Chaperonin-facilitated protein folding: optimization of rate and yield by an iterative annealing mechanism.

We develop a heuristic model for chaperonin-facilitated protein folding, the iterative annealing mechanism, based on theoretical descriptions of "rugged" conformational free energy landscapes for protein folding, and on experimental evidence that (i) folding proceeds by a nucleation mechanism whereby correct and incorrect nucleation lead to fast and slow folding kinetics, respectively, and (ii) chaperonins optimize the rate and yield of protein folding by an active ATP-dependent process. The chaperonins GroEL and GroES catalyze the folding of ribulose bisphosphate carboxylase at a rate proportional to the GroEL concentration. Kinetically trapped folding-incompetent conformers of ribulose bisphosphate carboxylase are converted to the native state in a reaction involving multiple rounds of quantized ATP hydrolysis by GroEL. We propose that chaperonins optimize protein folding by an iterative annealing mechanism; they repeatedly bind kinetically trapped conformers, randomly disrupt their structure, and release them in less folded states, allowing substrate proteins multiple opportunities to find pathways leading to the most thermodynamically stable state. By this mechanism, chaperonins greatly expand the range of environmental conditions in which folding to the native state is possible. We suggest that the development of this device for optimizing protein folding was an early and significant evolutionary event.

Prediction of the stability of DNA triplexes.

We present rules that allow one to predict the stability of DNA pyrimidine.purine.pyrimidine (Y.R.Y) triple helices on the basis of the sequence. The rules were derived from van't Hoff analysis of 23 oligonucleotide triplexes tested at a variety of pH values. To predict the enthalpy of triplex formation (delta H degrees), a simple nearest-neighbor model was found to be sufficient. However, to accurately predict the free energy of the triplex (delta G degrees), a combination model consisting of five parameters was needed. These parameters were (i) the delta G degrees for helix initiation, (ii) the delta G degrees for adding a T-A.T triple, (iii) the delta G degrees for adding a C(+)-G.C triple, (iv) the penalty for adjacent C bases, and (v) the pH dependence of the C(+)-G.C triple's stability. The fitted parameters are highly consistent with thermodynamic data from the basis set, generally predicting both delta H degrees and delta G degrees to within the experimental error. Examination of the parameters points out several interesting features. The combination model predicts that C(+) -G.C. triples are much more stabilizing than T-A.T triples below pH 7.0 and that the stability of the former increases approximately equal to 1 kcal/mol per pH unit as the pH is decreased. Surprisingly though, the most stable sequence is predicted to be a CT repeat, as adjacent C bases partially cancel the stability of one another. The parameters successfully predict tm values from other laboratories, with some interesting exceptions.

Dressed polyions, counterion condensation, and adsorption excess in polyelectrolyte solutions.

The phenomenon of Manning-Oosawa counterion condensation is given an explicit statistical mechanical and qualitative basis via a dressed polyelectrolyte formalism in connection with the topology of the electrostatic free-energy surface and is derived explicitly in terms of the adsorption excess of ions about the polyion via the nonlinear Poisson-Boltzmann equation. The approach is closely analogous to the theory of ion binding in micelles. Our results not only elucidate a Poisson-Boltzmann analysis, which shows that a fraction of the counterions lie within a finite volume around the polyion even if the volume of the system tends towards infinity, but also provide a direct link between Manning's theta-the number of condensed counterions for each polyion site-and a statistical thermodynamic quantity, namely, the adsorption excess per monomer.

Progress toward chemical accuracy in the computer simulation of condensed phase reactions.

We describe a procedure for the generation of chemically accurate computer-simulation models to study chemical reactions in the condensed phase. The process involves (i) the use of a coupled semiempirical quantum and classical molecular mechanics method to represent solutes and solvent, respectively; (ii) the optimization of semiempirical quantum mechanics (QM) parameters to produce a computationally efficient and chemically accurate QM model; (iii) the calibration of a quantum/classical microsolvation model using ab initio quantum theory; and (iv) the use of statistical mechanical principles and methods to simulate, on massively parallel computers, the thermodynamic properties of chemical reactions in aqueous solution. The utility of this process is demonstrated by the calculation of the enthalpy of reaction in vacuum and free energy change in aqueous solution for a proton transfer involving methanol, methoxide, imidazole, and imidazolium, which are functional groups involved with proton transfers in many biochemical systems. An optimized semiempirical QM model is produced, which results in the calculation of heats of formation of the above chemical species to within 1.0 kcal/mol (1 kcal = 4.18 kJ) of experimental values. The use of the calibrated QM and microsolvation QM/MM (molecular mechanics) models for the simulation of a proton transfer in aqueous solution gives a calculated free energy that is within 1.0 kcal/mol (12.2 calculated vs. 12.8 experimental) of a value estimated from experimental pKa values of the reacting species.

