Bacterial Outer-Membrane Vesicle as a Countermeasure

against Viral Infection

A Thesis Presented

by

Masoud Mahdisoltani

to

The Department of Civil and Environmental Engineering

in partial fulfillment of the requirements

for the degree of

Master of Science

in

Civil Engineering

Northeastern University

Boston, Massachusetts

August 2018

ii

ABSTRACT

To alleviate the effects of imposed stresses, bacterial populations employ a variety of

defensive mechanisms. Bacteriophage infection is one of the main threats to bacteria;

hence, bacteria evolved to have different strategies to fight against their infection.

Gram-negative bacteria release extracellular vesicles from their outer membrane. While

the reason behind the production of Outer-Membrane Vesicle (OMV), which costs energy

and resource for bacteria, is yet not fully understood, their same outer structure can serve

the bacterial population as decoys for reducing the viral infection rate. In this study, the

efficiency of OMVs as defensive agents against infection has been investigated to see

whether they can be considered as a biologically evolved defense mechanism. For this

purpose, mathematical models were used, and the average resource limitation

concentrations (a.k.a. R*) for the bacterium strain with OMVs and the strain without

OMVs were compared. It is observed that consuming resources for releasing OMVs

would benefit the bacterial population under certain conditions. This study uses

”equation based–computer developed” models simulating OMVs as anti-phage agents.

Findings from this research conform to the results from other studies which used

experimental methods.

In summary, when the population loss due to viral infection is significant, and resource

availability is not the main limiting factor, OMVs are helpful to bacteria to attenuate

infection; whereas OMVs presence in unfavorable conditions does not disprove these

findings as they have multiple functions. It is also noted in other studies that vesiculation

happens at a higher rate when bacteria are exposed to external stresses. These

observations validate the general idea of considering vesicles as a defense strategy and

introduces a possibility for quorum sensing involvement in their production by bacteria.

Applying quorum sensing as a regulator of OMV production, it is observed that adjusted

vesiculation based on phage infection serves in favor of bacterial population fitness.

iii

ACKNOWLEDGMENT

First of all, I want to express my sincere appreciation to Prof. Ferdi L. Hellweger, former

faculty at the Department of Civil and Environmental Engineering at Northeastern

University, and now Chair of Water Quality Engineering at the Technical University of

Berlin, who has been advising me for the most time of my master studies. His guidance

was of the essence to this research, and his mentorship provided me with insights beyond

the extents of it.

I surely should thank Prof. Ameet Pinto of the Department of Civil and Environmental

Engineering at Northeastern University, for advising me in the last stages of my thesis.

Concluding my work would not be possible without his kind support.

I would also like to acknowledge constructive comments of Prof. Philip Larese-Casanova

of the Department of Civil and Environmental Engineering at Northeastern University as

the reviewer of this thesis.

Last but not least, I extend my gratitude to my family, specially my parents, who provided

me with support and love which I cannot describe in words. I am dedicating this thesis to

them as a token of respect and appreciation.

iv

TABLE OF CONTENTS

LIST OF FIGURES v

LIST OF TABLES vi

LIST OF ACRONYMS vii

1 Introduction 11.1 Bacterial Cell Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Bacteriophage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Outer-Membrane Vesicles . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Bacterial Defense Mechanisms against Phage Infection . . . . . . . . . . . 61.5 Bacterially Speaking: Regulatory Mechanism for bacterial population . . . 7

2 Predator-Prey: Modeling of Bacteriophage-Bacterium Interaction 82.1 Fitness of OMVs as Anti-phage Agents . . . . . . . . . . . . . . . . . . . 8

3 Resource-Limited Growth, Competition, and Predation 103.1 Introducing OMVs to the Model . . . . . . . . . . . . . . . . . . . . . . . 103.2 Different States of the Model . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 R* as a Measure of Outer-Membrane Vesicles Fitness in Different Conditions 16

4 Marine Viruses and Heterotrophic Bacteria 204.1 Introducing OMVs to the Model . . . . . . . . . . . . . . . . . . . . . . . 214.2 Different States of the Model . . . . . . . . . . . . . . . . . . . . . . . . . 234.3 Measuring Outer-Membrane Vesicles Fitness . . . . . . . . . . . . . . . . 26

5 Quorum Sensing as a Regulator of Vesiculation Process 305.1 R* as a Measure of Outer-Membrane Vesicles Fitness . . . . . . . . . . . . 32

6 Conclusion 34

REFERENCES 36

v

LIST OF FIGURES

1.1 Prokaryotic cell structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Structure of bacteriophage . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Phage infection process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 OMV formation (vesiculation) process . . . . . . . . . . . . . . . . . . . . 5

3.1 Different states of the Levin, Stewart, and Chao (1977) Model. (a)Populations oscillating at equilibrium. (b) Populations stable at constantconcentrations. (c) Extinction of phages . . . . . . . . . . . . . . . . . . . 15

3.2 R* ratio in different habitat and OMVs variable versus the number ofreleased OMVs by bacteria in each division cycle . . . . . . . . . . . . . . 17

3.3 R* ratio in different habitat and OMVs variable versus g (extended interval) 18

4.1 Different states of Weitz et al. (2015a) Model. (a) Populations oscillatingtoward a stable equilibrium (b) Constant concentrations at equilibrium (c)Extinction of phages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 R* ratio of different habitat conditions and OMVs variables versus percentbiomass diverted to OMVs . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.3 Percent Loss due to Viral Infection (PLV) ratio of different habitatconditions and OMVs variables versus percent biomass diverted to OMVs . 28

5.1 Average Limiting Resource (R*) ratio for the QuorumSensing (QS)-regulated bacterium . . . . . . . . . . . . . . . . . . . . . . 33

vi

LIST OF TABLES

3.1 Average sizes of Escherichia coli (E. coli) cells and their OMVs . . . . . . 133.2 Parameter used for replicating different states of the model . . . . . . . . . 143.3 Minimum, Maximum and Average values for parameters varying in batch

computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.1 Values associated with different states of the model . . . . . . . . . . . . . 244.2 Minimum, Maximum and Average values for batch computations . . . . . . 29

5.1 Values associated with QS and vesiculation. . . . . . . . . . . . . . . . . . 32

vii

LIST OF ACRONYMS

E. coli Escherichia coli is a rod-shaped, gram-negative bacteria which some strainsof it are the cause of food poisoning.

