they can be uptaken by non-infected individuals. A surge in the

extrinsic concentration of vibriophages precipitates the end of each outbreak. It has been

suggested that predation from these vibriophages could drastically shorten the length of each

cholera outbreak as well as serve as a novel treatment option for suffering patients [2].

Furthermore, treatment with vibriophages would avoid damaging the native gut flora of the

patient, which can lead to further complications involving digestive issues and further infections

[3].

The hunt for alternative treatments to antibiotics is increasingly gaining urgency as the

rise in antibiotic resistance is poised to become the next global crisis [4]. Phage therapy has been

a known alternative to antibiotics for decades, even becoming a clinical treatment in the Soviet

Union in the 1960s [5]. However, lack of accessible scientific literature and the increasing

popularity of antibiotics shunted phage therapy into obscurity and it has only recently been re-

examined as a viable treatment option in light of the impending crisis. Phage therapy comes with

2

a slew of promising properties: phages are generally highly selective for their target hosts, they

can self-replicate and self-propagate through a bacterial population, and they can be used to

insert foreign DNA into target strains. The ability to affect the genome of the target pathogen can

be especially useful in minimizing the selective pressure responsible for developing resistance.

Using bacteriophages as adjuvants for antibiotics has been proven to be effective in eradicating

E. coli both in vitro and in vivo [6]. Further methods are possible to delay the evolution of phage

resistance, such as treatment with a phage cocktail containing several phage strains, targeting of

non-essential genes, and increasing the metabolic cost of developing resistance [4,6].

Other challenges present themselves in the pursuit of creating clinically relevant phage

therapies. Depending on the viral strain, phages can be difficult to isolate and characterize. Since

phages replicate in their hosts (highly dangerous pathogens), mass production would require high

security facilities [4]. Because of the inherent specificity of bacteriophages, no phage equivalent

to broad-spectrum antibiotics can be prescribed to the patient without diagnosis of the causative

bacterial strain. Phage therapy also encounters a delivery problem because of the potentially

inflammatory immune response to large virion doses. To tackle this issue, we turned to synthetic

biology in the aim of engineering bacteria to act as a tunable and targeted delivery system.

Common tools in synthetic biology have previously engineered bacteria to act as seek-and-

destroy systems for common pathogens [7,8,9]. These systems generally detect the bacterial

communication molecules secreted by the target strain (quorum-sensing autoinducers) and, upon

detection, release bacteriocins (small molecules that are lethal specifically against the target

strain) through either secretion or whole-cell lysis.

To help fight cholera infections, a probiotic E.coli strain can be recruited as the seek-and-

destroy vessel for vibriophage. Probiotics are bacterial strains that can confer a health benefit to

3

the host by creating a hostile environment for pathogens and promoting a healthy microecology

in the gut [10]. The E.coli strain Nissle 1917 [11] is one of the most widely studied probiotics

worldwide, it is commercially available and has been extensively studied as a treatment for

ulcerative colitis and acute diarrhea. In fact, a previous study by Duan and March in 2010

showed that a Nissle strain engineered to express one of the V.cholerae quorum-sensing

autoinducers was a highly effective pre-treatment for mice consequently fed V.cholerae [13].

Although further investigation is required to create clinical Nissle treatments, it is a promising

probiotic strain for use in synthetically designed phage therapy.

As in the case of the previously designed seek-and-destroy systems, our engineered

bacteria (EB) can use quorum-sensing to detect the target pathogens. Quorum-sensing

mechanisms use small membrane diffusible molecules (autoinducers) that are produced in each

bacterial cell and accumulate in extra- and intracellular space [12]. The concentration of

autoinducer increases as the bacterial population grows. Once a minimum threshold

concentration is reached, the autoinducers bind to receptor proteins which then regulate the

expression of genes that require coordination from the bacterial population. The best

characterized quorum-sensing system is also a common component used in synthetic biology

circuits: the LuxR/LuxI system. Natively, LuxI is a constitutively expressed synthase which

synthesizes the autoinducer acyl homo-serine lactone (AHL) from an abundant precursor

available in the cell. At high AHL concentrations, AHL binds to its receptor LuxR which then

dimerizes with another AHL:LuxR pair and then acts as a positive transcriptional regulator on

luxr promoters.

4

Figure 1. V.cholerae quorum-sensing architecture. a) At

low cell density, membrane bound autoinducer receptors

LuxPQ and CqsS act as kinases, phosphorylating

downstream proteins LuxU and LuxO, resulting in

production of four small RNAs (sRNA). The sRNAs inhibit

the production of a transcriptional activator, HapR. b) At

high cell density, AI-2 (produced by LuxS) binds to LuxPQ

and CAI-1 (produced by CqsA) binds to CqsS turning the

kinases into phosphatases. De-phosphorylation of LuxU and

LuxO results in transcription of quorum-sensing regulated

genes. See main text for details. Diagram based off

schematic from Ng and Bassler 2009 [14].

a) Low Cell Density

b) High Cell Density

Figure 2. Representation of LuxR/LuxI quorum-sensing

based population growth controller from You and Cox [34].

5

After the initial discovery of the LuxI/LuxR system in Vibrio fischerii, the databank of

identified quorum-sensing autoinducers grew to include oligopeptides, pseudomonas quinolone

signal (PQS), bradyoxetin, and the aptly named autoinducer-2 (AI-2), a furanosyl borate diester

[14]. The gene which codes for the AI-2 precursor synthase has been found in over 70 bacterial

species and is widely considered to be an interspecies communication molecule. AI-2 molecules

from one species has been known to affect quorum-regulated processes in other species [13]. In

fact, both E.coli and V.cholerae have the AI-2 precursor synthase. To avoid crosstalk and false

positives, a different QS channel must be used as the pathogen identifier in our EB.

The interspecies communication network is not the only quorum-sensing system in

V.cholerae (see Fig. 1). These bacteria also have an intraspecies channel which utilizes

oligopeptides as the diffusible autoinducers, namely the CqsS/CqsA network. CqsA synthesizes

the oligopeptide (S)-3-hydroxytridecan-4-one (CAI-1). CqsS is a two-component

phosphatase/kinase CAI-1 receptor. When unbound, CqsS acts as a kinase, phosphorylating the

downstream protein LuxO. LuxO regulates the expression of quorum-regulated small RNAs,

which in turn inhibit the production of HapR, an activator of downstream promoters [14]. As

concentrations of CAI-1 rise, the peptides bind to CqsS, swapping its function so that it

dephosphorylates its downstream targets and thus promotes expression of quorum-regulated

genes. Additionally, the LuxO protein integrates information from both inter- and intraspecies

communication since it is also phosphorylated by the AI-2 receptor LuxPQ. Whether or not

V.cholerae can differentiate between the two signals is unclear, although it is known that CAI-1

is a stronger signal transducer than AI-2 [14, 15]. The increased complexity of the CqsS/CqsA

system makes it more difficult to use in engineered circuits but its specificity for CAI-1 makes it

the favourable QS system for the EB.

6

The variety of available quorum-sensing systems and their relative specificity permits the

design of synthetic circuits that use parallel quorum-sensing systems for different uses. One of

the fears of using engineered bacteria for human clinical treatments, especially ones for

gastroenteric diseases that will result in expulsion of some engineered bacteria into the

environment, is their potential effect on the local ecology. This necessitates a population growth

controller, or self-activated death switch, to be programmed into the EB to avoid blooms in the

environment and to avoid overwhelming the immune system while still in the patient. Such a

population growth controller has previously been employed by You et al in 2004, who used a

lethal protein under regulation of a quorum-sensing system to create a strain of E.coli that can

only grow to a constrained carrying capacity (Fig. 2) [34]. Drawing from this controller and the

V.cholerae quorum-sensing system we can construct seek-and-destroy bacteria that would pose

limited environmental concerns if employed as a clinical treatment.

Our genetic network was therefore designed so that it could potentially fulfill several key

functions (Fig. 3). Firstly, our EB would have to be kept under a population growth inhibitor.

Secondly, they would enter the lytic cycle upon detecting a threshold level of V.cholerae.

Finally, entry into the lytic cycle would correspond to a halt of population growth restraint in

order to alleviate the metabolic load on the cells as well as avoiding killing of EB cells before

they have a chance to release vibriophages. All three functions can be accomplished through

quorum-sensing, with entry into the lytic cycle and population inhibition release both being

downstream of Vibrio cholerae CAI-1 detection and EB population regulation being controlled

by the LuxR/LuxI quorum-sensing system. The population controller in our design was modelled

from the You et al circuit [34], with LuxI and LuxR expressed constitutively and a CcdB protein

under control of the luxR promoter. The toxin CcdB acts by binding to DNA gyrase, a catalyzer

7

of DNA uncoiling [16]. Regulating the topological state of DNA is essential to bacteria as it

effects key processes such as transcription, DNA replication, and recombination [41, 42]. The

population control circuit would be mirrored by a similar system for the second and third

functions. Constitutive expression of CqsS and LuxU/O, coupled with a qrr4 promoter, would

allow the EB to regulate the expression of two proteins, Cro and CcdA, in response to the

presence of CAI-1. It is known that the Cro protein is a positive regulator of the lambda phage

lytic cycle [21]. Since the vibriophage life cycle is poorly understood, in our designed circuit,

Cro can represent a lysis-inducing protein. CcdA is the antitoxin counterpart to CcdB, binding to

CcdB and preventing it from binding to its target. In the absence of V.cholerae, the EB would

grow and accumulate AHL, leading to the expression of CcdB and cell death, thus maintaining a

limited population. Upon reaching a threshold concentration of CAI-1, the EB would be released

from the population growth inhibition by accumulation of CcdA and would enter the lytic stage

via expression of a lysis-inducing protein (Cro). It is likely that the environment in the patient’s

gut would be hostile enough not to warrant a population growth controller, since it is more

probable that our EB will struggle to gain a foothold in the flourishing native gut florae.

