# Unfolding under Pressure: An NMR Perspective

Annalisa Pastore, Piero Andrea Temussi

► To cite this version:

Annalisa Pastore, Piero Andrea Temussi. Unfolding under Pressure: An NMR Perspective. Chem-BioChem, 2023, 24 (16), pp.e202300164. 10.1002/cbic.202300164. hal-05094708

HAL Id: hal-05094708

https://hal.science/hal-05094708v1

Submitted on 3 Jun 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# Unfolding under Pressure: An NMR Perspective

Annalisa Pastore*<sup>[a, b]</sup> and Piero Andrea Temussi*<sup>[c]</sup>

This review aims to analyse the role of solution nuclear magnetic resonance spectroscopy in pressure-induced in vitro studies of protein unfolding. Although this transition has been neglected for many years because of technical difficulties, it provides important information about the forces that keep protein structure together. We first analyse what pressure unfolding is, then provide a critical overview of how NMR spectroscopy has contributed to the field and evaluate the

observables used in these studies. Finally, we discuss the commonalities and differences between pressure-, cold- and heat-induced unfolding. We conclude that, despite specific peculiarities, in both cold and pressure denaturation the important contribution of the state of hydration of nonpolar side chains is a major factor that determines the pressure dependence of the conformational stability of proteins.

## Introduction

Understanding why and how proteins fold or resist unfolding are two major directly intertwined challenges of modern biology. The transition of proteins from the ordered folded state to the unordered (unfolded) state can be induced by many causes, both in vivo and in vitro. Despite the attraction of in vivo studies, in vitro unfolding remains an important tool that has allowed generations of biophysicists to obtain information on this transition under controlled conditions and to understand the forces involved in the process.

In vitro studies can be roughly divided into those in which the unfolding agent is chemical and those in which it is physical.[1] The two agent types are intrinsically very different. At the base of the action of chemical unfolding agents there is inevitably a strong interaction between them and proteins, particularly when the protein is in the unfolded state.[2] However, the presence of concentrated chemical unfolding agents, such as the classical urea and guanidinium hydrochloride, has no direct counterpart in in vivo situations since no organism lives under these extreme conditions. It is thus hard to infer intrinsic tendencies of a protein to fold or unfold on the basis of chemical unfolding. On the contrary, the action of physical agents does not involve strong interactions with other molecules. The two main physical agents used to

unfold proteins in vitro are temperature and pressure. Proteins unfold when the temperature is raised (heat unfolding) but also when it is decreased (cold denaturation).[3,4] Unfolding caused by increase of pressure generally requires a rise from ambient pressure by thousands of bars. While most proteins do not usually experience extreme conditions, these studies can have direct biological relevance as they can for instance inform on the different forces that are experienced by proteins in thermophile, cryophile and barophile organisms as compared to the mesophile homologues.[5]

Initial in vitro studies, both using temperature and pressure perturbations, were performed with methods addressing global structural features, that is, the whole secondary and/or tertiary structure, for instance using circular dichroism spectroscopy or intrinsic fluorescence.[6] The possibility of using nuclear magnetic resonance spectroscopy has extended unfolding studies to the behaviour of individual residues, providing a sequence-specific map of local unfolding.[7,8] While protein unfolding has widely been analysed by NMR at high and, in more recent times, at low temperature,[9,10] still relatively few studies have addressed pressure unfolding by NMR, probably because of the technical difficulties to obtain this transition, plus the fact that the topic is often considered only a niche field, with relatively little direct interest for biological and/or biotechnological applications.

The present review aims at filling this gap by critically analysing the information obtained for the pressure unfolding transition by NMR and demonstrate how this technique can inform on important aspects of protein unfolding, among which the mechanism of unfolding at high pressure as compared to that of temperature (heat and cold) unfolding.

## What Is Pressure Unfolding?

It is common knowledge that, when exposed to hydrostatic pressures of thousands of bars, proteins lose their three-dimensional structure, that is, they unfold. The first studies on unfolding induced by a strong increase of pressure were published in the 1970s by Hawley[11] and by Zipp and

<figure><img src="image_3.png" /></figure>

<footnote>[a] A. Pastore
European Synchrotron Radiation Facilities
71 Ave des Martyrs, 38000 Grenoble (France)</footnote>

<footnote>[b] A. Pastore
The Wohl Institute,
King's College London
5 Cutcombe Rd, SE59RT London (UK)
E-mail: annalisa.1.pastore@kcl.ac.uk</footnote>

<footnote>[c] P. A. Temussi
University Federico II
via Cynthia, 80110 Naples (Italy)
E-mail: temussi@unina.it</footnote>

<footnote>© 2023 The Authors. ChemBioChem published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.</footnote>
<figure><img src="image_4.png" /></figure>

