State NMR Research Articles

Recent developments in deuterium solid-state NMR for the detection of slow motions in proteins

Slow timescale dynamics in proteins are essential for a variety of biological functions spanning ligand binding, enzymatic catalysis, protein folding and misfolding regulations, as well as protein–protein and protein–nucleic acid interactions. In this review, we focus on the experimental and theoretical developments of 2H static NMR methods applicable for studies of microsecond to millisecond motional modes in proteins, particularly rotating frame relaxation dispersion (R1ρ), quadrupolar Carr–Purcell–Meiboom–Gill (QCPMG) relaxation dispersion, and quadrupolar chemical exchange saturation transfer NMR experiments (Q-CEST). With applications chosen from amyloid-β fibrils, we show the complementarity of these approaches for elucidating the complexities of conformational ensembles in disordered domains in the non-crystalline solid state, with the employment of selective deuterium labels. Combined with recent advances in relaxation dispersion backbone measurements for 15N/13C/1H nuclei, these techniques provide powerful tools for studies of biologically relevant timescale dynamics in disordered domains in the solid state.

A static and dynamic NMR study of 10-hydrazino-BODIPY.

10-Hydrazino-BODIPY, BoNHNH2 , presents slow rotation about the C10-NH bond that results in anisochronous 1 H and 13 C NMR signals. The assignment of the different signals has been made using traditional two-dimensional methods as well as spin-spin coupling constants and confirmed by DFT calculations (B3LYP) using the 6-311++G(d,p) basis set. The rotational barrier has been determined in three pairs of proton signals and compared with the calculated barrier.

Combined High-Resolution Solid-State 1H/13C NMR Spectroscopy and 1H NMR Relaxometry for the Characterization of Kerogen Thermal Maturation

A key factor for the petroleum potential of source rock is the degree of chemical and physical structure evolution of its kerogen fraction through a range of maturation processes. In this study, various high-field, solid-state NMR methods have been applied to a series of kerogen isolates (type I) over a defined maturity range (vitrinite reflectance R₀ from 0.98 to 1.86%). Results obtained from ¹³C MAS NMR show that the sp²/sp³-hybridized carbon ratio of kerogen, here defined as the aromatic/aliphatic ratio, increases with increasing maturity. ¹H MAS NMR spectra contain partly overlapping aliphatic and aromatic resonances with distinct transverse relaxation behavior. In Hahn-echo experiments, the aromatic signal decays more slowly than the aliphatic signal, indicating that for these systems, transverse ¹H relaxation is rather controlled by local distances between hydrogen atoms than by molecular mobility. Similar relaxation differences are also found in static (nonspinning) ¹H Hahn-echo NMR experiments, here used to discriminate between phases with different proton mobilities and/or densities in the kerogen samples and, ultimately, between aromatic and aliphatic fractions. The distributions of the static transverse relaxation time (T₂), extracted from the Hahn-echo decays, are characterized by a short-T₂ peak (∼10 μs) and a long-T₂ peak (∼100 μs). The ratio between these two peaks correlates well with the aliphatic-to-aromatic signal intensity ratios in MAS NMR spectra of the corresponding kerogen samples, suggesting that a net decrease in kerogen proton density—occurring during maturation—is also reflected by ¹H NMR relaxation. For the investigated kerogen isolates, the long-T₂ peak in the T₂ distribution can be considered an indicator of aromatic content, which can be directly detected by measuring ¹H T₂ relaxation.

Temperature- and composition-dependent conformational transitions of amphipathic peptide–phospholipid nanodiscs

Nanodiscs are discoidal particles in which a lipid bilayer is encircled by amphipathic molecules such as proteins, peptides, or synthetic polymers. The apolipoprotein-A-I-derived peptide 18A is known to form nanodiscs in the presence of phospholipids, but the detailed mechanism of the formation and deformation of these nanodiscs in response to changes in the surrounding environment is not well understood. Here, we investigated the temperature- and composition-dependent structural changes of 18A–phosphatidylcholine complexes using fluorescence spectroscopy, dynamic light scattering, circular dichroism, static 31P NMR, and electron microscopy. We found that the nanodiscs in fast isotropic rotational motion increased in size above the gel-to-liquid-crystalline phase transition temperature of the lipid bilayers, resulting in the formation of enlarged nanodiscs and a lamellar phase. The lamellar phase was found to be oriented along the magnetic field. Further increase in temperature induced the formation of lipid vesicles. These transformations were explained using a transition model based on the migration of the peptide from the rim of the nanodiscs to the liquid-crystalline bilayer phase. The study outcomes provide a basis for understanding the design principles of discoidal nanostructures for structural biology and nanomedicine applications.

