Four-state Mechanism Research Articles

Calcium is a noncompetitive inhibitor of DMT1 on the intestinal iron absorption process: empirical evidence and mathematical modeling analysis.

Iron absorption is a complex and highly controlled process where DMT1 transports nonheme iron through the brush-border membrane of enterocytes to the cytoplasm but does not transport alkaline-earth metals such as calcium. However, it has been proposed that high concentrations of calcium in the diet could reduce iron bioavailability. In this work, we investigate the effect of intracellular and extracellular calcium on iron uptake by Caco-2 cells, as determined by calcein fluorescence quenching. We found that extracellular calcium inhibits iron uptake by Caco-2 cells in a concentration-dependent manner. Chelation of intracellular calcium with BAPTA did not affect iron uptake, which indicates that the inhibitory effect of calcium is not exerted through intracellular calcium signaling. Kinetic studies performed, provided evidence that calcium acts as a reversible noncompetitive inhibitor of the iron transport activity of DMT1. Based on these experimental results, a mathematical model was developed that considers the dynamics of noncompetitive inhibition using a four-state mechanism to describe the inhibitory effect of calcium on the DMT1 iron transport process in intestinal cells. The model accurately predicts the calcein fluorescence quenching dynamics observed experimentally after an iron challenge. Therefore, the proposed model structure is capable of representing the inhibitory effect of extracellular calcium on DMT1-mediated iron entry into the cLIP of Caco-2 cells. Considering the range of calcium concentrations that can inhibit iron uptake, the possible inhibition of dietary calcium on intestinal iron uptake is discussed.

Complex Folding Landscape of Apomyoglobin at Acidic pH Revealed by Ultrafast Kinetic Analysis of Core Mutants.

Under mildly acidic conditions (pH 4-4.5) apomyoglobin (apoMb) adopts a partially structured equilibrium state ( M-state) that structurally resembles a kinetic intermediate encountered at a late stage of folding to the native structure at neutral pH. We have previously reported that the M-state is formed rapidly (<1 ms) via a multistate process and thus offers a unique opportunity for exploring early stages of folding by both experimental and computational techniques. In order to gain structural insight into intermediates and barriers at the residue level, we studied the folding/unfolding kinetics of 12 apoMb mutants at pH 4.2 using fluorescence-detected ultrafast mixing techniques. Global analysis of the submillisecond folding/unfolding kinetics vs urea concentration for each variant, based on a sequential four-state mechanism ( U ⇔ I ⇔ L ⇔ M), allowed us to determine elementary rate constants and their dependence on urea concentration for most transitions. Comparison of the free energy diagrams constructed from the kinetic data of the mutants with that of wild-type apoMb yielded quantitative information on the effects of mutations on the free energy (ΔΔ G) of both intermediates and the first two kinetic barriers encountered during folding. Truncation of conserved aliphatic side chains on helices A, G, and H gives rise to a stepwise increase in ΔΔ G as the protein advances from U toward M, consistent with progressive stabilization of native-like contacts within the primary core of apoMb. Helix-helix contacts in the primary core contribute little to the first folding barrier ( U ⇔ I) and thus are not required for folding initiation but are critical for the stability of the late intermediate, L, and the M-state. Alanine substitution of hydrophobic residues at more peripheral helix-helix contact sites of the native structure, which are still absent or unstable in the M-state, shows both positive (destabilizing) and negative (stabilizing) ΔΔ G, indicating that non-native contacts are formed initially and weakened or lost as a result of subsequent structural rearrangement steps.

A Native-like Intermediate Serves as a Branching Point between the Folding and Aggregation Pathways of the Mouse Prion Protein

Transient folding intermediates and/or partially unfolded equilibrium states are thought to play a key role in the formation of protein aggregates. However, there is only indirect evidence linking accumulation of folding intermediates to aggregation, and the underlying mechanism remains to be elucidated. Here, we show that a partially unfolded state of the prion protein accumulates both as a stable equilibrium state at acidic pH (A-state) and as a late folding intermediate. With a time resolution of approximately 60 μs, we systematically studied the kinetics of folding and unfolding, starting from various initial conditions including the U-, N-, and A-states. Quantitative modeling showed that the observed kinetic data are completely consistent with a sequential four-state mechanism where the A-state is a late folding intermediate. Combined with previous evidence linking A-state accumulation to aggregation, the results indicate that this native-like state serves as a branching point between the folding and aggregation pathways.

