Tuning the collapse transition of weakly charged polymers by ion-specific screening and adsorption

A Unified Description of Salt Effects on the Liquid-Liquid Phase Separation of Proteins

Protein aggregation via liquid-liquid phase separation (LLPS) is ubiquitous in nature and is intimately connected to many human diseases. Although it is widely known that the addition of salt has crucial impacts on the LLPS of proteins, full understanding of the salt effects remains an outstanding challenge. Here, we develop a molecular theory that systematically incorporates the self-consistent field theory for charged macromolecules into the solution thermodynamics. The electrostatic interaction, hydrophobicity, ion solvation, and translational entropy are included in a unified framework. Our theory fully captures the long-standing puzzles of the nonmonotonic salt concentration dependence and the specific ion effect. We find that proteins show salting-out at low salt concentrations due to ionic screening. The solubility follows the inverse Hofmeister series. In the high salt concentration regime, protein continues salting-out for small ions but turns to salting-in for larger ions, accompanied by the reversal of the Hofmeister series. We reveal that the solubility at high salt concentrations is determined by the competition between the solvation energy and translational entropy of the ion. Furthermore, we derive an analytical criterion for determining the boundary between the salting-in and salting-out regimes, which is in good agreement with experimental results for various proteins and salt ions.

Specific ion effects on lignin adsorption and transport through cellulose confinements

The presence of ions in a solution is anticipated to induce distinct effects on macromolecules. Consequently, the tuning of adsorption and mass transfer of lignin molecules can be achieved by incorporating ions with chaotropic or kosmotropic characteristics. This study examines the adsorption and mass transfer behavior of lignin molecules across model cellulose membranes in presence of ions from the Hofmeister series. Experimental investigations encompassed the use of diffusion cells to quantify lignin's mass transfer through the membranes, and quartz crystal microbalance with dissipation (QCM-D) monitoring was used for adsorption studies. Notably, at high ion concentrations, the mass transport rate of lignin was observed to be lower in the presence of highly hydrated (kosmotropic) sulfate ions, conforming to the Hofmeister series. Intriguingly, this relationship was not apparent at lower ion concentrations. Furthermore, QCM-D experiments indicated that lignin displayed higher adsorption onto the cellulose surface when exposed to less hydrated (chaotropic) nitrate anions. This behavior can be rationalized by considering the system's increased entropy gain, facilitated by the release of adsorbed ions and water molecules from the cellulose surface upon lignin adsorption. This study highlights the complexity of ion-specific effects on mass transfer and adsorption processes and their dependency on ion concentrations.

Unraveling fluctuation in gelatin and monovalent salt systems: coulombic starvation

Fluctuations play a key role in biological systems. Here, fluctuations in gelatin intensify with increasing salt concentration. We find a redistribution of hydrogen bonds in protein-salt systems due to unfulfilled hydration of the charges of gelatin and salt-ions, termed as coulombic starvation. This yielded three regions; no starvation, starvation of gelatin, and both gelatin-salt. The system reaches equilibrium with all charges being partially hydrated. This will aid in interpreting protein-metal ion interactions and designing biomaterials.

Understanding specific ion effects and the Hofmeister series

Specific ion effects (SIE), encompassing the Hofmeister Series, have been known for more than 130 years since Hofmeister and Lewith's foundational work. SIEs are ubiquitous and are observed across the medical, biological, chemical and industrial sciences. Nevertheless, no general predictive theory has yet been able to explain ion specificity across these fields; it remains impossible to predict when, how, and to what magnitude, a SIE will be observed. In part, this is due to the complexity of real systems in which ions, counterions, solvents and cosolutes all play varying roles, which give rise to anomalies and reversals in anticipated SIEs. Herein we review the historical explanations for SIE in water and the key ion properties that have been attributed to them. Systems where the Hofmeister series is perturbed or reversed are explored, as is the behaviour of ions at the liquid-vapour interface. We discuss SIEs in mixed electrolytes, nonaqueous solvents, and in highly concentrated electrolyte solutions - exciting frontiers in this field with particular relevance to biological and electrochemical applications. We conclude the perspective by summarising the challenges and opportunities facing this SIE research that highlight potential pathways towards a general predictive theory of SIE.

Denaturation of proteins: electrostatic effects vs. hydration

The unfolding transition of proteins in aqueous solution containing various salts or uncharged solutes is a classical subject of biophysics. In many cases, this transition is a well-defined two-stage equilibrium process which can be described by a free energy of transition ΔG_u and a transition temperature T_m. For a long time, it has been known that solutes can change T_m profoundly. Here we present a phenomenological model that describes the change of T_m with the solute concentration c_s in terms of two effects: (i) the change of the number of correlated counterions Δn_ci and (ii) the change of hydration expressed through the parameter Δw and its dependence on temperature expressed through the parameter dΔc_p/dc_s. Proteins always carry charges and Δn_ci describes the uptake or release of counterions during the transition. Likewise, the parameter Δw measures the uptake or release of water during the transition. The transition takes place in a reservoir with a given salt concentration c_s that defines also the activity of water. The parameter Δn_ci is a measure for the gain or loss of free energy because of the release or uptake of ions and is related to purely entropic effects that scale with ln c_s. Δw describes the effect on ΔG_u through the loss or uptake of water molecules and contains enthalpic as well as entropic effects that scale with c_s. It is related to the enthalpy of transition ΔH_u through a Maxwell relation: the dependence of ΔH_u on c_s is proportional to the dependence of Δw on temperature. While ionic effects embodied in Δn_ci are independent of the kind of salt, the hydration effects described through Δw are directly related to Hofmeister effects of the various salt ions. A comparison with literature data underscores the general validity of the model.

