From independent modules to molten globules: observations on the nature of protein folding intermediates.
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Binding Sites↗
Biomedical subjects
J Skolnick
Publications and source records attributed to J Skolnick.
Insertion of peptide chains into lipid membranes: an off-lattice Monte Carlo dynamics model.
A combination of dynamic Monte Carlo simulation techniques with a hydropathy scale method for the prediction of the location of transmembrane fragments in membrane proteins is described. The new hydropathy scale proposed here is based on experimental data for the interactions of tripeptides with phospholipid membranes (Jacobs, R.E., White, S.H. Biochemistry 26:6127-6134, 1987) and the self-solvation effect in protein systems (Roseman, M.A. J. Mol. Biol. 200:513-522, 1988). The simulations give good predictions both for the state of association and the orientation of the peptide relative to the membrane surface of a number of peptides including Magain2, M2 delta, and melittin. Furthermore, for Pf1 bacteriophage coat protein, in accord with experiment, the simulations predict that the C-terminus forms a transmembrane helix and the N-terminus forms a helix which is adsorbed on the surface of the bilayer. Finally, the present series of simulations provide a number of insights into the mechanism of insertion of peptides into cell membranes.
Algorithms↗
Computer modeling and folding of four-helix bundles.
In the context of simplified models of globular proteins, the requirements for the unique folding to a four-helix bundle have been addressed through a new Monte Carlo procedure. In particular, the relative importance of secondary versus tertiary interactions in determining the nature of the folded structure is examined. Various cases spanning the extremes where tertiary interactions completely dominant to that where tertiary interactions are negligible have been explored. Not surprisingly, the folding to unique four-helix bundles is found to depend on an adequate balance of the secondary and tertiary interactions. Moreover, because the simplified model is composed of spheres representing alpha-carbons and side chains, the geometry of the latter being based on small real amino acids, the role played by the side chains, and the problems associated with packing and hard-core repulsions, are considered. Also, possible folding intermediates and their relationship with the experimentally observed molten globule state are explored. From these studies, a general set of rules is extracted which should aid in the further design of more detailed protein models adequate to more fully investigate the protein folding problem. Finally, the relationship between our conclusions and experimental work with specifically designed sequences is briefly discussed.
Amino Acid Sequence↗
De novo and inverse folding predictions of protein structure and dynamics.
In the last two years, the use of simplified models has facilitated major progress in the globular protein folding problem, viz., the prediction of the three-dimensional (3D) structure of a globular protein from its amino acid sequence. A number of groups have addressed the inverse folding problem where one examines the compatibility of a given sequence with a given (and already determined) structure. A comparison of extant inverse protein-folding algorithms is presented, and methodologies for identifying sequences likely to adopt identical folding topologies, even when they lack sequence homology, are described. Extension to produce structural templates or fingerprints from idealized structures is discussed, and for eight-membered beta-barrel proteins, it is shown that idealized fingerprints constructed from simple topology diagrams can correctly identify sequences having the appropriate topology. Furthermore, this inverse folding algorithm is generalized to predict elements of supersecondary structure including beta-hairpins, helical hairpins and alpha/beta/alpha fragments. Then, we describe a very high coordination number lattice model that can predict the 3D structure of a number of globular proteins de novo; i.e. using just the amino acid sequence. Applications to sequences designed by DeGrado and co-workers [Biophys. J., 61 (1992) A265] predict folding intermediates, native states and relative stabilities in accord with experiment. The methodology has also been applied to the four-helix bundle designed by Richardson and co-workers [Science, 249 (1990) 884] and a redesigned monomeric version of a naturally occurring four-helix dimer, rop. Based on comparison to the rop dimer, the simulations predict conformations with rms values of 3-4 A from native. Furthermore, the de novo algorithms can assess the stability of the folds predicted from the inverse algorithm, while the inverse folding algorithms can assess the quality of the de novo models. Thus, the synergism of the de novo and inverse folding algorithm approaches provides a set of complementary tools that will facilitate further progress on the protein-folding problem.
Algorithms↗
Regularities in interaction patterns of globular proteins.
