Lattice models protein folding kinetics

Abkevich, V. I., Gutin, A. M., and Shakhnovich, E. I., Free energy landscape for protein folding kinetics Intermediates, traps, and multiple pathways in theory and lattice model simulations. J. Chem. Phys. 101, 6052 (1994). 

A Sail, El Shakhnovich, M Karplus. Kinetics of protein folding A lattice model study of the requirements for folding to the native state. J Mol Biol 235 1614-1636, 1994. 

Sali A, E Shakhnovich and M Karplus 1994b. Kinetics of Protein Folding. A Lattice Model Study of the Requirements for Folding to the Native State. Journal of Molecular Biology 235.1614-1636... 

Hydration for the Kinetics and Thermodynamics of Protein Folding Simplified Lattice Models. 

Kinetics of Protein Folding A Lattice Model Analysis of Multiple Pathways with Intermediates. 

The fact that the folding (and unfolding) kinetics of relatively small, two-state proteins can be predicted with reasonable accuracy from global features of the native state like the contact order, stability, and number of contacts supports the idea that the details of protein structure are not required to capture the key features of protein folding, so that reduced representations should be adequate. However, the most widely used simple heteropolymer models, those restricted to a simple cubic lattice, predict that stability is more important than native structure, in contrast to the experimental data for proteins. In this section we seek to understand why lattice models differ from proteins in this regard. Doing so is of importance because complete details of the folding trajectories of such models... 

A. R. Dinner and M. Karplus, The thermodynamics and kinetics of protein folding A lattice model analysis of multiple pathways with intermediates. J. Phys. Chem. B 103, 7976-7994 (1999). 

To clarify the relevance of non-native intermediates in the folding of proteins dictated by the formation of disulfide bonds Camacho and Thirumalai [45] used lattice models. While these models are merely caricatures of proteins, they contain the specific effects that can be studied in microscopic detail. We used a two-dimensional lattice sequence consisting of hydrophobic (H), polar (P), and Cys (C) residues. If two C beads are near neighbors on the lattice, they can form a S-S bond with an associated energy gain of —with > 0. Thus, topological specificity is required for native S-S bond formation in this model. We have studied the folding kinetics of this model, which is perhaps the simplest model that can probe the characteristics of native and non-native disulfide bonded intermediates. 

In Section VIII, we incorporated into the lattice model features expected due to the presence of a macromolecular chain running throu the structure. We have not yet performed a kinetic analysis for this model according to the above description of protein dmaturation kinetics. It is to be expected that the conformations of Fig. 12 provide a sufficient set on which to perform the search for the slowest step in the fastest sequence of steps. The problon of performing this search is by no means a trivial one and we have not yet attempted to solve it Also there remains the problem of what is the rate of folding of a looped chain with respect to that of a chain with two free ends. (That is, if one wishes to consider such conformations in spite of the fact that these have relatively low statistical weights, i.e. low Kf.)... 

In conclusion, the results on myoglobin analyzed here tk) not provide a test of the various aspects of the theory developed in Section VIII, mainly for lack of supplementary data. Certainly we do not note discrepanci between the behavior tlK model and experimental results, but our criteria as to what constitutes dkcrepancy are not very stringent Tlte theory presents a particular point of view, which in these cases does allow one to gain a re onable qualitative understanding of the experiments. The basic point in the theory k the instability of the intermediates in the folding process this is well reproduced by the lattice model, which allows one to calculate the kinetic behavior of a cooperative system with results which may, hopefully, be applied to other cooperative systems and in particular to protein molecules. Further experimental studies are needed to establish whether this is in fact the case. 

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