Target Functions

First, the structure should explain the data. Apart from the energy or target function value returned by the refinement program, this check can be performed with some independent programs (e.g., AQUA/PROCHECK-NMR [90], MOLMOL [91]). The analysis of the deviations from the restraints used in calculating the structures is very useful in the process of assigning the NOE peaks and refining the restraint list. As indicators of the quality of the final structure they are less powerful, because violations have been checked and probably removed. A recent statistical survey of the quality of NMR structures found weak correlations between deviations from NMR restraints and other indicators of structure quality [88]. 

Figure 5 Optimization of the objective function in Modeller. Optimization of the objective function (curve) starts with a random or distorted model structure. The iteration number is indicated below each sample structure. The first approximately 2000 iterations coiTespond to the variable target function method [82] relying on the conjugate gradients technique. This approach first satisfies sequentially local restraints, then slowly introduces longer range restraints until the complete objective function IS optimized. In the remaining 4750 iterations, molecular dynamics with simulated annealing is used to refine the model [83]. CPU time needed to generate one model is about 2 mm for a 250 residue protein on a medium-sized workstation.

Number of Number of constraints RMSD (BB) Average target function (A) ... 

One straightforward choice for the X-ray target function is the least square residual that represent the discrepancy between the observed and model-predicted structure factors ... 

However, as pointed out by Read and others [23-27], use of residual as the target function is only justified for models that are very close to the true structure, which is often not the case in macromolecule refinements. An improved target function can be derived using the maximum likelihood formalism (MLF),... 

Figure 1.7 Derivatives of carboxylic acids can be prepared through the use of active intermediates that react with target functional groups to give acylated products.

Compounds having the same functionality on both ends are homobifunctional in nature and can be conjugated with the same target functionality on biomolecules, surfaces, or other molecules. Chapter 4 describes traditional homobifunctional compounds in detail, but the discrete PEG-based reagents are described here, because of their unique hydrophilic properties. 

Another perspective for production simulation is automatic capacity utilization optimization of multi-product systems. As discussed, this task may be very difficult because of the many different variables and boundary conditions. In an environment integrating optimization and simulation, the optimizer systematically varies the important decision variables in an external loop while the simulation model carries out production planning with the specified variables in the internal loop (see Gunther and Yang [3]). The target function, for example total costs or lead times, can be selected as required. The result of optimization is a detailed proposal for the sequence of the placed orders. 

One weakness of the developed model approach is the central, one-dimensional optimisation that assumes the same target function for all participants. The model identifies possible economic and environmental benefits of a hydrogen infrastructure build-up by determining the global optimum for the whole system instead of the... 

The role of the potential energy is taken by the Dyana target function [8, 28] that is defined such that it is zero if and only if all experimental distance constraints and torsion angle constraints are fulfilled and all nonbonded atom pairs satisfy a check for the absence of steric overlap. A conformation that satisfies the constraints more closely than another one will lead to a lower target function value. The exact definition of the Dyana target function is ... 

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