Computer Assisted Modeling Contributions of Computational Approaches to Elucidating Macromolecular Structure and Function (1987) / Chapter Skim
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6 Tertiary Structure of Proteins and Nucleic Acids: Theory
6 Tertiary Structure of Proteins and Nucleic Acids: Theory
Pages 69-105
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From page 69... ...
Thus, it is a challenge to chemists to understand how the interatomic interactions within the polypeptide chain and the interactions between the atoms of the chain and those of the surrounding solvent lead to the thermodynamically stable structure, that is, the one for which the statistical weight of the system is a maximum. The hypothesis that the statistical weight is a maximum immediately implies that some kind of optimization strategy is necessary to find the most stable structure.
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From page 70... ...
, armed from the presence of many local m~nima in the multidunensional energy surface. Although algorithms are available for minimizing an energy function of many variables, there are no efficient ones for passing from one local minimum, over a potential barrier, to the next local minunum and ultimately to the global niinimum of the potential energy in a very high dimensional space.
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From page 71... ...
(1978~. Potential Functions Many research groups have developed potential energy functions with which to carry out such computations on polypeptides, polysaccharides, polynucleotides, and synthetic polymers.
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From page 72... ...
Although potential functions could still be improved, those for which parameters have been determined in a self-consistent way have led to many computed structures that have subsequently been checked by experiment. For example, the computed structure of the colIagen-like poly(Gly-Pro-Pro)
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From page 73... ...
, but current efforts are being made to obtain such free energies from Monte CarIo and molecular dynamic studies of aqueous solutions of small molecules (see, e.g., Jorgensen et al., 1983~. The computation of free energies by these simulation techniques faces many theoretical obstacles, although this very active field of research is progressing quickly.
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From page 74... ...
The Monte CarIo method makes random changes in the conformational variables and accepts the new conformation according to various protocob that compute the energies before and after the random changes in the conformation. ~ molecular dynamics calculations, Newton's equations of motion for the atoms of the macromolecule (subject to interatomic forces determined by the potential functions)
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From page 75... ...
Then, the approx~nations are abandoned, and fuB-scale energy minimization, Monte CarIo, or molecular dynamics procedure ~ earned out. A variety of such procedures have been developed (Gibson and Scheraga, 1988~.
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From page 76... ...
has been verified by experiment (Sm~th-Gill et al., 1984~. These and other examples should give us confidence in the validity of the potential functions and computational methodology (Gibson and Scheraga, 1988~.
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From page 77... ...
Noguti and Go (1985) indicate how, with knowledge of the second-derivative matrix of the potential energy, the atomic coordinates can be effectively used to speed up the Monte CarIo process.
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From page 78... ...
The simulation requires two pieces of information at the outset: a starting conformation and potential energy function or forcefield. For a protein, current technology requires that the starting conformation be firmly based on experimental observation: because many conformations exist at local minimum energy, a conformation that is very different from the correct most stable conformation evolves too slowly to reach the correct conformation in the length of a typical calculation.
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From page 79... ...
Clearly, simulations cannot now span a time that is on the biological time scale of microseconds to seconds. Unavoidably, molecular dynamics simulations use simpie forcefields to span a longer time.
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From page 80... ...
Molecular dynamics simulations show r.nn.cliA-ral~^ ~:~ ~, ~ _ ~- HA VIl~i:~; Ut ;, "~`e to Increase our knowledge of structures proposed on the basis of incomplete information, particularly information derived interesting work has been reported on nucleic acids. However, the technical difficulties of working with tese highly charged molecules much exceed the difficulties encountered in simulations of proteins; given a limited amount of resources, it is understandable that technically less formidable problems have received priority.
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From page 81... ...
In this situation, additional information must be brought to bear, an obvious choice for this information being the constraints imposed on the structure by its chemistry and by the requirement of adequate interchain "packing." As these requirements are those observed in a typical molecular dynamics simulation, this has led to the development of a method of molecular dynamics with added constraints, i.e., the NOE distances. By varying the importance of the constraints that determine the conformation and varying the temperature (the total kinetic energy)
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From page 82... ...
Instead, its frequency was estimated by combining an analysis of the potential energy required to bend the hinge region with hydrodynamic consiclerations. In contrast, the breathing motion of myogiobin was observed in a molecular dynamics simulation of 100 picoseconds (10-~°sec)
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From page 83... ...
As this work has been refined with careful attention to detail and use of improved potential functions, the model's kinetic parameters have tended to approach the experimentally observed values. However, because the motion is so localized, this study of tyrosine ring flips may be the only well-developed example of its kind.
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From page 84... ...
The techniques have been am plied to proteins very recently, but already their use has shifted the emphasis of the simulation field to calculations of free energy differences. Several factors explain the great current interest in this application, the most important being the availability of many precise experimental data for a variety of equilibria that involve biological macromolecules and the unexpectedly excellent theoretical estimates that the simulations produce.
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From page 85... ...
~ S2 (solvated) ~ E-S2 the difference of the two free energy changes obtained from the simulations (indicated by vertical arrows)
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From page 86... ...