Barriers to protein folding: formation of buried polar interactions is a slow step in acquisition of structure.

In the MYL mutant of the Arc repressor dimer, sets of partially buried salt-bridge and hydrogen-bond interactions mediated by Arg-31, Glu-36, and Arg-40 in each subunit are replaced by hydrophobic interactions between Met-31, Tyr-36, and Leu-40. The MYL refolding/dimerization reaction differs from that of wild type in being 10- to 1250-fold faster, having an earlier transition state, and depending upon viscosity but not ionic strength. Formation of the wild-type salt bridges in a hydrophobic environment clearly imposes a kinetic barrier to folding, which can be lowered by high salt concentrations. The changes in the position of the transition state and viscosity dependence can be explained if denatured monomers interact to form a partially folded dimeric intermediate, which then continues folding to form the native dimer. The second step is postulated to be rate limiting for wild type. Replacing the salt bridge with hydrophobic interactions lowers this barrier for MYL. This makes the first kinetic barrier rate limiting for MYL refolding and creates a downhill free-energy landscape in which most molecules which reach the intermediate state continue to form native dimers.

Direct measurement of salt-bridge solvation energies using a peptide model system: implications for protein stability.

The solvation energies of salt bridges formed between the terminal carboxyl of the host pentapeptide AcWL- X-LL and the side chains of Arg or Lys in the guest (X) position have been measured. The energies were derived from octanol-to-buffer transfer free energies determined between pH 1 and pH 9. 13C NMR measurements show that the salt bridges form in the octanol phase, but not in the buffer phase, when the side chains and the terminal carboxyl group are charged. The free energy of salt-bridge formation in octanol is approximately -4 kcal/mol (1 cal = 4.184 J), which is equal to or slightly larger than the sum of the solvation energies of noninteracting pairs of charged side chains. This is about one-half the free energy that would result from replacing a charge pair in octanol with a pair of hydrophobic residues of moderate size. Therefore, salt bridging in octanol can change the favorable aqueous solvation energy of a pair of oppositely charged residues to neutral or slightly unfavorable but cannot provide the same free energy decrease as hydrophobic residues. This is consistent with recent computational and experimental studies of protein stability.

Protein-protein interaction: a genetic selection for compensating mutations at the barnase-barstar interface.

Barnase and barstar are trivial names of the extracellular RNase and its intracellular inhibitor produced by Bacillus amyloliquefaciens. Inhibition involves the formation of a very tight one-to-one complex of the two proteins. With the crystallographic solution of the structure of the barnase-barstar complex and the development of methods for measuring the free energy of binding, the pair can be used to study protein-protein recognition in detail. In this report, we describe the isolation of suppressor mutations in barstar that compensate for the loss in interaction energy caused by a mutation in barnase. Our suppressor search is based on in vivo selection for barstar variants that are able to protect host cells against the RNAse activity of those barnase mutants not properly inhibited by wild-type barstar. This approach utilizes a plasmid system in which barnase expression is tightly controlled to keep the mutant barnase gene silent. When expression of barnase is turned on, failure to form a complex between the mutant barnase and barstar has a lethal effect on host cells unless overcome by substitution of the wild-type barstar by a functional suppressor derivative. A set of barstar suppressors has been identified for barnase mutants with substitutions in two amino acid positions (residues 102 and 59), which are critically involved in both RNase activity and barstar binding. The mutations selected as suppressors could not have been predicted on the basis of the known protein structures. The single barstar mutation with the highest information content for inhibition of barnase (H102K) has the substitution Y30W. The reduction in binding caused by the R59E mutation in barnase can be partly reversed by changing Glu-76 of barstar, which forms a salt bridge with the Arg-59 in the wild-type complex, to arginine, thus completing an interchange of the two charges.

