Kinetics of unfolding and refolding of proteins. 3. Results for lysozyme

The kinetics of the reversible denaturation of lysozyme by guanidine hydrochloride have been studied over a wide range of pH and denaturant concentration. The results contrast sharply with those observed for cytochrome c. The interconversion of native (N) and denatured (D) states is strictly first-order in both directions under most conditions, showing that no intermediate forms of any kind accumulate to a significant extent during the reaction. At one pH (pH 2.6) experiments were extended to extreme denaturant concentrations, and under these conditions kinetic intermediates were observed. Analysis by the procedures of the first paper of this series Ikai &; Tanford 1973 showed that the principal intermediate observed at low denaturant concentration must be different from that observed at high denaturant concentration, and that both must be on the direct pathway from N to D. This suggests that the over-all reaction mechanism is of the form

and this mechanism is able to account for all of the observed results. The intermediate X₁ which accumulates transiently in the renaturation reaction at low concentrations of guanidine hydrochloride is spectrally very similar to the native state, i.e. it is probably a highly ordered state, but most of the interactions between surface acidic and basic groups, which are responsible for the anomalous titration behavior of native lysozyme, do not yet exist in this state. It is probable that the difference between the kinetics of refolding of lysozyme and cytochrome c may be ascribed to the existence of disulfide cross-links in lysozyme, which were intact in these experiments. These cross-links greatly limit the possible pathways for folding and thus make it much less likely that incorrectly folded states on dead-end pathways are readily accessible.     

The consistency principle in protein structure and pathways of folding

• 1.i) It is pointed out that various energy terms contributing to stabilize the native state of globular proteins are consistent in the first approximation with each other in the native state. This means that each energy term is individually minimized at the minimum point of the total energy. I proposed (1) to call this fact “the consistency principle in protein structure.”
• 2.ii) The fair success of various methods of prediction of the secondary structures in globular proteins from their amino acid sequence is often interpreted as indicating the dominance of the short-range interactions in determining the local structures of the polypeptide chains. Partly from such a point of view, the hierarchic condensation model has been popular for the process of protein folding. However the consistency principle indicates that the short-range interactions are just one type of intramolecular interaction which contributes to stabilization of the native structure together with other mutually consistent types of intramolecular interactions. Therefore the hierarchic condensation model is not necessarily a unique model of protein folding.
• 3.iii) Roles of a possible nonspecific globular state, stabilized by nonspecific long-range intramolecular interactions, in the folding process are discussed. It is expected that this nonspecific globular state is observed either as an equilibrium or a kinetic intermediate state between the unfolded and the folded native states. Observation as a kinetic intermediate state is expected to occur in experiments done under strongly refolding conditions. In this case the polypeptide chain in the unfolded state collapses into a nonspecific globule by the action of nonspecific long-range intramolecular interactions. Two possible mechanisms of the transition from the nonspecific globular state to the specific native folded state are discussed.
• 4.iv) In an experiment done under weakly refolding conditions, folding is expected to occur according to the embryo-nucleus model. This model is a refined version of the hierarchic condensation model. Refinement is done by taking into account the fact that the intermediate structures assumed in the hierarchic condensation model are unstable against both the native folded state and the unfolded state. A nucleus is an ordered structure of a certain size. Ordered structures of a size larger than a nucleus tend to fold further to become the native specific globule. Ordered structures of a size smaller than a nucleus tend to unfold. Embryos are intrinsically unstable ordered structures smaller than a nucleus. Folding occurs when embryos grow in size to become a nucleus. The intrinsic instability of embryos is the built-in mechanism to overcome the low resolving power of the short-range interactions in determining local conformations of the polypeptide chain.

