Investigation of spacer length effect on immobilized Escherichia coli pili-antibody molecular recognition by AFM

The immobilization of antibodies to sensor surfaces is critical in biochemical sensor development. In this study, Poly(ethylene glycol) (PEG) and Jeffamine spacers were employed to tether Escherichia coli K99 pilus antibody to silicon wafer surfaces for the purpose of improving the orientation of antibody as well as reducing the steric hindrance. To illustrate the effect of spacer length, a variety of linear polymers were used to covalently attach the antibodies to silicon surfaces. Atomic Force Microscopy (AFM) and X-ray photoelectron spectroscopy (XPS) were used to characterize the surface morphology and chemical composition at each reaction step. The effect of spacer length in improving the specificity of immobilized antibody was investigated by attaching E. coli on the end of an AFM tip. The distribution of unbinding force and rupture distance from the force-distance curves obtained by AFM showed that the introduction of PEG spacer facilitates bacterial recognition which can improve the incidence of interactions by up to 90%. J600 proved to be the most effective spacer overcoming the steric hindrance seen with direct immobilization of antibody. In addition, the force spectroscopy reveals the elementary force quantum of E. coli-antibody to be 0.3 nN.     

Antibody linking to atomic force microscope tips via disulfide bond formation

Covalent binding of bioligands to atomic force microscope (AFM) tips converts them into monomolecular biosensors by which cognate receptors can be localized on the sample surface and fine details of ligand-receptor interaction can be studied. Tethering of the bioligand to the AFM tip via a approximately 6 nm long, flexible poly(ethylene glycol) linker (PEG) allows the bioligand to freely reorient and to rapidly "scan" a large surface area while the tip is at or near the sample surface. In the standard coupling scheme, amino groups are first generated on the AFM tip. In the second step, these amino groups react with the amino-reactive ends of heterobifunctional PEG linkers. In the third step, the 2-pyridyl-S-S groups on the free ends of the PEG chains react with protein thiol groups to give stable disulfide bonds. In the present study, this standard coupling scheme has been critically examined, using biotinylated IgG with free thiols as the bioligand. AFM tips with PEG-tethered biotin-IgG were specifically recognized by avidin molecules that had been adsorbed to mica surfaces. The unbinding force distribution showed three maxima that reflected simultaneous unbinding of 1, 2, or 3 IgG-linked biotin residues from the avidin monolayer. The coupling scheme was well-reproduced on amino-functionalized silicon nitride chips, and the number of covalently bound biotin-IgG per microm2 was estimated by the amount of specifically bound ExtrAvidin-peroxidase conjugate. Coupling was evidently via disulfide bonds, since only biotin-IgG with free thiol groups was bound to the chips. The mechanism of protein thiol coupling to 2-pyridyl-S-S-PEG linkers on AFM tips was further examined by staging the coupling step in bulk solution and monitoring turnover by release of 2-pyridyl-SH which tautomerizes to 2-thiopyridone and absorbs light at 343 nm. These experiments predicted 10(3)-fold slower rates for the disulfide coupling step than actually observed on AFM tips and silicon nitride chips. The discrepancy was reconciled by assuming 10(3)-fold enrichment of protein on AFM tips via preadsorption, as is known to occur on comparable inorganic surfaces.     

Analysis of DNA and Zinc finger interactions using mechanical force spectroscopy

The unbinding force of Zif268-DNA complex has been studied by atomic force microscopy (AFM). DNA and Zif268 were covalently immobilized on the surfaces of an AFM tip and glass substrate, respectively. Confocal microscopy was used to confirm the successful immobilization of DNA. Because of the complexity of the protein-DNA interaction, parallel experiments were designed to discriminate specific interactions. For such experiments, a typical unbinding force of a single Zif268-DNA complex (approx 550 pN at 40 nN/s force loading rate) was evaluated.     