However, should the EB be expelled out of the patient and into the environment, the population

controller could prevent unwanted proliferation of EB.

8

1) Population Size Regulation

Figure 3. Seek-and-destroy circuit. Diagram of seek-and-destroy circuit performing its

two duties. 1) In the absence of V.cholerae QS molecules, the EB are limited by a

population growth inhibitor that is regulated by their own quorum-sensing autoinducers

(AHL). 2) At high enough concentrations of V.cholerae, EB express an antitoxin (CcdA)

to the population inhibitor (CcdB) and also express a lysis-inducing protein (Cro) to release

vibriophages. See full text for details.

2) Phage Production in Response to V.cholerae CAI-1

9

The dynamics of this theoretical design were simulated using a mathematical model to

analyze the behaviour of the circuit. To begin experimentally constructing the genetic circuit,

easily available BioBrick components and cell strains were used. BioBrick components are

nucleotide sequences of standard biological parts used in synthetic circuit design and are part of

the Registry of Standard Biological Parts [40]. To avoid handling dangerous cell strains, readily

available E.coli strains were used to represent the EB and V.cholerae. The focus was placed on

the construction and expression of individual circuit components within these cells, rather than

studying realistic pathogen and phage dynamics. The E.coli K-12 strain was used to represent EB

because K-12 exists in a lysogenic state with lambda phage that can serve as a surrogate

vibriophage. E.coli MG1665 cells were used to represent V.cholerae as they are susceptible to

infection by lambda phage virions. The BioBrick component characterized was an inducible lytic

cassette, composed of a T4 phage holin, lysozyme, and antiholin [40]. Holins are a class of

proteins that form pores in the inner cell membrane allowing lysozymes to diffuse through and

degrade the peptidoglycan wall. The lytic cassette was primarily considered as a bacterial

population growth controller and subsequently as a potential inducer of virion production. In this

study, it was first confirmed that traditional methods could be used to induce the K-12 cell strain

to produce lambda phages which could infect the MG1665 cells. A plasmid containing the lytic

cassette was then constructed and expressed in K-12 cells. Frequent loss-of-function mutations in

the construct made characterization of the lytic cassette difficult. Nevertheless, some evidence

was found that the lytic cassette caused cell death and entry of the K-12 cells into the lytic phase

of the lambda phage life cycle.

10

Methods and Materials

Reagents and Buffers

All reagents used for restriction digestions were from New England Biolabs ® (NEB),

and their protocols were followed. Unless otherwise specified, high fidelity versions of the

restriction enzymes were used. Transformations were done via electroporation, following the

Knight protocol from OpenWetWare [33]. Plasmid DNA isolations were performed using

Qiagen miniprep kits. All OD measurements were done using the Spectronic 200

Spectrophotometer from Thermo Scientific. E.coli strains were stored at -80°C in Luria-Bertani

(LB) medium containing 30% glycerol.

Induction of E.coli K-12 lysis with exposure to ultraviolet light

The E. coli strain K-12 (ATCC Number: 10798; genotype: F+ lambda+) was used as a

substitute for our engineered bacteria. The E.coli strain MG1665 (ATCC Number: 700926

genotype: F- lambda- ilvG- rfb-50 rph-1) was used as a target strain. Cultures were grown in LB

medium (Bio-Shop Canada) overnight at 37°C and then diluted 1:500 into 20mL of fresh

medium. Once the culture had reached exponential growth (Optical Density (OD) at 600 nm

≈0.4) the cultures were transferred to 9 cm Petri dishes and exposed to UV light (254nm

wavelength, 40 J/m2) for either 5 or 10 minutes. Cultures not exposed to UV were treated the

same except without irradiation. Petri dishes were gently shaken in a circular fashion during

irradiation. Irradiated cultures were then transferred into culture tubes that were wrapped in

aluminum foil to allow for growth in the absence of light. OD600 measurements were taken

every 20 minutes. OD measurements for UV assays were done on undiluted samples.

11

Infectivity Assay

MG1665 cultures were diluted 1:500 from overnight cultures in 20mL of fresh LB

roughly 2 hours before the assay. K-12 cultures were irradiated with UV for 5 min as described

above. Samples were collected 140 minutes after exposure to UV light, spun down for 10 min at

13,000xg, and the supernatant was added to MG1665 cultures which were in exponential growth

(OD600 ≈ 0.4). Samples added to growing MG1665 cultures were topped off with media to

3.0mL. OD600 was measured every 20 minutes.

The response of the spectrophotometer deviates from linearity above an OD600 reading of 1.0.

To avoid this situation, culture samples were diluted 1:3 to ensure OD readings below 1.0.

Phage Plaque Assay

Soft agar (½ concentration of normal agar) was dispensed in 3.0 mL aliquots into sterile

tubes and kept in solution in a 50°C water bath. To each tube, 0.3mL of MG1665 cells and

various volumes of K-12 culture supernatant were added. The tubes were poured onto pre-made

agar plates, quickly spread around to ensure even distribution, and incubated at 37°C overnight.

Assays performed for UV-induced prophage production from K-12 were done with supernatant

samples taken 120 minutes after irradiation. Assays performed for IPTG induction of the lytic

cassette used supernatant samples taken 240 minutes after induction.

Transformations and other plasmid making techniques

BioBrick components were taken from the 2012 Spring Distribution of the BioBrick

Repository and transformed through electroporation into electrocompetent cells. For plasmid

constructions, inserts were first amplified via PCR, using the PfuTurbo® Hotstart PCR Master

Mix from Agilent Technologies and purified using the Qiagen QIAquick PCR purification kit.

They were then digested using appropriate enzymes and then purified from an 0.8% agarose gel

12

using the Qiagen QIAquick Gel Purification kit and ligated into the plasmid backbone. Similarly,

plasmids were digested and purified from an agarose gel and dephosphorylated using NEB

Antarctic Phosphatase.

Plasmid samples were sent to The Center for Applied Genomics DNA Sequencing Facility for

sequencing with the following primers:

Forward pZ12_AatII_lseqp: 5’ CCGAAAAGTGCCACCTGA 3’

Reverse pZ12_Avr_rp: 5’ ATTACCGCCTTTGAGTGAGC 3’

Making the pZe12-K112808 plasmid for use as circuit component

The pZe12-luc backbone from Expressys (DE) is a reporter plasmid with an IPTG-

inducible luciferase (1.1). The BioBrick BBa_K112808 was amplified using the PCR primers so

that it could be ligated in between the KpnI and PacI sites of the pZe12-luc backbone:

Forward K112808_Fwd_KpnI: 5’GAGGGTACCCTTAAAAGGAGGGTCTATGGCAGGCAGCACC 3’

Reverse B012_Rev_PacI: 5’GAGCATTAATTAAATAAACGCAGAAAGGCCCACC 3’

Figure 4. Genetic map of pZe12-luc plasmid. The plasmid contains a luciferase coding region under a pLlacO-1 promoter, a colE1 origin of replication and an ampicillin resistance marker

AatIIXhoI

EcorI

KpnI

XbaI

AvrIISpeI

SacIt0 T1

RBS

luciferase

PLlacO-1

Apr

pZE12luc

colE1

13

Reverse P1A2_K12_Rev_PacI: 5’GCAGGTTAATTAAGCCTTTGAGTGAGCTGATACCGC 3’

For the two primers, PCR product sizes were 1.2kbp and 1.8kbp for B012_Rev_PacI and

P1A2_K12_Rec_PacI respectively.

Two different primer sets were used in amplifying the lytic cassette; one that included the

entirety of the cassette, and the other that truncated the original cassette after the second

terminator, BBa_B0012 (1.2). When the two constructs failed to be stable enough to express

reliably, a third construct was attempted that cut the lytic cassette at the end of the lysozyme

coding region (after component K112806) and removed all terminators, thus removing all

homology. However, this short construct was too unstable to survive in transformed cultures

even for short periods of time.

T4 holin T4 anti-holin Terminators

Constitutive promoter T4 lysozyme

Long Construct

Short Construct

Figure 5. Diagram showing subparts of the Long and Short constructs of the BBa_K112808 lytic cassette.

14

Mathematical Model

A nonlinear system of ordinary differential equations (1) was created to capture the key

kinetic dynamics of the proposed circuit in action in the presence of a pathogen culture. The

following general assumptions were adopted from the You et al mathematical model [35] for

their population growth controller when creating our model: bacterial populations grow

logistically and within a shared carrying capacity, quorum-sensing components of the circuit can

be represented by their diffusible autoinducers, and protein production and degradation rates

follow first order kinetics.

In this model, the EB population was split into two subgroups; either lysogenic E.coli that

are growing logistically and under inhibition from the population growth controller (E), or E.coli

(1)

A A

AA A A A AB

AA A

EB, lysogenic

V.cholerae, lysogenic

EB, lytic

V.cholerae, lytic

Phages

AHL

CAI-1

Lytic cassette

CcdB

CcdA

CcdA:CcdB

15

that have entered the lytic cycle (En). Lytic E.coli are assumed not to be dividing and have no

associated growth rate term. Entry into the lytic cycle of our EB is regulated by the quorum-

sensing diffusible molecules expressed natively by V.cholerae (CAI-1). CAI-1 concentrations

directly affect expression of the lysis inducing protein, Cro (R) and the protein CcdA (A), which

can dimerize with CcdB (B). CcdB expression is linearly regulate by AHL (L) concentrations.

