Introduction

As one of nature’s most abundant building blocks, protein materials exhibit properties including biocompatibility, mechanical tunability, and versatility for advanced applications1,2,3. However, the challenges of extraction and processing, which rely on harsh conditions or organic denaturants, often compromise protein integrity and introduce complexity to downstream applications4,5,6. As a consequence, over ten million tons of keratin-rich waste are generated annually and typically disposed of through incineration or landfilling7, regardless of their potential for applications ranging from textiles to tissue engineering scaffolds8,9. Alternatively, concentrated ions pairs such as lithium bromide (LiBr) have been proposed for decades to denature proteins like keratin and silk fibroin10,11. However, despite the substantial differences between inorganic ions and conventional organic denaturants such as urea or guanidinium, proteins denatured with LiBr are typically processed using similar methods, including dialysis or precipitation, which yield dispersed powders and consume large amounts of single-use denaturants12,13,14. The lack of mechanistic insight on how inorganic ions contribute to protein denaturation limits our ability to fully control and utilize processes to generate protein-based materials.

In the 19th century, Franz Hofmeister discovered the ‘Hofmeister Series’15,16, describing how various salts can either increase or decrease protein solubility in aqueous solutions. Interest in this phenomenon grew between the 1940s and 1960s, focusing on how concentrated inorganic ions affect protein stability and conformation10,17, with LiBr showing the most pronounced impact18,19,20. In recent years, extensive research has explored the interactions between water molecules and ions21,22, offering further insights into the origin of hydrophobicity and its influence on protein folding23,24,25, potentially driven by modifications in the intermolecular interactions of water26. However, a unified framework for understanding the triadic relationship between proteins, water, and solutes remains elusive27.

Here, we show that LiBr-treated keratin spontaneously aggregates into a stable gel and rapidly solidifies upon immersion in water, rather than remaining in a dispersed, solubilized state. This behavior challenges conventional models of protein denaturation, which typically attribute LiBr’s effect to direct interactions between lithium cations and proteins12,13,18,19,20. We hypothesize that concentrated LiBr solution denatures proteins through an indirect mechanism in contrast to direct protein binding. To test this, we compare the effects of LiBr with two other ion pairs, lithium chloride (LiCl) and sodium bromide (NaBr), on three proteins spanning different levels of structure complexity. Both experimental and theoretical analyses reveal that these differences stem from the ion pairs’ varying capabilities to disrupt the water network without directly binding to proteins, indicating a denaturation mechanism driven by entropy instead of enthalpy. Guided by this indirect mechanism, we design a separation process based on spontaneous aggregation and achieve closed-loop recycling of the LiBr solution. This method yields a stable keratin gel that rapidly transitions into solid state upon immersion in water, enabling the direct fabrication of engineered structures as an efficient means for protein regeneration.

Results

Spontaneous aggregation of keratin gel with rapid phase-transition capability

Recognizing the limitations of complex separation and fabrication processes in conventional extraction methods, we refined our previously reported process to extract keratin into a concentrated gel state that is capable of undergoing rapid phase transition into solid upon immersion in water based on our established protocol13 (Fig. 1a). Protein resources such as animal fragments or wool-based textiles are extracted by an aqueous solution of 8 M LiBr, with heat applied to accelerate reaction kinetics and prevent aggregation during extraction. A small amount of 1,4-dithiothreitol (DTT) is added as a reducing agent to break down the dense disulfide matrix in keratin. Notably, we observed spontaneous aggregation of keratin upon cooling without the need for additional chemicals, which enables the separation of a condensed gel phase through overnight sedimentation or centrifugation (Supplementary Fig. 1a).

Fig. 1: Spontaneous aggregation of keratin gel with rapid phase transition capability.
figure 1

a Extraction process of the room-temperature stable keratin gel using LiBr-induced denaturation. b Rheology measurements of the keratin gel, showing an increase in viscosity and shear-thinning property upon decrease of temperature. Data are presented as mean ± s.d. (n = 3 independently prepared keratin gel samples). c Keratin content of the aggregated gel after separation. Data are presented as mean ± s.d. (n = 6 independently prepared keratin gel samples). d Phase transition study illustrating the behavior of extracted keratin when immersed in water using coverslips with transparent well spacers. Keratin gel (i) obtained through LiBr extraction rapidly transitioned into a white solid phase, whereas keratin solution (ii) extracted with urea exhibited slow diffusion and remained soluble. Scale bar, 5 mm. e Facile manufacturing strategies including injection molding, film casting, dip coating, fiber spinning, and 3D printing. Scale bars, 1 cm (optical images), 300 µm (SEM images). Source data are provided as a Source Data file.

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The resulting keratin gel exhibits shear-thinning rheological properties (Fig. 1b) and contains a high concentration of 300–400 mg ml-1 (Fig. 1c and Supplementary Fig. 1b). This concentration is up to two orders of magnitude higher than that of typical protein gels that remain fluid at room temperature28, indicating a condensed protein aggregate state rather than a molecular dispersion. Upon immersion in water, the gel rapidly transitions to solid state within tens of seconds (Fig. 1d and Supplementary Movie 1). In contrast, keratin extracted using conventional organic denaturants (e.g., urea) remains non-processable until fully dialyzed and lyophilized, producing only dispersed powders without structural integrity (Supplementary Fig. 2)9,14. The gel’s fluidity, stability, and rapid hydration-driven phase transition enables a wide array of manufacturing methods, including injection molding, membrane casting, dip coating, fiber spinning, and 3D printing (Fig. 1e and Supplementary Fig. 3). Additionally, the temperature-dependent viscosity of the keratin gel enables tunable extrusion performance during 3D printing (Supplementary Fig. 4).

The distinct differences in behavior between our reported keratin gel and keratin extracted with organic denaturants like urea indicate divergent underlying mechanisms. Our previous hypotheses attributed the denaturation capability of LiBr solutions primarily to direct binding of lithium cations to the protein surface13. However, this explanation does not account for the spontaneous aggregation of denatured keratin, the densely aggregated nature, or its rapid phase transition into a renatured solid, as the dissociation kinetics of such interactions are slower than the observed timescale. These observations suggest a different mechanism that challenges the notion of direct binding between proteins and LiBr denaturants.

Universal denaturation capacity of LiBr

To investigate the denaturation mechanism of LiBr, we selected three proteins representing different levels of structural complexity (Fig. 2a), along with three different ionic solutes including LiBr, LiCl, and NaBr. We found markedly distinct solute effects for different proteins and salts across various concentrations, as evidenced by aggregation of denatured protein during turbidity measurements at 405 nm (Fig. 2b–d). The smallest protein tested, dihydrofolate reductase (DHFR) showed significant aggregation at 1 M LiBr and 5 M LiCl, but remained soluble at all NaBr concentrations (Fig. 2b and Supplementary Fig. 5). The relatively higher turbidity signal in LiCl than LiBr can be contributed to larger sizes of aggregates after denaturation. Starting from 2 M LiBr, we observed a gradual loss of secondary structure of DHFR such as α-helix (1650–1655 cm-1) and β-sheet/turns (1660–1690 cm-1), along with an increase in aggregated β-like random structures (1620–1630 cm-1) (Fig. 2e). The secondary structure loss of DHFR in 2 M LiBr was further confirmed by conformational kinetics measurement using Raman spectroscopy, where less-stable β-sheet disappeared first, followed by α-helix, with obvious accumulation of random structures (Fig. 2h, Supplementary Figs. 6 and 7). Both FTIR and tryptophan fluorescence measurement confirmed DHFR unfolding starting from ~5 M LiCl (Supplementary Fig. 8). In contrast, DHFR stayed well-folded for all concentrations of NaBr.