A phenomenological approach to the unfolding transition of proteins is given. The model treats quantitatively the effect of electrostatics as well as of hydration (Hofmeister effects).

Transfer learning of memory kernels for transferable coarse-graining of polymer dynamics

The present work concerns the transferability of coarse-grained (CG) modeling in reproducing the dynamic properties of the reference atomistic systems across a range of parameters. In particular, we focus on implicit-solvent CG modeling of polymer solutions. The CG model is based on the generalized Langevin equation, where the memory kernel plays the critical role in determining the dynamics in all time scales. Thus, we propose methods for transfer learning of memory kernels. The key ingredient of our methods is Gaussian process regression. By integration with the model order reduction via proper orthogonal decomposition and the active learning technique, the transfer learning can be practically efficient and requires minimum training data. Through two example polymer solution systems, we demonstrate the accuracy and efficiency of the proposed transfer learning methods in the construction of transferable memory kernels. The transferability allows for out-of-sample predictions, even in the extrapolated domain of parameters. Built on the transferable memory kernels, the CG models can reproduce the dynamic properties of polymers in all time scales at different thermodynamic conditions (such as temperature and solvent viscosity) and for different systems with varying concentrations and lengths of polymers.

Impact of Arginine-Phosphate Interactions on the Reentrant Condensation of Disordered Proteins

Re-entrant condensation results in the formation of a condensed protein regime between two critical ion concentrations. The process is driven by neutralization and inversion of the protein charge by oppositely charged ions. Re-entrant condensation of cationic proteins by the polyvalent anions, pyrophosphate and tripolyphosphate, has previously been observed, but not for citrate, which has similar charge and size compared to the polyphosphates. Therefore, besides electrostatic interactions, other specific interactions between the polyphosphate ions and proteins must contribute. Here, we show that additional attractive interactions between arginine and tripolyphosphate determine the re-entrant condensation and decondensation boundaries of the cationic, intrinsically disordered saliva protein, histatin 5. Furthermore, we show by small-angle X-ray scattering (SAXS) that polyvalent anions cause compaction of histatin 5, as would be expected based solely on electrostatic interactions. Hence, we conclude that arginine-phosphate-specific interactions not only regulate solution properties but also influence the conformational ensemble of histatin 5, which is shown to vary with the number of arginine residues. Together, the results presented here provide further insight into an organizational mechanism that can be used to tune protein interactions in solution of both naturally occurring and synthetic proteins.

Data-driven coarse-grained modeling of polymers in solution with structural and dynamic properties conserved

We present data-driven coarse-grained (CG) modeling for polymers in solution, which conserves the dynamic as well as structural properties of the underlying atomistic system. The CG modeling is built upon the framework of the generalized Langevin equation (GLE). The key is to determine each term in the GLE by directly linking it to atomistic data. In particular, we propose a two-stage Gaussian process-based Bayesian optimization method to infer the non-Markovian memory kernel from the data of the velocity autocorrelation function (VACF). Considering that the long-time behaviors of the VACF and memory kernel for polymer solutions can exhibit hydrodynamic scaling (algebraic decay with time), we further develop an active learning method to determine the emergence of hydrodynamic scaling, which can accelerate the inference process of the memory kernel. The proposed methods do not rely on how the mean force or CG potential in the GLE is constructed. Thus, we also compare two methods for constructing the CG potential: a deep learning method and the iterative Boltzmann inversion method. With the memory kernel and CG potential determined, the GLE is mapped onto an extended Markovian process to circumvent the expensive cost of directly solving the GLE. The accuracy and computational efficiency of the proposed CG modeling are assessed in a model star-polymer solution system at three representative concentrations. By comparing with the reference atomistic simulation results, we demonstrate that the proposed CG modeling can robustly and accurately reproduce the dynamic and structural properties of polymers in solution.

Theoretical and Computational Insight into Solvent and Specific Ion Effects for Polyelectrolytes: The Importance of Local Molecular Interactions

Polyelectrolytes in solution show a broad plethora of interesting effects. In this short review article, we focus on recent theoretical and computational findings regarding specific ion and solvent effects and their impact on the polyelectrolyte behavior. In contrast to standard mean field descriptions, the properties of polyelectrolytes are significantly influenced by crucial interactions with the solvent, co-solvent and ion species. The corresponding experimental and simulation results reveal a significant deviation from theoretical predictions, which also highlights the importance of charge transfer, dispersion and polarization interactions in combination with solvation mechanisms. We discuss recent theoretical and computational findings in addition to novel approaches which help broaden the applicability of simple mean field theories.

