NMR Linewidth Research Articles

Using NMR linewidth broadening for magnetic characterization of micrometer-size particles in silicone matrix

Standard magnetization measurements on samples of small magnetic particles may generate conflicting results. We compare the mass magnetization of MgZn ferrite particles in a compressed bulk material and in dry powder and find that at low fields the values can differ by as much as 50%. We show here that embedding the particles in a silicone matrix and measuring the NMR linewidth in combination with simulations establishes a new method to evaluate the magnetization of the particles at different fields and temperatures. The NMR results agree with the direct magnetization measurements of the powder samples and the magnetization measurements of the particles embedded in silicone. This work is motivated, in part, by studies on using small magnetic particles as MRI temperature indicators, and we compare the effectiveness of these particles for low-field and high-field MRI thermometry.

Insights into the Structure and Dynamics of Proteins from 19F Solution NMR Spectroscopy.

19F NMR spectroscopy has recently witnessed a resurgence as an attractive analytical tool for the study of the structure and dynamics of biomolecules in vitro and in cells, despite reports of its applications in biomolecular NMR since the 1970s. The high gyromagnetic ratio, large chemical shift dispersion, and complete absence of the spin 1/2 19F nucleus from biomolecules results in background-free, high-resolution 19F NMR spectra. The introduction of 19F probes in a few selected locations in biomolecules reduces spectral crowding despite its increased line width in comparison to typical 1H NMR line widths and allows rapid site-specific measurements from simple 1D spectra alone. The design and synthesis of novel 19F probes with reduced line widths and increased chemical shift sensitivity to the surrounding environment, together with advances in labeling techniques, NMR methodology, and hardware, have overcome several drawbacks of 19F NMR spectroscopy. The increased interest and widespread use of 19F NMR spectroscopy of biomolecules is gradually establishing it as a sensitive and high-resolution probe of biomolecular structure and dynamics, supplementing traditional 13C/15N-based methods. This Review focuses on the advances in 19F solution NMR spectroscopy of proteins in the past 5 years, with an emphasis on novel 19F tags and labeling techniques, NMR experiments to probe protein structure and conformational dynamics in vitro, and in-cell NMR applications.

Localized Shims Enable Low-Field Simultaneous Multinuclear NMR Spectroscopy.

This Article introduces a smart localized shimset, integrated with a radiofrequency (RF) microsolenoid and optimized as a single unit to locally achieve high-resolution NMR spectroscopy, as a significant advancement toward achieving parallel NMR spectroscopy. The shimset, consisting exclusively of linear shims, demonstrates the capability to improve NMR line width from 84 to 4 Hz in a 1.05 T preclinical MRI scanner. This enhancement enables the resolution of j-couplings in the sample while requiring a total power of 545 mW. Furthermore, a novel method is presented for concurrently obtaining multinuclear NMR spectra using a single RF channel. This approach allows for the utilization of high-sensitivity NMR signals as a reference to correct field drift, facilitating signal averaging in a permanent magnet NMR scanner that is prone to significant temperature-dependent drift.

Dissociation Kinetics and Antimicrobial Activity of Ofloxacin Antibiotic in Artificial Tears Via 1H-NMR, Raman, and UV-Vis Spectroscopic Analysis.

