How large are the volume changes accompanying protein transitions and binding?

The Protein Unfolded State: One, No One and One Hundred Thousand

Many in vitro studies, in which proteins have been unfolded by the action of a variety of physical or chemical agents, have led to the definition of a folded versus an unfolded state and to the question of what is the nature of the unfolded state. The unstructured nature of this state could suggest that "the" unfolded state is a unique entity which holds true for all kinds of unfolding processes. This assumption has to be questioned because the unfolding processes under different stress conditions are dictated by entirely different mechanisms. As a consequence, it can be easily understood that the final state, generically referred to as "the unfolded state", can be completely different for each of the unfolding processes. The present review examines recent data on the characteristics of the unfolded states emerging from experiments under different conditions, focusing specific attention to the level of compaction of the unfolded species.

Crowding revisited: Open questions and future perspectives

Although biophysical studies have traditionally been performed in diluted solutions, it was pointed out in the late 1990s that the cellular milieu contains several other macromolecules, creating a condition of molecular crowding. How crowding affects protein stability is an important question heatedly discussed over the past 20 years. Theoretical estimations have suggested a 5-20°C effect of fold stabilisation. This estimate, however, is at variance with what has been verified experimentally that proposes only a limited increase of stability, opening the question whether some of the assumptions taken for granted should be reconsidered. The present review critically analyses the causes of this discrepancy and discusses the limitations and implications of the current concept of crowding.

Interaction of the new inhibitor paxlovid (PF-07321332) and ivermectin with the monomer of the main protease SARS-CoV-2: A volumetric study based on molecular dynamics, elastic networks, classical thermodynamics and SPT

The COVID-19 pandemic has accelerated the study of drugs, most notably ivermectin and more recently Paxlovid (PF-07321332) which is in phase III clinical trials with experimental data showing covalent binding to the viral protease Mpro. Theoretical developments of catalytic site-directed docking support thermodynamically feasible non-covalent binding to Mpro. Here we show that Paxlovid binds non-covalently at regions other than the catalytic sites with energies stronger than reported and at the same binding site as the ivermectin B1a homologue, all through theoretical methodologies, including blind docking. We volumetrically characterize the non-covalent interaction of the ivermectin homologues (avermectins B1a and B1b) and Paxlovid with the mMpro monomer, through molecular dynamics and scaled particle theory (SPT). Using the fluctuation-dissipation theorem (FDT), we estimated the electric dipole moment fluctuations at the surface of each of complex involved in this study, with similar trends to that observed in the interaction volume. Using fluctuations of the intrinsic volume and the number of flexible fragments of proteins using anisotropic and Gaussian elastic networks (ANM+GNM) suggests the complexes with ivermectin are more dynamic and flexible than the unbound monomer. In contrast, the binding of Paxlovid to mMpro shows that the mMpro-PF complex is the least structurally dynamic of all the species measured in this investigation. The results support a differential molecular mechanism of the ivermectin and PF homologues in the mMpro monomer. Finally, the results showed that Paxlovid despite beingbound in different sites through covalent or non-covalent forms behaves similarly in terms of its structural flexibility and volumetric behaviour.

Conformational Rearrangements in the Redox Cycling of NADPH-Cytochrome P450 Reductase from Sorghum bicolor Explored with FRET and Pressure-Perturbation Spectroscopy

Simple Summary

NADPH-cytochrome P450 reductase (CPR) enzymes are known to undergo an ample conformational transition between the closed and open states in the process of their redox cycling. To explore the conformational landscape of CPR from the potential biofuel crop Sorghum bicolor (SbCPR), we incorporated a FRET donor/acceptor pair into the enzyme and employed rapid scanning stop-flow and pressure perturbation spectroscopy to characterize the equilibrium between its open and closed states at different stages of the redox cycle. Our results suggest the presence of several open conformational sub-states differing in the system volume change associated with the opening transition (ΔV⁰). Although the closed conformation always predominates in the conformational landscape, the population of the open conformations increases by order of magnitude upon the two-electron reduction and the formation of the disemiquinone state of the enzyme. In addition to elucidating the functional choreography of plant CPRs, our study demonstrates the high exploratory potential of a combination of the pressure-perturbation approach with the FRET-based monitoring of protein conformational transitions.

