Folding-unfolding of immunoglobulin domains in titin: a simple two-state model

The folding-unfolding reaction rate process in the giant protein titin is studied within a simple two-state model. The molecule is assumed to be stretched by an external force which modulates the potential barrier associated with the folded state. A two-state model for this process is assumed (i.e., the immunoglobulin domains are considered to be either folded or unfolded, with no intermediate states at all). Simple calculations yield a relation between the force and the pulling speed that agrees fairly well with data from experiments and Monte Carlo simulations performed recently. Moreover, in a regime involving ultrafast pulling, the results show that the detailed form of the potential barrier is irrelevant, a conclusion that agrees with the current theoretical work on molecular dynamics.     

An Optimisation of Asymmetry Evaluation of Molecules within the Folding-Unfolding Method

This article concerns the study of the folding-unfolding (Continuous Symmetry Measure, CSM) method of Avnir et al. (Zabrodsky, H.; Peleg, S.; Avnir, D. J. Am. Chem. Soc. 1992, 114, 7843) for quantitative evaluation of the asymmetry of molecular objects. It is shown that a series of modifications to the folding-unfolding method are expedient. An efficient solution for optimisation problems in the folding-unfolding method has been proposed. It allows a significant speed up of the calculations and provides better results. Differences in the behaviours of the original and optimised folding-unfolding methods for various molecular structures are investigated.     

Conformational exchange on the microsecond time scale in alpha-helix and beta-hairpin peptides measured by 13C NMR transverse relaxation

13C-NMR relaxation experiments (T(1), T(2), T(1)(rho), and NOE) were performed on selectively enriched residues in two peptides, one hydrophobic staple alpha-helix-forming peptide GFSKAELAKARAAKRGGY and one beta-hairpin-forming peptide RGITVNGKTYGR, in water and in water/trifluoroethanol (TFE). Exchange contributions, R(ex), to spin-spin relaxation rates for (13)C(alpha) and (13)C(beta) groups were derived and were ascribed to be mainly due to peptide folding-unfolding. To evaluate the exchange time, tau(ex), from R(ex), the chemical shift difference between folded and unfolded states, Deltadelta, and the populations of these states, p(i), were determined from the temperature dependence of (13)C chemical shifts. For both peptides, values for tau(ex) fell in the 1 micros to 10 micros range. Under conditions where the peptides are most folded (water/TFE, 5 degrees C), tau(ex) values for all residues in each respective peptide were essentially the same, supporting the presence of a global folding-unfolding exchange process. Rounded-up average tau(ex) values were 4 micros for the helix peptide and 9 micros for the hairpin peptide. This 2-3-fold difference in exchange times between helix and hairpin peptides is consistent with that observed for folding-unfolding of other small peptides.     

How cytochrome c folds, and why: submolecular foldon units and their stepwise sequential stabilization

Native state hydrogen exchange experiments have shown that the cytochrome c (Cyt c) protein consists of five cooperative folding-unfolding units, called foldons. These are named, in the order of increasing unfolding free energy, the nested-Yellow, Red, Yellow, Green, and Blue foldons. Previous results suggest that these units unfold in a stepwise sequential way so that each higher energy partially unfolded form includes all of the previously unfolded lower free energy units. If this is so, then selectively destabilizing any given foldon should equally destabilize each subsequent unfolding step above it in the unfolding ladder but leave the lower ones before it unaffected. To perform this test, we introduced the mutation Glu62Gly, which deletes a salt link in the Yellow unit and destabilizes the protein by 0.8 kcal/mol. Native state hydrogen exchange and other experiments show that the stability of the Yellow unit and the states above it in the free energy ladder are destabilized by about the same amount while the lower lying states are unaffected. These results help to confirm the sequential stepwise nature of the Cyt c unfolding pathway and therefore a similar refolding pathway. The steps in the pathway are dictated by the concerted folding-unfolding property of the individual unit foldons; the order of steps is determined by the sequential stabilization of progressively added foldons in the native context. Much related information for Cyt c strongly conforms with this mechanism. Its generality is supported by available information for other proteins.     

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.     

Dynamic light scattering studies of ribonuclease

Dynamic light scattering has been used to measure the translational diffusion coefficients of bovine pancreatic ribonuclease A as functions of temperature and concentration in the presence of 1 M Guanidine-HCl. Data was collected throughout a temperature range including the folding-unfolding transitions. Evidence of a pretransition "swelling" of the protein was observed. Entropy and enthalpy changes upon unfolding were obtained using a two-state model.     

