Structure adaptation

Niedermeier, C, Tavan, P. A structure-adapted multipole method for electrostatic interactions in protein dynamics. J. chem. Phys. 101 (1994) 734-748. 

Abstract. Molecular dynamics (MD) simulations of proteins provide descriptions of atomic motions, which allow to relate observable properties of proteins to microscopic processes. Unfortunately, such MD simulations require an enormous amount of computer time and, therefore, are limited to time scales of nanoseconds. We describe first a fast multiple time step structure adapted multipole method (FA-MUSAMM) to speed up the evaluation of the computationally most demanding Coulomb interactions in solvated protein models, secondly an application of this method aiming at a microscopic understanding of single molecule atomic force microscopy experiments, and, thirdly, a new method to predict slow conformational motions at microsecond time scales. 

As an example for an efficient yet quite accurate approximation, in the first part of our contribution we describe a combination of a structure adapted multipole method with a multiple time step scheme (FAMUSAMM — fast multistep structure adapted multipole method) and evaluate its performance. In the second part we present, as a recent application of this method, an MD study of a ligand-receptor unbinding process enforced by single molecule atomic force microscopy. Through comparison of computed unbinding forces with experimental data we evaluate the quality of the simulations. The third part sketches, as a perspective, one way to drastically extend accessible time scales if one restricts oneself to the study of conformational transitions, which arc ubiquitous in proteins and are the elementary steps of many functional conformational motions. 

Fig. 1. Structure adapted hierarchical description of Coulomb interactions in biological macromolecules. Filled circles (level 0) represent atoms, structural units (li vel 1) are surrounded by a single-line border, and clusters (level 2) are surrounded by a double-line border.

C. Niedermeier and P. Tavan. Fast version of the structure adapted multipole method — efficient calculation of electrostatic forces in protein dynamics. Mol. Sim., 17 57-66, 1996. 

A, B, and C, surrounded by a helices. The polypeptide chain is colored in sections from the N-terminus to facilitate following the chain tracing in the order green, blue, yellow, red and pink. The red region corresponds to the active site loop in the serpins which in ovalbumin is protruding like a handle out of the main body of the structure. (Adapted from R.W. Carrell et al.. Structure 2 257-270, 1994.)... 

Figure 8.23 The helix-turn-helix motifs of the subunits of both the PurR and the lac repressor subunits bind to the major groove of DNA with the N-terminus of the second helix, the recognition helix, pointing into the groove. The two hinge helices of each arm of the V-shaped tetramer bind adjacent to each other in the minor groove of DNA, which is wide and shallow due to distortion of the B-DNA structure. (Adapted from M.A. Schumacher et al.. Science 266 763-770, 1994.)...

A view down the fivefold symmetry axis of the icosahedtal structure (a) shows that the central capsomer is pentameric in shape and surrounded by five other capsomers as expected. The view down the pseudosixfold axis (h) shows, however, that the central capsomer is pentameric in shape and not hexameric as required for a T = 7 structure. (Adapted from 1. Rayment et al., Nature 295 110-115, 1982, hy copyright permission of Macmillan Magazines Limited.)... 

Fig. 10.1 Intelligent control system structure (adapted from Johnson and Picton).

Production System Structure (adapted from Reason 1990). 

FIGURE 6.39 Relative frequencies of occurrence of amino acid residues in m-helices, /3-sheets, and /S-turns in proteins of known structure. (Adapted from Belt, J E., and Belt, E. T, 1988, Proteins and. Enzymes, Englewood Cliffs, NJ Prentice-Hall.)... 

Burroughs AM, Allen KN, Dunaway-Mariano D et al (2006) Evolutionary genomics of the HAD superfamily understanding the structural adaptations and catalytic diversity in a superfamily of phosphoesterases and allied enzymes. J Mol Biol 361 1003-1034... 

Our work described in this section clearly illustrates the importance of the nature of the cations (size, charges, electronegativities), electronegativity differences, electronic factors, and matrix effects in the structural preferences of polar intermetallics. Interplay of these crucial factors lead to important structural adaptations and deformations. We anticipate exploratory synthesis studies along the ZintI border will further result in the discovery of novel crystal structures and unique chemical bonding descriptions. 

Williams PA, Cosme J, Sridhar V, Johnson EF, McRee DE. Mammalian microsomal cytochrome P450 monooxygenase structural adaptations for membrane binding and functional diversity. Mol Cell 2000 5 121-31. 