Least activation path for protein folding: investigation of staphylococcal nuclease folding by stopped-flow circular dichroism.

Is the pathway of protein folding determined by the relative stability of folding intermediates, or by the relative height of the activation barriers leading to these intermediates? This is a fundamental question for resolving the Levinthal paradox, which stated that protein folding by a random search mechanism would require a time too long to be plausible. To answer this question, we have studied the guanidinium chloride (GdmCl)-induced folding/unfolding of staphylococcal nuclease [(SNase, formerly EC 3.1.4.7; now called microbial nuclease or endonuclease, EC 3.1.31.1] by stopped-flow circular dichroism (CD) and differential scanning microcalorimetry (DSC). The data show that while the equilibrium transition is a quasi-two-state process, kinetics in the 2-ms to 500-s time range are triphasic. Data support the sequential mechanism for SNase folding: U3 <--> U2 <--> U1 <--> N0, where U1, U2, and U3 are substates of the unfolded protein and N0 is the native state. Analysis of the relative population of the U1, U2, and U3 species in 2.0 M GdmCl gives delta-G values for the U3 --> U2 reaction of +0.1 kcal/mol and for the U2 --> U1 reaction of -0.49 kcal/mol. The delta-G value for the U1 --> N0 reaction is calculated to be -4.5 kcal/mol from DSC data. The activation energy, enthalpy, and entropy for each kinetic step are also determined. These results allow us to make the following four conclusions. (i) Although the U1, U2, and U3 states are nearly isoenergetic, no random walk occurs among them during the folding. The pathway of folding is unique and sequential. In other words, the relative stability of the folding intermediates does not dictate the folding pathway. Instead, the folding is a descent toward the global free-energy minimum of the native state via the least activation path in the vast energy landscape. Barrier avoidance leads the way, and barrier height limits the rate. Thus, the Levinthal paradox is not applicable to the protein-folding problem. (ii) The main folding reaction (U1 --> N0), in which the peptide chain acquires most of its free energy (via van der Waals' contacts, hydrogen bonding, and electrostatic interactions), is a highly concerted process. These energy-acquiring events take place in a single kinetic phase. (iii) U1 appears to be a compact unfolded species; the rate of conversion of U2 to U1 depends on the viscosity of solution. (iv) All four relaxation times reported here depend on GdmCl concentrations: it is likely that none involve the cis/trans isomerization of prolines. Finally, a mechanism is presented in which formation of sheet-like chain conformations and a hydrophobic condensation event precede the main-chain folding reaction.

Crystal structure of the membrane-exposed domain from a respiratory quinol oxidase complex with an engineered dinuclear copper center.

Cytochrome oxidase is a membrane protein complex that catalyzes reduction of molecular oxygen to water and utilizes the free energy of this reaction to generate a transmembrane proton gradient during respiration. The electron entry site in subunit II is a mixed-valence dinuclear copper center in enzymes that oxidize cytochrome c. This center has been lost during the evolution of the quinoloxidizing branch of cytochrome oxidases but can be restored by engineering. Herein we describe the crystal structures of the periplasmic fragment from the wild-type subunit II (CyoA) of Escherichia coli quinol oxidase at 2.5-A resolution and of the mutant with the engineered dinuclear copper center (purple CyoA) at 2.3-A resolution. CyoA is folded as an 11-stranded mostly antiparallel beta-sandwich followed by three alpha-helices. The dinuclear copper center is located at the loops between strands beta 5-beta 6 and beta 9-beta 10. The two coppers are at a 2.5-A distance and symmetrically coordinated to the main ligands that are two bridging cysteines and two terminal histidines. The residues that are distinct in cytochrome c and quinol oxidases are around the dinuclear copper center. Structural comparison suggests a common ancestry for subunit II of cytochrome oxidase and blue copper-binding proteins.

Changing nucleosome positions through modification of the DNA rotational information.

The effects of the rotational information of DNA in determining the in vitro localization of nucleosomal core particles (ncps) have been studied in the Saccharomyces cerevisiae 5S rRNA repeat gene. We have altered the distribution of the phased series of flexibility signals present on this DNA by inserting a 25-bp tract, and we have analyzed the effects of this mutation on the distribution and on the frequencies of ncps, as compared with the wild type and a reference 21-bp insertion mutant. The variation of the standard free energy of nucleosome reconstitution was determined. The results show that the DNA rotational information is a major determinant of ncps positioning, define how many rotationally phased signals are required for the formation of a stable particle, and teach how to modify their distribution through the alteration of the rotational signals.

