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Rationale for using NMR to study water relations in foods and biological tissues
Review
Rationale for using NMR to study water relations in foods and biological tissues Herman J.e. Berendsen Water relations in hydrated biological materials are reflected in the magnetic resonance relaxation behaviour of water, but the relationship is not straightforward at all. The two types of relaxation behaviour that can be distinguished experimentally
(T, and T2) are related to different aspects of the interaction and motion of the water molecules. The presence of macromolecules complicates the interpretation of both kinds of relaxation and may cause erroneous conclusions if standard theories are applied. Measurements of T, are generally more reliable than T2 measurements, but can be complicated by spin diffusion processes. T2 relaxation can be complicated by slow diffusion among locally ordered regions in heterogeneous samples. In general, a model in which water exchanges rapidly between the first hydration layer of a macromolecule and all other water (the 'bulk' water) fits the experimental results as well as computer simulations. The water in the first hydration layer is slowed down in rotation and translation by a factor of 2-3, and interacts with the macromolecular protons while it diffuses through the system.
The state of water in cells, biological tissues, other biological materials and foods has long been a matter of discussion and controversy. There is no doubt that water plays an essential role in biological environments, but it has proved to be extremely difficult to characterize the properties of water in such heterogeneous and complex environments as biological tissues and materials I. The next step, to relate the characteristics of water to biological function, has almost never been made clearly and unambiguously. Many material and functional Herman J.e. Berendsen is at the BIOSON Research Institute, laboratory of Biophysical Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands. The author is Professor of physical chemistry and has been engaged in the study of water relations in biological tissues using nuclear magnetic resonance since 1962. Since 1976 his research interests have shifted to computer simulation of hydrated biological macromolecules using the methods of molecular dynamics.
202
©1992, Elsevier Science Publishers Ltd, (UK)
properties are strongly dependent on water content, which is related to water activity (measured by osmotic or vapour pressure). Felix Franks contributed a Viewpoint article on the validity of relating water activity to food safety and quality to this journal last year2, warning against a light-hearted faith in the general applicability of observed correlations between water activity and microbial growth potential. On the molecular level, water plays an essential role in the structure of proteins, polysaccharides, nucleic acids and lipid aggregates; structural integrity may be irreversibly lost once the water content drops below a critical value. Lyophilized material should retain a water content of at least several per cent in order to be able to rehydrate in a reversible manner. Collagen, for example, is irreversibly denatured when it is deprived of the few water molecules that stabilize its three-fold helical coil. Most proteins contain a few internally bound water molecules that are essential for the integrity of the native structure,
Nuclear spin relaxation NMR spectroscopy has been applied to water since its invention, because the water signal can so easily be measured and, due to the mobility of water molecules, can easily be distinguished from the signals of other constituents in a complex hydrated material. Relaxation properties can be accurately determined and, since they are somehow related to the molecular properties of water, it should be possible to derive relevant characteristics of water in tissues and foods from a careful interpretation of the nuclear spin relaxation of water. This challenge can only partially be met because of the complexity of the interactions; a less careful analysis may easily lead to erroneous conclusions if simple assumptions, made for simple applications, are assumed to hold in the complex case as well. In addition, it is often necessary to distinguish the various possible molecular causes that determine the relaxation behaviour experimentally, by changing water content, temperature, water isotopic composition or magnetic field strength. Let us consider first what is actually measured in NMR relaxation experiments, then look at the interactions on a molecular scale that determine the resonance characteristics and, finally, consider the kinetics of the behaviour of water. In order to draw the link between NMR and molecular events, it is very useful to , consider computer simulations of the molecular dynamics of water and hydrated biopolymers. A water NMR signal can -he characterized by three properties: • its resonance frequency; • its longitudinal relaxation behaviour, often given by the longitudinal or spin-lattice relaxation time, T,; • its transverse relaxation behaviour, often given by the transverse or spin-spin relaxation time, T2• Of these, the resonance frequency is the least informative. Separate water molecules are not seen because the water 1ll01ecules generally exchange quickly, Trends in Food Science & Technology August/September 1992 [Vol. 3)
and only a single resonance is observed. The basic theory of longitudinal and transverse relaxation is treated elsewhere in this issue 3 ; here we shall take a simple approach and consider the protons of the water molecules to resonate in a large external magnetic field, Bo, that is modified by a fluctuating local field, B,ocal ' This local field may be due to neighbouring nuclei, but it may also result from the exchange with a binding site at a macromolecule with a different chemical shift. The proton resonance properties are determined by the characteristics of this local field (its average value, and the magnitude and time dependence of its fluctuation). Considering each proton independently in its own fluctuating local field neglects some quantum-mechanical detail and is quantitatively not quite correct, but contains all the essential features of the problem.