OMV Outer-Membrane Vesicle is a spherical entity released from the membrane ofgram-negative bacteria.

PLV Percent Loss due to Viral Infection is the ratio of loss for the bacterial populationdue to viral infection over the population loss due to infection, wash-out or otherlimiting phenomena.

QS Quorum Sensing is a mechanism used by bacterial population to set up geneexpression for regulating the population responses and behaviors.

R* Average Limiting Resource is the resource concentration that restricts thepopulation of an organism.

1

Chapter 1

Introduction

Numerous microorganisms such as bacteria and viruses exist in the environments which are

critical players in the biogeochemical cycle (Sime-Ngando, 2014). The interaction between

bacteria and viruses has gained increasing attention recently (Almand, Moore, & Jaykus,

2017; Steed & Stappenbeck, 2014).

A bacterium is a single-celled microorganism which is a severe concern in regards to

water resources contamination and water-borne diseases (Cabral, 2010; Pandey, Kass,

Soupir, Biswas, & Singh, 2014). Viruses are infectious particles which affect all living

organisms including microorganism (Koonin, Senkevich, & Dolja, 2006). Bacteriophages

(a.k.a. phages), viruses that infect bacteria, affect the bacterial population in different

ways. Phages can retard the growth rate of the population, alter the key characteristics of

them (e.g., antibiotics resistance or converting non-pathogenic strains to pathogenic ones)

(Chaturongakul & Ounjai, 2014; Davies & Davies, 2010). Understanding the interaction

between bacteria and viruses can help to better perceive theses microorganisms

functioning and subsequently proper planning.

1.1 Bacterial Cell Structure

Bacteria are prokaryotic organisms consist of ”nucleoid (DNA), ribosomes, cell membrane,

cell wall, and a surface layer” (Salton & Kim, 1996). Figure 1.1 shows their typical cell

structure.

2

Figure 1.1: Prokaryotic cell structure (Source: Davidson (2015))

Based on the cell wall structure, bacteria divide into gram-negative and gram-positive.

Gram-negative bacterium has an outer membrane besides the peptidoglycan cell wall

(Nikaido & Nakae, 1980). The outer membrane provides the gram-negative bacteria with

an extra shield against severe environments (Ralf, P., & Patrick, 2002).

1.2 Bacteriophage

While we traditionally consider viruses as parasites causing diseases, they have been used

to eliminate pathogenic bacteria. They have also can have an adverse effect on the bacteria

and convert a non-pathogenic one to pathogenic (Kutter et al., 2010; Sinha, Grewal, & Roy,

2018). Therefore, it is essential to investigate their interaction with the bacteria to grasp

their role in the ecobiology system. The relationship between bacteria and phage can be

limited to a predator-prey system or be as complicated as their evolution path (Doetsch &

Cook, 1973; Onodera, 2010).

3

It has been discovered that viruses have the largest population of microorganisms not only

in natural water bodies but also on Earth, exceeding bacteria population by an order of

magnitude (Minsik & Sangryeol, 2012; Wommack & Colwell, 2000). Thus, they have an

impact on water quality studies concerning bacterial activities; however, their effect has

been mainly overlooked in the basis of current models (Boutilier, Jamieson, Gordon, &

Lake, 2011; Wong, Lee, & Hodgkiss, 2007).

Proteins of the outer membrane of gram-negative bacteria serve as receptors for phages.

Each bacteriophage can infect a limited number of hosts based on the existence of the

receptor (i.e., proteins of the membrane) on the membrane of the bacteria (Rakhuba,

Kolomiets, Dey, & Novik, 2010).

Most phages initiate their infection by tail adsorption to the bacterium wall (Chaturongakul

& Ounjai, 2014). It has been indicated that by far the majority of phages are tailed (Minsik

& Sangryeol, 2012). Hence, we focus on demonstrating tailed phages and their infection

process. Figure 1.2 shows a tailed phage structure.

Figure 1.2: Structure of bacteriophage (Source: D’Onofrio (2012))

4

Phage infects a bacterium by adsorbing to the cell wall, penetrating, introducing DNA or

RNA of it to the bacterium, and finally using bacterium as a host for replication (Lenski,

1988). Figure 1.3 illustrates the process of infection.

Figure 1.3: Phage infection process (Source: Viral Zone (Swiss Institute of

Bioinformatics) (2013))

It is a key concept to this research that the outer membrane of the gram-negative bacteria

performs as host receptors for the proteins on tails of the phage and that the adsorption

of phage to outer membrane is irreversible. In other words, phages infect any agent that

has the appropriate receptors, and once they infect the individual, whether it is a bacterium

or not, the process cannot be undone (Rakhuba et al., 2010; Silva, Storms, & Sauvageau,

2016). Moreover, Superinfection phenomenon (Roundy, Azar, Rossi, Weaver, & Vasilakis,

2017) is neglected in the model and each bacteria or OMV only gets infected once.

1.3 Outer-Membrane Vesicles

Gram-negative bacteria releases spherical entities of outer membrane ”filled with

periplasmic content” which are called OMVs. However, this is not exclusive to

gram-negative bacteria, and it has been observed that all forms of living organisms

—Eukarya, Archaea, and Bacteria— make ”membrane-enclosed” material (Jan, 2017;

Schwechheimer & Kuehn, 2015).

