Proton relaxation mechanisms and the measurements of r phi, r psi and transannular interproton distances in gramicidin S

Monoselective, Rio(SE), biselective, Rio(i,j), and nonselective proton spin-lattice relaxation rates have been measured for dilute solutions of gramicidin S in dimethyl sulfoxide and used to evaluate cross-relaxation rates (sigma ij = Rio(i,j)-Rio(SE)) and Fi ratios (Fi = Ri(NS)/Rio(SE)). The cross-relaxation parameters, sigma, and Fi ratios measured for backbone gramicidin S protons predict that the same correlation time, tau c = 1.2 X 10(-9)s, modulates all the dipolar proton-proton interactions and that these interactions represent the main source for the proton spin-lattice relaxation process. The larger relaxation rates for amide versus alpha-protons of the backbone are attributed to dipolar relaxation between 14N and its directly bonded protons and is an approximate measure of the extent of this. The intrabackbone proton-proton distances, evaluated from sigma values, were consistent with the antiparallel beta-plated sheet/beta II'-turn conformation previously proposed for gramicidin S in solution.     

Effects of internal motions on the development of the two-dimensional transferred nuclear Overhauser effect

Summary In this paper we address the influence of internal motions on the development of the transferred nuclear Overhauser effect in a ligand undergoing chemical exchange between a free and a bound state. We examine the effects of varying the effective correlation time as well as the motional order parameter for methyl group and phenyl ring rotations in the free and bound ligand conformations. The effect of decreasing the motional order for a proton pair on a methyl group or phenyl ring is to decrease the effective correlation time of the internuclear vector, and thus to decrease the cross-relaxation rate between the proton pair. This functions to dampen the effects of spin diffusion, especially in the bound ligand- where cross-relaxation rates are much faster than in the free ligand. The effect of changing the effective correlation time for methyl group motions has little effect on the build-up behaviour of the transferred nuclear Overhauser effect for small values of fraction bound, but a larger effect on how fast it decays. This effect is greater for internal motions in the free peptide than it is for internal motions in the bound peptide.Dedicated to the memory of Professor V.F. Bystrov     

Detection of internal motions in oligosaccharides by 1H relaxation measurements at different magnetic fields.

The effect of internal motions on proton relaxation data in oligosaccharides has been investigated experimentally. 1H steady-state and transient NOEs together with 13C T1's have been measured at two magnetic field strengths. The existence of internal motions leads to additional modulations of the dipolar interaction between proton pairs, thus producing a range of spectral density functions for these interactions. As a result, it is possible to show that protons relaxing through fixed distances have a different ratio of relaxation parameters, acquired at 500 and 300 MHz, compared to those relaxing through fluctuating distances. This approach has been used to unequivocally establish for two disaccharides the existence of internal motions on the time scale of the overall tumbling.     

Magnetic cross-relaxation among protons in protein solutions.

The magnetic spin-lattice relaxation rates of solvent water nuclei are known to increase upon addition of diamagnetic solute protein. This enhancement of the relaxation rate is a function of magnetic field, and the orientational relaxation time of the protein molecules can be deduced from analysis of the field-dependent relaxation rates. Although the nature of the interactions that convey information about the dynamics of protein motion to the solvent molecules is not established, it is known that there is a contribution to the relaxation rates of solvent protons that plays no role in the relaxation of solvent deuterons and 17O nuclei. We show here that the additional interaction arises from a cross-relaxation process between solvent and solute protons. We introduce a heuristic three-parameter model in which protein protons and solvent protons are considered as two separate thermodynamic systems that interact across the protein-solvent interface. The three parameters are the intrinsic relaxation rates of each system and a cross-relaxation term. The sign of the latter term must always be positive, for all values of magnetic field, in order for magnetization energy to flow from the hotter to the cooler system. We find that the magnetic field-dependence of the cross-relaxation contribution is much like that of the remaining solvent proton relaxation, i.e., about the same as the deuteron relaxation field dependence. This finding is not compatible with the predictions of expressions for the cross-relaxation that have been used by other authors, but not applied to data over a wide range of magnetic field strength. The model predicts that the relaxation behavior of both the protein protons and the solvent protons is the sum of two exponentials, the relative contributions of which would vary with protein concentration and solvent isotopic composition in a fashion suggestive of the presence of two classes of protein protons, when there is in reality only one. This finding has immediate implications for the interpretation of published proton relaxation rates in complex systems such as tissues; these data should be reexamined with cross-relaxation taken into account.     