Abstract

NADPH-cytochrome P450 reductase (CPR) from Sorghum bicolor (SbCPR) serves as an electron donor for cytochrome P450 essential for monolignol and lignin production in this biofuel crop. The CPR enzymes undergo an ample conformational transition between the closed and open states in their functioning. This transition is triggered by electron transfer between the FAD and FMN and provides access of the partner protein to the electron-donating FMN domain. To characterize the electron transfer mechanisms in the monolignol biosynthetic pathway better, we explore the conformational transitions in SbCPR with rapid scanning stop-flow and pressure-perturbation spectroscopy. We used FRET between a pair of donor and acceptor probes incorporated into the FAD and FMN domains of SbCPR, respectively, to characterize the equilibrium between the open and closed states and explore its modulation in connection with the redox state of the enzyme. We demonstrate that, although the closed conformation always predominates in the conformational landscape, the population of open state increases by order of magnitude upon the formation of the disemiquinone state. Our results are consistent with several open conformation sub-states differing in the volume change (ΔV⁰) of the opening transition. While the ΔV⁰ characteristic of the oxidized enzyme is as large as −88 mL/mol, the interaction of the enzyme with the nucleotide cofactor and the formation of the double-semiquinone state of CPR decrease this value to −34 and −18 mL/mol, respectively. This observation suggests that the interdomain electron transfer in CPR increases protein hydration, while promoting more open conformation. In addition to elucidating the functional choreography of plant CPRs, our study demonstrates the high exploratory potential of a combination of the pressure-perturbation approach with the FRET-based monitoring of protein conformational transitions.

Denaturant- or ligand-induced change in protein volume by pressure shift assay

A complete thermodynamic description of protein-ligand binding includes parameters related to pressure and temperature. The changes in protein volume and compressibility upon binding a ligand are pressure-related parameters that are...

Protein-Ligand Binding Volume Determined from a Single 2D NMR Spectrum with Increasing Pressure

Proteins undergo changes in their partial volumes in numerous biological processes such as enzymatic catalysis, unfolding–refolding, and ligand binding. The change in the protein volume upon ligand binding—a parameter termed the protein–ligand binding volume—can be extensively studied by high-pressure NMR spectroscopy. In this study, we developed a method to determine the protein–ligand binding volume from a single two-dimensional (2D) ¹H–¹⁵N heteronuclear single quantum coherence (HSQC) spectrum at different pressures, if the exchange between ligand-free and ligand-bound states of a protein is slow in the NMR time-scale. This approach required a significantly lower amount of protein and NMR time to determine the protein–ligand binding volume of two carbonic anhydrase isozymes upon binding their ligands. The proposed method can be used in other protein–ligand systems and expand the knowledge about protein volume changes upon small-molecule binding.

Characterization of the ergometric properties of commercial bioactive dairy peptides

The thermodynamic properties of bioactive peptides provide insights into their functional behavior and their biological efficacy. We conducted precise analyses of the density, the ultrasonic velocity and the relative attenuation of serial dilutions of three commercial dairy peptides prepared by enzymatic methods. From these we determined the partial specific volume and the partial specific adiabatic compressibility coefficient for the peptides. At concentrations greater than ~2.5 ​mg ​mL⁻¹, the apparent values for specific volume and adiabatic compressibility were constant, differing between the three peptides at ±3% for specific volume and ±70% for compressibility. Both specific volume and adiabatic compressibility were highly dependent on concentration, indicating the importance of precise low concentration measurements to obtain correct values for these thermodynamic parameters. From these parameters it was apparent that restructuring of water molecules around the peptides (and their associated counterions) led to compact solutes that were also incompressible. These thermodynamic analyses are critical for understanding how the properties and the beneficial effects of bioactive peptides are influenced by their chemical environment.

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Dissolved dairy peptide properties distinguishable from ergometric analyses.

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Specific volume and adiabatic compressibility evaluate bioactive peptide hydration.

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Commercial bioactive dairy peptides are compact and incompressible.

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Compactness and incompressibility of peptide affected by hydrogen-bonding amino acids.

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Solution concentration affects values of measured thermodynamic parameters.

Thermodynamic, kinetic, and structural parameterization of human carbonic anhydrase interactions toward enhanced inhibitor design