Direct immobilization of avidin protein on AFM tip functionalized by acrylic acid vapor at RF plasma

The atomic force microscopy (AFM) has been used as a force sensor to measure unbinding forces of single bound complexes in the nanonewton and piconewton range. Force spectroscopy measurements can be applied to study both intermolecular and intramolecular interactions of complex biological and synthetic macromolecules. Although the AFM has been extensively used as a nano force sensor, the commercially available cantilever is limited to silicon and silicon nitride. Those materials reduce the adhesion sensitivity with specific surface and/or molecule. Here, we functionalized the AFM tip with carboxylic groups by applying acrylic acid (AA) vapor at radio frequency plasma treatment at 100 W for 5 min. This method provides a remarkable sensitivity enhancement on the functional group interaction specificity. The functionalized tip was characterized by scanning electron microscopy. The electron beam high resolution images have not shown significant tip sharpness modification. Silicon wafers (1 0 0)-no treated and functionalized by AA plasma treatment-were characterized by Auger electron spectroscopy to elucidate the silicon surface sputtering and demonstrate functionalization. The Fourier transform-infrared spectroscopy spectrum shows a high absorbance of avidin protein over the silicon surface functionalized by AA plasma treatment.We carried out force spectroscopy assay to measure the unbinding force between the well-established pair biotin-avidin. At pulling speed of 2 μm/s, we measured the unbinding force of 106?±?23 pN, which is in good agreement with the literature, demonstrating the effectiveness of the tip functionalization by AA plasma treatment in biological studies.     

Dynamic response of glucagon/anti-glucagon pairs to pulling velocity and pH studied by atomic force microscopy

We used atomic force microscopy (AFM) to measure the unbinding force between antigen coupled to an AFM tip and antibody coated on the substrate surface. Dynamic responses of glucagon/anti-glucagon pairs with multiple pull-off steps to pH and pulling velocity were studied by AFM. Force-distance curves of a specific glucagon-anti-glucagon interaction system with mono-, di-, and multi-unbinding events were recorded, which may be attributed to a single, sequential or multiple breaking of interacting bond(s) between glucagon and anti-glucagon. We studied the dynamic response of glucagon-anti-glucagon pairs to various pulling velocities (16.7-166.7 nm/s). It was found that the mean value of the unbinding force was shifted toward higher values with increasing pulling velocity at each pH. This indicates that the friction force between glucagon and anti-glucagon may contribute to the unbinding force. Moreover, the dynamic response of glucagon-anti-glucagon pairs to pH (4-10) with different pulling velocities was studied. Within the acid range, the bond strength between the glucagon/anti-glucagon complex showed a rapid increase from pH 4 to 7 and reached a maximum (256.4+/-48.9 pN at 166.7 nm/s) at neutrality, followed by a sharp decrease with increasing pH (pH 7-10). This could be attributed to the conformational change that occurred in glucagon when the pH value in solution was varied from the reference level at neutrality. This study demonstrated that the pH dependence of multiple antigen-antibody bond-rupture forces could be measured by a force-based AFM biosensor. Unraveling the relationship between inter-molecular force and intra-molecular conformational change in acid, neutral, and alkaline environments may provide new directions for future application of force measurements by AFM in proteomics or in the development of a clinical cantilever-based mechanical biosensor.     

