Role of G326 in Determining the Aggregation Propensity of R3 Tau Repeat: Insights from Studies on R1R3 Tau Construct.

The Microtubule-binding repeat region (MTBR) of Tau has been studied extensively due to its pathological implications in neurodegenerative diseases like Alzheimer's disease. The pathological property of MTBR is mainly due to the R3 repeat's high propensity for self-aggregation, highlighting the critical molecular grammar of the repeat. Utilizing the R1R3 construct (WT) and its G326E mutant (EE), we determine the distinct characteristics of various peptide segments that modulate the aggregation propensity of the R3 repeat using NMR spectroscopy. Through time-dependent experiments, we have identified 317KVTSKCGS324 in R3 repeat as the aggregation initiating motif (AIM) due to its role at the initial stages of aggregation. The G326E mutation induces changes in conformation and dynamics at the AIM, thereby effectively abrogating the aggregation propensity of the R1R3 construct. We further corroborate our findings through MD simulations and propose that AIM is a robust site of interest for tauopathy drug design.

Modulation of Primary and Secondary Processes in Tau Fibril Formation by Salt-Induced Dynamics.

The initial stages of amyloid fibrilization begin with the monomers populating aggregation-prone conformers. Characterization of such aggregation-prone conformers is crucial in the study of neurodegenerative diseases. The current study characterizes the aggregation pathway of two tau protein constructs that have been recently demonstrated to form Alzheimer's (AD) fibril structures with divalent ions and chronic traumatic encephalopathy (CTE) fibril structures with monovalent ions. The results highlight the involvement of identical residues in both the primary and secondary processes of both AD and CTE fibril propagation. Nuclear magnetic resonance relaxation experiments reveal increased flexibility of the motifs 321KCGS within R3 and 364PGGGN within R4 in the presence of MgCl2/NaCl, correlating with faster aggregation kinetics and indicating efficient primary nucleation. Notably, the seeded aggregation kinetics of the tau monomers in the presence and absence of metal ions are strikingly different. This correlates with the overall sign of the 15N-ΔR2 profile specifying the dominant mechanism involved in the process of aggregation.

Sensing PEGylated Peptide Conformations Using a Protein Nanopore.

Membrane pores are exploited for the stochastic sensing of various analytes, and here, we use electrical recordings to explore the interaction of PEGylated peptides of different sizes with a protein pore, CymA. This wide-diameter natural pore comprises densely filled charged residues, facilitating electrophoretic binding of polyethylene glycol (PEG) tagged with a nonaarginine peptide. The small PEG 200 peptide conjugates produced monodisperse blockages and exhibited voltage-dependent translocation across the pores. Notably, the larger PEG 1000 and 2000 peptide conjugates yielded heterogeneous blockages, indicating a multitude of PEG conformations hindering their translocation through the pore. Furthermore, a much larger PEG 5000 peptide occludes the pore entrance, resulting in complete closure. The competitive binding of different PEGylated peptides with the same pore produced specific blockage signals reflecting their identity, size, and conformation. Our proposed model of sensing distinct polypeptide conformations corresponds to disordered protein unfolding, suggesting that this pore can find applications in proteomics.

NMR Relaxation Experiments Probe Monomer-Fibril Interaction and Identify Critical Interacting Residues Responsible for Distinct Tau Fibril Morphologies.

Tau aggregation is governed by secondary processes, a major pathological pathway for tau protein fibril propagation, yet its molecular mechanism remains unknown. This work uses saturation transfer and lifetime line-broadening experiments to identify the critical residues involved in these secondary processes. Distinct residue-specific NMR relaxation parameters were obtained for the truncated three repeat tau construct (K19) in equilibrium with structurally different, self-aggregated (saK19) or heparin-induced (hK19) fibrils. The interacting residues are restricted to R3 repeat for hK19 and to R3, R4, and R' repeats for saK19 fibrils. Furthermore, the relaxation profiles of tau monomers in equilibrium with the structurally comparable, in vitro pathological fibrils (tauAD and tauCTE) were similar but distinct from hK19 or saK19 fibrils. Thus, residue-specific relaxation identifies the important residues involved in the binding of monomers to the fibrils. The relaxation profile of the monomers in equilibrium with the NMR invisible fibril seeds potentially distinguishes the distinct structures of tau fibrils.