Vanadium incorporation from aqueous NH4VO3 solution into siliceous Beta zeolite determined by NMR with formation of V-single site zeolite catalysts for application in SCR of NO

The speciation of vanadium in initial aqueous NH4VO3 solutions as a function of pH and concentration, in supernatant and in wet solids were investigated by 51V static and MAS NMR. Two series of VSiBeta zeolite catalysts were prepared by a two-step postsynthesis procedure at pH = 2.5 and 6. 51V static and MAS NMR, 51V 3Q MAS NMR, DR UV–vis, XPS and EPR allowed determining the state of vanadium in both series of catalysts. The catalytic activity of VSiBeta catalysts in SCR of NO strongly depended on the state of the vanadium present. The V-single site V1.0SiBeta(I) and V1.4SiBeta(I) catalysts with isolated pseudo-tetrahedral V(V) were active in SCR of NO with NH3 process, with maximum NO conversion about 75 % at 773 K for V1.4SiBeta(I). In contrast, V1.0SiBeta(II) and V7.5SiBeta(I) catalysts containing pseudo-octahedral V(V) were much less active in SCR of NO and high amount of undesired N2O was produced.

In-situ reaction monitoring of a mechanochemical ball mill reaction with solid state NMR

We present an approach towards the in situ solid state NMR monitoring of mechanochemical reactions in a ball mill. A miniaturized vibration ball mill is integrated into the measuring coil of a home-built solid state NMR probe, allowing for static solid state NMR measurements during the mechanochemical reaction within the vessel. The setup allows to quantitatively follow the product evolution of a prototypical mechanochemical reaction, the formation of zinc phenylphosphonate from zinc acetate and phenylphosphonic acid. MAS NMR investigations on the final reaction mixture confirmed a reaction yield of 89% in a typical example. Thus, NMR spectroscopy may in the future provide complementary information about reaction mechanisms of mechanochemical reactions and team up with other analytical methods which have been employed to follow reactions in situ, such as Raman spectroscopy or X-ray diffraction.

Heterogeneous Polymer Dynamics Explored Using Static 1H NMR Spectra.

NMR spectroscopy continues to provide important molecular level details of dynamics in different polymer materials, ranging from rubbers to highly crosslinked composites. It has been argued that thermoset polymers containing dynamic and chemical heterogeneities can be fully cured at temperatures well below the final glass transition temperature (Tg). In this paper, we described the use of static solid-state 1H NMR spectroscopy to measure the activation of different chain dynamics as a function of temperature. Near Tg, increasing polymer segmental chain fluctuations lead to dynamic averaging of the local homonuclear proton-proton (1H-1H) dipolar couplings, as reflected in the reduction of the NMR line shape second moment (M2) when motions are faster than the magnitude of the dipolar coupling. In general, for polymer systems, distributions in the dynamic correlation times are commonly expected. To help identify the limitations and pitfalls of M2 analyses, the impact of activation energy or, equivalently, correlation time distributions, on the analysis of 1H NMR M2 temperature variations is explored. It is shown by using normalized reference curves that the distributions in dynamic activation energies can be measured from the M2 temperature behavior. An example of the M2 analysis for a series of thermosetting polymers with systematically varied dynamic heterogeneity is presented and discussed.

Optimized High-Yield Purification of Obesity-Associated Melanocortin 4 Receptor.

