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252--The A&EP Physics of Life Prof. Pollack Prelim I Fall 2007 October 16, 2007 Instructions: 1. Write legibly. If I cannot read your answer, you will not receive partial credit. 2. Work your solution in the space provided. If you need extra space, use the back of the page. If you need more space, there is extra paper in the front of the room. Please write your name on every sheet that you hand in. 3. Print your name on this line and sign the statement below. Name Academic integrity is expected of all students of Cornell University at all times, whether in the presence or absence of members of the faculty. Understanding this, I declare I shall not give, use or receive unauthorized aid in this examination Signature of Student Points: Shorter answer (25 points, 5 problems, 5 points each) 1. ____________ 2. ____________ 3. ____________ 4. ____________ 5. ____________ Total: ____________ Longer answer (75 points, 5 problems, 10-25 points each) 6. ____________ 7. ____________ 8. ____________ 9. ____________ 10. ____________ Total: ____________ TOTAL ____________ 1. Name four bonds that determine configuration or conformations of biological molecules? List them in order of their relative strength in water in kcal/mol. 2. What is the human genome project, and one of its major goals? 3. List the four most common elements found in cells. Name a fifth element commonly found in nucleotides? 4. What is the chemical difference between a saturated and unsaturated fat? 5. How does a virus work (~ two to three sentences will do) ? 1. (10 points) A probability distribution y = a x exists over the region x=0 to 4. a) If this is a normalized distribution, what is the value of a? b) What is the average value of x given this distribution function? your Give answers as numbers. 2. (15 points ) There are a large number, V slots in a 1-dimensional lattice. I place four particles in the slots. a. If the particles are distinguishable (e.g. they have different colors), how many distinct arrangements are there? If they are indistinguishable (all blue) how many different arrangements are there? b. c. If they are indistinguishable, how many ways can I arrange them so that the four particles are not in adjacent slots? Evaluate all of the factorials in your answers. 3. (15 points) As we learned, the phi and psi angles describe the conformations of an amino acid. Each angle can take on three values. a. How many different conformations exist for each amino acid? N amino acids are strung together into a protein. There is one folded conformation, the rest are considered unfolded. b. In how many conformations can the amino acid chain be found? c. What is the entropy associated with an unfolded chain? d. What is the entropy associated with the folded chain? 4. (15 points ). A system has four energy levels. E1=1, E2=2, E3=3 and E4=4. There are 4 particles in the system, and its internal energy U=10. a) Sketch the energy level diagram for this system. How many arrangements of the particles can be found if they are b) distinguishable? c) indistinguishable? 5. (20 points) In a biased random walk problem, the probability of taking a step to the left is q. In this case, q does not have to equal 0.5. A total of N steps are taken, with L to the left. a. What is the expression for the probability of taking L steps to the left out of a total of N steps, P(L,N)? b. Using ln[P(L,N)], calculate the most probable value of L (known as L*) as a function of N and q. c. What happens when q=0.5?

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