Evaluating the Catalytic Efficiency of the Human Membrane-type 1 Matrix Metalloproteinase (MMP-14) Using AuNP-Peptide Conjugates.

Interactions of plasmonic nanocolloids such as gold nanoparticles and nanorods with proximal dye emitters result in efficient quenching of the dye photoluminescence (PL). This has become a popular strategy for developing analytical biosensors relying on this quenching process for signal transduction. Here, we report on the use of stable PEGylated gold nanoparticles, covalently coupled to dye-labeled peptides, as sensitive optically addressable sensors for determining the catalytic efficiency of the human matrix metalloproteinase-14 (MMP-14), a cancer biomarker. We exploit real-time dye PL recovery triggered by MMP-14 hydrolysis of the AuNP-peptide-dye to extract quantitative analysis of the proteolysis kinetics. Sub-nanomolar limit of detections for MMP-14 has been achieved using our hybrid bioconjugates. In addition, we have used theoretical considerations within a diffusion-collision framework to derive enzyme substrate hydrolysis and inhibition kinetics equations, which allowed us to describe the complexity and irregularity of enzymatic proteolysis of nanosurface-immobilized peptide substrates. Our findings offer a great strategy for the development of highly sensitive and stable biosensors for cancer detection and imaging.

Quantum Dot-Peptide Conjugates as Energy Transfer Probes for Sensing the Proteolytic Activity of Matrix Metalloproteinase-14.

We detail the assembly and characterization of quantum dot (QD)-dye conjugates constructed using a peptide bridge specifically designed to recognize and interact with a breast cancer biomarker─matrix metalloproteinase-14 (MMP-14). The assembled QD conjugates are then used as optically addressable probes, relying on Förster resonance energy transfer (FRET) interactions as a transduction mechanism to detect the activity of MMP-14 in solution phase. The QDs were first coated with dithiolane poly(ethylene glycol) (PEG) bearing a carboxyl group that allows coupling via amide bond formation with different dye-labeled peptides. The analytical capability of the conjugates is enabled by correlating changes in the FRET efficiency with the conjugate valence and/or QD-to-dye separation distance, triggered and modulated by enzymatic proteolysis of surface-tethered peptides. The FRET probe exhibits great sensitivity to enzyme digestion with sub-nanomolar limit of detection. We further analyze the proteolysis data within the framework of the Michaelis-Menten model, which considers the fact that surface-attached peptides have a slower diffusion coefficient than free peptides. This results in reduced collision frequency and lower catalytic efficiency, kcat/KM. Our results suggest that our conjugate design is promising, effective, and potentially useful for in vivo analysis.

Characterizing the Brownian Diffusion of Nanocolloids and Molecular Solutions: Diffusion-Ordered NMR Spectroscopy vs Dynamic Light Scattering.

Hydrodynamic size is a characteristic dimension that reflects the Brownian diffusion of objects, such as proteins, macromolecules, and various colloids when dissolved/dispersed in fluid phases. This property is crucial when investigating the utility of colloidal nanocrystals and polymeric materials in biology. Dynamic light scattering (DLS) has been widely used to measure the diffusion coefficient and hydrodynamic size of such systems. Comparatively, diffusion-ordered NMR spectroscopy (DOSY-NMR) is a relatively new analytical method that has provided researchers with an alternative experimental approach to access such information. Here, we apply DLS and DOSY-NMR simultaneously to characterize the diffusion coefficient and hydrodynamic size of several sets of nanocolloids, including dispersions of gold nanoparticles and luminescent quantum dots that are surface-capped with either hydrophobic or hydrophilic coatings, as well as a monomer and a low-molecular-weight polymer. We compare, side by side, the findings acquired from each measurement, which has allowed us to identify the benefits and constraints of each technique. Our results show that the two approaches provide comparable data when larger size nanocolloids are probed. However, we find that DOSY is substantially more effective in characterizing nanocolloids that are fluorescent and/or have very small dimensions, as well as molecular-scale organic ligands, where DLS reaches its limit. Additionally, we find that, compared to DLS, DOSY tends to require higher solute concentrations and longer collection time to generate data with high signal-to-noise ratios.

Elucidating the Role of Surface Coating in the Promotion or Prevention of Protein Corona around Quantum Dots.