The structural adaptation of the skeleton is one of the most fascinating problems in the history of science. Galileo observed in 1638 that longer bones had to be thicker than shorter ones to have the same structural... 

Figure 7.6. When a force is applied to a bone of uniform structure (a), the structure adapts by the feedback mechanism shown in Figure 7.5 and forms a nonuniform structure to carry the load efficiently (b). The resulting structure resembles the familiar design of bridges and other man-made trusses (c).

The remainder of this chapter is structured as follows. In Section II the problem of deriving an estimate of an unknown function from empirical data is posed and studied in a theoretical level. Then, following Vapnik s original work (Vapnik, 1982), the problem is formulated in mathematical terms and the sources of the error related to any proposed solution to the estimation problem are identified. Considerations on how to reduce these errors show the inadequacy of the NN solutions and lead in Section III to the formulation of the basic algorithm whose new element is the pointwise presentation of the data and the dynamic evolution of the solution itself. The algorithm is subsequently refined by incorporating the novel idea of structural adaptation guided by the use of the L" error measure. The need... 

Theorem 2. Algorithm 1 will converge to Sj., and no further structural adaptation will be needed for any additional data points. 

The space-frequency localization of wavelets has lead other researchers as well (Pati, 1992 Zhang and Benveniste, 1992) in considering their use in a NN scheme. In their schemes, however, the determination of the network involves the solution of complicated optimization problem where not only the coefficients but also the wavelet scales and positions in the input space are unknown. Such an approach evidently defies the on-line character of the learning problem and renders any structural adaptation procedure impractical. In that case, those networks suffer from all the deficiencies of NNs for which the network structure is a static decision. 

The multiresolution framework allows us to reconsider more constructively some of the features of the structure adaptation algorithm. First, a strictly forward move in the ladder of subspaces [Eq. (8)] is not necessary. Due to localization, the structural correction can be sought in higher spaces before ail functions in the previous space are exhausted. This... 

Fig. 4.4 Atomistic representation of successive steps in the ECALE synthesis of CdTe on an Au substrate. Observe the deposition and stripping of Te for assembling the correct atomic planes of the zinc blende structure. (Adapted from [27])...

Figure 1.18 STM image (4 nm x 4 nm) showing the 2D cocrystalline structure consisting of an ordered array of 1 1 H-bonded complexes of (R,R)-tartrate and methylacetoacetate species on Ni l 1 1 givingachiral (3 11-3 4) structure. (Adapted with permission from Ref. [62], Copyright 2002, Elsevier.)...

If a case is found that matches the user s query closely, this is used to provide appropriate advice. If, on the other hand, there is no case that matches the problem presented by the user sufficiently closely, the system can try to modify a case that is present in the library to bring it into line with the user s query in what is known as structural adaptation, or it may be able to create a new solution using as a starting point a similar case from the past (derivational adaptation). 

The combined features of structural adaptation in a specific hybrid nanospace and of a dynamic supramolecular selection process make the dynamic-site membranes, presented in the third part, of general interest for the development of a specific approach toward nanomembranes of increasing structural selectivity. From the conceptual point of view these membranes express a synergistic adaptative behavior the addition of the most suitable alkali ion drives a constitutional evolution of the membrane toward the selection and amplification of a specific transport crown-ether superstructure in the presence of the solute that promoted its generation in the first place. It embodies a constitutional selfreorganization (self-adaptation) of the membrane configuration producing an adaptative response in the presence of its solute. This is the first example of dynamic smart membranes where a solute induces the preparation of its own selective membrane. 

Fig. 62. LEED pattern observed for UPD of Cd from a CdCl2 solution. The pattern is for a (v/7 x /7)A19.1°-Cd,Cl structure. The fractional order beams show some streaking, indicating some ordered disorder in the structure. Adapted from ref. [273],...

The use of the symbol E in 5.1 for the environment had a double objective. It stands there for general environments, and it also stands for the enzyme considered as a very specific environment to the chemical interconversion step [102, 172], In the theory discussed above catalysis is produced if the energy levels of the quantum precursor and successor states are shifted below the energy value corresponding to the same species in a reference surrounding medium. Both the catalytic environment E and the substrates S are molded into complementary surface states to form the complex between the active precursor complex Si and the enzyme structure adapted to it E-Si. In enzyme catalyzed reactions the special productive binding has been confussed with the possible mechanisms to attain it lock-key represents a static view while the induced fit concept... 

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