5

Beveridge (1999); Jan (2017) explain the process of OMV formation and introduce the

following theories for that matter:

• The lost covalent linkage between the outer membrane and peptidoglycan

• Partial accumulation of peptidoglycan under outer membrane

• Increase in the membrane curvature-inducing molecules

Based on the above hypotheses, OMVs production is initiated by a local change in the

outer membrane which leads to the formation of a bulge and finally releasing the vesicular

particle. Figure 1.4 shows a schematic of OMV formation. It can be observed that OMVs

have the same outer membrane specification as the bacteria.

Figure 1.4: OMV formation (vesiculation) process (Source: Roier, Zingl, Cakar,

Durakovic, et al. (2016))

Vesiculation costs bacterial population a significant amount of energy and resource (Roier,

Zingl, Cakar, & Schild, 2016). It is suggested that OMVs are involved in critical functions

of the bacterial population on different levels including bacteria-bacteria and bacteria-host

interactions (e.g., resource acquisition, horizontal gene transfer, protection against

6

antibiotics) (Kulkarni & Jagannadham, 2014; Kulkarni, Nagaraj, & Jagannadham, 2015;

Kulp & Kuehn, 2010; Roier, Zingl, Cakar, Durakovic, et al., 2016).

1.4 Bacterial Defense Mechanisms against Phage

Infection

Bacteria must respond to stressors to keep its growth rate above the survival rate

(MacDonald & Kuehn, 2013). To mitigate viral infection effects, bacteria employ

different strategies such as preventing phage attachment by concealing protein receptors

through mutation, preventing DNA entry by imitating superinfection effect

(superinfection exclusion) or even abortive infection which causes the death of the

infected bacterium but prevents phage replication. (Labrie, Samson, & Moineau, 2010;

Seed, 2015). More recently, Reyes-Robles et al. (2018) showed that OMVs could reduce

viral infection stress on the bacterial population. In their study, it is noted that OMVs are

non-replicating agents with the same outer structure as bacteria with outer-membrane

proteins and lipids and periplasmic content. It supports the hypothesis that phage may

infect an OMV and since it is not a replicating agent, that phage will be neutralized.

OMVs have the same membrane as one of the bacteria and therefore, phages may infect

them (refer to Chapter 1.3). Manning and Kuehn (2011) have also evaluated this

hypothesis and concluded that OMV contributes to the bacterial population by

”adsorption of antimicrobial peptides and bacteriophages” as an innate defense strategy.

Reyes-Robles et al. (2018) measured the decrease in the infection of phage for a particular

strain of Vibrio cholerae bacterium. They found out that presence of the specific types of

receptors (LPS) on OMVs associated with the specific type of the phage is required for them

to affect the infection rate. The observations were verified by measuring the infection rate

for three different phages in which the rate has decreased in the presence of OMVs by an

order of magnitude for all of them. These findings support the idea of considering OMVs as

a defense strategy for bacteria against viral infection; however, OMVs have been observed

to play various roles for bacterial population and therefore, their presence in non-infectious

environments is justified (Kulkarni & Jagannadham, 2014).

7

1.5 Bacterially Speaking: Regulatory Mechanism for

bacterial population

The bacterium can communicate within its population by producing signaling molecules

to regulate gene expressions due to changes in its population or to response to the presence

of other microorganisms. It has also been noted that viruses sense these chemicals

produced by bacteria and intercept the signals (Callaway, 2017; Forsythe, 2018; Miller &

Bassler, 2001). Evolutionary speaking, this points out that bacteria may use signaling

against viruses and, ergo phages has developed a method to intervene and neutralize that.

The mechanism of signaling by bacteria is called Quorum Sensing which enables them to

make the appropriate response when the population reaches to a certain level or a change

happens in the habitat or population (Monedero, Revilla-Guarinos, & Zuniga, 2017). The

term ”Bacterially Speaking” was used by Bassler and Losick (2006) to describe this

phenomenon. It is believed that QS is playing a more complicated role for bacterial

population, and have multiple functions for bacteria (Bassler & Losick, 2006; Monedero

et al., 2017; Oliver & Swords, 2015). Besides, various types and strains of bacteria (e.g.,

heterotrophs or autotrophs, gram-negative or gram-positive) has been observed to employ

QS as a regulatory mechanism (de Souza Santos, Salomon, Li, Krachler, & Orth, 2015;

Papenfort & Bassler, 2016; Rutherford & Bassler, 2012; Zhou, Lyu, Richlen, Anderson, &

Cai, 2016; Zohar & Kolodkin-Gal, 2015).

More interestingly, Høyland-Kroghsbo, Mærkedahl, and Svenningsen (2013) investigated

QS as an optimization method of bacterial defense strategies against bacteriophage

infection. In their research, it has been observed that E. coli activates or elevates its

anti-phage strategies in response to the presence of the predator (i.e., bacteriophage).

8

Chapter 2

Predator-Prey: Modeling of

Bacteriophage-Bacterium Interaction

There are two types of infection by bacteriophage: virulent and temperate. Temperate

phages insert their genome into the bacteria and replicate in the process of cell division.

While virulent phage kills the host when it reaches its burst size (Heilmann, Sneppen, &

Krishna, 2010). This study focuses on virulent phages. Therefore, predator-prey models of

bacteriophages-bacteria were selected to investigate OMVs as an anti-phage strategy.

These models generally are constructed by simulating bacteria growing on resources and

bacteriophages replicating by infecting bacteria. Infection can potentially wipe out

bacteria from its habitat upon certain conditions, which explains the existence of defense

strategies for bacteria. Apart from extinction, infection is a limiting factor for bacterial

growth; therefore, phages need to be restrained form infection to mitigate their adverse

effect on the growth rate of bacterial population.

2.1 Fitness of OMVs as Anti-phage Agents

We introduced OMVs as a variable which constrains phage infection; but, they also

decelerate bacterial growth rate by consuming resource (refer to Chapter 1.3 and

Chapter 1.4). Hence, there should be a method to measure the beneficence of OMVs.