Temperature dependence of the phosphorescence and of the thermally activated delayed fluorescence of 12C70 and 13C70 in amorphous polymer matrices. Is a second triplet involved?

The phosphorescence and thermally activated delayed fluorescence (TADF) lifetimes of 12C70 and 13C70 in two different glassy hydrocarbon polymers, one aliphatic (cyclic polyolefin) and one aromatic (polystyrene), were measured between −200 and 100 ºC. The temperature dependence of the lifetimes is equally well described by a three-state mechanism (ground state, S0, and two excited states in thermal equilibrium, T1 and S1, the lifetime of T1 being temperature dependent) and by a four-state mechanism (ground state, S0, and three excited states in thermal equilibrium, T1, T2 and S1, all with temperature-independent lifetimes). The estimated S1–T1 and T2–T1 energy gaps (four-state mechanism) are in good agreement with spectroscopic measurements. These and the determined quantum yield of triplet formation, 0.997 ± 0.001, are found to be essentially independent of the polymer matrix and of the isotopic composition of the fullerene. On the other hand, the lifetimes of both T1 and T2 (four-state mechanism) are weakly dependent on the polymer matrix but strongly vary with the fullerene isotopic composition, nearly doubling when going from 12C70 to 13C70. A parameter useful for the characterization of TADF, the on-set temperature T0, is also introduced.

A Two-State Model for the Dynamics of the Pyrophosphate Ion Release in Bacterial RNA Polymerase

The dynamics of the PPi release during the transcription elongation of bacterial RNA polymerase and its effects on the Trigger Loop (TL) opening motion are still elusive. Here, we built a Markov State Model (MSM) from extensive all-atom molecular dynamics (MD) simulations to investigate the mechanism of the PPi release. Our MSM has identified a simple two-state mechanism for the PPi release instead of a more complex four-state mechanism observed in RNA polymerase II (Pol II). We observed that the PPi release in bacterial RNA polymerase occurs at sub-microsecond timescale, which is ∼3-fold faster than that in Pol II. After escaping from the active site, the (Mg-PPi)2− group passes through a single elongated metastable region where several positively charged residues on the secondary channel provide favorable interactions. Surprisingly, we found that the PPi release is not coupled with the TL unfolding but correlates tightly with the side-chain rotation of the TL residue R1239. Our work sheds light on the dynamics underlying the transcription elongation of the bacterial RNA polymerase.

Sequential four‐state folding/unfolding of goat α‐lactalbumin and its N‐terminal variants

Equilibria and kinetics of folding/unfolding of α-lactalbumin and its two N-terminal variants were studied by circular dichroism spectroscopy. The two variants were wild-type recombinant and Glu1-deletion (E1M) variants expressed in Escherichia coli. The presence of an extra methionine at the N terminus in recombinant α-lactalbumin destabilized the protein by 2 kcal/mol, while the stability was recovered in the E1M variant in which Glu1 was replaced by Met1. Kinetic folding/unfolding reactions of the proteins, induced by stopped-flow concentration jumps of guanidine hydrochloride, indicated the presence of a burst-phase in refolding, and gave chevron plots with significant curvatures in both the folding and unfolding limbs. The folding-limb curvature was interpreted in terms of accumulation of the burst-phase intermediate. However, there was no burst phase observed in the unfolding kinetics to interpret the unfolding-limb curvature. We thus assumed a sequential four-state mechanism, in which the folding from the burst-phase intermediate takes place via two transition states separated by a high-energy intermediate. We estimated changes in the free energies of the burst-phase intermediate and two transition states, caused by the N-terminal variations and also by the presence of stabilizing calcium ions. The Φ values at the N terminus and at the Ca(2+)-binding site thus obtained increased successively during folding, demonstrating the validity of the sequential mechanism. The stability and the folding behavior of the E1M variant were essentially identical to those of the authentic protein, allowing us to use this variant as a pseudo-wild-type α-lactalbumin in future studies.