Simple model of protein folding kinetics.

A simple model of the kinetics of protein folding is presented. The reaction coordinate is the "correctness" of a configuration compared with the native state. The model has a gap in the energy spectrum, a large configurational entropy, a free energy barrier between folded and partially folded states, and a good thermodynamic folding transition. Folding kinetics is described by a master equation. The folding time is estimated by means of a local thermodynamic equilibrium assumption and then is calculated both numerically and analytically by solving the master equation. The folding time has a maximum near the folding transition temperature and can have a minimum at a lower temperature.

On the magnitude of the electrostatic contribution to ligand-DNA interactions.

A model based on the nonlinear Poisson-Boltzmann equation is used to study the electrostatic contribution to the binding free energy of a simple intercalating ligand, 3,8-diamino-6-phenylphenanthridine, to DNA. We find that the nonlinear Poisson-Boltzmann model accurately describes both the absolute magnitude of the pKa shift of 3,8-diamino-6-phenylphenanthridine observed upon intercalation and its variation with bulk salt concentration. Since the pKa shift is directly related to the total electrostatic binding free energy of the charged and neutral forms of the ligand, the accuracy of the calculations implies that the electrostatic contributions to binding are accurately predicted as well. Based on our results, we have developed a general physical description of the electrostatic contribution to ligand-DNA binding in which the electrostatic binding free energy is described as a balance between the coulombic attraction of a ligand to DNA and the disruption of solvent upon binding. Long-range coulombic forces associated with highly charged nucleic acids provide a strong driving force for the interaction of cationic ligands with DNA. These favorable electrostatic interactions are, however, largely compensated for by unfavorable changes in the solvation of both the ligand and the DNA upon binding. The formation of a ligand-DNA complex removes both charged and polar groups at the binding interface from pure solvent while it displaces salt from around the nucleic acid. As a result, the total electrostatic binding free energy is quite small. Consequently, nonpolar interactions, such as tight packing and hydrophobic forces, must play a significant role in ligand-DNA stability.

Effect of lactose solid-state on the aerosolization performance of drug-carrier mixtures

Lactose, in particular α-lactose monohydrate, is the most used carrier for inhalation. Its surface and solid-state properties are of paramount importance in determining drug aerosolization performance. However, these properties may be altered by processing, such as micronization, thus affecting the product performance and stability. The present research project focused on the study of the effect of lactose solid-state on the aerosolization performance of drug-carrier mixtures, giving particular attention to the impact of micronization on lactose physico-chemical properties. The formation of a fraction of hygroscopic anhydrous α-lactose, rather than amorphous lactose, as a consequence of the mechanical stress stemming from micronization was evidenced by 1H NMR, XRPD and DSC analyses performed on samples of micronized lactose. The development of a new DVS method capable to identify and quantify different forms of α-lactose (hygroscopic anhydrous, stable anhydrous and amorphous), even simultaneously present in the same sample, confirmed the results obtained with the above-mentioned techniques. The influence of lactose solid-state on drug respirability was then evaluated through the preparation and in vitro aerodynamic assessment of ternary and binary mixtures containing two different drugs. In particular, the use, as carriers, of anhydrous forms of α-lactose in place of the conventional α-lactose monohydrate resulted in significantly improved respirability in the case of salbutamol sulphate and poorer performance in the case of budesonide. In an attempt to rationalize the obtained results, IGC was selected as a tool to investigate possible variations in the surface energy of the studied lactose carriers and APIs. A direct correlation between the total surface free energy of lactose carriers and drug respirability was not found. However, salbutamol sulphate and budesonide exhibited different specific surface free energy, to which the difference in the aerosolization performance may be, at least in part, ascribed.

Equilibrium fluid-solid coexistence of hard spheres

We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibbs’ free energies depending on several crystalline order parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-solid interfaces). We are able to extrapolate to infinite volume the coexistence pressure [p_(co) = 11.5727(10)k_(B)T/σ^(3)] and the interfacial free energy [γ_({100}) = 0.636(11)k_(B)T/σ^(2)].

Tethered Monte Carlo: computing the effective potential without critical slowing down

We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two-dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L = 1024.