9

The average resource concentration which bacteria needs to maintain its population density

is called R*. Lower values of R* means that the population can survive on lower amounts

of resource available and thus they are in favor in comparison to other types\strains of

bacteria with higher R* value. Thereby, we measured the fitness of OMVs by comparing

R* for different bacterium strains. This idea leads to introducing R* ratio demonstrated in

Equation 2.1 which quantifies fitness of OMVs for bacteria.

R∗ ratio =R∗BacteriawithOMV

R∗BacteriawithoutOMV

(2.1)

In the same environment, R* ratio of less than one means that bacterial population which

produces OMVs can survive on a lower amount of resource which makes them favorable

over the ones without OMVs; therefore, in those environments, vesiculation can benefit the

bacteria to fight against viral infection to grow faster and survive.

Here, we considered carbon as the limiting resource in our models; while, as stated by

Levin et al. (1977) inorganic resources can also be limiting.

To neglect the effects of early fluctuations in the populations, we averaged resource for the

last 90 percent of whole simulation time. We used R* ratio for evaluation of OMVs fitness

as a defense mechanism in all of our models. In the next three chapters, models used in this

study and their results are presented.

10

Chapter 3

Resource-Limited Growth, Competition,

and Predation

A model for bacterial growth in an infectious environment has been developed by Levin et

al. (1977). This model considers the bacteria as the first order consumer of the resource

which is the prey for the phages (predator). They considered a latency between infection

and replication of phages (burst) which introduces infected bacteria to the model. Here, we

modified the original model (equations) to also include OMVs as a consumer of resources

(indirectly by reducing bacterial growth rate). Vesicles can also get infected. However,

phages will not be replicated by infecting OMVs and die as a result. Chapter 3.1 illustrates

the original equations and our modifications.

3.1 Introducing OMVs to the Model

Levin et al. (1977) constructed their model on the basis of consumption of the resource by

bacteria, a steady inflow of resource to the habitat and same rate of washout, and replication

of phages by infecting bacteria. Our modification introduced OMVs as another agent that

phages can infect, but they also impose a reduction on the bacterial growth by occupying

part of the resources. We assumed that OMVs do not affect the infection rate for the

bacteria ( by blocking phages from infection or being released from the outer membrane

when a phage is attached to it) and phages only get neutralized when they infect an OMV.

11

This model considers a constant inflow/washout for all the variables. Moreover, as noted

in Chapter 3 infected bacteria stays in the system until replicated viruses reach to their

burst size. Equations 3.1, 3.2, 3.3, 3.4, and 3.5 are the modified equations for our model

(modified parts are emboldened).

r = ρ(C − r)− φ(n+m) (3.1)

n = n

(φ

e(1 + fg)

)− ρn− γnp (3.2)

v = n

(φ

e(1 + fg)g

)− ρv− δvp (3.3)

m = γnp− ρm− γn′

(t−l)p′

(t−l)e−ρl (3.4)

p = bγn′

(t−l)p′

(t−l)e−ρl − ρp− γnp− δvp (3.5)

where:

r is the resource concentration in the habitat [ µgml

]

p is the virus population density [#pml

]

n is the bacterial population density [#nml

]

m is the infected bacterial population density [#mml

]

v is the OMV population density [#vml

]

12

C is the resource concentration in the storage [ µgml

]

ρ is the washout (inflow) rate [ 1hr

]

φ is the resource uptake function of the bacteria [ µghr#n

]

e is the unit resource needed for bacteria to reach its division size [ µg#n

]

f is the ratio of the resource needed to produce one OMV to e [µg#nµg#v

]

g is the number of OMVs produced in each division cycle [#v#n

]

γ is the viral infection rate for bacteria [ ml#hr#p#n

]

δ is the viral infection rate for OMV [ ml#hr#p#v

]

b is the burst size [#p#n

]

l is the latent period or the lag between the infection and burst [hr]

In the units of the variables ”#” followed by the type of the cell, represents the number of

cells; however, nominators for δ and γ units in Equations 3.2 and 3.3 differ from the ones

in Equation 3.5, so, the type of the cell has not been provided for these two parameters.

Resource uptake function of the bacteria also varies based on the resource available in the

habitat (Levin et al., 1977).

φ =P × rQ+ r

(3.6)

where:

P is the maximum growth rate [ µgml hr#n

]

Q is the resource that bacteria needs to reach to half of its maximum growth rate [ µgml

]

13

3.2 Different States of the Model

In this model, we investigated E. coli and T2 phage. Values for the variables of equations

and initial populations concentrations are retrieved from Levin et al. (1977).

To estimate values associated with OMVs (i.e., f , and δ), we used the volume ratio and

surface area ratio of vesicles to the ones of bacteria to find the ratio of over e and δ over γ,

respectively (Hoekstra, van der Laan, de Leij, & Witholt, 1976; Horstman & Kuehn, 2000;

Huang et al., 2016; Koleva & Hellweger, 2015; Pardo, Florez, Baker, Schertzer, & Mahler,

2015; Reshes, Vanounou, Fishov, & Feingold, 2008; Schwechheimer & Kuehn, 2015).

E. coli shape can be approximated by ”a cylinder with hemispherical caps” (Itan, Carmon,

Rabinovitch, Fishov, & Feingold, 2008). Refer to Table 3.1 for the numbers associated

with sizes of E. coli cell and its OMVs.

Table 3.1: Average sizes of E. coli cells and their OMVs

Variable Definition Average Size

2R Width of E. coli 1 µm

H Total height of E. coli 2 µm

h Cap height of E. coli 0.25 µm

2r Diameter of OMVs 100 ηm

We varied the variables based on the interval of sizes provided for bacteria and vesicles.

Moreover, we changed habitat conditions by varying resource concentration and washout

rate. Other variables which have been approximated by Levin et al. (1977) have not been

changed. Based on that, we investigate the efficiency of OMVs regarding the change in

number of OMVs per cycle, which is thoroughly described in Chapter 3.3.