Molecular interactions that produce local fields The interactions described below contribute to local magnetic fields in the case of a hydrated biomacromolecule. The type of motion that leads to fluctuation of the local field for each particular type of interaction is also indicated.
Intramolecular interaction between the two protons on one water molecule Since the distance between the two protons is practically constant, a local field of a given magnitude is produced (about 2 mT or 20 gauss), which fluctuates with the rotational motion of the water molecule. The local field is proportional to 3cos 2( tJ)-l, where tJ is the angle between the external magnetic field and the vector connecting the two protons. Its average value is zero, which means that the effect vanishes as the molecules approach very fast rotational motion (happily so, because otherwise high-resolution NMR spectroscopy in solution would not be possible!). The magnitude of this kind of interaction is proportional to the proton concentration if experiments are performed in a H 20/D 20 mixture. Intermolecular interaction between two protons on different water molecules In this case, not only the direction of interaction, but also the distance between the protons, and hence the magnitude of the local field, changes because of the diffusional motion of the water molecules. The magnitude of the intramolecular proton-proton interaction is proportional to the proton concentration in H zO/D 20 mixtures. Interaction between a water proton and a proton (or other magnetic nucleus) in a macromolecule In this case, the local field is governed by two properties: the behaviour of the protons in the macromolecules, which have their own interactions with their environment; and the time dependence of the distance between the water proton and the macromolecule (again, the diffusional motion of the water molecule). One can view the water proton as moving in a local Trends in Food Science & Technology August/September 1992 [Vol. 3J
field produced by magnetic nuclei (essentially only protons) in the macromolecule. The effect on relaxation is independent of the isotopic ratio.
Exchange between a water proton and a proton bound to the macromolecule When such exchange processes occur, a particular proton will spend a fraction of its lifetime not bound to water, but bound to a macromolecule via an oxygen, nitrogen or sulphur atom. When bound to a macromolecular group, it may experience a different local field due to the difference in chemical shift. While in all the cases described above the local field results from the dipolar field of other nuclei and, hence, is independent of the external field, in this case the local field is proportional to the external field. This fact may be used to distinguish this particular type of molecular interaction by conducting the NMR experiment at different magnetic field strengths; the mixing of water with heavy water does not influence the relaxation behaviour in this case. There may be other factors that contribute to local magnetic fields in addition to the ones mentioned above, but they apply only in special cases that will not be considered here. The most important case is the presence of unpaired electrons in the macromolecule or solution in the form of paramagnetic ions or free radicals. Such paramagnetic centres strongly influence the relaxation behaviour of nearby protons.
