Model landscape

Thereby, the features of the a-relaxation observed by different techniques are different projections of the actual structural a-relaxation. Since the glass transition occurs when this relaxation freezes, the investigation of the dynamics of this process is of crucial interest in order to understand the intriguing phenomenon of the glass transition. The only microscopic theory available to date dealing with this transition is the so-called mode coupling theory (MCT) (see, e.g. [95,96,106] and references therein) recently, landscape models (see, e.g. [107-110]) have also been proposed to account for some of its features. 

In management science, use of rugged landscape models has been brought to bear on questions concerning the adaptability of organizations, optimal organizational structure, the co-evolution of organizations, and further topics. 

Mackay CE, Pastorok R A. 2002. Landscape models aquatic and terrestrial. In Pastorok RA, Bartell SM, Ferson S, Ginzburg LR, editors. Ecological modeling in risk assessment. Boca Raton (FL) Lewis Publishers, p 149-180. 

Voinov A, Voinov H, Costamza R. 1999. Landscape modelling of surface water flow flow 2 Patuxent watershed case study. Ecol Model 119 211-230. 

At present, many popular applied molecular evolution protocols do not involve mutation or recombination. The laboratory technique-based models presented in this section are of this type. Incorporating mutation requires fitness landscape models or some other means of relating molecular properties to particular sequences. The more abstract models reviewed later allow for mutation and recombination and are based heavily on landscape structure. The models in the present section are based on affinity distribution p(Ka), the probability that a ligand chosen at random from the library has affinity Ka. 

Landscape models are much more abstract than the laboratory technique-based models. As extensive as theory about evolution and optimization on fitness landscapes has become, there is still little work on matching a search algorithm to landscape properties. Additionally, much of this work is based on landscape properties that are presently very difficult to measure with any statistical significance for molecular landscapes. For these reasons, and for reasons of limited space, the landscape search results will be explained in much less detail than the laboratory-based techniques. This section is divided into four parts (i) definitions of terms used in fitness landscape studies and caveats about then-misuse (ii) review of models for fitness landscapes (iii) results from studies of search on fitness landscapes and (iv) conclusions from these results. 

Quite often, a model is capable of producing all possible landscapes however, for the vast majority of landscapes, the probability of the model producing them is extremely low. The quality of a fitness landscape model is determined by how closely its landscape probabilities match those of the problem being considered. 

NK model The NK model is a simple landscape model that allows arbitrary degrees of correlation between 0 and 1 [4,92,93], The sequence space is an N-dimensional space... 

Fig. 15. Example of frustration in an NK fitness landscape model. The tables list the fitness contributions for sites 3 and 4 as a function of their K = 2 epistatic inputs and their own values. The highest fitness contribution for fi requires [a2.a,.a4] =[1,0,0], while for f4 it requires [a3,a4,a5]= [1,0,1]. These two constraints cannot be mutually satisfied, leading to frustration. As K increases, the number of such conflicts rises and results in an increasingly rugged landscape whose peaks are of increasingly lower average fitness.

A completely different class of landscape models has developed from studies of RNA secondary structure folding (recent review in Ref. 66, software available in Ref. 102). These studies are reviewed by Schuster elsewhere in this collection, so I will only summarize certain relevant results here. 

The first limitation is that the landscape models are very abstract. Their results apply to molecular search in a general way, but are difficult to relate to laboratory concerns. Ideally, future work will combine the mathematical rigor of landscape-based search with the chemical and experimental details of the laboratory technique-based models. Some work along these lines has started with calculating mutation rates for SELEX schemes based on RNA secondary structure landscape models [114],... 

The REM, NK and p-spin models all are attempts to capture the important statistical properties of true molecular landscapes in a simple model. Because they contain no biophysical information, they are limited in how well they can achieve this. The block model is an important step in removing some of the simplifications in these models, as it allows for nonstationary properties that can be matched to different regions of molecules. Ideally, landscape models can be based on experimental data. Unfortunately, despite the tremendous interest in molecular optimization, there is still relatively little data that can be used this way. As more data are collected on the effects of substitutions in protein structural and loop regions, antibody CDRs and framework regions, etc., a block or other type of model can be developed that uses appropriate fitness functions for each block. Combined efforts by theoreticians and experimentalists may also help devise experiments that measure key true affinity landscape properties without excessive laboratory effort. 

Fig. 24. 2H NMR data for TOL at various temperatures T< 7R (a) measured (points) and simulated within the energy-landscape model (dashed lines) correlation functions / COK(fnbp — 80 is) (b) and (c) measured (solid lines) and simulated (dashed lines) 2H NMR spectra for solid-echo delays tp = 100 and 200 ps, respectively. (Adapted from Ref. 110.)...

Fig. 25. Distribution V(x) characterizing the full opening angles of the cones in the energy-landscape model of the / -process in TOL. (Adapted from Ref. 110.)...

Two types of uropathogenic E. coli bacterial pili, P and type 1, which are predominantly expressed by E. coli in the upper and lower urinary tracts, have been scrutinized in some detail using FMOT. A model for the bond opening of the LL bond in the helix-like structure as well as the opening of the HT bond between consecutive subunits in the rod, based upon an energy landscape model and a kinetic model (of sticky-chain type) for the bond opening,... 

Plotkin, S. S., Wang, J., and Wolynes, P. G., Correlated energy landscape model for finite, random heteropolymers. Phys. Rev. E 53, 6271 (1996). 

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