Fig. 2: Concentrated LiBr solutions induce universal protein conformational change and cause denaturation.
figure 2

a Schematics of DHFR, fibronectin, and α-keratin (wool), representing three levels of structural complexity. b–d Turbidity assay of three respective proteins measured by OD405, suggesting different denaturation capabilities of LiBr, LiCl, and NaBr. Data are normalized by the highest OD405 values of respective proteins and presented as mean (n = 4 independently prepared protein solutions). e–g FTIR of the amide I band indicate a gradual loss of secondary structure upon increasing of LiBr concentration. h Percentage change of the secondary structure in DHFR in 2 M LiBr, deconvoluted from the amide I band of Raman spectra. i DLS measurement of the hydrodynamic radius of fibronectin with increasing LiBr concentration, indicating an extension of quaternary structure followed by aggregation. Box plots represent the interquartile range (25th to 75th percentile), with the center line indicating the median. Whiskers extend to the minimum and maximum values. (n = 6 independently prepared protein solutions). j SEM image of wool prior (i) and after (ii) denaturation with 8 M LiBr. Scale bars, 50 µm. Source data are provided as a Source Data file.

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To elucidate whether ionic solutes can affect conformations of proteins with more complex, hierarchically ordered structures, we examined fibronectin. This protein, a critical component for cell-extracellular matrix29. has more recently been explored as a synthetic building material30,31 because of its unique structure-function relationships. Fibronectin is comprised of two covalently linked extensible arms formed by β-sheet domains that can undergo quaternary structure changes from globular to extended state32 (Fig. 2a middle). With the increase of protein structural complexity, higher concentrations of LiBr and LiCl (7 M and 8 M, respectively) were required to induce aggregation of fibronectin (Fig. 2c and Supplementary Fig. 9), where secondary structure loss was also confirmed by FTIR spectra (Fig. 2f and Supplementary Fig. 10a, b). Before denaturation, protein conformational changes were observed through dynamic light scattering (DLS) measurements of the hydrodynamic radius Rh (Fig. 2i), where fibronectin transitions from the globular state (Rh ~8 nm) to the extended state (Rh ~23 nm) at a lower concentration of LiBr around 2 M. Combining the loss of the secondary and tertiary structure observed in FTIR and the quaternary structure extension shown via DLS, we can identify sequential changes in protein structure as the concentration of LiBr increases (Supplementary Fig. 10c).

In contrast to DHFR and fibronectin, keratin possesses hierarchical structure ranging from α-helices at the nanometer scale to protofibrils and filaments at the micrometer scale. A turbidity map generated from 24-h soaking of wool in salt solutions showed that visible signal can only be observed at high concentrations of LiBr (Fig. 2d). FTIR spectra further indicated complete denaturation of both α-keratin from wool and β-keratin from goose feathers, irrespective of their different native configurations (Fig. 2g). Finally, scanning electron microscope (SEM) images of wool before and after treatment with 8 M LiBr, LiCl, and NaBr also corroborate our turbidity measurement findings, where only concentrated LiBr induces denaturation of keratin (Fig. 2j, Supplementary Figs. 11 and 12). These results show that despite their chemical similarities, the denaturation potency of these ion pairs follow a consistent order across all tested proteins, with LiBr as the strongest and NaBr as the least potent.

Indirect solute effects

Protein conformational change or denaturation is a complex process where entropy and enthalpy contribute to the overall free energy balance. At lower concentrations of denaturants, entropy and enthalpy balance to favor the native state; however, at higher concentrations, they tend towards the unfolded state33. To elucidate the thermodynamic mechanisms of protein denaturation by LiBr, we conducted isothermal titration calorimetry (ITC) experiments to measure the enthalpic contribution from direct LiBr solute-protein interactions, with commonly used denaturants urea and guanidine hydrochloride (GdnHCl) as a control. Pronounced heat release was detected upon injection of urea or GdnHCl into samples containing DHFR and fibronectin (Fig. 3a, b and Supplementary Fig. 13). Enthalpy changes, dependent on protein sizes and exposures of hydrophobic domains (~ −7 kCal mol-1 for DHFR and ~ −14 kCal mol-1 for fibronectin), correspond to the formation of 1–2 or 3–4 hydrogen bonds with protein per organic denaturant molecule, respectively. These results are consistent with previous studies34,35, where enthalpy-driven mechanisms of protein denaturation by urea or GdnHCl were established. In contrast, no enthalpy change from direct interaction with proteins was detected when LiBr solution was injected into protein samples under identical protocols, suggesting that solute ions here do not engage in noticeable direct interactions with proteins. Given that LiBr, being a universal and potent denaturant, does not contribute enthalpically to protein free energy, we hypothesize that LiBr shifts the proteins conformation towards denaturation by affecting the structure of water network.

Fig. 3: Protein conformational changes come from indirect solute effects manifested as water network entropy.
figure 3

Reaction enthalpy of interactions between proteins (a, DHFR, b, fibronectin) and denaturants (LiBr, urea, and GdnHCl) as measured by isothermal titration calorimetry. Data are presented as mean ± s.d. (n = 3 independently prepared protein and denaturant solutions). c Distributions of molecular entropy of water molecules in 7 M LiBr, LiCl, and NaBr from MD simulations. d Total water entropy penalty decrease in different concentrations of LiBr, LiCl, and NaBr solutions. Data are obtained from MD simulations and calculated via the analytical model (Eq. 1). Data are presented as mean ± s.d. (n = 3 independent simulation runs), however, the error bars are smaller than the data point size. e Schematics of different ion effects on water structures. For LiBr and LiCl, high charge density of Li+ ion results in localized (trapped) water molecules and disrupted water network (i), while NaBr induces a more global effect without breaking water network (ii). f Contribution of water network entropy penalty decrease to the total water entropy penalty decrease. g Strong correlation between the theoretical value of water network entropy penalty decrease and the protein denaturation ratio observed from FTIR experiments in LiBr and LiCl solutions. The Pearson correlation coefficient is shown with a two-tailed P value of \(3.44\times {10}^{-11}\). Dashed line represents the best fit. h Free energy landscape of an α-helix peptide (20 amino acids) in pure water and 1, 4, 7 M LiBr from MD simulations. Source data are provided as a Source Data file.

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Mechanism of entropy-driven protein denaturation

To investigate the hypothesis that concentrated ion pairs alter the water network structure, we performed molecular dynamics (MD) simulations to model the distribution of water molecules in the presence of ions (See Methods and Supplementary Table 1 for details). First, we confirmed that local water density around ions (Supplementary Fig. 14) in our simulations agrees well with previous X-ray and neutron diffraction experimental results36. The cooperativity of ion hydration37 was also observed, where local water structures influenced not only by individual ions but also their counterions.

We further examined how changes in water behavior around ions affect the entropy of the water network by calculating molecular water entropy based on TIP3P38 model using Two-Phase Thermodynamic (2PT) method, which has been shown to accurately replicate experimental entropy values39. In both LiBr and LiCl solutions, two distinct populations of water molecules are observed (Fig. 3c). As suggested by evidence of local effects of Li+ ions40, the subset characterized by lower average entropy is identified as ion-bound water, whereas the other, possessing higher entropy, is identified as free water that constitutes the hydrogen bonded water network. LiBr solution also demonstrates a higher proportion of ion-bound water compared to LiCl solution (Fig. 3ei and Supplementary Fig. 15a, b). This enhanced capacity of Li+ ions to sequester water in LiBr could stem from the more effective separation between Li+ and Br- ions21,22,36, attributable to the lower charge density of Br- ions and the substantial size disparity between Li+ and Br- ions. In contrast, the NaBr solution exhibits a single population suggesting to the intact hydrogen bond network of pure water (Fig. 3eii and Supplementary Fig. 15c), which could potentially be explained by the absence of localized high charge density22,37.