Kauzmann.[12] In the 1980s, most experimental studies on proteins under pressure were continued in the laboratory of Hui Ben Hoa.[13] Protein high-pressure NMR spectroscopy was pioneered in the 1990s by Jonas and Jonas[14] and then more recently expanded by several other authors.[15-18] All of these researchers assumed it to be obvious, as thermodynamics requires, that, in the pressure-induced unfolding process, the volume of the unfolded species must be smaller than that of the corresponding folded species. However, very little is known about the folded and unfolded states during the very long lag phase before transition, that is, in the region between the pressure of 1 bar (0.1 MPa) and those (of several kilobar) that determine unfolding. An interesting hint can be found in the first paper describing pressure unfolding. Hawley[11] quoted earlier papers on the influence of pressure on proteins: "pressure denaturation of proteins exhibits some unusual and interesting characteristics. It has been observed, for example, that while very high pressures (7500 atm or ca. 750 MPa) invariably produce protein denaturation, moderate pressures (1000 atm or ca. 10 MPa) may stabilise the native form, thereby increasing the temperature required for heat denaturation".[19,20] What these words suggest is that the first effect of increasing pressure could be to have an intermediate state, still folded, more compact and therefore more stable at moderated values of pressure. This conjecture might look counterintuitive for some if we applied the very idea of le Chatelier's principle according to which we should think that the unfolded state should be in equilibrium with the folded state in a simple two-way situation. This is certainly true but it might also be reasonable to think that the events occurring in the initial phase of the unfolded population versus pressure curve might not host at all the unfolded state. More work will be needed to explore the Hawley's hypothesis.

## How Can Pressure NMR Be Achieved?

Several different approaches have been applied to reach high pressures on the NMR spectrometer that, of course, have largely evolved through time. Early designs for high-pressure NMR spectroscopy were based on a setup called the "autoclave" method in which the entire radio frequency transmitter and detection coils were placed in a high-pressure nonmagnetic

vessel.[21] This approach allowed to reach pressures of about 9 kbar (900 MPa) but was hardly compatible with some of the hardware and did not allow multidimensional NMR.[22] An alternative approach was based on pressure-resistant sample cells, instead of pressure-resistant probes. This could be used on any commercial NMR probes and allowed the measurement of multidimensional and multinuclear experiments with high field homogeneity but required the delicate hand-made manufacturing of quartz cells and fairly concentrated protein samples.[15,23]

In the 1990s, large-volume NMR tubes were developed using either sapphire or ceramic tubes with a safety valve.[24]

Currently, the high-pressure sample cells commercially available are made of aluminium-toughened zirconia and mounted on a self-sealing nonmagnetic valve (Daedalus Innovation™). These tubes can reach pressures as high as up to 300 MPa and can be used on any commercial NMR probe with a sensitivity of about 50% that of standard 3 mm diameter NMR tubes. Pressure is transmitted by mineral oil. Despite the smaller range of pressures reachable, these cells provide a flexible and convenient tool that greatly facilitate pressure NMR studies. For a more detailed description of these designs the reader can refer to the exhaustive review by Roche et al.[25]

## What Can We Learn about Pressure Unfolding by NMR?

When comparing studies of protein unfolding caused by different physical forces, it is immediately clear that the data available for pressure unfolding regard a much smaller number of proteins than for both heat and cold denaturation, even though the latter is a poorly described phenomenon.[1,10,26] This is partly due to the technical difficulties of spectroscopic measurements at high hydrostatic pressure, in particular for NMR studies, as well illustrated by Roche et al.[25] Another difference that is immediately clear is the use of different parameters to monitor unfolding. The great majority of studies on protein unfolding with techniques other than NMR characterises the transition from the folded to the unfolded states using a single averaged parameter: for instance, in studies monitoring temperature unfolding by circular dichroism or

<figure><img src="image_5.png" /></figure>

Piero Andrea Temussi is a visiting professor at King's College London. He was a professor of chemistry at the University of Naples Federico II from 1963 to 2010. In 2019, he became a member of the Academia Europaea. He has published more than 200 primary publications and was one of the first scientists to introduce biological NMR spectroscopy in Italy. His past interests centred on opioid peptides and sweet compounds. More recently, he has developed an interest in protein folding and molecular crowding.

<figure><img src="image_6.png" /></figure>

Annalisa Pastore is a physical chemist by training currently working at the European Synchrotron Radiation Facility of Grenoble and is also a visiting professor at King's College London. Over the last 30 years, she has been a structural biologist who has used different and complementary biochemical, biophysical and bioinformatics tools. Her research focuses mainly on the study of the structural biology of neuroscience and neurodegeneration. She was elected an EMBO member in 2000 and a member of the Academia Europaea in 2013.
fluorescence, the process is usually described by the temperature at which there is the coexistence of equal amounts of the two states. This temperature is described as the transition midpoint and is usually indicated as Tm. This parameter was mainly used as a measure of protein temperature stability. The possibility of using this parameter in lieu of the more conventional and natural difference of free energy (ΔG) was suggested in the seminal paper by Becktel and Schellman,[3] with precise indications of its limitations, but it was then generally adopted also in cases in which it is not strictly applicable.[27] Interestingly, a similar parameter was not adopted in pressure-induced studies among early studies; that is, very few papers on pressure unfolding adopted a similar criterion based on the pressure at which the folded and unfolded populations are equal. Different criteria to study the process were followed instead as detailed in the next paragraph.

