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Article ; Online: Reply to "Comment on 'Hydration and mobility of trehalose in aqueous solution'".

Halle, Bertil

The journal of physical chemistry. B

2014 Volume 118, Issue 36, Page(s) 10806–10812

MeSH term(s)	Trehalose/chemistry
Chemical Substances	Trehalose (B8WCK70T7I)
Language	English
Publishing date	2014-09-11
Publishing country	United States
Document type	Comment ; Journal Article ; Research Support, Non-U.S. Gov't
ISSN	1520-5207
ISSN (online)	1520-5207
DOI	10.1021/jp5083467
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Compressibility of the protein-water interface.

Persson, Filip / Halle, Bertil

The Journal of chemical physics

2018 Volume 148, Issue 21, Page(s) 215102

Abstract: The compressibility of a protein relates to its stability, flexibility, and hydrophobic interactions, but the measurement, interpretation, and computation of this important thermodynamic parameter present technical and conceptual challenges. Here, we ... ...

Abstract	The compressibility of a protein relates to its stability, flexibility, and hydrophobic interactions, but the measurement, interpretation, and computation of this important thermodynamic parameter present technical and conceptual challenges. Here, we present a theoretical analysis of protein compressibility and apply it to molecular dynamics simulations of four globular proteins. Using additively weighted Voronoi tessellation, we decompose the solution compressibility into contributions from the protein and its hydration shells. We find that positively cross-correlated protein-water volume fluctuations account for more than half of the protein compressibility that governs the protein's pressure response, while the self correlations correspond to small (∼0.7%) fluctuations of the protein volume. The self compressibility is nearly the same as for ice, whereas the total protein compressibility, including cross correlations, is ∼45% of the bulk-water value. Taking the inhomogeneous solvent density into account, we decompose the experimentally accessible protein partial compressibility into intrinsic, hydration, and molecular exchange contributions and show how they can be computed with good statistical accuracy despite the dominant bulk-water contribution. The exchange contribution describes how the protein solution responds to an applied pressure by redistributing water molecules from lower to higher density; it is negligibly small for native proteins, but potentially important for non-native states. Because the hydration shell is an open system, the conventional closed-system compressibility definitions yield a pseudo-compressibility. We define an intrinsic shell compressibility, unaffected by occupation number fluctuations, and show that it approaches the bulk-water value exponentially with a decay "length" of one shell, less than the bulk-water compressibility correlation length. In the first hydration shell, the intrinsic compressibility is 25%-30% lower than in bulk water, whereas its self part is 15%-20% lower. These large reductions are caused mainly by the proximity to the more rigid protein and are not a consequence of the perturbed water structure.
MeSH term(s)	Animals ; Biomechanical Phenomena ; Cattle ; Mechanical Phenomena ; Molecular Dynamics Simulation ; Proteins/chemistry ; Surface Properties ; Water/chemistry
Chemical Substances	Proteins ; Water (059QF0KO0R)
Language	English
Publishing date	2018-06-07
Publishing country	United States
Document type	Journal Article
ZDB-ID	3113-6
ISSN	1089-7690 ; 0021-9606
ISSN (online)	1089-7690
ISSN	0021-9606
DOI	10.1063/1.5026774
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Article ; Online: Nuclear magnetic relaxation by the dipolar EMOR mechanism: Multi-spin systems.

Chang, Zhiwei / Halle, Bertil

The Journal of chemical physics

2017 Volume 147, Issue 8, Page(s) 84203

Abstract: In aqueous systems with immobilized macromolecules, including biological tissues, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole- ... ...

