Computer-based analysis of the binding steps in protein complex formation

Computer models were used to examine whether and under what conditions the multimeric protein complex is inhibited by high concentrations of one of its components—an effect analogous to the prozone phenomenon in precipitin tests. A series of idealized simple “ball-and-stick” structures representing small oligomeric complexes of protein molecules formed by reversible binding reactions were analyzed to determine the binding steps leading to each structure. The equilibrium state of each system was then determined over a range of starting concentrations and Kds and the steady-state concentration of structurally complete oligomer calculated for each situation. A strong inhibitory effect at high concentrations was shown by any protein molecule forming a bridge between two or more separable parts of the complex. By contrast, proteins linked to the outside of the complex by a single bond showed no inhibition whatsoever at any concentration. Nonbridging, multivalent proteins in the body of the complex could show an inhibitory effect or not depending on the structure of the complex and the strength of its bonds. On the basis of this study, we suggest that the prozone phenomenon will occur widely in living cells and that it could be a crucial factor in the regulation of protein complex formation.

NMR investigation of ferricytochrome c unfolding: Detection of an equilibrium unfolding intermediate and residual structure in the denatured state

Horse ferricytochrome c (cyt c) undergoes exchange of one of its axial heme ligands (Met-80) for one or more non-native ligands under denaturing conditions. We have used 1H NMR spectroscopy to detect two conformations of paramagnetic cyt c with non-native heme ligation through a range of urea concentrations. One non-native form is an equilibrium unfolding intermediate observed under partially denaturing conditions and is attributed to replacement of Met-80 with one or more Lys side chains. The second non-native form, in which the native Met ligand is replaced by a His, is observed under strongly denaturing conditions. Thermodynamic analysis of these data indicates a relatively small ΔG (17 kJ/mol) for the transition from native to the Lys-ligated intermediate and a significantly larger ΔG (47 kJ/mol) for the transition from native to the His-ligated species. Although CD and fluorescence data indicate that the equilibrium unfolding of cyt c is a two-state process, these NMR results implicate an intermediate with His-Lys ligation.

Partial molar volume, surface area, and hydration changes for equilibrium unfolding and formation of aggregation transition state: High-pressure and cosolute studies on recombinant human IFN-γ

The equilibrium dissociation of recombinant human IFN-γ was monitored as a function of pressure and sucrose concentration. The partial molar volume change for dissociation was −209 ± 13 ml/mol of dimer. The specific molar surface area change for dissociation was 12.7 ± 1.6 nm2/molecule of dimer. The first-order aggregation rate of recombinant human IFN-γ in 0.45 M guanidine hydrochloride was studied as a function of sucrose concentration and pressure. Aggregation proceeded through a transition-state species, N*. Sucrose reduced aggregation rate by shifting the equilibrium between native state (N) and N* toward the more compact N. Pressure increased aggregation rate through increased solvation of the protein, which exposes more surface area, thus shifting the equilibrium away from N toward N*. The changes in partial molar volume and specific molar surface area between the N* and N were −41 ± 9 ml/mol of dimer and 3.5 ± 0.2 nm2/molecule, respectively. Thus, the structural change required for the formation of the transition state for aggregation is small relative to the difference between N and the dissociated state. Changes in waters of hydration were estimated from both specific molar surface area and partial molar volume data. From partial molar volume data, estimates were 25 and 128 mol H2O/mol dimer for formation of the aggregation transition state and for dissociation, respectively. From surface area data, estimates were 27 and 98 mol H2O/mol dimer. Osmotic stress theory yielded values ≈4-fold larger for both transitions.

Preferential exclusion of sucrose from recombinant interleukin-1 receptor antagonist: Role in restricted conformational mobility and compaction of native state

Understanding the mechanism for sucrose-induced protein stabilization is important in many diverse fields, ranging from biochemistry and environmental physiology to pharmaceutical science. Timasheff and Lee [Lee, J. C. & Timasheff, S. N. (1981) J. Biol. Chem. 256, 7193–7201] have established that thermodynamic stabilization of proteins by sucrose is due to preferential exclusion of the sugar from the protein’s surface, which increases protein chemical potential. The current study measures the preferential exclusion of 1 M sucrose from a protein drug, recombinant interleukin 1 receptor antagonist (rhIL-1ra). It is proposed that the degree of preferential exclusion and increase in chemical potential are directly proportional to the protein surface area and that, hence, the system will favor the protein state with the smallest surface area. This mechanism explains the observed sucrose-induced restriction of rhIL-1ra conformational fluctuations, which were studied by hydrogen–deuterium exchange and cysteine reactivity measurements. Furthermore, infrared spectroscopy of rhlL-1ra suggested that a more ordered native conformation is induced by sucrose. Electron paramagnetic resonance spectroscopy demonstrated that in the presence of sucrose, spin-labeled cysteine 116 becomes more buried in the protein’s interior and that the hydrodynamic diameter of the protein is reduced. The preferential exclusion of sucrose from the protein and the resulting shift in the equilibrium between protein states toward the most compact conformation account for sucrose-induced effects on rhIL-1ra.

Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

A transient expansion of the native state precedes aggregation of recombinant human interferon-γ

Aggregation of proteins, even under conditions favoring the native state, is a ubiquitous problem in biotechnology and biomedical engineering. Providing a mechanistic basis for the pathways that lead to aggregation should allow development of rational approaches for its prevention. We have chosen recombinant human interferon-γ (rhIFN-γ) as a model protein for a mechanistic study of aggregation. In the presence of 0.9 M guanidinium hydrochloride, rhIFN-γ aggregates with first order kinetics, a process that is inhibited by addition of sucrose. We describe a pathway that accounts for both the observed first-order aggregation of rhIFN-γ and the effect of sucrose. In this pathway, aggregation proceeds through a transient expansion of the native state. Sucrose shifts the equilibrium within the ensemble of rhIFN-γ native conformations to favor the most compact native species over more expanded ones, thus stabilizing rhIFN-γ against aggregation. This phenomenon is attributed to the preferential exclusion of sucrose from the protein surface. In addition, kinetic analysis combined with solution thermodynamics shows that only a small (9%) expansion surface area is needed to form the transient native state that precedes aggregation. The approaches used here link thermodynamics and aggregation kinetics to provide a powerful tool for understanding both the pathway of protein aggregation and the rational use of excipients to inhibit the process.