Introduction: The hydrogen-bonded networks play a significant role in influencing several physicochemical properties of ofloxacin in artificial tears (ATs), including density, pH, viscosity, and self-diffusion coefficients. The activities of the ofloxacin antibiotic with Ats mixtures are not solely determined by their concentration but are also influenced by the strength of the hydrogen bonding network which highlight the importance of considering factors such as excessive tear production and dry eye conditions when formulating appropriate dosages of ofloxacin antibiotics for eye drops. Objectives: Investigating the physicochemical properties of ofloxacin-ATs mixtures, which serve as a model for understanding the impact of hydrogen bonding on the antimicrobial activity of ofloxacin antibiotic eye drops. Determine the antimicrobial activities of the ofloxacin-Ats mixture with different concentration of ofloxacin. Methods: The ofloxacin-ATs mixtures were analyzed using 1H-NMR, Raman, and UV-Vis spectroscopies, with variation of ofloxacin concentration to study its dissociation kinetics in ATs, mimicking its behavior in human eye tears. The investigation includes comprehensive analysis of 1H-NMR spectral data, self-diffusion coefficients, Raman spectroscopy, UV-Vis spectroscopy, liquid viscosity, and acidity, providing a comprehensive assessment of the physicochemical properties. Results: Analysis of NMR chemical shifts, linewidths, and self-diffusion coefficient curves reveals distinct patterns, with peaks or minima observed around 0.6 ofloxacin mole fraction dissociated in ATs, indicating a strong correlation with the hydrogen bonding network. Additionally, the pH data exhibits a similar trend to viscosity, suggesting an influence of the hydrogen bonding network on protonic ion concentrations. Antibacterial activity of the ofloxacin-ATs mixtures is evaluated through growth rate analysis against Salmonella typhimurium, considering varying concentrations with mole fractions of 0.1, 0.4, 0.6, 0.8, and 0.9. Conclusions: The antibiotic-ATs mixture with a mole fraction of 0.6 ofloxacin exhibited lower activity compared to mixtures with mole fractions of 0.1 and 0.4, despite its lower concentration. The activities of the mixtures are not solely dependent on concentration but are also influenced by the strength of the hydrogen bonding network. These findings emphasize the importance of considering tear over-secretion and dry eye problems when designing appropriate doses of ofloxacin antibiotics for eye drop formulations.

An easy-built Halbach magnet for LF-NMR with high homogeneity using optimized target-field passive shimming method

The aim of this work is to develop a Halbach magnet that possesses characteristics such as easy-built, low cost and high homogeneity for use in a portable low-field NMR (LF-NMR) system. Considering portability, a 4-ring Halbach magnet was designed through simulation and mechanical modelling, which was successfully constructed in a general laboratory setting. The obtained field strength (B0) was 0.169 T, with an initial homogeneity of 8204 ppm within a sphere with a diameter of 20 mm. To enhance robustness, efficiency and effectiveness of shimming, an optimized target-field passive shimming method was proposed. Subsequently, the homemade spectrometer was used to run NMR experiments on the Halbach magnet. The 1H NMR linewidths of water samples became significantly narrower after passive shimming, e.g., the linewidth of a sample with a diameter of 3 mm and a length of 3 mm reduced from 452.3 Hz (62.5 ppm) to 12.9 Hz (1.8 ppm), which was much less than 102 Hz. The NMR results demonstrate that the proposed passive shimming method can achieve high homogeneity, and the developed Halbach magnet is capable of satisfying numerous LF-NMR applications.

Magnetometer-Detected Nuclear Magnetic Resonance of Photochemically Hyperpolarized Molecules.

Photochemically induced dynamic nuclear polarization (photo-CIDNP) enables nuclear spin ordering by irradiating samples with light. Polarized spins are conventionally detected via high-field chemical-shift-resolved NMR (above 0.1 T). In this Letter, we demonstrate in situ low-field photo-CIDNP measurements using a magnetically shielded fast-field-cycling NMR setup detecting Larmor precession via atomic magnetometers. For solutions comprising mM concentrations of the photochemically polarized molecules, hyperpolarized 1H magnetization is detected by pulse-acquired NMR spectroscopy. The observed NMR line widths are about 5 times narrower than normally anticipated in high-field NMR and are systematically affected by light irradiation during the acquisition period, reflecting a reduction of the transverse relaxation time constant, T2*, on the order of 10%. Magnetometer-detected photo-CIDNP spectroscopy enables straightforward observation of spin-chemistry processes in the ambient field range from a few nT to tens of mT. Potential applications of this measuring modality are discussed.

Large Reduction in the a-axis Knight Shift on UTe2 with Tc = 2.1 K

Spin susceptibility in the superconducting (SC) state was measured in the higher-quality sample of uranium-based superconductor UTe$_2$ by using Knight-shift measurements for a magnetic field $H$ along all three crystalline axes. In the higher-quality sample, the SC transition temperature $T_{\rm c}$ is about 2.1 K, and the residual electronic term in the specific heat is almost zero. The NMR linewidth becomes narrower and is almost half of that in the previous sample with $T_{\rm c} \sim 1.6$ K when $H \parallel a$ and $c$. Although the Knight-shift behavior was not so different from the previous results for $H \parallel b$, and $c$, a large reduction in Knight shift along the $a$ axis was observed, in contrast with the previous $a$-axis Knight shift result. We discuss the origin of the difference between the previous and present results, and the possible SC state derived from the present results.