The prominent differences in both water network size and denaturation capability between LiBr, LiCl, NaBr, and pure water, point out to a change in water network entropy as a possible culprit. To further highlight this concept, we developed an analytical model describing the decrease of total entropy penalty from water molecules in solution \((\Delta \Delta {S}^{{{\rm{water}}}})\), which drives the overall free energy balance towards the denatured state.

$$\Delta \Delta {S}^{{{\rm{water}}}}=\Delta \Delta {S}^{{{\rm{translation}}}}+\Delta \Delta {S}^{{{\rm{rotation}}}}+\Delta \Delta {S}^{{{\rm{vibration}}}}-4{k}_{{{{\rm{B}}}}}{{\mathrm{ln}}}\phi$$
(1)

Here, \(\Delta \Delta {S}^{{{\rm{translation}}}}\), \(\Delta \Delta {S}^{{{\rm{rotation}}}}\), and \(\Delta \Delta {S}^{{{\rm{vibration}}}}\) represent the entropy penalty decrease from individual water molecules and \(-4{k}_{{{{\rm{B}}}}}{{\mathrm{ln}}}\phi\) denotes the entropy penalty decrease of water as a collective network (\({\Delta \Delta S}^{{{{\rm{network}}}}}\)), with \(\phi\) representing the ratio of water network sizes in ionic solutions and pure water (see Methods for derivation of Eq. 1 and further details).

The total decrease of water entropy penalty from different ion pairs can be calculated using Eq. 1 with values of individual contributions obtained from molecular dynamics simulation (Fig. 3d and Supplementary Fig. 16). Notably, the decrease of the water network entropy penalty \(\Delta \Delta {S}^{{{{\rm{network}}}}}\) appears to be the predominant factor over contributions of rotational and translational entropy of individual water molecules, especially for LiBr and LiCl, the two potent protein denaturants (Fig. 3f). Considering only translational and rotational entropy is also insufficient to account for either the extent or the trend of denaturation capability observed among LiBr, LiCl, NaBr, and pure water (Supplementary Fig. 17). This key factor has been underestimated in several previous studies, potentiating considerable debate regarding the effects of solutes on water dynamics and protein unfolding41,42. Furthermore, the theoretically calculated \(\Delta \Delta {S}^{{{{\rm{network}}}}}\) and the experimentally observed ratio of denatured and native α-helix around 1650–1655 cm-1 from FTIR in LiBr and LiCl solutions showed a strong correlation with the Pearson correlation coefficient of 0.9058 (Fig. 3g). In contrast, contributions from rotational and translational entropy exhibited a weaker correlation (Supplementary Fig. 18), with minimal contributions to the total decrease of water entropy and misalignment with the denaturation capabilities of different salt solutions. The strong quantitative agreement between theoretical predictions and experimental results suggests the universal predictive capability of the water network model across various ion types and concentrations, particularly at conditions where water network entropy plays a dominant role. For salts and concentrations where \(\Delta \Delta {S}^{{{{\rm{network}}}}}\) is less than 10 J mol⁻¹ K⁻¹, our model predicts no denaturation or indicates that water network entropy is not the primary driving force behind any observed denaturation, as exemplified by NaBr.

Finally, protein free energy landscapes at different LiBr concentrations were constructed using well-tempered metadynamics simulation43, where a stable α-helix peptide of 20 amino acids was adopted as a model protein (Fig. 3h and Supplementary Figs. 19–23). The increase of ion concentrations shifts the free energy landscapes towards unfolded conformations and lowers the energy barrier for unfolding. Unfolding free energy changes (\(\Delta \Delta G\)) of this model protein in LiBr solutions relative to that in pure water show quantitative agreement with entropic contribution of water calculated from analytical model (Supplementary Fig. 24), which lends further support to entropy-driven theory of the denaturation capacity of LiBr. In summary, solute-induced water network disruption potentiates the reduction of entropy penalty when proteins sequester water molecules from bulk water network during unfolding. This mechanism explains the rapid phase transition of the keratin gel upon transfer to water, where renaturation occurs quickly in the absence of directly bound denaturants. In contrast, keratin extracted with organic denaturants remains soluble due to persistent protein–denaturant interactions.

Mechanical tunability and shape-memory of regenerated keratin

The ability to form a homogenous object through rapid phase transition enables the direct fabrication of keratin materials with tunable mechanical properties via crosslinking. After extraction, the disulfide bonds in keratin are reduced to thiol groups, thereby endowing the regenerated keratin material with adjustable covalent crosslinking through oxidation. For instance, low level of crosslinking allows the α-helices to rearrange more freely under stress (Fig. 4a), while formation of disulfide crosslinking restrains such arrangement (Fig. 4d) As a result, reduced keratin preserves a high flexibility with a modulus of 124.3 ± 18.8 kPa and a fracture strain of 435 ± 61%, whereas oxidized keratin demonstrates a higher modulus of 1.35 ± 0.11 MPa and a reduced fracture strain of 95 ± 9% (Fig. 4b, e and Supplementary Fig. 25). Differences between the two conditions reveal the effect of disulfide crosslinking on the α-helix network of regenerated keratin, providing the material with tunable mechanical properties from ductile to elastic (Fig. 4c).

Fig. 4: Tunable mechanical properties and shape-memory effect of regenerated keratin.
figure 4

a Schematic of the α-keratin in reduced state and directional rearrangement of α-helices induced by stretching. b Cyclic loading of reduced keratin to 50% strain. c Stress-strain curves of reduced and oxidized keratin until fracture. Scale bars, 2 mm. d Schematic of the α-keratin in oxidized state and uncoiling of helices upon stretch. e Cyclic loading of oxidized keratin to 50% strain. f Change of secondary structure percentage under 50% strain quantified from Raman deconvolution of amide I band. A more significant decrease of α-helix can be observed within oxidized sample, indicating the uncoiling of helices into metastable β-sheets. Data are presented as mean ± s.d. (n = 3 independently prepared keratin film samples). g Schematic of the shape memory effect triggered by hydration signal. h Demonstration of shape memory effect with a badge model and a tensegrity structure. Scale bars, 3 cm. Source data are provided as a Source Data file.

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Prior studies revealed that uniaxial strain can induce reversible uncoiling of α-helix into metastable β-like structures within anisotropic bio-based elastomer44,45. Similarly, Raman spectroscopy of keratin samples under 50% strain suggests that most secondary structures remain unchanged within reduced keratin upon stretching, whereas a more discernible loss of α-helix domains and an increase of β/random structures can be observed in oxidized keratin (Fig. 4f). This transition between coiled helix and uncoiled strands can also lead to a shape-memory effect facilitated by formation and decay of hydrogen bonds (Fig. 4g), which has been investigated and confirmed in our previous studies by Cera et al.13. The shape-memory capability of regenerated keratin material is demonstrated both as a standalone object and as components of complex tensegrity structures (Fig. 4h, Supplementary Fig. 26, and Supplementary Movies 2–4).

Closed-loop recycling of LiBr solution

Since the LiBr does not induce denaturation via direct interactions, the resulting solution can be continuously recycled in a closed loop, which not only eliminates pollution from waste organics but also reduces the consumption and cost of denaturants (Fig. 5a). To test the cyclic stability of the closed-loop recycling protocol, we performed multiple iterations of extraction using both wool (mainly α-keratin) and goose feathers (mainly β-keratin). The extraction yield remains consistently around 40% over five cycles (Fig. 5b), while the first cycle shows a slightly lower yield, likely due to a small portion of keratin remaining in the solution after separation. This residual keratin is carried over and included as part of the input for subsequent cycles, resulting in more consistent yields from the second cycle onward. The composition of the recycled LiBr solution was further confirmed through thermogravimetric analysis (TGA), which showed no significant difference between weight loss profiles of the original 8 M LiBr solution and the recycled solution after five cycles (Fig. 5c). Additionally, FTIR of the emitted gas during thermogravimetric analysis (TG-FTIR) revealed that the gas consistently remained as water vapor across various heating stages (Fig. 5d, e). This stable composition of recycled solution can be attributed to the minimal consumption of LiBr under the indirect denaturation mechanism.