Longitudinal and transverse spin relaxation It is important at this point to relate the two types of spin relaxation to the rate of fluctuation of the local magnetic field. The longitudinal relaxation time gives the timecourse with which the protons exchange energy with the environment (a spin-lattice relaxation). If this timecourse is exponential, one can define a spin-lattice relaxation time (T,), which is often of the order of one second. T, is determined by local field fluctuations at the resonance frequency, say 100 MHz. This means that processes with time constants in the nanosecond range effectively increase the relaxation rate (decrease T,); both much faster and much slower processes are ineffective. For water molecules interacting with macromolecules and diffusing in the environment of a macromolecule, there is a slow component of the interaction with the macromolecule. Its time dependence is such that the resulting relaxation rate (determined by frequency components at the resonance frequency) is inversely proportional to the square root of the resonance frequency, indicating a diffusional process. Protons in macromolecules can often mutually exchange their energies quite rapidly by a process called spin diffusion. This process causes all coupled protons to act as one reservoir, and tends to make all individual T, values equal. In such a case, T, is not determined by the local fluctuating fields, but by the presence of particular 'sinks': protons with motions in the effective frequency range. In macromolecules, rotating methyl groups form such sinks. If spin diffusion is present, the spin-lattice relaxation is generally found to deviate 203
from exponential behaviour; non-exponential behaviour is a warning that spin diffusion is taking place. The transverse relaxation, on the other hand, is the result of interactions between spins that conserve the total energy (spin-spin relaxation). It is a kind of dephasing process: protons that resonate initially in phase will get out of phase in the course of time because each proton experiences a fluctuating field and hence a fluctuating resonance frequency. The transverse relaxation rate is proportional to the mean square deviation of the resonance frequency (thus, to the square of the magnitude of the local field) and is also proportional to the correlation time of the local field fluctuation. The slower the field fluctuates, the faster the dephasing progresses and the shorter the transverse relaxation time T2 becomes. A short T2 also means a broad resonance. Unlike the case of spin-lattice relaxation, there is no limit or optimum to the process of spin-spin relaxation. The T2 behaviour is more local than the T) behaviour and is not complicated by the process of spin diffusion. However, in heterogeneous macromolecular systems, T2 has its own complication, which is often overlooked). Consider a structure with local order, extending over a size of tens of nanometers, as sketched in Fig. 1. Many macromolecular or lipid aggregates fall into this class. If water resides in a structurally ordered local region, the local field does not average to zero, but a certain small average field (L1B) remains, which gives rise to a splitting of the resonance signal. In macroscopically ordered systems, such as hydrated collagen4 or DNA fibres, such resonance splittings (in the range of a few hundred
.
,
':.'i.fi!!.(.: ......... . ... .
. . . ..
....~. . :.~:...~ ... . . . . . .. .. . ... ..
,
milligauss) are commonly observed. But in a macroscopically disordered system, water molecules diffuse slowly between locally ordered regions, producing slowly fluctuating components of the local fields. These slow components decrease T2 while not influencing T) at all. It is clear from the foregoing that the interpretation of the spin relaxation behaviour of water in heterogeneous hydrated biomacromolecular systems is not straightforward. Particular care must be exercised if standard formulae are being used to interpret T) and T2 in terms of molecular motion. The best (but also the most tedious) procedure is to determine experimentally which molecular interaction is dominantly responsible for the observed effects, by changing the appropriate experimental parameter. For example, don't interpret a T) value in terms of rotational rate of water motion unless you have verified by a deuterium exchange experiment that T) is inversely proportional to the proton mole fraction. It is likely not to be! Then measure at another frequency to see if exchange with chemically different sites is important. If it is not, attribute the relaxation to interactions between water and macromolecular protons - but beware of spin diffusion among the macromolecular protons. Don't interpret the T2 of water in heterogeneous but locally ordered systems at all.
Macromolecular hydration exchange model What happens if the water content of a sample containing macromolecules is varied? Let us assume that there are two types of water molecules: bound and free, which are in fast exchange. The spin-lattice relaxation rate, R) (R) = 1IT) is a weighted average of the relaxation rates of the two kinds of water molecules. Thus, R) is a linear function of the fraction (f) of bound water (relative to the total amount of water), which is proportional to II P where Pw is the water content in grams per 100 grams dry weight. Such a relationship is indeed observed, for example, in bovine serum albumin (BSA) solutions containing up to 30% protein (Kamman, R.L., PhD thesis, University of Groningen, The Netherlands, 1987). A large number of studies of BSA in which both water content and frequency were varied have been shown to fit the macromolecular hydration exchange model, in addition to exhibiting the 'inverse square root of frequency' behaviour typical of water molecules diffusing around a macromolecule with which they interact. The 'bound' water of the BSA system amounts to -50 g per 100 g protein. The division into two kinds of water is a simplification: in fact there are many kinds of binding with varying strength-, but NMR relaxation will not be able to resolve them further. W'
.