Obesity has emerged as a global public health challenge associated with increased risk of hyperlipidemia and hypertension. It contributes to high sympathetic activity and increased catecholamine levels. The hypothalamic melanocortin system is known to regulate the energy homeostasis. The role of melanocortin 4 receptor (MC4R) has been demonstrated pharmacologically and in animal studies, which showed that severe obesity in MC4R knockout mice was caused by increased food intake and decreased energy consumption. Over 70 multiple different mis- -sense and nonsense mutations in hMC4R have been found at a high frequency of 2-8% in severe early onset or hereditary obesity. The single amino acid variation (D90N) located in the second transmembrane domain (TM2) of MC4R results in accelerated growth and childhood onset obesity. Interestingly, the functional characterization of D90N hMC4R mutant TM2 (m-hMC4R-TM2) revealed normal cell surface expression and binding with agonist similar to the hMC4R wild-type TM2 (wt-hMC4R-TM2) but loss of signal transduction mediated via Gs/adenylyl cyclase activation. It is essential to delineate the three-dimensional structure of MC4Rs in order to elucidate their functional aspects. In this study, we demonstrate the optimized expression and isolation of wt/m-hMC4R-TM2 proteins under different chemical cleavage reaction times and purification procedures via SDS precipitation. The solid-state NMR spectroscopy was carried out to study the structure of wt/m-hMC4R- TM2 protein in the anisotropic phospholipid bicelles. The KSI-wt/m-hMC4R-TM2 fusion proteins developed in cell culture with LB medium. In order to isolate the expressed fusion protein from the cell, ultrasonication, Ni-NTA affinity chromatography, dialysis, and lyophilization techniques were used. Then, to obtain a protein with higher purity and higher yield, the CNBr chemical cleavage time was subdivided into 30 minutes, 1 h, 2 h, 3 h, and 4 h. Purification process was performed using FPLC, and 100 mM KCl and dialysis were used to remove the SDS. CD spectrometer, MALDI-TOF, solution-state NMR, and solid-state NMR were used to confirmed purity and structure of the wt/m-hMC4R-TM2. The precipitation method was used to remove the SDS bound to proteins as KCl-SDS. We optimized the 2 h cleavage reaction times for both wt-hMC4R-TM2 and m-hMC4R-TM2 depending on the purity based on mass spectra and 1H-15N HSQC spectra and the yield after final purification. The 1D 1H-15N CP (Cross polarization) solid-state NMR spectra suggest that the wt/m-hMC4R- TM2 undergo rotational diffusion around a perpendicular axis along the bilayer normal. We expressed wt/m-hMC4R-TM2 in E.coli and optimized the isolation and purification process, especially CNBr chemical cleavage time. The efficiency of KCl-SDS precipitation was confirmed via MALDI-TOF MS and the pure proteins obtained using this method were characterized by CD spectroscopy and solution-state NMR. The results of 1H-15N HSQC spectra in solution- state NMR also show the probability for structural studies. The 1D 1H-15N CP solid-state NMR spectra indicate that most of the residues in both the wt/m-hMC4R-TM2 peptides are integrated into the membrane.

An investigation of the long-range and local structure of sub-stoichiometric zirconium carbide sintered at different temperatures

ZrC1−x (sub-stoichiometric zirconium carbide), a group IV transition metal carbide, is being considered for various high temperature applications. Departure from stoichiometry changes the thermo-physical response of the material. Reported thermo-physical properties exhibit, in some cases, a degree of scatter with one likely contributor to this being the uncertainty in the C/Zr ratio of the samples produced. Conventional, methods for assigning C/Zr to samples are determined either by nominal stochiometric ratios or combustion carbon analysis. In this study, a range of stoichiometries of hot-pressed ZrC1−x were examined by SEM, XRD, Raman spectroscopy and static 13C NMR spectroscopy and used as a basis to correct the C/Zr. Graphite, amorphous, and ZrC1−x carbon signatures are observed in the 13C NMR spectra of samples and are determined to vary in intensity with sintering temperature and stoichiometry. In this study a method is outlined to quantify the stoichiometry of ZrC1−x and free carbon phases, providing an improvement over the sole use and reliance of widely adopted bulk carbon combustion analysis. We report significantly lower C/Zr values determined by 13C NMR analysis compared with carbon analyser and nominal methods. Furthermore, the location of carbon disassociated from the ZrC1−x structure is analysed using SEM and Raman spectroscopy.