## How Is Pressure Unfolding Characterised in NMR Studies?

As described by Dubois et al.,[18] the consequences of pressure perturbation on proteins have been studied for many years by means of optical spectroscopies such as circular dichroism,[28] fluorescence,[29] or FTIR spectroscopy[30] that by their very nature yield global information on the state of the system, essentially on the relative populations of the folded and unfolded states at a given pressure. Similarly to the optical spectroscopies quoted above, global information on protein folding can also be obtained by measuring the area of the so-called ring-shifted peaks of 1D NMR spectra.[9,10] In addition, multidimensional (2D) NMR provides multiple probes in the protein structure, giving access to local, residue-specific information.[7]

In most cases of unfolding studies, it is possible to assume a two-state equilibrium in which the changes of population of either folded or unfolded forms (F or U) are well fitted by a sigmoidal curve. In unfolding studies caused by temperature variations it was shown[7,31] that the fitting of the sigmoidal curves can be best performed using a modified Gibbs Helmholtz equation (1):

$$ \Delta G = \Delta H_m \left[ 1 - \frac{T}{T_m} \right] + \Delta C_p \left\{ (T - T_m) - T \ln \left[ \frac{T}{T_m} \right] \right\} $$

Dubois et al.[18] showed that in pressure unfolding studies it is possible to derive an equation relating the populations of folded and unfolded studies to the free energy and the pressure variation.

If one chooses to follow the increase with pressure of a resonance corresponding to the unfolded species in the 1D NMR spectrum, lF stands for the intensity of the corresponding NMR line in the folded spectrum at 1 bar (0.1 MPa; lF = lmin), whereas lu corresponds to the intensity of the same line at high pressure, when the protein is fully unfolded (lu = lmax).

The equilibrium Equation (2) is:

$$ K_{eq} = \frac{U}{F} = \frac{l_F - l}{l - l_u} $$

Combining this equation with equations that give the free energy changes from F to U at pressure p and p0 (p0 = 1 bar) gives the characteristic equation (3) for a two-state equilibrium:

$$ I = \frac{l_F + l_u e^{-[\Delta G^0 + (p - p^0)\Delta V^0]/RT}}{1 + e^{-[\Delta G^0 + (p - p^0)\Delta V^0]/RT}} $$

Where ΔV0 is the partial molar volume change.

## An Historical Excursus of Protein Unfolding by NMR

If we consider the historical work by the group of Jiri Jonas, one of the first of these papers dealt with the influence of pressure on lysozyme.[32] The authors studied the pressure unfolding of lysozyme, with and without the presence of a substrate (tri-N-acetylglucosamine), using the resonances of five residues, His15, Leu17, Trp28, Cys64 and Trp108, and calculated the reaction volumes (ΔV) for each residue. The equilibrium constants (Ka) were measured from peak areas (H15_ε1 has both folded and unfolded peaks visible in a slow exchange regime). The data of folded and unfolded populations can be plotted in linear form as ln Keq versus pressure. The equilibrium constants for denaturation (Keq) were calculated from the NMR data as follows:

$$ K_{eq} = \frac{\% \text{ denatured form}}{\% \text{ native form}} $$

The slopes of the lines are related to ΔV, the reaction volume, by [Eq. (4)]

$$ p \Delta V = RT \ln K_{eq} $$

where p is pressure, R is the gas constant, and T is temperature in Kelvin.

Small but statistically significant differences in ΔV were found for residues located in different regions of the protein. The possibility to detect these differences for individual residues was considered the main result of these experiments. While this conclusion might look obvious after thirty years, it was certainly not trivial at the time.

The values of equilibrium constants found in this pressure unfolding work were consistent with those quoted in the literature.[33] Great emphasis was also given to the values of reaction values, also called partial molar volume change, for individual residues (ΔV0). The importance of these values for unfolding was probably exaggerated. It is not clear whether there is a relationship between the influence of pressure on reaction values and unfolding. To make a simple comparison, there is no obvious relationship between the influence of
<figure><img src="image_7.png" /></figure>

temperature on the mobility of side chains (often external) and temperature unfolding, which is crucially dependent on the behaviour of core residues.

The emphasis on individual $\Delta V$ values was also exploited in a paper, dealing with both NMR and fluorescence, published at about the same time,[34] where the authors investigated the effects of substituting Cys residues with Gly in the pressure denaturation of staphylococcal nuclease. The authors studied distinct interconverting conformations arising from the population of both cis and trans Xaa-Pro peptide bonds (His46-Pro47 and Lys116-Pro117) which are summarised in Evans et al.[35] These conformations did not reveal any simple relationship between the position of the cis/trans equilibrium in the folded state and the heterogeneity of the fluorescence decay.

However, the specific dynamic properties of each mutant, as revealed by time-resolved fluorescence, did appear to be correlated with the partial molar volume changes of denaturation of the specific residue. Mutation to glycines of either (or both) of the prolines that exhibited structural heterogeneity greatly altered the stability of the protein.

