Two-state folding over a weak free-energy barrier

We present a Monte Carlo study of a model protein with 54 amino acids that folds directly to its native three-helix-bundle state without forming any well-defined intermediate state. The free-energy barrier separating the native and unfolded states of this protein is found to be weak, even at the folding temperature. Nevertheless, we find that melting curves to a good approximation can be described in terms of a simple two-state system, and that the relaxation behavior is close to single exponential. The motion along individual reaction coordinates is roughly diffusive on timescales beyond the reconfiguration time for a single helix. A simple estimate based on diffusion in a square-well potential predicts the relaxation time within a factor of two.     

Ramachandran free-energy surfaces for disaccharides: trehalose, a case study

We present calculated potential of mean force surfaces for rotation about phi, psi dihedral angles of the alpha(1<-->1)alpha-glycosidic linkage in the disaccharide trehalose (alpha-D-Glc-(1<-->1)-alpha-D-Glc) in both vacuum and aqueous solution. The effects of aqueous solvation upon the alpha(1<-->1)alpha-glycosidic linkage are investigated through comparison of the vacuum and aqueous solution free-energy surfaces. These surfaces reveal that trehalose is restricted to a single minimum-energy conformation in both vacuum and solution. The exceptional rigidity of this disaccharide in solution may provide a molecular rationale for the antidesiccant properties of trehalose glasses.     

Docking enzyme-inhibitor complexes using a preference-based free-energy surface

We present a docking scheme that utilizes both a surface complementarity screen as well as an energetic criterion based on surface area burial. Twenty rigid enzyme/inhibitor complexes with known coordinate sets are arbitrarily separated and reassembled to an average all-atom rms (root mean square) deviation of 1.0 Å from the native complexes. Docking is accomplished by a hierarchical search of geometrically compatible triplets of surface normals on each molecule. A pruned tree of possible bound configurations is built up using successive consideration of larger and larger triplets. The best scoring configurations are then passed through a free-energy screen where the lowest energy member is selected as the predicted native state. The free energy approximation is derived from observations of surface burial by atom pairs across the interface of known enzyme/inhibitor complexes. The occurrence of specific atom-atom surface burial, for a set of complexes with well-defined secondary structure both in the bound and unbound states, is parameterized to mimic the free energy of binding. The docking procedure guides the inhibitor into its native state using orientation and distance-dependent functions that reproduce the ideal model of free energies with an average rms deviation of 0.9 kcal/mol. For all systems studied, this docking procedure identifies a single, unique minimum energy configuration that is highly compatible with the native state. © 1996 Wiley-Liss, Inc.     

Three-state protein folding: experimental determination of free-energy profile

When considering protein folding with a transient intermediate, a difficulty arises as to determination of the rates of separate transitions. Here we overcome this problem, using the kinetic studies of the unfolding/refolding reactions of the three-state protein apomyoglobin as a model. Amplitudes of the protein refolding kinetic burst phase corresponding to the transition from the unfolded (U) to intermediate (I) state, that occurs prior to the native state (N) formation, allow us to estimate relative populations of the rapidly converting states at various final urea concentrations. On the basis of these proportions, a complicated experimental chevron plot has been deconvolved into the urea-dependent rates of the I<-->N and U<-->N transitions to give the dependence of free energies of the main transition state and of all three (N, I, and U) stable states on urea concentration.     

Use of multistate Bennett acceptance ratio method for free-energy calculations from enhanced sampling and free-energy perturbation

Multistate Bennett acceptance ratio (MBAR) works as a method to analyze molecular dynamics (MD) simulation data after the simulations have been finished. It is widely used to estimate free-energy changes between different states and averaged properties at the states of interest. MBAR allows us to treat a wide range of states from those at different temperature/pressure to those with different model parameters. Due to the broad applicability, the MBAR equations are rather difficult to apply for free-energy calculations using different types of MD simulations including enhanced conformational sampling methods and free-energy perturbation. In this review, we first summarize the basic theory of the MBAR equations and categorize the representative usages into the following four: (i) perturbation, (ii) scaling, (iii) accumulation, and (iv) full potential energy. For each, we explain how to prepare input data using MD simulation trajectories for solving the MBAR equations. MBAR is also useful to estimate reliable free-energy differences using MD trajectories based on a semi-empirical quantum mechanics/molecular mechanics (QM/MM) model and ab initio QM/MM energy calculations on the MD snapshots. We also explain how to use the MBAR software in the GENESIS package, which we call mbar_analysis, for the four representative cases. The proposed estimations of free-energy changes and thermodynamic averages are effective and useful for various biomolecular systems.     