Fig. 5: Closed-loop recycling of LiBr solution.
figure 5

a, Schematic showing the regeneration protocol of keratin waste with closed-loop recycling of LiBr solution. b Extraction yield of keratin extracted from wool and keratin extracted from goose feathers. Data are presented as mean ± s.d. (n = 7 for wool, n = 3 for feathers, independent extraction experiments). c Comparison of the TGA profile shows no major change in the LiBr solution after 5 cycles of extraction. d, e TG-FTIR of the LiBr solution recycled after keratin separation. f Environmental impact assessment of producing 1 kg keratin via agriculture (raw wool), urea extraction, and this work. Calculations conducted using the Intergovernmental Panel on Climate Change (IPCC) 100-year time horizon global warming potentials (GWP 100a) with ecoinvent 3.9.1 database. Detailed calculations described in Supplementary Tables 3 and 4. g Different keratin samples were regenerated from (i) wool, (ii) goose feathers, (iii) wool clothes, and (iv) human hair. Keratin samples were shaped into the word describing their sources using the injection molding method. Scale bars, 1 cm. Source data are provided as a Source Data file.

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In contrast to conventionally employed enthalpy-driven denaturants (e.g., urea, GdnHCl), the entropy-driven denaturation mechanism addresses key limitations in protein regeneration, including waste and pollution from single-use organic chemicals and the complexity of fabrication processes (Supplementary Table 2). Compared to the significant environmental impact of traditional agricultural practices and protein extraction using urea, the regeneration process with LiBr offers substantial reductions in greenhouse gas emissions due to the recyclability of its key chemicals46 (Fig. 5f and Supplementary Tables 3−4). To demonstrate the versatility of this approach, we extracted keratin from various protein waste sources including wool, feathers, wool clothes, and human hair, regenerated them into the word-shaped structures representing their sources and investigated their mechanical properties (Fig. 5g and Supplementary Fig. 27).

Discussion

The effect of water networks on protein conformation and stability has long been a subject of extensive debate. Inspired by our observations of the unique properties of keratin gel and building on the foundational work dating back to the 19th century ‘Hofmeister Series’, we investigated the molecular mechanisms of protein denaturation driven by inorganic ions pairs like LiBr. Notably, our ITC experiments revealed no direct interactions between proteins and ionic solutes despite the significant potency of LiBr as a universal denaturant. Combining experimental, computational and theoretical approaches, we confirm an entropy-driven denaturation mechanism through the disruption of water network, distinct from the conventional denaturation model involving direct binding of organic denaturants to proteins (Supplementary Fig. 28).

Building upon the entropy-driven mechanism and our previous procedure13, we designed an efficient strategy for upcycling keratin from diverse protein sources with closed-loop recycling of LiBr denaturants. The resulting keratin gel is compatible with a wide array of fabrication techniques, providing tunable mechanical properties and hydration-triggered shape-memory capabilities, while avoiding the usage of single-used organic denaturants. This interdisciplinary study, which combines a clear molecular-level mechanism with practical applications, paves the way for future valorization of underutilized protein resources and the development of protein-based smart materials.

Methods

Escherichia coli dihydrofolate reductase expression

Cell culture

E. coli dihydrofolate reductase (DHFR, UniProt: P0ABQ4) (wild-type or W30C mutant) was overexpressed in BL21(DE3) E. coli cells. The plasmid was synthesized by GenScript Biotech with pET-28a(+) vector and C-terminus 6xHis-tag. All the cell culture were conducted in Terrific Broth (TB) medium (BD Difco™), supplemented with glycerol (0.4% v/v, RPI), glucose (4 g L-1, Sigma-Aldrich), MOPS (25 mM, Sigma-Aldrich, pH = 7.2), citric acid (0.4 mM, VWR Chemicals BDH®), ferric ammonium citrate (40 µl L-1, 1% w/v, AMRESCO), and kanamycin (50 µg ml-1, Millipore-Sigma). All the concentrations denoted here are final concentrations. 2% v/v frozen cell stock solution of BL21(DE3) E. coli cells transformed with DHFR (wild-type or W30C mutant) plasmid was used for a small overnight (~12 h) culture at 37 °C with shaking at 250 rpm. Overnight culture solution (2% v/v) was used to start the production culture, initially at 37 °C with shaking at 250 rpm. After 3.5 h at which the cell growth started the mid-log phase with an optical density of around 0.6 at 600 nm, isopropyl β-D-thiogalactopyranoside (100 µM, IPTG, RPI) was added to induce the protein overexpression. The temperature was decreased to 18 °C, with shaker speed kept as 250 rpm. The cell pellets were harvested after 12-h low-temperature protein overexpression through centrifugation.

Protein purification

Three different buffers were used in DHFR protein purification: Lysis buffer [100 mM bicine (Sigma-Aldrich), 5 mM imidazole (Millipore-Sigma OmniPur®), 250 mM NaCl (VWR Chemicals BDH®), pH = 9]; Buffer A [20 mM Tris (J.T. Baker™), 5 mM imidazole, 250 mM NaCl, pH = 8.5]; Buffer B [20 mM Tris, 50 mM imidazole, 250 mM NaCl, pH = 8]. Cell pellet (1 g, from 50 ml cell culture solution) was resuspended in lysis buffer (1.5 ml), supplemented with Nuclease (0.01 % v/v, Millipore-Sigma Benzonase®), Protease Inhibitor Cocktail Set II (1% v/v, Millipore-Sigma Calbiochem®), and lysozyme (1 mg ml-1, Thermo Fisher Scientific). All the concentrations denoted here are final concentrations. The resuspended solution was then sonicated, centrifuged with supernatant collected. cOmplete™ His-Tag Purification Resin (Roche) was used to further isolate DHFR protein from supernatant in gravity flow columns (Bio-Rad). Buffer A was first used to wash away non-bound proteins and other cell debris, followed by elution of Buffer B, where DHFR was washed out and collected. Only the fractions with A280/A260 > 1.7 were pooled based on the absorbance measurement with a NanoDrop spectrophotometer (Thermo Fisher Scientific). DHFR was then washed into Tris buffered saline (20 mM, pH = 7.0, with 250 mM NaCl) and concentrated into the final concentration (3 mg ml-1) using ultrafilter (Sartorius Vivaspin®). Mass spectrometry (Bruker Impact II q-TOF) was used to confirm that DHFR (both wild-type and W30C mutant) was successfully synthesized and purified, after which protein solution was aliquoted and stored in -70 °C.

Rheology test

Rheology measurements were performed using a Discovery HR-20 rheometer (TA Instruments) equipped with a 40 mm diameter, 2° cone-plate geometry. Prior to measurements, keratin gel samples were equilibrated at the designated temperature for 10 min to ensure equilibrium. Shear rate sweeps were conducted from 0.1 to 100 s⁻¹ at constant temperature.

During shear rate sweeps, steady-state sensing was enabled, with a sample period of 10 s a 5% tolerance, and a maximum equilibration time of 90 s at each shear rate. This ensured that viscosity values were recorded only after the sample reached steady-state flow conditions. Data collection and analysis were performed using TRIOS software (v.5.6.0.87, TA Instruments).