Abstract	In aqueous systems with immobilized macromolecules, including biological tissues, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. Starting from the stochastic Liouville equation, we have previously developed a rigorous EMOR relaxation theory for dipole-coupled two-spin and three-spin systems. Here, we extend the stochastic Liouville theory to four-spin systems and use these exact results as a guide for constructing an approximate multi-spin theory, valid for spin systems of arbitrary size. This so-called generalized stochastic Redfield equation (GSRE) theory includes the effects of longitudinal-transverse cross-mode relaxation, which gives rise to an inverted step in the relaxation dispersion profile, and coherent spin mode transfer among solid-like spins, which may be regarded as generalized spin diffusion. The GSRE theory is compared to an existing theory, based on the extended Solomon equations, which does not incorporate these phenomena. Relaxation dispersion profiles are computed from the GSRE theory for systems of up to 16 protons, taken from protein crystal structures. These profiles span the range from the motional narrowing limit, where the coherent mode transfer plays a major role, to the ultra-slow motion limit, where the zero-field rate is closely related to the strong-collision limit of the dipolar relaxation rate. Although a quantitative analysis of experimental data is beyond the scope of this work, it is clear from the magnitude of the predicted relaxation rate and the shape of the relaxation dispersion profile that the dipolar EMOR mechanism is the principal cause of water-
Language	English
Publishing date	2017-08-28
Publishing country	United States
Document type	Journal Article
ZDB-ID	3113-6
ISSN	1089-7690 ; 0021-9606
ISSN (online)	1089-7690
ISSN	0021-9606
DOI	10.1063/1.4991687
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Article ; Online: How proteins modify water dynamics.

Persson, Filip / Söderhjelm, Pär / Halle, Bertil

The Journal of chemical physics

2018 Volume 148, Issue 21, Page(s) 215103

Abstract: Much of biology happens at the protein-water interface, so all dynamical processes in this region are of fundamental importance. Local structural fluctuations in the hydration layer can be probed ... ...

Abstract	Much of biology happens at the protein-water interface, so all dynamical processes in this region are of fundamental importance. Local structural fluctuations in the hydration layer can be probed by
MeSH term(s)	Electricity ; Molecular Dynamics Simulation ; Protein Conformation ; Proteins/chemistry ; Rotation ; Water/chemistry
Chemical Substances	Proteins ; Water (059QF0KO0R)
Language	English
Publishing date	2018-06-07
Publishing country	United States
Document type	Journal Article
ZDB-ID	3113-6
ISSN	1089-7690 ; 0021-9606
ISSN (online)	1089-7690
ISSN	0021-9606
DOI	10.1063/1.5026861
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Article ; Online: The geometry of protein hydration.

Persson, Filip / Söderhjelm, Pär / Halle, Bertil

The Journal of chemical physics

2018 Volume 148, Issue 21, Page(s) 215101

Abstract: Based on molecular dynamics simulations of four globular proteins in dilute aqueous solution, with three different water models, we examine several, essentially geometrical, aspects of the protein-water interface that remain controversial or incompletely ...

Abstract	Based on molecular dynamics simulations of four globular proteins in dilute aqueous solution, with three different water models, we examine several, essentially geometrical, aspects of the protein-water interface that remain controversial or incompletely understood. First, we compare different hydration shell definitions, based on spatial or topological proximity criteria. We find that the best method for constructing monolayer shells with nearly complete coverage is to use a 5 Å water-carbon cutoff and a 4 Å water-water cutoff. Using this method, we determine a mean interfacial water area of 11.1 Å
MeSH term(s)	Bacterial Proteins/chemistry ; Molecular Dynamics Simulation ; Protein Domains ; Water/chemistry
Chemical Substances	Bacterial Proteins ; IgG Fc-binding protein, Streptococcus ; Water (059QF0KO0R)
Language	English
Publishing date	2018-06-07
Publishing country	United States
Document type	Journal Article
ZDB-ID	3113-6
ISSN	1089-7690 ; 0021-9606
ISSN (online)	1089-7690
ISSN	0021-9606
DOI	10.1063/1.5026744
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Nuclear magnetic relaxation by the dipolar EMOR mechanism: General theory with applications to two-spin systems.