Great efforts were also put into a theme very popular at the same time, that is, the so-called molten globule state. This folding intermediate, described as a collapsed state with secondary but not tertiary structure, was very much in fashion in the 1990s, whereas has now lost much of its original emphasis. Peng et al.[36] studied different denatured states of the Arc repressor and found that increasing pressure triggered sequential structural variations of the repressor. Upon increasing pressure (up to 5.0 kbar or 500 MPa), the native dimer dissociated and formed a denatured monomer with all features typical of a molten globule: the aromatic region of the 1D $^1H$ NMR spectra of the pressure-induced monomer of Arc repressor underwent a substantial line broadening with strong overlap of the resonances, indicating the presence of a number of different interconverting conformations in an intermediate exchange rate regime (Figure 1). The chemical shifts were considerably different from those of the native dimer as well as from those of the thermally or chemically unfolded monomer. Retention of substantial secondary structure was indicated by the presence of several nuclear Overhauser effects (NOEs) in two-dimensional

NOESY spectra. Some of the NOEs were observed in the $\beta$-sheet region of the spectrum, suggesting that the inter-subunit $\beta$-sheet (residues 6–14) in the native dimer would be replaced by an intra-molecular $\beta$-sheet. The pressure-induced state was also fairly compact at variance with the high temperature and urea unfolded states which were shown to be both less structured and more expanded conformations. This study was interesting because it illustrated the almost unique potentialities of pressure unfolding, with respect to other types of unfolding, to stabilise and characterise folding intermediates.

## Pressure Jump Experiments: The New Frontier

In 1995, Vidugiris et al.[37] studied staphylococcal nuclease by pressure jump experiments, on the belief that direct information about the structural properties of the transition state could be obtained from determination of the activation volumes for the folding and unfolding transitions.[37] The authors found that the volume of the protein-solvent system is larger in the transition state than in either the folded or unfolded states and concluded that their results also supported a molten globule-like model for the transition state of the nuclease in which the polypeptide chain is in a collapsed, loosely packed, solvent-excluded structure. This article was followed by a few other studies of pressure unfolding in which pressure jump experiments were used, albeit mainly followed by spectroscopic techniques different from NMR.

For instance, Kitahara et al.[38] reported the real-time observation of pressure-jump unfolding kinetics carried out by fluorescence and complemented by 2D NMR spectroscopy on a small oncogene product, P13$^{MTCP1}$ (Figure 2). Below approximately 200 MPa, pressure caused continuous, nonlinear shifts of many of the $^{15}$N and $^1H$ correlations, suggesting the presence of folded conformers in rapid equilibrium with the basic native structure. Above approximately 200 MPa, pressure caused a sharp decrease in the intensity of the folded protein signals, while the peaks corresponding to disordered structures increased, yielding a free energy of unfolding variation of $6.0 \text{ kcal mol}^{-1}$ and an associated volume change of $-100 \text{ mL mol}^{-1}$, in agreement with the fluorescence result.

The paucity of pressure-jump NMR experiments was probably due to the difficulty of coordinating pressure jumps with

<figure><img src="image_8.png" /><figcaption>**Figure 1.** Schematic representation of the pressure-induced dissociation of the native dimer of the arc repressor (PDB ID: 1ARQ) to a molten-globule monomer through dissociation of the $\beta$-sheet (indicated with a dashed box). The process was highlighted by a substantial broadening of the NMR spectra. The picture is adapted and interpreted from ref. [36]. Copyright: 1993, National Academy of Science.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 2.** Steady-state fluorescence of the intrinsic tryptophan emission and high-pressure NMR was used by Kitahara et al. to carry out equilibrium pressure-induced unfolding studies to look for alternative folded conformers of P13$^{MTCP1}$. The two techniques concomitantly indicated the formation of a kinetic unfolding intermediate.</figcaption></figure>
<figure><img src="image_10.png" /></figure>

intrinsic times of pulse sequences. In 2011, Kremer et al.[39] introduced an innovative way to generate pressure jump experiments inside the very radio frequency pulse sequences. They designed a microprocessor-controlled pressure jump unit that is able to introduce fast, strong pressure changes at any point of a pulse sequence. Repetitive pressure changes of 80 MPa in the sample tube are thus feasible in less than 30 ms. Two general forms of these experiments were proposed: the pressure perturbation transient state spectroscopy (PPTSS) and the pressure perturbation state correlation spectroscopy (PPSCS). PPTSS can be used to measure the rate constants and the activation energies and activation volumes for the transition between different conformational states including the folded and unfolded state of proteins, for polymerisation-depolymerisation processes, and for ligand binding at atomic resolution. PPSCS spectroscopy correlates the NMR parameters of different pressure-induced states of the system, thus allowing the measurement of properties of a given pressure induced state such as a folding intermediate in a different state, for example, the folded state.

Possible applications of PPTSS proposed in the article are the determination of rate constants in folding/unfolding experiments. In PPSCS, rapid pressure changes inside the pulse sequence can be used to correlate spin states at different pressures. An example for such a PPSCS experiment is the application of a pressure jump in a [¹H,¹⁵N] HSQC at the interface between t₁ and t₂ time evolution. The experiment allows the correlation of chemical shifts of all protein amide groups at one pressure with the corresponding chemical shifts at another pressure.

To demonstrate both types of experiments, Kremer et al.[39] presented the application of PPTSS and of PPSCS to the pressure-induced denaturation/refolding of an active centre mutant of the histidine-containing phosphocarrier protein (HPr) protein from *Staphylococcus carnosus*.40) They observed the results by 1D NMR spectroscopy after increasing the pressure from ambient pressure to 80 MPa and vice versa.