Turbidity assay

Turbidity measurements at OD405 were performed using a Biotek PowerWave HT 340 microplate reader. For each condition, protein solutions was mixed with solutions of LiBr, LiCl, and NaBr (Sigma-Aldrich) to the final concentration of DHFR (0.4 mg ml-1) or human fibronectin (0.1 mg ml-1, BD Biosciences), and added in a 96-well plate (100 µl). Samples were then immediately placed into the microplate reader and OD405 was continuously measured for 1 h at room temperature. For keratin, cleaned wool (80 mg, R. H. Lindsay Wool Company) was soaked into salt solutions (4 ml) with DTT (0.1 M, Sigma-Aldrich) in quartz cuvettes, then heated to 70 °C to accelerate the denaturation kinetics. Samples of the solutions were taken at 24 h and 48 h, added into 96-well plate, and cooled at room temperature before OD405 measurement. Photos recording the condition of the solution were taken after cooling for 1 h.

FTIR and TG-FTIR

All FTIR measurements were conducted using a Nicolet iS50 FTIR spectrometer. Protein solutions with DHFR (1 mg ml-1), fibronectin (0.5 mg ml-1), or keratin (1 mg ml-1, α-keratin from Angora wool, R. H. Lindsay Wool Company; β-keratin from goose feathers, Dream Solutions USA), respectively, were prepared with a gradient of LiBr concentrations (0 to 8 M), then stabilized for at least 3 h to achieve structural equilibrium prior to measurements. During acquisition, background information was initially recorded by applying pure LiBr solutions onto the ATR crystal, which was then replaced by the corresponding protein solutions, with a total of 64 scans collected for each sample. Solid samples, including regenerated keratins and raw materials, were measured using the same ATR-FTIR setup. Gas phase FTIR coupled with TGA was collected using the same equipment connected to the Discovery TGA 550. Data analysis and background subtraction were carried out with OMNIC v.9.2.86 software. To calculate the ratio of protein denaturation for Fig. 3g and Supplementary Fig. 18, we measured the intensity change at 1652.5 cm⁻¹, corresponding to the denaturation of α-helix structure.

Raman spectroscopy

Raman experiments were performed with a Horiba LabRam HR Evolution Raman confocal system (633 nm excitation, 50x, 0.5NA, 13 mW). For DHFR experiment, a customized imaging chamber made by sandwiching a 1 mm thick PDMS (Sylgard™ 184, Dow Corning) well between glass slides (Supplementary Fig. 6) was loaded with a solution of DHFR (3 mg ml-1) and LiBr (2 M). Each spectrum was collected with 600 gr mm-1, 180 s acquisition time and 2 accumulations. For solid samples, 1800 gr mm-1, 60 s acquisition and 4 accumulations were used. Data collection and analysis were carried out with Labspec v.6.5.1 software.

Dynamic light scattering

DLS experiments were performed using a Malvern Zeitasizer Pro system. Fibronectin (0.5 mg ml-1) in LiBr solutions were filtered to remove dust before transferred into cuvettes (40 µl, Malvern Panalytical) and measured 3 h after preparation. This stabilization time allows fibronectin to adopt a stable conformation under the given conditions. A shorter duration (e.g., less than 10 min) results in high variability in DLS measurements due to ongoing conformational changes, while an extended incubation (e.g., beyond 24 h) also increases variance as fibronectin molecules tend to aggregate over time.

Keratin solutions (diluted to 1 mg ml-1 after extraction) were filtered, then transferred into cuvettes (1 ml, Malvern Panalytical). Samples were heated to 70 °C for 30 min and then held at the designated temperature for 10 min prior to measurement. The stabilization time was intentionally kept shorter than that used for fibronectin to capture temperature-dependent aggregation kinetics. Extending this period (e.g., to 3 h) would lead to extensive aggregation at all temperatures, obscuring differences in aggregation behavior across the temperature range. Data collection and analysis were carried out with ZS Xplorer v.3.0.0.53 software.

Scanning electron microscopy

Samples were mounted on a 12.5 mm diameter SEM stub covered with carbon tape, then sputtered-coated with Pt/Pd with an EMS 150 T ES sputter coater with 10 nm thickness. SEM images were taken with a Zeiss Gemini 360 field emission scanning electron microscope with an electric high tension of 3 kV and SE2 detector.

Isothermal titration calorimetry

ITC experiments were conducted using a Malvern Panalytical MicroCal VP-ITC. During the experiments, the sample chamber was filled with 1.8 ml of DHFR solution (1 mg ml-1, W30C mutant) or fibronectin solution (0.5 mg ml-1), while the syringe was loaded with solutions of LiBr (100 µM), urea (100 µM), or GdnHCl (100 µM), respectively. Corresponding control experiments were performed by titrating milli-Q water into the same concentration of protein solution to measure and subtract the dilution heat of proteins. Additionally, parallel control groups were also performed by titrating ligands into a chamber filled with milli-Q water to measure the dilution heat of ligands, which were found to be significantly smaller than the detectable binding enthalpy between proteins and ligands (Supplementary Fig. 13). Each individual run comprised titrating ligand solution (7 µl) 25 times into the chamber, with a duration of 12 s, and interval of 240 s, a filter period of 2 s, a stir speed of 309, and temperature controlled at 30 °C. Data collection and analysis including baseline adjustment and integration of enthalpy were carried out with VPViewer2000 v.1.29.1 software.

Molecular dynamics simulations

General simulation setup

All the molecular dynamics simulations were conducted with NAMD 2.1447 software and analyzed and visualized with VMD 1.9.348, unless otherwise denoted. Amber ff14SB force field49 were used for atomistic protein simulation, combined with TIP3P water model50 for explicit solvation and Li/Merz ion parameters51 for monovalent ions. All initial configurations of simulation box were prepared using tLEaP program52, followed by minimization, heating, constant pressure (NPT) equilibration, and constant volume (NVT) equilibration. All the production simulations were run under constant particle number, constant volume, and constant temperature (i.e., canonical ensemble (NVT)). Periodic boundary condition was applied to prevent the boundary effect. Langevin thermostat with damping coefficient of 1 ps-1 was used to control simulation temperature as 298 K, without coupling hydrogen atoms. Electrostatic and van der Waals interactions were cut off beyond 12 Å. Particle Mesh Ewald (PME) method was employed to deal with long-range electrostatic interactions. Rigid bond constraints between hydrogen and any other atoms were applied through SHAKE/RATTLE algorithm. The integration time step was set as 2 fs with short-range nonbonded forces updated every 2 fs and long-range electrostatic forces updated every 4 fs. Software and models are summarized in Supplementary Table 1.

Initial configuration preparation and equilibration

To ensure that total number of ions and water molecules are correctly determined for all salts and concentrations, we first decided the simulation box sizes and thus ion numbers. All the simulation boxes were fixed to the size with three dimensions around 50 Å. Water molecules were initially placed using tLEaP program52, the numbers of which were then adjusted according to volume changes after 100 ps minimization, 200 ps heating, and 2 ns constant pressure (NPT) equilibration. After the water molecule number corrections, another round of 100 ps minimization, 200 ps heating, 2 ns constant pressure (NPT) equilibration, plus 2 ns constant volume (NVT) equilibration, were conducted to ensure the correct setup and complete equilibration of simulation systems.

Water structure characterization

The equilibrated initial configurations containing water molecules and ions were prepared as stated above. The production simulations for water structure characterization were run for 100 ns with trajectories recorded every 10 ps. The radial distribution function g(r) between cations (or anions) and oxygen atoms of water can be used to characterize local water structure around ions. It was calculated via VMD and averaged among all cations (or anions) and all trajectory frames with the definition as

$$g\left(r\right)=\frac{d{n}_{r}}{4\pi {r}^{2}\bullet {dr}\bullet {\rho }_{{{\rm{bulk}}}}}$$
(2)

where \(d{n}_{r}\) is the number of oxygen atoms of water within the shell of thickness at the distance \(r\), \(4\pi {r}^{2}\bullet {dr}\) is the volume of the shell, \({\rho }_{{{\rm{bulk}}}}\) is the bulk average density of oxygen atoms of water in the simulation box.