Internal motional averaging and three-dimensional structure determination by nuclear magnetic resonance.

Dynamic averaging effects from internal motions on interproton distances estimated from nuclear Overhauser effects (NOE) are determined by using a molecular dynamics simulation of lysozyme. Generalized order parameters measuring angular averaging and radial averaging parameters are calculated. The product of these two parameters describes the full averaging effects on cross-relaxation. Analysis of 2778 non-methyl NOE interactions from the protein interior and surface indicates that distances estimated by assuming a rigid molecule have less than 10% error for 89% of the NOE interactions. However, analysis of 1854 methyl interactions found that only 68% of the distances estimated from cross-relaxation rates would have less than 10% error. Qualitative evaluation of distances according to strong, medium and weak NOE intensities, when used to define only the upper bound for interproton separation, would misassign less than 1% of the distance constraints because of motional averaging. Internal motions do not obscure the identification of secondary structure, although some instances of significant averaging effects were found for interactions in alpha-helical regions. Interresidue NOEs for amino acids more than three residues apart in the primary sequence are more extensively averaged than intraresidue or short-range interresidue NOEs. Intraresidue interactions exhibit a greater degree of angular averaging than those involving interresidue proton pairs. An internal motion does not equally affect all NOE interactions for a particular proton. Thus, incorporation of averaging parameters in nuclear magnetic resonance structure determination procedures must be made on a proton-pair-wise basis. On the basis of the motional averaging results, particular fixed-distance proton pairs in proteins are suggested for use as distance references. A small percentage of NOE pairs localized to three regions of the protein exhibit extreme averaging effects from internal motions. The regions and types of motions involved are described.     

Distance estimates from paramagnetic enhancements of nuclear relaxation in linear and flexible model peptides.

The distance dependence of electron-nuclear dipole-dipole coupling was tested using a series of poly-L-proline based peptides of different length. The poly-proline based peptides were synthesized with a nitroxide spin label on the N-terminus and a tryptophan on the C-terminus, and paramagnetic enhancements of nuclear spin-lattice relaxation rates were measured for the aromatic protons on the tryptophan as a function of the number of proline spacers in the sequence. As expected, paramagnetic enhancements decrease with distance, but the distances deduced from the NMR relaxation rates were shorter than expected for every peptide studied compared to a rigid linear poly-L-proline type II helix structure. Calculations of cross-relaxation rates indicate that this difference is not the result of spin-diffusion or the creation of a spin-temperature gradient in the proton spins caused by the nitroxide. Molecular dynamics simulations were used to estimate dynamically averaged value of (2). These weighted average distances were close to the experimentally determined distances, and suggest that molecular motion may account for differences between the rigid linear models and the distances implied by the NMR relaxation data. A poly-L-prolone peptide synthesized with a central glycine hinge showed dramatic relaxation rate enhancements compared to the peptide of the same length lacking the hinge. Molecular dynamics simulations for the hinged peptide support the notion that the NMR data is a representation of the weighted average distance, which in this case is much shorter than that expected for an extended conformation. These results demonstrate that intermoment distances based on NMR relaxation rates provide a sensitive indicator of intramolecular motions.     

Errors in RNA NOESY distance measurements in chimeric and hybrid duplexes: differences in RNA and DNA proton relaxation.

Nuclear magnetic resonance experiments reveal that the base H8/H6 protons of oligoribonucleotides (RNA) have T1 relaxation times that are distinctly longer than those of oligodeoxyribonucleotides (DNA). Similarly, the T1 values for the RNA H1' protons are approximately twice those of the corresponding DNA H1' protons. These relaxation differences persist in single duplexes containing covalently linked RNA and DNA segments and cause serious overestimation of distances involving RNA protons in typical NOESY spectra collected with a duty cycle of 2-3 s. NMR and circular dichroism experiments indicate that the segments of RNA maintain their A-form geometry even in the interior of DNA-RNA-DNA chimeric duplexes, suggesting that the relaxation times are correlated with the type of helix topology. The difference in local proton density is the major cause of the longer nonselective T1s of RNA compared to DNA, although small differences in internal motion cannot be completely ruled out. Fortunately, any internal motion differences that might exist are shown to be too small to affect cross-relaxation rates, and therefore reliable distance data can be obtained from time-dependent NOESY data sets provided an adequately long relaxation delay is used. In hybrid or chimeric RNA-DNA duplexes, if the longer RNA relaxation times are not taken into account in the recycle delay of NOESY pulse sequences, serious errors in measuring RNA proton distances are introduced.     