EBlysogenic

AHL ccdB

Phages Lytic Cassette

ccdB:ccdAdimer

V.cholerae lysogenic

CAI-1 ccdA

EBlytic

V.choleraelytic

Detect and Eradicate

Pop. Growth Regulation

Figure 6. Diagram of seek-and-destroy mathematical model. In the red box are the molecular components for the population growth regulation. In the blue box are components for detection and eradication of V.cholerae, including the pathogens and phages themselves

16

Similarly, V.cholerae can either grow logistically (D) or, after infection with vibriophages, enter

a lytic stage from which they burst to release more vibriophage particles (Dn). Similar to lytic

EB, lytic V.cholerae have no growth term. Vibriophages (P) can either be taken up by uninfected

V.cholerae or degraded through first order kinetics. Production of phage particles is dependent

on a burst size (β) and a cell lysis rate (b). Similarly to the You et al model, both quorum-sensing

regulated proteins are proportional to the concentration of diffusible autoinducer produced

linearly by the bacterial populations. In the population controller, the EB death rate is linearly

related to the CcdB concentration and the switch from lysogeny to lysis is also linearly

dependent on the concentration of the Cro protein. CcdA and CcdB binding dynamics are

described by an association and disassociation constant. For simplicity, the CcdA:CcdB dimer

(AB) was not given a degradation term, it was assumed that the dimer dissociates and the

individual molecules degrade independently. Numerical simulations were performed using

Matlab’s stiff ODE solver “ode15s”, which is a variable order solver based on numerical

differentiation formulas (see Matlab documentation for details). Steady state values were

numerically solved using the “fsolve” function with starting conditions near but not equal to

some of the final concentrations taken from numerical simulations (S3.1-3.2).

The majority of parameter values were taken from the following sources: the population

regulation model by You et al [34] and the V.cholerae and vibriophage infection model from

Jensen et al [2]. The CcdB and CcdA binding coefficient was taken from Dao and Charlier [16],

the dissociation coefficient was approximated to be on the lower end of the range for the

association values. CcdA production rate was assumed to be the same as that for CcdB but the

degradation term was doubled since CcdA is much more unstable than CcdB [16]. Lysis

inducing protein (R) was given identical kinetics as CcdB, as it was assumed that its lethal

17

functionality would be similar to the toxic CcdB’s effect on the cell. Finally, lysis rates were

initially taken from a bacteriophage model by Cox and Rees [35] and Maynard and Birch [18].

See supplementary figures for a full table of parameter values.

In models where different species operate on widely disparate time-scales, quasi-steady

state can be assumed for the faster species. To apply the quasi-steady state assumption the

following model components were solved analytically for steady state and then substituted in the

other equations: CcdB, CcdA, CcdA:CcdB, Cro, AHL, and CAI-1. This resulted in a simplified

model of only 5 players: all four bacterial species and vibriophages (2). A further simplification

was made by setting the two lytic bacterial specie concentrations (En and Dn) to steady state,

under the assumption that once the cell commits to lysis it dies within a doubling time (on

average, 40 minutes after induction) [17] (3). For legibility, coefficients in (3) were substituted

as described in (4).

(2)

(3)

18

Where,

To update some of the unknown coefficient values, a lambda phage infection model was

fitted to the experimental data from the infectivity assay (5). This model was slightly modified

from the Maynard and Birch model [18], a non-dimensional ODE system describing three

players: uninfected cells, phage, and infected lysogenic cells. Uninfected E.coli (E) grew

logistically at rate, kE, to some carrying capacity, K. They were infected at a rate, ki, and a

fraction, f, entered lysis. Cells that chose lysogeny (D) grew at a rate, kD, to a carrying capacity

of KD. Lysogenic cells could also be superinfected with lambda phage at the same rate, ki, as

uninfected cells. Lambda phage (P) burst from infected cells that chose lysis at some burst size,

b. Values for growth rate and carrying capacity were taken from fitting a logistical growth model

(4)

(5)

19

to growth curves for the bacterial cultures. Experimental data values were normalized to the

calculated carrying capacity and the model was then fit to the data using a system of trial and

error. Once the closest fit was achieved (as measured by coefficient of determination), the rate of

lysis in infected cells was re-calculated to be applicable to our model of the entire proposed seek-

and-destroy circuit. See supplementary methods for dimensional model (S1.3).

20

Results

Inducible lambda phage production in E.coli K-12

Exposure to ultraviolet radiation has been shown to induce entry into the lytic phase in

lysogenic bacteria, by creating pyrimidine dimers in DNA [19]. These mutated sites can be

repaired if the cell is exposed to sunlight, activating DNA photolyase which catalyzes the

cleavage of the cyclobutane ring of the pyrimidine dimers [20]. Sites which are not repaired

become single stranded DNA sites that act as SOS signals. The RecA protein binds to these sites,

forms multidimensional helical filaments, and is activated. Active RecA acquires protease

activity through which it activates downstream proteins that can then affect cell cycle regulation,

stop DNA synthesis, and instigate error-prone DNA replication. RecA also cleaves CI, the lytic

repressor, allowing initiation of the lambda phage lytic cycle [21]. UV-inducible cell lysis,

specific to K-12 cells, was confirmed by tracking OD600 levels of E.coli K-12 and MG1665

cultures exposed to either 5 or 10 minutes of UV light (Fig. 7A). Exposure to UV light had no

discernible effect on growth of MG1665 cultures, demonstrating that UV exposure itself at this

dose was not harmful to the cells. In contrast, K-12 cultures showed a dramatic drop in OD600

80 minutes after exposure to UV light, with a more drastic drop for the culture exposed for 5

minutes. Cultures exposed to UV light recovered after the drop in OD600 (about 2 hours after

being irradiated). This recovery can be attributed to a subpopulation of E.coli K-12 cells that did

not complete the lysis switch, either due to a weak SOS signal or a lack of DNA damage to begin

with.

21

0 50 100 150 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (min)

OD60

0

MG 0minMG 5minMG 10minK12 0minK12 5minK12 10min

Figure 7. UV induction of lambda prophage. A) OD 600 of K-12 and MG1665 cultures exposed to 0,5 or 10 minutes of UV light. B) K-12 culture irradiated for either 0 (ctrl) or 5 minutes (UV). Samples of the supernatant were taken 120 minutes after UV exposure and added to MG1665 culture C) at time 0. For each sample, 3.0mL was added to the MG1665 culture: either 3.0mL of K-12 supernatant or 1.5mL of LB + 1.5mL of supernatant. Negative control is 3.0mL of LB added to MG1665 culture (MG ctrl). OD measurements were done on undiluted samples. Each data line represents a single replicate.

A

0 50 100 150 200

0.4

0.5

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0.7

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0.9

1

1.1

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K12 0 minK12 5 min

0 20 40 60 80 100 120 140 1600.2

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Time (min)

OD 600

MG CtrlMG K12 ctrl 1.5mLMG K12 ctrl 3.0mLMG K12 UV 1.5mLMG K12 UV 3.0mL

B

C

22

To confirm the production of lambda virions, supernatants of lysed K-12 cultures were

added to growing MG1665 cultures in an infectivity assay (Fig. 7B-C). Supernatant samples

were taken from K-12 cultures exposed to UV light for 5 minutes since that exposure time

resulted in the more drastic drop in OD600 and thus probably allowing for greater virion yield.

MG1665 cultures grown with supernatant from lysing K-12 cells showed a volume-dependent

growth rate impediment. Lambda phage is a temperate phage, meaning that infected MG1665

cells can enter a lysogenic state instead of lysing. This could explain the lack of a drop in OD600

levels for the MG1665 culture. The reduction in growth rate of the MG1665 cultures could

therefore be attributed to a small percentage of infected cells randomly lysing rather than

integrating the lambda phage into their genome, or it could be attributed to the metabolic strain

of infection slowing down the cell cycle [22].

As a final confirmation that lambda phage was infecting the MG1665 cultures, a phage

plaque assay was performed (Fig. 8). Briefly, isolated supernatant from lysing or non-lysing K-

12 cultures was added to growing MG1665 cultures and then plated in soft agar (see Methods).

No plaques formed in the control plate (no UV exposure) and only a few plaques formed on the

experimental plate. The low number of plaques could be attributed again to the low incidence of

lysis being chosen over lysogeny. Despite the low number of phage plaques and the MG1665

behaviour in the infectivity assay, it can be concluded the E.coli K-12 strain can be induced to

enter the lytic life stage and create lambda virions which can infect MG1665 cells, in accordance

with established literature [21].

23

0.5 mL 1.0 mL 1.5 mL

Figure 8. Phage Plaque Assay for UV induced K-12. K-12 cultures were irradiated for 5 minutes and supernatant samples were taken 120 minutes later. Different volumes of supernatant samples were added to MG1665 plated on soft agar. A) Plaque count for all plates. B) Photos of plates with UV induced K-12 samples. Plaque count represents a single assay

A

B

SSE = 0.0603 r2 = 0.8611

SSE = 0.0052 r2 = 0.9462 SSE = 0.0697

r2 = 0.6457

Figure 9. Fitting infection model to infectivity assay data. Data points represent OD 600 measurements from infectivity assay of K-12 induced to lyse via UV and MG1665. Data points were normalized to calculated carrying capacity (see main text for details). Solid lines represent model predictions. Sum of squared errors of prediction (SSE) and the coefficient of determination (r2) for each data set and appropriate model prediction is inset. A) Ctrl represents MG1665 culture grown with supernatant from non-irradiated K-12 cultures. Infected represents MG1665 cultures grown with 3.0 mL of supernatant of K-12 cultures exposed to 5 min of UV. B) Data represents growth of MG1665 cultures grown with 1.5mL of supernatant of irradiated K-12 culture + 1.5mL of LB.

