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Z Luthey-Schulten

Publications and source records attributed to Z Luthey-Schulten.

13 recordsLinked to original sources
PubMed2002

Folding funnels: the key to robust protein structure prediction.

Natural proteins fold because their free energy landscapes are funneled to their native states. The degree to which a model energy function for protein structure prediction can avoid the multiple minima problem and reliably yield at least low-resolution predictions is also dependent on the topography of the energy landscape. We show that the degree of funneling can be quantitatively expressed in terms of a few averaged properties of the landscape. This allows us to optimize simplified energy functions for protein structure prediction even in the absence of homology information. Here we outline the optimization procedure in the context of associative memory energy functions originally introduced for tertiary structure recognition and demonstrate that even partially funneled landscapes lead to qualitatively correct, low-resolution predictions.

Computational Biology↗
PubMed2000

Associative memory hamiltonians for structure prediction without homology: alpha-helical proteins.

Energy landscape theory is used to obtain optimized energy functions for predicting protein structure, without using homology information. At short sequence separation the energy functions are associative memory Hamiltonians constructed from a database of folding patterns in nonhomologous proteins and at large separations they have the form of simple pair potentials. The lowest energy minima provide reasonably accurate tertiary structures even though no homologous proteins are included in the construction of the Hamiltonian. We also quantify the funnel-like nature of these energy functions by using free energy profiles obtained by the multiple histogram method.

Computer Simulation↗
PubMed1999

Backbone dynamics, fast folding, and secondary structure formation in helical proteins and peptides.

We discuss the construction of a simple, off-lattice model protein with a comparatively detailed representation of the protein backbone, and use it to address some general aspects of the folding kinetics of a small helical protein and two peptide fragments. The model makes use of an associative memory hamiltonian to smoothly interpolate between the limits of a native contact only, or Go, potential and a statistical pair potential derived from a database of known structures. We have observed qualitatively different behavior in these two limits. In the Go limit, we see apparently barrier-less folding. As we increase the roughness of the model energy landscape, we can observe the emergence of the characteristic activated temperature dependence previously seen in lattice studies and analytical theories. We are also able to study the dependence of the folding kinetics on local interactions such as hydrogen bonds, and we discuss the implications of these results for the formation of secondary structure at intermediate stages of the folding reaction.

Bacterial Proteins↗
PubMed1998

Self-consistently optimized energy functions for protein structure prediction by molecular dynamics.

The protein energy landscape theory is used to obtain optimal energy functions for protein structure prediction via simulated annealing. The analysis here takes advantage of a more complete statistical characterization of the protein energy landscape and thereby improves on previous approximations. This schema partially takes into account correlations in the energy landscape. It also incorporates the relationships between folding dynamics and characteristic energy scales that control the collapse of the proteins and modulate rigidity of short-range interactions. Simulated annealing for the optimal energy functions, which are associative memory hamiltonians using a database of folding patterns, generally leads to quantitatively correct structures. In some cases the algorithm achieves "creativity," i.e., structures result that are better than any homolog in the database.

Artificial Intelligence↗
PubMed1997

The foldon universe: a survey of structural similarity and self-recognition of independently folding units.

We have identified independently folding units, so called "foldons", from non-homologous proteins representing different folds. We applied simple statistical arguments in order to estimate the size of the foldon universe required to construct all foldable proteins. Various alignment procedures yield about 2600 foldons in the natural protein universe but this estimate is shown to be rather sensitive to the chosen cut-off value for structural similarity. We showed that foldon matching-modelling can reproduce the major part of the main chain of several proteins with a structural similarity measure Q-score of about 0.4 and an r.m.s. error of about 5 A, although the accuracy of structure prediction has been limited so far by the small size of foldon data set. The prediction score may be increased if one uses the set of protein fragments with optimized sequence-structure relationships, in other works, minimally frustrated segments. To quantify the degree of frustration of the structures of foldons from our database, we searched for those foldons which recognize their own sequence and structure upon threading. As a result we found that about half of the foldons from our data set recognize themselves as the best choice upon threading and therefore are individually minimally frustrated. We showed that there is a close connection between the Q-score of self recognition and the relative foldability (Theta) of the folding units. Foldons having high Q-score and Theta values are expected to be formed in the early phase of the folding process and be observed as stable intermediates under appropriate experimental conditions.