The rapid switch of pressure was improved by a brilliant hardware development.[41] These authors started by the consideration that it had proven difficult to safely jump the pressure in an NMR sample cell by kilobar amounts faster than the time required for protein folding. To circumvent this limitation, they succeeded in developing a system that is capable of rapidly (1–3 ms) switching back and forth between 1 bar (0.1 MPa) and pressures as high as 2.7 kbar (270 MPa). This process can be repeated tens of thousands of times, only limited by mechanical wear of the system. When applied to folding and unfolding processes of a pressure sensitised ubiquitin, their method provided interesting insights on these processes.[41] They for instance studied the state of proteins abruptly transferred from high pressure (2.5 kbar or 250 MPa) to ambient pressure to examine the recovered unfolded state at ambient temperature. The authors found that "At first sight, the unfolded ubiquitin structure under native conditions behaves rather similar to the pressure-denatured state and to a fully disordered 'random coil'." This conclusion was motivated by the fact that secondary chemical shifts did not show any significant correlation to the

corresponding ones of the folded state. In addition, they found that amide relaxation rates are similar to those of the protein denatured by 8 M urea.[42] As reported by these authors, plateau values in the central part of the ubiquitin sequence, are R₁ = 1.57 s⁻¹ and R₂ = 3.48 ± 0.50 s⁻¹. These values are much lower than those expected for a structured protein, and reflect the unfolded character of ubiquitin at pH 2 and 8 M urea.

This observation is interesting from a chemical physics point of view as it confirms that the unfolded state promoted by chemical denaturants behaves like a synthetic polymer, because their hydrogen bonding groups are completely saturated by the denaturant.

## Cold Denaturation Studies of Proteins at High Pressure

Another interesting aspect of high-pressure studies is the possibility to access protein cold denaturation. The first observation that low temperatures can lower the stability of proteins is as old as 1930 when Hopkins[43] observed that the rate of denaturation of ovalbumin by urea is higher at zero degrees than at ambient temperature and rationalised on the basis of the stability curve, that is the plot of ΔG as a function of temperature, introduced by Becktel and Schellman[3] and by the Russian scientist Privalov.[4] Based on thermodynamics concepts, Privalov theorised that all proteins undergo both cold and heat transition, but the former is much less accessible because most mesophile proteins cold denature at temperatures well below the water freezing point at ambient pressure. The possibility to observe cold denaturation more easily by increasing the pressure is explained by the fact that at high pressure it is possible to study water solutions below zero degrees without water freezing. Zhang et al.[44] studied for instance the reversible cold, heat, and pressure unfolding of RNase A and the RNase A-inhibitor complex by 1D and 2D ¹H NMR spectroscopy. It is important to note that the effect of increasing the pressure is not simply to decrease the temperature of water freezing but also, and more importantly, to *increase* the cold denaturation temperature of the protein, as described in several papers.[45] There is an apparent synergy between temperature decrease and pressure increase, hinting at a common denaturation mechanism (Figure 3). In other words, it seems plausible that the effect of pressure is also to favour the interaction of water molecules with hydrophobic groups, thus making it possible to have this interaction at higher temperatures.

The reversible pressure denaturation experiments in the pressure range from 1 bar (or 0.1 MPa) to 5 kbar (or 500 MPa) were carried out at pH 2.0 and 10 °C. The cold denaturation was carried out at 3 kbar (300 MPa), cooling down the protein solution to –25 °C without freezing. The experimental data allowed the authors to construct the pressure versus temperature phase diagram of RNase A. The data suggested the possibility that all three denaturation processes (cold, heat, and pressure) lead to non-cooperative unfolding of this protein. The
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 3.** Phase diagram of RNase A at pH 2.0 (inspired by Figure 7 of Zhang et al.[44]).</figcaption></figure>

appearance of a new histidine resonance in the cold-denatured and pressure-denatured RNase A spectra, compared to the absence of this resonance in the heat-denatured state, indicated that the pressure- and cold-denatured states, but not the heat-denatured state, may contain partially folded intermediates. Stable hydrogen-bonded structures protecting the backbone amide hydrogens from solvent exchange were observed in the pressure-denatured state.

The same protein was also studied by Yamaguchi et al.[46] These authors used the His epsilon proton resonances as reporter groups to measure fractions of folded and unfolded species. Gibbs energy differences were obtained as functions of pressure for different temperatures and as functions of temperature for different pressures. The volume increase upon unfolding, ΔV, was negative and temperature-dependent, decreasing from −10 mLmol⁻¹ at 7.5 °C to −30 mLmol⁻¹ at 37 °C. From the least-squares fitting of the experimental Gibbs energy differences to a theoretical expression holding pressure and ΔCp, they determined best-fit values of ΔG, ΔH, ΔS and ΔCp for different values of pressure in the temperature range 7.5 to 40 °C. The authors found that ΔCp is pressure dependent, decreasing from 1.79 kcalmol⁻¹K⁻¹ at 1 atm (0.1 MPa) to 1.08 kcalmol⁻¹K⁻¹ at 2000 atm (ca. 200 MPa). The paper of Yamaguchi[46] introduced a significant change in the parameters used to describe pressure induced unfolding because it described the whole process on rigorous thermodynamic terms, including the use of stability curves.[3] This choice determined a trend, since most papers on pressure unfolding published afterwards adopted a similar approach, also because a large number of contributions during the last fifteen years come from the same Akasaka laboratory. Similar approaches were anyway adopted also in other laboratories.[47]

