Grand-reaction method for simulations of ionization equilibria coupled to ion partitioning

Landsgesell, Jonas; Rud, Oleg; Hebbeker, Pascal; Lunkad, Raju; Košovan, Peter; Holm, Christian

doi:10.26434/chemrxiv.9741746

“…To account for the acid-base equilibrium and coupling to the reservoir, we use the grand-reaction Monte Carlo method, introduced in Ref. 27 . We represent the acid-base ionization reaction as…”

Section: Particle-based Models (Md)mentioning

confidence: 99%

“…[44][45][46][47] The CG models of our current study have been used before to model strong polyelectrolyte hydrogels with fixed ionization. 20,24,25 To study weak polyelectrolyte hydrogels, we now combine these models with the grand-reaction Monte Carlo (G-RxMC) method, which we introduced a year ago, 27 Thus, our current study for the first time combines a particle-based model of a weak polyelectrolyte hydrogel with an explicit model of acid-base reactions coupled to a reservoir of ionic solution. This set-up enables the comparison of predictions of swelling and ionization properties of weak polyelectrolyte hydrogels on different levels of approximation, starting from the ideal gas, through the mean-field, up to an explicit-particle representation.…”

Section: Introductionmentioning

confidence: 99%

The pH-dependent Swelling of Weak Polyelectrolyte Hydrogels Modeled at Different Levels of Resolution

Landsgesell

¹

,

Beyer

²

,

Hebbeker

³

et al. 2022

Preprint

Self Cite

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The swelling of polyelectrolyte hydrogels has been often explained using simple models derived from the Flory-Rehner model. While these models qualitatively predict the experimentally observed trends, they also introduce strong approximations and neglect some important contributions. Consequently, they sometimes incorrectly ascribe the observed trends to contributions which are of minor importance under the given conditions. In this work, we investigate the swelling properties of weak (pH-responsive) polyelectrolyte gels at various pH and salt concentrations, using a hierarchy of models, gradually introducing various approximations. For the first time, we introduce a three-dimensional particle-based model which accounts for the topology of the hydrogel network, for electrostatic interactions between gel segments and small ions and for acid-base equilibrium coupled to the Donnan partitioning of small ions. This model is the most accurate one, therefore, we use it as a reference when assessing the effect of various approximations. As the first approximation, we introduce the affine deformation, which allows us to replace the network of many chains by a single chain, while retaining the particle-based representation. In the next step, we use the mean-field approximation to replace particles by density fields, combining the Poisson-Boltzmann equation with elastic stretching of the chain. Finally, we introduce an ideal gel model by neglecting the electrostatics while retaining all other features of the previous model. Comparing predictions from all four models allows us to understand which contributions dominate at high or low pH or salt concentrations. We observe that the field-based models overestimate the ionization degree of the gel because they underestimate the electrostatic interactions. Nevertheless, a cancellation of effects on the electrostatic interactions and Donnan partitioning causes that both particle-based and field-based models consistently predict the swelling of the gels as a function of pH and salt concentration. Thus, we can conclude that any of the employed models can rationalize the known experimental trends in gel swelling, however, only the particle-based models fully account for the true effects causing these trends. The full understanding of differences between various models is important when interpreting experimental results in the framework of existing theories and for ascribing the observed trends to particular contributions, such as the Donnan partitioning of ions, osmotic pressure or electrostatic interactions.

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“…With this, we also assume that any conformational changes do not contribute in a major fashion, which should be a valid approximation for proteins, unlike, for instance, in the case of polyelectrolyte chains [40,41] or protein-RNA complexation [42]. Nonetheless, this effect should be investigated further also in proteins, and recent advances in Monte Carlo and molecular dynamics simulations that include efficient computations of charge regulation effects should be of great aid in this [3,[43][44][45]. Constant-pH molecular dynamics simulations of protein protonisation behaviour would also allow to explore the question of protein protonisation fluctuations fully at the appropriate level without any linearization assumptions while providing a good comparison for the predictions of our model.…”

