Cytochrome c(551) as a model system for protein folding

Considerable progress was made over the last few years in understanding the mechanism of folding of cytochrome c₅₅₁, a small acidic hemeprotein from Pseudomonas aeruginosa. Comparison of our results with those obtained by others on horse heart cytochrome c allows to draw some general conclusions on the structural features that are common determinants in the folding of members of the cytochrome c family.     

Cytochrome c551 as a model system for protein folding

Considerable progress was made over the last few years in understanding the mechanism of folding of cytochrome c₅₅₁, a small acidic hemeprotein from Pseudomonas aeruginosa. Comparison of our results with those obtained by others on horse heart cytochrome c allows to draw some general conclusions on the structural features that are common determinants in the folding of members of the cytochrome c family.     

Retinal proteins as model systems for membrane protein folding

Experimental folding studies of membrane proteins are more challenging than water-soluble proteins because of the higher hydrophobicity content of membrane embedded sequences and the need to provide a hydrophobic milieu for the transmembrane regions. The first challenge is their denaturation: due to the thermodynamic instability of polar groups in the membrane, secondary structures in membrane proteins are more difficult to disrupt than in soluble proteins. The second challenge is to refold from the denatured states. Successful refolding of membrane proteins has almost always been from very subtly denatured states. Therefore, it can be useful to analyze membrane protein folding using computational methods, and we will provide results obtained with simulated unfolding of membrane protein structures using the Floppy Inclusions and Rigid Substructure Topography (FIRST) method. Computational methods have the advantage that they allow a direct comparison between diverse membrane proteins. We will review here both, experimental and FIRST studies of the retinal binding proteins bacteriorhodopsin and mammalian rhodopsin, and discuss the extension of the findings to deriving hypotheses on the mechanisms of folding of membrane proteins in general. This article is part of a Special Issue entitled: Retinal Proteins—You can teach an old dog new tricks.     

Equilibrium folding and unfolding pathways for a model protein

The folding–unfolding process of reduced bovine pancreatic trypsin inhibitor was investigated with an idealized model employing approximate free energies. The protein is regarded to consist of only C^α and C^β atoms. The backbone dihedral angles are the only conformational variables and are permitted to take discrete values at every 10°. Intraresidue energies consist of two terms: an empirical part taken from the observed frequency distributions of (?,ψ) and an additional favorable energy assigned to the native conformation of each residue. Interresidue interactions are simplified by assuming that there is an attractive energy operative only between residue pairs in close contact in the native structure. A total of 230,000 molecular conformations, with no atomic overlaps, ranging from the native state to the denatured state, are randomly generated by changing the sampling bias. Each conformation is classified according to its conformational energy, F; a conformational entropy, S(F) is estimated for each value of F from the number of samples. The dependence of S(F) on energy reveals that the folding–unfolding transition for this idealized model is an “all-or-none” type; this is attributable to the specific long-range interactions. Interresidue contact probabilities, averaged over samples representing various stages of folding, serve to characterize folding intermediates. Most probable equilibrium pathways for the folding–unfolding transition are constructed by connecting conformationally similar intermediates. The specific details obtained for bovine pancreatic trypsin inhibitor are as follows: (1) Folding begins with the appearance of nativelike medium-range contacts at a β-turn and at the α-helix. (2) These grow to include the native pair of interacting β-strands. This state includes intact regular secondary conformations, as well as the interstrand sheet contacts, and corresponds to an activated state with the highest free energy on the pathway. (3) Additional native long-range contacts are completely formed either toward the amino terminus or toward the carboxyl terminus. (4) In a final step, the missing contacts appear. Although these folding pathways for this model are not consistent with experimental reports, it does indicate multiple folding pathways. The method is general and can be applied to any set of calculated conformational energies and furthermore permits investigation of gross folding features.     