Implicit-solvent coarse-grained modeling for polymer solutions via Mori-Zwanzig formalism

We present a bottom-up coarse-graining (CG) method to establish implicit-solvent CG modeling for polymers in solution, which conserves the dynamic properties of the reference microscopic system. In particular, tens to hundreds of bonded polymer atoms (or Lennard-Jones beads) are coarse-grained as one CG particle, and the solvent degrees of freedom are eliminated. The dynamics of the CG system is governed by the generalized Langevin equation (GLE) derived via the Mori-Zwanzig formalism, by which the CG variables can be directly and rigorously linked to the microscopic dynamics generated by molecular dynamics (MD) simulations. The solvent-mediated dynamics of polymers is modeled by the non-Markovian stochastic dynamics in GLE, where the memory kernel can be computed from the MD trajectories. To circumvent the difficulty in direct evaluation of the memory term and generation of colored noise, we exploit the equivalence between the non-Markovian dynamics and Markovian dynamics in an extended space. To this end, the CG system is supplemented with auxiliary variables that are coupled linearly to the momentum and among themselves, subject to uncorrelated Gaussian white noise. A high-order time-integration scheme is used to solve the extended dynamics to further accelerate the CG simulations. To assess, validate, and demonstrate the established implicit-solvent CG modeling, we have applied it to study four different types of polymers in solution. The dynamic properties of polymers characterized by the velocity autocorrelation function, diffusion coefficient, and mean square displacement as functions of time are evaluated in both CG and MD simulations. Results show that the extended dynamics with auxiliary variables can construct arbitrarily high-order CG models to reproduce dynamic properties of the reference microscopic system and to characterize long-time dynamics of polymers in solution.

In situ study of the competitive adsorption of ions at an organic-aqueous two-phase interface: the essential role of the Hofmeister effect

Understanding of the microcosmic essence of the competitive adsorption of different ions at liquid/liquid interfaces is of crucial importance for the elucidation of the unique chemical reactivities or selectivities of ions in numerous heterogeneous chemical processes. However, the knowledge of the microscopic mechanism behind the competitive adsorption of ions at the liquid/liquid interface is lacking. Herein, the competitive adsorption of various inorganic salt anions at organic-aqueous two-phase interfaces has been investigated as compared to that of the CrO42- ions by total internal reflection UV-visible (TIR-UV) spectroscopy since CrO42- ions are detectable by UV-visible spectroscopy and have a relatively poor interface propensity as compared to other chaotropic ions. Experimental results indicate that the interface propensities of different salt anions to the organic/aqueous phase interface follow the Hofmeister series. Molecular dynamics simulations further provided molecular-level evidence for role of the Hofmeister series of ions in the competitive adsorption of salt anions at organic-aqueous two-phase interfaces; the present study provided the first-hand experimental evidence demonstrating the occurrence of the Hofmeister series effect at the organic/aqueous two-phase interfaces, influencing the competitive adsorption of different salt ions; moreover, it is expected to offer a basis for the development of new strategies for the regulation of the chemical reactivity and selectivity of ions at organic/aqueous phase interfaces by introduction of other ions for competitive adsorption.

Water-Mediated Nanostructures for Enhanced MRI: Impact of Water Dynamics on Relaxometric Properties of Gd-DTPA

Recently, rational design of a new class of contrast agents (CAs), based on biopolymers (hydrogels), have received considerable attention in Magnetic Resonance Imaging (MRI) diagnostic field. Several strategies have been adopted to improve relaxivity without chemical modification of the commercial CAs, however, understanding the MRI enhancement mechanism remains a challenge. Methods: A multidisciplinary approach is used to highlight the basic principles ruling biopolymer-CA interactions in the perspective of their influence on the relaxometric properties of the CA. Changes in polymer conformation and thermodynamic interactions of CAs and polymers in aqueous solutions are detected by isothermal titration calorimetric (ITC) measurements and later, these interactions are investigated at the molecular level using NMR to better understand the involved phenomena. Water molecular dynamics of these systems is also studied using Differential Scanning Calorimetry (DSC). To observe relaxometric properties variations, we have monitored the MRI enhancement of the examined structures over all the experiments. The study of polymer-CA solutions reveals that thermodynamic interactions between biopolymers and CAs could be used to improve MRI Gd-based CA efficiency. High-Pressure Homogenization is used to obtain nanoparticles. Results: The effect of the hydration of the hydrogel structure on the relaxometric properties, called Hydrodenticity and its application to the nanomedicine field, is exploited. The explanation of this concept takes place through several key aspects underlying biopolymer-CA's interactions mediated by the water. In addition, Hydrodenticity is applied to develop Gadolinium-based polymer nanovectors with size around 200 nm with improved MRI relaxation time (10-times). Conclusions: The experimental results indicate that the entrapment of metal chelates in hydrogel nanostructures offers a versatile platform for developing different high performing CAs for disease diagnosis.