Team:Paris/Analysis/Construction2

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Model Construction

Introduction

In this section, we investigate possible improvements of the core system. Our objective is twofold : the system has to provide sustained oscillations and these oscillations should be synchronized amongst a population of cells. To this aim we explore designs inspired by quorum sensing and model in a chemostat cell growth and species diffusion outside cells. We consider two models relaying on different designs principles.

↓ To joint our quest for alternatives click here! ↑

	Same environment
	Using a chemostat
	Same starting point
	The core system
	We keep 3 interactions
	Same quorum sensing mechanism
	LasI indirectly activates envZ via HSL
Alternative One		Alternative Two

Two copies of envZ		No modifications, i.e. a single copy of envZ

FlhDC and Flia active one of the copies of envZ		FlhDC and Flia active lasI

EnvZ inhibits the expression of lasI		EnvZ does not inhibit the expression of lasI

This system ends up with 2 modules		This system consists of a single module

Modeling Alternatives

The proposed models are:

Bimodular System	Unimodular System

unimodular system figure remark: LasI should be producing HSL

In the first system, we use a modular design. We consider that the core system is one of the modules of the system and that the other module is a three gene oscillator system presented in [Garcia-Ojalvo] that accounts for quorum sensing. We call this alternative the 'bimodular system'.

In the second system, namely the 'unimodular system', we rewire the architecture of the core system to introduce delay via HSL export in the environment in a single circuit.

Both the bimodular and unimodular systems describe events that happen not only at the cellular level (as in the core system) but also at the population level due to interactions needed between a cell and its environment.

In the following sections, we first describe the common part among the two proposed models and then focus our attention to the alternatives description where the characteristics that are exclusive to each of the modeling alternatives are presented.

Common Description

Use of chemostat:

Use of quorum sensing:

Use of some interactions from the core system:

↓ read more on common dynamics... ↑

Common Dynamics: Chemostat

The variation of cells' concentration in the chemostat over time can be expressed in terms of a production (positive) term and degradation (negative) terms:

For the production term, we use a logistic equation to model cell growth, according to standard assumptions. The behaviour obtained is the following one: at low population density, the concentration of cells in the chemostat (c) increase exponentially with a growth rate α_cell and at high population density, the population reaches a maximum concentration, c_max.

For the degradation term, we consider that c decrease proportionally to both a dilution phenomena cause by the renewal of the medium in the chemostat (D_renewal) and cell death (d).

Common Dynamics: Quorum Sensing

In order to model the quorum sensing dynamics, we consider that:

1) Inside a cell, the HSL concentration increases proportionally to the concentration of LasI and decreases according to both a degradation term (proportional to the internal HSL concentration) and a transport term (proportional to the difference between the internal and external concentration of HSL). Thus, the equation for the internal HSL concentration is:

2) Outside the cells, HSL is accumulated with the same transport term that we use in the previous equation. The degradation of HSL in the external medium and the dilution controlled via the chemostat accounts for HSL external decrease. So the external HSL concentration is given by:

that is equivalent to:

where

and

Common Network Dynamics: FlhDC and Flia

FlhDC and Flia are regulated in the same way in both systems. FlhDC is produced under the influence of EnvZ via an inhibition. Flia is regulated for its self and FlhDC.

Alternatives Description

Bimodular System	Unimodular System
Core system coupled with an oscillator:	Modified core system that accounts for quorum sensing:

↓ read more on alternatives description... ↑

HSL mediated coupled oscillators	HSL mediated simple oscillator
a) The expression of lasI is under the control of the same promotor that used for FlhDC.	a) The expression of lasI is regulated by FlhDC and Flia (as in the core system)

b) The expression of envZ depends on both the activation from FlhDC and Flia (as in the core system) and the concentration of HSL present in the cell.	b) The expression of envZ depends only on the concentration of HSL present in the cell.

Kinetic parameter values

The following table sumarize our findings. Theses parameters values are used during the simulations. Most them are found in literature others are obtained from further analysis.

Parameters

Chemostat	Parameter	Meaning	Original Value	Normalized Value	Unit	Source
	α_cell	Growth rate	0.0198	1	min^-1	wet-lab
	c_max	Carrying capacity for cell growth	0.1	0.1	µm³	[3]
	D_renewal	Dilution rate	0.00198	0.1	min^-1	wet-lab ([3])
	d	Death rate	0.0099	0.5	min^-1	wet-lab

Quorum Sensing	Parameter	Meaning	Original Value	Normalized Value	Unit	Source
	γ_HSL	Degradation rate	0.0053	0.2690	min^-1	wet-lab
	γ_{HSL_ext}	Degradation rate	0.0106	0.5380	min^-1	[2]
	β_HSL	Production rate	0.3168	16	min^-1	∅
	η	Diffusion rate	10	505	min^-1	[2]
	n_HSL	Hill coefficient		4		[3]
	θ_HSL	Hill characteristic concentration for the second operator		0.5	c.u	[3]

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 |[[Image:Unimo.png|250px]]
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+'''unimodular system figure remark: LasI should be producing HSL'''
 *In the first system, we use a modular design. We consider that the core system is one of the modules of the system and that the other module is a three gene oscillator system presented in [[Team:Paris/Modeling/BOB#Bibliography|[Garcia-Ojalvo]]] that accounts for quorum sensing. We call this alternative the 'bimodular system'.