A B

24

In an effort to draw kinetic parameter data from these infection assays, a mathematical

model was modified to fit the data (Fig. 9). First, a logistic growth model was fit to MG1665

growth curves to get parameter values for growth rate and carrying capacity. OD600

measurements from the infectivity assay were then normalized to the carrying capacity and a

non-dimensional version of the infection model was fit to the data from the MG1665 culture

grown in the 3.0mL supernatant sample of the lysing K-12 culture, i.e. the MG1665 culture that

should be infected by lambda phage particles released from K-12. While the model could

accurately capture the dynamics of this infected culture (as shown by the high coefficient of

determination (r2) score) it was less accurate in predicting growth of the uninfected (or control)

culture. Furthermore, when these parameter values were tested against data from the MG1665

culture grown in only 1.5mL of lysing K-12 supernatant, the model became even more

inaccurate (r2 = 0.6457). Regardless, a parameter value for the lysis rate of E.coli cells that have

entered the lytic state was pulled from the fitted model for use in updating the mathematical

model of the seek-and-destroy EB circuit. See supplementary for a list of parameter values

(S1.2).

BioBrick Lytic Cassette

To begin constructing the seek-and-destroy circuit, a lytic cassette from BioBricks was

chosen for characterization. This cassette is composed of a promoterless T4 lysozyme and T4

holin, and a T4 antiholin under control of a constitutive promoter. The cassette contains three

terminators in total, BBa_B0010 and BBa_B0012 after the T4 lysozyme coding sequence, and

BBa_B0010 at the end of the cassette. In an effort to reduce sequence repetition, two different

versions of this cassette were created; one containing the entirety of the original cassette (called

Long) and one stopping at the first terminator (called Short) (see s1.2 in Methods).These

25

constructs were ligated into a pZe12-luc backbone, under a pLacO promoter and transformed

into K-12 cells (plasmids: pZe12-K112808L and pZe12-K112808S for the Long and Short

construct respectively). It was hypothesized that chemically inducing the expression of this lytic

cassette could consequently induce prophage production in the K-12, suggesting a role as the

vibriophage releasing component of our designed EB. If expression of the lytic cassette failed to

result in lambda virion production, it could still play a role in EB population control.

26

Figure 10. Expressing the lytic cassette A) IPTG toxicity assay for K-12 pZe12-luc and B) MG1665 pZe12-luc cultures. C) IPTG induction of K-12 pZe12-K112808L and D) K-12 pZe12-K112808S. Graphs show average and standard deviation of three trials. OD 600 measurements were made on a 1:3 dilution of samples in LB.

A

B

C

D

27

Growth of K-12 and MG1665 cultures was monitored in the presence of different IPTG

concentrations to check for potential IPTG toxicity (Fig. 10A-B). Although IPTG has been

known to reduce some protein synthesis [23] in E.coli strains, it did not seem to have detrimental

effects on growth of K-12 and MG1665 cultures as measured by OD600. When IPTG was added

to K-12 cells transformed with the lytic cassettes pZe12-K112808L or pZe12-K112808S, the

highest concentration of IPTG (5mM) showed some growth inhibition for both constructs (Fig.

10C-D). No difference could be seen between the pZe12-K112808L and the pZe12-K112808S

strains. It was expected that the lytic cassettes would be much more sensitive [40] to smaller

IPTG concentrations. The lack of response in the transformed cultures is possibly due to

mutations in the plasmid that lead to a loss of function. DNA sequencing of the plasmid DNA

retrieved from transformed cells revealed that both Long and Short were lacking the coding

sequences for the lytic cassette, although the promoter region was still intact. The slower growth

rate of cultures being grown at 5mM IPTG might be attributed to a subpopulation of the culture

which maintain a functional lysis cassette and are being killed, since IPTG itself was shown to

have no negative effect on K-12 growth rate. The lack of difference between the Long and Short

constructs could be attributed to both constructs having different physiological disadvantages.

The high level of sequence similarity in the long construct and the metabolic strain of holin and

lysozyme leakage in the short construct result in two different selective pressures that both drive

the cells to eliminate the cassette. Since the cultures being tested come from overnight dilutions,

there is sufficient time for the bacterial populations to lose the original plasmid structure.

28

Although the lytic cassette was an ineffective and difficult-to-employ technique for

population regulation, it was hoped that expressing the cassette would prove to be sufficient to

induce virion production in the K-12 cells. The infectivity assay was not performed since it was

difficult to pinpoint when maximal virion release would be occurring. The infectivity assay also

previously proved to lack sensitivity to small amounts of lambda phage. To test for trace

amounts of phage particles the phage plaque assay was performed instead (Fig. 11). In a series of

such assays, occasional plaques appeared in trials with 5mM IPTG for the pZe12-K112808L

construct. The lack of plaques in any of the control plates would seem to indicate that IPTG

induction of the lytic cassette is responsible for production of some phage particles.

Figure 11. Phage Plaque Assay for lytic cassette constructs. Total count of visible plaques for MG1665 cultures plated with various volumes of K-12 pZe12-K112808L (A) and K-12 pZe12-K112808S (B) supernatant, 240 minutes after induction with either 0 or 5 mM of IPTG. Shown is total plaque count for 3 trials (A) and for 1 trial (B).

A) pZe12-K112808L

B) pZe12-K112808S

29

Mathematical Model

In order to predict our EB’s hypothetical ability to eradicate Vibrio cholera, a

mathematical model was created to simulate the dynamics of the proposed circuit in action in the

presence of Vibrio cholerae. The model was analyzed analytically in three cases: zero initial EB

concentration, zero initial V.cholerae concentration, or both bacterial populations are present

(Fig. 12A). In the first case, the pathogen grows to carrying capacity. In the second case, the EB

exhibit dampened oscillations around the steady state which, due to the population regulation

circuit, is some fraction of the carrying capacity. This steady state is determined by the various

kinetic rates of the molecular components of the population regulation circuit (AHL and CcdB)

(S.1.4). Stability analysis of these steady states is made complicated by the high-dimensionality

of the mathematical model. Eigenvalues for this state could not be solved analytically. Numerical

eigenvalue solutions implied that both cases where only one of the bacterial players is present are

stable. Whereas ODE systems of 3 equations or fewer have been well characterized, it is difficult

to draw concrete stability information from 11 eigenvalues. In both single-strain steady states,

the eigenvalues in those cases are 10 negative to 1 positive. Intuitively, if V.cholerae is growing

at the environment’s carrying capacity, introduced EB would find themselves quickly

outcompeted without successfully denting the pathogen population. The case where all model

players are at a concentration of zero also underwent stability analysis. It would be hypothesized

that this state would be unstable since even a slight deviation from the origin by either of the

bacterial populations would drive the system to one of the other steady states. However, the

eigenvalues did not reflect this, with all but two being negative, implying some stability to the

system (S2.5).

30

Analytical solutions of a third steady state where EB and V.cholerae are both present

were impossible to find, as confirmed with Matlab’s symbolic equation solver. Numerical

solutions showed that for a variety of initial conditions the pathogen population would be

completely eradicated and the EB would settle into its constrained density after exhibiting

dampened oscillations (Fig. 12A). This is the same steady state as the second case described

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

1.2

CFU

s/mL no

rmalized

to C

arrying Cap

acity

Time (hrs)

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rmalized

to C

arrying Cap

acity

Time (hrs)

0 5 10 15 20 25 300

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s/mL no

rmalized

to C

arrying Cap

acity

Time (hrs)

0 5 10 15 20 25 300

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1

1.2

CFU

s/mL no

rmalized

to C

arrying Cap

acity

Time (hrs)

A

B D

0 → 1 E.coli

V.cholerae

C

Figure 12. Numerical simulations of full mathematical model. A) Varying initial concentrations of bacterial players, from 0 → carrying capacity for E.coli (black to blue lines) and simultaneously from carrying capacity → 0 for V.cholerae (orange → green). B) Varying rate of production for lysis inducing protein, from 0 to 5 in increments of 0.5 (black to blue). C) Varying rate of degradation for lysis inducing protein from 0 to 5 in increments of 0.5 (black to blue). D) Varying rate of entry into lysis from 0 to 0.048 in increments of 0.0048 (black to blue). Graphs show non-lysing bacterial concentrations (i.e.: E and D) normalized to carrying capacity for 30 hours. Inset graphs show V.cholerae concentrations for first minutes of simulation.

Initial Concentrations dR: 0 → 5

vR: 0 → 5 η: 0 → 0.048

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.2

0.4

0.6

0.8

1

1.2

CFU

s/mL no

rmalized

to Carrying Ca

pacity

Time (hrs)

0 0.1

0 0.05 0.1 0.150

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rmalized

to C

arrying Ca

pacity

Time (hrs)

0 0.15

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rmalized

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acity

Time (hrs)

0 0.15

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acity

Time (hrs)

0 0.15

31

above. The model was then simulated for different variable values, specifically: lysis rate, Cro

production and degradation, and CAI-1 production and degradation. (S2.1 and Fig. 12B-D). All

of these parameters could not be found in literature. For these parameters, no bifurcations could

be found in the ranges tested. These simulations all resembled those of the initial parameter value

simulations, with variable tuning affecting the dynamics of the bacterial populations but never

the final state of the system.

In an effort to simplify the analysis of our mathematical model, quasi-steady state was

assumed for all molecular players, resulting in a five-equation system. Quasi-steady state could

be applied since changes in transcription and translation levels occur on the order of minutes,

whereas bacterial population growth, lysis, and response to lethal proteins occur on the order of a

bacterial generation time (anything from 15-60 minutes). Solving this reduced system gave the

same final concentrations as the previous system (Fig. 13). Eigenvalue analysis easier to

decipher, with consistently negative eigenvalues for this steady state across the entire range of

parameter values tested, with the exception of very low (not biologically relevant) values (S2.2).

If we continue to assume quasi-steady state for the lytic populations of the EB and

V.cholerae, we can reduce the system further to three equations. Numerical simulations of this

system proved to be unrealistic, with V.cholerae concentrations plummeting almost

instantaneously to zero regardless of initial conditions (Fig. 14). Conversely, numerical solutions

for the steady states concurred with those of the previous model versions and steady state

stability analysis showed this steady state to be stable, with the exception of parameter values

near zero (S2.3).