.. ... ..
I/:~··:·
Molecul.ar dynamics simulations of hydrated Fig. 1 macromolecules Heterogeneous material with local order (represented by parallel lines) causes water molecules (represented by dots) to diffuse from one ordered region to another, providing the low-frequency components of the local field fluctuations that contribute to the transverse relaxation.
204
Recently, it has become possible to simulate complex molecular systems such as hydrated biological macromolecules with the methods of molecular dynamics (e.g. see Ref. 5 and references therein). This amounts to solving Newton's equations of motion for thousands of atoms and for tens of thousands of time steps, based on
Trends in Food Science & Technology August/September 1992 [Vol. 3)
a description of the potential energy in terms of the coordinates of all atoms. Such simulations, after validation by comparison with experiment, yield extremely detailed insights into the dynamic molecular events. For example, the hydration structure of bovine pancreatic trypsin inhibitor has been simulated in aqueous solution, as well as in the hydrated crystalline state (Zwanenburg, G., unpublished). The results are summarized below. If we define 'hydration water' as all water molecules that have at least one protein atom as a nearest neighbour, then the hydration water of bovine pancreatic trypsin inhibitor amounts to -100 g per 100 g protein (but note that this is a small protein of 54 amino acids with a relatively large surface area). This hydration water is the only water that significantly deviates in its dynamic behaviour from bulk water. Its rotational correlation time is, on average, 2-3 times longer than in the bulk solution, for both water next to a hydrophobic protein atom and water next to a hydrophilic protein atom. The diffusion coefficient cannot be accurately determined (the simulations are too short for a detailed analysis), but will follow the same pattern because there is a strong correlation between rotational and translational motion in water. The macromolecular exchange model (Fig. 2) with two kinds of water seems to be a valid model, based both on molecular dynamics results and on experimental relaxation studies of protein solutions. Dry material, containing less than 50% water, may behave differently. In this case there are more than two kinds of water, and the water molecules exchange between various kinds of bound states. There is no component corresponding to bulk water, and lifetimes in bound states may extend into the microsecond range' .
Conclusion Interpretation of the relaxation behaviour of water in complex systems containing hydrophilic macromolecules is by no means a straightforward exercise. Nevertheless, by careful analysis and experimental variation, the proper molecular explanation of the observed effects can be discerned and analysed. The thoughtless application of textbook equations may lead to erroneous conclusions. Interpretations should be kept as simple as possible and one should use simple models only: NMR relaxation is not an information-intensive technique that
macromol ecule
fast exchange
free water
o
bound water
Fig. 2 The two-state macromolecular hydration exchange model assumes one layer of 'bound' water with modified properties in fast exchange with 'free' water. The bound water is 2-3 times slower than free water and amounts to -50 g per 100 g macromolecule.
allows very detailed conclusions. However, this does not restrict the pragmatic use of relaxation characteristics, for example in the optimization of contrast in NMR imaging, where the manipulation of relaxation analysis can considerably enhance its usefulness.
References 2 3 4 5
Berendsen, H.J.C. (1975) in Water, A Comprehensive Treatise (Franks, F., ed.), pp. 293-330, Plenum Press Franks, F. (1991) Trends Food Sci. Technol. 2, 68-72 Hemminga, M. (1992) Trends Food Sci. Technol. 3, 179-186 Berendsen, H.J.C. and Grigera, J.R. (1979) Biopolymers 18, 47-57 Van Gunsteren, W.F. and Berendsen, H.J.C. (1990) Angew. Chem.lnt. Ed. Engl. 29, 992--1023
In next month's issue Progress in the identification of irradiated foods, by M.H. Stevenson Tracer studies of nutrient availability using 'naturally enriched' DC-labelled substrates, by Brian A. McGaw Peptide-specific Maillard reaction products: a new pathway for flavor chemistry, by Henry V. Izzo and Chi-Tang Ho pH of low-moisture solids, by Leonard N. Bell and Theodore P. Labuza
Trends in Food Science & Technology August/September 1992 [Vol. 3J
205
Rationale for using NMR to study water relations in foods and biological tissues Herman J.e. Berendsen Water relations in hydrated biological materials are reflected in the magnetic resonance relaxation behaviour of water, but the relationship is not straightforward at all. The two types of relaxation behaviour that can be distinguished experimentally
(T, and T2) are related to different aspects of the interaction and motion of the water molecules. The presence of macromolecules complicates the interpretation of both kinds of relaxation and may cause erroneous conclusions if standard theories are applied. Measurements of T, are generally more reliable than T2 measurements, but can be complicated by spin diffusion processes. T2 relaxation can be complicated by slow diffusion among locally ordered regions in heterogeneous samples. In general, a model in which water exchanges rapidly between the first hydration layer of a macromolecule and all other water (the 'bulk' water) fits the experimental results as well as computer simulations. The water in the first hydration layer is slowed down in rotation and translation by a factor of 2-3, and interacts with the macromolecular protons while it diffuses through the system.