Finite one-dimensional spin systems as models of biopolymers

New models are proposed for describing various properties of biopolymers, especially those of proteins and nucleic acids. Each model is constituted of a set of spins arranged on a chain, and each pair of spins produces an interaction. We examine the transitions of these spin systems between the ground state and the disordered state. It is found that the transitions of the present spin systems demonstrate various properties in response to values of the so-called interaction energy. If we define interaction energy parameters with no so-called frustration, the system exhibits two-state transitions, similar to the folding-unfolding transition of small proteins. The addition of frustrations to the model produces effects similar to those of mutations in proteins. On the other hand, if the interactions between two spins attenuate as a function of their separation along the chain, the transition of the system has characteristics similar to those of nucleic acids. Thus, the present spin systems can offer a unified view of the folding-unfolding transition of biopolymers in terms of differences in the pairwise interactions between spins. Based on our models, we propose a condition for two-state transition behavior for proteins.     

Fast tree search for a triangular lattice model of protein folding

Using a triangular lattice model to study the designability of protein folding, we overcame the parity problem of previous cubic lattice model and enumerated all the sequences and compact structures on a simple two-dimensional triangular lattice model of size 4 5 6 5 4. We used two types of amino acids, hydrophobic and polar, to make up the sequences, and achieved 223W212 different sequences excluding the reverse symmetry sequences. The total string number of distinct compact structures was 219,093, excluding reflection symmetry in the self-avoiding path of length 24 triangular lattice model. Based on this model, we applied a fast search algorithm by constructing a cluster tree. The algorithm decreased the computation by computing the objective energy of non-leaf nodes. The parallel experiments proved that the fast tree search algorithm yielded an exponential speed-up in the model of size 4 5 6 5 4. Designability analysis was performed to understand the search result.     

Diffusion–collision model for protein folding

The basic equations for the elementary step in the diffusion–collision–coalescence model of protein folding are derived for the case of two radially diffusing spherical microdomains. Refinements and biological implications of the mechanism are considered; included are detailed discussions of the parameters of the model, the possibilities of rotational diffusion and surface diffusion in one or two dimensions, the nature of the microdomains, and the application of the model to protein unfolding.     

Dynamics of unfolded polypeptide chains as model for the earliest steps in protein folding

The rate of formation of intramolecular interactions in unfolded proteins determines how fast conformational space can be explored during folding. Characterization of the dynamics of unfolded proteins is therefore essential for the understanding of the earliest steps in protein folding. We used triplet-triplet energy transfer to measure formation of intrachain contacts in different unfolded polypeptide chains. The time constants (1/k) for contact formation over short distances are almost independent of chain length, with a maximum value of about 5 ns for flexible glycine-rich chains and of 12 ns for stiffer chains. The rates of contact formation over longer distances decrease with increasing chain length, indicating different rate-limiting steps for motions over short and long chain segments. The effect of the amino acid sequence on local chain dynamics was probed by using a series of host-guest peptides. Formation of local contacts is only sixfold slower around the stiffest amino acid (proline) compared to the most flexible amino acid (glycine). Good solvents for polypeptide chains like EtOH, GdmCl and urea were found to slow intrachain diffusion and to decrease chain stiffness. These data allow us to determine the time constants for formation of the earliest intrachain contacts during protein folding.     

Water as a conformational editor in protein folding

As molecules approach one another in aqueous solution, desolvation free energy barriers to association are encountered. Experiments suggest these (de)solvation effects contribute to the free energy barriers separating the folded and unfolded states of protein molecules. To explore their influence on the energy landscapes of protein folding reactions, we have incorporated desolvation barriers into a semi-realistic, off-lattice protein model that uses a simplified physico-chemical force-field determined solely by the sequence of amino acids. Monte Carlo sampling techniques were used to study the effects on the thermodynamics and kinetics of folding of a number of systems, diverse in structure and sequence. In each case, desolvation barriers increase the stability of the native conformation and the cooperativity of the major folding/unfolding transition. The folding times of these systems are reduced significantly upon inclusion of desolvation barriers, demonstrating that the particulate nature of the solvent engenders a more defined route to the native fold.     

HPr as a model protein in structure, interaction, folding and stability studies

The small size and lack of disulphide bonds or cofactors in the Histidine-containing phosphocarrier protein (HPr) makes it an attractive system with which to study structure, interaction to its enzymatic partners, and its stability and folding. Here we give an overview on the immense work that has been performed on this protein and we will show that HPr has been widely used as a model protein to study important aspects in modern Structural Biology.     

Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus

A lattice model with side chains was used to investigate protein folding with computer simulations. In this model, we rigorously demonstrate the existence of a specific folding nucleus. This nucleus contains specific interactions not present in the native state that, when weakened, slow folding but do not change protein stability. Such a decoupling of folding kinetics from thermodynamics has been observed experimentally for real proteins. From our results, we conclude that specific non-native interactions in the transition state would give rise to straight phi-values that are negative or larger than unity. Furthermore, we demonstrate that residue Ile 34 in src SH3, which has been shown to be kinetically, but not thermodynamically, important, is universally conserved in proteins with the SH3 fold. This is a clear example of evolution optimizing the folding rate of a protein independent of its stability and function.     

Squeezed exponential kinetics to describe a nonglassy downhill folding as observed in a lattice protein model

We previously studied the so-called strange kinetics in the two-dimensional lattice HP model. To further study the strange kinetics, folding processes of a 27-mer cubic lattice protein model with Gō potential were investigated by simulating how the bundle of folding trajectories, consisting of a number of independent Monte Carlo simulations, evolves as the folding reaction proceeds, covering a wide range of temperature. Three realms of folding kinetics were observed depending on temperature. Although at temperatures where folding was two-state-like, the kinetics was conventional single exponential, we found that the time course data were well represented by a squeezed (or "shrunken") exponential function, exp [-(t/tau)beta] with beta > 1, at temperatures lower than the folding temperature, where folding was fastest and of a nonglassy downhill type. The squeezed exponential kinetics was found to pertain to the subdiffusion on the nonglassy downhill free energy surface and presents a marked contrast both to the single exponential kinetics and to the stretched exponential kinetics that was observed at lower temperatures where folding was also downhill but topological frustration came into effect. The observed temperature dependence of the folding kinetics suggests that some small single-domain proteins may follow the squeezed exponential kinetics at about the room temperature.     

Models for protein folding and nature's choice of protein as catalyst

The study of protein folding and unfolding pathways lends a fascinating dimension to protein biochemistry. Several models for protein folding have been postulated. Two powerful probes used in protein folding study are far UV-CD monitored stopped flow kinetics and pulse hydrogen exchange in conjunction with NMR. The formation of molten globule, which is an intermediate possessing secondary structure but not a well packed tertiary structure, is now emerging as a common feature on the folding pathway of many proteins. The molten globule is recognized by a class of molecules called chaperones which act as accelerators of protein folding. This article ends by elucidating why proteins are Nature's choice as catalysts.     

Exploring zipping and assembly as a protein folding principle

It has been proposed that proteins fold by a process called "Zipping and Assembly" (Z&A). Zipping refers to the growth of local substructures within the chain, and assembly refers to the coming together of already-formed pieces. Our interest here is in whether Z&A is a general method that can fold most of sequence space, to global minima, efficiently. Using the HP model, we can address this question by enumerating full conformation and sequence spaces. We find that Z&A reaches the global energy minimum native states, even though it searches only a very small fraction of conformational space, for most sequences in the full sequence space. We find that Z&A, a mechanism-based search, is more efficient in our tests than the replica exchange search method. Folding efficiency is increased for chains having: (a) small loop-closure steps, consistent with observations by Plaxco et al. 1998;277;985-994 that folding rates correlate with contact order, (b) neither too few nor too many nucleation sites per chain, and (c) assembly steps that do not occur too early in the folding process. We find that the efficiency increases with chain length, although our range of chain lengths is limited. We believe these insights may be useful for developing faster protein conformational search algorithms.     

Evidence for a molten globule state as a general intermediate in protein folding

The folding of globular proteins occurs through intermediate states whose characterisation provides information about the mechanism of folding. A major class of intermediate states is the compact 'molten globule', whose characteristics have been studied intensively in those conditions in which it is stable (at acid pH, high temperatures and intermediate concentrations of strong denaturants). In studies involving bovine carbonic anhydrase, human alpha-lact-albumin, bovine beta-lactoglobulin, yeast phosphoglycerate kinase, beta-lactamase from Staphylococcus aureus and recombinant human interleukin 1 beta, we have demonstrated that a transient intermediate which accumulates during refolding is compact and has the properties of the 'molten globule' state. We show that it is formed within 0.1-0.2 s. These proteins belong to different structural types (beta, alpha + beta and alpha/beta), with and without disulphide bridges and they include proteins with quite different times of complete folding (from seconds to decades of minutes). We propose that the formation of the transient molten globule state occurs early on the pathway of folding of all globular proteins.     

