Can protein unfolding simulate protein folding?
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Computer Simulation↗
Biomedical subjects
A V Finkelstein
Publications and source records attributed to A V Finkelstein.
Residue-residue mean-force potentials for protein structure recognition.
We present two new sets of energy functions for protein structure recognition, given the primary sequence of amino acids along the polypeptide chain. The first set of potentials is based on the positions of alpha- and the second on positions of beta- and alpha-carbon atoms of amino acid residues. The potentials are derived using a theory of Boltzmann-like statistics of protein structure. The energy terms incorporate both long-range interactions between residues remote along a chain and short-range interactions between near neighbors. Distance dependence is approximated by a piecewise constant function defined on intervals of equal size. The size of the interval is optimized to preserve as much detail as possible without introducing excessive error due to limited statistics. A database of 214 non-homologous proteins was used both for the derivation of the potentials, and for the 'threading' test originally suggested by Hendlich et al. (1990) J. Mol. Biol., 216, 167-180. Special care is taken to avoid systematic error in this test. For threading, we used 100 non-homologous protein chains of 60-205 residues. The energy of each of the native structures was compared with the energy of 43,000 to 19,000 alternative structures generated by threading. Of these 100 native structures, 92 have the lowest energy with alpha-carbon-based potentials and, even more, 98 of these 100 structures, have the lowest energy with the beta- and alpha-carbon based potentials.
Databases, Factual↗
Accurate mean-force pairwise-residue potentials for discrimination of protein folds.
We present two new sets of energy functions for protein structure recognition. The first set of potentials is based on the positions of alpha- and the second on positions of beta-carbon atoms of amino acid residues. The potentials are derived using a theory of Boltzmann-like statistics of protein structure by Finkelstein et al. The energy terms incorporate both long-range interactions between residues remote along a chain and short-range interactions between near neighbors. Distance-dependence is approximated by a piecewise constant function defined on intervals of equal size. The size of this interval is optimized. A database of 222 non-homologous proteins was used both for the derivation of the potentials, and for the "threading" test originally suggested by Hendlich et al. For threading, we used 102 non-homologous protein chains of 60 to 200 residues. The energy of each of the native structures was compared with the energy of 45 to 20 thousand alternative structures generated by threading. Of these 102 native structures 94 have the lowest energy with alpha-carbon-based potentials, and even more, 100 of these 102 structures, have the lowest energy with the beta-carbon-based potentials.
Computer Simulation↗
Adjusting potential energy functions for lattice models of chain molecules.
Lattice models of proteins can approximate off-lattice structure to arbitrary precision with RMS (root mean squared) deviations roughly equal to half the lattice spacing (Rykunov et al., Proteins 22:100-109, 1995; Reva et al., J. Comp. Biol., 1996). However, even small distortions in the positions of chain links lead to significant errors in lattice-based energy calculations (Reva et al., J. Comp. Chem., 1996). These errors arise mainly from rigid interactions (such as steric repulsion) which change their energies considerably at a range which is much smaller than the usual accuracy of lattice modeling (> 1.0 A). To reduce this error, we suggest a procedure of adjusting energy functions to a given lattice. The general approach is illustrated with energy calculations based on pairwise potentials by Kolinski et al. (J. Chem. Phys. 98:1-14, 1993). At all the lattice spacings, from 0.5-3.8 A, the lattice-adjusted potentials improve the accuracy of lattice-based energy calculations and increase the correlations between off-lattice and lattice energies.
Models, Chemical↗
Building self-avoiding lattice models of proteins using a self-consistent field optimization.
