By Alexander V. Yakubovich
There are approximately a hundred 000 various protein sequences encoded within the human genome, each one with its personal particular fold. figuring out how a newly shaped polypeptide series reveals its technique to the proper fold is without doubt one of the maximum demanding situations within the glossy structural biology. the purpose of this thesis is to supply novel insights into protein folding through contemplating the matter from the viewpoint of statistical mechanics.
The thesis begins by means of investigating the basic levels of freedom in polypeptides which are answerable for the conformational transitions. this data is then utilized within the statistical mechanics description of helix↔coil transitions in polypeptides. ultimately, the theoretical formalism is generalized to the case of proteins in an aqueous atmosphere. the main novelty of this paintings lies in combining (a) a formalism in keeping with primary actual houses of the approach and (b) the ensuing probability of describing the folding↔unfolding transitions quantitatively. The transparent actual nature of the formalism opens find out how to additional purposes in a wide number of structures and processes.
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Extra info for Theory of Phase Transitions in Polypeptides and Proteins
Example text
Physical Review E, 011909, 1–7. 4. , & Hutter, J. (2000). Structure and mechanism in protein science: a guide to enzyme catalysis and protein folding. Julich: John von Neumann Institute for Computing. 5. -J. (2000). Ab initio methods for electron correlation in molecules. In J. ), Modern methods and algorithms of quantum chemistry (pp. 397–434). Julich, Germany: John von Neumann Institute for Computing. 6. , & Gross, E. (2004). Time-dependent density functional theory. Annual Review of Physical Chemistry, 55, 427–455.
It is worth noting that for some conformations of alanine hexapeptide the angles ϕ and ψ change significantly when the relaxation of all degrees of freedom in the system are accounting for (see for example conformations 1, 5 in Fig. 8a and conformations 2, 4 in Fig. 8b). 2 Conformational Properties of Alanine and Glycine Chains 37 Fig. 8 Potential energy surface for the alanine hexapeptide with the sheet secondary structure (part a) and with the helix secondary structure (part b) calculated by the B3LYP/6-31G(2d,p) method.
48) This is the normal form of the general HF equation. 48) can be written out explicitly Z 1 − ∇ 2 − + UHF |a = εa |a . 49) Each term here can be given a simple physical interpretation. The first term represents the kinetic energy of electron a and Z/r its attraction to the nucleus. The potential UHF represents the average Coulomb and the exchange interaction of electron a with other electrons in the atom. 49) and similar equations, the molecular orbitals, φi , are often approximated by a linear combination of a pre-defined set of single-electron functions, χμ , known as basis functions.