     

Time-resolved small-angle X-ray scattering study of the folding dynamics of barnase

Structural changes of barnase during folding were investigated using time-resolved small-angle X-ray scattering (SAXS). The folding of barnase involves a burst-phase intermediate, sometimes designated as the denatured state under physiological conditions, D_phys, and a second hidden intermediate. Equilibrium SAXS measurements showed that the radius of gyration (R_g) of the guanidine unfolded state (U) is 26.9 ± 0.7 Å, which remains largely constant over a wide denaturant concentration range. Time-resolved SAXS measurements showed that the R_g value extrapolated from kinetic R_g data to time zero, R_g,0, is 24.3 ± 0.1 Å, which is smaller than that of U but which is expanded from that of folding intermediates of other proteins with similar chain lengths (19 Å). After the burst-phase change, a single-exponential reduction in R_g² was observed, which corresponds to the formation of the native state for the major component containing the native trans proline isomer. We estimated R_g of the minor component of D_phys containing the non-native cis proline isomer (D_phys,cis) to be 25.7 ± 0.6 Å. Moreover, R_g of the major component of D_phys containing the native proline isomer (D_phys,tra) was estimated as 23.9 ± 0.2 Å based on R_g,0. Consequently, both components of the burst-phase intermediate of barnase (D_phys,tra and D_phys,cis) are still largely expanded. It was inferred that D_phys possesses the N-terminal helix and the center of the β-sheet formed independently and that the formation of the remainder of the protein occurs in the slower phase.     

Kinetic folding of Haloferax volcanii and Escherichia coli dihydrofolate reductases: haloadaptation by unfolded state destabilization at high ionic strength

Salts affect protein stability by multiple mechanisms (e.g., the Hofmeister effect, preferential hydration, electrostatic effects and weak ion binding). These mechanisms can affect the stability of both the native state and the unfolded state. Previous equilibrium stability studies demonstrated that KCl stabilizes dihydrofolate reductases (DHFRs) from Escherichia coli (ecDHFR, E. coli DHFR) and Haloferax volcanii (hvDHFR1, H. volcanii DHFR encoded by the hdrA gene) with similar efficacies, despite adaptation to disparate physiological ionic strengths (0.2 M versus 2 M). Kinetic studies can provide insights on whether equilibrium effects reflect native state stabilization or unfolded state destabilization. Similar kinetic mechanisms describe the folding of urea-denatured ecDHFR and hvDHFR1: a 5-ms stopped-flow burst-phase species that folds to the native state through two sequential intermediates with relaxation times of 0.1-3 s and 25-100 s. The latter kinetic step is very similar to that observed for the refolding of hvDHFR1 from low ionic strength. The unfolding of hvDHFR1 at low ionic strength is relatively slow, suggesting kinetic stabilization as observed for some thermophilic enzymes. Increased KCl concentrations slow the urea-induced unfolding of ecDHFR and hvDHFR1, but much less than expected from equilibrium studies. Unfolding rates extrapolated to 0 M denaturant, k_unf(H₂O), are relatively independent of ionic strength, demonstrating that the KCl-induced stabilization of ecDHFR and hvDHFR1 results predominantly from destabilization of the unfolded state. This supports the hypothesis from previous equilibrium studies that haloadaptation harnesses the effects of elevated salt concentrations on the properties of the aqueous solvent to enhance protein stability.     

Rabbit liver fructose-1,6-bisphosphatase: location of an active site lysyl residue in the COOH-terminal fragment generated by a lysosomal proteinase

Digestion of native rabbit liver fructose-1,6-bisphosphatase (Fru-P₂ase, EC 3.1.3.11) with a membrane-bound proteinase from rat liver lysosomes yields a fragment of M_r = 9850. This peptide contains the COOH terminus of the Fru-P₂ase polypeptide chain and also the cyanogen bromide peptide (BrCN5) carrying the active site lysyl residue. The sequence of BrCN5 and its location with respect to the COOH terminus of the polypeptide chain have been determined. The active site lysyl residue is located at approximately residue ?54 from the COOH terminus. The bond hydrolyzed by the lysosomal proteinase is located between residues ?88 and ?89 from the COOH terminus.     