The state of water in cells, biological tissues, other biological materials and foods has long been a matter of discussion and controversy. There is no doubt that water plays an essential role in biological environments, but it has proved to be extremely difficult to characterize the properties of water in such heterogeneous and complex environments as biological tissues and materials I. The next step, to relate the characteristics of water to biological function, has almost never been made clearly and unambiguously. Many material and functional Herman J.e. Berendsen is at the BIOSON Research Institute, laboratory of Biophysical Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands. The author is Professor of physical chemistry and has been engaged in the study of water relations in biological tissues using nuclear magnetic resonance since 1962. Since 1976 his research interests have shifted to computer simulation of hydrated biological macromolecules using the methods of molecular dynamics.
202
©1992, Elsevier Science Publishers Ltd, (UK)
properties are strongly dependent on water content, which is related to water activity (measured by osmotic or vapour pressure). Felix Franks contributed a Viewpoint article on the validity of relating water activity to food safety and quality to this journal last year2, warning against a light-hearted faith in the general applicability of observed correlations between water activity and microbial growth potential. On the molecular level, water plays an essential role in the structure of proteins, polysaccharides, nucleic acids and lipid aggregates; structural integrity may be irreversibly lost once the water content drops below a critical value. Lyophilized material should retain a water content of at least several per cent in order to be able to rehydrate in a reversible manner. Collagen, for example, is irreversibly denatured when it is deprived of the few water molecules that stabilize its three-fold helical coil. Most proteins contain a few internally bound water molecules that are essential for the integrity of the native structure,
Nuclear spin relaxation NMR spectroscopy has been applied to water since its invention, because the water signal can so easily be measured and, due to the mobility of water molecules, can easily be distinguished from the signals of other constituents in a complex hydrated material. Relaxation properties can be accurately determined and, since they are somehow related to the molecular properties of water, it should be possible to derive relevant characteristics of water in tissues and foods from a careful interpretation of the nuclear spin relaxation of water. This challenge can only partially be met because of the complexity of the interactions; a less careful analysis may easily lead to erroneous conclusions if simple assumptions, made for simple applications, are assumed to hold in the complex case as well. In addition, it is often necessary to distinguish the various possible molecular causes that determine the relaxation behaviour experimentally, by changing water content, temperature, water isotopic composition or magnetic field strength. Let us consider first what is actually measured in NMR relaxation experiments, then look at the interactions on a molecular scale that determine the resonance characteristics and, finally, consider the kinetics of the behaviour of water. In order to draw the link between NMR and molecular events, it is very useful to , consider computer simulations of the molecular dynamics of water and hydrated biopolymers. A water NMR signal can -he characterized by three properties: • its resonance frequency; • its longitudinal relaxation behaviour, often given by the longitudinal or spin-lattice relaxation time, T,; • its transverse relaxation behaviour, often given by the transverse or spin-spin relaxation time, T2• Of these, the resonance frequency is the least informative. Separate water molecules are not seen because the water 1ll01ecules generally exchange quickly, Trends in Food Science & Technology August/September 1992 [Vol. 3)
and only a single resonance is observed. The basic theory of longitudinal and transverse relaxation is treated elsewhere in this issue 3 ; here we shall take a simple approach and consider the protons of the water molecules to resonate in a large external magnetic field, Bo, that is modified by a fluctuating local field, B,ocal ' This local field may be due to neighbouring nuclei, but it may also result from the exchange with a binding site at a macromolecule with a different chemical shift. The proton resonance properties are determined by the characteristics of this local field (its average value, and the magnitude and time dependence of its fluctuation). Considering each proton independently in its own fluctuating local field neglects some quantum-mechanical detail and is quantitatively not quite correct, but contains all the essential features of the problem.