32

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

1.2

CFU

s/mL no

rmalized

to C

arrying Cap

acity

Time (hrs)

0 5 10 15 20 25 300

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s/mL no

rmalized

to C

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acity

Time (hrs)

0 5 10 15 20 25 300

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1

1.2

CFU

s/mL no

rmalized

to C

arrying Cap

acity

Time (hrs)

0 →1

E.coli

V.cholerae

Figure 13. Numerical simulations of reduced mathematical model. A) Varying initial concentrations of bacterial players, from 0→carrying capacity for E.coli (black to blue lines) and simultaneously carrying capacity→0 for V.cholerae (orange→green). B) Varying rate of production for lysis inducing protein, from 0→5 in increments of 0.5 (black to blue). C) Varying rate of degradation for lysis inducing protein from 0→5 in increments of 0.5 (black to blue). Graphs show non-lysing bacterial concentrations normalized to carrying capacity. Insets show V.cholerae concentrations for the first 0.15 hrs.

Initial Concentrations A

vR:0 →5 B

dR:0 →5 C

0 0.150

0.5

1

0 0.150

1

0 0.150

1

33

Finally, the full model was simulated with the parameter value lifted from the fitted

infection model. However, since the parameter value for calculated lysis rate was so low (~10-11)

it effectively removed the EB’s ability to react to V.cholerae presence. For all initial conditions,

the two bacterial populations would grow to their respective carrying capacities such that their

total concentrations equalled the system’s carrying capacity (S2.4).

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

1.2

CFU

s/m

L no

rmalized

to C

arry

ing Cap

acity

Time (hrs)

0 →1 E.coli

V.cholerae

Initial Concentrations

Figure 14. Numerical simulations of 3-ODE model. Varying initial concentrations of bacterial players, from 0 to carrying capacity for E.coli (black to blue lines) and simultaneously from carrying capacity→0 for V.cholerae (orange→green). Graph shows non-lysing bacterial concentrations normalized to carrying capacity. Inset shows V.cholerae concentration for first 0.15 hrs of simulation.

0 0.150

1

34

Discussion

As antibiotic-resistant bacteria begin to cusp on the verge of a global epidemic, serious

pursuits are being undertaken into alternative treatments. Phage therapy, first investigated over

seven decades ago, is now being reconsidered as a promising new alternative. One of the main

challenges in employing phage therapy is production and delivery of the virions. To address this

challenge, we turned to synthetic biology to design a bacterial vessel to seek out target pathogens

and release the deadly phages.

The bacterial strain of choice used to represent the seek-and-destroy engineered bacteria

(EB) was E.coli K-12, which is in a lysogenic state with the lambda phage. It was shown that

exposure to UV light at 254 nm for 5 minutes was sufficient to induce the cells to lyse. Though

the results were not definitive, infectivity assays and phage plaque assays supported established

literature claiming that UV exposure results in prophage induction [21]. In a previous study on

UV lysis induction in E.coli WU3610, it was shown that at high doses of UV (~6.4J/m2) about

75% of lysogenic bacteria become infective centers [24]. Since the UV dose used in induction of

K-12 was nearly 6.5 times greater, we can assume that a high percentage of the population was

induced, as long as the cells have competent lambda phage. The surprising scarcity of plaques

formed in the phage plaque assay is perhaps not only due to a lack of lytic induction but also a

sub-optimal protocol resulting in only a fraction of the available phages being added to the

susceptible MG1665 culture. Furthermore, below a certain threshold of lysing cells, plaques

would not be visible due to being overgrown by adjacent lysogenic [25] E.coli. Further

confirmation of phage presence could have been attained by performing PCR amplifications for

lambda phage DNA on samples that were hypothesized to contain phage particles.

35

In an effort to gather more biologically relevant parameter values for simulations of the

circuit design, a phage infection model was fit to the above-mentioned infectivity assay. A few

remarks are required here about the fallibility of forced model fitting. According to a paper by

Gunawardena in 2014 [38], when fitting a model to experimental data, only about 20% of the

parameters are well constrained by the fit. In order to prove the model’s accuracy, it is necessary

to constrain it on one set of experimental data points and to prove its validity by having it then

predict a second data set. Unfortunately in the case of fitting the infection model to the in vivo

data, only a single data set exists for each experimental condition. Any set of parameters can be

forced to fit a data set without reflecting any biologically relevant values. Therefore, although the

model was forced to fit one set of measurements accurately, because it lost accuracy when

compared to other experimental measurements its results must be viewed with skepticism.

The BioBrick lytic cassette BBa_K112808 was designed to cause cell death through an

onslaught on bacterial cell walls. It has the potential to fulfill two roles in a seek-and-destroy

genetic circuit: population growth inhibition and induction of phage production. Analysis of

BBa_K112808 functionality in vivo was made difficult by frequent loss-of-function mutations

due to the structure of the BioBrick component and the plasmid backbone used. The loss-of-

function mutations were determined to be prevalent in the cultures by nucleotide sequencing.

One of the drawbacks of construction of synthetic genetic circuits is the use of a registry of

standard components. This often results in part repetition, especially in more complicated

components with polycistronic regions or multiple promoters. In the case of the BBa_K112808

lytic cassette, the terminator BBa_B0010 is repeated at the end of both coding regions (i.e. after

the T4 lysozyme and after the T4 anti-holin). Sequence similarities between proximate DNA

segments, especially ones of such great length (80bp), will frequently result in replication

36

slippage and cause homologous recombination [27]. The greater the metabolic load of the

transformed plasmid on the host system, the greater the selective pressure to destroy the

synthetic circuit. A previous study into evolutionary stability of BioBricks in E.coli MG1665

cells found that plasmids could lose functionality as quickly as overnight for constructs with a

high metabolic load [27,38]. The lethal nature of the proteins under the inducible promoter serve

as a strong selective pressure for the bacterial cells. The lac promoter is known to be leaky [43]

and the pZe12-luc backbone is a high copy plasmid, together this results in a significant amount

of leakage of the cassette. Thus, attempts to remove the repeated terminator and constitutive

antiholin part of the lytic cassette were not sufficient to create a stable plasmid. The shorter

construct, pZe12-K112808S, which lacks the repeated BBa_B0010 component, also lacks the

antiholin coding sequence. Since the antiholin’s primary function is to nullify any leakage from

the holin gene, the shorter construct therefore leaks lethal proteins, resulting in an urgent

selective pressure against the plasmid. Future circuit engineering would require more stable

elements, not only for in vitro or in vivo characterization but also for any potential therapeutic

uses. Attempting to coerce bacteria into exhibiting selfless behaviour is counter to their frantic

scrabble for survival and it remains a constant engineering challenge.

Although our experimental findings could not decisively demonstrate the lytic cassette’s

ability to diminish population concentration, previous experiments [40] demonstrate that it can

efficiently exterminate a bacterial population. What is less evident is whether the cassette is

sufficient for induction of the lambda lytic phase, since the isolated plaques from the phage

plaque assay for BBa_K112808 are inconclusive proof. The lysogenic-lytic switch for lambda

phage is a carefully regulated process with known triggers for induction of prophage production,

such as: changes in environmental nutrient level, DNA mutation, and high multiplicity of

37

infection (number of lambda phages in a single cell) [21,24,25]. The lambda phage life cycle

decision can be condensed to the opposing activities of two repressor proteins, Cro and CI, on

the OR promoter region (Fig. 15). This bidirectional promoter region expresses genes required

for lysogeny in one direction and genes required for lysis in the other. At the moment of

infection, the lytic/lysogenic decision is made based on the ratio of Cro to CI concentration, with

Cro repressing the lysogenic pathway and CI repressing the lytic. Whereas Cro concentrations

are not subject to intense regulation, CI levels are determined by cell status at the moment of

infection. Among the first genes transcribed after infection is CII, a lysogeny transcription

activator which promotes transcription of cI from the PRE promoter. The CII protein is

susceptible to degradation by host proteases and its concentration reflects the host’s state. Even

after lysogeny is established, it is known that certain factors can induce a switch to lysis through

their effects on the stability of CII [21,28]. For example, low cAMP concentrations result in

higher activity of the bacterial protease HflB which decreases the concentration of CII, allowing

for OR123 to escape repression and for the phage to enter lysis.

While no literature addressing the direct effect of cell wall degradation on CII stability

has been found to date, one can speculate on the cell’s reactions to such a drastic upheaval. One

can imagine that the porosity of the walls could lead to a scattering of cAMP molecules leading

to an increased degradation of CII. A known inducer of lysis is protein denaturing through heat

shock [39], which could be similar to secretion of proteins through the damaged walls. It remains

to be elucidated whether the experimentally observed phage plaque is a testament to the lytic

cassette’s ability to produce viable virions or whether the lonely plaque stands as a marker of

biological noise.

38

a

b

c

Figure 15. Lysis/Lysogeny switch in lambda phage. a) Short operator region of the lambda phage genome containing three binding sites (OR1-3). Binding to the PRM promoter region results in transcription to the left, which includes transcribing the cI protein. Conversely, binding to the PR promoter region results in transcription of the right side and thus the Cro protein. b) As CI concentrations increase, cI dimers bind first to the OR1 site, then the OR2 site and block the RNA polymerase from binding to the PR promoter. Consequent transcription of the left hand side of genes results in lysogeny. c) With increasing Cro concentrations, Cro dimers bind to OR3

resulting in transcription of the right hand side genes, leading to lysis. d) Binding affinities for CI and Cro as their respective concentrations increase.

Cro cI

OR3 OR2 OR1

lysis

Increasing cI conc.