The aim of rational drug design is to develop small molecules using a quantitative approach to optimize affinity. This should enhance the development of chemical compounds that would specifically, selectively, reversibly, and with high affinity interact with a target protein. It is not yet possible to develop such compounds using computational (i.e., in silico) approach and instead the lead molecules are discovered in high-throughput screening searches of large compound libraries. The main reason why in silico methods are not capable to deliver is our poor understanding of the compound structure-thermodynamics and structure-kinetics correlations. There is a need for databases of intrinsic binding parameters (e.g., the change upon binding in standard Gibbs energy (ΔGint), enthalpy (ΔHint), entropy (ΔSint), volume (ΔVintr), heat capacity (ΔCp,int), association rate (ka,int), and dissociation rate (kd,int)) between a series of closely related proteins and a chemically diverse, but pharmacophoric group-guided library of compounds together with the co-crystal structures that could help explain the structure-energetics correlations and rationally design novel compounds. Assembly of these data will facilitate attempts to provide correlations and train data for modeling of compound binding. Here, we report large datasets of the intrinsic thermodynamic and kinetic data including over 400 primary sulfonamide compound binding to a family of 12 catalytically active human carbonic anhydrases (CA). Thermodynamic parameters have been determined by the fluorescent thermal shift assay, isothermal titration calorimetry, and by the stopped-flow assay of the inhibition of enzymatic activity. Kinetic measurements were performed using surface plasmon resonance. Intrinsic thermodynamic and kinetic parameters of binding were determined by dissecting the binding-linked protonation reactions of the protein and sulfonamide. The compound structure-thermodynamics and kinetics correlations reported here helped to discover compounds that exhibited picomolar affinities, hour-long residence times, and million-fold selectivities over non-target CA isoforms. Drug-lead compounds are suggested for anticancer target CA IX and CA XII, antiglaucoma CA IV, antiobesity CA VA and CA VB, and other isoforms. Together with 85 X-ray crystallographic structures of 60 compounds bound to six CA isoforms, the database should be of help to continue developing the principles of rational target-based drug design.

Uncovering dehydration in cytochrome c refolding from urea- and guanidine hydrochloride-denatured unfolded state by high pressure spectroscopy

To investigate the dehydration associated with protein folding, the partial molar volume changes for protein unfolding (ΔV_u) in cytochrome c (Cyt c) were determined using high pressure absorption spectroscopy. ΔV_u values for the unfolding to urea- and guanidine hydrochloride (GdnHCl)-denatured Cyt c were estimated to be 56±5 and 29±1 mL mol⁻¹, respectively. Considering that the volume change for hydration of hydrophobic groups is positive and that Cyt c has a covalently bonded heme, a positive ΔV_u reflects the primary contribution of the hydration of heme. Because of the marked tendency of guanidium ions to interact with hydrophobic groups, a smaller number of water molecules were hydrated with hydrophobic groups in GdnHCl-denatured Cyt c than in urea-denatured Cyt c, resulting in the smaller positive ΔV_u. On the other hand, urea is a relatively weak denaturant and urea-denatured Cyt c is not completely hydrated, which retains the partially folded structures. To unfold such partial structures, we introduced a mutation near the heme binding site, His26, to Gln, resulting in a negatively shifted ΔV_u (4±2 mL mol⁻¹) in urea-denatured Cyt c. The formation of the more solvated and less structured state in the urea-denatured mutant enhanced hydration to the hydrophilic groups in the unfolding process. Therefore, we confirmed the hydration of amino acid residues in the protein unfolding of Cyt c by estimating ΔV_u, which allows us to discuss the hydrated structures in the denatured states of proteins.

Binding of l-Argininamide to a DNA Aptamer: A Volumetric Study

We use a combination of volumetric and spectroscopic techniques to characterize the binding of l-argininamide to its aptamer, the 24-base DNA hairpin 5'-d(GATCGAAACGTAGCGCCTTCGATC)-3'. The binding causes increases in volume, Δ V, and adiabatic compressibility, Δ K_S, of 12 ± 7 cm³ mol^-1 bar and (73 ± 8) × 10^-4 cm³ mol^-1 bar^-1, respectively. These volumetric results combined with structural data reveal that the binding is accompanied by release of 73 ± 27 waters from the hydration shells of the interacting molecules to the bulk. We use the estimated change in hydration to estimate the hydration, Δ S_hyd, and configurational, Δ S_conf, contributions to the binding entropy. The large and unfavorable change in configurational entropy, Δ S_conf, is nearly compensated by a favorable change in the hydration contribution, Δ S_hyd.

