ps6_molecular-mechanicsF07

# ps6_molecular-mechanicsF07 - of T For students taking 2.37...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.370/2.37 Molecular Mechanics Fall 2007 PROBLEM SET 6 DUE: Friday, November 2 Assignments from Molecular Driving Forces For students taking 2.370 1. Chapter 10, problem 7 2. Chapter 10, problem 9 3. Chapter 10, problem 11 4. Chapter 12, problem 2 5. In this problem we examine a simpliﬁed model for the unwinding of double- stranded DNA molecules. The DNA has N links; each link has a state in which it is closed with energy 0, and a state in which it is open with energy ε . The DNA can only unwind from the left; in other words, the s th link can open if all the links to the left (1,2,3,. ..,s-1) are open. (a) Show that the partition function of a DNA molecule is 1 - exp( - ( N + 1) ε/kT ) 1 - exp( - ε/kT ) (b) In the limit ε ± kT ﬁnd the average number of open links as a function

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Unformatted text preview: of T For students taking 2.37 1. Chapter 10, problem 7 2. Chapter 10, problem 9 3. Chapter 10, problem 11 4. Chapter 11, problem 7 5. Chapter 12, problem 2 6. In this problem we examine a simplied model for the unwinding of double-stranded DNA molecules. The DNA has N links; each link has a state in which it is closed with energy 0, and a state in which it is open with energy . The DNA can only unwind from the left; in other words, the s th link can open if all the links to the left (1,2,3,. ..,s-1) are open. (a) Show that the partition function of a DNA molecule is 1-exp(-( N + 1) /kT ) 1-exp(-/kT ) (b) In the limit kT nd the average number of open links as a function of T...
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## This note was uploaded on 10/06/2011 for the course MECHANICAL 2.37 taught by Professor Hadjiconstantinou during the Fall '07 term at MIT.

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ps6_molecular-mechanicsF07 - of T For students taking 2.37...

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