Structurally Induced Chirality of an Achiral Chromophore on Self-Assembled Nanofibers: A Twist Makes It Chiral.

The surface domains of self-assembled amphiphiles are well-organized and can perform many physical, chemical, and biological functions. Here, we present the significance of chiral surface domains of these self-assemblies in transferring chirality to achiral chromophores. These aspects are probed using l- and d-isomers of alkyl alanine amphiphiles which self-assemble in water as nanofibers, possessing a negative surface charge. When bound on these nanofibers, positively charged cyanine dyes (CY524 and CY600), each having two quinoline rings bridged by conjugated double bonds, show contrasting chiroptical features. Interestingly, CY600 displays a bisignated circular dichroic (CD) signal with mirror-image symmetry, while CY524 is CD silent. Molecular dynamics simulations reveal that the model cylindrical micelles (CM) derived from the two isomers exhibit surface chirality and the chromophores are buried as monomers in mirror-imaged pockets on their surfaces. The monomeric nature of template-bound chromophores and their binding reversibility are established by concentration- and temperature-dependent spectroscopies and calorimetry. On the CM, CY524 displays two equally populated conformers with opposite sense, whereas CY600 is present as two pairs of twisted conformers in each of which one is in excess, due to differences in weak dye-amphiphile hydrogen bonding interactions. Infrared and NMR spectroscopies support these findings. Reduction of electronic conjugation caused by the twist establishes the two quinoline rings as independent entities. On-resonance coupling between the transition dipoles of these units generates bisignated CD signals with mirror-image symmetry. The results presented herein provide insight on the little-known structurally induced chirality of achiral chromophores through transfer of chiral surface information.

Kinetochore-microtubule attachment in human cells is regulated by the interaction of a conserved motif of Ska1 with EB1.

The kinetochore establishes the linkage between chromosomes and the spindle microtubule plus ends during mitosis. In vertebrates, the spindle-kinetochore-associated (Ska1,2,3) complex stabilizes kinetochore attachment with the microtubule plus ends, but how Ska is recruited to and stabilized at the kinetochore-microtubule interface is not understood. Here, our results show that interaction of Ska1 with the general microtubule plus end-associated protein EB1 through a conserved motif regulates Ska recruitment to kinetochores in human cells. Ska1 forms a stable complex with EB1 via interaction with the motif in its N-terminal disordered loop region. Disruption of this interaction either by deleting or mutating the motif disrupts Ska complex recruitment to kinetochores and induces chromosome alignment defects, but it does not affect Ska complex assembly. Atomic-force microscopy imaging revealed that Ska1 is anchored to the C-terminal region of the EB1 dimer through its loop and thereby promotes formation of extended structures. Furthermore, our NMR data showed that the Ska1 motif binds to the residues in EB1 that are the binding sites of other plus end targeting proteins that are recruited to microtubules by EB1 through a similar conserved motif. Collectively, our results demonstrate that EB1-mediated Ska1 recruitment onto the microtubule serves as a general mechanism for the formation of vertebrate kinetochore-microtubule attachments and metaphase chromosome alignment.

Sequence-Dependent Conformational Properties of PGGG Motif in Tau Repeats: Insights from Molecular Dynamics Simulations of Narrow Pick Filament.

Tauopathies are a class of neurodegenerative diseases correlated with the presence of pathological Tau fibrils as a diagnostic marker. The microtubule-binding repeat region of Tau protein, which includes R1, R2, R3, and R4 repeats, constitutes the core of these fibrils. Each repeat consists of a semiconserved C-terminal hexapeptide flanked by KxGS and PGGG motifs. Previous studies have shown the influence of these peptides on protein aggregation, yet their repeat-specific properties are less explored. Using molecular dynamics, we probed the sequence-specific influence of the C-terminal hexapeptide (264ENLKHQ269) in determining the compact local conformation of the R1 repeat of the narrow Pick filament (NPF) with a homologous E264G mutation. In addition to that, we also studied the influence of 262S phosphorylation on this conformation as the phosphorylation is proposed to alleviate the pathogenesis of Pick's disease. Interestingly, we determined that E264G mutation induces a conformational shift of 270PGGG273 from a turn to a random coil. This conformational dependence is experimentally verified with the R1R3-E264G mutant construct, which displayed accelerated aggregation compared with the R1R3 wild-type construct. A significant delay in aggregation of the R1R3-G326E mutant further demonstrates the importance of 326G in determining the conformation of the R3 repeat. Thus, we conclude that the conformational properties of the PGGG motif in Tau repeats are strongly dependent on the repeat-specific sequence of the C-terminal hexapeptide.