Parahydrogen-Induced Carbon-13 Radiofrequency Amplification by Stimulated Emission of Radiation.

The feasibility of Carbon-13 Radiofrequency (RF) Amplification by Stimulated Emission of Radiation (C-13 RASER) is demonstrated on a bolus of liquid hyperpolarized ethyl [1-13 C]acetate. Hyperpolarized ethyl [1-13 C]acetate was prepared via pairwise addition of parahydrogen to vinyl [1-13 C]acetate and polarization transfer from nascent parahydrogen-derived protons to the carbon-13 nucleus via magnetic field cycling yielding C-13 nuclear spin polarization of approximately 6 %. RASER signals were detected from samples with concentration ranging from 0.12 to 1 M concentration using a non-cryogenic 1.4T NMR spectrometer equipped with a radio-frequency detection coil with a quality factor (Q) of 32 without any modifications. C-13 RASER signals were observed for several minutes on a single bolus of hyperpolarized substrate to achieve 21 mHz NMR linewidths. The feasibility of creating long-lasting C-13 RASER on biomolecular carriers opens a wide range of new opportunities for the rapidly expanding field of C-13 magnetic resonance hyperpolarization.

Parahydrogen‐Induced Carbon‐13 Radiofrequency Amplification by Stimulated Emission of Radiation

AbstractThe feasibility of Carbon‐13 Radiofrequency (RF) Amplification by Stimulated Emission of Radiation (C‐13 RASER) is demonstrated on a bolus of liquid hyperpolarized ethyl [1‐13C]acetate. Hyperpolarized ethyl [1‐13C]acetate was prepared via pairwise addition of parahydrogen to vinyl [1‐13C]acetate and polarization transfer from nascent parahydrogen‐derived protons to the carbon‐13 nucleus via magnetic field cycling yielding C‐13 nuclear spin polarization of approximately 6 %. RASER signals were detected from samples with concentration ranging from 0.12 to 1 M concentration using a non‐cryogenic 1.4T NMR spectrometer equipped with a radio‐frequency detection coil with a quality factor (Q) of 32 without any modifications. C‐13 RASER signals were observed for several minutes on a single bolus of hyperpolarized substrate to achieve 21 mHz NMR linewidths. The feasibility of creating long‐lasting C‐13 RASER on biomolecular carriers opens a wide range of new opportunities for the rapidly expanding field of C‐13 magnetic resonance hyperpolarization.

Molecular Parameters Promoting High Relaxivity in Cluster-Nanocarrier Magnetic Resonance Imaging Contrast Agents.

We have investigated the mechanism of relaxivity for two magnetic resonance imaging contrast agents that both employ a cluster-nanocarrier design. The first system termed Mn8Fe4-coPS comprises the cluster Mn8Fe4O12(L)16(H2O)4 or Mn8Fe4 (1) (L = carboxylate) co-polymerized with polystyrene to form ∼75 nm nanobeads. The second system termed Mn3Bpy-PAm used the cluster Mn3(O2CCH3)6(Bpy)2 or Mn3Bpy (2) where Bpy = 2,2'-bipyridine, entrapped in ∼180 nm polyacrylamide nanobeads. Here, we investigate the rate of water exchange of the two clusters, and corresponding cluster-nanocarriers, in order to elucidate the mechanism of relaxivity in the cluster-nanocarrier. Swift-Connick analysis of O-17 NMR was used to determine the water exchange rates of the clusters and cluster-nanocarriers. We found distinct differences in the water exchange rate between Mn8Fe4 and Mn8Fe4-coPS, and we utilized these differences to elucidate the nanobead structure. Using the transverse relaxivity from O-17 NMR line widths, we were able to determine the hydration state of the Mn3Bpy (2) cluster as well as Mn3Bpy-PAm. Using these hydration states in the Swift-Connick analysis of O-17 NMR, we found the water exchange rate to be extremely close in value for the cluster Mn3Bpy and cluster-nanocarrier Mn3Bpy-PAm.