Putting the Piezolyte Hypothesis under Pressure

A group of small molecules that stabilize proteins against high hydrostatic pressure has been classified as piezolytes, a subset of stabilizing cosolutes. This distinction would imply that piezolytes counteract the effects of high hydrostatic pressure through effects on the volumetric properties of the protein. The purpose of this study was to determine if cosolutes proposed to be piezolytes have an effect on the volumetric properties of proteins through direct experimental measurements of volume changes upon unfolding of model proteins lysozyme and ribonuclease A, in solutions containing varying cosolute concentrations. Solutions containing the proposed piezolytes glutamate, sarcosine, and betaine were used, as well as solutions containing the denaturants guanidinium hydrochloride and urea. Changes in thermostability were monitored using differential scanning calorimetry whereas changes in volume were monitored using pressure perturbation calorimetry. Our findings indicate that increasing stabilizing cosolute concentration increases the stability and transition temperature of the protein, but does not change the temperature dependence of volume changes upon unfolding. The results suggest that the pressure stability of a protein in solution is not directly affected by the presence of these proposed piezolytes, and so they cannot be granted this distinction.

The Emperor's new clothes: Myths and truths of in-cell NMR

In-cell NMR is a technique developed to study the structure and dynamical behavior of biological macromolecules in their natural environment, circumventing all isolation and purification steps. In principle, the potentialities of the technique are enormous, not only for the possibility of bypassing all purification steps but, even more importantly, for the wealth of information that can be gained from directly monitoring interactions among biological macromolecules in a natural cell. Here, we review critically the promises, successes and limits of this technique as it stands now. Interestingly, many of the problems of NMR in bacterial cells stem from the artificially high concentration of the protein under study whose overexpression is anyway necessary to select it from the background. This has, as a consequence, that when overexpressed, most globular proteins, do not show an NMR spectrum, limiting the applicability of the technique to intrinsically unfolded or specifically behaving proteins. The outlook for in-cell NMR of eukaryotic cells is more promising and is possibly the most attracting aspect for the future.

Quantifying non-specific interactions between flavour and food biomolecules

Non-specific protein–flavour interactions can be captured by assumption-free statistical thermodynamics.

Conformational Mobility in Cytochrome P450 3A4 Explored by Pressure-Perturbation EPR Spectroscopy

We used high hydrostatic pressure as a tool for exploring the conformational landscape of human cytochrome P450 3A4 (CYP3A4) by electron paramagnetic resonance and fluorescence spectroscopy. Site-directed incorporation of a luminescence resonance energy transfer donor-acceptor pair allowed us to identify a pressure-dependent equilibrium between two states of the enzyme, where an increase in pressure increased the spatial separation between the two distantly located fluorophores. This transition is characterized by volume change (ΔV°) and P1/2 values of -36.8 ± 5.0 mL/mol and 1.45 ± 0.33 kbar, respectively, which corresponds to a Keq° of 0.13 ± 0.06, so that only 15% of the enzyme adopts the pressure-promoted conformation at ambient pressure. This pressure-promoted displacement of the equilibrium is eliminated by the addition of testosterone, an allosteric activator. Using site-directed spin labeling, we demonstrated that the pressure- and testosterone-sensitive transition is also revealed by pressure-induced changes in the electron paramagnetic resonance spectra of a nitroxide side chain placed at position 85 or 409 of the enzyme. Furthermore, we observed a pressure-induced displacement of the emission maxima of a solvatochromic fluorophore (7-diethylamino-3-((((2-maleimidyl)ethyl)amino)carbonyl) coumarin) placed at the same positions, which suggests a relocation to a more polar environment. Taken together, the results reveal an effector-dependent conformational equilibrium between open and closed states of CYP3A4 that involves a pronounced change at the interface between the region of α-helices A/A' and the meander loop of the enzyme, where residues 85 and 409 are located. Our study demonstrates the high potential of pressure-perturbation strategies for studying protein conformational landscapes.

Protein Ensembles: How Does Nature Harness Thermodynamic Fluctuations for Life? The Diverse Functional Roles of Conformational Ensembles in the Cell

All soluble proteins populate conformational ensembles that together constitute the native state. Their fluctuations in water are intrinsic thermodynamic phenomena, and the distributions of the states on the energy landscape are determined by statistical thermodynamics; however, they are optimized to perform their biological functions. In this review we briefly describe advances in free energy landscape studies of protein conformational ensembles. Experimental (nuclear magnetic resonance, small-angle X-ray scattering, single-molecule spectroscopy, and cryo-electron microscopy) and computational (replica-exchange molecular dynamics, metadynamics, and Markov state models) approaches have made great progress in recent years. These address the challenging characterization of the highly flexible and heterogeneous protein ensembles. We focus on structural aspects of protein conformational distributions, from collective motions of single- and multi-domain proteins, intrinsically disordered proteins, to multiprotein complexes. Importantly, we highlight recent studies that illustrate functional adjustment of protein conformational ensembles in the crowded cellular environment. We center on the role of the ensemble in recognition of small- and macro-molecules (protein and RNA/DNA) and emphasize emerging concepts of protein dynamics in enzyme catalysis. Overall, protein ensembles link fundamental physicochemical principles and protein behavior and the cellular network and its regulation.