Water entropy calculation

The equilibrated initial configurations containing water molecules and ions were prepared as stated above. The production simulations for water entropy calculation were run for 20 ps39 with trajectories recorded every 2 fs. All the water entropy calculations were conducted based on Two-Phase Thermodynamic (2PT) model39,53 using corresponding open source program54. The resulting histograms were fit with two Gaussian distributions with no boundary conditions. Initial values of peak centers were determined using local minima of 2nd derivative. For LiBr and LiCl, fitting achieved convergence with Chi-Square tolerance value of 10−6. For NaBr, one peak will collapse to zero and only a single peak remained upon convergence.

Protein free energy landscape construction

To examine changes in free energy that drive denaturation, we used metadynamics simulation to explore the free energy landscape of the complex molecular system including water, ions, and protein. A short alanine-based peptide with 20 amino acids (AAAAKAAAAKAAAAKAAAAK), which has been confirmed experimentally55 to have a stable alpha helix structure in pure water, was adopted as the model protein to study the difference of protein free energy landscapes under different concentrations of LiBr. We used ColabFold v1.5.556 to obtain the initial atomistic protein structure, with N-terminus acetylated and C-terminus amidated using PyMOL 2.5.5. The equilibrated initial configurations containing protein, water molecules and ions were prepared as stated above. Well-tempered metadynamics simulations were implemented for protein free energy landscape construction using Colvars module43 on top of standard molecular dynamics simulations as stated above. Root mean square displacement (RMSD) from the backbone of native alpha helix protein structure was selected as the collective variable to guide the sampling of unfolded confirmations. After the first run of metadynamics simulation, two more protein conformations (Supplementary Fig. 19a) with medium RMSD (6 Å) and large RMSD (12 Å) respectively, were chosen as two other start structures. In total, nine metadynamics simulations for each LiBr concentration, started from three different initial protein conformations, were conducted. Each simulation was run for around 2 µs with trajectory recorded every 100 ps (Supplementary Fig. 19b, c). Convergence of metadynamics simulations was examined using block analysis via the open-source, community-developed PLUMED library, version 2.8.357.

Rigorous criteria have been implemented to ensure the accuracy of free energy landscapes derived from metadynamics simulations (Supplementary Figs. 20–23). Initially, simulations are conducted until the collective variable (CV) iterates over its entire possible range, in this case, 0 to 12.5 Å (first column). Secondly, the final height of the Gaussian bias potential added at each CV position must be less than \(5\times {10}^{-3}\) kCal M-1 (second column). Lastly, the convergence of the simulations is further confirmed by observing a plateau in the average standard deviation of the potential of mean force (PMF) as calculated from block analysis, with increasing block sizes (third column). Six converged simulations out of nine for each LiBr concentration were used for final protein free energy landscape construction.

Keratin extraction protocol

The pretreatment of keratin-rich sources (Angora wool, Merino wool shirt, and feathers from the R. H. Lindsay Wool Company, Merino Tech, and Dream Solutions USA, respectively. Hair samples collected from local barber shop) involves washing with ethanol (VWR 200 proof) in a Soxhlet extractor for 48 h to remove organic residues, followed by rinsing with water and allowing the material to dry at room temperature overnight. Subsequently, long wool fibers were cut into smaller fragments (less than 1 cm in length) to facilitate dispersion in solution. During the extraction process, keratin fragments (10 g) were suspended in an aqueous solution (150 ml, 8 M LiBr, and 0.1 M DTT). The suspension was stirred at 350 rpm for 36 h in an insulated environment at 90 °C. Afterwards, insoluble residues were filtered through cotton cloth with 80/180 µm mesh size while still hot, then stored at 4 °C overnight. A viscous, gel phase of aggregated keratin was observed, and centrifugation (1800 g, 4 °C) further separated the mixture into an upper phase of LiBr solution and a lower phase of keratin gel. The LiBr solution could then be easily collected and reused in the following extraction cycle along with a new batch of keratin source and DTT. A small amount of LiBr stock solution (8 M) were added to compensate the solution loss from filtration process in order to maintain the total volume at 150 ml after every cycle.

The keratin content of the aggregated gel was measured by taking 1 ml of gel and allowing it to fully solidify in water, freeze-dried, then lyophilized to obtain a dehydrated solid and measure its weight. It was found that 1 ml of keratin gel contains 392.8 ± 18.6 mg of α-keratin or 347.9 ± 23.7 mg of β-keratin (n = 6). To calculate the extraction yield, the volume of the keratin gel obtained from each batch was measured, multiplied by the corresponding content, and divided by the initial weight of keratin fragments. The denatured keratin gel could be stably stored at 4 °C in the absence of oxygen, with a shelf life longer than 6 months in absence of oxygen. To further assess the robustness of the process, we performed first-cycle keratin extractions from wool after different time points: 24 h, 36 h, and 48 h. The corresponding yields were 22.4%, 33.2%, and 32.5% (n = 2), indicating that an extraction time longer than 24 h is necessary for complete dissolution, while extending the duration to 48 h does not result in a significant increase in yield.

The urea extraction of keratin followed the exact same procedure as LiBr extraction, except substituting the LiBr (8 M) with Urea (8 M). The resulting solution after hot filtration remained homogenous and did not undergo spontaneous aggregation. Keratin/urea solution was dialyzed against DI water using 10,000 Mw cut-off dialysis cassettes (Thermo Scientific, Slide-A-Lyzer 10 K) with water bath changed every 12 h. The resulting concentrated solution was then lyophilized overnight, yielding dispersed keratin powder (Supplementary Fig. 2).

Thermogravimetric analysis

TGA of the LiBr solution prior to the 1st cycle and the recycled LiBr solution after the 5th cycle were conducted with a Discovery TGA 550. Solution (~30 mg) was loaded onto a platinum HT sample pan, stabilized under nitrogen flow for 10 min before measurement. Experiments were performed by heating samples to 100 °C at a rate of 5 °C min−1, then to 600 °C at a rate of 10 °C min−1 in an air flow of 90 ml min−1. The mass of the sample was continuously measured while the evolving gas from the sample was analyzed simultaneously by TG-FTIR. Data collection and analysis were carried out with TRIOS v.5.2.2 software.

Keratin sample preparation

All samples were regenerated using α-keratin gel unless otherwise noted. The reverse mold for injection molding was created by casting PDMS (Sylgard™ 184, Dow Corning) around a 3D printed logo. Keratin gel was injected into the mold and transferred into a water bath until solidified. Membrane casting and dip coating followed a similar process by casting a layer of gel on glass coverslip or coating targets, then transferred into a water bath. Fiber spinning was achieved by injecting the gel through a 21 gauge needle (BD PrecisionGlide™) at a constant rate of 0.1 ml min−1 into a bath of NaH2PO4 solution (0.4 M, Sigma-Aldrich) to accelerate the phase transition process. 3D printing was carried out using a Cellink BIO X 3D printer. The keratin gel was extruded into a supporting bath of Pluronic F127 (25% w/v, BASF) under an absolute pressure of 50 kPa and through 20 or 25 gauge needles (Nordson EFD Precision Tips) that was moving at a speed of 4 mm s−1. The bath was then removed by cooling and rinsing with water.

Keratin samples for mechanical tests, Raman and polarized Raman spectra were prepared by film casting a layer of keratin gel onto glass coverslips with a thickness around 0.4 mm, then transferred into a water bath to solidify the gel. Oxidized samples were fabricated by further transferring into H2O2 solution (1% v/v) for 1 h to reconnect the disulfide bonds. Finally, samples were sectioned into 5 × 20 mm rectangles and stored in water prior to measurements.