Effect of AMPs MSI-78 and BP100 on the lipid acyl chains of 2H-labeled intact Gram positive bacteria

The lipid bilayer disrupting effect of antimicrobial peptides (AMPs) has been widely studied in model-lipid systems by applying biophysical techniques such as 2H NMR spectroscopy. Real bacteria cell envelopes contain non-lipid components, such as peptidoglycan, and thus it is important to assess the effects of such non-lipid components on the lipid-disrupting effects of AMPs. To this end, our group and other have developed methods that promote uptake of deuterium-labeled acyl chains in bacterial cells to produce 2H-membrane-enriched Bacillus subtilis. In this work, we studied changes in the static 2H NMR spectra of B. subtilis induced by the AMPs MSI-78 and BP100. Addition of both AMPs resulted in the increase of lipid acyl chain disorder consistent with disruption of the bacterial membrane. In addition, the peptide to lipid molar ratios (P:L) that give rise to observable effects fall between the P:L molar ratios necessary to generate membrane disruption in model-lipid-only systems and the P:L molar ratios needed to inhibit bacterial cell growth. This observation supports a role for the non-lipid components in modulating the AMP-lipid interactions.

Experimental Comparison of Solid-state NMR Spectra for Quadrupolar Nuclei Using Various Spin-echo Sequences

Static solid-state NMR spectra for quadrupolar nuclei were compared using various spin-echo sequences, as well as a single pulse sequence. 47/49Ti spectra of TiO2 and 2H spectra of deuterium-labele...

1H NMR linewidths of small organic guest molecules physisorbed on different mesoporous silicas

The excessive linewidths of 1H NMR spectra of solids is a longstanding difficulty. Organic molecules (crystalline at room temperatures) of different chemical characters (camphor, menthol, HMB, HMTA, biphenyl, terphenyl, anthracene, perylene, etc.) have been confined or physisorbed in regular (MCM-41, SBA-15) and irregular (aerogel) silica mesopores. Unexpectedly, steadily decreasing proton NMR linewidths have been observed upon increasing pore sizes. Comparison of the static 1H NMR spectra of the confined and “free” bulk molecules showed an impressive resolution improvement (a factor of 5–10). Static 1H NMR and 2H magic angle spinning (MAS) spectra pointed out the increased molecular mobility as origin. In a qualitative approach the possible reasons of mobility have been thoroughly discussed. The increased mobility seems to be easiest achievable in aerogel and so, in the future, this extreme light mesoporous silica nanomaterial (MSN) may be considered as “active” filling material in solid state NMR spectroscopy. Since sensitivity is not an issue in 1H MAS measurements the proposal - simultaneous dilution of the dense 1H–1H spin network and increasing the molecular mobility of the molecules of interest by confinement or physisorption in/on silica mesopores - may find applications, especially in laboratories where high magnetic fields and state of art ultra-fast MAS rotation are not available.

The influence of TiO2 on the structure and properties of sodium-zinc phosphate glasses

xTiO2–(40-x)ZnO–10Na2O–50P2O5 glasses were prepared up to x = 20. The stabilizing effect of titanium on the phosphate glasses was tested. The structure of the glasses was studied by Raman, both 31P and 23Na MAS NMR spectroscopies and 31P static NMR. The increasing titanium content caused the change in the metaphosphate structure into pyrophosphate. The amount of reduced titanium was detected by electron paramagnetic resonance to be less than 0.5% and the coordination polyhedron of titanium was identified as the tetragonally distorted octahedron with some trigonal deformation. The results of basic thermoanalytical values, density and microhardness confirmed the anticipated influence of titanium on the strengthening of the glass network. The influence of titanium on surface layer thickness and solubility was tested in demineralized water and in a saline solution. It was determined that even a concentration of 1mol% TiO2 significantly decreases the degradation rate and thickness of the surface layer. The thickness of the surface layer of glass without titanium was found to be about 40 µm and the thickness of the surface layer of glass with 1 mol% TiO2 was found to be close to 7 µm. The results obtained correlate well with the significant stabilizing effect of titanium. It is possible to conclude that the determination of surface layer thickness does not depend on the solvent but only on the chemical composition.