Nonspecific interactions in biological media can lead to the formation of a protein corona around nanocolloids, which tends to alter their behavior and limit their effectiveness when used as probes for imaging or sensing applications. Yet, understanding the corona buildup has been challenging. We hereby investigate these interactions using luminescent quantum dots (QDs) as a model nanocolloid system, where we carefully vary the nature of the hydrophilic block in the surface coating, while maintaining the same dihydrolipoic acid (DHLA) bidentate coordinating motif. We first use agarose gel electrophoresis to track changes in the mobility shift upon exposure of the QDs to protein-rich media. We find that QDs capped with DHLA (which presents a hydrophobic alkyl chain terminated with a carboxyl group) promote corona formation, in a concentration-dependent manner. However, when a polyethylene glycol block or a zwitterion group is appended onto DHLA, it yields a coating that prevents corona buildup. Our results clearly confirm that nonspecific interactions with protein-rich media are strongly dependent on the nature of the hydrophilic motif used. Additional gel experiments using SDS-PAGE have allowed further characterization of the corona protein, and showed that mainly a soft corona forms around the DHLA-capped QDs. These findings will be highly informative when designing nanocolloids that can find potential use in biological applications.

Modification of Poly(maleic anhydride)-Based Polymers with H2N-R Nucleophiles: Addition or Substitution Reaction?

Reacting poly(maleic anhydride)-based polymers with H2N-R nucleophiles is a flexible and highly effective approach for preparing a variety of multifunctional, multicoordinating, and multireactive polymers. The exact transformation of the anhydride ring during this addition reaction is still an open question. In this report, we characterize the transformation of a representative block copolymer, poly(isobutylene- alt-maleic anhydride), with a few H2N-R nucleophiles. In particular, we test the effects of varying a few reaction parameters/conditions (e.g., temperature, solvent, reaction time, and addition of thionyl chloride) on the nature of the anhydride transformation and bond formed between the polymer and the lateral R groups. The resulting polymers are characterized using a combination of analytical techniques including FT-IR, one- and two-dimensional NMR, and gel electrophoresis. We find that the ring opening transformation occurs under mild conditions. Conversely, cyclic imide transformation can take place for reactions carried out at high temperature (e.g., in DMF under refluxing conditions). We also find that use of a protic solvent, such as methanol, or addition of thionyl chloride (SOCl2) to the reaction mixture under refluxing conditions can promote cyclic imide transformation. The cyclic imide transformation is nonetheless partial, as carboxyl groups could still be accounted for in the resulting compounds. Depending on the type of transformation, the resulting polymer can exhibit a few distinct properties, such as net charge buildup along the chain, or the appearance of weak UV-vis absorption and fluorescence properties. These findings are useful for understanding the properties exhibited by polymer materials prepared via this flexible and highly effective route using anhydride containing polymers and oligomers.

Intracellular Delivery of Gold Nanocolloids Promoted by a Chemically Conjugated Anticancer Peptide.

We report on the ability of a chemically synthesized anticancer peptide, SVS-1, to promote the rapid uptake of gold nanorods (AuNRs) and gold nanoparticles (AuNPs) by live HeLa cells. For this, AuNPs and AuNRs, surface ligated with a multicoordinating polymer that presents several amine groups per ligand, are simultaneously reacted with SVS-1 and Texas-Red dye; the latter allows fluorescence visualization of the nanocrystals. Using epifluorescence microscopy, we find that incubation of the SVS-1-conjugated AuNPs and AuNRs with a model cancer cell line yields extended staining throughout the cell cytoplasm, even at low conjugate concentrations (∼0.1 nM). Furthermore, uptake is specific to the SVS-1-conjugated nanocrystals. Additional endocytosis inhibition experiments, where cells have been incubated with the conjugates at 4 °C or in the presence of endocytic inhibitors, show that significant levels of conjugate uptake persist. These results combined indicate an uptake mechanism that does not necessarily rely on endocytosis, a promising finding with implications for the use of nanomaterials in the field of biology and nanomedicine.

Efficient Assembly of Quantum Dots with Homogenous Glycans Derived from Natural N-Linked Glycoproteins.