Denaturant-induced movement of the transition state of protein folding revealed by high-pressure stopped-flow measurements

The small all-β protein tendamistat folds and unfolds with two-state kinetics. We determined the volume changes associated with the folding process by performing kinetic and equilibrium measurements at variable pressure between 0.1 and 100 MPa (1 to 1,000 bar). GdmCl-induced equilibrium unfolding transitions reveal that the volume of the native state is increased by 41.4 ± 2.0 cm3/mol relative to the unfolded state. This value is virtually independent of denaturant concentration. The use of a high-pressure stopped-flow instrument enabled us to measure the activation volumes for the refolding (ΔVf0‡) and unfolding reaction (ΔVu0‡) over a broad range of GdmCl concentrations. The volume of the transition state is 60% native-like (ΔVf0‡ = 25.0 ± 1.2 cm3/mol) in the absence of denaturant, indicating partial solvent accessibility of the core residues. The volume of the transition state increases linearly with denaturant concentration and exceeds the volume of the native state above 6 M GdmCl. This result argues for a largely desolvated transition state with packing deficiencies at high denaturant concentrations and shows that the structure of the transition state depends strongly on the experimental conditions.

An equilibrium statistical model for the spreading phase of open-ocean convection

A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading phase of open-ocean convection. The theory depends only on bulk conserved quantities such as energy, circulation, and the range of values of potential vorticity in each layer. The simplest theory is formulated for a uniform cooling event over the entire basin that triggers a homogeneous random distribution of convective towers. For a small Rossby deformation radius typical for open-ocean convection sites, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection, with a stabilizing barotropic rim current and localized temperature anomaly.

Three-dimensional domain swapping in p13suc1 occurs in the unfolded state and is controlled by conserved proline residues

p13suc1 has two native states, a monomer and a domain-swapped dimer. We show that their folding pathways are connected by the denatured state, which introduces a kinetic barrier between monomer and dimer under native conditions. The barrier is lowered under conditions that speed up unfolding, thereby allowing, to our knowledge for the first time, a quantitative dissection of the energetics of domain swapping. The monomer–dimer equilibrium is controlled by two conserved prolines in the hinge loop that connects the exchanging domains. These two residues exploit backbone strain to specifically direct dimer formation while preventing higher-order oligomerization. Thus, the loop acts as a loaded molecular spring that releases tension in the monomer by adopting its alternative conformation in the dimer. There is an excellent correlation between domain swapping and aggregation, suggesting they share a common mechanism. These insights have allowed us to redesign the domain-swapping propensity of suc1 from a fully monomeric to a fully dimeric protein.

The pKa of His-24 in the folding transition state of apomyoglobin

In native apomyoglobin, His-24 cannot be protonated, although at pH 4 the native protein forms a molten globule folding intermediate in which the histidine residues are readily protonated. The inability to protonate His-24 in the native protein dramatically affects the unfolding/refolding kinetics, as demonstrated by simulations for a simple model. Kinetic data for wild type and for a mutant lacking His-24 are analyzed. The pKa values of histidine residues in native apomyoglobin are known from earlier studies, and the average histidine pKa in the molten globule is determined from the pH dependence of the equilibrium between the native and molten globule forms. Analysis of the pH-dependent unfolding/refolding kinetics reveals that the average pKa of the histidine residues, including His-24, is closely similar in the folding transition state to the value found in the molten globule intermediate. Consequently, protonation of His-24 is not a barrier to refolding of the molten globule to the native protein. Instead, the normal pKa of His-24 in the transition state, coupled with its inaccessibility in the native state, promotes fast unfolding at low pH. The analysis of the wild-type results is confirmed and extended by using the wild-type parameters to fit the unfolding kinetics of a mutant lacking His-24.

Ultrafast diffraction and structural dynamics: The nature of complex molecules far from equilibrium

Studies of molecular structures at or near their equilibrium configurations have long provided information on their geometry in terms of bond distances and angles. Far-from-equilibrium structures are relatively unknown—especially for complex systems—and generally, neither their dynamics nor their average geometries can be extrapolated from equilibrium values. For such nonequilibrium structures, vibrational amplitudes and bond distances play a central role in phenomena such as energy redistribution and chemical reactivity. Ultrafast electron diffraction, which was developed to study transient molecular structures, provides a direct method for probing the nature of complex molecules far from equilibrium. Here we present our ultrafast electron diffraction observations of transient structures for two cyclic hydrocarbons. At high internal energies of ≈4 eV, these molecules display markedly different behavior. For 1,3,5-cycloheptatriene, excitation results in the formation of hot ground-state structures with bond distances similar to those of the initial structure, but with nearly three times the average vibrational amplitude. Energy is redistributed within 5 ps, but with a negative temperature characterizing the nonequilibrium population. In contrast, the ring-opening reaction of 1,3-cyclohexadiene is shown to result in hot structures with a C—C bond distance of over 1.7 Å, which is 0.2 Å away from any expected equilibrium value. Even up to 400 ps, energy remains trapped in large-amplitude motions comprised of torsion and asymmetric stretching. These studies promise a new direction for studying structural dynamics in nonequilibrium complex systems.