Molecular interactions that produce local fields The interactions described below contribute to local magnetic fields in the case of a hydrated biomacromolecule. The type of motion that leads to fluctuation of the local field for each particular type of interaction is also indicated.
Intramolecular interaction between the two protons on one water molecule Since the distance between the two protons is practically constant, a local field of a given magnitude is produced (about 2 mT or 20 gauss), which fluctuates with the rotational motion of the water molecule. The local field is proportional to 3cos 2( tJ)-l, where tJ is the angle between the external magnetic field and the vector connecting the two protons. Its average value is zero, which means that the effect vanishes as the molecules approach very fast rotational motion (happily so, because otherwise high-resolution NMR spectroscopy in solution would not be possible!). The magnitude of this kind of interaction is proportional to the proton concentration if experiments are performed in a H 20/D 20 mixture. Intermolecular interaction between two protons on different water molecules In this case, not only the direction of interaction, but also the distance between the protons, and hence the magnitude of the local field, changes because of the diffusional motion of the water molecules. The magnitude of the intramolecular proton-proton interaction is proportional to the proton concentration in H zO/D 20 mixtures. Interaction between a water proton and a proton (or other magnetic nucleus) in a macromolecule In this case, the local field is governed by two properties: the behaviour of the protons in the macromolecules, which have their own interactions with their environment; and the time dependence of the distance between the water proton and the macromolecule (again, the diffusional motion of the water molecule). One can view the water proton as moving in a local Trends in Food Science & Technology August/September 1992 [Vol. 3J
field produced by magnetic nuclei (essentially only protons) in the macromolecule. The effect on relaxation is independent of the isotopic ratio.
Exchange between a water proton and a proton bound to the macromolecule When such exchange processes occur, a particular proton will spend a fraction of its lifetime not bound to water, but bound to a macromolecule via an oxygen, nitrogen or sulphur atom. When bound to a macromolecular group, it may experience a different local field due to the difference in chemical shift. While in all the cases described above the local field results from the dipolar field of other nuclei and, hence, is independent of the external field, in this case the local field is proportional to the external field. This fact may be used to distinguish this particular type of molecular interaction by conducting the NMR experiment at different magnetic field strengths; the mixing of water with heavy water does not influence the relaxation behaviour in this case. There may be other factors that contribute to local magnetic fields in addition to the ones mentioned above, but they apply only in special cases that will not be considered here. The most important case is the presence of unpaired electrons in the macromolecule or solution in the form of paramagnetic ions or free radicals. Such paramagnetic centres strongly influence the relaxation behaviour of nearby protons.