Ligand-Induced Ground- and Excited-State Chirality in Silicon Nanoparticles: Surface Interactions Matter.

Silicon-based light-emitting materials have emerged as a favorable substitute to various organic and inorganic systems due to silicon's high natural abundance, low toxicity, and excellent biocompatibility. However, efforts on the design of free-standing silicon nanoparticles with chiral non-racemic absorption and emission attributes are rather scare. Herein, we unravel the structural requirements for ligand-induced chirality in silicon-based nanomaterials by functionalizing with D- and L-isomers of a bifunctional ligand, namely, tryptophan. The structural aspects of these systems are established using high-resolution high-angle annular dark-field imaging in the scanning transmission electron microscopy mode, solid-state nuclear magnetic resonance, Fourier transform infrared, and X-ray photoelectron spectroscopy. Silicon nanoparticles capped with L- and D-isomers of tryptophan displayed positive and negative monosignated circular dichroic signals and circularly polarized luminescence indicating their ground- and excited-state chirality. Various studies supported by density functional theory calculations signify that the functionalization of indole ring nitrogen on the silicon surface plays a decisive role in modifying the chiroptical characteristics by generating emissive charge-transfer states. The chiroptical responses originate from the multipoint interactions of tryptophan with the nanoparticle surface through the indole nitrogen and -CO2- groups that can transmit an enantiomeric structural imprint on the silicon surface. However, chiroptical properties are not observed in phenylalanine- and alanine-capped silicon nanoparticles, which are devoid of Si-N bonds and chiral footprints. Thus, the ground- and excited-state chiroptics in tryptophan-capped silicon nanoparticles originates from the collective effect of ligand-bound emissive charge-transfer states and chiral footprints. Being the first report on the circularly polarized luminescence in silicon nanoparticles, this work will open newer possibilities in the field of chirality.

Examining the Transient Dark State in Protein-Quantum Dot Interaction by Relaxation-Based Solution NMR.

We probed the "dark" state involved in the protein-quantum dot (QD) interaction using a relaxation-based solution nuclear magnetic resonance (NMR) approach. We examined the dynamics and exchange kinetics of the ubiquitin-CdTe model system, which undergoes a fast exchange in the transverse relaxation time scale. We applied the recently developed dark-state exchange saturation transfer (DEST), lifetime line broadening (ΔR2), and exchange-induced chemical shift (δex) solution NMR techniques to obtain a residue-specific binding behavior of the protein on the QD surface. The variation in the estimated 15N-R2bound values clearly shows the dynamic nature of bound Ub. Upon mapping the amino acid residues showing a faster relaxation rate on the electrostatic potential surface of the protein, we have determined that the interaction is preferably electrostatic, and the amino acid residues involved in binding lie on the positively charged surface of the protein. We believe that our experimental approach should provide more in-depth knowledge to engineer new hybrid protein-QD systems in the future.

Mapping the Fibril Core of the Prion Subdomain of the Mammalian CPEB3 that is Involved in Long Term Memory Retention.

Long-term memory storage is modulated by the prion nature of CPEB3 forming the molecular basis for the maintenance of synaptic facilitation. Here we report that the first prion sub-domain PRD1 of mouse CPEB3 can autonomously form amyloid fibrils in vitro and punctate-like structures in vivo. A ninety-four amino acid sequence within the PRD1 domain, PRD1-core, displays high propensity towards aggregation and associated amyloid characteristics. PRD1-core is characterized using electron microscopy, X-ray diffraction, and solution-state NMR deuterium exchange experiments. Secondary structure elements deduced from solid-state NMR reveal a ß-rich core comprising of forty amino acids at the N-terminus of PRD1-core. The synthesized twenty-three amino acid long peptide containing the longest rigid segment (E124-H145) of the PRD1-core rapidly self-aggregates and forms fibrils, indicating a limited aggregation-prone region that could potentially activate the aggregation of the full-length protein. This study provides the first step in identifying the structural trigger for the CPEB3 aggregation process.