Spatially Resolved Spin–Lattice Relaxation Times and Line Widths in Manganese-Grafted Detonation Nanodiamonds

We report on a novel approach that allows determining the spatially resolved nuclear spin–lattice relaxation times and NMR line widths in nanomaterials. The approach was applied to a newly synthesized nanomaterial─detonation nanodiamonds with manganese ions directly grafted to the surface of the nanodiamond particles. The interaction of the carbon nuclear spins with paramagnetic Mn2+ ions results in acceleration of nuclear spin–lattice relaxation and broadening of the 13C resonance line. Using spin dephasing experiments, we were able to determine the layer-by-layer contributions of the paramagnetic Mn2+ions to the spin–lattice relaxation time and line width of the carbon spins positioned at different depths from the diamond surface. Developed for nanodiamonds, this approach is more general and can be successfully applied to study the distribution of nuclear relaxation rates and line broadening and for mapping magnetic interactions inside various nanoparticles, being of practical use in various nanotechnologies.

Solvation and Ion-Pairing Effects of Choline Acetate Electrolyte in Protic and Aprotic Solvents Studied by NMR Titrations.

Choline‐based electrolytes have been proposed as environmentally friendly and low‐cost alternatives for secondary zinc air batteries. Choline acetate [Ch]+[OAc]− in protic (D2O) and aprotic (DMSO‐d6) solvents has been studied by means of concentration‐dependent 1H NMR, viscosity, and density measurements. The viscosities have been calculated on the basis of the Jones‐Dole equation and showed that the dominant contribution originates from short‐range ion‐solvent interactions. Site‐specific association affinities were assigned from NMR chemical shift titrations. In DMSO‐d6, the hydroxyl group of choline was found to have the smallest dissociation constant followed by the methyl group of acetate. The corresponding Gibbs energies at low concentration were found to be in agreement with a solvent‐separated ion pair (2SIP) configuration, whereas at concentrations above 300 mM, a solvent‐shared ion pair (SIP) configuration was assigned. For [Ch]+[OAc]− in D2O, association effects were found to be weaker, attributed to the high dielectric constant of the solvent. On time scales on the order of 100 ms, NMR linewidth perturbations indicated a change in the local rotational dynamics of the ions, attributed to short‐range cation‐solvent interactions and not to solvent viscosity. At 184 mM, ∼ 40 % of the cations in DMSO‐d6 and ∼ 10 % in D2O were found to exhibit short‐range interactions, as indicated by the linewidth perturbations. It was found that at about 300 mM, the ions in DMSO‐d6 exhibit a transition from free to collective translational dynamics on time scales on the order of 400 ms. In DMSO‐d6, both ions were found to be almost equally solvated, whereas in D2O solvation of acetate was stronger, as indicated by the obtained effective hydrodynamic radii. For [Ch]+[OAc]− in DMSO‐d6, the results suggest a solvent‐shared ion association with weak H‐bonding interactions for concentrations between 0.3–1 M. Overall, the extent of ion association in solvents such as DMSO is not expected to significantly limit charge transport and hinder the performance of choline‐based electrolytes.

Site preferences and ion dynamics in lithium chalcohalide solid solutions with argyrodite structure: I. A multinuclear solid state NMR study of the system Li6PS5-xSexI and of Li6AsS5I

Abstract A comprehensive multinuclear (7Li, 31P, 75As, 77Se, 127I) NMR study has been conducted to characterize local structural configurations and atomic distributions in the crystallographically ordered solid solutions of composition Li6PS5-x Se x I (0 ≤ x ≤ 1) and in Li6AsS5I. Throughout the composition range, structural ordering between the atoms on the Wyckoff sites 4a and 4c is maintained, with the I− ions exclusively occupying the 4a sites. 31P magic-angle spinning nuclear magnetic resonance (MAS NMR) can serve to differentiate between the various possible PS4-n Se n 3− tetrahedral units in a quantitative fashion, indicating a preference of P-S relative to P-Se bonding. Each individual PS4-n Se n 3− tetrahedron is represented by a peak cluster containing up to five resonances, representing the five different configurations in which the PCh4 3− units are surrounded by the four closest chalcogenide anions occupying the 4c sites; the distribution of S2− and Se2− over these sites is close to statistical. Non-linear 7Li chemical shift trends as a function of x are interpreted to indicate that the Coulombic traps created by sulfur-rich PS4-n Se n 3− ions (n ≥ 2) within the energy landscape of the lithium ions are deeper than those of the other anionic species present (i.e. selenium-richer PCh4 3− tetrahedra, isolated chalcogenide or iodide ions), causing the Li+ ions to spend on average more time near them. Temperature dependent static 7Li NMR linewidths measured on Li6PS5I and Li6AsS5I indicate a two-step motional narrowing process characterized by a clear dynamic distinction between a more rapid localized intra-cage process and a slower, long-range inter-cage process. In the solid solutions this differentiation gradually disappears, leading to an overall increase of lithium ionic mobility with increasing selenium content, which can be attributed to the influences of higher anionic polarizability and a widening of the lithium migration pathways caused by lattice expansion. Furthermore, the low-temperature phase transition in Li6PS5I, which tends to immobilize the lithium ions below 170 K, is suppressed in the solid solutions. The results offer interesting new insights into the -structure/ionic mobility correlations in this new class of compounds.