The tensegrity structure for the shape memory demonstration was created by oxidizing keratin films in a curled permanent state to as compression units. These units were then interconnected with nylon threads (Singer®) to serve as tension units (Supplementary Fig. 29). Samples were fixed in a distorted temporary state by desiccating for 90 min with addition of external stress.

Mechanical tests

Tensile testing were performed with a CellScale biaxial tester with 2.5 N load cells using keratin film samples described in the prior section. For cyclic stretching curves, samples were tested at a strain rate of 5% per second to a maximum of 50% for 10 cycles. For yield strain measurements, samples were tested at a strain rate of 5% until fracture. Sample thickness was measured with a Mitutoyo Absolute Digimatic digital caliper. The modulus of reduced and oxidized samples was calculated within the 0–50% strain region.

Environmental impact assessment

Global warming potential from different keratin production and regeneration methods in kg CO2-eq was conducted using the Intergovernmental Panel on Climate Change Global Warming Potentials (IPCC GWP100a, V1.02) with ecoinvent 3.9.1 database44 in SimaPro 9.5. Detailed calculation described in Supplementary Tables 3 and 4.

Statistics and reproducibility

Experimental errors are reported as the standard deviation unless otherwise specified, with n referring to the number of analyzed samples as indicated in the figure legends. All representative experiments and micrographs, such as those shown in Figs. 1d, e, 2j, 4h, 5g, were independently repeated at least three times with similar results.

Analytical model of entropy penalty decrease

The protein unfolding reaction is defined as

$$F\leftrightarrows U$$
(3)

where \(F\) is the folded state and \(U\) is the unfolded state. For folded proteins, since they can maintain stable structures in pure water solution, the free energy change \(\Delta {G}_{{{\rm{pure}}}}\) of the unfolding reaction in deionized pure water should be positive, i.e.,

$$\Delta {G}_{{{\rm{pure}}}} > 0$$
(4)

According to the unfolding experiments presented in this work, LiBr has the strongest capability of unfolding (denaturing) proteins, followed by LiCl. NaBr cannot denature those tested proteins in this work. Therefore, the free energy changes of the unfolding reaction in different solution environments can be ranked as follow,

$$\Delta {G}_{{{\rm{LiBr}}}} < \Delta {G}_{{{\rm{LiCl}}}} < \Delta {G}_{{{\rm{NaBr}}}} < \Delta {G}_{{{\rm{pure}}}}$$
(5)

where \(\Delta {G}_{{{\rm{LiBr}}}}\) and \(\Delta {G}_{{{\rm{LiCl}}}}\) for some proteins in high concentration salt solutions are negative (i.e., the unfolding reaction is favored).

The difference between free energy changes of the unfolding reaction in salt solutions \(\Delta {G}_{{{\rm{salt}}}}\) and that in pure water \(\Delta {G}_{{{\rm{pure}}}}\) can be written as

$$\Delta \Delta G =\Delta {G}_{{{\rm{salt}}}}-\Delta {G}_{{{\rm{pure}}}} < 0\\ =\Delta {H}_{{{\rm{salt}}}}-\Delta {H}_{{{\rm{pure}}}}-T\Delta {S}_{{{\rm{salt}}}}-\left(-T\Delta {S}_{{{\rm{pure}}}}\right)\\ =\Delta \Delta H-T\Delta \Delta S$$
(6)

where enthalpy change difference \(\Delta \Delta H\) equals to 0 given the ITC data (Fig. 3a, b) that no direct interaction between proteins and ions was observed. Thus, we have

$$\Delta \Delta G=-T\Delta \Delta S < 0$$
(7)

where \(\Delta \Delta S\) is the entropy penalty decrease due to high concentration salts and should be positive.

Entropy penalty decrease caused by high concentration salts can be written as

$$\Delta \Delta S =\Delta {S}_{{{\rm{salt}}}}-\Delta {S}_{{{\rm{pure}}}} > 0\\ =\Delta {S}_{{{\rm{salt}}}}^{{{\rm{protein}}}}+\Delta {S}_{{{\rm{salt}}}}^{{{\rm{water}}}}-\left(\Delta {S}_{{{\rm{pure}}}}^{{{\rm{protein}}}}+\Delta {S}_{{{\rm{pure}}}}^{{{\rm{water}}}}\right)\\ =\Delta {S}_{{{\rm{salt}}}}^{{{\rm{water}}}}-\Delta {S}_{{{\rm{pure}}}}^{{{\rm{water}}}}$$
(8)

where protein conformational entropy changes \(\Delta {S}^{{{\rm{protein}}}}\) during unfolding is independent of solutions and thus cancel with each other, \(\Delta {S}^{{{\rm{water}}}}\) is the entropy change of water in the solution.

The entropy change of water molecules in the solution \({S}^{{{\rm{water}}}}\) is composed of two parts, i.e., molecular entropy and network entropy. Molecular entropy is composed of translational, rotational, and vibrational entropy of individual water molecules themselves. Network entropy comes from the collective behavior of water network, which considers different combinations water molecules can have to form a network. Therefore, the total entropy change of water during protein unfolding can be expressed as

$$\Delta {S}^{{{\rm{water}}}}=\Delta {S}^{{{\rm{translation}}}}+\Delta {S}^{{{\rm{rotation}}}}+\Delta {S}^{{{\rm{vibration}}}}+\Delta {S}^{{{\rm{network}}}}$$
(9)

Consider a water network with \({N}^{{{\rm{network}}}}\) water molecules (i.e., water molecules that are not bound by either proteins or ions), for a water molecule within this network, there are \({N}^{{{\rm{network}}}}-1\) ways to form the first hydrogen bond with any other water molecules, \({N}^{{{\rm{network}}}}-2\) ways to form the second hydrogen bond, \({N}^{{{\rm{network}}}}-3\) ways to form the third hydrogen bond, and \({N}^{{{\rm{network}}}}-4\) ways to form the second hydrogen bond. Therefore, the total combinations of a water molecule forming hydrogen bonds with other water molecules can be expressed as

$$\Omega=\left({N}^{{{\rm{network}}}}-1\right)\left({N}^{{{\rm{network}}}}-2\right)\left({N}^{{{\rm{network}}}}-3\right)\left({N}^{{{\rm{network}}}}-4\right)$$
(10)

which can also be interpreted as the number of microstates available to each water molecule within the network, in terms of hydrogen bond formation. This formulation assumes that one water molecule can form four hydrogen bonds with other four distinct water molecules in the network.

Then the associated network entropy of a water molecule (i.e., combinatorial entropy of forming hydrogen bonds within the network) is

$${S}^{{{\rm{network}}}}={k}_{{{{\rm{B}}}}}\,{{{\mathrm{ln}}}}\left(\Omega \right)={k}_{{{{\rm{B}}}}}\,{{{\mathrm{ln}}}}\left(\left({N}^{{{\rm{network}}}}-1\right)\left({N}^{{{\rm{network}}}}-2\right)\left({N}^{{{\rm{network}}}}-3\right)\left({N}^{{{\rm{network}}}}-4\right)\right)$$
(11)

As proteins unfold, they must take water molecules from the surrounding hydrogen-bond network. This process incurs an entropic penalty, as the captured water molecules experience a significant loss in degrees of freedom—including the reduction in the number of possible hydrogen-bonding configurations with neighboring water molecules. If we assume that a water molecule loses all of its hydrogen-bonding interactions within the network upon being sequestered by the unfolding protein, its number of accessible microstates, with respect to hydrogen bond formation, effectively reduces to one. Consequently, the entropy change associated with a single water molecule during protein unfolding—referred to here as the network entropy penalty—can be expressed as:

$$\Delta {S}^{{{\rm{network}}}}=-{k}_{{{{\rm{B}}}}}\,{{{\mathrm{ln}}}}\left(\left({N}^{{{\rm{network}}}}-1\right)\left({N}^{{{\rm{network}}}}-2\right)\left({N}^{{{\rm{network}}}}-3\right)\left({N}^{{{\rm{network}}}}-4\right)\right)$$
(12)