Longitudinal and transverse spin relaxation It is important at this point to relate the two types of spin relaxation to the rate of fluctuation of the local magnetic field. The longitudinal relaxation time gives the timecourse with which the protons exchange energy with the environment (a spin-lattice relaxation). If this timecourse is exponential, one can define a spin-lattice relaxation time (T,), which is often of the order of one second. T, is determined by local field fluctuations at the resonance frequency, say 100 MHz. This means that processes with time constants in the nanosecond range effectively increase the relaxation rate (decrease T,); both much faster and much slower processes are ineffective. For water molecules interacting with macromolecules and diffusing in the environment of a macromolecule, there is a slow component of the interaction with the macromolecule. Its time dependence is such that the resulting relaxation rate (determined by frequency components at the resonance frequency) is inversely proportional to the square root of the resonance frequency, indicating a diffusional process. Protons in macromolecules can often mutually exchange their energies quite rapidly by a process called spin diffusion. This process causes all coupled protons to act as one reservoir, and tends to make all individual T, values equal. In such a case, T, is not determined by the local fluctuating fields, but by the presence of particular 'sinks': protons with motions in the effective frequency range. In macromolecules, rotating methyl groups form such sinks. If spin diffusion is present, the spin-lattice relaxation is generally found to deviate 203
from exponential behaviour; non-exponential behaviour is a warning that spin diffusion is taking place. The transverse relaxation, on the other hand, is the result of interactions between spins that conserve the total energy (spin-spin relaxation). It is a kind of dephasing process: protons that resonate initially in phase will get out of phase in the course of time because each proton experiences a fluctuating field and hence a fluctuating resonance frequency. The transverse relaxation rate is proportional to the mean square deviation of the resonance frequency (thus, to the square of the magnitude of the local field) and is also proportional to the correlation time of the local field fluctuation. The slower the field fluctuates, the faster the dephasing progresses and the shorter the transverse relaxation time T2 becomes. A short T2 also means a broad resonance. Unlike the case of spin-lattice relaxation, there is no limit or optimum to the process of spin-spin relaxation. The T2 behaviour is more local than the T) behaviour and is not complicated by the process of spin diffusion. However, in heterogeneous macromolecular systems, T2 has its own complication, which is often overlooked). Consider a structure with local order, extending over a size of tens of nanometers, as sketched in Fig. 1. Many macromolecular or lipid aggregates fall into this class. If water resides in a structurally ordered local region, the local field does not average to zero, but a certain small average field (L1B) remains, which gives rise to a splitting of the resonance signal. In macroscopically ordered systems, such as hydrated collagen4 or DNA fibres, such resonance splittings (in the range of a few hundred
.
,
':.'i.fi!!.(.: ......... . ... .
. . . ..
....~. . :.~:...~ ... . . . . . .. .. . ... ..
,
milligauss) are commonly observed. But in a macroscopically disordered system, water molecules diffuse slowly between locally ordered regions, producing slowly fluctuating components of the local fields. These slow components decrease T2 while not influencing T) at all. It is clear from the foregoing that the interpretation of the spin relaxation behaviour of water in heterogeneous hydrated biomacromolecular systems is not straightforward. Particular care must be exercised if standard formulae are being used to interpret T) and T2 in terms of molecular motion. The best (but also the most tedious) procedure is to determine experimentally which molecular interaction is dominantly responsible for the observed effects, by changing the appropriate experimental parameter. For example, don't interpret a T) value in terms of rotational rate of water motion unless you have verified by a deuterium exchange experiment that T) is inversely proportional to the proton mole fraction. It is likely not to be! Then measure at another frequency to see if exchange with chemically different sites is important. If it is not, attribute the relaxation to interactions between water and macromolecular protons - but beware of spin diffusion among the macromolecular protons. Don't interpret the T2 of water in heterogeneous but locally ordered systems at all.
Macromolecular hydration exchange model What happens if the water content of a sample containing macromolecules is varied? Let us assume that there are two types of water molecules: bound and free, which are in fast exchange. The spin-lattice relaxation rate, R) (R) = 1IT) is a weighted average of the relaxation rates of the two kinds of water molecules. Thus, R) is a linear function of the fraction (f) of bound water (relative to the total amount of water), which is proportional to II P where Pw is the water content in grams per 100 grams dry weight. Such a relationship is indeed observed, for example, in bovine serum albumin (BSA) solutions containing up to 30% protein (Kamman, R.L., PhD thesis, University of Groningen, The Netherlands, 1987). A large number of studies of BSA in which both water content and frequency were varied have been shown to fit the macromolecular hydration exchange model, in addition to exhibiting the 'inverse square root of frequency' behaviour typical of water molecules diffusing around a macromolecule with which they interact. The 'bound' water of the BSA system amounts to -50 g per 100 g protein. The division into two kinds of water is a simplification: in fact there are many kinds of binding with varying strength-, but NMR relaxation will not be able to resolve them further. W'
.