## Mechanism of Unfolding under Pressure

As seen in the pressure studies described above, there has been a constant search for all possible causes that can lead to a decrease in the volume of the folded state in the pressure-induced transition. In the paper by Yamaguchi et al.,[46] an interesting suggestion is that the state of hydration of nonpolar side-chains upon unfolding of the protein is a major factor that

determines the pressure dependence of the conformational stability of a protein. A few years later, a theoretical paper proposed explicitly that pressure denaturation of proteins can be explained by the pressure destabilisation of hydrophobic aggregates.[48] The validity of a common mechanism for cold denaturation and pressure unfolding has been more recently supported by a detailed MD study of a 32 monomer polymer.[49]

This hypothesis was contrasted by a different proposal advanced by Frye and Royer.[50] These authors investigated the pressure-induced unfolding of a three-point mutant of S-nase in which the internal cavity size was altered. The experimentally determined volume changes of unfolding for the mutants suggested that loss of internal void volume upon unfolding could represent the major contributing factor to the value of the volume change of S-nase unfolding. In support of this suggestion, the authors quoted their previous work that demonstrated that for S-nase, neither "electrostriction" of charged and polar groups that become exposed to solvent upon unfolding nor polar or nonpolar hydration contributes significantly to the value of the volume change of unfolding.[51] The experimentally determined volume changes of unfolding for the S-nase mutant studied in 1998 suggested that loss of internal void volume upon unfolding could represent the major contributing factor to the value of the volume change of S-nase unfolding.

This suggestion was followed up in several papers[52–55] and is often regarded as the basic explanation of pressure unfolding. At the basis of this approach there is the belief that the changes from a folded to an unfolded state can be followed monotonously starting from the structure of the folded state. However, there is no evidence that other mechanisms of unfolding follow a similar pathway. In particular, this belief is contrary to the mechanism of temperature unfolding that is based on the disruption of the hydrophobic core mediated by the increased molecular motions.[4]

From a thermodynamic perspective, that is valid both for cold and heat unfolding, albeit with different origins, was clearly explained by Privalov[4] (Figure 4). This author wrote, "An important consequence of the fact that the van der Waals and

<figure><img src="image_13.png" /><figcaption>**Figure 4.** Pictorial representation of Privalov's theory on the effects of cold denaturation. When the temperature is decreased, the hydrophobic forces decrease, while hydration becomes increasingly important up to the opening of the hydrophobic core and unfolding. We would argue that a similar model could be extended to pressure unfolding.</figcaption></figure>
<figure><img src="image_14.png" /></figure>

hydration effects contribute to the hydrophobic effect with opposite signs is the biphasic character of this integral effect. Indeed, since the van der Waals interaction is a short range one and the hydration effect is a long range one, it is evident that the 'hydrophobic interaction' should be attractive at short distances and repulsive at long distances (exceeding the size of a water molecule). This might be one of the reasons for the extreme cooperativity of the tightly packed native protein domain which is disrupted in the 'all-or-none' way and always involves the penetration of water inside the protein structure." The author thus indicated that the nature of the unfolded ensemble can be seen as a direct consequence of a similar catastrophic "explosion" of the hydrophobic core, which can be considered as independent from what happens during the lag phase. Accordingly, Zhou and Hall[56] suggested the formation of an unfolded state formed by a completely disordered "necklace" chain, whose volume would indeed be smaller than that of the folded state.

It seems likely that also pressure-induced unfolding follows a similar route, as proposed by Hummer et al., who suggested the similarity between cold and pressure unfolding.[48] An indirect confirmation of this similarity comes from experiments on Yfh1, a protein that undergoes cold denaturation in (quasi)physiological conditions at temperatures above water freezing.[10] In the case of Yfh1, we have shown that the mechanism of unfolding can be attributed in great part to the presence, on the surface, of an electrostatic hinge that favours the entrance of water molecules toward the hydrophobic core when decreasing the temperature.[57,58] We recently studied the pressure unfolding of this protein by fluorescence studies based on the intrinsic fluorescence of the two tryptophan residues in the sequence.[59] We found significant peculiarities: pressure unfolding of Yfh1 occurs at pressures far smaller than those exhibited by most proteins. The midpoint of the transition for Yfh1 lies in fact around 100 bar (or 10 MPa).[59] as compared to the 1–2 kbar (or 100–200 MPa) observed on other systems. It is thus tempting to attribute the facility of pressure unfolding of the protein to the presence of the hinge that favours the entrance of water molecules, consistent with a mechanism of unfolding based on the disruption of the hydrophobic core by water molecules at moderate pressures. A more detailed analysis of the mechanism awaits the use of NMR to understand how the transition might occur.

