Constrained energy minimization

M Levitt. Protein folding by constrained energy minimization and molecular dynamics. J Mol Biol 170 723-764, 1983. 

We can design a linear matched filter such that the desired target signal s is passed through while the average filter output energy is minimized. The solution to this minimization problem was shown in " and was called Constrained Energy Minimization... 

Thirup 15 Ca-Ca distances of 3 residues on either side of loop 31 protein database constrained energy minimization of fragments 0—4 aa in length well-modeled... 

The average structure for the ADA-8H complex generated after energy minimization and equilibration with 20 ps of MD simulation showed considerable movement of atoms in the vicinity of the zinc ion when these residues were not constrained. Virtual bonds between zinc and the atoms that coordinate to the zinc ion were added to provide necessary atomic constraints prior to energy minimization and MD simulations. After constraints were applied, the average structure was similar to the X-ray... 

Rather than minimize the energy function o(P) = (P, H) by varying over the set of fe-matrices, there is a dual formulation where the bottom eigenvalue /lo(H + S) of the matrix H + S is maximized over the set of Pauli matrices S e The dual formulation can be derived using Lagrange s method, which requires converting the constrained energy problem to an unconstrained one. If... 

The coefficients in Eq. 19.7 may be taken as constants independent of the form of the distribution of cluster sizes. The relationship between the two coefficients fa and qaa+i may then be obtained by imposing an artificial constraint on the system no clusters are allowed to grow beyond a limiting size, Af m, which is considerably larger than the critical size Afc. At the same time, all clusters of size below this limit are allowed to equilibrate with respect to one another so that detailed balance is achieved between them and all fluxes in cluster space go to zero. A new distribution of cluster sizes, N q, will be produced in this constrained system. It is assumed that the same free-energy minimization procedure used previously to find the size distribution under true equilibrium conditions, and which led to Eq. 19.6, may be used for the constrained system, resulting in... 

Click on Calculate. Energy minimization with the N-C-C-N torsion constrained initially at 60°, then at 55° and so on will begin. The results will appear in tabular and graphical forms in windows as shown in Fig. 17.15.5 and 17.15.6. If there are asterisks in the Minimum not reached column increase the number of cycles in the optimization controls and repeat the calculations. 

The mathematical formulation leads to a constrained Gibbs energy minimization problem, subject to conservation of the total amounts of the individual chemical elements that make up the chemical species This constraint is incorporated into the problem via the method of Lagrange multipliers Details of the procedure are given elsewhere W ... 

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