Direct Observation of the Self-Aggregation of R3R4 Bi-repeat of Tau Protein.

Different cryo-EM derived atomic models of in vivo tau filaments from patients with tauopathies consisted of R3 and R4 repeats of the microtubule-binding domain. In comparison, only the R3 repeat forms the core of the heparin-induced fibrils of the three repeat tau isoforms. For developing therapeutics, it is desirable to have an in vitro tau aggregation system producing fibrils corresponding to the disease morphology. Here we report the self-aggregation of truncated tau segment R3R4 peptide without requiring heparin for aggregation induction. We used NMR spectroscopy and other biophysical methods to monitor the self-aggregation of R3R4. We identified the hexapeptide region in R3 and ß-turn region in R4 as the aggregation initiating region of the protein. The solid-state NMR of self-aggregated R3R4 fibrils demonstrated that in addition to R3 residues, residues of R4 were also part of the fibril filaments. The presence of both R3 and R4 residues in the aggregation process and the core of fibril filaments suggest that the aggregation of R3R4 might resemble the in vivo aggregation process.

SxIP binding disrupts the constitutive homodimer interface of EB1 and stabilizes EB1 monomer.

SxIP is a microtubule tip localizing signal found in many +TIP proteins that bind to the hydrophobic cavity of the C-terminal domain of end binding protein 1 (EB1) and then positively regulate the microtubule plus-end tracking of EBs. However, the exact mechanism of microtubule activation of EBs in the presence of SxIP signaling motif is not known. Here, we studied the effect of SxIP peptide on the native conformation of EB1 in solution. Using various NMR experiments, we found that SxIP peptide promoted the dissociation of natively formed EB1 dimer. We also discovered that I224A mutation of EB1 resulted in an unfolded C-terminal domain, which upon binding with the SxIP motif folded to its native structure. Molecular dynamics simulations also confirmed the relative structural stability of EB1 monomer in the SxIP bound state. Residual dipolar couplings and heteronuclear NOE analysis suggested that the binding of SxIP peptide at the C-terminal domain of EB1 decreased the dynamics and conformational flexibility of the N-terminal domain involved in EB1-microtubule interaction. The SxIP-induced disruption of the dimeric interactions in EB1, coupled with the reduction in conformational flexibility of the N-terminal domain of EB1, might facilitate the microtubule association of EB1.

Residual Dipolar-Coupling-Based Conformational Comparison of Noncovalent Ubiquitin Homodimer with Covalently Linked Diubiquitin.

Although the conformation of the polymer chain of Ubiquitin (Ub) mainly depends on the type of isopeptide linkage connecting two Ub molecules, the non-covalent (noncovalent) interaction between two Ub molecules within the chain could also tune their conformational preference. Here, we studied the conformation of noncovalently formed Ub dimers in solution using residual dipolar couplings (RDCs). Comparing the RDC derived alignment tensor of the noncovalently formed dimer with the two most abundant (K11 and K48) covalent linked Ub dimers revealed that the conformation of K11 linked and noncovalent Ub dimers were similar. Between the various NMR and crystal structures of K11 linked Ub dimers, RDC tensor analysis showed that the structure of K11 linked dimer crystalized at neutral pH is similar to noncovalent dimer. Analogous to the experimental study, the comparison of predicted order matrix of various covalent Ub dimers with that of the experimentally determined order matrix of noncovalent Ub dimer also suggests that the conformation of K11 linked dimers crystalized at neutral pH is similar to the noncovalent dimer.

GTP-binding facilitates EB1 recruitment onto microtubules by relieving its auto-inhibition.

Microtubule plus end-binding protein, EB1 is a key regulator of microtubule dynamics. Auto-inhibitory interaction in EB1 has previously been shown to inhibit its ability to bind to microtubules and regulate microtubule dynamics. However, the factors that promote its microtubule regulatory activity by over-coming the auto-inhibition are less known. Here, we show that GTP plays a critical role in promoting the microtubule-targeting activity of EB1 by suppressing its auto-inhibition. Our biophysical data demonstrate that GTP binds to EB1 at a distinct site in its conserved N-terminal domain. Detailed analyses reveal that GTP-binding suppresses the intra-molecular inhibitory interaction between the globular N-terminus and the C-terminal coiled-coil domain. We further show that mutation of the GTP-binding site residues in N-terminus weakens the affinity for GTP, but also for the C-terminus, indicating overlapping binding sites. Confocal imaging and biochemical analysis reveal that EB1 localization on the microtubules is significantly increased upon mutations of the GTP-binding site residues. The results demonstrate a unique role of GTP in facilitating EB1 interaction with the microtubules by relieving its intra-molecular inhibition. They also implicate that GTP-binding may regulate the functions of EB1 on the cellular microtubules.