## Conclusions

In this review, we have discussed pressure unfolding and how NMR can contribute to our understanding of the mechanisms that determine the transition. We have also compared pressure unfolding with cold and heat denaturation, analysing differences and commonalities. We have shown that the sequence of events may be very different in different types of unfolding. In heat-induced unfolding, increasing temperature induces increasing motion while stabilising the hydrophobic forces, until the entropic component becomes prevalent, and the structure unfolds. In cold denaturation, the hydrophobic forces become

increasingly weaker, while interactions with the solvent increase because the enthalpy of interaction of water with nonpolar residues increases as temperature decreases,[4] up to opening of the core and unfolding. Pressure unfolding would occur instead first by favouring the attracting forces (hydrophobic and electrostatic) by compression, and then suddenly, through a catastrophic event, by deforming the structure to the point of implosion as a consequence of the entrance of water molecules into the hydrophobic core. Despite the specific peculiarities, it is clear that hydration plays a key role in both cold and pressure-induced unfolding, suggesting that these transitions, although intrinsically different, rely on similar essential aspects. More studies are nevertheless needed to determine the molecular details of these transitions.

## Acknowledgements

We are greatly indebted to Christian Roumestand of the University of Montpellier and Judith Peters of the University of Grenoble Alps for helpful discussions.

## Conflict of Interests

The authors declare no conflict of interest.

## Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

**Keywords:** biophysics · frataxin · NMR spectroscopy · pressure · protein unfolding · Yfh1

[1] L. J. Lapidus, *F1000Research* **2017**, *6*, 1723.

[2] H. Gong, G. D. Rose, *Proc. Natl. Acad. Sci. USA* **2008**, *105*, 3321–6.

[3] W. J. Becktel, J. A. Schellman, *Bopolymers*. **1987**, *26*, 1859–77.

[4] P. L. Privalov, *Crit. Rev. Biochem. Mol. Biol*. **1990**, *25*, 281–305.

[5] R. Jaenicke, *Eur. J. Biochem*. **1991**, *202*, 715–28.

[6] A. S. Politou, A. Pastore, P. A. Temussi, *ChemPhysChem* **2022**, *23*, e202100520.

[7] R. Puglisi, O. Brylski, C. Alfano, S. R. Martin, A. Pastore, P. A. Temussi, *Commun. Chem.* **2020**, *3*, 100.

[8] R. Puglisi, G. Karunanithy, D. F. Hansen, A. Pastore, P. A. Temussi, *Commun. Chem.* **2021**, *4*, s42004-021-00566-3.

[9] T. Szyperski, J. L. Mills, D. Perl, J. Balbach, *Eur. Biophys. J.* **2006**, *35*, 363–6.

[10] A. Pastore, S. R. Martin, A. Politou, K. C. Kondapalli, T. Stemmler, P. A. Temussi, *J. Am. Chem. Soc.* **2007**, *129*, 5374–5.

[11] S. A. Hawley, *Biochemistry* **1971**, *10*, 2436–42.

[12] A. Zipp, W. Kauzmann, *Biochemistry* **1973**, *12*, 4217–28.

[13] G. Hui Bon Hoa, P. Douzou, N. Dahan, C. Balny, *Anal. Biochem.* **1982**, *120*, 125–35.

[14] J. Jonas, A. Jonas, *Annu. Rev. Biophys. Biomol. Struct.* **1994**, *23*, 287–318.

[15] K. Akasaka, *Chem. Rev.* **2006**, *106*, 1814–35.

[16] H. R. Kalbitzer, *Subcell. Biochem.* **2015**, *72*, 179–97.

[17] J. Roche, M. Dellarole, C. A. Royer, C. Roumestand, *Subcell. Biochem.* **2015**, *72*, 261–78.

[18] C. Dubois, I. Herrada, P. Barthe, C. Roumestand, *Molecules* **2020**, *25*, 5551.
<figure><img src="image_15.png" /></figure>

[19] F. H. Johnson, D. H. Campbell, *J. Biol. Chem.* **1946**, *163*, 689-98.

[20] C. Suzuki, K. Kitamura, K. Suzuki, J. Osugi, *Rev. Phys. Chem. Jap.* **1962**, *32*, 30.

[21] G. B. Benedek, E. M. Purcell, *J. Chem. Phys.* **22**, 1954, 2003-2012.

[22] L. Ballard, C. Reiner, J. Jonas, *J. Magn. Reson.* **1996**, *123*, 81-86.

[23] M. W. Lassalle, K. Akasaka, *Methods Mol. Biol.* **2007**, *350*, 21-38.

[24] M. B. Erlach, C. E. Munte, W. Kremer, R. Hartl, D. Rochelt, D. Niesner, H. R. Kalbitzer, *J. Magn. Reson.* **2010**, *204*, 196-199.

[25] J. Roche, C. A. Royer, C. Roumestand, *Prog. Nucl. Magn. Reson. Spectrosc.* **2017**, *102-103*, 15-31.

[26] M. Adrover, V. Esposito, G. Martorell, A. Pastore, P. A. Temussi, *J. Am. Chem. Soc.* **2010**, *132*, 16240-6.

[27] A. Pastore, P. A. Temussi, *J. Am. Chem. Soc.* **2022**, *144*, 22352-22357.

[28] M. T. Lerch, J. Horwitz, J. McCoy, W. L. Hubbell, *Proc. Natl. Acad. Sci. USA* **2013**, *110*, E4714-22.

[29] M. Dellarole, C. A. Royer, *Methods Mol. Biol.* **2014**, *1076*, 53-74.

