The Chain Method

The Chain method initially calculates the energy at a series of points placed at regular intervals (tfmax) along a suitable reaction coordinate. This may either he a straight line, 

The Locally Updated Planes (LUP) minimization is related to the chain method, but the relaxation is here done in the hyperplane perpendicular to the reaction coordinate, rather than along a line defined by the gradient. Furthermore, all the points are moved in each iteration, rather than one at a time. 

The Conjugate Peak Refinement (CPR) method may be considered as a dynamical version of the chain method, where points are added or removed based on a sequence of maximizations along line segments and minimizations along the conjugate directions. 

In practice it may not be possible to minimize the energy in the conjugate directions, since the energy surface in general is not quadratic. Once the gradient 

In the Self Penalty Walk (SPW) method the whole reaction path is approximated by minimizing the average energy along the path, given as a line integral between the reactant and product geometries (R and P). 

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Figure 14.8 Illustration of the chain method. Initial points along the path are denoted by jc, and relaxed points are denoted by ...

N C The Locally Updated Planes (LUP) minimization " is related to the chain method, but... 

Biopolymers such as proteins have a hierarchical structure (this can be compared to semicrystalline polymers. Section 2.7.2). The primary structure is simply the sequence of amino-acid residues in the polymer chain. This is created during the synthesis of each molecule, and is memorized , in other words it is not destroyed by thermal motion of the chain. Methods for determining primary structure have now been discovered, and even automated. The secondary structure of biopolymers results from hydrogen bonding between -CO and -HN groups. This leads to the so-called a and (3 structures of proteins. An a-helix and p-sheet are sketched in Fig. 6.13. The tertiary structure refers to the overall arrangement of the macromolecule, an example is shown in Fig. 6.14. 

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