Team:Edinburgh/Phage Replication

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Phage Replication

A basic activity in biorefinery consists of the degradation of cellulose, due to the presence of enzymes. We are not only concerned with the activities and the amount of enzymes, but also with metabolism and activities of bacteriophage.

Contents

M13 Replication

M13 is a filamentous bacteriophage: a worm-like virus approximately 1 um long with a 10 nm diameter that infects only E.coli.

  • The viral particle consists of a single-stranded, closed circular DNA core surround by a protein coat.
  • Prior to virus assembly, the coat proteins are fixed in the bacterial membrane by transmembrane domains.
  • During assembly, viral DNA is extruded through the membrane and concomitantly enveloped by coat proteins.
  • The ends of the assembled virus are capped by four minor coat proteins, and the length of the filament is covered by several thousand copies of the major coat protein(P8).
From Slonczewski and Foster (2010).
  • The M13 phage attacks E. coli (host), multiplies in the host cell cytoplasm, and is released without causing the bacteria’s death (non-lytic).

Phage dynamic model

  • dx/dt=a*k1*x-b*v*x
(Rate of change of quantity of uninfected E. coli equals to the uninfected E. coli replicate itself minus the E. coli infected by M13 phage.）
  • dy/dt=a*k2*y+b*v*x
（Rate of change of quantity of infected E. coli equals to the quantity of infected E. coli replicate itself plus the E. coli infected by M13 phage.）
  • dv/dt=c*y-b*v*x-m*v
（Rate of change of quantity of free phage equals to the phage released by infected E. coli minus the phage which is to infect an E. coli and the decayed phage.）
X(t) — uninfected E. coli
Y(t) — infected E. coli
V(t) — free phage
a — replication coefficient of E. coli
b — transmission coefficient of phage
c — replication coefficient of phage
m — decay rate of phage
K1, K2 — account for the difference of the rate of replication between infected E.coli and uninfected E.coli


Simulations

The MATLAB code uses a Runge-Kutta method of order four to solve the system.

simulation value: x0=2.00E3 y0=v0=2.00E5
The above figure shows a simulation going over 15 hours.
The simulation shows when the amount of uninfected E.coli is significantly smaller than others, the infected E. coli population dominates.
simulation value: x0=v0=2.00E5 y0=2.00E3
The above figure shows a simulation going over 15 hours.
The simulation shows when the amount of infected E.coli is significantly smaller than others, the infected E. coli population dominates as well.
simulation value: x0=y0=v0=2.00E5



References


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