Hofmeister effect on thermo-responsive poly(propylene oxide): Role of polymer molecular weight and concentration

Although a vast amount of research has been dedicated to investigate the Hofmeister effect on the stability of polymer solutions, a clear understanding of the role of polymer properties in this phenomenon is still missing. Here, the Hofmeister effect of NaCl (destabilizing) and NaSCN (stabilizing) salts on aqueous solutions of poly(propylene oxide) (PPO) is studied. Four different molecular weights of PPO were investigated, to determine how the variation in the polymer coil size affects the Hofmeister effect. The investigation was further conducted for different PPO concentrations, in order to understand the effect of inter-chain interactions on the response to addition of salt. The temperature-driven phase separation of the solutions was monitored by differential scanning calorimetry, which provides the precise value of the phase separation temperature, as well as the enthalpy change accompanied with the transition. It was observed that increasing the molecular weight weakens the effect of the both salts, which is interpreted in terms of a scaling law between the molecular weight and the accessible surface area of the polymers. Increasing the PPO concentration further diminished the NaCl effect, but amplified the NaSCN effect. This difference is attributed to an electrostatic stabilization mechanism in the case of NaSCN.

Driving Forces in Pressure-Induced Protein Transitions

The molecular mechanisms underlying pressure-induced protein denaturation can be analyzed based on the pressure-dependent differences in the apparent volume occupied by amino acids inside the protein and when exposed to water in an unfolded conformation. This chapter presents a volumetric analysis of the peptide group and the 20 naturally occurring amino acid side chains in the interior of the native state, the micelle-like interior of the pressure-induced denatured state, and in the unfolded conformation modeled by low-molecular analogs of proteins. The transfer of a peptide group from the protein interior to water becomes increasingly favorable as pressure increases. This observation classifies solvation of peptide groups as a major driving force in pressure-induced protein denaturation. Polar side chains do not appear to exhibit significant pressure-dependent changes in their preference for the protein interior or solvent. The transfer of nonpolar side chains from the protein interior to water becomes more unfavorable as pressure increases. An inference can be drawn that a sizeable population of nonpolar side chains remains buried inside a solvent-inaccessible core of the pressure-induced denatured state. At elevated pressures this core, owing to the absence of structural constraints, may become packed almost as tightly as the interior of the native state. The presence and partial disappearance of large intraglobular voids is another driving force facilitating pressure-induced protein denaturation. Volumetric data presented here have implications for the kinetics of protein folding and shed light on the nature of the folding transition state ensembles.

Ultrasonic and densimetric characterization of the association of cyclic AMP with the cAMP-binding domain of the exchange protein EPAC1

We employed a combination of densimetric and ultrasonic velocimetric techniques to characterize the volumetric properties of the association of the cAMP-binding domain (CBD) of EPAC1 with cAMP at 25 °C in a pH 7.6 buffer. The binding of cAMP to the CBD of EPAC1 is accompanied by changes in volume, ΔV, and adiabatic compressibility, ΔKS, of -59 ± 4 cm(3) mol(-1) and (34 ± 9) × 10(-4) cm(3) mol(-1) bar(-1), respectively. We use these volumetric results in conjunction with the structural data to estimate a change in hydration, Δnh, accompanying the binding. We calculate that approximately 103 water molecules are released to the bulk from the associating surfaces of the protein and the ligand. This number is ∼30% larger than the number of water molecules in direct contact with the associating surfaces while also being within the error of our Δnh determination. Therefore, we conclude that cAMP binding to EPAC1 may involve, in addition to the waters from within the first coordination sphere, also some waters from the second coordination sphere of the protein and cAMP. Our analysis of the compressibility data reveals that the protein becomes more rigid and less dynamic upon the cAMP binding as reflected in a 4 ± 0.5% decrease in its intrinsic coefficient of adiabatic compressibility. Finally, we estimate the hydration, ΔShyd, and configurational, ΔSconf, contributions to the binding entropy, ΔSb. We find that the binding entropy is determined by the fine balance between the ΔShyd and ΔSconf terms. In general, we discuss insights that are derived from a combination of volumetric and structural properties, in particular, emphasizing how measured changes in volume and compressibility can be interpreted in terms of hydration and dynamic properties of EPAC1 in its apo- and holo-forms.