Chang, Zhiwei / Halle, Bertil

The Journal of chemical physics

2016 Volume 144, Issue 8, Page(s) 84202

Abstract: In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole- ... ...

Abstract	In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. We have embarked on a systematic program to develop, from the stochastic Liouville equation, a general and rigorous theory that can describe relaxation by the dipolar EMOR mechanism over the full range of exchange rates, dipole coupling strengths, and Larmor frequencies. Here, we present a general theoretical framework applicable to spin systems of arbitrary size with symmetric or asymmetric exchange. So far, the dipolar EMOR theory is only available for a two-spin system with symmetric exchange. Asymmetric exchange, when the spin system is fragmented by the exchange, introduces new and unexpected phenomena. Notably, the anisotropic dipole couplings of non-exchanging spins break the axial symmetry in spin Liouville space, thereby opening up new relaxation channels in the locally anisotropic sites, including longitudinal-transverse cross relaxation. Such cross-mode relaxation operates only at low fields; at higher fields it becomes nonsecular, leading to an unusual inverted relaxation dispersion that splits the extreme-narrowing regime into two sub-regimes. The general dipolar EMOR theory is illustrated here by a detailed analysis of the asymmetric two-spin case, for which we present relaxation dispersion profiles over a wide range of conditions as well as analytical results for integral relaxation rates and time-dependent spin modes in the zero-field and motional-narrowing regimes. The general theoretical framework presented here will enable a quantitative analysis of frequency-dependent water-proton longitudinal relaxation in model systems with immobilized macromolecules and, ultimately, will provide a rigorous link between relaxation-based magnetic resonance image contrast and molecular parameters.
MeSH term(s)	Hydroxides/chemistry ; Proton Magnetic Resonance Spectroscopy/standards ; Reference Standards ; Stochastic Processes ; Water/chemistry
Chemical Substances	Hydroxides ; Water (059QF0KO0R) ; hydroxide ion (9159UV381P)
Language	English
Publishing date	2016-02-28
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	3113-6
ISSN	1089-7690 ; 0021-9606
ISSN (online)	1089-7690
ISSN	0021-9606
DOI	10.1063/1.4942026
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Nuclear magnetic relaxation by the dipolar EMOR mechanism: Three-spin systems.

Chang, Zhiwei / Halle, Bertil

The Journal of chemical physics

2016 Volume 145, Issue 3, Page(s) 34202

Abstract	In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. Starting from the stochastic Liouville equation, we have developed a non-perturbative theory that can describe relaxation by the dipolar EMOR mechanism over the full range of exchange rates, dipole couplings, and Larmor frequencies. Here, we implement the general dipolar EMOR theory for a macromolecule-bound three-spin system, where one, two, or all three spins exchange with the bulk solution phase. In contrast to the previously studied two-spin system with a single dipole coupling, there are now three dipole couplings, so relaxation is affected by distinct correlations as well as by self-correlations. Moreover, relaxation can now couple the magnetizations with three-spin modes and, in the presence of a static dipole coupling, with two-spin modes. As a result of this complexity, three secondary dispersion steps with different physical origins can appear in the longitudinal relaxation dispersion profile, in addition to the primary dispersion step at the Larmor frequency matching the exchange rate. Furthermore, and in contrast to the two-spin system, longitudinal relaxation can be significantly affected by chemical shifts and by the odd-valued ("imaginary") part of the spectral density function. We anticipate that the detailed studies of two-spin and three-spin systems that have now been completed will provide the foundation for developing an approximate multi-spin dipolar EMOR theory sufficiently accurate and computationally efficient to allow quantitative molecular-level interpretation of frequency-dependent water-proton longitudinal relaxation data from biophysical model systems and soft biological tissue.
MeSH term(s)	Algorithms ; Models, Theoretical ; Nuclear Magnetic Resonance, Biomolecular/methods ; Stochastic Processes ; Water/chemistry
Chemical Substances	Water (059QF0KO0R)
Language	English
Publishing date	2016-07-21
Publishing country	United States
Document type	Journal Article
ZDB-ID	3113-6
ISSN	1089-7690 ; 0021-9606
ISSN (online)	1089-7690
ISSN	0021-9606
DOI	10.1063/1.4955423
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Article ; Online: The physical basis of model-free analysis of NMR relaxation data from proteins and complex fluids.