Based on the habitat situation (resource concentration at storage and washout rate) there

are two major states possible for Levin et al. (1977) model:

1. Concentrations at equilibrium

14

(a) Stable oscillations

(b) Constant concentrations

2. Extinction of the strains (bacterium or phage)

Table 3.2 shows sets of variables for each of the states as mentioned earlier. Values for

r, p, n, m, and v are the initial values which the model has been set up with them and ρ

is a random variable with a normal distribution. Figure 3.1 demonstrates the populations

dynamic for each set of variables presented in the table.

Table 3.2: Parameter used for replicating different states of the model

Variable Stable Oscillation Constant Concentrations Extinction of Strains

r 0.0 0.0 0.0

p 2.0E+6 2.0E+6 2.0E+6

n 3.5E+4 3.5E+4 3.5E+4

m 0 0 0

v 0 0 0

C 7.0E+1 3.5E+1 2.2E+1

ρ N(3.5E-1, 5.0E-3) N(3.5E-1, 5.0E-3) N(3.5E-1, 5.0E-3)

e 1.35E-4 1.35E-4 1.35E-4

f N/A 1.0E-5 1.0E-5

g 0 10 10

γ 3.12E-8 3.12E-8 3.12E-8

δ N/A 3.12E-11 3.12E-11

b 9.8E+1 9.8E+1 9.8E+1

l 5.0E-1 5.0E-1 5.0E-1

P 9.96E-5 9.96E-5 9.96E-5

Q 4.0E0 4.0E0 4.0E0

15

(a)

1e+02

1e+04

1e+06

0 500 1000 1500 2000Time (hr)

Co

nce

ntr

atio

n

(ce

ll/m

l o

r µ

g/m

l)

ResourceBacteriaInf. BacteriaBacteriophage

(b)

1e+02

1e+04

1e+06

0 500 1000 1500 2000Time (hr)

Co

nce

ntr

atio

n

(ce

ll/m

l o

r µ

g/m

l)

ResourceBacteriaInf. BacteriaBacteriophageOMVsInf. OMVs

(c)

1e+00

1e+02

1e+04

1e+06

0 500 1000 1500 2000Time (hr)

Co

nce

ntr

atio

n

(ce

ll/m

l o

r µ

g/m

l)

ResourceBacteriaInf. BacteriaBacteriophageOMVsInf. OMVs

Figure 3.1: Different states of the Levin et al. (1977) Model. (a) Populations oscillating at

equilibrium. (b) Population stable at constant concentrations. (c) Extinction of phages. To

find the values associated with these graphs refer to Table 3.2

16

3.3 R* as a Measure of Outer-Membrane Vesicles Fitness

in Different Conditions

To investigate the efficiency of OMVs in different environments, we varied some aspects

of the model and compared the R* of the population which produces OMVs to the one of

the population which does not produce them and calculated R* ratio.

For each parameter, we assumed three values at maximum, minimum and mean. While

using one variable at maximum or minimum the other ones were at their mean. At each

batch computation, we increased the number of produced OMVs per cycle (i.e., g) to see

the trend of OMVs fitness. Table 3.3 shows the three values mentioned above for each

parameter. Initial concentrations of the cells, e, δ, b, l, P , and Q are the same as values

presented in Table 3.2 for stable oscillation.

Table 3.3: Minimum, Maximum and Average values for parameters varying in batch

computations

Variable Maximum Value Mean Value Minimum Value

C 1.1E+2 7.0E+1 2.5E+1

ρ N(5.0E-1, 5.0E-3) N(3.5E-1, 5.0E-3) N(1.5E-1, 5.0E-3)

f 9.45E-6 1.35E-6 1.40E-8

δ 6.24E-10 2.18E-10 3.12E-11

Figure 3.2 and Figure 3.3 show the R* ratio for batch computations in different habitat

situations. Points below one are the ones which OMVs are beneficial to bacteria.

It can be observed from Figure 3.2 that when the resource concentration at storage is at its

maximum, OMVs are beneficial to bacteria since producing them does not limit the growth

of bacterial population due to lack of resource. Despite that, when C is at its minimum,

vesiculation cost has a much higher effect on availability resource for growing process,

17

1.0

0

0.9

8

1.0

2

01

02

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18

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7

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3

01

00

20

03

00

40

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)

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19

and therefore, the cost/benefit ratio falls below one. It can be seen from the graph that

increasing number of OMVs per cycle will result in R* ratio soaring for C at its minimum.

On the other hand, when washout is at its minimum, bacterial population is highly

benefiting from vesiculation. It can be described by the fact that lower washout means

higher population density and consequently, a higher rate of infection. In high infectious

habitat, employing a defense strategy becomes extensively important. That is why that

minimum washout has the lowest values for R* ratio.

Moreover, the size of vesicles is another critical variable for the amount of resource used

for the production of them and their infection rate. It is observed that when size is at

its minimum, vesicles are benefiting the bacterial population. Smaller OMVs means less

resource allocated to them; although, it also means lower infection rate for vesicles, their

specific surface area increases which eventually plays in favor of the bacterium.

Figure 3.3 demonstrates that ultimately, by increasing the number of OMVs per cycle,

vesicles will lose their beneficence. Increasing g is equivalent of allocating more resource

to vesiculation which, at some point, will result in the cost of vesiculation surpassing their

benefit to bacteria and subsequently, rising R* ratio.

20

Chapter 4

Marine Viruses and Heterotrophic

Bacteria

Weitz et al. (2015a) introduced another system of nonlinear ODE equations to model a

multitrophic environment and study the effects of marine viruses on these biological

systems. In the original model, Weitz et al. (2015a) included ”heterotrophs,

cyanobacteria, eukaryotic autotrophs, zooplanktons and viruses along with organic and

inorganic nutrients”. This model also considers virulent phages as same as Levin et al.

(1977) model.

To simplify the model, we only considered heterotrophs and their specific type of virus.