Phospholipid packing and conformation in small vesicles revealed by two-dimensional 1H nuclear magnetic resonance cross-relaxation spectroscopy.

Two-dimensional 1H-NMR spectroscopy has been used to examine cross-relaxation in sonicated phospholipid vesicle systems. The observed pattern of proton cross-relaxation reveals several important features of these vesicle systems. For example, cross-relaxation rates on each monolayer of the vesicle system can be resolved and reflect the expected geometric packing constraints of the vesicle system. Small but significant magnetization-exchange is also seen to develop between the headgroup N-methyl resonance and the terminal methyl resonance. Spectra taken with deuterated lipids indicate that this exchange is not mediated by spin-diffusion down the length of the alkyl chains. Since spin-diffusion is the only process that is expected to facilitate magnetization-exchange over distances of 15-20 A, a close proximity of headgroup and terminal methyl protons in a fraction of the membrane lipid is indicated by these results. This could occur by events such as lipid interdigitation or alkyl chain bends that terminate lipid alkyl chain ends near the membrane surface.     

Solution structure of a LewisX analogue by off-resonance 1H NMR spectroscopy without use of an internal distance reference

Summary A recent ¹H NMR method has been applied to the determination of the solution structure and internal dynamics of a synthetic mixed C/O trisaccharide related to sialyl Lewis^x. Varying the rf field offset in ROESY-type experiments enabled the measurement of longitudinal and transverse dipolar cross-relaxation rates with high accuracy. Assuming that for each proton pair the motion could be represented by a single exponential autocorrelation function, it was possible to derive geometrical parameters (r) and dynamic parameters _cp. With this assumption, 224 cross-relaxation rates have been transformed into 30 interproton distance constraints and 30 dipolar correlation times. The distance constraints have been used in a simulated-annealing procedure. This trisaccharide exhibits a structure close to the O-glycosidic analogue, but its flexibility seems highly reduced. On the basis of the determined structure and dynamics, it is shown that no conformational exchange occurs, the molecule existing in the form of a unique family in aqueous solution. In order to assess the quality of the resulting structures and to validate this new experimental procedure of distance extraction, we finally compare these solution structures to the ones obtained using three different sets of distances deduced from three choices of internal reference. It appears that this procedure allows the determination of the most precise and accurate solution.Abbreviations COSY correlation spectroscopy - NOE nuclear Overhauser enhancement - NOESY nuclear Overhauser enhancement spectroscopy; rmsd, root-mean-square deviation - ROESY rotating frame Overhauser enhancement spectroscopy - SLe^x sialyl Lewis^x - TOCSY total correlation spectroscopy     

NMR distance measurements in DNA duplexes: sugars and bases have the same correlation times

To evaluate whether the sugar moieties of short DNA duplexes exhibit local motion of sufficient amplitude to affect interproton distance measurements, we have carried out a series of time-dependent NOESY experiments at increasingly shorter mixing times on dodecamer DNA duplexes. By use of the cytosine H5-H6 vector as a known distance in the bases and the geminal 2'H-2'H vector as a known distance in the sugars, the corresponding apparent cross-relaxation rates were sampled at various mixing times. While the ratio of the inverse sixth power of these two fixed distances is in the range 6-7, when the system is sampled at 100 ms the apparent initial rate of growth of the 2'H-2'H NOESY crosspeak is only 1.9-2.0 times faster than that of the H5-H6 crosspeak--in agreement with the results of Clore and Gronenborn [Clore, G. M., & Gronenborn, A. M. (1984) FEBS Lett. 172, 219; (1984) FEBS Lett. 175, 117] and of Gronenborn and Clore [Gronenborn, A. M., & Clore, G. M. (1985) Prog. NMR Spectrosc. 17, 1]. This observation was interpreted to indicate the existence of internal mobility with a 3-fold shorter correlation time for the sugar moieties in DNA and led to the use of this shorter correlation time to estimate sugar-sugar proton distances and many sugar-base proton distances in subsequent DNA structure determination. We have examined 2'H-2"H cross-relaxation and H5-H6 cross-relaxation at 100, 90, 60, 30, and 15 ms in dodecamer DNA duplexes.(ABSTRACT TRUNCATED AT 250 WORDS)     

