BME 100 Computer project 3_nigel

BME 100 Computer project 3_nigel - BME 100 Computer Project...

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BME 100 Computer Project 3: Modeling a Genetic Oscillator BME 100 Computer project 3: Modeling a genetic oscillator: Repressilator Nigel Chou A) Since units of s nM = dt dM i , therefore units of s 1 , s nM = = m o d k j K , j P and j M are nM (given) The terms in j K and j P cancel out, therefore units of s nM = k Since units of s nM = dt dP i , therefore units of s 1 = = p p d k These results are summarized in table 1. Table 1: Dimensions of parameters Parameter Units K j nM P j nM M i nM k nM s -1 k 0 nM s -1 d m s -1 k p s -1 d p s -1 B) Let m m d d dt t d 1 = = τ The units are 1 s s 1 = = - (dimensionless) Let j j j K P p = dt dP K dt dp i j i 1 = The units are 1 nM/nM = = j p (dimensionless) Let j i p p i K M d k m = 1 dt dM K dt dm i j i 1 = The units are, 1 nM/nM = = j m (dimensionless) 1 The reason for this choice will is that it allows us to pull out a constant (β) from the second equation, as we shall see later. 1
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BME 100 Computer Project 3: Modeling a Genetic Oscillator Also, K i = K j since all three reaction have the same kinetics Equation 1 i n j j i p p j m p p n j j m p p i m n j j j m p p i j m p p i j p p i m p K M d k K d d k k p K d d k k M d k k P k K d d k dt dM K d d k d dt dt dM K d k d dm - + + = - + + = - + + = = = 0 0 0 1 1 ) 1 ( α τ By observing the above equation, we get: j m p p K d d k k = and j m p p K d d k k 0 0 = The units are 1 nM s s ) s (nM s 1 1 1 1 = = - - - - and 1 nM s s ) s (nM s 1 1 1 1 0 = = - - - - , thus both are dimensionless Equation 2 ) ( ) ( ) ( 1 ) ( 1 ) ( 1 1 1 i i i i m p i p i p m j i p j i p p p m i p i p p p j m i j m i i i p m p m d d p d m d d K P d K M d k d d P d M d d k K d dt dP K d d dt dt dP K d dp - = - = - = = - = - = = = β By observing the above equation, we get: m p d d = The units are 1 s s 1 1 = = - - thus it is also dimensionless. C)
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BME 100 Computer project 3_nigel - BME 100 Computer Project...

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