Linking of sensor molecules with amino groups to amino-functionalized AFM tips

The measuring tip of an atomic force microscope (AFM) can be upgraded to a specific biosensor by attaching one or a few biomolecules to the apex of the tip. The biofunctionalized tip is then used to map cognate target molecules on a sample surface or to study biophysical parameters of interaction with the target molecules. The functionality of tip-bound sensor molecules is greatly enhanced if they are linked via a thin, flexible polymer chain. In a typical scheme of tip functionalization, reactive groups are first generated on the tip surface, a bifunctional cross-linker is then attached with one of its two reactive ends, and finally the probe molecule of interest is coupled to the free end of the cross-linker. Unfortunately, the most popular functional group generated on the tip surface is the amino group, while at the same time, the only useful coupling functions of many biomolecules (such as antibodies) are also NH(2) groups. In the past, various tricks or detours were applied to minimize the undesired bivalent reaction of bifunctional linkers with adjacent NH(2) groups on the tip surface. In the present study, an uncompromising solution to this problem was found with the help of a new cross-linker ("acetal-PEG-NHS") which possesses one activated carboxyl group and one acetal-protected benzaldehyde function. The activated carboxyl ensures rapid unilateral attachment to the amino-functionalized tip, and only then is the terminal acetal group converted into the amino-reactive benzaldehyde function by mild treatment (1% citric acid, 1-10 min) which does not harm the AFM tip. As an exception, AFM tips with magnetic coating become demagnetized in 1% citric acid. This problem was solved by deprotecting the acetal group before coupling the PEG linker to the AFM tip. Bivalent binding of the corresponding linker ("aldehyde-PEG-NHS") to adjacent NH(2) groups on the tip was largely suppressed by high linker concentrations. In this way, magnetic AFM tips could be functionalized with an ethylene diamine derivative of ATP which showed specific interaction with mitochondrial uncoupling protein 1 (UCP1) that had been purified and reconstituted in a mica-supported planar lipid bilayer.     

Measurement of interaction force between nanoarrayed integrin alphavbeta3 and immobilized vitronectin on the cantilever tip

Protein nanoarrays containing integrin alphavbeta3 or BSA were fabricated on ProLinker-coated Au surface by dip-pen nanolithography (DPN). An atomic force microscope (AFM) tip coated with ProLinker was modified by vitronectin. We measured the interaction force between nanoarrayed integrin alphavbeta3 or BSA and immobilized vitronectin on the cantilever tip by employing tethering-unbinding method. The unbinding force between integrin alphavbeta3 and vitronectin (1087+/-62 pN) was much higher than that of between BSA and vitronectin (643+/-74 pN). These results demonstrate that one can distinguish a specific protein interaction from non-specific interactions by means of force measurement on the molecular interactions between the nanoarrayed protein and its interacting protein on the AFM tip.     

Mechanical force analysis of peptide interactions using atomic force microscopy

Some peptides have previously been reported to bind low molecular weight chemicals. One such peptide with the amino acid sequence His-Ala-Ser-Tyr-Ser was selectively screened from a phage library and bound to a cationic porphyrin, 5,10,15,20-tetrakis(N-methylpyridinium-4-yl)-21H,23H-porphine (TMpyP), with a binding constant of 10(5) M(-1) (J. Kawakami, T. Kitano, and N. Sugimoto, Chemical Communications, 1999, pp. 1765-1766). The proposed binding was due to pi-electron stacking from two aromatic amino acids of histidine and tyrosine. In this study, the weak interactions between TMpyP and the peptide were further investigated by force curve analysis using atomic force microscopy (AFM). The mechanical force required to unbind the peptide-porphyrin complex was measured by vertical movement of the AFM tip. Peptide self-assembled monolayers were formed on both a gold-coated mica substrate and a gold-coated AFM tip. The TMpyPs could bind between the two peptide layers when the peptide-immobilized AFM tip contacted the peptide-immobilized substrate in solution containing TMpyP. In the retracting process a force that ruptured the interaction between TMpyPs and peptides was observed. The unbinding force values correlated to the concentration of TMpyP. A detection limit of 100 ng/mL porphyrin was obtained for the force measurement, and was similar to surface plasmon resonance sensor detection limits. Furthermore, we calculated the product of the observed force and the length of the molecular elongation to determine the work required to unbind the complexes. The obtained values of unbinding work were in a reasonable range compared to the binding energy of porphyrin-peptide.     

