Team:UC Berkeley/Modeling

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(Difference between revisions)

Revision as of 05:36, 25 October 2008

The kinetics of the Lambda phage lysis device was modeled to help our team gain an insight into the behavior of our system. The below equations describe our system

Where P1 and P2 approximate the mRNA promoter strength and /omega_mH and mH are the degradation rates for holin and antiholin respectively. kH , kAH and kc represent the rate constants for holin and antiholin formation and the coupling rate for the holin-antiholin dimer.

The literature indicates that at the time of lysis, cells infected with lambda phage have approximately 1000 holin proteins. Therefore, the critical concentration of holin (Hc) was set at 1000 holin proteins per cell.

At steady state,

The system can be simplified into the following transfer function

Where $\Omega_H$, $\Omega_{AH}$ and $\phi$ are represented by the following collections of constants

Using MatLab, graphs of the system were produced

@@ Line 4: / Line 4: @@
-[[Image:test1.jpg]]
+[[Image:cdb1.jpg]]
+Where P1 and P2 approximate the mRNA promoter strength and /omega_mH and mH are the degradation rates for holin and antiholin respectively. kH , kAH and kc represent the rate constants for holin and antiholin formation and the coupling rate for the holin-antiholin dimer.
+The literature indicates that at the time of lysis, cells infected with lambda phage have approximately 1000 holin proteins. Therefore, the critical concentration of holin (Hc) was set at 1000 holin proteins per cell.
+At steady state,
-Where P1 and P2 approximate the mRNA promoter strength and mH and mH are the degradation rates for holin and antiholin respectively. kH , kAH and kc represent the rate constants for holin and antiholin formation and the coupling rate for the holin-antiholin dimer.
-The literature indicates that at the time of lysis, cells infected with lambda phage have approximately 1000 holin proteins. Therefore, the critical concentration of holin (Hc) was set at 1000 holin proteins per cell.
-At steady state, <math> {d[~]}{dt}=0 </math>
+[[Image:cdb2.jpg]]
-The above equations were set equal to zero. The system was simplified into three dimensionless numbers
+The system can be simplified into the following transfer function
-	H = k HPH		AH = k AHPAH		      = ku+ 
+[[Image:cdb3.jpg]]
-	          mH		           mAH			 kc
-and the following transfer function,
+Where $\Omega_H$, $\Omega_{AH}$ and $\phi$ are represented by the following collections of constants
-	[H] – (H – AH + )[H] – H = 0
+[[Image:cdb4.jpg]]
 Using MatLab, graphs of the system were produced