The entropy penalty decreases originated from the shrinkage of intact water network size in high salt concentration systems can be expressed as

$$\Delta \Delta {S}^{{{\rm{network}}}} =\Delta {S}_{{{\rm{salt}}}}^{{{\rm{network}}}}-\Delta {S}_{{{\rm{pure}}}}^{{{\rm{network}}}}\\ =-{k}_{{{{\rm{B}}}}}{{{\mathrm{ln}}}}\left(\frac{\left({N}_{{{\rm{salt}}}}^{{{\rm{network}}}}-1\right)\left({N}_{{{\rm{salt}}}}^{{{\rm{network}}}}-2\right)\left({N}_{{{\rm{salt}}}}^{{{\rm{network}}}}-3\right)\left({N}_{{{\rm{salt}}}}^{{{\rm{network}}}}-4\right)}{\left({N}_{{{\rm{pure}}}}^{{{\rm{total}}}}-1\right)\left({N}_{{{\rm{pure}}}}^{{{\rm{total}}}}-2\right)\left({N}_{{{\rm{pure}}}}^{{{\rm{total}}}}-3\right)\left({N}_{{{\rm{pure}}}}^{{{\rm{total}}}}-4\right)}\right)\\ \doteq -4{k}_{{{{\rm{B}}}}}{{{\mathrm{ln}}}}\left(\frac{{N}_{{{\rm{salt}}}}^{{{\rm{network}}}}}{{N}_{{{\rm{pure}}}}^{{{\rm{total}}}}}\right)\\ =-4{k}_{{{{\rm{B}}}}}{{\mathrm{ln}}}\phi$$
(13)

where \({N}_{{{\rm{pure}}}}^{{{\rm{total}}}}\) is the total number of water molecules in pure water systems as all water molecules here are considered as part of the water network, both \({N}_{{{\rm{salt}}}}^{{{\rm{network}}}}\) and \({N}_{{{\rm{pure}}}}^{{{\rm{total}}}}\) are normally much larger than 1 (i.e., \(\gg 1\)), \(\phi=\frac{{N}_{{{\rm{salt}}}}^{{{\rm{network}}}}}{{N}_{{{\rm{pure}}}}^{{{\rm{total}}}}}\) is the ratio of free water number in salt solution to that of pure water system.

Finally, we have

$$\Delta \Delta {S}^{{{\rm{water}}}} =\Delta {S}_{{{\rm{salt}}}}^{{{\rm{water}}}}-\Delta {S}_{{{\rm{pure}}}}^{{{\rm{water}}}}\\ =\Delta \Delta {S}^{{{\rm{translation}}}}+\Delta \Delta {S}^{{{\rm{rotation}}}}+\Delta \Delta {S}^{{{\rm{vibration}}}}+\Delta {S}^{{{\rm{network}}}}\\ =\Delta \Delta {S}^{{{\rm{translation}}}}+\Delta \Delta {S}^{{{\rm{rotation}}}}+\Delta \Delta {S}^{{{\rm{vibration}}}}-4{k}_{{{{\rm{B}}}}}{{\mathrm{ln}}}\phi$$
(14)

where \(\Delta \Delta {S}^{{{\rm{translation}}}}\), \(\Delta \Delta {S}^{{{\rm{rotation}}}}\), and \(\Delta \Delta {S}^{{{\rm{vibration}}}}\) can be expressed as follows,

$$\Delta \Delta {S}^{{{{\rm{j}}}}} =\Delta {S}_{{{\rm{salt}}}}^{{{{\rm{j}}}}}-\Delta {S}_{{{\rm{pure}}}}^{{{{\rm{j}}}}}\\ =\left({S}_{{{\rm{salt}}}}^{{{{\rm{j}}}}-{{\rm{bound}}}}-{S}_{{{\rm{salt}}}}^{{{{\rm{j}}}}-{{\rm{unbound}}}}\right)-\left({S}_{{{\rm{pure}}}}^{{{{\rm{j}}}}-{{\rm{bound}}}}-{S}_{{{\rm{pure}}}}^{{{{\rm{j}}}}-{{\rm{unbound}}}}\right)\\ ={S}_{{{\rm{pure}}}}^{{{{\rm{j}}}}-{{\rm{unbound}}}}-{S}_{{{\rm{salt}}}}^{{{{\rm{j}}}}-{{\rm{unbound}}}}$$
(15)

where \({{{\rm{j}}}}\) denotes translational or rotational or vibrational components of water entropy, \(\Delta {S}_{{{\rm{salt}}}/{{\rm{pure}}}}^{{{{\rm{j}}}}}\) denotes the water molecular entropy changes during protein unfolding in salt solutions or pure water, with the following definition,

$$\Delta {S}_{{{\rm{salt}}}/{{\rm{pure}}}}^{{{{\rm{j}}}}}={S}_{{{\rm{salt}}}/{{\rm{pure}}}}^{{{{\rm{j}}}}-{{\rm{bound}}}}-{S}_{{{\rm{salt}}}/{{\rm{pure}}}}^{{{{\rm{j}}}}-{{\rm{unbound}}}}$$
(16)

where “bound” and “unbound” represent whether the water molecule is bound or unbound to protein. The entropy of protein-bound water molecules \({S}_{{{\rm{salt}}}}^{{{{\rm{j}}}}-{{\rm{bound}}}}\) and \({S}_{{{\rm{pure}}}}^{{{{\rm{j}}}}-{{\rm{bound}}}}\) are assumed to be independent of their solution environments and thus cancel out each other. \({S}_{{{\rm{salt}}}/{{\rm{pure}}}}^{{{{\rm{j}}}}-{{\rm{unbound}}}}\) can be obtained from 2PT analysis through averaging over all water molecules.

All the parameters in Eq. 14 (\(\Delta \Delta {S}^{{{\rm{translation}}}}\), \(\Delta \Delta {S}^{{{\rm{rotation}}}}\), \(\Delta \Delta {S}^{{{\rm{vibration}}}}\), and \(\phi\)) can be obtained through molecular dynamics simulation and Two-Phase Thermodynamic (2PT) calculation39,54. The numerical calculation heavily depends on the correct counting of water molecule number in network (i.e., \({N}^{{{\rm{network}}}}\)). Rather than arbitrarily defining whether a water molecule belongs to the water network based on a distance cutoff from the ions, we identified the number of water molecules in network based on their entropy values, which is more physically meaningful and helps avoid overcounting. The entropy distributions for water molecules under different salt conditions and concentrations can be obtained via 2PT analysis as shown in Fig. 3c and Supplementary Fig. 15. LiBr and LiCl solutions exhibit clear bimodal distributions, while pure water and NaBr solutions display a single peak. We interpret the higher-entropy population as water molecules in network and the lower-entropy population as ion-bound water molecules, since ion binding restricts the degrees of freedom of water molecules. All distributions were fitted with Gaussian functions, and the number of free water molecules was determined from the proportion of the higher-entropy peak.

It is important to note that translational entropy and network entropy are distinct and independent components; both should be considered when analyzing the entropic contribution of water. Translational entropy reflects the number of spatial positions a water molecule can occupy in three-dimensional space. In contrast, network entropy quantifies the number of possible hydrogen-bonding configurations a water molecule can adopt with other water molecules, based solely on graph connectivity, without regard to spatial coordinates. In other words, regardless of a water molecule’s location in space, there always exist \(\Omega\) distinct configurations through which it can engage in hydrogen bonding, provided it remains part of the hydrogen-bonded network.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.