We have also introduced OMVs to the model by the same approach used in Chapter 3.

The reason for this simplification is that we wanted merely to consider the effects of

vesiculation on the process. Including multiple agents besides bacterium and phage would

increase the sensibility of the model to changes and it cannot be affirmed that changes are

happening due to the presence of OMVs. Although it is possible to model OMVs in

complex environments, it is not in the scales of this research.

Additionally, we added a washout rate to account for competition that we omitted by

removing other cell types. It is crucial to notice that competition among microorganism is

an essential player in biological systems (Gregory et al., 2017) and neglecting that from

the model without placing another limiting factor on growing cycle of bacteria will result

in an unrealistically high concentration of cells which affects the robustness of results.

21

4.1 Introducing OMVs to the Model

In Weitz et al. (2015a) model the amount of biomass converted to bacteria has been

considered to present their growth. To account for vesiculation, we modified this term by

adding a coefficient which accounts for the percentage of the biomass converted to OMVs.

Same as Chapter 3.1, OMV kills viruses while considering a lower infection rate for

OMVs based on their size. As mentioned earlier, we added washout as a replacement for

the excluded competition. Equations 4.1, 4.2, 4.3, 4.4, and 4.5 show the system of

equations representing this model. To find the original equations refer to Weitz et al.

(2015b).

H =µxonH

xon +Kon× 1

1 + f− φHHP −monH −minH − ωH (4.1)

P = βφHHP −mpP − φV V P − ωP (4.2)

V =µxonH

xon +Kon× f

1 + f× g − φV V P − ωV (4.3)

xon = −ω(xon − xsub)−qHε× µxonH

xon +Kon+ (4.4)

qPmPP + qHmonH + (qH − β qp)φHHP

xin = −ω(xin − xsub) +qH(1− ε)

ε× µxonH

xon +Kon+ qHminH (4.5)

22

where:

H is a heterotrophic bacteria density[#HL

]

P is the virus population density [#PL

]

V is the OMV population density [#VL

]

ω is the mixing (washout) rate [ 1day

]

φH is the viral lysis rate of the phage-bacterium [ L# day

]

φV is the viral lysis rate of the phage-vesicle [ L# day

]

β is the phage burst size [#P#H

]

mP is the viral decay rate [ 1day

]

f is the fraction of resource (biomass) allocated to OMVs [N/A]

g is the conversion ratio of bacterial biomass to OMVs based on f [#V#H

]

qH is the nitrogen content of bacteria [µmolN#H

]

qP is the nitrogen content of phage [µmolN#P

]

xon is the organic resource density [µmolL

]

xin is the inorganic resource density [µmolNL

]

µ is the maximum growth rate of heterotrophs [ 1day

]

Kon is the half saturation constant [µmolL

]

mon is the organic loss rate of bacteria [day

]

min is the bacterial respiration rate [day

]

23

ε is the efficiency of resource uptake by bacteria [N/A]

xsub is the deep inorganic N concentration or organic resource (C) concentration at

storage [µmolL

]

Equation 4.6 illustrates the relationship between conversion ratio of biomass to OMVs with

percent biomass diverted to vesiculation.

g =f

f(4.6)

where:

f is the average ratio of volume of OMVs to the one of bacteria [#H#V

]

Since E. coli is a heterotrophic bacteria (Gregory et al., 2017), we used the same numbers

for the relative size of OMVs to one of the bacteria (refer to Chapter 3.2) to estimate values

of f and φV .

4.2 Different States of the Model

The same major states are possible for this model as well as the model in Chapter 3.

However, it has been observed that the model will eventually reach a point that

fluctuations in the concentrations will stop and populations reach to stable and constant

values.

Figure 4.1 demonstrates three different examples of this model. Values associated with

these figures are presented in Table 4.1. By looking at these values, it is evident that xsubas the primary parameter of providing bacteria with resource plays a vital role affecting the

outcome of the model. This observation is another illustration of the fact earlier mentioned

that by removing other competitors, resource concentration becomes exclusively vital.

It can be observed from Figure 4.1.a and other variations of the model parameters (results

not shown) that oscillation in densities is not permanent and after some time densities will

be stabilized.

24

Table 4.1: Values associated with different states of the model

Variable Stable Oscillation Constant Concentrations Extinction of Strains

H 5.00E+8 5.00E+8 5.00E+8

P 2.0E+10 2.0E+10 2.0E+10

V 0.00E0 0.00E0 0.00E0

ω N(1.6E-1, 5.0E-3) N(1.6E-1, 5.0E-3) N(1.6E-1, 5.0E-3)

φH 4.40E-11 4.40E-11 4.40E-11

φV 5.40E-14 5.40E-14 5.40E-14

β 4.5E+1 4.5E+1 5.0E+1

mP 1.70E-1 1.70E-1 1.70E-1

f 5.10E-2 5.05E-3 5.05E-3

f 5.04E-5 5.04E-5 5.04E-5

qH 2.00E-9 2.00E-9 2.00E-9

qP 2.00E-12 2.00E-12 2.00E-12

xon 3.00E0 3.00E0 3.00E0

xin 2.00E0 2.00E0 2.00E0

µ 5.10E-1 5.10E-1 5.10E-1

Kon 4.0E0 4.0E0 4.0E0

mon 9.40E-1 9.40E-1 9.40E-1

min 6.90E-3 6.90E-3 6.90E-3

ε 2.00E-1 2.00E-1 2.00E-1

xsub 8.50E0 3.00E0 2.00E0

25

(a)

1e+02

1e+05

1e+08

1e+11

0 200 400 600Time (day)

Co

nce

ntr

atio

n

(ce

ll/L

or

µm

ol/L

)

BacteriaOMVBacteriophageOrganic ResourceInorganic Resource

(b)

1e+02

1e+05

1e+08

1e+11

0 200 400 600Time (day)

Co

nce

ntr

atio

n

(ce

ll/L

or

µm

ol/L

)

BacteriaOMVBacteriophageOrganic ResourceInorganic Resource

(c)

1e+00

1e+04

1e+08

0 200 400 600Time (day)

Co

nce

ntr

atio

n

(ce

ll/L

or

µm

ol/L

)

BacteriaOMVBacteriophageOrganic ResourceInorganic Resource

Figure 4.1: Different states of Weitz et al. (2015a) Model. (a) Populations oscillating

toward a stable equilibrium (b) Constant concentrations at equilibrium (c) Extinction of

phages. To find the values associated with these graphs refer to Table 4.1

26

Moreover, concentrations of inorganic resources are higher than organic resource

concentrations for all the three graphs in Figure 4.1 which validates considering organic

resource as the limiting factor.