Prognosis of Developments The success of the free energy sunulations has suddenly changed the scope and emphasis of molecular dynamics simulations. The early simulations either clarified properties of proteins that were difficult to study experimentally (kinetics and dynamics on the picosecond time scale)
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From page 87... ...
Apart from drug and protein design, others within and outside of industry will apply these techniques to the broad problems of protein-protein and protein-nucleic acid recognition, by using a combination of molecular dynamics simulations and the results of site-directed mutagenesis. Once we have dealt with the problem of rationalizing these equilibria in terms of molecular interactions in atomic detail, our attention will shift to the application of the newly acquired skills to problems of the dynamics of interaction of proteins with other molecules, which will presumably require just as much computer time.
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From page 88... ...
SOLVATION AND ELECT1tOSTATICS IN COMPUTER SIMULATION O1? BIOPOLY-:1IS Biomolecular systems function in viva in an aqueous solution environment.
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From page 89... ...
In particular, we must take into account the significant role played by the environment in determining the strength of ligand binding, as well as the relative stability (free energy) of the varied structures that must be encountered during protein folding and that may accompany function.
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From page 90... ...
Carrying out such studies requires specialized sampling techniques, termed umbrella sanding, that allow the accurate determination of relative populations of conformers that are separated from one another by significant free energy barriers. Such techniques and their efficient use are the products of recent research on simulations of molecular mode!
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From page 91... ...
. Recently, a number of studies have been carried out that aimed to evaluate directly the relative hydration free energies of small molecules, amino acids, and nucleotide bases (Bash et al., 1987a; Jorgensen and Ravimohan, 1985; Lybrand et al., 1986; Singh et al., 1987~.
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From page 92... ...
This does not imply that results obtained, for example, for polypeptide conformational equilibria would have comparable relative errors, but it does indicate that caution is warranted, and that further mode] development ~ necessary.
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From page 93... ...
This added "hydration shell" term introduces a free energy bonus or penalty associated with the close approach of solute atoms, typically proportional to the overlap volume of the first salvation shells of the approaching polypeptide atoms. This approach is closely analogous to the method widely used in models of ionic solutions pioneered by Friedman et al.
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From page 94... ...
It is known, for example, that for ionic solutions, a detailed molecular solvent treatment of the interionic potential of mean force does not closely resemble the hydration shell model, although both are consistent with observed thermodynamics (Pettitt and Roseky, 1986~. The true effective potential exhibits large oscillations as a function of distance.
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From page 95... ...
would require roughly 1,000 hours of supercomputer time. TO the case of nucleic acids, an intermediate ground state exists that is not relevant for many proteins.
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From page 96... ...
An example of significant recent progress along these lines is the work of Pack and coworkers (Klein and Pack, 1983~. They have used an algorithm for solution of the Poisson-Boltzmann equation for the ionic distributions around a detailed DNA model, and from such distributions the relevant free energies of different conformations are, in principle, obtainable.
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From page 97... ...
Therefore, we should continue to encourage both experiment and theory for both macromolecular and smaller mode} compounds. We cannot expect an immediate and completely satisfactory way to account for the influence of the solution environment on
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From page 98... ...
To explore adequately events such as protein folding that occur on much longer time scales (or involve vast conformational exploration) , these computational improvements would still be inadequate by many orders of magnitude.
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From page 99... ...
In summary, the rapid progress in our ability to describe the environmental aspects of bipolymer systems gives solid ground for optimism that this element of biomolecular modeling will not impede development of useful predictive methods. However, for the most challenging aspects, we are at least several years away from demonstrating the ability to mimic accurately solution environmental effects.
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From page 100... ...
The amino acids on the surface of the protein can be easily substituted. Energy minimization and/or molecular dynamics are sufficient to reduce the errors caused by any changes in surface sidechain conformation.
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From page 101... ...
Alwyn Jones at Uppsala has done this and recently integrated it into FRODO, his modeling program. After Al the changes have been made either by graphic methods or by using a loop library, extensive molecular dynamics simulation is generally used to improve the quality of the model.
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From page 102... ...
Exon Shnffling Many recently evolved proteins exhibit evidence of "exon shuffling.~ In this phenomenon, mosaic proteins result from the genom~c rearrangement of segments that encode small portions of different proteins. For such proteins, it ~ thought that the pew tide segments, which often range from 30 to 90 amino acids in length, all fold independently (DoolittIe, 1985~; as such, they constitute domains in the truest sense.
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From page 103... ...
PATTERN RECOGNITION AND ARTIFICIAL INT1:~LIGENCE We differentiate the techniques of pattern recognition from those of artificial intelligence, especially its subdiscipline of expert systems. Pattern recognition is usually defined as including numerical techniques for clustering observed data into binary or higher order categories (but see below)
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From page 104... ...
These techniques involve, for example, the presentation of threedimensional protein structures in the form of C-alpha distance maps (Kuntz, 1975; Rao and Rossmann, 1973) to infer the presence of secondary and super secondary structures and location of intron/exon boundaries (Go, 1981~.
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From page 105... ...
We are hopeful that they yield good first-order approximations that can be refined by the energy minimization and molecular dynamics calculations.
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