Halle, Bertil

The Journal of chemical physics

2009 Volume 131, Issue 22, Page(s) 224507

Abstract: NMR relaxation experiments have provided a wealth of information about molecular motions in macromolecules and ordered fluids. Even though a rigorous theory of spin relaxation is available, the complexity of the investigated systems often makes the ... ...

Abstract	NMR relaxation experiments have provided a wealth of information about molecular motions in macromolecules and ordered fluids. Even though a rigorous theory of spin relaxation is available, the complexity of the investigated systems often makes the interpretation of limited datasets challenging and ambiguous. To allow physically meaningful information to be extracted from the data without commitment to detailed dynamical models, several versions of a model-free (MF) approach to data analysis have been developed. During the past 2 decades, the MF approach has been used in the vast majority of all NMR relaxation studies of internal motions in proteins and other macromolecules, and it has also played an important role in studies of colloidal systems. Although the MF approach has been almost universally adopted, substantial disagreement remains about its physical foundations and range of validity. It is our aim here to clarify these issues. To this end, we first present rigorous derivations of the three well-known MF formulas for the time correlation function relevant for isotropic solutions. These derivations are more general than the original ones, thereby substantially extending the range of validity of the MF approach. We point out several common misconceptions and explain the physical significance of the approximations involved. In particular, we discuss symmetry requirements and the dynamical decoupling approximation that plays a key role in the MF approach. We also derive a new MF formula, applicable to anisotropic fluids and solids, including microcrystalline protein samples. The so-called slowly relaxing local structure (SRLS) model has been advanced as an alternative to the MF approach that does not require dynamical decoupling of internal and global motions. To resolve the existing controversy about the relative merits of the SRLS model and the MF approach, we formulate and solve a planar version of the SRLS model. The analytical solution of this model reveals the unphysical consequences of the symmetrical two-body Smoluchowski equation as applied to protein dynamics, thus refuting the widely held belief that the SRLS model is more accurate than the MF approach. The different results obtained by analyzing data with these two approaches therefore do not indicate the importance of dynamical coupling between internal and global motions. Finally, we explore the two principal mechanisms of dynamical coupling in proteins: torque-mediated and friction-mediated coupling. We argue by way of specific analytically solvable models that torque-mediated coupling (which the SRLS model attempts to capture) is unimportant because the relatively slow internal motions that might couple to the global motion tend to be intermittent (jumplike) in character, whereas friction-mediated coupling (which neither the SRLS model nor the MF approach incorporates) may be important for proteins with unstructured parts or flexibly connected domains.
MeSH term(s)	Colloids/chemistry ; Macromolecular Substances/chemistry ; Magnetic Resonance Spectroscopy ; Models, Chemical ; Proteins/chemistry
Chemical Substances	Colloids ; Macromolecular Substances ; Proteins
Language	English
Publishing date	2009-12-14
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	3113-6
ISSN	1089-7690 ; 0021-9606
ISSN (online)	1089-7690
ISSN	0021-9606
DOI	10.1063/1.3269991
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: The spatial range of protein hydration.

Persson, Filip / Söderhjelm, Pär / Halle, Bertil

The Journal of chemical physics

2018 Volume 148, Issue 21, Page(s) 215104

Abstract: Proteins interact with their aqueous surroundings, thereby modifying the physical properties of the solvent. The extent of this perturbation has been investigated by numerous methods in the past half-century, but a consensus has still not emerged ... ...