High-pressure macromolecular crystallography and NMR: status, achievements and prospects

Biomacromolecules are thermodynamic entities that exist in general as an equilibrium mixture of the basic folded state and various higher-energy substates including all functionally relevant ones. Under physiological conditions, however, the higher-energy substates are usually undetectable on spectroscopy, as their equilibrium populations are extremely low. Hydrostatic pressure gives a general solution to this problem. As proteins generally have smaller partial molar volumes in higher-energy states than in the basic folded state, pressure can shift the equilibrium toward the former substantially, and allows their direct detection and analysis with X-ray crystallography or NMR spectroscopy at elevated pressures. These techniques are now mature, and their status and selected applications are presented with future prospects.

Parsing partial molar volumes of small molecules: a molecular dynamics study

We used molecular dynamics (MD) simulations in conjunction with the Kirkwood-Buff theory to compute the partial molar volumes for a number of small solutes of various chemical natures. We repeated our computations using modified pair potentials, first, in the absence of the Coulombic term and, second, in the absence of the Coulombic and the attractive Lennard-Jones terms. Comparison of our results with experimental data and the volumetric results of Monte Carlo simulation with hard sphere potentials and scaled particle theory-based computations led us to conclude that, for small solutes, the partial molar volume computed with the Lennard-Jones potential in the absence of the Coulombic term nearly coincides with the cavity volume. On the other hand, MD simulations carried out with the pair interaction potentials containing only the repulsive Lennard-Jones term produce unrealistically large partial molar volumes of solutes that are close to their excluded volumes. Our simulation results are in good agreement with the reported schemes for parsing partial molar volume data on small solutes. In particular, our determined interaction volumes() and the thickness of the thermal volume for individual compounds are in good agreement with empirical estimates. This work is the first computational study that supports and lends credence to the practical algorithms of parsing partial molar volume data that are currently in use for molecular interpretations of volumetric data.

Volumetric measurements in binary solvents: theory to experiment

Interactions of proteins and protein groups with water-soluble cosolvents have been studied for the last 50 years with a variety of theoretical and experimental methods. The contribution of volumetric techniques to these studies is relatively modest, although volumetric properties of solutes are sensitive to the entire spectrum of solute-solvent and solute-cosolvent interactions. This deficiency is partly related to formidable experimental difficulties related to conducting volumetric measurements at high cosolvent concentrations and partly to the lack of the theoretical framework within which volumetric results can be rationalized in terms of solute-solvent and solute-cosolvent interactions. However, recent years have witnessed a revival of interest in application of the volumetric approach to characterization of solute-solvent interactions in protein solutions in binary mixtures. This review presents an overview of recent advances in the field, focusing on both the theoretical and the experimental developments. While presenting the current state of the art, it also outlines the strategy for future volumetric studies that will result in new insights into the old problem of interactions of proteins with protecting and denaturing osmolytes.

On the physical meaning of the isothermal titration calorimetry measurements in calorimeters with full cells

We have performed a detailed study of the thermodynamics of the titration process in an isothermal titration calorimeter with full cells. We show that the relationship between the enthalpy and the heat measured is better described in terms of the equation Δ H = W_inj + Q (where W_inj is the work necessary to carry out the titration) than in terms of ΔH = Q. Moreover, we show that the heat of interaction between two components is related to the partial enthalpy of interaction at infinite dilution of the titrant component, as well as to its partial volume of interaction at infinite dilution.

Study of the binding between lysozyme and C10-TAB: determination and interpretation of the partial properties of protein and surfactant at infinite dilution

This work examines the binding in aqueous solution, through the experimental determination of specific volumes and specific adiabatic compressibility coefficients, of decyltrimethylammonium bromide to lysozyme and to non-charged polymeric particles (which have been specially synthesized by emulsion polymerization). A method was developed to calculate the specific partial properties at infinite dilution and it was shown that a Gibbs-Duhem type equation holds at this limit for two solutes. With this equation, it is possible to relate the behavior of the partial properties along different binding types at a constant temperature. It was found that the first binding type, specific with high affinity, is related to a significant reduction of surfactant compressibility. The second binding type is accompanied by the unfolding of the protein and the third one is qualitatively identical to the binding of the surfactant to non-charged polymeric particles.