Kinetics of the unfolding-folding transition of Bacillus subtilislevansucrase precursor

The reversible folding-unfolding transition of mature and precursor forms of Bacillus subtilis levansucrase were compared under physiological conditions of pH and temperature. The time constant of the folding reaction was not modified by the presence of the signal sequence and the precursor in the native form was slightly more resistant to the denaturing action of urea. However, the folding pathway could be different for each protein since a domain of the mature levansucrase underwent an independent transition which is not observed during the renaturation process of prelevansucrase.     

A spectroscopic analysis of the thermally induced folding-unfolding transition of beta-trypsin.

Absorption and fluorescence changes were used to monitor the thermally induced folding-unfolding transition of beta-trypsin. These parameters reflect changes in the microenvironment of different subsets of the four tryptophanyl residues of this protein. The thermal transition was found to be sequential.     

Site-specific variations in RNA folding thermodynamics visualized by 2-aminopurine fluorescence

The fluorescent base analogue 2-aminopurine (2-AP) is commonly used to study specific conformational and protein binding events involving nucleic acids. Here, combinations of steady-state and time-resolved fluorescence spectroscopy of 2-AP were employed to monitor conformational transitions within a model hairpin RNA from diverse structural perspectives. RNA substrates adopting stable, unambiguous secondary structures were labeled with 2-AP at an unpaired base, within the loop, or inside the base-paired stem. Steady-state fluorescence was monitored as the RNA hairpins made the transitions between folded and unfolded conformations using thermal denaturation, urea titration, and cation-mediated folding. Unstructured control RNA substrates permitted the effects of higher-order RNA structures on 2-AP fluorescence to be distinguished from stimulus-dependent changes in intrinsic 2-AP photophysics and/or interactions with adjacent residues. Thermodynamic parameters describing local conformational changes were thus resolved from multiple perspectives within the model RNA hairpin. These data provided energetic bases for construction of folding mechanisms, which varied among different folding-unfolding stimuli. Time-resolved fluorescence studies further revealed that 2-AP exhibits characteristic signatures of component fluorescence lifetimes and respective fractional contributions in different RNA structural contexts. Together, these studies demonstrate localized conformational events contributing to RNA folding and unfolding that could not be observed by approaches monitoring only global structural transitions.     

Mapping the energy landscape of repeat proteins using NMR-detected hydrogen exchange

Repeat proteins contain tandem arrays of a simple structural motif. In contrast to globular proteins, repeat proteins are stabilized only by interactions between residues that are relatively close together in the sequence, with no ”long-range” interactions. Our work focuses on the tetratricopeptide repeat (TPR), a 34 amino acid helix-turn-helix motif found in tandem arrays in many natural proteins. Earlier, we reported the design and characterization of a series of consensus TPR (CTPR) proteins, which are built as arrays of multiple tandem copies of a 34 amino acid consensus sequence. Here, we present the results of extensive hydrogen exchange (HX) studies of the folding-unfolding behavior of two CTPR proteins (CTPR2 and CTPR3). We used HX to detect and characterize partially folded species that are populated at low frequency in the nominally folded state. We show that for both proteins the equilibrium folding-unfolding transition is non-two-state, but sequential, with the outermost helices showing a significantly higher probability than inner helices of being unfolded. We show that the experimentally observed unfolding behavior is consistent with the predictions of a simple Ising model, in which individual helices are treated as ”spin-equivalents”. The results that we present have general implications for our understanding of the thermodynamic properties of repeat proteins.     

Secretion of Bacillus subtilis levansucrase. Fe(III) could act as a cofactor in an efficient coupling of the folding and translocation processes.

The refolding of levansucrase denatured by urea was studied as a possible model for the second step of the secretion pathway of this protein. The folding-unfolding transition was monitored by measuring intrinsic fluorescence and resistance to proteolysis. Both methods provided the same estimation for the unfolding free energy of levansucrase, delta GD, which was 30.1 +/- 1.7 kJ.mol-1 (7.2 +/- 0.4 kcal.mol-1) at pH 7 in 0.1 M-potassium phosphate buffer. The rate of refolding was greatly enhanced by Fe3+, whereas the Fe3+ chelator EDTA prevented correct refolding. Fe3+ allowed the protein to reach its folded form in medium in which the dielectric constant had been lowered by ethanol. The efficiency in vivo of the export of levansucrase bearing an amino acid modification which blocks the second step of the translocation pathway was greatly increased by high concentrations of Fe3+ in the culture medium. Assuming that the protein folding governs the second step of the secretion process of levansucrase, we discuss from an irreversible thermodynamic point of view the possible role of Fe3+ in the efficient coupling of the two events.     