Zn2+ Interrupts R4-R3 Association Leading to Accelerated Aggregation of Tau Protein.

Direct binding of divalent metal ion, especially Zn2+ , have been shown to increase the rate of tau aggregation and enhance tau toxicity in cells. Hence, understanding the molecular basis of the Zn2+ -accelerated tau aggregation can potentially determine the molecular interactions modulating tau aggregation. Herein, we show that Zn2+ coordinates through the cysteine in R3 repeat and significantly accelerates the aggregation rate of the three repeat tau constructs (K19) but that the coordination is incapable of increasing the aggregation rate of the 20 amino acid peptide derived from the R3 repeat (R3) of tau. The NMR characterization of the binding of Zn2+ to K19, together with the aggregation studies with K19, R3 and R4 peptides, reveal the presence of an aggregation-inhibitory interaction between the R3 and R4 repeat of K19. Our data show that binding of Zn2+ to R3 repeat of tau, weaken the aggregation-inhibiting influence between R3 and R4 repeats, leading to faster aggregation of tau protein.

Direct Observation of Aggregation-Induced Backbone Conformational Changes in Tau Peptides.

In tau proteins, the hexapeptides in the R2 and R3 repeats are known to initiate tau fibril formation, which causes a class of neurodegenerative diseases called the taupathies. We show that in R3, in addition to the presence of the hexapeptides, the correct turn conformation upstream to it is also essential for producing prion-like fibrils that are capable of propagation. A time-dependent NMR aggregation assay of a slow fibril forming R3-S316P peptide revealed a trans to cis equilibrium shift in the peptide-bond conformation preceding P316 during the growth phase of the aggregation process. S316 was identified as the key residue in the turn that confers templating capacity on R3 fibrils to accelerate the aggregation of the R3-S316P peptide. These results on the specific interactions and conformational changes responsible for tau aggregation could prove useful for developing an efficient therapeutic intervention in Alzheimer's disease.

Recovery of bulk proton magnetization and sensitivity enhancement in ultrafast magic-angle spinning solid-state NMR.

The sensitivity of solid-state NMR experiments is limited by the proton magnetization recovery delay and by the duty cycle of the instrument. Ultrafast magic-angle spinning (MAS) can improve the duty cycle by employing experiments with low-power radio frequency (RF) irradiation which reduce RF heating. On the other hand, schemes to reduce the magnetization recovery delay have been proposed for low MAS rates, but the enhancements rely on selective transfers where the bulk of the (1)H magnetization pool does not contribute to the transfer. We demonstrate here that significant sensitivity enhancements for selective and broadband experiments are obtained at ultrafast MAS by preservation and recovery of bulk (1)H magnetization. We used [(13)C, (15)N]-labeled glutamine as a model compound, spinning in a 1.3 mm rotor at a MAS frequency of 65 kHz. Using low-power (1)H RF (13.4 kHz), we obtain efficient (1)H spin locking and (1)H-(13)C decoupling at ultrafast MAS. As a result, large amounts of (1)H magnetization, from 35% to 42% of the initial polarization, are preserved after cross-polarization and decoupling. Restoring this magnetization to the longitudinal axis using a flip-back pulse leads to an enhancement of the sensitivity, an increase ranging from 14% to 21% in the maximal achievable sensitivity regime and from 24% to 50% in the fast pulsing regime, and to a shortening of the optimal recycling delay to 68% of its original duration. The analysis of the recovery and sensitivity curves reveals that the sensitivity gains do not rely on a selective transfer where few protons contribute but rather on careful conservation of bulk (1)H magnetization. This makes our method compatible with broadband experiments and uniformly labeled materials, in contrast to the enhancement schemes proposed for low MAS. We tested seven different cross-polarization schemes and determined that recovery of bulk (1)H magnetization is a general method for sensitivity enhancement. The physical insight gained about the behavior of proton magnetization sharing under spin lock will be helpful to break further sensitivity boundaries, when even higher external magnetic fields and faster spinning rates are employed.