Coating inorganic nanoparticles with polyethylene glycol (PEG)-appended ligands, as means to preserve their physical characteristics and promote steric interactions with biological systems, including enhanced aqueous solubility and reduced immunogenicity, has been explored by several groups. Conversely, macromolecules present in the human serum and on the surface of cells are densely coated with hydrophilic glycans that act to reduce nonspecific interactions, while facilitating specific binding and interactions. In particular, N-linked glycans are abundant on the surface of most serum proteins and are composed of a branched architecture that is typically characterized by a significant level of molecular heterogeneity. Here we provide two distinct methodologies, covalent bioconjugation and self-assembly, to functionalize two types of Quantum Dots with a homogeneous, complex-type N-linked glycan terminated with a sialic acid moiety. A detailed physical and functional characterization of these glycan-coated nanoparticles has been performed. Our findings support the potential use of such fluorescent platforms to sense glycan-involved biological processes, such as lectin recognition and sialidase-mediated hydrolysis.

Photochemical transformation of lipoic acid-based ligands: probing the effects of solvent, ligand structure, oxygen and pH.

We have combined optical absorption with the Ellman's test to identify the parameters that affect the transformation of the 5-membered dithiolanes to thiols in lipoic acid (LA) and its derivatives during UV-irradiation. We found that the nature and polarity of the solvent, the structure of the ligands, acidity of the medium and oxygen can drastically affect the amount of photogenerated thiols. These findings are highly relevant to the understanding of the photochemical transformation of this biologically relevant compound, and would benefit the increasing use of LA-based ligands for the surface functionalization of various nanomaterials.

Enhanced Uptake of Luminescent Quantum Dots by Live Cells Mediated by a Membrane-Active Peptide.

The steady progress made over the past three decades in growing a variety of inorganic nanomaterials, with discreet control over their size and photophysical properties, has been exploited to develop several imaging and sensing applications. However, full integration of these materials into biology has been hampered by the complexity of delivering them into cells. In this report, we demonstrate the effectiveness of a chemically synthesized anticancer peptide to facilitate the rapid delivery of luminescent quantum dots (QDs) into live cells. We combine fluorescence imaging microscopy, flow cytometry, and specific endocytosis inhibition experiments to probe QD-peptide conjugate uptake by different cell lines. We consistently find that a sizable fraction of the internalized conjugates does not co-localize with endosomes or the nuclei. These findings are extremely promising for the potential integration of various nanomaterials into biological systems.

The roles of surface chemistry, dissolution rate, and delivered dose in the cytotoxicity of copper nanoparticles.

The understanding of nanoparticle (NP) cytotoxicity is challenging because of incomplete information about physicochemical changes particles undergo once they come into contact with biological fluids. It is therefore essential to characterize changes in NP properties to better understand their biological fate and effects in mammalian cells. In this paper, we present a study on the effect of particle surface oxidation and dissolution rates of Cu NPs. Particle dissolution, cell-associated Cu doses, and oxidative stress responses in A549 luciferase reporter cells were examined for Cu NPs modified with mercaptocarboxylic acids with different carbon chain lengths and a thiotic acid appended-PEG ligand (TA). We found that these Cu NPs released ionic species together with small particles upon oxidation and that surface chemistry influenced the morphology and dissolution rate. The dissolution rate was also shown to impact both the cellular Cu dosimetry and associated oxidative stress responses. The convergent results from dissolution and dosimetry measurements demonstrate that both intracellular and extracellular (i.e., NP uptake-independent) release of ionic species from Cu NPs greatly affect the cytotoxicity.

Margatoxin-bound quantum dots as a novel inhibitor of the voltage-gated ion channel Kv1.3.

Venom-derived ion channel inhibitors have strong channel selectivity, potency, and stability; however, tracking delivery to their target can be challenging. Herein, we utilized luminescent quantum dots (QDs) conjugated to margatoxin (MgTx) as a traceable vehicle to target a voltage-dependent potassium channel, Kv1.3, which has a select distribution and well-characterized role in immunity, glucose metabolism, and sensory ability. We screened both unconjugated (MgTx) and conjugated MgTx (QD-MgTx) for their ability to inhibit Shaker channels Kv1.1 to Kv1.7 using patch-clamp electrophysiology in HEK293 cells. Our data indicate that MgTx inhibits 79% of the outward current in Kv1.3-transfected cells and that the QD-MgTx conjugate is able to achieve a similar level of block, albeit a slightly reduced efficacy (66%) and at a slower time course (50% block by 10.9 ± 1.1 min, MgTx; vs. 15.3 ± 1.2 min, QD-MgTx). Like the unbound peptide, the QD-MgTx conjugate inhibits both Kv1.3 and Kv1.2 at a 1 nM concentration, whereas it does not inhibit other screened Shaker channels. We tested the ability of QD-MgTx to inhibit native Kv1.3 expressed in the mouse olfactory bulb (OB). In brain slices of the OB, the conjugate acted similarly to MgTx to inhibit Kv1.3, causing an increased action potential firing frequency attributed to decreased intraburst duration rather than interspike interval. Our data demonstrate a retention of known biophysical properties associated with block of the vestibule of Kv1.3 by QD-MgTx conjugate compared to that of MgTx, inferring QDs could provide a useful tool to deliver ion channel inhibitors to targeted tissues in vivo.