Increasing cro conc.

d

39

Should it be confirmed that population regulation components of our circuit cannot

double as the lysis inducing factor, alternative methods need to be explored. While it was

initially thought that overexpression of the lysogenic repressor Cro would be sufficient to enter

lysis, further research into the lysogenic/lytic decision mechanism suggests that this would not be

a reliable inducer. The lysogeny/lysis operator region contains three binding sites overlapping

the PR and PRM promoters. The two repressors (Cro and CI) have different affinities for the

binding sites, with cI preferring OR1 >OR2>OR3 and Cro preferring OR3>OR2=OR1 [21]. For an

E.coli cell existing in a lysogenic state, CI is bound to OR1 and OR2 and, at high concentrations,

to OR3 (Fig. 15). In order for lysis to be initiated, Cro needs to bind to OR3 with OR2 and OR1

free so that the RNA polymerase can bind to PR and begin transcribing lytic genes. Expressing

Cro might allow it to bind to the transiently free OR3 site, but it would require two consecutive

stochastic releases of OR2 and OR1 from CI. This is unlikely since CI dimers bound at OR1 help

stabilize CI bound at OR2. In order to induce lysis, some upstream protein would have to be

expressed that destabilizes CI. Of course, such a protein, once identified, might be specific for

lambda prophage induction and an analogue would have to be found for vibriophages. As of

now, little literature exists about the vibriophage life cycle, presenting a significant hurdle in

harnessing these phages for therapeutic use.

The next challenge that arises is the projected clinical efficiency of a small EB culture

eradicating a Vibrio cholerae infection. This question is answered, at least partly, through the

mathematical simulation of the EB system. Although many of the coefficients used in the model

were approximated or estimated, bifurcation analysis shows that it is only at extreme values

(non-biologically relevant) that the EB fails to eradicate the Vibrio cholerae. Obvious limitations

of our mathematical model come to mind when placing all our confidence in its conclusions,

40

including the computational challenges of simulating the eleven non-linear differential equations

with disparate time scales and the complexity involved in drawing conclusions from steady state

stability analyses. To reduce the complexity of the model and begin stressing it outside its

previous comfort zone, the quasi-steady state assumption was applied. This assumption is

applicable for systems with time-separation and claims that the molecular species with fast

dynamics can be considered to be in a steady-state concentration [29]. The simplified model

corroborated the findings from the original model, proving that the initial model’s behaviour was

not an artifact of its computational limitations. Numerical simulations and eigenvalue values

would indicate that from all but trivial initial conditions, our EB can demolish the pathogens.

The most interesting finding from the model is that a very small population of phages is

sufficient to quickly and efficiently kill the pathogen culture. In the Jensen model of vibriophage

growth during a cholera outbreak, an initial phage concentration of 106 virions/L was enough to

cut the duration of the outbreak in half and reduce the number of infected individuals [2]. This

was equal to less than one virion per pathogenic cell. Thus, even when initial conditions are such

that EB concentration is a small percentage of V.cholerae concentration, the self-propagating

nature of the vibriophages always pushes the pathogens to extinction.

In order to place our confidence in the results attained from our mathematical model we

need to re-evaluate the assumptions upon which the model is based. Physical laws predetermine

what conclusions can be drawn from a set of assumptions since a mathematical model can only

follow logical, consecutive steps to its resolution [38].

Firstly, the numerical representation of the quorum-sensing is a potential

oversimplification of the multi-component systems. In the case of the LuxR/LuxI circuit, the

You et al paper [34] assumed that activity of the circuit was limited by AHL concentrations since

41

LuxR and LuxI are expressed in abundance relative to the autoinducer concentration

fluctuations. It was similarly assumed that, despite differences in quorum-sensing architecture,

the CqsS/CqsA/CAI-1 quorum-sensing component of the seek-and-destroy circuit could be

described with the same mathematical equations. Both QS components are regulated by the

levels of their respective autoinducers. On the other hand, a more recent paper by Weber and

Buceta [30], which studied the effect of stochastic noise on the LuxR/LuxI quorum-sensing

system, found that variations in LuxR levels drove phenotypic variability and determined

quorum-sensing switch precision. Despite these contradicting theories, we would be inclined to

trust the You et al model because of its ability to accurately predict the dynamics of their

population growth controller. However, the conclusions drawn from the experimental data were

re-examined in a later study by Marguet and You in 2010 [31]. An investigation into possible

underlying causes of the observed population oscillations in cells containing the LuxI/LuxR-

ccdB circuit revealed that plasmids containing only the lethal ccdB were sufficient to produce

those oscillations. Plasmid amplification due to RNA Polymerase I level increase and decreased

division rates at high population densities caused the drastic bacterial population fluctuations

previously seen. Pointing out logical flaws in the model assumptions promises to be a

prodigious task. However, the fact that the original three-equation model was able to accurately

describe experimental behaviour suggests that it is still useful as a predictive tool.

Secondly, although the utilization of the quasi-steady state assumption (QSSA) was

useful in confirming stability analysis of steady states, the nature of the designed EB circuit leads

us to question the validity of using the QSSA. Quasi-steady state has been mostly applied in

biochemical [32] modeling when describing enzyme reactions or enzyme and substrate

interactions. Application of the QSSA can potentially cause the loss of dynamical behaviour by

42

oversimplification. Indeed, the reduced 5-equation version of the model did not show the

population oscillations of the EB culture present in the full 11-equation model. In fact, despite

the difference in time-scales between the different model species, assuming quasi-steady state

obfuscates the relationship between the molecular components and the bacterial players in the

model. However, although applying the QSSA to the model reduces its ability to capture

behavioural dynamics, it remains a useful tool as a steady-state stability analyzer.

In light of these contradictions and doubts one might begin to wonder whether

mathematical modeling is an exercise in futility. However, if we are to truly consider synthetic

biology an engineering discipline, then theoretical testing of our designs is mandatory. These in

silico experiments could be instrumental in identifying which circuit components need to be

tightly regulated. Furthermore, predicting different model behaviours would allow us to identify

why an unexpected experimental result might be occurring. Mathematical models are useful

tools that can clarify experimental results and uncover correlations that are not intuitively

evident.

43

Conclusion

Synthetic biology is a relatively young field, one whose boundaries expand daily as potential

circuit components and designs are characterized and created. It has within it the potential to

introduce revolutionary new medical treatments for crises that we are struggling to prevent. The

spread of antibiotic resistant bacterial strains threatens to make many standard clinical treatments

obsolete. By turning to synthetic biology praxes, we can design seek-and-destroy bacteria that

act as vessels to deliver phages to targeted pathogens. Such a genetic circuit was therefore

designed that used quorum-sensing molecules to regulate its two main functions; controlling the

growth of the seek-and-destroy bacteria and lysing upon detection of the target pathogen. To

realize the circuit, a mathematical model was developed to probe the design and assembly of the

circuit was begun in vivo with available circuit components.

Firstly, our chosen representative strain for our EB (K-12) was confirmed to be prophage

inducible via traditional methods. Secondly, construction on the seek-and-destroy circuit began

with a BioBrick lytic cassette. Characterization of this cassette was made difficult due to

frequent loss-of-function mutations but preliminary results hint towards the cassette having the

dual function of being a population regulator and a phage releaser. Whether or not we want those

two functions coupled in our EB circuit requires further investigation. Finally, a mathematical

simulation of the proposed circuit implied that the parasitic nature of vibriophages make them an

excellent avenue for study in creating realistic phage therapy treatments.

Although synthetic biology promises to be an important and novel tool in our biological

problem-solving arsenal, it comes with its own plethora of unique and perhaps still unidentified

challenges. The instability of synthetic circuits in such selfish organisms as bacteria make them

unreliable and uncooperative. Ambitious synthetic biologists are constantly working towards a

44

standardized method of circuit construction so that we can predict and avoid possible causes of

circuit failure. Though mathematical models, detailed databanks, and optimized computer

programs will allow us to maximize our chances of success for each original circuit design, the

persnickety nature of biology means that we cannot uncouple theoretical design maxims from

experimental trial and error. A two-pronged attack of theory and wet-lab tinkering will help us

use synthetic biology to provide solutions for a wide variety of global problems.

45

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List of Supplementary Figures S1.1 Table of parameter values for mathematical model of seek-and-destroy circuit 49

S1.2 Table of parameter values for infection model 50

S1.3 Dimensional version of infection model 50

S1.4 Analytical steady state of EB under population growth control 51

S2.1 Further numerical simulations of 11-ODE math model 52

S2.2 Numerical simulations of 5-ODE system 54

S2.3 Numerical simulations for 3-ODE system 55

S2.4 Numerical simulations for full model with parameter value pulled from infection model 56

S2.5 Eigenvalues 56

S3.1 Matlab code for numerical simulations 57

S3.2 Matlab code for steady state analysis 59

S3.3 Matlab code for fitting infection model to infectivity assay data 62

49

Supplementary

S.1.1 Table of parameter values for mathematical model of seek-and-destroy circuit

Variable Description Value Unit Source kE E.coli growth rate 0.97 1/h You [35] mx Carrying capacity 1.24*109 CFU/mL You [35] d death rate due to

ccdB 0.0004 nM/(mL*h) You [35]

vL AHL production rate 4.80*10-7 nM/(mL*h) You [35] dL AHL degradation

rate 0.64 1/h You [35]

vC CAI-1 production rate

4.80*10-7 nM/(mL*h) set to be the same as vL

dC CAI-1 degradation rate

0.64 1/h set to be the same as dL

vB ccdB production rate 5 1/h You [35] dB ccdB degradation

rate 2 1/h You [35]

kD V.cholerae growth rate

0.25 1/h Jensen [2]

kON ccdB:ccdA association rate

0.1 1/nM Dao [16]

kOFF ccdB:ccdA disassociation rate

0.001 1/nM Based off of Dao [16] findings. Approximated

vA ccdA production rate 5 1/h set to be the same as vB dA ccdA degradation

rate 4 1/h double dB

β1 virion burst size from E.coli

100 virions/(CFU/mL) Jensen [2]

