429-2009-Q4key - 580.429 SBE3 2009 Quiz 4 Name: Section...

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Unformatted text preview: 580.429 SBE3 2009 Quiz 4 Name: Section meeting time: Section meeting location: (2 pts) 1. A cell responds to an external stimulus S (t ) that can be controlled experimentally. We ! apply a signal S (t ) = S0 sin(! t ) . What is the Laplace transform S ( s ) ? ! S ( s ) = S0! / ( s 2 + ! 2 ) ! (3 pts) 2. A protein X responds to the stimulus with activation dynamics X (t ) = kS (t ) ! " X (t ) . Assuming that the protein is inactive at time 0 and the signal is absent before time 0, what is the ! Laplace transform X ( s ) in terms of k, ! , S0 , " ? ! X (s) = k " S0 2 s +! s +"2 (3 pts) 3. What is X (t ) ? X (t ) = k! S0 e"# t / (# 2 + ! 2 ) + ( kS0 / # 2 + ! 2 ) sin[! t " tan "1 (! / # )] (2 pts) 4. What is the gain (amplitude of X )/(amplitude of S ), and what is the phase delay? gain = k / ! 2 + " 2 phase delay = tan !1 (" / # ) ...
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