1H- and 2H-NMR study of bovine serum albumin solutions

Frozen, native and denatured bovine serum albumin solutions have been studied with a wide-band NMR pulse spectrometer. Both macromolecular and water protons spin-spin and spin-lattice relaxation times--t2m, t1m, t2w, t1w--have been measured between 170 and 360 K. In the native sample, the t2m process is the tumbling rate of the bovine serum albumin molecules. It gives to the spin-lattice relaxation an omega 0(-2) frequency dependence at room temperature in the studied frequency range, 6-90 MHz. An additional process contributes to t1m-1; it arises from internal backbone or segmental motions and provides a lower frequency behaviour. On denaturation, bovine serum albumin molecules lose their tumbling motion and form a rigid network, while internal backbone motions seem unaffected. Calorimetric Cp measurement confirms the occurrence of a phase transition upon denaturation. 1H and 2H spin-lattice relaxation times of water protons depend mainly on bound water mobility. 1H and 2H t2w depend also on the tertiary structure of bovine serum albumin and on its mobility, because of a fast exchange process between water and some protein protons (or deutons), while a cross-relaxation process between protein and water protons contributes to 1H t1w. Denaturation has no influence on bound water motional properties and bound water population.     

Nuclear Overhauser effect and cross-relaxation rate determinations of dihedral and transannular interproton distances in the decapeptide tyrocidine A.

The following interproton distances are reported for the decapeptide tyrocidine A in solution: (a) r(phi) distances between NH(i) and H alpha (i), (b) r(psi) distances between NH (i + 1) and H alpha (i), (c) r(phi psi) distances between NH(i + 1) and NH(i), (d) NH in equilibrium NH transannular distances, (e) H alpha in equilibrium H alpha transannular distances, (f) r x 1 distances between H alpha and H beta protons, (g) NH(i) in equilibrium H beta (i) distances, (h) NH (i + 1) in equilibrium H beta (i) distances, (i) carboxamide-backbone protons and carboxamide-side chain proton distances, (j) side chain proton-side chain proton distances. The procedures for distance calculations were: NOE ratios and calibration distances, sigma ratios and calibration distances, and correlation times and sigma parameters. The cross-relaxation parameters were obtained from the product, say, of NOE 1 leads to 2 and the monoselective relaxation rate of proton 2; the NOEs were measured by NOE difference spectroscopy. The data are consistent with a type I beta-turn/ type II' beta-turn/ approximately antiparallel beta-pleated sheet conformation of tyrocidine A in solution and the NOEs, cross-relaxation parameters, and interproton distances serve as distinguishing criteria for beta-turn and beta-pleated sheet conformations. It should be borne in mind that measurement of only r phi and r psi distances for a decapeptide only defines the ( phi, psi)-space in terms of 4(10) possible conformations; the distances b-j served to reduce the degeneracy in possible (phi, psi)-space to one tyrocidine A conformation. The latter conformation is consistent with that derived from scalar coupling constants, hydrogen bonding studies, and proton-chromophore distance measurement, and closely resembles the conformation of gramicidin S.     

A view of dynamics changes in the molten globule-native folding step by quasielastic neutron scattering

In order to understand the changes in protein dynamics that occur in the final stages of protein folding, we have used neutron scattering to probe the differences between a protein in its folded state and the molten globule states. The internal dynamics of bovine alpha-lactalbumin (BLA) and its molten globules (MBLA) have been examined using incoherent, quasielastic neutron scattering (IQNS). The IQNS results show length scale dependent, pico-second dynamics changes on length scales from 3.3 to 60 A studied. On shorter-length scales, the non-exchangeable protons undergo jump motions over potential barriers, as those involved in side-chain rotamer changes. The mean potential barrier to local jump motions is higher in BLA than in MBLA, as might be expected. On longer length scales, the protons undergo spatially restricted diffusive motions with the diffusive motions being more restricted in BLA than in MBLA. Both BLA and MBLA have similar mean square amplitudes of high frequency motions comparable to the chemical bond vibrational motions. Bond vibrational motions thus do not change significantly upon folding. Interestingly, the quasielastic scattering intensities show pronounced maxima for both BLA and MBLA, suggesting that "clusters" of atoms are moving collectively within the proteins on picosecond time scales. The correlation length, or "the cluster size", of such atom clusters moving collectively is dramatically reduced in the molten globules with the correlation length being 6.9 A in MBLA shorter than that of 18 A in BLA. Such collective motions may be important for the stability of the folded state, and may influence the protein folding pathways from the molten globules.     