The description of protein structure in the language of side chain contact maps is shown to offer many advantages over more traditional approaches. Because it focuses on side chain interactions, it aids in the discovery, study and classification of similarities between interactions defining particular protein folds and offers new insights into the rules of protein structure. For example, there is a small number of characteristic patterns of interactions between protein supersecondary structural fragments, which can be seen in various non-related proteins. Furthermore, the overlap of the side chain contact maps of two proteins provides a new measure of protein structure similarity. As shown in several examples, alignments based on contact map overlaps are a powerful alternative to other structure-based alignments.
Computer Simulation↗
Sequence-structure matching in globular proteins: application to supersecondary and tertiary structure determination.
A methodology designed to address the inverse globular protein-folding problem (the identification of which sequences are compatible with a given three-dimensional structure) is described. By using a library of protein finger-prints, defined by the side chain interaction pattern, it is possible to match each structure to its own sequence in an exhaustive data base search. It is shown that this is a permissive requirement for the validation of the methodology. To pass the more rigorous test of identifying proteins that are not close sequence homologs, but that have similar structure, the method has been extended to include insertions and deletions in the sequence, which is compared to the fingerprint. This allows for the identification of sequences having little or no sequence homology to the fingerprint. Examples include plastocyanin/azurin/pseudoazurin, the globin family, different families of proteases and cytochromes, including cytochromes c' and b-562, actinidin/papain, and lysozyme/alpha-lactalbumin. Turning to supersecondary structure prediction, we find that alpha/beta/alpha fragments possess sufficient specificity to identify their own and related sequences. By threading a beta-hairpin through a sequence, it is possible to predict the location of such hairpins and turns with remarkable fidelity. Thus, the method greatly extends existing techniques for the prediction of both global structural homology and local supersecondary structure.
Amino Acid Sequence↗
Spontaneous insertion of polypeptide chains into membranes: a Monte Carlo model.
The Monte Carlo dynamics method was used to examine the process of protein insertion into model cell membranes. The water and lipid environments were taken into account via an effective medium approximation based on coordinate-dependent hydrophobic and hydrogen bond potentials. The polypeptide chain was represented in a full-backbone atom representation as a chain of diamond lattice vectors. The simulations support the idea that to a good approximation insertion may be depicted as a spontaneous thermodynamic process. The mechanism of membrane insertion of a simple lattice protein chain exhibits many features of theoretical predictions and is in good accord with experimental data. In the model, insertion begins with adsorption of the chain onto the interface, followed by the formation of helical fragments. These fragments, having partially saturated internal hydrogen bonds, can be transported into the lipid phase and then form transbilayer structures.
Cell Membrane↗
Topology fingerprint approach to the inverse protein folding problem.
We describe the most general solution to date of the problem of matching globular protein sequences to the appropriate three-dimensional structures. The screening template, against which sequences are tested, is provided by a protein "structural fingerprint" library based on the contact map and the buried/exposed pattern of residues. Then, a lattice Monte Carlo algorithm validates or dismisses the stability of the proposed fold. Examples of known structural similarities between proteins having weakly or unrelated sequences such as the globins and phycocyanins, the eight-member alpha/beta fold of triose phosphate isomerase and even a close structural equivalence between azurin and immunoglobulins are found.
Algorithms↗
Simulations of the folding pathway of triose phosphate isomerase-type alpha/beta barrel proteins.
Simulations of the folding pathways of two large alpha/beta proteins, the alpha subunit of tryptophan synthase and triose phosphate isomerase, are reported using the knight's walk lattice model of globular proteins and Monte Carlo dynamics. Starting from randomly generated unfolded states and with no assumptions regarding the nature of the folding intermediates, for the tryptophan synthase subunit these simulations predict, in agreement with experiment, the existence and location of a stable equilibrium intermediate comprised of six beta strands on the amino terminus of the molecule. For the case of triose phosphate isomerase, the simulations predict that both amino- and carboxyl-terminal intermediates should be observed. In a significant modification of previous lattice models, this model includes a full heavy atom side chain description and is capable of representing native conformations at the level of 2.5- to 3-A rms deviation for the C alpha positions, as compared to the crystal structure. With a well-balanced compromise between accuracy of the protein description and the computer requirements necessary to perform simulations spanning biologically significant amounts of time, the lattice model described here brings the possibility of studying important biological processes to present-day computers.