[30] J. Torrent, P. Rubens, M. Ribó, K. Heremans, M. Vilanova, *Protein Sci.* **2001**, *10*, 725-34.

[31] S. R. Martin, V. Esposito, P. De Los Rios, A. Pastore, P. A. Temussi, *J. Am. Chem. Soc.* **2008**, *130*, 9963-70.

[32] S. D. Samarasinghe, D. M. Campbell, A. Jonas, J. Jonas, *Biochemistry* **1992**, *31*, 7773-8.

[33] R. E. Wedin, M. Delepierre, C. M. Dobson, F. M. Poulsen, *Biochemistry* **1982**, *21*, 1098-103.

[34] C. A. Royer, A. P. Hinck, S. N. Loh, K. E. Prehoda, X. Peng, J. Jonas, J. L. Markley, *Biochemistry* **1993**, *32*, 5222-32.

[35] P. A. Evans, C. M. Dobson, R. A. Kautz, G. Hatfull, R. O. Fox, *Nature* **1987**, *329*, 266-8.

[36] X. Peng, J. Jonas, J. L. Silva, *Proc. Natl. Acad. Sci. USA* **1993**, *90*, 1776-80.

[37] G. J. Vidugiris, J. L. Markley, C. A. Royer, *Biochemistry* **1995**, *34*, 4909-12.

[38] R. Kitahara, C. Royer, H. Yamada, M. Boyer, J. L. Saldana, K. Akasaka, C. Roumestand, *J. Mol. Biol.* **2002**, *320*, 609-28.

[39] W. Kremer, M. Arnold, C. E. Munte, R. Hartl, M. B. Erlach, J. Koehler, A. Meier, H. R. Kalbitzer, *J. Am. Chem. Soc.* **2011**, *133*, 13646-51.

[40] A. Möglich, B. Koch, W. Gronwald, W. Hengstenberg, E. Brunner, H. R. Kalbitzer, *Eur. J. Biochem.* **2004**, *271*, 4815-24.

[41] C. Charlier, T. R. Alderson, J. M. Courtney, J. Ying, P. Anfinrud, A. Bax, *Proc. Natl. Acad. Sci. USA* **2018**, *115*, E4169-E4178.

[42] J. Wirmer, W. Peti, H. Schwalbe, *J. Biomol. NMR* **2006**, *35*, 175-86.

[43] F. G. Hopkins, *Nature* **1930**, *126*, 383.

[44] J. Zhang, X. Peng, A. Jonas, J. Jonas, *Biochemistry* **1995**, *34*, 8631-41.

[45] J. Jonas, *Biochim. Biophys. Acta* **2002**, *1595*, 145-59.

[46] T. Yamaguchi, H. Yamada, K. Akasaka, *J. Mol. Biol.* **1995**, *250*, 689-94.

[47] I. Herrada, P. Barthe, M. Vanheusden, K. DeGuillen, L. Mammri, S. Delbecq, F. Rico, C. Roumestand, *Biophys. J.* **2018**, *115*, 341-352.

[48] G. Hummer, S. Garde, A. E. Garcia, M. E. Paulaitis, L. R. Pratt, *Proc. Natl. Acad. Sci. USA* **1998**, *95*, 1552-5.

[49] P. Das, S. Matysiak, *J. Phys. Chem. B* **2012**, *116*, 5342-8.

[50] K. J. Frye, C. A. Royer, *Protein Sci.* **1998**, *7*, 2217-22.

[51] K. J. Frye, C. S. Perman, C. A. Royer, *Biochemistry* **1996**, *35*, 10234-9.

[52] Y. O. Kamatari, L. J. Smith, C. M. Dobson, K. Akasaka, *Biophys. Chem.* **2011**, *156*, 24-30.

[53] Roche J, Caro JA, Norberto DR, Barthe P, Roumestand C, Schlessman JL, Garcia AE, Garcia-Moreno BE, Royer CA, *Proc. Natl. Acad. Sci. USA* **2012**, *109*, 6945-50.

[54] N. V. Nucci, B. Fuglestad, E. A. Athanasoula, A. J. Wand, *Proc. Natl. Acad. Sci. USA* **2014**, *111*, 3846-51.

[55] M. Xue, T. Wakamoto, C. Kejlberg, Y. Yoshimura, T. A. Nielsen, M. W. Risør, K. W. Sanggaard, R. Kitahara, F. A. A. Mulder, *Proc. Natl. Acad. Sci. USA* **2019**, *116*, 21031-21036.

[56] Y. Zhou, C. K. Hall, *Biopolymers* **1996**, *38*, 273-284.

[57] D. Sanfelice, R. Puglisi, S. R. Martin, L. Di Bari, A. Pastore, P. A. Temussi, *PLoS One* **2014**, *9*, e95801.

[58] A. Bitonti, R. Puglisi, M. Meli, S. R. Martin, G. Colombo, P. A. Temussi, A. Pastore, *J. Am. Chem. Soc.* **2022**, *144*, 7198-7207.

[59] R. Puglisi, P. Cioni, E. Gabellieri, G. Presciuttini, A. Pastore, P. A. Temussi, *Biophys. J.* **2022**, *121*, 1502-1511.

Revised manuscript received: May 6, 2023

Accepted manuscript online: May 8, 2023

Version of record online: May 8, 2023