4.3 Measuring Outer-Membrane Vesicles Fitness

Here, again, we used R* ratio to determine the efficiency of OMVs. Varying specific

parameters and changing the percent biomass diverted to OMVs, their fitness trend and

their contribution as an innate defense strategy against bacteriophages has been illustrated.

We have also calculated the loss of bacterial population due to infection to quantify OMVs

effect on neutralizing viruses. PLV is formulated in Equation 4.7.

PLV =φHHP

φHHP +monH +minH + ωH(4.7)

If PLV ratio, presented in Equation 4.8, is less than 1 it means that OMVs have successfully

weakened viral infection rate; however, this does not guarantee that they are beneficial for

bacterial population since resource consumption have an adverse effect on bacterial growth

rate which would outcompete their beneficence.

PLV ratio =PLVBacteriawithOMV

PLVBacteriawithoutOMV(4.8)

Varying parameters are shown in Table 4.2. For each batch computation, all parameters

except one are set to their average value. Other parameters of the model are presumed to be

constant and as same as the values provided for constant concentration state in Table 4.1.

Figure 4.2 and Figure 4.3 display the R* and PLV ratio, respectively, for batch

computations in different conditions.

27

1.0

0

0.9

8

1.0

2

0.0

%2

.5%

5.0

%7

.5%

10

.0%

Bio

ma

ss C

onve

rte

d t

o O

MV

s (

%)

R* ratio

Pa

ram

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t avg

Wa

sh

−o

ut

at

min

Wa

sh

−o

ut

at

ma

xS

ize

of

OM

V a

t m

inS

ize

of

OM

V a

t m

ax

Re

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urc

e C

on

c.

at

min

Re

so

urc

e C

on

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re4.

2:R

*ra

tioof

diff

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ondi

tions

and

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Vs

vari

able

sve

rsus

perc

entb

iom

ass

dive

rted

toO

MV

s

28

1.0

0.9

1.1

0.0

%2

.5%

5.0

%7

.5%

10

.0%

Bio

ma

ss C

onve

rte

d t

o O

MV

s (

%)

PLV ratio

Pa

ram

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rs a

t avg

Wa

sh

−o

ut

at

min

Wa

sh

−o

ut

at

ma

xS

ize

of

OM

V a

t m

inS

ize

of

OM

V a

t m

ax

Re

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urc

e C

on

c.

at

min

Re

so

urc

e C

on

c.

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re4.

3:PL

Vra

tioof

diff

eren

thab

itatc

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tions

and

OM

Vs

vari

able

sve

rsus

perc

entb

iom

ass

dive

rted

toO

MV

s

29

Table 4.2: Minimum, Maximum and Average values for batch computations

Variable Maximum Value Mean Value Minimum Value

ω 1.00E-2 1.55E-1 3.00E-1

φV 1.00E-13 5.40E-14 8.00E-15

Xsub 1.50E+1 8.50E+1 2.00E0

Points below one for R* ratio are the ones which OMVs are benefiting bacteria on a higher

level than their cost. On the other hand, PLV ratio less than one in Figure 4.3 cannot be

interpreted as same as R* ratio. Although, PLV ratio of less than one means that viruses

kill bacterium without OMVs on a higher rate but, as noted before, producing OMVs may

impose a higher cost than their benefit.

Figure 4.2 presents similar results to the ones observed in the Chapter 3 model. Again,

more resource ensures that OMVs beneficence would be at a higher level and verifies that

when the resource does not limit bacterial growth, anti-phage mechanisms are favorable.

Moreover, a higher density of populations due to lower washout also translates into a more

infectious environment and therefor vesiculation will be advantageous. The main

difference observed here is that when percent biomass diverted to OMVs is not significant,

their effect is not notable for some conditions and R* stays around 1. Moreover, when

parameters are at their average, vesiculation can benefit the bacterial population which

was not the case for the model in Chapter 3.

Comparing Figure 4.2 and Figure 4.3 it is evident that higher PLV does not necessarily put

vesicles in favor of bacterium. It is because PLV does not take the cost of vesiculation into

account and only represents their contribution to counteracting phages. Nevertheless, we

can see that even when PLV is indirectly affected by habitat situation due to the presence of

bacterial population density in its function. The lowest PLV ratio is for minimum washout

which is caused by high density of cells and an increased number of infections.

30

Chapter 5

Quorum Sensing as a Regulator of

Vesiculation Process

Quorum sensing (QS) has been proved to be involved in the regulation of anti-infection

mechanisms of bacteria (Høyland-Kroghsbo et al., 2013). In this chapter, we investigate

the possibility QS triggering/adjusting vesiculation in response to phage infection. In

summary, we considered that infected bacteria produces signaling molecules cautioning

its population about phages. Later, healthy bacteria produces OMVs as decoys for phages.

The concentration of signaling molecules regulates the number of vesicles released from

the outer membrane.

We used a similar function for production of signaling molecules to the one presented by

Barbarossa and Kuttler (2016); however, we only considered one type signaling molecule

which is released by the infected bacterium and did not included delay and assumed that

decay is simulated within washout. The number of produced OMVs (i.e., g) later has

been related to the concentration of QS molecules. For that relationship, we have used a

hyperbolic function as same as the one presented by Monod (1950) for resource uptake

function. We have also included the size of OMVs (i.e., f ) in this equation to consider the

amount of biomass spent on their production.