Main-chain Dynamics of a Partially Folded Protein:15N NMR Relaxation Measurements of Hen Egg White Lysozyme Denatured in Trifluoroethanol

¹⁵N NMR relaxation measurements have been used to study the dynamic behaviour of the main-chain of hen lysozyme in a partially folded state, formed in a 70% (v/v) trifluoroethanol (TFE)/30% water mixture at 37°C and pH 2. This state is characterised by helical secondary structure in the absence of extensive tertiary interactions. The NMR relaxation data were interpreted by mapping of spectral density functions and by derivation of segmental as well as global order parameters. The results imply that the dynamics of lysozyme in TFE can, at least for the great majority of residues, be adequately described by internal motions which are superimposed on an overall isotropic tumbling of the molecule. Although the dynamic behaviour shows substantial variations along the polypeptide chain, it correlates well with the conformational preferences identified in the TFE state by other NMR parameters. Segments of the polypeptide chain which are part of persistent helical structures are highly restricted in their motion (S²> 0.8, with effective internal correlation times τ_e< 200 ps) but are also found to experience conformational exchange on a millisecond timescale. Regions which are stabilised in less persistent helical structure possess greater flexibility (0.6 <S²< 0.8, 200 ps < τ_e< 1 ns) and those which lack defined conformational preferences are highly flexible (S²< 0.6, τ_e∼1 ns). The dynamic behaviour of the main-chain was found to be correlated with other local features of the polypeptide chain, including hydrophobicity and the position of the disulphide bridges. Despite the absence of extensive tertiary interactions, preferential stabilisation of native-like secondary structure by TFE results in a pattern of main-chain dynamics which is similar to that of the native state.     

Ligand exchange during unfolding of cytochrome c.

The productive folding pathway of cytochrome c passes through an obligatory HW intermediate in which the heme is coordinated by a solvent water molecule and a native ligand, His-18, prior to the formation of the folded HM state with both the native His-18 and Met-80 heme coordination. Two off pathway intermediates, a five-coordinated state (5C) and a bis-histidine state (HH), were also identified during the folding reaction. In the present work, the thermodynamics and the kinetics of the unfolding reaction of cytochrome c were investigated with resonance Raman scattering, tryptophan fluorescence spectroscopy, and circular dichroism. The objective of these experiments was to determine if the protein opens up and diverges into the differing heme ligation states through a many pathway mechanism or if it passes through intermediate states analogous to those observed during the folding reaction. Equilibrium unfolding results indicate that, in contrast to 5C, the stability of HH with respect to HW decreases as the concentration of GdnHCl increases. The difference in their response to the denaturant indicates that the polypeptide structure of 5C is relatively loose as compared with HH in which the polypeptide is misfolded. Time-resolved resonance Raman measurements show that strikingly similar ligand exchange reactions occur during unfolding as were observed during folding. Combined with fluorescence data, a kinetic model is proposed in which local structural rearrangements controlled by heme ligand exchange reactions appear prior to the global relaxation of the polypeptide chain.     

Kinetics of renaturation and self-assembly of intermediates on the pathway of folding of the β2-subunit of Escherichia coli tryptophan-synthetase

The kinetics of renaturation of the β₂-subunit of Escherichia coli tryptophan-synthetase (l-serine hydrolyase (adding indole) E.C. 4.2.1.20) and those of its two proteolytic fragments F₁ and F₂ are studied and compared. Steps corresponding to the refolding of F₁, to the association of the folded F₁ and F₂ fragments, and to an isomerization of the associated protein are identified. These steps are ordered on the pathway of renaturation and some of their kinetic parameters are determined. This leads to a tentative kinetic model for the renaturation of nicked-β₂ starting from the denatured F₁ and F₂ fragments.The step corresponding to the refolding of the F₁ domain, as well as that corresponding to the last rate-limiting isomerization leading to the native protein, is shown to be the same in the refolding of the entire, uncleaved β₂-protein. It is concluded that the refolded F₁ fragment corresponds to a folding intermediate on the pathway of renaturation of the β₂-subunit.     