Chemical, mineralogical and structural features of native and expanded perlite from Macedonia

The physico-mechanical, chemical and mineralogical characteristics of volcanic glass (perlite) from the Mariovo region (Macedonia) as well as the mineralogical changes that occur during its thermal treatment were investigated to demonstrate its utilization for industrial use. The native perlite was characterized by chemical analysis, X-ray powder diffraction (XRPD), infrared (IR) spectroscopy, thermal analysis (TGA/DTA), scanning electron microscopy (SEM-EDX), transmission electron microscopy (TEM), and solid- state NMR. The chemical examination suggests that the perlite represents an acidic volcanic rock with a high percentage of SiO2 (72.45%), high in alkali metal oxides (4.21 wt.% K2O, 3.56 wt.% Na2O), with a loss of ignition 3.54 wt.%. Results from the XRPD indicated major amorphous behaviour, with low amounts of feldspars, quartz, and cristobalite. SEM examinations revealed glassy structure with presence of certain pores (dimensions ranging from 50–100 μm). The determined expansion coefficient was 20 times its original volume. XRPD of expanded perlite compared to the native perlite depicted new intensive peaks of cristobalite. SEM and TEM revealed irregular morphology with broken or ragged edges. On the basis of the chemical and mineralogical composition, the studied perlite is classified as an appropriate material suitable as ceramic flux to lower the sintering temperature.

The influence of the stereochemistry and C-end chemical modification of dermorphin derivatives on the peptide-phospholipid interactions

In this work the conformation of dermorphin, Tyr-D-Ala-Phe-Gly-Tyr-Pro-Ser-NH2, an opioid peptide and its analogues with different stereochemistry of alanine and different C-terminus is studied in aqueous and membrane environments. Using two-dimensional NMR techniques we demonstrate that in D2O/H2O peptides with D-alanine have extended conformation, while for the L-isomers more compact conformation is preferred. The analysis of ROESY HR MAS spectra of the peptides interacting with the DMPC bilayer indicates that both stereoisomers have still more extended conformation compared to aqueous phase, as shown by much weaker intermolecular interactions. The influence of Ala residue stereochemistry is also reflected in the interactions of the studied peptides with model membranes, as shown by the 31P NMR static spectra, in which the shapes of the phosphorus NMR signals originating from D-isomers correspond to spherically shaped vesicles in the presence of external magnetic field, in comparison to a more elongated ones observed for L-isomers, while TEM photographs shows that upon addition of D-isomers larger lipid vesicles are formed, in contrast to smaller ones for L-isomers. The location of aromatic fragments of dermorphins in the membrane is determined based on static 2H NMR and 1H1H RFDR MAS experiments. All aromatic rings were found to be inserted in the hydrophobic part of the bilayer, with the exception of the Tyr5 rings of D-Ala dermorphins. The influence of the C-terminal modification was found to be almost imperceptible.

Effect of Post-Translational Modifications and Mutations on Amyloid-β Fibrils Dynamics at N Terminus

We investigate the variability in the dynamics of the disordered N-terminal domain of amyloid-β fibrils (Aβ), comprising residues 1–16 of Aβ1–40, due to post-translational modifications and mutations in the β-bend regions known to modulate aggregation properties. Using 2H static solid-state NMR approaches, we compare the dynamics in the wild-type Aβ fibrils in the threefold symmetric polymorph with the fibrils from three post-translational modification sequences: isoaspartate-D7, the phosphorylation of S8, and an N-terminal truncation ΔE3. Additional comparisons are made with the mutants in the β-bend region (residues 21–23) corresponding to the familial Osaka E22Δ deletion and D23N Iowa mutation. We also include the aggregates induced by Zn2+ ions. The dynamics are probed at the F4 and G9 positions. The main motional model involves two free states undergoing diffusion and conformational exchanges with the bound state in which the diffusion is quenched because of transient interactions involving fibril core and other intrastrand contacts. The fraction of the bound state increases in a sigmoidal fashion with a decrease in temperature. There is clear variability in the dynamics: the phosphorylation of S8 variant is the most rigid at the G9 site in line with structural studies, the ΔE3 fibrils are more flexible at the G9 site in line with the morphological fragmentation pattern, the Zn-induced aggregates are the most mobile, and the two β-bend mutants have the strongest changes at the F4 site toward higher rigidity. Overall, the changes underlie the potential role of conformational ensembles in setting the stage for aggregation-prone states.

Experiments with direct detection of multiple FIDs.