Multy-state protein: Determination of carbonic anhydrase free-energy landscape

Studies of the folding pathway of large proteins whose kinetics is complicated due to the formation of several intermediate states are most frequently impeded or totally impossible because of rapid folding phase occurring during instrument dead time. In this paper the obtaining of energy characteristics of one of such proteins—carbonic anhydrase B—is reported. Tryptophan fluorescence and absorption methods have been used to measure the folding and unfolding kinetics of carbonic anhydrase B at different urea concentrations. In spite of the fact that the formation of the initial intermediate state of this protein takes place during the instrument dead time, the population of this state has been estimated in a wide range of urea concentrations. The use of the population of the rapidly formed intermediate state and the effective rates of slow phases of the protein folding/unfolding permitted us to calculate free energies of all the protein states and the height of energy barriers between them. It has been shown that folding of carbonic anhydrase B can be described by a consecutive reaction scheme. The possibility to obtain energy characteristics of carbonic anhydrase would allow studying structural characteristics of both intermediate and transition states via site-directed mutations.     

Folding free-energy landscape of a 10-residue mini-protein, chignolin

Chignolin is an artificial mini-protein composed of 10 residues (GYDPETGTWG) that has been shown to cooperatively fold into a beta-hairpin structure in water. We extensively explored the conformational space of chignolin using a 180-ns multicanonical molecular dynamics (MD) simulation and analyzed its folding free-energy landscape. In the MD trajectory, we found structures that satisfy 99% of the experimental restraints and are quite close to the experimentally determined structures with C(alpha) root-mean-square-deviations of less than 0.5 Angstroms. These structures formed a large cluster in the conformational space with the largest probability of existence, agreeing well with the experiment.     

Amyloid beta-protein monomer folding: free-energy surfaces reveal alloform-specific differences

Alloform-specific differences in structural dynamics between amyloid β-protein (Aβ) 40 and Aβ42 appear to underlie the pathogenesis of Alzheimer's disease. To elucidate these differences, we performed microsecond timescale replica-exchange molecular dynamics simulations to sample the conformational space of the Aβ monomer and constructed its free-energy surface. We find that neither peptide monomer is unstructured, but rather that each may be described as a unique statistical coil in which five relatively independent folding units exist, comprising residues 1-5, 10-13, 17-22, 28-37, and 39-42, which are connected by four turn structures. The free-energy surfaces of both peptides are characterized by two large basins, comprising conformers with either substantial α-helix or β-sheet content. Conformational transitions within and between these basins are rapid. The two additional hydrophobic residues at the Aβ42 C-terminus, Ile41 and Ala42, significantly increase contacts within the C-terminus, and between the C-terminus and the central hydrophobic cluster (Leu17-Ala21). As a result, the β-structure of Aβ42 is more stable than that of Aβ40, and the conformational equilibrium in Aβ42 shifts towards β-structure. These results suggest that drugs stabilizing α-helical Aβ conformers (or destabilizing the β-sheet state) would block formation of neurotoxic oligomers. The atomic-resolution conformer structures determined in our simulations may serve as useful targets for this purpose. The conformers also provide starting points for simulations of Aβ oligomerization—a process postulated to be the key pathogenetic event in Alzheimer's disease.     

Electrostatic effects on the free-energy balance in folding a ribosome-inactivating protein

Electrostatics of globular proteins provides structural integrity as well as specificity of biological function. This dual role is particularly striking for ricin A-chain (RTA), an N-glycosidase which hydrolyzes a single adenine base from a conserved region of rRNA. The reported X-ray crystallographic structure of the RTA mutant E177A demonstrated a remarkable rescue of charge balance in the active site, achieved by the rotation of a second glutamic acid (Glu-208) into the vacated space. To understand this conformational reorganization, molecular-dynamics simulations were applied to estimate relative free energies that govern the thermodynamic stability of E177A together with mutants E177Q and E177D. The simulations anticipate that while E177A is a non-conservative substitution, the protein is more stable than the other two mutants. However, the structural plasticity of the RTA active site is not obtained penalty-free, rather E177A among the mutants shows the largest unfavorable net change in the electrostatic contribution to folding. Of the E177A folded state, reorganization of Glu-208 lowers the electrostatic cost of the free-energy change, yet interestingly, protein interactions oppose the rotational shift, while solvent effects favor the transition.     