Microsecond Folding Dynamics of Apomyoglobin at Acidic pH

Apomyolgobin (apoMb) is an important model for understanding the folding mechanism of helical proteins. This study focuses on a partially structured state of sperm whale apoMb populated at pH 4.2 (M-state), which structurally resembles a late kinetic intermediate in the formation of the native state (N) at higher pH. The thermodynamics and cooperativity of apoMb folding at pH 4.2 and 6.2 were studied by global analysis of the urea-induced unfolding transitions monitored by tryptophan fluorescence and circular dichroism. The kinetics of folding and unfolding of apoMb at pH 4.2 was measured over a time window from 40 to 850 μs, using fluorescence-detected continuous-flow measurements. Our observation of biphasic kinetics provides clear evidence for rapid (<100 μs) accumulation of previously unresolved intermediate states in both refolding and unfolding experiments. Quantitative kinetic modeling of the results, using a four-state mechanism with two intermediates on a direct route between the unfolded and folded states (U↔I↔L↔M), gave new insight into the conformational states and barriers that precede the rate-limiting step in the formation of the N-state of apoMb.

Last In, First Out: THE ROLE OF COFACTOR BINDING IN FLAVODOXIN FOLDING

Although many proteins require the binding of a ligand to be functional, the role of ligand binding during folding is scarcely investigated. Here, we have reported the influence of the flavin mononucleotide (FMN) cofactor on the global stability and folding kinetics of Azotobacter vinelandii holoflavodoxin. Earlier studies have revealed that A. vinelandii apoflavodoxin kinetically folds according to the four-state mechanism: I(1) <=> unfolded apoflavodoxin <=> I(2) <=> native apoflavodoxin. I(1)an off-pathway molten globule-like is intermediate that populates during denaturant-induced equilibrium unfolding; I(2) is a high energy on-pathway folding intermediate that never populates to a significant extent. Here, we have presented extensive denaturant-induced equilibrium unfolding data of holoflavodoxin, holoflavodoxin with excess FMN, and apoflavodoxin as well as kinetic folding and unfolding data of holoflavodoxin. All folding data are excellently described by a five-state mechanism: I(1) + FMN <=> unfolded apoflavodoxin + FMN <=> I(2) + FMN <=> native apoflavodoxin + FMN<=> holoflavodoxin. The last step in flavodoxin folding is thus the binding of FMN to native apoflavodoxin. I(1),I(2), and unfolded apoflavodoxin do not interact to a significantextent with FMN. The autonomous formation of native apoflavodoxin is essential during holoflavodoxin folding. Excess FMN does not accelerate holoflavodoxin folding, and FMN does not act as a nucleation site for folding. The stability of holoflavodoxin is so high that even under strongly denaturing conditions FMN needs to be released first before global unfolding of the protein can occur.

Acid-induced Unfolding of the Amino-terminal Domains of the Lethal and Edema Factors of Anthrax Toxin

The two enzymatic components of anthrax toxin, lethal factor (LF) and edema factor (EF), are transported to the cytosol of mammalian cells by the third component, protective antigen (PA). A heptameric form of PA binds LF and/or EF and, under the acidic conditions encountered in endosomes, generates a membrane-spanning pore that is thought to serve as a passageway for these enzymes to enter the cytosol. The pore contains a 14-stranded transmembrane beta-barrel that is too narrow to accommodate a fully folded protein, necessitating that LF and EF unfold, at least partly, in order to pass. Here, we describe the pH-dependence of the unfolding of LF(N) and EF(N), the 30kDa N-terminal PA-binding domains, and minimal translocatable units, of LF and EF. Equilibrium chemical denaturation studies using fluorescence and circular dichroism spectroscopy show that each protein unfolds via a four-state mechanism: N<-->I<-->J<-->U. The acid-induced N-->I transition occurs within the pH range of the endosome (pH 5-6). The I state predominates at lower pH values, and the J and U states are populated significantly only in the presence of denaturant. The I state is compact and has characteristics of a molten globule, as shown by its retention of significant secondary structure and its ability to bind an apolar fluorophore. The N-->I transition leads to an overall 60% increase in buried surface area exposure. The J state is expanded significantly and has diminished secondary structure content. We analyze the different protonation states of LF(N) and EF(N) in terms of a linked equilibrium proton binding model and discuss the implications of our findings for the mechanism of acidic pH-induced translocation of anthrax toxin. Finally, analysis of the structure of the transmembrane beta-barrel of PA shows that it can accommodate alpha-helix, and we suggest that the steric constraints and composition of the lumen may promote alpha-helix formation.