Equations 5.1 and 5.2 demonstrate the functions for the concentration of signaling

molecules and the number of produced OMVs (i. e. g), respectively. The rest of the model

is as same the one presented in Chapter 3.

31

S = αm+ βS2

K2S + S2

m− ρS (5.1)

g = g0 +Kf/f

Kg + SS (5.2)

where:

S is the concentration of signaling molecules [ µgml

]

α is the basic production rate of signaling molecules (S) by infected bacteria [ µg#mml

]

β is the feedback regulated constant for production of signaling molecules (S) [ µg#mml

]

KS is the saturation constant for signaling molecules (S) [ µgml

]

g0 is the baseline number of produced OMVs per cycle [#v#n

]

Kf is the critical threshold for the size of OMVs [N/A]

Kg is the critical threshold for the number of OMVs based on the concentration of

signaling molecules (S) [ µgml

]

To estimate the values of the parameters introduced above, we optimized the model while

other parameters were fixed at their average. In the process of optimization, the best value,

in regards to maximization of R* ratio, for each parameter has been selected independently,

and limited sensitivity analysis has been performed to tune values. Table 5.1 shows the

optimized values. The initial concentration of S is set to 0. To find the other variables and

their values refer to Table 3.2.

32

Table 5.1: Values associated with QS and vesiculation.

Variable Starting Value Optimized Value

α 5.00E0 1.00E+2

β 5.00E+2 9.90E+3

KS 1.00E-6 1.00E-12

g0 1.00E0 3.00E0

Kf 1.80E-4 1.80E-5

Kg 1.00E+3 1.00E+6

5.1 R* as a Measure of Outer-Membrane Vesicles Fitness

Here, we used a similar approach to the one used in Chapter 3.3. The same number as the

ones presented in Table 3.3 are used for batch computations. However, here we had no

control over the number of OMVs produced. Therefore, for each parameter, we had only

one R* ratio instead of a trend. To minimize the effect of randomness existing in ρ we used

averaged R* for five different random seed number. Figure 5.1 shows R* for parameters at

their minimum, mean, and maximum.

Figure 5.1 reveals that quorum sensing regulation can highly benefit bacteria to produce

OMVs in the event of phage infection effectively. Comparing R* ratio of parameters at the

average from this figure to Figure 3.2, it is obvious that an unfavorable habitat situation for

vesiculation can be transformed into vesicles being advantageous. It is due to fluctuations

in the number of OMVs produced per cycle based on the intensity of infection. Firstly,

not many vesicles are produced by bacteria. Afterwards, the number of OMVs increases in

response to the rise in infected cells. Later, vesiculation rate plummets as the infection rate

is decreasing. Hence, bacteria does not over-allocate its resources to vesiculation. On the

other hand, we see that highly unfavorable situations still have R* ratio of greater than one.

33

Figure 5.1: R* ratio for the QS-regulated bacterium

Number of reasons can be responsible for quorum sensing not benefiting the bacterial

population in our model at those situations. For instance, considering a baseline number

of vesicles, overlooking robust optimization methods for QS parameters, and simplifying

QS function which results in the production of signaling molecules merely based on

infected bacteria and with no regards to bacterial population status itself undermine the

QS effectiveness. Moreover, we see that R* ratio is not at its minimum for the favorable

situations.

Apart from the aforementioned reasons, overlooking delay in the process of producing

signaling molecules can be a source for that. In our function, any change in the infected

bacterial population will be instantly reflected in the QS molecules concentration; therefore,

local fluctuation in the population will immediately affect the vesiculation process.

However, as mentioned before, OMVs are not only considered to be defensive agents and

other applications have been discovered for them. By and large, it is reasonable to identify

QS as a valuable regulatory mechanism for bacteria to adapt to habitat situation and build

its strategies, including vesiculation, on the basis of that.

34

Chapter 6

Conclusion

Releasing extracellular entities from the outer membrane of gram-negative bacteria can

neutralize phages and contribute to bacterial population aptitude for growing. At the same

time, resource and energy allocated to the production of Outer-Membrane Vesicle (OMV)

slow down the growth rate.

In this study, we investigated the fitness of OMVs as a strategy for bacteria to fight against

phage predation. Using mathematical models to simulate bacterium-bacteriophage

interaction and modifying them to include OMVs, Average Limiting Resource (R*) of the

bacterium strains with OMVs has been compared to one of the strain without vesicles.

Results from the first two models (Chapter 3 and Chapter 4) show that vesiculation

benefits the bacterial population in high infectious habitat. Moreover, when the resource

availability is not the primary limiting factor for bacterial growth or when production of

OMVs does not impose a high cost on bacterial growth, vesicles are useful for diminishing

viral infection rate. On the other hand, in the low infectious environment or low resource

concentrations, amount of biomass available to bacteria for growth becomes the limiting

parameter and therefore, allocating it to the production of OMVs adversely affect the

bacterial population. Additionally, bacteria do not profit from producing larger OMVs as

they have a lower specific surface area and thus, their cost is higher than their benefit.

In the last model in Chapter 5, quorum sensing has been studied as a regulation for

producing OMVs. It has been observed that bacteria can highly benefit from Quorum

35

Sensing (QS) to tailor vesiculation in different conditions. Comparing the results from

Chapter 3 to the ones in Chapter 5 demonstrates improvements in R* ratio which verifies

that QS is an effective tool for bacteria to fine-tune its defensive strategies. It is crucial to

note that many other roles are known for OMVs and bacteria will produce them in

different conditions which may not necessarily benefit them regarding counteracting

bacteriophages but serving them in other ways.

Overall, the results of this study prove that OMVs can be considered as defensive agents

for bacteria against viral infection; however, their beneficence depends on the conditions

of the surrounding environment.

36

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