Physical-chemical properties of actin in different structural states. New ideas about its folding-unfolding pathways

Results of actin folding-unfolding pathways examination and characterization of intermediate and misfolded states are summarized. Properties of microenvironments and peculiarities of location of tryptophan residues in protein are analysed in detail. This allowed to conclude that the main contribution to the bulk fluorescence of native protein is made by internal tryptophan residues Trp 340 and Trp 356, localized in hydrophobic regions, while tryptophan residues Trp 79 and Trp 86 are quenched. It has been shown that inactivated actin, previously regarded as an intermediate state between native and completely unfolded state of protein is in reality a misfolded aggregated state. The properties of actin in this state were characterized in detail. In particular, it is shown that inactivated actin is a monodisperse associate consisting of 15 monomer unit. Two earlier unknown intermediate states, which precede completely unfolding of protein macromolecule and formation of inactivated actin, were visualized. A new scheme of folding-unfolding processes was proposed. It is shown that the reason of anomalous effects, which are recorded for actin in solutions with small concentrations of GdnHCl, is a specific interaction of actin with a denaturant.     

Structural characterization of yeast acidic ribosomal P proteins forming the P1A-P2B heterocomplex

Acidic ribosomal P proteins form a distinct lateral protuberance on the 60S ribosomal subunit. In yeast, this structure is composed of two heterocomplexes (P1A-P2B and P1B-P2A) attached to the ribosome with the aid of the P0 protein. In solution, the isolated P proteins P1A and P2B have a flexible structure with some characteristics of a molten globule [Zurdo, J., et al. (2000) Biochemistry 39, 8935-8943]. In this report, the structure of P1A-P2B heterocomplex from Saccharomyces cerevisiae is investigated by means of size-exclusion chromatography, chemical cross-linking, circular dichroism, light scattering, and fluorescence spectroscopy. The circular dichroism experiment shows that the complex could be ranked in the tertiary class of all-alpha proteins, with an average alpha-helical content of approximately 65%. Heat and urea denaturation experiments reveal that the P1A-P2B complex, unlike the isolated proteins, has a full cooperative transition which can be fitted into a two-state folding-unfolding model. The behavior of the complex in the presence of 2,2,2-trifluoroethanol also resembles a two-state folding-unfolding transition, further supporting the idea that the heterocomplex contains well-packed side chains. In conclusion, the P1A-P2B heterocomplex, unlike the isolated proteins, has a well-defined hydrophobic core. Consequently, the complex can put up its structure without additional ribosomal components, so the heterodimeric complex reflects the intrinsic properties of the two analyzed proteins, indicating thus that this is the only possible configuration of the P1A and P2B proteins on the ribosomal stalk structure.     

Optical tweezers as a probe for oligodeoxyribonucleotide structuration

The aim of this work is to investigate if the optical tweezers (OT) are suitable as a diagnostic tool for monitoring the oligodeoxyribonucleotide (ODN) structural behavior in solution. Preliminary experiments, performed on the quadruplex formed by the ODN sequence TGGGGT, showed that the OT can be used as a probe for ODN structuration by monitoring the medium viscosity changes associated with ODN folding-unfolding processes.     

Folding units govern the cytochrome c alkaline transition

The alkaline transition of cytochrome c is a model for protein structural switching in which the normal heme ligand is replaced by another group. Stopped flow data following a jump to high pH detect two slow kinetic phases, suggesting two rate-limiting structure changes. Results described here indicate that these events are controlled by the same structural unfolding reactions that account for the first two steps in the reversible unfolding pathway of cytochrome c. These and other results show that the cooperative folding-unfolding behavior of protein foldons can account for a variety of functional activities in addition to determining folding pathways.     

Theoretical study of a landscape of protein folding-unfolding pathways. Folding rates at midtransition

This paper presents a new method for calculating the folding-unfolding rates of globular proteins. The method is based on solution of kinetic equations for a network of folding-unfolding pathways of the proteins. The rates are calculated in the point of thermodynamic equilibrium between the native and completely unfolded states. The method has been applied to all the proteins listed by Jackson [Jackson, S. E. (1998) Folding Des. 3, R81-R91] and some peptides. Although the studied protein chains differ by more than 1 order of magnitude in size and exhibit two- as well as three-state kinetics in water, and their folding rates cover more than 11 orders of magnitude, the theoretical estimates are reasonable close to the experimentally measured folding rates in midtransition (the correlation coefficient being as high as 0.78). This means that the presented theory (having no adjustable parameters at all) is consistent with the experimental observations.     