Animals↗
Prediction of protein secondary structure by neural networks: encoding short and long range patterns of amino acid packing.
A complex, cascaded neural network designed to predict the secondary structure of globular proteins has been developed. Information about the local buried-unburied pattern and the average tendency of the particular types of amino acids to be buried inside the globule were used. Nonspecific information about long distance contact maps was also employed. These modifications result in a noticeable improvement (3-9%) of prediction accuracy. The best result for the average success ratio for the testing set of nonhomologous proteins was 68.3% (with corresponding Matthews' coefficients, C alpha,beta,coil equal to 0.60, 0.47, 0.43, respectively).
Amino Acid Sequence↗
Dynamic Monte Carlo simulations of a new lattice model of globular protein folding, structure and dynamics.
A long-standing problem of molecular biology is the prediction of globular protein tertiary structure from the primary sequence. In the context of a new, 24-nearest-neighbor lattice model of proteins that includes both alpha and beta-carbon atoms, the requirements for folding to a unique four-member beta-barrel, four-helix bundles and a model alpha/beta-bundle have been explored. A number of distinct situations are examined, but the common requirements for the formation of a unique native conformation are tertiary interactions plus the presence of relatively small (but not irrelevant) intrinsic turn preferences that select out the native conformer from a manifold of compact states. When side-chains are explicitly included, there are many conformations having the same or a slightly greater number of side-chain contacts as in the native conformation, and it is the local intrinsic turn preferences that produce the conformational selectivity on collapse. The local preference for helix or beta-sheet secondary structure may be at odds with the secondary structure ultimately found in the native conformation. The requisite intrinsic turn populations are about 0.3% for beta-proteins, 2% for mixed alpha/beta-proteins and 6% for helix bundles. In addition, an idealized model of an allosteric conformational transition has been examined. Folding occurs predominantly by a sequential on-site assembly mechanism with folding initiating either at a turn or from an isolated helix or beta-strand (where appropriate). For helical and beta-protein models, similar folding pathways were obtained in diamond lattice simulations, using an entirely different set of local Monte Carlo moves. This argues strongly that the results are universal; that is, they are independent of lattice, protein model or the particular realization of Monte Carlo dynamics. Overall, these simulations demonstrate that the folding of all known protein motifs can be achieved in the context of a single class of lattice models that includes realistic backbone structures and idealized side-chains.
Algorithms↗
Dynamic Monte Carlo simulations of globular protein folding. Model studies of in vivo assembly of four helix bundles and four member beta-barrels.
As part of an ongoing series of dynamic Monte Carlo simulations of globular protein folding, the nature of the folding pathway, of model four-member beta-barrels and four-helix bundles, under highly idealized conditions in vivo, has been examined. The ribosome is crudely modeled as an inert hard wall on to which the model protein chain is attached. Three cases are considered in detail. The first corresponds to post-translational assembly in which the fully synthesized chain is tethered to the wall and starts out under strongly denaturing conditions. The system is cooled down, and the chain is allowed to fold. Interestingly, the helical motif prefers to assemble parallel to the wall, whereas the beta-barrel, predominantly assembles with its principal axis perpendicular to the wall. In the former case, the dominant intermediate, the helical hairpin, is different from that in free solution, a three-helix bundle. The wall acts to reduce the expanse of configuration space that must be searched and aids in folding. Two situations that might lead to co-translational folding are also simulated. In the first case, to eliminate wall effects, the chain is slowly synthesized in free solution, and in the second case, it is slowly synthesized from the wall. In all cases, the chains are observed to fold post-translationally. While partially folded intermediates are observed during synthesis, they lack the stability to survive until chain synthesis is complete. The implications of these results for the folding in vivo of real protein chains is discussed, and a model of multiple domain protein folding is proposed.
Models, Structural↗
Dynamic Monte Carlo simulations of globular protein folding/unfolding pathways. I. Six-member, Greek key beta-barrel proteins.
