7/25/2019 NCBS Comprehension Exam 2012, June Answers 2 3

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Q3 Answer

Sketch out the long-term behaviour of all the solutions to the following dynamical

system:

x=x2+ y 21y=(xy )

Your answer should include all fixed points and saddle separatrices if any! Also write

down in words the nature of each fixed point! "You should start with nullclines to

break up the plane into different regions and try to find the direction of flow within

each region! #his should be sufficient to guess what all tra$ectories look like! You may

lineari%e the system if you wish but it is not necessary!&

Ans:

#here are two fixed points the one on the left is a spiral sink the one on the right is a

saddle whose unstable separatrices determine the basin of the sink!

3! 'e know that a ds()A protein binds only to certain ds()As but among those

binders we do not find a consensus se*uence! +xplain!

Ans: "#he important thing is to notice that this is a *uestion about ds()A rather thanss()A, and that the protein does not bind ss()A! owever that second part was

implied in the name rather than explicitly stated in the *uestion! #herefore . accepted

answers in which the protein bound to base-paired regions of ss()A!&

#here are many options!

/! #he se*uence specificity could be provided by the binding of some other protein

which stabili%es the interaction of (01/2/ to the ds()A! .f there is more than one

such accessory protein with different se*uence specificities then on the whole we

would not find a consensus se*uence!

! .f the binding to (01/2/ is sensitive to the se*uence but the energetics comesfrom dinucleotides then no consensus would emerge from averaging!