Question

Using MATLAB

Consider a paramagnetic system of N elementary dipoles (with dipole moment μ) that can only have states of parallel ↑ or antiparallel ↓ to the applied magnetic field B. The energies associated with each dipole is ±μ-B, the lower energy state being when the dipole is parallel to the B field. The macrostate state of the system will be defined by Nt, or equivalently, the total energy: The multiplicity of a given macrostate of a paramagnet is given by: (a) For a system of 100 dipoles: (i) Calculate and plot the energy U/uB and entropy S/k of each macrostate of the system (ii) Plot the entropy S/k as a function of the energy UjuB (ii) Using a centred finite difference scheme, for each macrostate, calculate the dimensionless temperature kT/uE kT S+1-S-1) (iv) Plot the dimensionless temperature kTJuB as a function of U/NIB. Discuss your results including an interpretation of the sign of the dimensionless temperature (v) Using a centred finite difference scheme, calculate and plot the heat capacity C/Nk as a function of the sionless temperature kT/uB (b) Repeat for a system of 300 dipoles. Discuss any differences.

Answer 1

Solution: 1. The direction of the dipole pointing towards the axis of alpha helix. a-helices often occur with the N-terminal end bound by a 2. Yes the Glu or Asp amino acid at the N- terminus matter for the stability of an alpha helix segment.g-helices often occurwith the N-terminal end bound by a negatively charged group, these groups can be glutamate or aspartate, or sometimes a phosphate ion. These groups act as micro- dipoles interacting electrostatically with such groups leading to set of interactions between local micro dipoles such as C-OH-N thereby they disturb the stability of the alpha helix 3. Yes there are amino acids that stabilize the alpha helix. For example: alanine, leucine, isoleucine and valine. These amino acids contain unnatural aliphatic side chains having linear side chains with two, three, or four carbons are as strongly helix stabilizing as the single methyl in alanine and that all linear side chains are stronger helix promoters than leucine. Restriction in conformational freedom of a side chain imposed by alpha-helix formation is a major component of the role of a side chain in stabilizing helical structure. 4. The helices stabilize the ion in the positive ion channel and these positive ion channel are lined lined mainly by hydrophobic amino acids from the inner helix and hence no strong hydrogen- bonding donor or acceptor groups are available for the water molecules surrounding the ion.