Aqueous Growth of Gold Clusters with Tunable Fluorescence Using Photochemically Modified Lipoic Acid-Based Ligands.

We report a one-phase aqueous growth of fluorescent gold nanoclusters (AuNCs) with tunable emission in the visible spectrum, using a ligand scaffold that is made of poly(ethylene glycol) segment appended with a metal coordinating lipoic acid at one end and a functional group at the other end. This synthetic scheme exploits the ability of the UV-induced photochemical transformation of LA-based ligands to provide DHLA and other thiol byproducts that exhibit great affinity to metal nanoparticles, obviating the need for chemical reduction of the dithiolane ring using classical reducing agents. The influence of various experimental conditions, including the photoirradiation time, gold precursor-to-ligand molar ratios, time of reaction, temperature, and the medium pH, on the growth of AuNCs has been systematically investigated. The photophysical properties, size, and structural characterization were carried out using UV-vis absorption and fluorescence spectroscopy, TEM, DOSY-NMR, and X-ray photoelectron spectroscopy. The hydrodynamic size (RH) obtained by DOSY-NMR indicates that the size of these clusters follows the trend anticipated from the absorption and PL data, with RH(red) > RH(yellow) > RH(blue). The tunable emission and size of these gold nanoclusters combined with their high biocompatibility would make them greatly promising for potential use in imaging and sensing applications.

Bio-orthogonal Coupling as a Means of Quantifying the Ligand Density on Hydrophilic Quantum Dots.

We describe the synthesis of two metal-coordinating ligands that present one or two lipoic acid (LA) anchors, a hydrophilic polyethylene glycol (PEG) segment and a terminal reactive group made of an azide or an aldehyde, two functionalities with great utility in bio-orthogonal coupling techniques. These ligands were introduced onto the QD surfaces using a combination of photochemical ligation and mixed cap exchange strategy, where control over the fraction of azide and aldehyde groups per nanocrystal can be easily achieved: LA-PEG-CHO, LA-PEG-N3, and bis(LA)-PEG-CHO. We then demonstrate the application of two novel bio-orthogonal coupling strategies directly on luminescent quantum dot (QD) surfaces that use click chemistry and hydrazone ligation under catalyst-free conditions. We applied the highly efficient hydrazone ligation to couple 2-hydrozinopyridine (2-HP) to aldehyde-functionalized QDs, which produces a stable hydrazone chromophore with a well-defined optical signature. This unique optical feature has enabled us to extract a measure for the ligand density on the QDs for a few distinct sizes and for different ligand architectures, namely mono-LA-PEG and bis(LA)-PEG. We found that the foot-print-area per ligand was unaffected by the nanocrystal size but strongly depended on the ligand coordination number. Additionally, we showed that when the two bio-orthogonal functionalities (aldehyde and azide) are combined on the same QD platform, the nanocrystal can be specifically reacted with two distinct targets and with great specificity. This design yields QD platforms with distinct chemoselectivities that are greatly promising for use as carriers for in vivo imaging and delivery.

Controlling the Architecture, Coordination, and Reactivity of Nanoparticle Coating Utilizing an Amino Acid Central Scaffold.