The triplex-hairpin transition in cytosine-rich DNA

We present a theoretical study of the self-complementary single-stranded 30-mer d(TC*TTC*C*TTTTCCTTCTC*CCGAGAAGGTTTT) (PDB ID: 1b4y) that was designed to form an intramolecular triplex by folding back twice on itself. At neutral pH the molecule exists in a duplex hairpin conformation, whereas at acidic pH the cytosines labeled by an asterisk (*) are protonated, forming Hoogsteen hydrogen bonds with guanine of a GC Watson-Crick basepair to generate a triplex. As a first step in an investigation of the energetics of the triplex-hairpin transition, we applied the Bashford-Karplus multiple site model of protonation to calculate the titration curves for the two conformations. Based on these data, a two-state model is used to study the equilibrium properties of transition. Although this model properly describes the thermodynamics of the protonation-deprotonation steps that drive the folding-unfolding of the oligomer, it cannot provide insight into the time-dependent mechanism of the process. A series of molecular dynamics simulations using the ff94 force field of the AMBER 6.0 package was therefore run to explore the dynamics of the folding/unfolding pathway. The molecular dynamics method was combined with Poisson-Boltzmann calculations to determine when a change in protonation state was warranted during a trajectory. This revealed a sequence of elementary protonation steps during the folding/unfolding transition and suggests a strong coupling between ionization and folding in cytosine-rich triple-helical triplexes.     

Detection and characterization of partially unfolded oligomers of the SH3 domain of alpha-spectrin

For the purpose of equilibrium and kinetic folding-unfolding studies, the SH3 domain of alpha-spectrin (spc-SH3) has long been considered a classic two-state folding protein. In this work we have indeed observed that the thermal unfolding curves of spc-SH3 measured at pH 3.0 by differential scanning calorimetry, circular dichroism, and NMR follow apparently the two-state model when each unfolding profile is considered individually. Nevertheless, we have found that protein concentration has a marked effect upon the thermal unfolding profiles. This effect cannot be properly explained in terms of the two-state unfolding model and can only be interpreted in terms of the accumulation of intermediate associated states in equilibrium with the monomeric native and unfolded states. By chemical cross-linking and pulsed-field gradient NMR diffusion experiments we have been able to confirm the existence of associated states formed during spc-SH3 unfolding. A three-state model, in which a dimeric intermediate state is assumed to be significantly populated, provides the simplest interpretation of the whole set of thermal unfolding data and affords a satisfactory explanation for the concentration effects observed. Whereas at low concentrations the population of the associated intermediate state is negligible and the unfolding process consequently takes place in a two-state fashion, at concentrations above approximately 0.5 mM the population of the intermediate state becomes significant at temperatures between 45 degrees C and 80 degrees C and reaches up to 50% at the largest concentration investigated. The thermodynamic properties of the intermediate state implied by this analysis fall in between those of the unfolded state and the native ones, indicating a considerably disordered conformation, which appears to be stabilized by oligomerization.     

Evaluation of feeding strategies in carbon-regulated secondary metabolite production through mathematical modeling

There is now growing evidence that the production of many secondary metabolic by microorganisms is subjected to carbon-catabolite regulation. Even though the exact mode of this regulation is not yet clear, an engineering analysis of the production process is still possible based upon a suitable hypothesis. By way of simulation of penicillin fermentation data obtained from the literature, a mechanistic model involving a substrate inhibition kinetics of product formation has been verified in this paper. Such a model has been found successful not only in predicting simple sugar-feeding strategy, but also a complicated computer guided strategy based upon controlling biomass growth rates in the tropo and idiophases. Using this model, for strategies for sugar feeding into penicillin fermentation have been investigated. These results show that similar penicillin productivities can be obtained using any of these strategies provided fermentations are carried out under optimal conditions corresponding to the strategy chosen. Effect of maximum oxygen transfer capacity of the fermentor under the conditions of fungal growth has been incorporated using an upper limit of biomass concentration on achievement of which the fermentations must be stopped due to serious oxygen limitations. Results of model simulations with such limits throw light upon the way in which different fermentors may behave with respect to product formation.     

Morphology and productivity of filamentous fungi

Cultivation processes involving filamentous fungi have been optimised for decades to obtain high product yields. Several bulk chemicals like citric acid and penicillin are produced this way. A simple adaptation of cultivation parameters for new production processes is not possible though. Models explaining the correlation between process-dependent growth behaviour and productivity are therefore necessary to prevent long-lasting empiric test series. Yet, filamentous growth consists of a complex microscopic differentiation process from conidia to hyphae resulting in various macroscopically visible appearances. Early approaches to model this morphologic development are recapitulated in this review to explain current trends in this area of research. Tailoring morphology by adjusting process parameters is one side of the coin, but an ideal morphology has not even been found. This article reviews several reasons for this fact starting with nutrient supply in a fungal culture and presents recent advances in the investigation of fungal metabolism. It illustrates the challenge to unfold the relationship between morphology and productivity.