.. ... ..
I/:~··:·
Molecul.ar dynamics simulations of hydrated Fig. 1 macromolecules Heterogeneous material with local order (represented by parallel lines) causes water molecules (represented by dots) to diffuse from one ordered region to another, providing the low-frequency components of the local field fluctuations that contribute to the transverse relaxation.
204
Recently, it has become possible to simulate complex molecular systems such as hydrated biological macromolecules with the methods of molecular dynamics (e.g. see Ref. 5 and references therein). This amounts to solving Newton's equations of motion for thousands of atoms and for tens of thousands of time steps, based on
Trends in Food Science & Technology August/September 1992 [Vol. 3)
a description of the potential energy in terms of the coordinates of all atoms. Such simulations, after validation by comparison with experiment, yield extremely detailed insights into the dynamic molecular events. For example, the hydration structure of bovine pancreatic trypsin inhibitor has been simulated in aqueous solution, as well as in the hydrated crystalline state (Zwanenburg, G., unpublished). The results are summarized below. If we define 'hydration water' as all water molecules that have at least one protein atom as a nearest neighbour, then the hydration water of bovine pancreatic trypsin inhibitor amounts to -100 g per 100 g protein (but note that this is a small protein of 54 amino acids with a relatively large surface area). This hydration water is the only water that significantly deviates in its dynamic behaviour from bulk water. Its rotational correlation time is, on average, 2-3 times longer than in the bulk solution, for both water next to a hydrophobic protein atom and water next to a hydrophilic protein atom. The diffusion coefficient cannot be accurately determined (the simulations are too short for a detailed analysis), but will follow the same pattern because there is a strong correlation between rotational and translational motion in water. The macromolecular exchange model (Fig. 2) with two kinds of water seems to be a valid model, based both on molecular dynamics results and on experimental relaxation studies of protein solutions. Dry material, containing less than 50% water, may behave differently. In this case there are more than two kinds of water, and the water molecules exchange between various kinds of bound states. There is no component corresponding to bulk water, and lifetimes in bound states may extend into the microsecond range' .
Conclusion Interpretation of the relaxation behaviour of water in complex systems containing hydrophilic macromolecules is by no means a straightforward exercise. Nevertheless, by careful analysis and experimental variation, the proper molecular explanation of the observed effects can be discerned and analysed. The thoughtless application of textbook equations may lead to erroneous conclusions. Interpretations should be kept as simple as possible and one should use simple models only: NMR relaxation is not an information-intensive technique that
macromol ecule
fast exchange
free water
o
bound water
Fig. 2 The two-state macromolecular hydration exchange model assumes one layer of 'bound' water with modified properties in fast exchange with 'free' water. The bound water is 2-3 times slower than free water and amounts to -50 g per 100 g macromolecule.
allows very detailed conclusions. However, this does not restrict the pragmatic use of relaxation characteristics, for example in the optimization of contrast in NMR imaging, where the manipulation of relaxation analysis can considerably enhance its usefulness.
References 2 3 4 5
Berendsen, H.J.C. (1975) in Water, A Comprehensive Treatise (Franks, F., ed.), pp. 293-330, Plenum Press Franks, F. (1991) Trends Food Sci. Technol. 2, 68-72 Hemminga, M. (1992) Trends Food Sci. Technol. 3, 179-186 Berendsen, H.J.C. and Grigera, J.R. (1979) Biopolymers 18, 47-57 Van Gunsteren, W.F. and Berendsen, H.J.C. (1990) Angew. Chem.lnt. Ed. Engl. 29, 992--1023
In next month's issue Progress in the identification of irradiated foods, by M.H. Stevenson Tracer studies of nutrient availability using 'naturally enriched' DC-labelled substrates, by Brian A. McGaw Peptide-specific Maillard reaction products: a new pathway for flavor chemistry, by Henry V. Izzo and Chi-Tang Ho pH of low-moisture solids, by Leonard N. Bell and Theodore P. Labuza
Trends in Food Science & Technology August/September 1992 [Vol. 3J
205