Kinetic mechanism of folding and unfolding of Rhodobacter capsulatus cytochrome c2.

In spite of marginal sequence homology, cytochrome c2 from photosynthetic bacteria and the mitochondrial cytochromes c exhibit some striking structural similarities, including the tertiary arrangement of the three main helices. To compare the folding mechanisms for these two distantly related groups of proteins, equilibrium and kinetic measurements of the folding/unfolding reaction of cytochrome c2 from Rhodobacter capsulatus were performed as a function of guanidine hydrochloride (GuHCl) concentration in the absence and presence of a stabilizing salt, sodium sulfate. Quenching of the fluorescence of Trp67 by the heme was used as a conformational probe. Kinetic complexities due to non-native histidine ligation are avoided, since cytochrome c2 contains only one histidine, His17, which forms the axial heme ligand under native and denaturing conditions. Quantitative kinetic modeling showed that both equilibrium and kinetic results are consistent with a minimal four-state mechanism with two sequential intermediates. The observation of a large decrease in fluorescence during the 2-ms dead-time of the stopped-flow measurement (burst phase) at low GuHCl concentration, followed by a sigmoidal recovery of the initial amplitude toward the unfolding transition region, is attributed to a well-populated compact folding intermediate in rapid exchange with unfolded molecules. A nearly denaturant-independent process at low GuHCl concentrations reflects the rate-limiting conversion of a compact intermediate to the native state. At high GuHCl concentrations, a process with little denaturant dependence is attributed to the rate-limiting Met96-iron deligation process during unfolding, which is supported by the kinetics of imidazole binding. The strong GuHCl-dependence of folding and unfolding rates near the midpoint of the equilibrium transition is attributed to destabilization of each intermediate and their transition states in folding and unfolding. Addition of sodium sulfate shifts the rate profile to higher denaturant concentration, which can be understood in terms of the relative stabilizing effect of the salt on partially and fully folded states.

Presteady-state kinetics and carrier-mediated transport: A theoretical analysis

Kinetic studies of cotransport mechanisms have so far been limited to the conventional steady-state approach which does not allow in general to resolve either isomerization or rate-limiting steps and to determine the values of the individual rate constants for the elementary reactions involved along a given transport pathway. Such questions can only be answered using presteady-state or relaxation experiments which, for technical reasons, have not yet been introduced into the field of cotransport kinetics. However, since two recent reports seem compatible with the observation of such transient kinetics, it would appear that theoretical studies are needed to evaluate the validity of such claims and to critically evaluate the expectations from a presteady-state approach. We thus report such a study which was performed on a simple four-state mechanism of carrier-mediated transport. The time-dependent equation for zero-trans substrate uptake was thus derived and then extended to models with p intermediary steps. It is concluded that (p-1) exponential terms will describe the approach to the steady state but that such equations have low analytical value since the parameters of the flux equation cannot be expressed in terms of the individual rate constants of the elementary reactions for models with p greater than 5. We thus propose realistic simplifications based on the time-scale separation hypothesis which allows replacement of the rate constants of the rapid steps by their equilibrium constants, thereby reducing the complexity of the kinetic system. Assuming that only one relaxation can be observed, this treatment generates approximate models for which analytical expressions can easily be derived and simulated through computer modeling. When performed on the four-state mechanism of carrier-mediated transport, the simulations demonstrate the validity of the approximate solutions derived according to this hypothesis. Moreover, our approach clearly shows that presteady-state kinetics, should they become applicable to (co)transport kinetics, could be invaluable in determining more precise transport mechanisms.