Team:LCG-UNAM-Mexico:odes
From 2009.igem.org
(Difference between revisions)
(→Assumptions) |
|||
(12 intermediate revisions not shown) | |||
Line 4: | Line 4: | ||
|-valign="top" border="0" | |-valign="top" border="0" | ||
|width="900px" style="padding: 0 20px 0 0;"| | |width="900px" style="padding: 0 20px 0 0;"| | ||
- | |||
='''Deterministic population dynamics model'''= | ='''Deterministic population dynamics model'''= | ||
- | Some bacteriophages are parasites of bacteria, and as such, must prudently exploit their resources (in this case bacteria) to avoid killing bacterium before reproduce enough copies of itself. It has been suggested that parasites have evolved to tune their degree of virulence (amount of damage the parasite causes to the host) to achieve a balance between rapid reproduction and a prudent use of resources [[Team:LCG-UNAM-Mexico:odes#References | [1]]]. It is this fine balance which we intend to break increasing the virulence of phage in such a way that kills the bacterium so fast that the phage is unable to assemble their own copies.<br><br> | + | Some bacteriophages are parasites of bacteria, and as such, must prudently exploit their resources (in this case bacteria) to avoid killing bacterium before reproduce enough copies of itself. It has been suggested that parasites have evolved to tune their degree of virulence (amount of damage the parasite causes to the host) to achieve a balance between rapid reproduction and a prudent use of resources [[Team:LCG-UNAM-Mexico:odes#References | [1]]]. It is this fine balance which we intend to break, increasing the virulence of phage in such a way that kills the bacterium so fast that the phage is unable to assemble their own copies.<br><br> |
- | As a first approach | + | As a first approach, the infection process was mathematically modeled with a system of differential equations.<br><br> |
It is important to consider that the amount of phages at a given moment 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 [http://en.wikipedia.org/wiki/Delay_differential_equation DELAY DIFFERENTIAL EQUATIONS (DDE)] based on the system proposed by [[Team:LCG-UNAM-Mexico:odes#References | Beretta [2]]]. The use of DDE allows us to update the system depending on the states of the system in previous points in time. | It is important to consider that the amount of phages at a given moment 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 [http://en.wikipedia.org/wiki/Delay_differential_equation DELAY DIFFERENTIAL EQUATIONS (DDE)] based on the system proposed by [[Team:LCG-UNAM-Mexico:odes#References | Beretta [2]]]. The use of DDE allows us to update the system depending on the states of the system in previous points in time. | ||
Line 26: | Line 25: | ||
==Populations== | ==Populations== | ||
- | <center> | + | <br><center> |
<html><head><title>Population</title> | <html><head><title>Population</title> | ||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> | <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> | ||
Line 415: | Line 414: | ||
[[Image:6e05_0_0.png|400px|thumb|center|Normal growth of ''E. coli'' without phages in the medium. Bacterial population grows according to a logistic equation.]] | [[Image:6e05_0_0.png|400px|thumb|center|Normal growth of ''E. coli'' without phages in the medium. Bacterial population grows according to a logistic equation.]] | ||
|} | |} | ||
- | <center>Initial population vector set to '''[6e05 0 0]'''.<br> As there are no phages present, the infected and phage populations does not increase.</center><br><br> | + | <center>Initial population vector set to '''[6e05 0 0]'''.<br> As there are no phages present, the infected and phage populations does not increase and ''E. coli'' grows normally.</center><br><br> |
{| | {| | ||
- | |||
| [[Image:Zoom_6e05_0_1_5.png|400px|thumb|right|Behavior of an infection in a wild type ''E. coli''.]] | | [[Image:Zoom_6e05_0_1_5.png|400px|thumb|right|Behavior of an infection in a wild type ''E. coli''.]] | ||
+ | | [[Image:6e05_0_1_5.png|400px|thumb|left|Behavior of an infection in a wild type ''E. coli''.]] | ||
|} | |} | ||
{| | {| | ||
- | <center>Initial population vector set to '''[6e05 0 1]'''. <br> | + | <center>Initial population vector set to '''[6e05 0 1]'''. <br>Susceptibles bacteria becomes infected when phages are added. Bacterial death is only caused by phage lysis product, therefore, the death rate is set to one time the inverse of the latency period ('''μi=5''').</center><br><br> |
|} | |} | ||
<br> | <br> | ||
- | [[Image:6e05_0_1_25.png|400px|thumb|center|]] | + | [[Image:6e05_0_1_25.png|400px|thumb|center|Behavior of an infection in an engineered ''E. coli''.]] |
- | <center>Initial population vector set to '''[6e05 0 1]'''. <br> | + | <center>Initial population vector set to '''[6e05 0 1]'''. <br>when T7 infects a bacterium |
+ | which has the suicide circuit, '''μi''' (mortality rate caused by suicide system) is increased, host bacteria die before the phages reproduce itself. The mortality parameter estimated caused by the toxin is five times the inverse of the latency period ('''μi=25''').</center> | ||
|} | |} | ||
<br> | <br> | ||
+ | |||
==Assumptions== | ==Assumptions== | ||
Line 441: | Line 442: | ||
[1] Frank, S. A. 1996 Models of parasite virulence. Q. Rev. Biol. 71, 37–78.<br> | [1] Frank, S. A. 1996 Models of parasite virulence. Q. Rev. Biol. 71, 37–78.<br> | ||
[2] E. Beretta, Y. Kuang (2001): Modeling and Analysis of a Marine Bacteriophage Infection with Latency Period. Nonlinear Analysis : Real World Applications, 2, 35-74<br> | [2] E. Beretta, Y. Kuang (2001): Modeling and Analysis of a Marine Bacteriophage Infection with Latency Period. Nonlinear Analysis : Real World Applications, 2, 35-74<br> | ||
- | [3] L.F. Shampine and S. Thompson, Solving DDEs in MATLAB | + | [3] L.F. Shampine and S. Thompson, Solving DDEs in MATLAB.<br> |
- | [4] Heineman, R., Springman, R., Bull, J. (2008). Optimal Foraging by Bacteriophages through Host Avoidance | + | [4] Heineman, R., Springman, R., Bull, J. (2008). Optimal Foraging by Bacteriophages through Host Avoidance. The American Naturalist, 171(4), E149-E157. <br> |
[5] De Paepe M, Taddei F (2006) Viruses' life history: Towards a mechanistic basis of a trade-off between survival and reproduction among phages. PLoS Biol 4(7): e193. DOI: 10.1371/journal.pbio.0040193.<br> | [5] De Paepe M, Taddei F (2006) Viruses' life history: Towards a mechanistic basis of a trade-off between survival and reproduction among phages. PLoS Biol 4(7): e193. DOI: 10.1371/journal.pbio.0040193.<br> | ||
|} | |} | ||
- | |||
<!--Do not remove the first and last lines in this page!-->{{Template:LCG_bottom_Netscape}} | <!--Do not remove the first and last lines in this page!-->{{Template:LCG_bottom_Netscape}} |
Latest revision as of 14:01, 21 October 2009