# ps_2 - MASSACHUSETTS INSTITUE OF TECHNOLOGY Molecular...

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MASSACHUSETTS INSTITUE OF TECHNOLOGY Molecular, Cellular and Tissue Biomechanics BEH.410 / 2.978J / 6.524J / 10.537J Problem Set #2 Issued: 2/21/03 Due: 3/5/03 (in class) Please staple each problem separately as we will have different graders grading each problem. Also please put your name on each problem! Problem #1 Microtubule Structure Problem 2.5 in Boal Problem #2 Entropic Elasticity of a 1-D Polymer Chain Model In class we discussed the freely jointed chain in 3-dimensions as a model for flexible polymers. Here will consider a more simple model of a 1-D polymer chain. The chain is composed of N links of length b. Each link has a two state variable σ which equals +1 if the link points forward and –1 if it points backward. The total chain N extension is then z = b i . i = 1 a) What is the probability P( σ 1 , σ 2 ,… σ N ) of a given conformation (set of { σ 1 , σ 2 ,… σ N }) when a constant force f is applied at the chain ends ? b) Prove that <z>/Nb = tanh(fb/kT). Note: tanh(x) = (e x -e -x )/(e x +e -x ). c) Compare the spring constant for the1-D chain and 3-D chain in the linear regime (small forces).

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