Pulse schemes with direct observation of multiple free induction decays (FIDs) offer a dramatic increase in the spectral information content of NMR experiments and often yield substantial improvement in measurement sensitivity per unit time. Availability of multiple receivers on the state-of-the-art commercial spectrometers allows spectra from different nuclear species to be recorded in parallel routinely. Experiments with multi-FID detection have been designed with both, homonuclear and multinuclear acquisition. We provide a brief overview of such techniques designed for applications in liquid- and solid- state NMR as well as in hyperpolarized samples. Here we show how these techniques have led to design of experiments that allow structure elucidation of small molecules and resonance assignment in proteins from a single measurement. Probes with multiple RF micro-coils routed to multiple NMR receivers provide an alternative way of increasing the throughput of modern NMR systems. Solid-state NMR experiments have also benefited immensely from both parallel and simultaneous FID acquisition in a variety of multi-dimensional pulse schemes. We believe that multi-FID detection will become an essential component of the future NMR methodologies effectively increasing the information content of NMR experiments and reducing the cost of NMR analysis.

Solid-state NMR reveals a comprehensive view of the dynamics of the flexible, disordered N-terminal domain of amyloid-β fibrils

Amyloid fibril deposits observed in Alzheimer's disease comprise amyloid-β (Aβ) protein possessing a structured hydrophobic core and a disordered N-terminal domain (residues 1-16). The internal flexibility of the disordered domain is likely essential for Aβ aggregation. Here, we used 2H static solid-state NMR methods to probe the dynamics of selected side chains of the N-terminal domain of Aβ1-40 fibrils. Line shape and relaxation data suggested a two-state model in which the domain's free state undergoes a diffusive motion that is quenched in the bound state, likely because of transient interactions with the structured C-terminal domain. At 37 °C, we observed freezing of the dynamics progressively along the Aβ sequence, with the fraction of the bound state increasing and the rate of diffusion decreasing. We also found that without solvation, the diffusive motion is quenched. The solvent acted as a plasticizer reminiscent of its role in the onset of global dynamics in globular proteins. As the temperature was lowered, the fraction of the bound state exhibited sigmoidal behavior. The midpoint of the freezing curve coincided with the bulk solvent freezing for the N-terminal residues and increased further along the sequence. Using 2H R1ρ measurements, we determined the conformational exchange rate constant between the free and bound states under physiological conditions. Zinc-induced aggregation leads to the enhancement of the dynamics, manifested by the faster conformational exchange, faster diffusion, and lower freezing-curve midpoints.

Preparation, Thermal, and Physical Properties of Perovskite-Type (C3H7NH3)2CdCl4 Crystals

To investigate the thermal and physical properties of perovskite-type (C3H7NH3)2CdCl4, its temperature-dependent chemical shifts and spin–lattice relaxation times are measured using thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), magic angle spinning nuclear magnetic resonance (MAS NMR), and static NMR methods. Above 300 K, two phase transitions are observed at 398 K and 538 K. Each proton and carbon in the (C3H7NH3) cation is distinguished in the MAS NMR results. The environments around 1H, 13C, and 14N do not change with temperature according to the NMR spectra. In contrast, the resonance frequency of 113Cd in the CdCl6 octahedra decreases with increasing temperature, indicating an environmental change. The uniaxial rotations for 1H and 13C have high mobility at both high and low temperatures, and these are related to the phase transitions. In addition, the molecular motion of 113Cd in the anion becomes activated upon raising the temperature.

2H NMR Reveals Liquid State-Like Dynamics of Arene Guests Inside Hexameric Pyrogallol[4]arene Capsules in the Solid State.

The dynamics of guests in molecular encapsulation complexes have been studied extensively in solution, but the corresponding behavior of those guests when the capsules are present in the solid state is not as well understood. Here we report on comparative solution 1H and solid-state 2H NMR measurements of encapsulation complexes of fluorene(-d 2), fluoranthene(-d 10), and pyrene-(-d 10) in pyrogallol[4]arene hexamers assembled in the solid state by ball milling. In solution, the 1H spectra show that these rigid guests tumble and exchange positions quickly within the capsules' interiors, with the exception of pyrene, which has slower tumbling and positional exchange. Static solid-state 2H NMR using the deuterated guests shows that, when the capsules are in the solid state, their guests retain the liquid state-like dynamics observed for the capsules in solution. When the pyrogallol[4]arene hexamers' pendant decyl groups were substituted with propyl groups, guest dynamics in the solid state were slowed. We propose that these pendant alkyl groups form an interdigitated and dynamic waxy domain surrounding the capsules in the solid state, and that the greater mobility of the decyl groups is translated across the walls of the host, resulting in more rapid guest dynamics in the capsules' interiors.