Folding Pathways of the Tetrahymena Ribozyme

Like many structured RNAs, the Tetrahymena group I intron ribozyme folds through multiple pathways and intermediates. Under standard conditions in vitro, a small fraction reaches the native state (N) with k_obs ≈ 0.6 min^− 1, while the remainder forms a long-lived misfolded conformation (M) thought to differ in topology. These alternative outcomes reflect a pathway that branches late in folding, after disruption of a trapped intermediate (I_trap). Here we use catalytic activity to probe the folding transitions from I_trap to the native and misfolded states. We show that mutations predicted to weaken the core helix P3 do not increase the rate of folding from I_trap but they increase the fraction that reaches the native state rather than forming the misfolded state. Thus, P3 is disrupted during folding to the native state but not to the misfolded state, and P3 disruption occurs after the rate-limiting step. Interestingly, P3-strengthening mutants also increase native folding. Additional experiments show that these mutants are rapidly committed to folding to the native state, although they reach the native state with approximately the same rate constant as the wild-type ribozyme (~ 1 min^− 1). Thus, the P3-strengthening mutants populate a distinct pathway that includes at least one intermediate but avoids the M state, most likely because P3 and the correct topology are formed early. Our results highlight multiple pathways in RNA folding and illustrate how kinetic competitions between rapid events can have long-lasting effects because the “choice” is enforced by energy barriers that grow larger as folding progresses.     

Chloroplast translocations in Lemna trisulca L. induced by continuous irradiation and by light pulses

The analytical model describing the steady state position of chloroplasts in dependence of fluence rate as well as the chloroplast response to single strong light pulses has been proposed. The model is based on the following assumptions: 1. Irradiation of the cell generates the state X in the cell membrane region, proportional to the local fluence rate. After switching on the light, the value of X increases exponentially with the time constant of about 3 min. The dark decay of X is also exponential with the same time constant. The level of X controls all kinds of chloroplast arrangements. 2. The state X generates two further states: Y ₁ and Y ₂, the first of them representing attraction forces for chloroplasts and the second representing repulsion forces. Empirical equations have been found for both Y states. The fluence rate response curve can be described with the use of functions Y ₁ and Y ₂. 3. The kinetic analysis requires the introduction of two additional functions Z in order to account for delays and time dispersion of the chloroplast movement in response to driving and resistance factors. The computer program for the proposed model was developed and the results of calculations were compared with experimental data (fluence rate response curve and pulse effects) with satisfactory agreement. Initially no attempt was made to ascribe any physical meaning to the postulated states. Some suggestions in this respect are mentioned in the discussion.     

Mechanisms of the multiphasic kinetics in the folding and unfolding of globular proteins

The multiphasic kinetics of the protein folding and unfolding processes are examined for a “cluster model” with only two thermodynamically stable macroscopic states, native (N) and denatured (D), which are essentially distributions of microscopic states. The simplest kinetic schemes consistent with the model are: N-(fast) → I-(slow) → D for unfolding and N ← (fast)-D₂ ← (slow)-D₁ for refolding. The fast phase during the unfolding process can be visualized as the redistribution of the native population N to I within its free energy valley. Then, this population crosses over the free energy barrier to the denatured state D in the slow phase. Therefore, the macrostate I is a kinetic intermediate which is not stable at equilibrium. For the refolding process, the initial equilibrium distribution of the denatured state D appears to be separated into D₁ and D₂ in the final condition because of the change in position of the free energy barrier. The fast refolding species D₂ is due to the “leak” from the broadly distributed D state, while the rest is the slow refolding species D₁, which must overpass the free energy barrier to reach N. At an early stage of the folding process the amino acid chain is considered to be composed of several locally ordered regions, which we call clusters, connected by random coil chain parts. Thus, the denatured state contains different sizes and distributions of clusters depending on the external condition. A later stage of the folding process is the association of smaller clusters. The native state is expressed by a maximum-size cluster with possible fluctuation sites reflecting this association. A general discussion is given of the correlation between the kinetics and thermodynamics of proteins from the overall shape of the free energy function. The cluster model provides a conceptual link between the folding kinetics and the structural patterns of globular proteins derived from the X-ray crystallographic data.     

Interaction of SecB with intermediates along the folding pathway of maltose-binding protein.