Autologous cancer vaccine: a novel formulation

A novel cancer vaccine consisting of fixed autologous cancer tissue-fragments, microparticles encapsulating cytokines, and an adjuvant was developed. In a Phase I/IIa clinical trial, vaccination to patients after resection of hepatocellular carcinoma induced significantly longer time before the first recurrence than that in historical control patients operated in the same department (P < 0.05). This formulation will be promising against recurrence of many types of human cancers.     

Control, regulation and thermodynamics of free-energy transduction

The quantitative formalism called Metabolic Control Theory makes it possible to be precise in discussions of metabolic control. To illustrate this, I will mention 2 experimental systems where free energy is converted from one form to another, i.e., bacteriorhodopsin liposomes and mitochondrial oxidative phosphorylation. More specifically I shall discuss how the distribution of the control of fluxes, concentrations and potentials, among the various enzymes (catalysts) in these systems has been measured and how this distribution can be understood in terms of the enzyme properties. From the outset, Metabolic Control Theory was valid for branched metabolic pathways with non-linear kinetics. Yet, it seemed to be limited to metabolic pathways without enzyme-enzyme interactions and to steady states. It is now clear that these limitations were apparent only and recent extensions to Metabolic Control Theory deal explicitly with enzyme-enzyme interaction and with transient-time analysis. Other limitations are inherent. For instance, Metabolic Control Theory pays for its clarity and exactness by being limited to small modulations. Mosaic Non Equilibrium Thermodynamics and Biochemical System Analysis are formalisms that deal with larger changes, at the cost of accuracy and exactness.     

Spatially resolved free-energy contributions of native fold and molten-globule-like Crambin

The folding stability of a protein is governed by the free-energy difference between its folded and unfolded states, which results from a delicate balance of much larger but almost compensating enthalpic and entropic contributions. The balance can therefore easily be shifted by an external disturbance, such as a mutation of a single amino acid or a change of temperature, in which case the protein unfolds. Effects such as cold denaturation, in which a protein unfolds because of cooling, provide evidence that proteins are strongly stabilized by the solvent entropy contribution to the free-energy balance. However, the molecular mechanisms behind this solvent-driven stability, their quantitative contribution in relation to other free-energy contributions, and how the involved solvent thermodynamics is affected by individual amino acids are largely unclear. Therefore, we addressed these questions using atomistic molecular dynamics simulations of the small protein Crambin in its native fold and a molten-globule-like conformation, which here served as a model for the unfolded state. The free-energy difference between these conformations was decomposed into enthalpic and entropic contributions from the protein and spatially resolved solvent contributions using the nonparametric method Per|Mut. From the spatial resolution, we quantified the local effects on the solvent free-energy difference at each amino acid and identified dependencies of the local enthalpy and entropy on the protein curvature. We identified a strong stabilization of the native fold by almost 500 kJ mol⁻¹ due to the solvent entropy, revealing it as an essential contribution to the total free-energy difference of (53 ± 84) kJ mol⁻¹. Remarkably, more than half of the solvent entropy contribution arose from induced water correlations.     

Determination of the free-energy change for repair of a DNA phosphodiester bond

The repair of phosphodiester bonds in nicked DNA is catalyzed by DNA ligases. Ligation is coupled to cleavage of a phosphoanhydride bond in a nucleotide cofactor resulting in a thermodynamically favorable process. A free energy value for phosphodiester bond formation was calculated using the reversibility of the T4 DNA ligase reaction. The relative number of DNA nicks to phosphodiester bonds in a circular plasmid DNA, formed during this reaction at fixed concentrations of ATP to AMP and PP(i), was quantified. At 25 degrees C, pH 7, the equilibrium constant (K(eq)) for the ligation reaction is 3.89 x 10(4) m. This value corresponds to a standard free energy (DeltaG degrees ') of -6.3 kcal mol(-1). By subtracting the known energy contribution due to hydrolysis of ATP to AMP and PP(i), DeltaG degrees ' for the hydrolysis of a DNA phosphodiester bond is -5.3 kcal mol(-1).     