β2 virion burst size from V.cholerae

100 virions/(CFU/mL) Jensen [2]

ω phage degradation rate

0.028 1/h Jensen [2]

q infection rate for V.cholerae

3.36*10-5 mL*h/virion Jensen [2]

b1 lysis rate for E.coli 1.5 1/h Cox [37] b2 lysis rate for

V.cholerae 1.5 1/h Cox [37]

vR cro production rate 5 1/h set to be equal to vB dR cro degradation rate 2 1/h set to be equal to dB η rate of entry into

lysis state for E.coli 0.023 nM/(mL*h) Smith [39]

50

S.1.2 Table of parameter values for infection model

Variable Description Non-dimensional

value

Source Dimensional Value

Unit

kE growth rate of uninfected E.coli

0.5 From fitting growth curve to logistic growth

0.5 1/h

f fraction of cells which choose lysis over lysogeny upon infection

0.35 estimated N/A N/A

b virion burst size of lysing cell

25 estimated 25 virions/CFU/m

L kD growth rate of

lysogenic E.coli 0.18 estimated 0.18 1/h

K carrying capacity for non-infected E.coli

1.33 From fitting growth curve to logistic growth

1.24*109 CFU/mL

KD carrying capacity for lysogenic E.coli

0.6 estimated 5.58*108 CFU/mL

ki lysis rate for cells in lytic state

0.1 estimated 7.83*10-11 1/h

P0 Phage count at time = 0 20 estimated N/A N/A dp degradation rate of

phage 0.1 estimated 7.83*10-11 1/h

S.1.3 Dimensional version of infection model

A non-dimensional version of (1) was created, as seen in main Methods, by substituting (2) into (1).

(1) (2)

51

S.1.4 Analytical steady state of EB under population growth control.

All other species at steady state are equal to zero. Subscript of “s” stands for steady state

concentration for EB (E) ccdB (B) and AHL (L).

52

S.2.1 Further numerical simulations of 11-ODE math model

vC: 0 → 9.8*10-7

dC: 0 → 1.28

eigenvalues

vC: 0 → 9.8*10-7

eigenvalues

dC: 0 → 1.28

0 ->1 E.coli

V.cholerae

A)

B)

53

Numerical simulations of full 11-ODE model of EB seek-and-destroy circuit and associated

eigenvalues at the resting steady state for each simulation. Black to blue lines represent E.coli

concentration normalized to carrying capacity, with increasing parameter values. Green to

orange lines represent V.cholerae concentration normalized to carrying capacity, with increasing

parameter values. Initial conditions are 1.24*108 CFU/mL for EB, 1.24*109 CFU/mL for

V.cholerae and zero for all other species. On the right of all numerical simulations are visual

representations of the real components of the eigenvalues, grey representing negative values and

black representing positive values. Each column represents one set of eigenvalues for each

parameter value. A) Increasing rate of CAI-1 production (vC) from 0 →9.8*10-7 nM/(mL*h) in

increments of 9.8*10-8 nM/(mL*h). B) Increasing rate of CAI-1 degradation (dC) from 0→1.28

1/h in increments of 0.128 1/h. C) Increasing rate of lysis (b1 and b2) from 0→2 1/h in

increments of 0.2 1/h.

b1 and b2: 0 → 2.0

b1 and b2: 0 → 2.0

eigenvalues

C)

54

S.2.2 Numerical simulations of 5-ODE system.

Similar conditions to S.2.1 but for the 5-ODE math model and only showing parameter value

variations for lysis rate A) b1 and b2 and for CAI-1 production rate B) vC.

b1 and b2: 0 → 2.0

b1 and b2: 0 → 2.0

eigenvalues

vC: 0 → 9.8*10-7

vC: 0 → 9.8*10-7

eigenvalues

A)

B)

55

S.2.3 Numerical simulations for 3-ODE system.

Similar to S.2.1 and S.2.3. Only showing parameter variation for CAI-1 production rate, vC.

Simulations of other parameter variations were computationally impossible.

vC: 0 → 9.8*10-7

vC: 0 → 9.8*10-7

eigenvalues

56

S.2.4 Numerical simulation for full model with parameter value pulled from infection model

Similar to S.2.1-3. All parameter values set at initial values with the exception of the rate of lysis

(b1 and b2) which are set to 7.8*10-11 1/h as determined from fitting the infection model to the

data from the K-12 and MG1665 UV infectivity assay. Shown on the left are numerical

simulations with black → blue lines representing increasing EB concentrations as normalized to

carrying capacity. Simultaneously, orange → green lines represent decreasing V.cholerae

concentrations, also normalized to carrying capacity. On the right, each column in the matrix

represents a set of eigenvalues for that condition (i.e. column 2 shows eigenvalues for E0 =

0.2*mx and D0 = 0.8*mx). Grey represents negative values and black represents positive values

for the real parts of the eigenvalues.

S.2.5 Eigenvalues for steady state where all species are zero, for 11-ODE model with initial

parameter values

Initial concentration: EB ↑ as V.cholerae ↓

eigenvalues

λ1 = -7*10-11

λ2 = -3.99

λ3 = -2.00

λ4 = -2.0

λ5 = -0.64 λ6 = -0.64

λ7 = -0.028

λ8 = -0.001

λ9 = -7*10-11

λ10 = 0.25

λ11 = 0.97

57

S.3.1 Matlab code for numerical simulations

ODEs for full 11-equation seek-and-destroy model function dydt = pmod(t,y) %Assigning all variables global kE mx d z kD q b1 b2 Bet1 Bet2 w vl dl vc dc va da vb d_b vr dr kon koff; E = y(1); D = y(2); En = y(3);Dn = y(4);P = y(5);L = y(6); C = y(7); R = y(8);B = y(9); A = y(10);Ab = y(11); dydt = [kE*(E*(1-(E+En+D+Dn)/mx)-d*E*B-z*R*E); kD*D*(1-(E+En+D+Dn)/mx)-q*P*D; z*R*E-b1*En; q*P*D-b2*Dn; Bet1*b1*En+Bet2*b2*Dn-q*P*D-w*P; vl*E-dl*L; vc*D-dc*C; vr*C-dr*R; vb*L+koff*Ab-d_b*B-kon*A*B; va*C-da*A-kon*A*B+koff*Ab; kon*A*B-koff*Ab;]; end

Call_pmod takes one argument, allowing one parameter value to be varied with each call of the function

function [T,Y] = call_pmod(b) %Assigning values to all variables global kE mx d z kD q b1 b2 Bet1 Bet2 w vl dl vc dc va da vb d_b vr dr kon koff; kE = 0.97; mx = 1.24e9; d = .004; z = 0.023; kD = 0.25; q = 3.36E-5; b1 = 1.5; b2 = 1.5; Bet1 = 100; Bet2 = 100; w = 0.028; vl = 4.8E-7;dl = 0.64; vc = 4.8E-7; dc = 0.64; va = 5; da = 4; vb = 5; d_b = 2; vr = 5; dr = 2;kon = 10^(-1);koff = 0.001; %Setting up initial conditions tspan = [0 60]; y0 = zeros(11,1); y0(1:2) = [b*mx (1-b)*mx]; [T,Y] = ode15s(@pmod,tspan,y0); end

Performing a numerical simulation of the pmod function on a range of parameter values. This is

a script called numsimviz.m hold on for i=0:0.1:1 [T,Y] = call_pmod(i); plot(T,Y(:,1)/1.24E9,'color',[0 0 i]); plot(T,Y(:,2)/1.24E9,'color',[(1-i) 0.5 0]);

58

end ylabel('CFUs/mL normalized to Carrying Capacity'); xlabel('Time (hrs)');

After first quasi-steady state approximation, model is reduced to 5 equations. function [T,Y] = moleculargone(b) %Using quasisteady state on all molecular players reduces system to 5 %dimensions kE = 0.97; mx = 1.24*10^9; d = 0.004; r = 0.023; kD = 0.25;q = 3.36e-5; b1 = 1.5; b2 = 1.5; Bet1 = 80; Bet2 = 80;w = 0.33; vl = 4.8*10^-7; dl = 0.639; vc = 4.8*10^-7*2*b; dc = 0.639; va = 5; da = 4; vb = 5; db = 2; vr = 5; dr = 2; kon = 10^(-1);koff = 10^(-5); function dydt = myfun(t,y) E = y(1);D=y(2);En=y(3);Dn=y(4);P=y(5);

dydt = [kE*E*(1-(E+En+D+Dn)/mx)-d*vb*vl/(db*dl)*E*E-r*vr*vc/(dr*dc)*D*E;

kD*D*(1-(E+En+D+Dn)/mx)-q*P*D; r*vr*vc/(dr*dc)*D*E-b1*En; q*P*D-b2*Dn; Bet1*b1*En+Bet2*b2*Dn-q*P*D-w*P;]; end tspan = [0 60]; y = zeros(5,1); y(1:2) = [0.1*mx mx]; [T,Y] = ode15s(@myfun,tspan,y); end

For numerical simulations, numsimviz is used but with line 3 changed to [T,Y] = moleculargone(i); Another application of the quasi-steady state equilibrium reduces the model to 3 equations:

function [T,Y] = solvtrzyeqns(b) kE = 0.97; mx = 1.24*10^9; d = 0.004; r = 0.023; kD = 0.25;q = 3.36e-5; b1 = 1.5; b2 = 1.5; Bet1 = 80; Bet2 = 80;w = 0.33; vl = 4.8*10^-7; dl = 0.639; vc = 4.8*10^-7*2*b; dc = 0.639; va = 5; da = 4; vb = 5; db = 2; vr = 5; dr = 2; kon = 10^(-1);koff = 10^(-5); a1 = r*vr*vc/(dr*dc*b1); a2 = q/b2; a3 = d*vc*vb/(db*dc); a4 = r*vr*vc/(dr*dc); y1 = Bet1*a4; y2 = Bet2*q; function dydt = myfunc(t,y) dydt = [kE*y(1)*(1-(y(1)+y(2)+a1*y(2)*y(1)+a2*y(3)*y(2))/mx)-a3*y(1)^2-a4*y(2)*y(1); kD*y(2)*(1-(y(1)+y(2)+a1*y(2)*y(1)+a2*y(3)*y(2))/mx)-q*y(3)*y(2); y1*y(2)*y(1)+y2*y(3)*y(2)-q*y(3)*y(2)-w*y(3);]; end y0 = zeros(3,1); y0(1:2) = [b*mx (1-b)*mx]; tspan = [0 60];