Myoglobin as a model system for designing heme protein based blood substitutes

The ligand binding properties and resistances to denaturation of >300 different site-directed mutants of sperm whale, pig, and human myoglobin have been examined over the past 15 years. This library of recombinant proteins has been used to derive chemical mechanisms for ligand binding and to examine the factors governing holo- and apoglobin stability. We have also examined the effects of mutagenesis on the dioxygenation of NO by MbO(2) to form NO(3)(-) and metMb. This reaction rapidly detoxifies NO and is a key physiological function of both myoglobins and hemoglobins. The mechanisms derived for O(2) binding and NO dioxygenation have been used to design safer, more efficient, and more stable heme protein-prototypes for use as O(2) delivery pharmaceuticals in transfusion therapy (i.e. blood substitutes). An interactive database is being developed (http://olsonnt1.bioc.rice.edu/web/myoglobinhome.asp) to allow rapid access to the ligand binding parameters, stability properties, and crystal structures of the entire set of recombinant myoglobins. The long-range goal is to use this library for developing general protein engineering principles and for designing individual heme proteins for specific pharmacological and industrial uses.     

Low-throughput model design of protein folding inhibitors

The stabilization energy of proteins in their native conformation is not distributed uniformly among all the amino acids, but is concentrated in few (short) fragments, fragments which play a key role in the folding process and in the stability of the protein. Peptides displaying the same sequence as these key fragments can compete with the formation of the most important native contacts, destabilizing the protein and thus inhibiting its biological activity. We present an essentially automatic method to individuate such peptidic inhibitors based on a low-throughput screening of the fragments which build the target protein. The efficiency and generality of the method is tested on proteins Src-SH3, G, CI2, and HIV-1-PR with the help of a simplified computational model. In each of the cases studied, we find few peptides displaying strong inhibitory properties, properties which are quite robust with respect to point mutations. The possibility of implementing the method through low-throughput experimental screening of the target protein is discussed.     

A heteropolymer model study for the mechanism of protein folding

A heteropolymer model of randomly self-interacting chains in two dimensions is studied with numerical simulations in order to elucidate the folding mechanism of protein. We find that the model occasionally shows folding propensity depending on the sequence of random numbers given to the chain. We study the thermodynamic and kinematic roles in the folding mechanism by grouping the local energy minima found in the simulations into clusters according to the similarity of their conformations. It is suggested that the local minima to which some heteropolymers show a folding tendency are always the lowest energy states of the energy spectrum within a cluster, though which cluster is selected depends on the sequence. For the eight random sequences we study, we find that the energy gap between the ground state and excited states is little correlated with folding or nonfolding. We rather find that folding propensities are correlated with the global structure of the average energy surface, implying a dominant kinetic role in the folding mechanism, although thermal factors cannot be ignored as the mechanism of choosing the ground state within a cluster of states connected by small deformations. We suggest that a hierarchical cluster structure plays an important role in selecting a unique folded state out of the huge number of local minima of heteropolymers. © 1997 John Wiley & Sons, Inc.     

Kinetics of intermolecular interaction during protein folding of reduced cytochrome c

Kinetics of intermolecular interaction between reduced cytochrome c (Cyt c) protein and solvent during the protein-refolding process is studied by monitoring the time dependence of apparent diffusion coefficient (D) using the pulsed-laser-induced transient grating technique. The refolding was triggered by photoinduced reduction of unfolded Fe(III) Cyt c in 3.5 M guanidine hydrochloride (GdnHCl) solution and the change in the diffusion coefficient was monitored in time domain. The relationship between D and the protein conformations under equilibrium condition were investigated at various GdnHCl concentrations using a photolabeling reagent. The time dependence of the observed transient grating signal was analyzed using these data and two models: a continuous change model of the intermolecular interaction and a two-state model. It was found that the TG signals in various time ranges can be consistently reproduced well by the two-state model. The dynamics of D is expressed well by a single exponential function with a rate constant of 22 +/- 7 s(-1) in a whole time range. The folding process of Cyt c is discussed based on these observations.