Anisotropic rotation in nucleic acid fragments: significance for determination of structures from NMR data

Proton-proton relaxation rate constants depend on the angle between the internuclear vector and the principal axis of rotation in symmetric top molecules. It is possible to determine to rotational correlation times of the equivalent ellipsoid for DNA fragments from a knowledge of the axial ratio and the cross-relaxation rate constant for the cytosine H6-H5 vectors. The cross-relaxation rate constants for the cytosine H6-H5 vectors have been measured in the 14-base-pair sequence dGCTGTTGACAATTA.dTAATTGTCAACAGC at four temperatures. The results, along with literature data for DNA fragments ranging from 6 to 20 base pairs can be accounted for by a simple hydrodynamic equation based on the formalism of Woessner (1962). The measured cross-relaxation rate constant is independent of position in the sequence and is consistent with the absence of large amplitude internal motions on the Larmor time scale. All the data can be described by a simple hydrodynamic model, which accounts for the rotational anisotropy of the DNA fragments and allows the correlation time for end-over-end tumbling to be determined if the approximate rise per base pair is known. This is the correlation time that dominates the spectral density functions for internucleotide vectors and is significantly different from that calculated for a sphere of the same hydrodynamic volume for fragments containing more than about 14 base pairs. This method therefore allows NOE intensities used for structure calculation of nucleic acids to be treated more rigorously. Offprint requests to: A.N. Lane     

Three-dimensional structure of a DNA hairpin in solution: two-dimensional NMR studies and distance geometry calculations on d(CGCGTTTTCGCG)

The three-dimensional structure of d(CGCGTTTTCGCG) in solution has been determined from proton NMR data by using distance geometry methods. The rate of dipolar cross-relaxation between protons close together in space is used to calculate distances between proton pairs within 5 A of each other; these distances are used as input to a distance geometry algorithm that embeds this distance matrix in three-dimensional space. The resulting refined structures that best agree with the input distances are all very similar to each other and show that the DNA sequence forms a hairpin in solution; the bases of the loop region are stacked, and the stem region forms a right-handed helix. The advantages and limitations of the technique, as well as the computer requirements of the algorithm, are discussed.     

Structure determination of a DNA octamer in solution by NMR spectroscopy. Effect of fast local motions.

NMR structures of biomolecules are primarily based on nuclear Overhauser effects (NOEs) between protons. For the interpretation of NOEs in terms of distances, usually the assumption of a single rotational correlation time corresponding to a rigid molecule approximation is made. Here we investigate the effect of fast internal motions of the interproton vectors in the context of the relaxation matrix approach for structure determination of biomolecules. From molecular dynamics simulations generalized order parameters were calculated for the DNA octamer d(GCGTTCGC).d(CGCAACGC), and these were used in the calculation of NOE intensities. The magnitudes of the order parameters showed some variation for the different types of interproton vectors. The lowest values were observed for the interresidue base H6/H8-H2" proton vectors (S2 = 0.60), while the cytosine H5-H6 interproton vectors were among the most motionally restricted (S2 = 0.92). Inclusion of the motion of the interproton vectors resulted in a much better agreement between theoretically calculated NOE spectra and the experimental spectra measured by 2D NOE spectroscopy. The interproton distances changed only slightly, with a maximum of 10%; nevertheless, the changes were significant and resulted in constraints that were better satisfied. The structure of the DNA octamer was determined by using restrained molecular dynamics simulations with H2O as a solvent, with and without the inclusion of local internal motions. Starting from A- or B-DNA, the structures showed a high local convergence (0.86 A), while the global convergence for the octamer was ca. 2.6 A.     

