Predictive theory

J.D. Bryngelson, When is a potential accurate enough for structure prediction Theory and application to a random heteropolymer model of protein folding, J. Ghem. Phys. 100 (1994), 6038-6045. 

This clearly overstates the potential of demographic study to provide a mechanistic understanding of plant responses to environments and, if implemented, would lead to unnecessary delay in the development of generalising principles. The remainder of this chapter is founded on the assumption that the most direct route to a coherent predictive theory of plant responses to stress is likely to involve a synthesis of insights derived from plant population biology, ecophysiology, and many other fields of botanical endeavour. 

Vrentas, JS Duda, JL, Diffusion in Polymer-Solvent Systems. I. Reexamination of the Free-Volume Theory, Journal of Polymer Science Polymer Physics Edition 15, 403, 1977. Vrentas, JS Duda, JL, Diffusion in Polymer-Solvent Systems. II. A Predictive Theory for the Dependence of Diffusion Coefficients on Temperature, Concentration, and Molecnlar Weight, Journal of Polymer Science Polymer Physics Edition 15, 417, 1977. 

One tool for working toward this objective is molecular mechanics. In this approach, the bonds in a molecule are treated as classical objects, with continuous interaction potentials (sometimes called force fields) that can be developed empirically or calculated by quantum theory. This is a powerful method that allows the application of predictive theory to much larger systems if sufficiently accurate and robust force fields can be developed. Predicting the structures of proteins and polymers is an important objective, but at present this often requires prohibitively large calculations. Molecular mechanics with classical interaction potentials has been the principal tool in the development of molecular models of polymer dynamics. The ability to model isolated polymer molecules (in dilute solution) is well developed, but fundamental molecular mechanics models of dense systems of entangled polymers remains an important goal. 

At this point, we have completed the presentation of the key equations which will be crucial to the development of a predictive theory of molecular structure. These equations will form the basis for determining the relative stability of isomers, the relative stabilization of a cationic, radical or anionic center by substituents, etc. On the other hand, the differential expressions (9) to (12) will form the basis for determining how substitution affects the relative stability of isomers, the relative stabilization of cationic, radical and anionic centers, etc. It is then obvious that a working knowledge of Eqs. (1) to (6) presupposes a great familiarity with the key quantities involved in these equations, namely, orbital energies and interaction matrix elements. 

This section may be concluded by the statement that flexible dendrimers are predicted to exhibit a strongly fluctuating structure in solution. According to these studies the endgroups are not strictly located at the surface of the molecules but may also fold back into the interior of the dendrimer. It must be noted that this conclusion originates from models which idealize the dendritic architecture in terms of model parameter common in polymer theory [ 14,15]. In this respect theory may not lead to fully quantitative predictions. Theory, however, certainly arrives at correct qualitative conclusions which are largely backed by available experimental evidence as shown further below. 

Gibilaro, L.G., Fluidization-dynamics the formulation and applications of a predictive theory for the fluidized state, Butterworth-Heinemann, Oxford, 2001. 

Forster s theory [1], has enabled the efficiency of EET to be predicted and analyzed. The significance of Forster s formulation is evinced by the numerous and diverse areas of study that have been impacted by his paper. This predictive theory was turned on its head by Stryer and Haugland [17], who showed that distances in the range of 2-50 nm between molecular tags in a protein could be measured by a spectroscopic ruler known as fluorescence resonance energy transfer (FRET). Similar kinds of experiments have been employed to analyze the structure and dynamics of interfaces in blends of polymers. 

So, an accurate predictive theory should satisfiy the following equality ... 

At its most satisfying level, a statistical thermodynamic theory would begin by specifying realistic interaction potentials for the molecular components of a complex mixture and from these potentials the thermodynamic functions and phase behavior would be predicted without further approximation. For the next decade or so, there is little hope to accomplish such a theory for microstructured fluids. However, predictive theories can be obtained with the aid of elemental structures models. Also, lattice models... 

Obtaining these desired output parameters involves two steps. In the first step, tests are conducted on the target system in order to obtain a set of measured values for macroscopic properties such as temperature, pH, ultrasonic attenuation, etc. In the second, the previously measured data are analysed in order to compute the desired microscopic properties. Such analysis requires three tools a model dispersion, a prediction theory and an analysis engine. 

A prediction theory consists of a set of equations that describes some of the measurable macroscopic properties in terms of the microscopic properties of the model system. 

While there are no currently approved therapeutic protein or peptide products for delivery via the pulmonary route into the systemic circulation, the data on the efficiency, reproducibility, and safety of molecules such as insulin are particularly encouraging. From a molecular perspective, there is a general trend in the reduction of the rate and extent of absorption with increasing molecular weight, but predictive theories are lacking due to our poor understanding of the complexity and multitude of channels of entry of drugs from the respiratory tract into the systemic circulation. 

Miller In my paper in particular, what I am striving for is a theory of -loadings. I want to explain why some mental adaptations are so much more dependent on than others, and why some are more variable and heritable. If we can have a predictive theory which says which mental adaptations are and aren t, this is a step forward in understanding intelligence. 

Spalding, G.E. 1971. Predictive theory of coion transport accompanying particle diffusion controlled ion exchange. J. Chem. Phys. 55 4991-4995. 

The richness of interactions and their nonlinear character lead to critical quantitative relationships that characterize systemic behavior. Only a quantitatively precise language like mathematics has the power to elucidate these design principles and the structure to represent them in an efficient manner. Mathematical methods can be employed to make rigorous comparisons, which in turn form the basis for predictive theories of alternative design. 

Outer-sphere electron transfer is one of the simplest reaction types because no bonds are broken or formed. It is therefore not surprising that this class of reactions was the subject of early kinetic theories. More than 30 years ago Marcus (1965) derived a predictive theory for the rate constants of os redox reactions in homogeneous and heterogeneous systems. A didactic introduction was later given by the same author (Marcus, 1975), and Sutin (1986) reviewed modern refinements of the theory. 

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