NMR determination of Van Hove singularity and Lifshitz transitions in the nodal-line semimetal ZrSiTe

We have applied nuclear magnetic resonance spectroscopy to study the distinctive network of nodal lines in the Dirac semimetal ZrSiTe. The low-$T$ behavior is dominated by a symmetry-protected nodal line, with NMR providing a sensitive probe of the diamagnetic response of the associated carriers. A sharp low-$T$ minimum in NMR shift and $(T_1T)^{-1}$ provides a quantitative measure of the dispersionless, quasi-2D behavior of this nodal line. We also identify a van Hove singularity closely connected to this nodal line, and an associated $T$-induced Lifshitz transition. A disconnect in the NMR shift and line width at this temperature indicates the change in electronic behavior associated with this topological change. These features have an orientation-dependent behavior indicating a field-dependent scaling of the associated band energies.

Molecular Motion of Azetidinium Ion and Phase Transition in [(CH2)3NH2]2KCo(CN)6 with Double Perovskite Structure

Abstract Molecular dynamics of azetidinium ion (AzH+), a four-membered-ring ammonium, in a cyano-bridged double perovskite compound (AzH)2KCo(CN)6 is studied by spin-lattice relaxation time measurements of 1H NMR as well as 14N NQR in relation to the phase transition associated with considerable change of dielectric property. AzH+ ions are in static and dynamic disorder, respectively, below and above Tc = 199 K. Below Tc, a ring-puckering motion of AzH+ takes place with the activation energy Ea = 17.5 kJ mol−1 and the correlation time τc/s = 2.8 × 10−14 exp(Ea/RT). On the other hand, from sudden decrease of 1H NMR linewidth above Tc, a C3 reorientation of AzH+ ion is shown to be activated in high-temperature phase. The activation energy of the C3 reorientation is estimated to be 18 kJ mol−1 from the temperature dependences of 1H NMR as well as 14N NQR spin-lattice relaxation times T1 and T1Q.

A Magic Angle Spinning Activated 17O DNP Raser.

In the raser effect, a sample spontaneously emits continuous radiofrequency radiation, allowing exceptionally narrow NMR line widths to be recorded without applying pulses. To achieve this phenomenon, a large negative magnetization must be induced, which we show here can be achieved for the 17O magnetization of isotopically labeled Gd-doped CeO2 using solid effect dynamic nuclear polarization (DNP), at high field and 110 K. This allows a 2 mHz line width to be measured, which is limited only by the magnetic field stability. The raser effect can be reversibly activated and deactivated by magic angle spinning (MAS), which modulates the nuclear spin coherence lifetime. The use of MAS DNP to enable the raser effect should be further applicable to other systems and nuclei.

Selective observation of spin and charge dynamics in an organic superconductor λ−(BETS)2GaCl4 using Ga69,71 NMR measurements