Section: Discussionmentioning

confidence: 99%

Site Correlations, Capacitance, and Polarizability From Protein Protonation Fluctuations

Božič

¹

,

Podgornik

²

2021

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We generalize the Kirkwood-Shumaker theory of protonisation fluctuation for an anisotropic distribution of dissociable charges on a globular protein. The fluctuations of the total charge and the total dipole moment, in contrast to their average values, depend on the same proton occupancy correlator, thus exhibiting a similar dependence also on the solution pH. This has important consequences for the Kirkwood-Shumaker interaction and its dependence on the bathing solution conditions.

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“…The ionization reaction is modeled using the reaction ensemble formalism, a Monte-Carlo procedure, in which the identity of HA is changed to Aand an H + is inserted into the system, based on the acceptance probabilities described in Refs. 27,53 . The system is coupled to a reservoir by inserting and deleting ion pairs, formally represented as chemical reactions…”

Section: Particle-based Models (Md)mentioning

confidence: 99%

“…The equilibrium constants of these reactions are determined by the reservoir pH and salt concentration, as detailed in Refs. 27,62 . All particle-based simulations are performed using the simulation software ESPResSo.…”

Section: Particle-based Models (Md)mentioning

confidence: 99%

The pH-dependent Swelling of Weak Polyelectrolyte Hydrogels Modeled at Different Levels of Resolution

Landsgesell

¹

,

Beyer

²

,

Hebbeker

³

et al. 2021

Preprint

Self Cite

0

View full text Add to dashboard Cite

The swelling of polyelectrolyte hydrogels has been often explained using simple models derived from the Flory-Rehner model. While these models qualitatively predict the experimentally observed trends, they also introduce strong approximations and neglect some important contributions. Consequently, they sometimes incorrectly ascribe the observed trends to contributions which are of minor importance under the given conditions. In this work, we investigate the swelling properties of weak (pH-responsive) polyelectrolyte gels at various pH and salt concentrations, using a hierarchy of models, gradually introducing various approximations. For the first time, we introduce a three-dimensional particle-based model which accounts for the topology of the hydrogel network, for electrostatic interactions between gel segments and small ions and for acid-base equilibrium coupled to the Donnan partitioning of small ions. This model is the most accurate one, therefore, we use it as a reference when assessing the effect of various approximations. As the first approximation, we introduce the affine deformation, which allows us to replace the network of many chains by a single chain, while retaining the particle-based representation. In the next step, we use the mean-field approximation to replace particles by density fields, combining the Poisson-Boltzmann equation with elastic stretching of the chain. Finally, we introduce an ideal gel model by neglecting the electrostatics while retaining all other features of the previous model. Comparing predictions from all four models allows us to understand which contributions dominate at high or low pH or salt concentrations. We observe that the field-based models overestimate the ionization degree of the gel because they underestimate the electrostatic interactions. Nevertheless, a cancellation of effects on the electrostatic interactions and Donnan partitioning causes that both particle-based and field-based models consistently predict the swelling of the gels as a function of pH and salt concentration. Thus, we can conclude that any of the employed models can rationalize the known experimental trends in gel swelling, however, only the particle-based models fully account for the true effects causing these trends. The full understanding of differences between various models is important when interpreting experimental results in the framework of existing theories and for ascribing the observed trends to particular contributions, such as the Donnan partitioning of ions, osmotic pressure or electrostatic interactions.

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Grand-reaction method for simulations of ionization equilibria coupled to ion partitioning

Cited by 13 publications

References 3 publications

The pH-dependent Swelling of Weak Polyelectrolyte Hydrogels Modeled at Different Levels of Resolution

The pH-dependent Swelling of Weak Polyelectrolyte Hydrogels Modeled at Different Levels of Resolution

Site Correlations, Capacitance, and Polarizability From Protein Protonation Fluctuations

The pH-dependent Swelling of Weak Polyelectrolyte Hydrogels Modeled at Different Levels of Resolution

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