Hydration in protein folding: thermal unfolding/refolding of human serum albumin

Human serum albumin (HSA) is known to undergo both reversible and irreversible thermal unfolding and refolding, depending upon the experimental conditions (end temperature) at neutral pH. In this report we have used high precision densimetric and ultrasonic measurements to determine the apparent specific volume (phi v) and compressibility (phi k) of HSA at different unfolded and refolded states at two different end temperatures, 55 degrees C and 70 degrees C. The unfolded and refolded states were characterized using dynamic light scattering (DLS), circular dichroism (CD), picosecond-resolved fluorescence decay, and anisotropy of the single-tryptophan residue in HSA (Trp214). Both the unfolded states were allowed to refold by cooling wherein the former and latter processes were found to be reversible and irreversible, respectively, in nature. The results obtained from the densimetric and ultrasonic measurements reveal that the apparent specific volume and compressibility of the protein in the reversible protein unfolding process is preserved upon restoration of HSA to ambient temperature. However, a significant change in phi v and phi k occurs in the process of irreversible protein refolding (from 70 to 20 degrees C). The experimental observation is rationalized in terms of the exposure of domain IIA to an aqueous environment, resulting in the swelling of the protein to a higher hydrodynamic diameter. Our studies attempt to explore the extent of hydration associated with the structural integrity of the popular protein HSA.

Unfolding and refolding of bovine serum albumin at acid pH: ultrasound and structural studies

Serum albumin is the most abundant protein in the circulatory system. The ability of albumins to undergo a reversible conformational transition, observed with changes in pH, is conserved in distantly related species, suggesting for it a major physiological role possibly related to the transport of small molecules including drugs. We have followed changes of bovine serum albumin (BSA) in volume by densimetry and in adiabatic compressibility during its conformational transition from pH 7-2, using ultrasound measurements. In parallel, circular dichroism was measured. The volume and adiabatic compressibility decrease from pH 4 to 2. The change in ellipticity shows a decrease over the same pH range from 70% to 40% of its alpha-helix content. Sorbitol, at concentrations from 0 to 2 M, led to the progressive restoration of BSA volume and compressibility values, as well as a substantial recovery of its original alpha-helix content. This finding implies that the compressibility variation observed reflects the conformational changes during the transition. The mutual interactions of the mechanical properties and structural features of BSA reported here are important in biotechnology for research in material sciences and for the design and the development of new, tailor-made drug carriers.

Probing the Transition State Ensemble of a Protein Folding Reaction by Pressure-Dependent NMR Relaxation Dispersion

The F61A/A90G mutant of a redesigned form of apocytochrome b562 folds by an apparent two-state mechanism. We have used the pressure dependence of 15N NMR relaxation dispersion rate profiles to study the changes in volumetric parameters that accompany the folding reaction of this protein at 45 degrees C. The experiments were performed under conditions where the folding/unfolding equilibrium could be studied at each pressure without addition of denaturants. The exquisite sensitivity of the methodology to small changes in folding/unfolding rates facilitated the use of relatively low-pressure values (between 1 and 270 bar) so that pressure-induced changes to the unfolded state ensemble could be minimized. A volume change for unfolding of -81 mL/mol is measured (at 1 bar), a factor of 1.4 larger (in absolute value) than the volume difference between the transition state ensemble (TSE) and the unfolded state. Notably, the changes in the free energy difference between folded and unfolded states and in the activation free energy for folding were not linear with pressure. Thus, the difference in the isothermal compressibility upon unfolding (-0.11 mL mol(-1) bar(-1)) and, for the first time, the compressibility of the TSE relative to the unfolded state (0.15 mL mol(-1) bar(-1)) could be calculated. The results argue for a TSE that is collapsed but loosely packed relative to the folded state and significantly hydrated, suggesting that the release of water occurs after the rate-limiting step in protein folding. The notion of a collapsed and hydrated TSE is consistent with expectations based on earlier temperature-dependent folding studies, showing that the barrier to folding at 45 degrees C is entropic (Choy, W. Y.; Zhou, Z.; Bai, Y.; Kay, L. E. J. Am. Chem. Soc. 2005, 127, 5066-5072).

Dehydration in the Folding of Reduced Cytochrome c Revealed by the Electron-Transfer-Triggered Folding under High Pressure

We determined the activation volume associated with protein folding of reduced cytochrome c from the collapsed intermediate to the native state. The folding rate was followed by a change in the absorption (420 nm) at various pressures between 0.1 and 200 MPa and at various concentrations of denaturant (guanidine hydrochloride) between 3.2 and 4.0 M. Dependence of the folding rate on both these factors revealed that the activation volume at ambient pressure in the absence of denaturant is negative (DeltaVf0 = -14 (+/-8) cm3.mol-1). Such a negative activation volume can be accounted for by a decrease in volume resulting from the dehydration of hydrophobic groups, primarily the heme group. Dehydration, which increases the entropy of the protein system, compensates for a decrease in the entropy accompanying the formation of the more compact and ordered transition state. We, therefore, propose that the positive change in the activation entropy for the folding reaction is due to the dehydration of hydrophobic groups. Furthermore, dehydration entropically promotes the protein folding reaction.