For the unconventional organic superconductor $\ensuremath{\lambda}\text{\ensuremath{-}}{(\mathrm{BETS})}_{2}{\mathrm{GaCl}}_{4}$ [BETS = bis(ethylenedithio) tetraselenafulvalene], the importance of both spin and charge degrees of freedom has been discussed based on the broadening of the NMR linewidth due to charge disproportionation and the occurrence of a spin-density-wave phase near the superconducting phase. NMR with the nuclear spin of $1/2$, previously used for studying organic conductors, is an effective method for revealing electronic states microscopically; however, it cannot distinguish between charge and spin anomalies. To resolve this problem, in this paper, we performed $^{69,71}\mathrm{Ga}$-NMR measurements, which enabled us to study both charge and spin dynamics using different gyromagnetic ratios and quadrupole moments between two isotopes. The spin-lattice relaxation rate is dominated by electric-field gradient fluctuations originating from molecular dynamics above 150 K and, below this temperature, it is dominated by spin fluctuations derived from the $\ensuremath{\pi}$ electrons of BETS layers. This change in the relaxation mechanism is considered to be due to the development of interactions between ${\mathrm{GaCl}}_{4}$ ions and BETS layers upon freezing of the molecular motion by cooling. Below 150 K, the contribution of spin fluctuations monotonically increases, and no increase in the charge fluctuation was observed, suggesting that the spin degree of freedom plays a major role in low-temperature physical properties. Our findings will aid theoretical studies on superconducting properties.

Protein Side-Chain-DNA Contacts Probed by Fast Magic-Angle Spinning NMR.

Protein–nucleic acid interactions are essential in a variety of biological events ranging from the replication of genomic DNA to the synthesis of proteins. Noncovalent interactions guide such molecular recognition events, and protons are often at the center of them, particularly due to their capability of forming hydrogen bonds to the nucleic acid phosphate groups. Fast magic-angle spinning experiments (100 kHz) reduce the proton NMR line width in solid-state NMR of fully protonated protein–DNA complexes to such an extent that resolved proton signals from side-chains coordinating the DNA can be detected. We describe a set of NMR experiments focusing on the detection of protein side-chains from lysine, arginine, and aromatic amino acids and discuss the conclusions that can be obtained on their role in DNA coordination. We studied the 39 kDa enzyme of the archaeal pRN1 primase complexed with DNA and characterize protein–DNA contacts in the presence and absence of bound ATP molecules.

A Practical Review of NMR Lineshapes for Spin-1/2 and Quadrupolar Nuclei in Disordered Materials.

NMR is a powerful spectroscopic method that can provide information on the structural disorder in solids, complementing scattering and diffraction techniques. The structural disorder in solids can generate a dispersion of local magnetic and electric fields, resulting in a distribution of isotropic chemical shift δiso and quadrupolar coupling CQ. For spin-1/2 nuclei, the NMR linewidth and shape under high-resolution magic-angle spinning (MAS) reflects the distributions of isotropic chemical shift, providing a rich source of disorder information. For quadrupolar nuclei, the second-order quadrupolar broadening remains present even under MAS. In addition to isotropic chemical shift, structural disorder can impact the electric field gradient (EFG) and consequently the quadrupolar NMR parameters. The distributions of quadrupolar coupling and isotropic chemical shift are superimposed with the second-order quadrupolar broadening, but can be potentially characterized by MQMAS (multiple-quantum magic-angle spinning) spectroscopy. We review analyses of NMR lineshapes in 2D DQ–SQ (double-quantum single-quantum) and MQMAS spectroscopies, to provide a guide for more general lineshape analysis. In addition, methods to enhance the spectral resolution and sensitivity for quadrupolar nuclei are discussed, including NMR pulse techniques and the application of high magnetic fields. The role of magnetic field strength and its impact on the strategy of determining optimum NMR methods for disorder characterization are also discussed.

1H detection of heteronuclear dipolar oscillations with water suppression in single crystal peptide and oriented protein samples

Oriented sample solid-state NMR is a complementary approach to protein structure determination with the distinct advantage that it can be applied to supramolecular assemblies, such as viruses and membrane proteins, under near-native conditions, which generally include high levels of hydration as found in living systems. Thus, in order to perform 1H detected versions of multi-dimensional experiments water suppression techniques must be integrated into the pulse sequences. For example, 1H-windowed detection of 1H-15N dipolar couplings enable multi-dimensional NMR experiments to be performed. Here we show that the addition of a solvent suppression pulse during the z-filter interval greatly improves the sensitivity of the experiments by suppressing the 1H signals from water present. This is demonstrated here with a crystal sample submerged in water and then extended to proteins. The combination of solvent-suppressed 1H detected PISEMO and the use of a strip shield-solenoid coil probe configuration provides a two-fold sensitivity enhancement in both the crystal sample and Pf1 coat protein sample compared to the 15N direct detection method. Here we also examine protein NMR line-widths and sensitivity enhancements in the context of window detected separated local field experiments for protein samples.