Team:LCG-UNAM-Mexico:odes

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='''The Project'''=
='''The Project'''=
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Bacteriophage infection represents an interesting process in science and industry. The idea of being able to contend at a population level with such infections is the main motivation for the development of our project.<br>
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As a first approach for our problem, the infection was mathematically modeled with a system of equations.
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We propose a population level approach relaying on a defense system delivered by an engineered version of the enterobacteria phage P4. The purpose of the defense construction is to make a bacteria to hold back the process of infection by triggering a cellular death response when a cell encounters a specific component of the infective phage. Such response will be fast enough to stop the formation process of viral particles, thus preventing the phage proliferation and population decline.<br>
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It is important to consider that the amount of phages on a point in time depends on the amount of phages on a previous point in time due to the latency period (once the phage has inserted its genome, it requires a period of time to redirect the molecular machinery of the bacteria, reproduce and start assembling). To tackle this problem, we modeled the phage infection using a system of DELAY DIFFERENTIAL EQUATIONS (DDE) based on the system proposed by Beretta. The use of DDE allows us to update the system according to the states of the systems in previous points in time.
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Delivery of the defense system take advantage of the satellite properties of P4 phage. This means that a P4 phage engineered with the defense construction will be able to infect an ''E.coli'' strain which harbors some genes from the helper phage P2 that are used for complementing and completing P4 life cycle, hence creating a production line of our version of P4.<br>
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It is noteworthy that the success of system, on a population level, depends on the efficiency of our suicide system after a bacteria has been infected by a phage. To include this in our model, our system of equations must consider the mortality rate of bacteria after they have been infected by a phage (it is precisely this parameter which we are trying to modify experimentally).              
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On the other hand the defense system will consist of DNA and RNA degradation by toxins which will be transcribed by T3 or T7 RNA-Polymerases fast enough to stop phage assembly and scattering in the environment. Simultaneously, a quorum sensing signal will be difunding to the non-infected bacterias acting as a transcriptional activator of an antisense RNA against bacteriophage's transcriptional machinery , hence "warning" the population to prepare against further T3 or T7 infection.<br>
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Furthermore, we will implement a stochastic population model based on the basic properties of the bacterial cells and the phages such as movement, reproduction, etc. The model will make simulations of the infection processes and quantification of the efficiency of our system possible.<br>
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In an infection we have three distinct populations:
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- Not infected bacteria (susceptible to be infected)
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- Bacteria that have already been infected
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- Bacteriophages
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S              Susceptible bacterial population                              Bacteria/volume
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I              Infected population                        Bacteria/volume
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P            Free phages                      Phage/volume
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alpha    Growth rate constant of bacteria population      1              hr^-1
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C            Carrying capacity              1.25e+09              Bacteria/volume
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k              Adsorption rate                2.1000e-007        ml/hr
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b            Burst size            200        Number of phages
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mp        Phage decay rate            2.1000e-007        2.1000e-007        hr^-1
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mi          Infected bacteria death rate      Parameter to modified in our project    hr^-1
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tau        Latency period  0.2          hr
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In this modeling approach we assume that:
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-One phage is only able to infect one bacterium.
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-Bacteria and phages are well mixed (in equilibrium), neglecting the spatial considerations
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Revision as of 06:11, 18 October 2009


The Project

As a first approach for our problem, the infection was mathematically modeled with a system of equations.

It is important to consider that the amount of phages on a point in time depends on the amount of phages on a previous point in time due to the latency period (once the phage has inserted its genome, it requires a period of time to redirect the molecular machinery of the bacteria, reproduce and start assembling). To tackle this problem, we modeled the phage infection using a system of DELAY DIFFERENTIAL EQUATIONS (DDE) based on the system proposed by Beretta. The use of DDE allows us to update the system according to the states of the systems in previous points in time.

It is noteworthy that the success of system, on a population level, depends on the efficiency of our suicide system after a bacteria has been infected by a phage. To include this in our model, our system of equations must consider the mortality rate of bacteria after they have been infected by a phage (it is precisely this parameter which we are trying to modify experimentally).

In an infection we have three distinct populations:

- Not infected bacteria (susceptible to be infected)

- Bacteria that have already been infected

- Bacteriophages

S Susceptible bacterial population Bacteria/volume

I Infected population Bacteria/volume

P Free phages Phage/volume

alpha Growth rate constant of bacteria population 1 hr^-1

C Carrying capacity 1.25e+09 Bacteria/volume

k Adsorption rate 2.1000e-007 ml/hr

b Burst size 200 Number of phages

mp Phage decay rate 2.1000e-007 2.1000e-007 hr^-1

mi Infected bacteria death rate Parameter to modified in our project hr^-1

tau Latency period 0.2 hr





In this modeling approach we assume that:

-One phage is only able to infect one bacterium.

-Bacteria and phages are well mixed (in equilibrium), neglecting the spatial considerations

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