We present an algorithm to build self-avoiding lattice models of chain molecules with low RMS deviation from their actual 3D structures. To find the optimal coordinates for the lattice chain model, we minimize a function that consists of three terms: (1) the sum of squared deviations of link coordinates on a lattice from their off-lattice values, (2) the sum of "short-range" terms, penalizing violation of chain connectivity, and (3) the sum of "long-range" repulsive terms, penalizing chain self-intersections. We treat this function as a chain molecule "energy" and minimize it using self-consistent field (SCF) theory to represent the pairwise link repulsions as 3D fields acting on the links. The statistical mechanics of chain molecules enables computation of the chain distribution in this field on the lattice. The field is refined by iteration to become self-consistent with the chain distribution, then dynamic programming is used to find the optimal lattice model as the "lowest-energy" chain pathway in this SCF. We have tested the method on one of the coarsest (and most difficult) lattices used for model building on proteins of all structural types and show that the method is adequate for building self-avoiding models of proteins with low RMS deviations from the actual structures.
Algorithms↗
Search for the most stable folds of protein chains: I. Application of a self-consistent molecular field theory to a problem of protein three-dimensional structure prediction.
We present a general approach to the prediction of 3-D folds of protein chains from their amino acid sequences. The approach is based on the use of the self-consistent molecular field theory for long-range interactions, the use of 1-D statistical mechanics for short-range interactions and on the discovery that there is and should only be a relatively small discrete set of folding patterns. This makes it possible to examine the full variety of 'potentially stable' folds and to determine the thermodynamically stable structure. In this paper, we give the general theoretical background of the approach. The encouraging results of the application of this approach to beta-domains are described in another paper.
Models, Molecular↗
Search for the most stable folds of protein chains: II. Computation of stable architectures of beta-proteins using a self-consistent molecular field theory.
In a preceding paper we presented a novel approach to computation of 3-D folds of protein chains from their amino acid sequences. This approach is a physically correct generalization of the 'threading' methods. It is based on a self-consistent molecular field theory and on a physical theory of protein folding patterns, which make it possible to examine all the variety of 'potentially stable' folding patterns and all the variety of the chain conformations within each of them and to determine the thermodynamically stable structure. In this paper, we apply this approach to single out stable folding patterns and conformations for the chains of beta-sandwich proteins and show that the similarity of the calculated and observed structures is usually rather close.
Amino Acid Sequence↗
Accurate general method for lattice approximation of three-dimensional structure of a chain molecule.
An algorithm based on dynamic programming gives the lattice models having the minimal RMS deviations from the actual folds of protein (RNA, etc.) chains for a given lattice and a given orientation of the macromolecule relative to the lattice. The algorithm is applicable for 3-D lattices of any kind. The accuracy of the lattice approximation increases when the distance between neighbor chain links is not rigidly fixed. Special repulsive potentials facilitate generation of self-avoiding lattice chains. The results of model building show the efficiency and precision of this proposed general method when compared with others.
Algorithms↗
Why do protein architectures have Boltzmann-like statistics?
A theoretical study has shown that the occurrence of various structural elements in stable folds of random copolymers is exponentially dependent on the own energy of the element. A similar occurrence-on-energy dependence is observed in globular proteins from the level of amino acid conformations to the level of overall architectures. Thus, the structural features stabilized by many random sequences are typical of globular proteins while the features rarely observed in proteins are those which are stabilized by only a minor part of the random sequences.
Computer Simulation↗
Perfect temperature for protein structure prediction and folding.
We have investigated the influence of the "noise" of inevitable errors in energetic parameters on protein structure prediction. Because of this noise, only a part of all the interactions operating in a protein chain can be taken into account, and therefore a search for the energy minimum becomes inadequate for protein structure prediction. One can rather rely on statistical mechanics: a calculation carried out at a temperature T* somewhat below that of protein melting gives the best possible, though always approximate prediction. The early stages of protein folding also "take into account" only a part of all the interactions; consequently, the same temperature T* is favorable for the self-organization of native-like intermediates in protein folding.
Computer Simulation↗
Boltzmann-like statistics of protein architectures. Origins and consequences.
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Algorithms↗
Constructing lattice models of protein chains with side groups.
An algorithm to construct lattice models of polymers with side chains is presented. A search for the global minimum of the error function for a given lattice-to-chain orientation is done by dynamic programming, making the search both fast and complete. Application of the algorithm is illustrated by constructing lattice models for 12 proteins of different sizes and structural types.