In the context of a simplified diamond lattice model of a six-member, Greek key beta-barrel protein that is closely related in topology to plastocyanin, the nature of the folding and unfolding pathways have been investigated using dynamic Monte Carlo techniques. The mechanism of Greek key assembly is best described as punctuated "on site construction". Folding typically starts at or near a beta-turn, and then the beta-strands sequentially form by using existing folded structure as a scaffold onto which subsequent tertiary structure assembles. On average, beta-strands tend to zip up from one tight bend to the next. After the four-member, beta-barrel assembles, there is a long pause as the random coil portion of the chain containing the long loop thrahes about trying to find the native state. Thus, there is an entropic barrier that must be surmounted. However, while a given piece of the protein may be folding, another section may be unfolding. A competition therefore exists to assemble a fairly stable intermediate before it dissolves. Folding may initiate at any of the tight turns, but the turn closer to the N terminus seems to be preferred due to well-known excluded volume effects. When the protein first starts to fold, there are a multiplicity of folding pathways, but the number of options is reduced as the system gets closer to the native state. In the early stages, the excluded volume effect exerted by the already assembled protein helps subsequent assembly. Then, near the native conformation, the folded parts reduce the accessible conformational space available to the remaining unfolded sections. Unfolding essentially occurs in reverse. Employing a simple statistical mechanical theory, the configurational free energy along the reaction co-ordinate for this model has been constructed. The free energy surface, in agreement with the simulations, provides the following predictions. The transition state is quite near the native state, and consists of five of the six beta-strands being fully assembled, with the remaining long loop plus sixth beta-strand in place, but only partially assembled. It is separated from the beta-barrel intermediate by a free energy barrier of mainly entropic origin and from the native state by a barrier that is primarily energetic in origin. The latter feature is in agreement with the "Cardboard Box" model described by Goldenberg and Creighton but, unlike their model, the transition state is not a high-energy distorted form of the native state.(ABSTRACT TRUNCATED AT 250 WORDS)
Algorithms↗
Dynamic Monte Carlo simulations of globular protein folding/unfolding pathways. II. Alpha-helical motifs.
Dynamic Monte Carlo simulations of the folding pathways of alpha-helical protein motifs have been undertaken in the context of a diamond lattice model of globular proteins. The first question addressed in the nature of the assembly process of an alpha-helical hairpin. While the hairpin could, in principle, be formed via the diffusion-collision-adhesion of isolated performed helices, this is not the dominant mechanism of assembly found in the simulations. Rather, the helices that form native hairpins are constructed on-site, with folding initiating at or near the turn in almost all cases. Next, the folding/unfolding pathways of four-helix bundles having tight bends and one and two long loops in the native state are explored. Once again, an on-site construction mechanism of folding obtains, with a hairpin forming first, followed by the formation of a three-helix bundle, and finally the fourth helix of the native bundle assembles. Unfolding is essentially the reverse of folding. A simplified analytic theory is developed that reproduces the equilibrium folding transitions obtained from the simulations remarkably well and, for the dominant folding pathway, correctly identifies the intermediates seen in the simulations. The analytic theory provides the free energy along the reaction co-ordinate and identifies the transition state for all three motifs as being quite close to the native state, with three of the four helices assembled, and approximately one turn of the fourth helix in place. The transition state is separated from the native conformation by a free-energy barrier of mainly energetic origin and from the denatured state by a barrier of mainly entropic origin. The general features of the folding pathway seen in all variants of the model four-helix bundles are similar to those observed in the folding of beta-barrel, Greek key proteins; this suggests that many of the qualitative aspects of folding are invariant to the particular native state topology and secondary structure.
Algorithms↗
Monte Carlo studies on equilibrium globular protein folding. II. Beta-barrel globular protein models.