Disparate HDV ribozyme crystal structures represent intermediates on a rugged free-energy landscape

The hepatitis delta virus (HDV) ribozyme is a member of the class of small, self-cleaving catalytic RNAs found in a wide range of genomes from HDV to human. Both pre- and post-catalysis (precursor and product) crystal structures of the cis-acting genomic HDV ribozyme have been determined. These structures, together with extensive solution probing, have suggested that a significant conformational change accompanies catalysis. A recent crystal structure of a trans-acting precursor, obtained at low pH and by molecular replacement from the previous product conformation, conforms to the product, raising the possibility that it represents an activated conformer past the conformational change. Here, using fluorescence resonance energy transfer (FRET), we discovered that cleavage of this ribozyme at physiological pH is accompanied by a structural lengthening in magnitude comparable to previous trans-acting HDV ribozymes. Conformational heterogeneity observed by FRET in solution appears to have been removed upon crystallization. Analysis of a total of 1.8 µsec of molecular dynamics (MD) simulations showed that the crystallographically unresolved cleavage site conformation is likely correctly modeled after the hammerhead ribozyme, but that crystal contacts and the removal of several 2′-oxygens near the scissile phosphate compromise catalytic in-line fitness. A cis-acting version of the ribozyme exhibits a more dynamic active site, while a G-1 residue upstream of the scissile phosphate favors poor fitness, allowing us to rationalize corresponding changes in catalytic activity. Based on these data, we propose that the available crystal structures of the HDV ribozyme represent intermediates on an overall rugged RNA folding free-energy landscape.     

Understanding protein folding via free-energy surfaces from theory and experiment

The ability of protein molecules to fold into their highly structured functional states is one of the most remarkable evolutionary achievements of biology. In recent years, our understanding of the way in which this complex self-assembly process takes place has increased dramatically. Much of the reason for this advance has been the development of energy surfaces (landscapes), which allow the folding reaction to be described and visualized in a meaningful manner. Analysis of these surfaces, derived from the constructive interplay between theory and experiment, has led to the development of a unified mechanism for folding and a recognition of the underlying factors that control the rates and products of the folding process.     

Moving from Complaints to Action: Oppositional Consciousness and Collective Action in a Political Community

This article analyzes the process of youth political activism and development by drawing on ethnographic research on Asian and Pacific Islander youth activists. Young people revealed that collective action begins with a critical analysis of their lived experiences with inequalities. Their actions also involved oppositional consciousness that was nurtured in social justice-oriented community organizations. Tracking youth's successful efforts for school reform, I show how oppositional consciousness is realized and what activism looks like in practice.  [youth activism, oppositional consciousness, social–educational change, Asian and Pacific Islanders]     

Energy metabolism and ATP free-energy change of the intertidal wormSipunculus nudus below a critical temperature

The intertidal wormSipunculus nudus was exposed to various temperatures for an analysis of the integrated changes in energy and acid-base status. Animals were incubated in sea water or maintained for up to 8 days at 4 and 0°C while dwelling in the sediment. Cannulation of the animals prior to experimentation allowed the analysis of blood gas parameters ( , and pH). fell to 0 torr within 8 days at 0°C. A simultaneous reduction of ventilatory activity was derived from measurements of the pattern of coelomic fluid pressure changes associated with ventilatory movements. The increase in and an onset of anaerobic metabolism, indicated by the accumulation of end products like acetate and propionate both in the coelomic fluid and the body wall musculature, led to the development of a progressive acidosis and a deviation from the alphastat regulation of intracellular pH seen in unburied animals. The drop in intracellular pH together with the depletion of the adenylates and the phosphagen, phospho-l-arginine, reflect a significant decrease in the Gibb's free-energy change of ATP hydrolysis. These changes are interpreted to indicate lethal cold injuries, because recovery was not possible when the animals were returned to 12°C after more than 2 days of exposure to 0°C. A low critical temperature indicating the onset of cold-induced anaerobiosis is concluded to exist below 4°C owing to the insufficient response of the ventilatory system to the developing hypoxia.