NMR analysis of carbohydrates with model-free spectral densities: the dispersion range revisited

Over the past decade molecular mechanics and molecular dynamics studies have demonstrated considerable flexibility for carbohydrates. In order to interpret the corresponding NMR parameters, which correspond to a time-averaged or 'virtual' conformer, it is necessary to simulate the experimental data using the averaged geometrical representation obtained with molecular modelling methods. This structural information can be transformed into theoretical NMR data using empirical Karplus-type equations for the scalar coupling constants and the appropriate formalism for the relaxation parameters. In the case of relaxation data, the 'model-free' spectral densities have been widely used in order to account for the internal motions in sugars. Several studies have been conducted with truncated model-free spectral densities based on the assumption that internal motion is very fast with respect to overall tumbling. In this report we present experimental and theoretical evidence that suggests that this approach is not justified. Indeed, recent results show that even in the case of moderate-sized carbohydrates internal motions are occurring on the same timescale as molecular reorientation. Simulations of relaxation parameters (NOESY volumes, proton cross-relaxation rates, carbon T1 and nOe values) in the dispersion range (0.1<Tc<5 ns) show that rates of internal motion can be fairly precisely defined with respect to overall tumbling. Experimental data for a variety of oligosaccharides clearly indicate similar timescales for internal and overall motion. This revised version was published online in August 2006 with corrections to the Cover Date.     

N.m.r. assignments and temperature-dependent conformational transitions of a mutant trp operator-promoter in solution.

A total of 145 protons in the mutant trp operator-promoter sequence CGTACTGATTAATCAGTACG were assigned by one-dimensional and two-dimensional n.m.r. methods. Except at the sites of mutation (underlined), the chemical shifts and other n.m.r. parameters are very similar to those observed in the symmetrized wild-type sequence [Lefèvre, Lane & Jardetzky (1987) Biochemistry 26, 5076-5090]. Spin-spin-relaxation rate constants of the resolved base protons and intra- and inter-nucleotide nuclear-Overhauser-enhancement intensities argue for a sequence-dependent structure similar to that of the wild-type, except at and close to the sites of the mutation. The overall tumbling time as a function of temperature was determined from cross-relaxation rate constants for the H-6-H-5 vectors of the four cytosine residues. The values are consistent with the oligonucleotide maintaining a double-helical conformation over the entire temperature range 5-45 degrees C, and that internal motions of the bases are of small amplitude on the subnanosecond time scale. The temperature-dependence of chemical shifts, spin-spin-relaxation rate constants and cross-relaxation rate constants show the occurrence of two conformational transitions localized to the TTAA sequence in the centre of the molecule. The thermodynamics of the transition at the lower temperature (tm = 16 degrees C) were analysed according to a two-state process. The mid-point temperature is about 6 degrees C higher than in the wild-type sequence. The conformational transition does not lead to rupture of the Watson-Crick hydrogen bonds, but probably involves changes in the propellor twists of T.A-9 and T.A-10. The second transition occurs at about 40 degrees C, but cannot be fully characterized. This conformational variability seems to be a property of the sequence TTAA, and may have functional significance in bacterial promoters.     

Effect of cell arrangement and interstitial volume fraction on the diffusivity of monoclonal antibodies in tissue.

We present theoretical calculations relating the effective diffusivity of monoclonal antibodies in tissue (Deff) to the actual diffusivity in the interstitium (Dint) and the interstitial volume fraction phi. Measured diffusivity values are effective values, deduced from concentration profiles with the tissue treated as a continuum. By using homogenization theory, the ratio Deff/Dint is calculated for a range of interstitial volume fractions from 10 to 65%. It is assumed that only diffusion in the interstitial spaces between cells contributes to the effective diffusivity. The geometries considered have cuboidal cells arranged periodically, with uniform gaps between cells. Deff/Dint is found to generally be between (2/3) phi and phi for these geometries. In general, the pathways for diffusion between cells are not straight. The effect of winding pathways on Deff/Dint is examined by varying the arrangement of the cells, and found to be slight. Also, the estimates of Deff/Dint are shown to be insensitive to typical nonuniformities in the widths of gaps between cells. From our calculations and from published experimental measurements of the effective diffusivity of an IgG polyclonal antibody both in water and in tumor tissue, we deduce that the diffusivity of this molecule in the interstitium is one-tenth to one-twentieth its diffusivity in water. We also conclude that exclusion of molecules from cells (an effect independent of molecular weight) contributes as much as interstitial hindrance to the reduction of effective diffusivity, for small interstitial volume fractions (around 20%). This suggests that the increase in the rate of delivery to tissues resulting from the use of smaller molecular-weight molecules (such as antibody fragments or bifunctional antibodies) may be less than expected.