SecB, a molecular chaperone involved in protein export in Escherichia coli, displays the remarkable ability to selectively bind many different polypeptide ligands whose only common feature is that of being nonnative. The selectivity is explained in part by a kinetic partitioning between the folding of a polypeptide and its association with SecB. SecB has no affinity for native, stably folded polypeptides but interacts tightly with polypeptides that are nonnative. In order to better understand the nature of the binding, we have examined the interaction of SecB with intermediates along the folding pathway of maltose-binding protein. Taking advantage of forms of maltose-binding protein that are altered in their folding properties, we show that the first intermediate in folding, represented by the collapsed state, binds to SecB, and that the polypeptide remains active as a ligand until it crosses the final energy barrier to attain the native state.     

Synthesis and properties of horseradish peroxidase copolymers

Conditions for copolymerization of native and sodium periodate-oxidized horseradish peroxidase (HTP; EC 1.11.1.7) have been optimized. Copolymerization products have been characterized electrophoretically, spectrally, and kinetically. Copolymers containing 2–3, 4, 5–7, and 9–10 molecules of the enzyme were found among the products of polymerization. The copolymers had lower values of D ₄₀₃/D ₂₈₀ than HRP. The copolymers had more ordered structures than the original HRP. Comparison of the thermal stability and kinetic characteristics of the fractions differing in the ratio of copolymers to the monomeric enzyme demonstrated that the polymeric products were more stable than HRP (in terms of resistance to high temperature or inhibitory effects of H₂O₂), but their kinetic activity was, on the whole, lower than that of the original enzyme.     

Microsecond Barrier-Limited Chain Collapse Observed by Time-Resolved FRET and SAXS

It is generally held that random-coil polypeptide chains undergo a barrier-less continuous collapse when the solvent conditions are changed to favor the fully folded native conformation. We test this hypothesis by probing intramolecular distance distributions during folding in one of the paradigms of folding reactions, that of cytochrome c. The Trp59-to-heme distance was probed by time-resolved Förster resonance energy transfer in the microsecond time range of refolding. Contrary to expectation, a state with a Trp59–heme distance close to that of the guanidinium hydrochloride (GdnHCl) denatured state is present after ~ 27 μs of folding. A concomitant decrease in the population of this state and an increase in the population of a compact high-FRET (Förster resonance energy transfer) state (efficiency > 90%) show that the collapse is barrier limited. Small-angle X-ray scattering (SAXS) measurements over a similar time range show that the radius of gyration under native favoring conditions is comparable to that of the GdnHCl denatured unfolded state. An independent comprehensive global thermodynamic analysis reveals that marginally stable partially folded structures are also present in the nominally unfolded GdnHCl denatured state. These observations suggest that specifically collapsed intermediate structures with low stability in rapid equilibrium with the unfolded state may contribute to the apparent chain contraction observed in previous fluorescence studies using steady-state detection. In the absence of significant dynamic averaging of marginally stable partially folded states and with the use of probes sensitive to distance distributions, barrier-limited chain contraction is observed upon transfer of the GdnHCl denatured state ensemble to native-like conditions.     

Molecular weight and symmetry of the pyruvate dehydrogenase multienzyme complex of Escherichia coli.

The molecular weight and polypeptide chain stoichiometry of the native pyruvate dehydrogenase multienzyme complex from Escherichia coli were determined by independent techniques. The translational diffusion coefficient (D^o_20,w) of the complex was measured by laser light intensity fluctuation spectroscopy and found to be 0.90 (±0.02) × 10^?11m²/s. When this was combined in the Svedberg equation with the measured sedimentation coefficient (s^o_20,w = 60.2 (±0.4) S) and partial specific volume ($\text{v}\text{?}\text{= 0.735 (±0.01)}\text{ml/g}$), the molecular weight of the intact native complex was calculated to be 6.1 (±0.3) × 10⁶. The polypeptide chain stoichiometry (pyruvate decarboxylase: lipoate acetyltransferase: lipoamide dehydrogenase) of the same sample of pyruvate dehydrogenase complex was measured by the radioamidination technique of Bates et al. (1975) and found to be 1.56:1.0:0.78.From this stoichiometry and the published polypeptide chain molecular weights estimated by sodium dodecyl sulphate/polyacrylamide gel electrophoresis, a minimum chemical molecular weight of 283,000 was calculated. This structure must therefore be repeated approximately 22 times to make up the native complex, a number which is in good agreement with the expected repeat of 24 times if the lipoate acetyltransferase core component has octahedral symmetry. It is consistent with what appears in the electron microscope to be trimer-clustering of the lipoate acetyltransferase chains at the corners of a cube. It rules out any structure based on 16 lipoate acetyltransferase chains comprising the enzyme core.The preparation of pyruvate dehydrogenase complex was polydisperse: in addition to the major component, two minor components with sedimentation coefficients (s^o_20,w) of 90.3 (±0.9) S and 19.8 (±0.3) S were observed. Together they comprised about 17% of the total protein in the enzyme sample. Both were in slowly reversible equilibrium with the major 60.2 S component but appeared to be enzymically active in the whole complex reaction. The faster-sedimenting species is probably a dimer of the complex, whereas the slower-sedimenting species has the properties of an incomplete aggregate of the component enzymes of the complex based on a trimer of the lipoate acetyltransferase chain.     

