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Announcements

Announcements. Seminar: Professor Roberto Car, Princeton University "The H-bond network in water and ice" Olin 101, Thursday Sept 23 rd 4:00pm. Zip Model. A particular example of the simple helix formation models. The only allowed states are those with contigious stretches of 1’s:.

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Announcements

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  1. Announcements Seminar: Professor Roberto Car, Princeton University "The H-bond network in water and ice" Olin 101, Thursday Sept 23rd 4:00pm

  2. Zip Model A particular example of the simple helix formation models The only allowed states are those with contigious stretches of 1’s: There are 2 parameters: the nucleation parameter, s, and the propagation parameter, s. As N increases the number of allowed states compared to possible states decreases

  3. Zip Model Each allowed state contributes to the partition function. A state contributes either 1 {the entirely unfolded state}, or ssm , where m is the number of 1’s {the size of the folded stretch}. Why do we multiply? What is the partition function for N=3? What is the partition function for N=2? Can you derive a expression for wk? How would this differ if we allowed all states?

  4. Zip Model The second sum is s times the derivative of the first sum. Hence, If I figure out the first sum I virtually am done. From your favorite book on series,

  5. Zip Model: Helical Fraction Since we know the partition function, we can compute many quantities. One of particular interest is the helical fraction. Why? The probability of having k monomers folded is: How? The helical fraction, q, is defined as:

  6. Zip Model: Helical Fraction The helical fraction, q, is defined as:

  7. Zip Model to Zimm-Bragg What assumption of the zip model does Zimm-Bragg remove? In order to calculate the partition function, the easiest way is to work with a transition matrix. A transition matrix tells us about the weight of the next monomer in terms of the initial monomer What if I had more than nearest neighbor interactions?

  8. Zimm-Bragg The easiest way to work with the Zimm-Bragg model is to diagonalize the transition matrix, as then the last term just becomes: For large N, Helical fraction,

  9. Zimm-Bragg We can now examine what happens to the experimental observable {q} as a function of the nucleation parameter. What does this mean physically? Helical fraction, Interpret these two regimesb

  10. Zimm-Bragg We can now examine what happens to the experimental observable {q} as a function of the nucleation parameter. What does this mean physically? Helical fraction, Interpret these two regimes

  11. Molecular dynamics Use a force field to determine the potential and numerically propagate Newton’s equations of motions within that potential. Start with random velocities picked from a Maxwell-Boltzmann distribution Define the temperature as: Each degree of freedom is given a temperature taken randomly from an MB distribution If the approximation to the canonical ensemble breaks down {i.e. temperature changes too much}, then reassign or rescale the temperatures What do I mean by a degree of freedom? Do I mean the potential terms from the force field?

  12. Molecular dynamics Use newton’s equations of motion at each time-step: Where is the force field? How do I use this to actually change the coordinates?

  13. Molecular dynamics: Numerics In order to use these equations, I need to do numeric derivatives

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