A straightforward method for stereospecific assignment of val and leu prochiral methyl groups by solid-state NMR: Scrambling in the [2-13C]Glucose labeling scheme.

The unambiguous stereospecific assignment of the prochiral methyl groups in Val and Leu plays an important role in the structural investigation of proteins by NMR. Here, we present a straightforward method for their stereospecific solid-state NMR assignment based on [2-(13)C]Glucose ([2-(13)C]Glc) as the sole carbon source during protein expression. The approach is fundamentally based on the stereo-selective biosynthetic pathway of Val and Leu, and the co-presence of [2-(13)C]pyruvate produced mainly by glycolysis and [3-(13)C]/[1,3-(13)C]pyruvate most probably formed through scrambling in the pentose phosphate pathway. As a consequence, the isotope spin pairs (13)Cß-(13)Cγ2 and (13)Cα-(13)Cγ1 in Val, and (13)Cγ-(13)Cδ2 and (13)Cß-(13)Cδ1 in Leu are obtained. The approach is successfully demonstrated with the stereospecific assignment of the methyl groups of Val and Leu of type 3 secretion system PrgI needles and microcrystalline ubiquitin.

ß-Sheet core of tau paired helical filaments revealed by solid-state NMR.

One of the hallmarks of Alzheimer's disease is the self-assembly of the microtubule-associated protein tau into fibers termed "paired helical filaments" (PHFs). However, the structural basis of PHF assembly at atomic detail is largely unknown. Here, we applied solid-state nuclear magnetic resonance (ssNMR) spectroscopy to investigate in vitro assembled PHFs from a truncated three-repeat tau isoform (K19) that represents the core of PHFs. We found that the rigid core of the fibrils is formed by amino acids V306 to S324, only 18 out of 99 residues, and comprises three ß-strands connected by two short kinks. The first ß-strand is formed by the well-studied hexapeptide motif VQIVYK that is known to self-aggregate in a steric zipper arrangement. Results on mixed [(15)N:(13)C]-labeled K19 fibrils show that ß-strands are stacked in a parallel, in-register manner. Disulfide bridges formed between C322 residues of different molecules lead to a disturbance of the ß-sheet structure, and polymorphism in ssNMR spectra is observed. In particular, residues K321-S324 exhibit two sets of resonances. Experiments on K19 C322A PHFs further confirm the influence of disulfide bond formation on the core structure. Our structural data are supported by H/D exchange NMR measurements on K19 as well as a truncated four-repeat isoform of tau (K18). Site-directed mutagenesis studies show that single-point mutations within the three different ß-strands result in a significant loss of PHF aggregation efficiency, highlighting the importance of the ß-structure-rich regions for tau aggregation.

Tailored low-power cross-polarization under fast magic-angle spinning.

High static magnetic fields and very fast magic-angle spinning (MAS) promise to improve resolution and sensitivity of solid-state NMR experiments. The fast MAS regime has permitted the development of low-power cross-polarization schemes, such as second-order cross-polarization (SOCP), which prevent heat deposition in the sample. Those schemes are however limited in bandwidth, as weak radio-frequency (RF) fields only cover a small chemical shift range for rare nuclei (e.g. (13)C). Another consideration is that the efficiency of cross-polarization is very sensitive to magnetization decay that occurs during the spin-lock pulse on the abundant nuclei (e.g. (1)H). Having characterized this decay in glutamine at 60 kHz MAS, we propose two complementary strategies to tailor cross-polarization to desired spectral regions at low RF power. In the case of multiple sites with small chemical shift dispersion, a larger bandwidth for SOCP is obtained by slightly increasing the RF power while avoiding recoupling conditions that lead to fast spin-lock decay. In the case of two spectral regions with large chemical shift offset, an extension of the existing low-power schemes, called MOD-CP, is introduced. It consists of a spin-lock on (1)H and an amplitude-modulated spin-lock on the rare nucleus. The range of excited chemical shifts is assessed by experimental excitation profiles and numerical simulation of an I(2)S spin system. All SOCP-based schemes exhibit higher sensitivity than high-power CP schemes, as demonstrated on solid (glutamine) and semi-solid (hydrated, micro-crystalline ubiquitin) samples.