Structural Characteristic of the Initial Unfolded State on Refolding Determines Catalytic Efficiency of the Folded Protein in Presence of Osmolytes

Osmolytes are low molecular weight organic molecules accumulated by organisms to assist proper protein folding, and to provide protection to the structural integrity of proteins under denaturing stress conditions. It is known that osmolyte-induced protein folding is brought by unfavorable interaction of osmolytes with the denatured/unfolded states. The interaction of osmolyte with the native state does not significantly contribute to the osmolyte-induced protein folding. We have therefore investigated if different denatured states of a protein (generated by different denaturing agents) interact differently with the osmolytes to induce protein folding. We observed that osmolyte-assisted refolding of protein obtained from heat-induced denatured state produces native molecules with higher enzyme activity than those initiated from GdmCl- or urea-induced denatured state indicating that the structural property of the initial denatured state during refolding by osmolytes determines the catalytic efficiency of the folded protein molecule. These conclusions have been reached from the systematic measurements of enzymatic kinetic parameters (K _m and k _cat), thermodynamic stability (T _m and ΔH _m) and secondary and tertiary structures of the folded native proteins obtained from refolding of various denatured states (due to heat-, urea- and GdmCl-induced denaturation) of RNase-A in the presence of various osmolytes.     

Protein folding in vitro and in the cellular environment

The main concepts concerning protein folding have been developed from in vitro refolding studies. They state that the folding of a polypeptide chain is a spontaneous process depending only on the amino-acid sequence in a given environment. It is thermodynamically controlled and driven by the hydrophobic effect. Consequently, it has been accepted that the in vitro refolding process is a valuable model to understand the mechanisms involved during the folding of a nascent polypeptide chain in the cell. Although it does not invalidate the main rules deduced from the in vitro studies, the discovery of molecular chaperones has led to a re-evaluation of this last point. Indeed, in cells molecular chaperones are able to mediate the folding of polypeptide chains and the assembly of subunits in oligomeric proteins. The possible mechanisms by which these folding helpers act are discussed in the light of the data available in the literature. The folding process is assisted in the cell in different ways, preventing premature folding of the polypeptide chain and suppressing the incorrectly folded species and aggregates. Molecular chaperones bind to incompletely folded proteins in a conformation which suggests that the latter are in the "molten globule" state. However, very little is known about the recognition process.     

Kinetic traps in the folding of beta alpha-repeat proteins: CheY initially misfolds before accessing the native conformation

The βα-repeat class of proteins, represented by the (βα)₈ barrel and the α/β/α sandwich, are among the most common structural platforms in biology. Previous studies on the folding mechanisms of these motifs have revealed or suggested that the initial event involves the submillisecond formation of a kinetically trapped species that must at least partially unfold before productive folding to the respective native conformation can occur. To test the generality of these observations, CheY, a bacterial response regulator, was subjected to an extensive analysis of its folding reactions. Although earlier studies had proposed the formation of an off-pathway intermediate, the data available were not sufficient to rule out an alternative on-pathway mechanism. A global analysis of single- and double-jump kinetic data, combined with equilibrium unfolding data, was used to show that CheY folds and unfolds through two parallel channels defined by the state of isomerization of a prolyl peptide bond in the active site. Each channel involves a stable, highly structured folding intermediate whose kinetic properties are better described as the properties of an off-pathway species. Both intermediates subsequently flow through the unfolded state ensemble and adopt the native cis-prolyl isomer prior to forming the native state. Initial collapse to off-pathway folding intermediates is a common feature of the folding mechanisms of βα-repeat proteins, perhaps reflecting the favored partitioning to locally determined substructures that cannot directly access the native conformation. Productive folding requires the dissipation of these prematurely folded substructures as a prelude to forming the larger-scale transition state that leads to the native conformation. Results from Gō-modeling studies in the accompanying paper elaborate on the topological frustration in the folding free-energy landscape of CheY.     