Abstract	Proteins interact with their aqueous surroundings, thereby modifying the physical properties of the solvent. The extent of this perturbation has been investigated by numerous methods in the past half-century, but a consensus has still not emerged regarding the spatial range of the perturbation. To a large extent, the disparate views found in the current literature can be traced to the lack of a rigorous definition of the perturbation range. Stating that a particular solvent property differs from its bulk value at a certain distance from the protein is not particularly helpful since such findings depend on the sensitivity and precision of the technique used to probe the system. What is needed is a well-defined decay length, an intrinsic property of the protein in a dilute aqueous solution, that specifies the length scale on which a given physical property approaches its bulk-water value. Based on molecular dynamics simulations of four small globular proteins, we present such an analysis of the structural and dynamic properties of the hydrogen-bonded solvent network. The results demonstrate unequivocally that the solvent perturbation is short-ranged, with all investigated properties having exponential decay lengths of less than one hydration shell. The short range of the perturbation is a consequence of the high energy density of bulk water, rendering this solvent highly resistant to structural perturbations. The electric field from the protein, which under certain conditions can be long-ranged, induces a weak alignment of water dipoles, which, however, is merely the linear dielectric response of bulk water and, therefore, should not be thought of as a structural perturbation. By decomposing the first hydration shell into polarity-based subsets, we find that the hydration structure of the nonpolar parts of the protein surface is similar to that of small nonpolar solutes. For all four examined proteins, the mean number of water-water hydrogen bonds in the nonpolar subset is within 1% of the value in bulk water, suggesting that the fragmentation and topography of the nonpolar protein-water interface has evolved to minimize the propensity for protein aggregation by reducing the unfavorable free energy of hydrophobic hydration.
MeSH term(s)	Entropy ; Hydrogen Bonding ; Hydrophobic and Hydrophilic Interactions ; Proteins/chemistry ; Solvents/chemistry ; Water/chemistry
Chemical Substances	Proteins ; Solvents ; Water (059QF0KO0R)
Language	English
Publishing date	2018-06-07
Publishing country	United States
Document type	Journal Article
ZDB-ID	3113-6
ISSN	1089-7690 ; 0021-9606
ISSN (online)	1089-7690
ISSN	0021-9606
DOI	10.1063/1.5031005
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Longitudinal relaxation in dipole-coupled homonuclear three-spin systems: Distinct correlations and odd spectral densities.

Chang, Zhiwei / Halle, Bertil

The Journal of chemical physics

2015 Volume 143, Issue 23, Page(s) 234201

Abstract: A system of three dipole-coupled spins exhibits a surprisingly intricate relaxation behavior. Following Hubbard's pioneering 1958 study, many authors have investigated different aspects of this problem. Nevertheless, on revisiting this classic relaxation ...

Abstract	A system of three dipole-coupled spins exhibits a surprisingly intricate relaxation behavior. Following Hubbard's pioneering 1958 study, many authors have investigated different aspects of this problem. Nevertheless, on revisiting this classic relaxation problem, we obtain several new results, some of which are at variance with conventional wisdom. Most notably from a fundamental point of view, we find that the odd-valued spectral density function influences longitudinal relaxation. We also show that the effective longitudinal relaxation rate for a non-isochronous three-spin system can exhibit an unusual inverted dispersion step. To clarify these and other issues, we present a comprehensive theoretical treatment of longitudinal relaxation in a three-spin system of arbitrary geometry and with arbitrary rotational dynamics. By using the Liouville-space formulation of Bloch-Wangsness-Redfield theory and a basis of irreducible spherical tensor operators, we show that the number of relaxation components in the different cases can be deduced from symmetry arguments. For the isochronous case, we present the relaxation matrix in analytical form, whereas, for the non-isochronous case, we employ a computationally efficient approach based on the stochastic Liouville equation.
Language	English
Publishing date	2015-12-21
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	3113-6
ISSN	1089-7690 ; 0021-9606
ISSN (online)	1089-7690
ISSN	0021-9606
DOI	10.1063/1.4937377
Database	MEDical Literature Analysis and Retrieval System OnLINE

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