Compressibility changes accompanying conformational transitions of apomyoglobin

We used high-precision density and ultrasonic velocity measurements to characterize the native (N), molten globule (MG), and unfolded (U) conformations of apomyoglobin. The molten globule states that were studied in this work include the MG(pH4)(NaCl) state observed at pH 4 and 20 mM NaCl, the MG(pH4)(NaTCA) state observed at pH 4 and 20 mM sodium trichloracetate (NaTCA), the MG(pH2)(NaCl) state observed at pH 2 and 200 mM NaCl, and the MG(pH2)(NaTCA) state observed at pH 2 and 20 mM NaTCA. We used our densimetric and acoustic data to evaluate changes in adiabatic compressibility associated with the acid- or salt-induced N-to-MG, MG-to-U, MG-to-MG, and U-to-MG transitions of the protein. The N-to-MG(pH4)(NaCl) and N-to-MG(pH4)(NaTCA) transitions are accompanied by decreases in compressibility of -(3.0 +/- 0.6) x 10(-6) and -(2.0 +/- 0.6) x 10(-6) cm3 g(-1)bar(-1), respectively. The N-to-MG(pH2)(NaCl) and N-to-MG(pH2)(NaTCA) transitions are associated with compressibility changes of -(4.9 +/- 1.1) x 10(-6) and (0.7 +/- 0.9) x 10(-6) cm3 g(-1) bar(-1), respectively. We interpret these data in terms of the degree of unfolding of the various molten globule forms of apomyoglobin. In general, our compressibility data reveal significant disparities between the various equilibrium molten globule states of apomyoglobin while also quantitatively characterizing each of these states. Volumetric insights provided by our data facilitate gaining a better understanding of the folding pathways, intermediates, and kinetics of apomyoglobin folding.

The Kirkwood–Buff theory and the effect of cosolvents on biochemical reactions

Cosolvents added to aqueous solutions of biomolecules profoundly affect protein stability, as well as biochemical equilibria. Some cosolvents, such as urea and guanidine hydrochloride, denature proteins, whereas others, such as osmolytes and crowders, stabilize the native structures of proteins. The way cosolvents interact with biomolecules is crucial information required to understand the cosolvent effect at a molecular level. We present a statistical mechanical framework based upon Kirkwood-Buff theory, which enables one to extract this picture from experimental data. The combination of two experimental results, namely, the cosolvent-induced equilibrium shift and the partial molar volume change upon the reaction, supplimented by the structural change, is shown to yield the number of water and cosolvent molecules bound or released during a reaction. Previously, denaturation experiments (e.g., m-value analysis) were analyzed by empirical and stoichiometric solvent-binding models, while the effects of osmolytes and crowders were analyzed by the approximate molecular crowding approach for low cosolvent concentration. Here we synthesize these previous approaches in a rigorous statistical mechanical treatment, which is applicable at any cosolvent concentration. The usefulness and accuracy of previous approaches was also evaluated.

The extended interface: measuring non-local effects in biomolecular interactions

Improvements in the sensitivity and availability of biophysical techniques for the detection of the formation of complexes in solution are revealing that the effects of binding are not restricted to the direct contacts between the biomolecules or even to a localised site. Rather, information about the binding event is transmitted throughout the biomolecules and the surrounding solution through changes in the hydrogen bonding, hydration and electrostatic field as the complex is formed. Calorimetric, volumetric and NMR methods are beginning to provide a quantitative view of the nature and thermodynamic consequences of this extended interface, and the resulting data pose a major challenge for computational models of binding.

Evolutionary Computer Programming of Protein Folding and Structure Predictions

In order to understand the mechanism of protein folding and to assist the rational de-novo design of fast-folding, non-aggregating and stable artificial enzymes it is very helpful to be able to simulate protein folding reactions and to predict the structures of proteins and other biomacromolecules. Here, we use a method of computer programming called "evolutionary computer programming" in which a program evolves depending on the evolutionary pressure exerted on the program. In the case of the presented application of this method on a computer program for folding simulations, the evolutionary pressure exerted was towards faster finding deep minima in the energy landscape of protein folding. Already after 20 evolution steps, the evolved program was able to find deep minima in the energy landscape more than 10 times faster than the original program prior to the evolution process.