Virtual Sponge Models

Introduction

In this section we model the water flux in living sponges. As we could not test our constructs in living sponges (sponges are fragile organisms, bringing them to paris and then growing them is complicated), we relied on models in order to find out: what would be the effectiveness of our constructs in living sponges ?

More precisely we are interested in finding: what is the quantity of compound that is in contact with our bacterium ?

With this quantity and the number of bacteria in the sponge, we can the connect with the models developed for PCB and phenol (TODO) sensing and then relate the sensing capacity to the concentration of compound in the surrounding water.

To answer this question, we built two different model :

1. A simple model where we consider only water flows without trying to take into acount the very specific geometry of the sponge.
2. A 2D diffusion model where we take into acount the geometry of the sponge.

Throughout this section we base our study on the Spongia Officinalis species, because i) there are evidences that pseudovibrio bacteria live inside (TODO: cite) and ii) its is a quite common type of sponge.

Model 1: Simple Fluxes

For this model, we make simple computations based on the intake and expeled quantities of water. Our main assumptions are the following :

1. Bacteria are uniformely distributed in the sponge
2. Compounds diffuse instantly inside the sponge (the quantity of compound in the same everywhere inside)

These two assumptions imply that each bacterium is in contact with the same quantity of compound.

Model Formulation

We call φ_in (in ml/h/cm³) the quantity of compounds (<= 0.2 μm) filtered by a sponge of volume V (cm³). The compound is present at concentration C (mol.ml^-1). Then the quantity of compound in contact with the bacteria, Q (mol.h^-1), is:

Q = φ_inVC

Parameters

Name	Value	Unit	Ref
φin	[0.1-0.3]	cm3(water).cm-3(sponge).s-1	WATER TRANSPORT, RESPIRATION AND ENERGETICS OF THREE TROPICAL MARINE SPONGES
V	[66.8-116]	cm3	Filtering activity of Spongia officinalis var. adriatica (Schmidt) (Porifera, Demospongiae) on bacterioplankton: Implications for bioremediation of polluted seawater

Results

We present in Figure1 the results obtained for different parameter sets (min, mean and max values). The value of Q increases linearly with the concentration and is in the range of the μmol.

The equations for the three lines in Figure1 are the following:

• Red: y = 0.00668x
• Green: y = 0.01828x
• Blue: y = 0.0348x

Model 2: 2D diffusion

For this second model we want to take into account the geometry of the sponge. For the equations and geometry to be tractable we will consider a 2D slice of a sponge. Our assumptions are the following :

1. Bacteria are uniformely distributed in the sponge (as for model 1)
2. Sponge geometry is approximated as a sphere
3. The interior of the sponge is a uniform medium in which the compound diffuse isotropically with a coefficient D