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Common Dynamics: Chemostat |
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The variation of cells' concentration in the chemostat over time can be expressed in terms of a production (positive) term and degradation (negative) terms: |
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For the production term, we use a logistic equation to model cell growth, according to standard assumptions. The behaiviour obtained is the following one: at low population density, the concentration of cells in the chemostat (c) increase exponentialy with a growth rate αcell and at high population density, the population reaches a maximum concentration, cmax.
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For the degradation term, we consider that c decrease proportionaly to both a dilution phenomena cause by the renewal of the medium in the chemostat (Drenewal) and cell death (d).
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Common Dynamics: Quorum Sensing |
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In order to model the quorum sensing dynamics, we consider that: |
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1) Inside a cell, the HSL concentration increases proportionaly 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 beetwen the internal and external concentration of HSL). Thus, the equation for the internal HSL concentration is: |
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2) Outside the cells, HSL is cumulated with the same transport term tah we use in the previous equation. The degradation of HSL in the external medium and the dilution controled via the chemostat accounts for HSL external decrease. So the external HSL concentration is given by: |
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that is equivalent to: |
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where  and  |
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Common Network Dynamics: FlhDC and Flia |
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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. |
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| Bimodular System |
Unimodular System |
| 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). |
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| 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 varies as a function of the concentration of HSL present in the cell. |
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