Amino Acid Sequence↗
PubMed1997

Structural basis for thermostability and identification of potential active site residues for adenylate kinases from the archaeal genus Methanococcus.

Sequence comparisons of highly related archaeal adenylate kinases (AKs) from the mesophilic Methanococcus voltae, the moderate thermophile Methanococcus thermolithotrophicus, and two extreme thermophiles Methanococcus igneus and Methanococcus jannaschii, allow identification of interactions responsible for the large variation in temperatures for optimal catalytic activity and thermostabilities observed for these proteins. The tertiary structures of the methanococcal AKs have been predicted by using homology modeling to further investigate the potential role of specific interactions on thermal stability and activity. The alignments for the methanococcal AKs have been generated by using an energy-based sequence-structure threading procedure against high-resolution crystal structures of eukaryotic, eubacterial, and mitochondrial adenylate and uridylate (UK) kinases. From these alignments, full atomic model structures have been produced using the program MODELLER. The final structures allow identification of potential active site interactions and place a polyproline region near the active site, both of which are unique to the archaeal AKs. Based on these model structures, the additional polar residues present in the thermophiles could contribute four additional salt bridges and a higher negative surface charge. Since only one of these possible salt bridges is interior, they do not appear significantly to the thermal stability. Instead, our model structures indicate that a larger and more hydrophobic core, due to a specific increase in aliphatic amino acid content and aliphatic side chain volume, in the thermophilic AKs is responsible for increased thermal stability.

Adenylate Kinase↗
PubMed1997

Theory of protein folding: the energy landscape perspective.

The energy landscape theory of protein folding is a statistical description of a protein's potential surface. It assumes that folding occurs through organizing an ensemble of structures rather than through only a few uniquely defined structural intermediates. It suggests that the most realistic model of a protein is a minimally frustrated heteropolymer with a rugged funnel-like landscape biased toward the native structure. This statistical description has been developed using tools from the statistical mechanics of disordered systems, polymers, and phase transitions of finite systems. We review here its analytical background and contrast the phenomena in homopolymers, random heteropolymers, and protein-like heteropolymers that are kinetically and thermodynamically capable of folding. The connection between these statistical concepts and the results of minimalist models used in computer simulations is discussed. The review concludes with a brief discussion of how the theory helps in the interpretation of results from fast folding experiments and in the practical task of protein structure prediction.

Amino Acid Sequence↗
PubMed1996

Foldons, protein structural modules, and exons.

Foldons, which are kinetically competent, quasi-independently folding units of a protein, may be defined using energy landscape analysis. Foldons can be identified by maxima in a scan of the ratio of a contiguous segment's energetic stability gap to the energy variance of that segment's molten globule states, reflecting the requirement of minimal frustration. The predicted foldons are compared with the exons and structural modules for 16 of the 30 proteins studied. Statistical analysis indicates a strong correlation between the energetically determined foldons and Go's geometrically defined structural modules, but there are marked sequence-dependent effects. There is only a weak correlation of foldons to exons. For gammaII-crystallin, myoglobin, barnase, alpha-lactalbumin, and cytochrome c the foldons and some noncontiguous clusters of foldons compare well with intermediates observed in experiment.

Algorithms↗
PubMed1996

Self-consistently optimized statistical mechanical energy functions for sequence structure alignment.