An analysis of incorrectly folded protein models. Implications for structure predictions

Proteins with homologous amino acid sequences have similar folds and it has been assumed that an unknown three-dimensional structure can be obtained from a known homologous structure by substituting new side-chains into the polypeptide chain backbone, followed by relatively small adjustment of the model. To examine this approach of structure prediction and, more generally, to isolate the characteristics of native proteins, we constructed two incorrectly folded protein models. Sea-worm hemerythrin and the variable domain of mouse immunoglobulin K-chain, two proteins with no sequence homology, were chosen for study; the former is composed of a bundle of four alpha-helices and the latter consists of two 4-stranded beta-sheets. Using an automatic computer procedure, hemerythrin side-chains were substituted into the immunoglobulin domain and vice versa. The structures were energy-minimized with the program CHARMM and the resulting structures compared with the correctly folded forms. It was found that the incorrect side-chains can be incorporated readily into both types of structures (alpha-helices, beta-sheets) with only small structural adjustments. After constrained energy-minimization, which led to an average atomic co-ordinate shift of no more than 0.7 to 0.9 A, the incorrectly folded models arrived at potential energy values comparable to those of the correct structures. Detailed analysis of the energy results shows that the incorrect structures have less stabilizing electrostatic, van der Waals' and hydrogen-bonding interactions. The difference is particularly pronounced when the electrostatic and van der Waals' energy terms are calculated by modified equations that include an approximate representation of solvent effects. The incorrectly folded structures also have a significantly larger solvent-accessible surface and a greater fraction of non-polar side-chain atoms exposed to solvent. Examination of their interior shows that the packing of side-chains at the secondary structure interfaces, although corresponding to sterically allowed conformations, deviates from the characteristics found in normal proteins. The analysis of incorrectly folded structures has made it clear that the absence of bad non-bonded contacts, though necessary, is not sufficient to demonstrate the validity of model-built structures and that modeling of homologous structures has to be accompanied by a thorough quantitative evaluation of the results. Further, certain features that characterize native proteins are made evident by their absence in misfolded models.     

Electron transfer in reaction centers of Rhodopseudomonas sphaeroides. I. Determination of the charge recombination pathway of D+QAQ−B and free energy and kinetic relations between Q−AQB and QAQ−B

The electron-transfer reactions and thermodynamic equilibria involving the quinone acceptor complex in bacterial reaction centers from R. sphaeroides were investigated. The reactions are described by the scheme: We found that the charge recombination pathway of D⁺Q_AQ^?_B proceeds via the intermediate state D⁺Q^?_AQ_B, the direct pathway contributing less than approx. 5% to the observed recombination rate. The method used to obtain this result was based on a comparison of the kinetics predicted for the indirect pathway (given by the product k_AD-times the fraction of reaction centers in the Q^?_AQ_B state) with the observed recombination rate, k^obs_{D⁺ →D}. The kinetic measurements were used to obtain the pH dependence (6.1 ? pH ? 11.7) of the free energy difference between the states Q^?_AQ_B and Q_AQ^?_B. At low pH (less than 9) Q_AQ^?_B is stabilized relative to Q^?_AQ_B by 67 meV, whereas at high pH Q^?_AQ_B is energetically favored. Both Q^?_A and Q^?_B associate with a proton, with pK values of 9.8 and 11.3, respectively. The stronger interaction of the proton with Q^?_B provides the driving force for the forward electron transfer.