We have developed a versatile strategy to prepare a series of multicoordinating and multifunctional ligands optimized for the surface-functionalization of luminescent quantum dots (QDs) and gold nanoparticles (AuNPs) alike. Our chemical design relies on the modification of l-aspartic acid precursor to controllably combine, through simple peptide coupling chemistry, one or two lipoic acid (LA) groups and poly(ethylene glycol) (PEG) moieties in the same ligand. This route has provided two sets of modular ligands: (i) bis(LA)-PEG, which presents two lipoic acids (higher coordination) appended onto a single end-functionalized PEG, and (ii) LA-(PEG)2 made of two PEG moieties (higher branching, with various end reactive groups) appended onto a single lipoic acid. These ligands are combined with a new photoligation strategy to yield hydrophilic and reactive QDs that are colloidally stable over a broad range of conditions, including storage at nanomolar concentration and under ambient conditions. AuNPs capped with these ligands exhibit excellent stability in various biological conditions and improved resistance against NaCN digestion. This route also provides compact nanocrystals with tunable surface reactivity. As such, we have covalently coupled QDs capped with bis(LA)-PEG-COOH to transferrin to facilitate intracellular uptake. We have also characterized and quantified the coupling of dye-labeled peptides to QD surfaces using fluorescence resonance energy transfer interactions in QD-peptide-dye assemblies.

Preparation of compact biocompatible quantum dots using multicoordinating molecular-scale ligands based on a zwitterionic hydrophilic motif and lipoic acid anchors.

Luminescent quantum dots (QDs) can potentially be used for many biological experiments, provided that they are constructed in such a way as to be stable in biological matrices. Furthermore, QDs that are compact in size and easy to couple to biomolecules can be readily used for applications ranging from protein tracking to vasculature imaging. In this protocol, we describe the preparation of ligands comprising either one or two lipoic acid (LA) groups chemically linked to a zwitterion moiety. These ligands are then used to functionalize luminescent QDs via a photochemical transformation of LA. This route produces nanocrystals that are compact in size and stable over a broad range of conditions. In addition, the resulting QDs are readily self-assembled with polyhistidine-appended proteins. This mode of conjugation maintains the protein biological activity and its orientation, yielding highly promising fluorescent conjugates that can be used for imaging and sensing. The protocol in its entirety can be completed in 3 weeks.

Photoligation of an amphiphilic polymer with mixed coordination provides compact and reactive quantum dots.

We introduce a new set of multicoordinating polymers as ligands that combine two distinct metal-chelating groups, lipoic acid and imidazole, for the surface functionalization of QDs. These ligands combine the benefits of thiol and imidazole coordination to reduce issues of thiol oxidation and weak binding affinity of imidazole. The ligand design relies on the introduction of controllable numbers of lipoic acid and histamine anchors, along with hydrophilic moieties and reactive functionalities, onto a poly(isobutylene-alt-maleic anhydride) chain via a one-step nucleophilic addition reaction. We further demonstrate that this design is fully compatible with a novel and mild photoligation strategy to promote the in situ ligand exchange and phase transfer of hydrophobic QDs to aqueous media under borohydride-free conditions. Ligation with these polymers provides highly fluorescent QDs that exhibit great long-term colloidal stability over a wide range of conditions, including a broad pH range (3-13), storage at nanomolar concentration, under ambient conditions, in 100% growth media, and in the presence of competing agents with strong reducing property. We further show that incorporating reactive groups in the ligands permits covalent conjugation of fluorescent dye and redox-active dopamine to the QDs, producing fluorescent platforms where emission is controlled/tuned by Förster Resonance Energy Transfer (FRET) or pH-dependent charge transfer (CT) interactions. Finally, the polymer-coated QDs have been coupled to cell-penetrating peptides to facilitate intracellular uptake, while subsequent cytotoxicity tests show no apparent decrease in cell viability.

UV and sunlight driven photoligation of quantum dots: understanding the photochemical transformation of the ligands.