In the context of dynamic Monte Carlo simulations on a model protein confined to a tetrahedral lattice, the interplay of protein size and tertiary structure, and the requirements for an all-or-none transition to a unique native state, are investigated. Small model proteins having a primary sequence consisting of a central bend neutral region flanked by two tails having an alternating hydrophobic/hydrophilic pattern of residues are seen to undergo a continuous transition to a beta-hairpin collapsed state. On increasing the length of the tails, the beta-hairpin structural motif is found to be in equilibrium with a four-member beta-barrel. Further increase of the tail length results in the shift of the structural equilibrium to the four-member beta-barrel. The random coil to beta-barrel transition is of an all-or-none character, but while the central turn is always the desired native bend, the location of the turns involving the two external strands is variable. That is, beta-barrels having the external stands that are two residues out of register are also observed in the transition region. Introduction into the primary sequence of two additional regions that are at the very least neutral toward turn formation produces an all-or-none transition to the unique, native, four-member beta-barrel. Various factors that can augment the stability of the native conformation are explored. Overall, these folding simulations strongly indicate that the general rules of globular protein folding are rather robust--namely, one requires a general pattern of hydrophobic/hydrophilic residues that allow the protein to have a well-defined interior and exterior and the presence of regions in the amino acid sequence that at the very least are locally indifferent to turn formation. Since no site-specific interactions between hydrophobic and hydrophilic residues are required to produce a unique four-member beta-barrel, these simulations strongly suggest that site specificity is involved in structural fine-tuning.
Algorithms↗
Monte Carlo studies on equilibrium globular protein folding. III. The four helix bundle.
The nature of the equilibrium conformational transition from the denatured state to a four-member alpha-helical bundle was studied employing a dynamic Monte Carlo algorithm in which the model protein chain was confined to a tetrahedral lattice. The model chain was allowed to hunt over all phase space, the target native state was not assumed a priori, and no site-specific interactions were introduced. The exterior vs the interior part of the protein is distinguished by the pattern of hydrophilic and hydrophobic interactions encoded into the primary sequence. The importance of a statistical preference for forming bends, as a function of bend location in the primary sequence, and helical wheel type cooperative interactions were examined, and the necessary conditions for collapse of the chain to the unique native structure were investigated. It was found that an amphipathic pattern of hydrophobic/hydrophilic interactions along with a statistical preference of the central residues for bend formation are sufficient to obtain the four-helix bundle. The transition to the native state has an all-or-none character.
Algorithms↗
Dynamic Monte Carlo study of the folding of a six-stranded Greek key globular protein.
To help elucidate the general rules of equilibrium globular protein folding, dynamic Monte Carlo simulations of a model beta-barrel globular protein having the six-stranded Greek key motif characteristic of real globular proteins were undertaken. The model protein possesses a typical beta-barrel amino acid sequence; however, all residues of a given type (e.g. hydrophobic residues) are identical. Even in the absence of site-specific interactions, starting from a high-temperature denatured state, these models undergo an all-or-none transition to a structurally unique six-stranded beta-barrel. These simulations suggest that the general rules of globular protein folding are rather robust in that the overall tertiary structure is determined by the general pattern of hydrophobic, hydrophilic, and turn-type residues, with site-specific interactions mainly involved in structural fine tuning of a given topology. Finally, these studies suggest that loops may play an important role in producing a unique native state. Depending on the stability of the native conformation of the long loop in the Greek key, the conformational transition can be described by a two-state, three-state, or even larger number of multiple equilibrium states model.
Models, Molecular↗
Monte Carlo simulation of equilibrium globular protein folding: alpha-helical bundles with long loops.
To help elucidate the general rules of globular protein folding, computer simulations of the conformational transition in model proteins having the left-handed, four-helix bundle motif in which the helices are joined by one or two long loops, as in apoferritin and somatotropin, respectively, have been undertaken. In the context of simple tetrahedral lattice protein models, these unique native helix bundle motifs can be obtained by a set of interactions similar to those found in previous simulations of the folding of four-member alpha-helical bundles with tight bends and beta-barrel proteins including the Greek key motif. The essential features sufficient to produce the four-helix bundle motif with long loops are as follows: (i) a general pattern of hydrophobic and hydrophilic type residues which differentiate the interior from the exterior of the molecule; (ii) the existence of hydrophilic regions in the amino acid sequence that, on the basis of short-range interactions, are indifferent to loop formation but that interact favorably with all the exterior residues of the helix bundle. Thus, these simulations indicate that, to reproduce all varieties of the left-handed four-helix bundle motif, site-specific interactions are not required.
Algorithms↗