59

options = odeset('NonNegative',[1 2 3]); [T,Y] = ode15s(@myfunc,tspan,y0); end

For numerical simulations, numsimviz is used but with line 3 changed to [T,Y] = solvtrzyeqns(i); S.3.2 Matlab code for steady state analysis

For each set of parameter values, the steady state is solved for using “fsolve”. Eigenvalues at

these steady states are then calculated and written to an excel file. function [eigs] = solvepmod() kE = 0.97; mx = 1.24e9; d = .004; z = 0.023; kD = 0.25; q = 3.36E-5; b1 = 1.5; b2 = 1.5; Bet1 = 100; Bet2 = 100; w = 0.028; vl = 4.8E-7;dl = 0.64; vc = 4.8E-7; dc = 0.64; va = 5; da = 4; vb = 5; d_b = 2; vr = 5; dr = 2;kon = 10^(-1);koff = 0.001; function dydt = myfun(y) E = y(1); D = y(2); En = y(3);Dn = y(4);P = y(5);L = y(6); C = y(7); R = y(8);B = y(9); A = y(10);Ab = y(11); dydt = [kE*(E*(1-(E+En+D+Dn)/mx)-d*E*B-z*R*E); kD*D*(1-(E+En+D+Dn)/mx)-q*P*D; z*R*E-b1*En; q*P*D-b2*Dn; Bet1*b1*En+Bet2*b2*Dn-q*P*D-w*P; vl*E-dl*L; vc*D-dc*C; vr*C-dr*R; vb*L-d_b*B-kon*A*B+koff*Ab; va*C-da*A-kon*A*B+koff*Ab; kon*A*B-koff*Ab;]; end y0 = zeros(11,1); tspan = [0 60]; y0(1:2) = [0.1*mx 0.1*mx]; y0(6:11) = 300; options = optimset('MaxFunEvals',50000,'MaxIter',4000); eigmatrix = zeros(11,22); j = 1; solmatrix = zeros(11,11); s = 1; for i=0:0.1:1; y0(1:2) = [0*mx 0*mx]; [sol] = fsolve(@myfun,y0,options);

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solmatrix(:,s) = sol; s = s+1; v = [kE,mx,d,z,kD,q,b1,b2,Bet1,Bet2,w,vl,dl,vc,dc,vr,dr,vb,d_b,kon,koff,va,da]; J = myjacob(v,sol'); eigs = eig(J); eigmatrix(:,j) = real(eigs); eigmatrix(:,j+1) = imag(eigs); j = j+2; end xlswrite('/Thesis/evals.xlsx',eigmatrix,9); xlswrite('/Thesis/evals.xlsx',solmatrix,10); end

Similarly, for the 5-equation ODE system steady state analysis: function molgoneigs() %Looking for bifurcations again for molecular qss system kE = 0.97; mx = 1.24*10^9; d = 0.004; r = 0.023; kD = 0.25;q = 3.36e-5; b1 = 1.5; b2 = 1.5; Bet1 = 80; Bet2 = 80;w = 0.33; vl = 4.8*10^-7; dl = 0.639; vc = 4.8*10^-7; dc = 0.639; va = 5; da = 4; vb = 5; db = 2; vr = 5; dr = 2; kon = 10^(-1);koff = 10^(-5); function dydt = myfun(y) E = y(1);D=y(2);En=y(3);Dn=y(4);P=y(5); dydt = [kE*E*(1-(E+En+D+Dn)/mx)-d*vb*vl/(db*dl)*E*E-r*vr*vc/(dr*dc)*D*E; kD*D*(1-(E+En+D+Dn)/mx)-q*P*D; r*vr*vc/(dr*dc)*D*E-b1*En; q*P*D-b2*Dn; Bet1*b1*En+Bet2*b2*Dn-q*P*D-w*P;]; end eigmatrix = zeros(5,22); j = 1; solmatrix = zeros(5,11); s = 1; y0 = zeros(5,1); y0(1:2) = [0.1*mx 0.1*mx]; options = optimset('MaxFunEvals',50000,'MaxIter',40000); for i=0:0.1:1; vc = i*2*4.8E-7; [sol] = fsolve(@myfun,y0,options); solmatrix(:,s) = sol; s = s+1; v = [kE mx (d*vb*vl/(db*dl)) (r*vr*vc/(dr*dc)) kD q b1 b2 Bet1 Bet2 w]; J = molgoneJacob(v,sol'); eigs = eig(J); eigmatrix(:,j) = real(eigs); eigmatrix(:,j+1) = imag(eigs); j = j+2; end xlswrite('/Thesis/molgone_evals.xlsx',eigmatrix,3);

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xlswrite('/Thesis/molgone_evals.xlsx',solmatrix,4); end

And for the 3-equation model: function trzyeigens() %Looking for bifurcations again for trzy eqn system function dydt = myfun(y) E = y(1);D=y(2);P=y(3); dydt = [kE*E*(1-(E+D+a1*D*E+a2*P*D)/mx)-a3*E^2-a4*D*E; kD*D*(1-(E+D+a1*D*E+a2*P*D)/mx)-q*P*D; y1*D*E+y2*P*D-q*P*D-w*P;]; end eigmatrix = zeros(3,22); j = 1; solmatrix = zeros(3,11); s = 1; y0 = zeros(3,1); y0(1:2) = [0.1*1.24E9 0.0*1.24E9]; options = optimset('MaxFunEvals',50000,'MaxIter',40000); for i=0:0.1:1; kE = 0.97; mx = 1.24*10^9; d = 0.004; r = 0.023; kD = 0.25;q = 3.36e-5; b1 = 1.5; b2 = 1.5; Bet1 = 80; Bet2 = 80;w = 0.33; vl = 4.8*10^-7; dl = 0.639; vc = 4.8*10^-7; dc = 0.639*2*i; va = 5; da = 4; vb = 5; db = 2; vr = 5;dr = 2; kon = 10^(-1);koff = 10^(-5); a1 = r*vr*vc/(dr*dc*b1); a2 = q/b2; a3 = d*vc*vb/(db*dc); a4 = r*vr*vc/(dr*dc); y1 = Bet1*a4; y2 = Bet2*q; [sol] = fsolve(@myfun,y0,options); solmatrix(:,s) = sol; s = s+1; v = [kE mx a1 a2 kD a3 a4 q y1 y2 w]; J = trzyJacob(v,sol'); eigs = eig(J); eigmatrix(:,j) = real(eigs); eigmatrix(:,j+1) = imag(eigs); j = j+2; end xlswrite('/Thesis/3_evals.xlsx',eigmatrix,3); xlswrite('/Thesis/3_evals.xlsx',solmatrix,4); end

The appropriate excel sheet was read and the eigenvalue values were visualized as a two-colour

matrix. This script is called eigenvalueviz.m numbs = xlsread('/Thesis/evals.xlsx',9); xvals = numbs(1,:); xvals(isnan(xvals)) = []; reals = numbs(:,1:2:end);

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reals = reals./abs(reals); imagesc(reals);

S.3.3 Matlab code for fitting infection model to infectivity assay data.

To calculate growth rate and carrying capacity of K-12 and MG1165, the Matlab Open Curve

Fitting app was used (“cftool”). function [] = maynard_nodil() %This one will be immutable. It's the first infection trial. %data points ctrl = [0.389 0.524 0.729 1.02 1.16 1.24 1.24]; inf = [0.389 0.36 0.409 0.49 0.582 0.703 0.821]; % Where x3 is the 1.5mL trial ctrl = ctrl/1.25; inf = inf/1.25; % time = 0:20:20*6; time = 0:6; kE = 0.5; %from fitting ctrl f = 0.35; b = 25; kD = 0.18; Kd = 0.6; K = 1.33; %from fitting ctrl ki = 0.1; Po = 20; dp = 0.1; function dydt = myfun(t,y); E = y(1); P = y(2); D = y(3); dydt = [E*(1-(E+D))-ki/kE*E*P; K/kE*(b*ki*E*P*f-ki*D*P-ki*E*P-dp*P); ki/kE*(1-f)*E*P+kD/kE*D*(1-(E+D)/(Kd*K));]; end y0 = [ctrl(1);0;0]; [t,y] = ode23s(@myfun,[0 6],y0); modc = interp1(t,(y(:,1)+y(:,3)),time); SSE = (modc-ctrl); SSE = sum(SSE.^2) h1 = plot(time,ctrl,'^'); hold on plot(t,(y(:,1)+y(:,3)),'blue'); y0 = [inf(1); Po; 0]; [t,y] = ode23s(@myfun,[0 6],y0); modi = interp1(t,(y(:,1)+y(:,3)),time); SSE = (modi-inf); SSE = sum(SSE.^2) h2 = plot(time,inf,'r+'); [ax,h3,h4] =plotyy(t,(y(:,1)+y(:,3)),t,y(:,2)); set(h3,'color','red'); set(h4,'color','green'); ylabel(ax(1),'OD 600'); ylabel(ax(2),'Phage/mL'); legend([h1 h2 h4],{'Ctrl','Infected','Phage Particles'}); end