A quantitative form of the principle of minimal frustration is used to obtain from a database analysis statistical mechanical energy functions and gap parameters for aligning sequences to three-dimensional structures. The analysis that partially takes into account correlations in the energy landscape improves upon the previous approximations of Goldstein et al. (1994, 1995) (Goldstein R, Luthey-Schulten Z, Wolynes P, 1994, Proceedings of the 27th Hawaii International Conference on System Sciences. Los Alamitos, California: IEEE Computer Society Press. pp 306-315; Goldstein R, Luthey-Schulten Z, Wolynes P, 1995, In: Elber R, ed. New developments in theoretical studies of proteins. Singapore: World Scientific). The energy function allows for ordering of alignments based on the compatibility of a sequence to be in a given structure (i.e., lowest energy) and therefore removes the necessity of using percent identity or similarity as scoring parameters. The alignments produced by the energy function on distant homologues with low percent identity (less than 21%) are generally better than those generated with evolutionary information. The lowest energy alignment generated with the energy function for sequences containing prosite signatures but unknown structures is a structure containing the same prosite signature, providing a check on the robustness of the algorithm. Finally, the energy function can make use of known experimental evidence as constraints within the alignment algorithm to aid in finding the correct structural alignment.

Data Interpretation, Statistical↗
PubMed1996

Protein folding funnels: the nature of the transition state ensemble.

BACKGROUND: Energy landscape theory predicts that the folding funnel for a small fast-folding alpha-helical protein will have a transition state half-way to the native state. Estimates of the position of the transition state along an appropriate reaction coordinate can be obtained from linear free energy relationships observed for folding and unfolding rate constants as a function of denaturant concentration. The experimental results of Huang and Oas for lambda repressor, Fersht and collaborators for C12, and Gray and collaborators for cytochrome c indicate a free energy barrier midway between the folded and unfolded regions. This barrier arises from an entropic bottleneck for the folding process. RESULTS: In keeping with the experimental results, lattice simulations based on the folding funnel description show that the transition state is not just a single conformation, but rather an ensemble of a relatively large number of configurations that can be described by specific values of one or a few order parameters (e.g. the fraction of native contacts). Analysis of this transition state or bottleneck region from our lattice simulations and from atomistic models for small alpha-helical proteins by Boczko and Brooks indicates a broad distribution for native contact participation in the transition state ensemble centered around 50%. Importantly, however, the lattice-simulated transition state ensemble does include some particularly hot contacts, as seen in the experiments, which have been termed by others a folding nucleus. CONCLUSIONS: Linear free energy relations provide a crude spectroscopy of the transition state, allowing us to infer the values of a reaction coordinate based on the fraction of native contacts. This bottleneck may be thought of as a collection of delocalized nuclei where different native contacts will have different degrees of participation. The agreement between the experimental results and the theoretical predictions provides strong support for the landscape analysis.

Animals↗
PubMed1995

Toward an outline of the topography of a realistic protein-folding funnel.

Experimental information on the structure and dynamics of molten globules gives estimates for the energy landscape's characteristics for folding highly helical proteins, when supplemented by a theory of the helix-coil transition in collapsed heteropolymers. A law of corresponding states relating simulations on small lattice models to real proteins possessing many more degrees of freedom results. This correspondence reveals parallels between "minimalist" lattice results and recent experimental results for the degree of native character of the folding transition state and molten globule and also pinpoints the needs of further experiments.

Computer Simulation↗
PubMedDate not supplied

On the structure of hisH: protein structure prediction in the context of structural and functional genomics.

We predict a structure of the glutamine amidotransferase subunit (hisH) of imidazole glycerol phosphate synthase (IGPS) which catalyzes the fifth step of the histidine biosynthesis in Escherichia coli. The model is constructed using an energy-based threading program augmented by a multiple sequence to structure profile analysis. In developing our model we identified a conserved core region within hisH and a variable domain which is the likely site of interaction with the synthase subunit (hisF) of IGPS. Information available from structural and functional genomics studies was used to improve the structure prediction, to discuss parallels between histidine biosynthesis and other amino acid and nucleotide metabolic pathways, and to better understand the protein-protein interactions between the hisH and hisF domains of IGPS. This work allows us to develop a preliminary model for the structure of the entire IGPS holoenzyme.

Acetyltransferases↗