Algorithms↗
Predicted beta-structure stability parameters under experimental test.
Recently, beta-structure stability parameters have been measured for all 20 natural amino acids, separately for the edge and separately for the internal beta-sheet positions. Theoretical estimations of all these stability parameters have been obtained earlier on the basis of the molecular theory. Comparison shows a good concordance between the recent experimental results and the earlier theoretical predictions.
Amino Acids↗
Folding of chains with random and edited sequences: similarities and differences.
We have investigated the process of protein folding by Monte-Carlo simulation of folding occurring in a simple 3D lattice model of a protein globule. We have found the range of 'optimal' temperatures where the native fold is achieved by the Monte-Carlo process much faster than that by exhaustive sorting of all the chain folds. The 'optimal' temperatures are essentially the same for different random and 'edited' sequences (for the latter, the native fold energy is separated by a considerable gap from the energies of other low-energy folds; for random sequences, this gap is negligible). At the 'optimal' temperatures, the 'edited' chains attain their native fold faster than the random ones. However, the essence is that the native folds of 'edited' chains are thermodynamically stable at temperatures optimal for fast folding, while the native folds of random chains are unstable at the temperatures optimal for fast folding; also, at low temperatures where the native folds of random chains are stable, folding kinetics is very slow. Consequently, stable native folds are formed slowly by random sequences and rapidly by the 'edited' ones.
Computer Simulation↗
A new approach to artificial and modified proteins: theory-based design, synthesis in a cell-free system and fast testing of structural properties by radiolabels.
A novel approach to the creation of artificial and modified proteins has been elaborated. The approach includes a sequence design based on the molecular theory of protein secondary structure and folding patterns, gene expression in a cell-free system and testing of structural properties of the synthesized polypeptides at a nanogram level using radiolabelled chains. The approach has been applied to a new synthetic protein albebetin which has been designed to form a 3-D fold which does not contradict any structural rule but has been never observed up to now in natural proteins. Using size-exclusion chromatography, urea-gradient electrophoresis and limited proteolysis of a radiolabelled chain, it has been shown that the artificial protein is nearly as compact as natural proteins, cooperatively unfolds at high urea concentrations and has some structural features of a definite structure consistent with the designed one. As albebetin has been designed as consisting of two structural repeats, a 'half-albebetin' (one of these repeats) has also been synthesized and studied. It was shown that 'half-albebetin' is also compact.
Amino Acid Sequence↗
Secondary structure of globular proteins at the early and the final stages in protein folding.
The ellipticities for an early transient intermediate in refolding observed by kinetic circular dichroism measurements at 220-225 nm for 14 different proteins are summarized, and the ellipticity values are compared with those for the final native proteins and also with the ellipticities expected from a physical theory of protein and polypeptide secondary structure. The results show that a substantial part of the protein secondary structure is in general formed in the earliest detectable intermediate in refolding and that the ellipticities in both the native and the intermediate states are consistent with the physical theory of protein secondary structure.
Animals↗
Why are the same protein folds used to perform different functions?
A small number of folding patterns describe in outline most of the known protein globules, the same folds being found in non-homologous proteins with different functions. We show that the 'popular' folding patterns are those which, due to some thermodynamic advantages of their structure, can be stabilized by a lot of random sequences. In contrast, the folds which are rarely or never observed in natural globular proteins can be stabilized only by a tiny number of random sequences. The advantageous folds are few, they tolerate various primary structures, and therefore they can and ought to perform different functions. A connection between the inherent 'weak points' of protein folding patterns and positions of active sites are discussed.
Binding Sites↗
Computation of biopolymers: a general approach to different problems.
A comparative analysis of some effective algorithms widely used in analysis, computation and comparison of chain molecules is presented. A notion of a stream in an oriented hypergraph is introduced, which generalizes a notion of a path in a graph. All considered algorithms looking over exponential sets of structures in polynomial time can be described as variants of a general algorithm of analysis of paths in graphs and of streams in oriented hypergraphs.
Algorithms↗