We have recently reported that photoinduced ligation of ZnS-overcoated quantum dots (QDs) offers a promising strategy to promote the phase transfer of these materials to polar and aqueous media using multidentate lipoic acid (LA)-modified ligands. In this study we investigate the importance of the underlying parameters that control this process, in particular, whether or not photoexcited QDs play a direct role in the photoinduced ligation. We find that irradiation of the ligand alone prior to mixing with hydrophobic QDs is sufficient to promote ligand exchange. Furthermore, photoligation onto QDs can also be carried out simply by using sunlight. Combining the use of Ellman's test with matrix-assisted laser desorption/ionization and electrospray ionization mass spectrometry, we probe the nature of the photochemical transformation of the ligands. We find that irradiation (using either a UV photoreactor or sunlight) alters the nature of the disulfide groups in the lipoic acid, yielding a different product mixture than what is observed for chemically reduced ligands. Irradiation of the ligand in solution generates a mixture of monomeric and oligomeric compounds. Ligation onto the QDs selectively favors oligomers, presumably due to their higher coordination onto the metal-rich QD surfaces. We also show that photoligation using mixed ligands allows the preparation of reactive nanocrystals. The resulting QDs are coupled to proteins and peptides and tested for cellular staining. This optically controlled ligation of QDs combined with the availability of a variety of multidentate and multifunctional LA-modified ligands open new opportunities for developing fluorescent platforms with great promises for use in imaging and sensor design.

Strategies for interfacing inorganic nanocrystals with biological systems based on polymer-coating.

Interfacing inorganic nanoparticles and biological systems with the aim of developing novel imaging and sensing platforms has generated great interest and much activity. However, the effectiveness of this approach hinges on the ability of the surface ligands to promote water-dispersion of the nanoparticles with long term colloidal stability in buffer media. These surface ligands protect the nanostructures from the harsh biological environment, while allowing coupling to target molecules, which can be biological in nature (e.g., proteins and peptides) or exhibit specific photo-physical characteristics (e.g., a dye or a redox-active molecule). Amphiphilic block polymers have provided researchers with versatile molecular platforms with tunable size, composition and chemical properties. Hence, several groups have developed a wide range of polymers as ligands or micelle capsules to promote the transfer of a variety of inorganic nanomaterials to buffer media (including magnetic nanoparticles and semiconductor nanocrystals) and render them biocompatible. In this review, we first summarize the established synthetic routes to grow high quality nanocrystals of semiconductors, metals and metal oxides. We then provide a critical evaluation of the recent developments in the design, optimization and use of various amphiphilic copolymers to surface functionalize the above nanocrystals, along with the strategies used to conjugate them to target biomolecules. We finally conclude by providing a summary of the most promising applications of these polymer-coated inorganic platforms in sensor design, and imaging of cells and tissues.

Photoligation combined with zwitterion-modified lipoic acid ligands provides compact and biocompatible quantum dots.

We describe the design and synthesis of a series of compact ligands made of lipoic acid (LA)-based coordinating anchors and hydrophilic zwitterion groups. This ligand design is combined with a novel photoligation strategy to promote the transfer of QDs to polar and buffer media. This approach has provided hydrophilic QDs that exhibit great colloidal stability over a broad range of pHs and in the presence of cell culture media. Our photoligation strategy drastically improves previous phase transfer methods by eliminating the need for chemical reduction of the dithiolane ring using NaBH4 prior to the cap exchange, and it is adapted to several LA-based ligands. We also found that QDs stabilized with these compact zwitterionic ligands are fully compatible with metal-histidine-driven self-assembly where the protein activity is maintained after forming conjugation with the QDs.

Design of a multi-dopamine-modified polymer ligand optimally suited for interfacing magnetic nanoparticles with biological systems.

We have designed a set of multifunctional and multicoordinating polymer ligands that are optimally suited for surface functionalizing iron oxide and potentially other magnetic nanoparticles (NPs) and promoting their integration into biological systems. The amphiphilic polymers are prepared by coupling (via nucleophilic addition) several amine-terminated dopamine anchoring groups, poly(ethylene glycol) moieties, and reactive groups onto a poly(isobutylene-alt-maleic anhydride) (PIMA) chain. This design greatly benefits from the highly efficient and reagent-free one-step reaction of maleic anhydride groups with amine-containing molecules. The availability of several dopamine groups in the same ligand greatly enhances the ligand affinity, via multiple coordination, to the magnetic NPs, while the hydrophilic and reactive groups promote colloidal stability in buffer media and allow subsequent conjugation with target biomolecules. Iron oxide nanoparticles ligand exchanged with these polymer ligands have a compact hydrodynamic size and exhibit enhanced long-term colloidal stability over the pH range of 4-12 and in the presence of excess electrolytes. Nanoparticles ligated with terminally reactive polymers have been easily coupled to target dyes and tested in live cell imaging with no measurable cytotoxicity. Finally, the resulting hydrophilic nanoparticles exhibit large and size-dependent r2 relaxivity values.