Adsorption characteristics of P(3HB) depolymerase as evaluated by surface plasmon resonance and atomic force microscopy

Molecular recognition of poly[(R)-3-hydroxybutyrate] (P(3HB)) depolymerase from Ralstonia pickettii T1 to the surfaces of biodegradable aliphatic polyesters such as P(3HB) and poly(L-lactic acid) (PLLA) was examined from the viewpoints of kinetics and dynamics. To determine the kinetic parameters on the interaction between the substrate-binding domain (SBD) of P(3HB) depolymerase and various polymer substrates with different chemical structures, surface plasmon resonance (SPR) measurements were performed. On the other hand, using an atomic force microscopic (AFM) cantilever tip functionalized with the SBD of P(3HB) depolymerase, the mechanical parameters such as unbinding force to the polymer surfaces were measured. Both the SPR and AFM measurements showed that the SBD has a high affinity to P(3HB) and PLLA. From the results of kinetics and dynamics, the energy potential landscape of SBD-polymer interaction was disclosed on the basis of a phenomenological model, and the mechanism of the interaction was discussed.     

Dynamic response of HPV16/anti-HPV16 pairs with unbinding events studied by atomic force microscopy

This paper proposes an effective approach to distinguish whether samples include Human Papilloma virus type-16 (HPV16) by Atomic force microscopy (AFM). AFM is an important instrument in nanobiotechnology field. At first we identified the HPV16 by Polymerase chain reaction (PCR) analysis and Western blotting from specimen of the HPV patient (E12) and the normal (C2), and then we used an AFM to observe the surface ultrastructure by tapping mode and to measure the unbinding force between HPV16 coupled to an AFM tip and anti-HPV16 L1 coated on the substrate surface by contact mode. The experimental results by tapping mode show that the size of a single HPV viron was similar to its SEM image from the previous literatures; moreover, based on the purposed methods and the analysis, two obvious findings that we can determine whether or not the subject is a HPV patient can be derived from the results; one is based on the distribution of unbinding forces, and the other is based on the distribution of the stiffness. Furthermore, the proposed method could be a useful technique for further investigating the potential role among subtypes of HPVs in the oncogenesis of human cervical cancer.     

Detection and localization of single molecular recognition events using atomic force microscopy

Because of its piconewton force sensitivity and nanometer positional accuracy, the atomic force microscope (AFM) has emerged as a powerful tool for exploring the forces and the dynamics of the interaction between individual ligands and receptors, either on isolated molecules or on cellular surfaces. These studies require attaching specific biomolecules or cells on AFM tips and on solid supports and measuring the unbinding forces between the modified surfaces using AFM force spectroscopy. In this review, we describe the current methodology for molecular recognition studies using the AFM, with an emphasis on strategies available for preparing AFM tips and samples, and on procedures for detecting and localizing single molecular recognition events.     

Single molecular dynamic interactions between glycophorin A and lectin as probed by atomic force microscopy

Glycophorin A (GpA) is one of the most abundant transmembrane proteins in human erythrocytes and its interaction with lectins has been studied as model systems for erythrocyte related biological processes. We performed a force measurement study using the force mode of atomic force microscopy (AFM) to investigate the single molecular level biophysical mechanisms involved in GpA-lectin interactions. GpA was mounted on a mica surface or natively presented on the erythrocyte membrane and probed with an AFM tip coated with the monomeric but multivalent Psathyrella velutina lectin (PVL) through covalent crosslinkers. A dynamic force spectroscopy study revealed similar interaction properties in both cases, with the unbinding force centering around 60 pN with a weak loading rate dependence. Hence we identified the presence of one energy barrier in the unbinding process. Force profile analysis showed that more than 70% of GpAs are free of cytoskeletal associations in agreement with previous reports.     

Elucidation of the effect of aptamer immobilization strategies on the interaction between cell and its aptamer using atomic force spectroscopy

The immobilization strategy of cell‐specific aptamers is of great importance for studying the interaction between a cell and its aptamer. However, because of the difficulty of studying living cell, there have not been any systematic reports about the effect of immobilization strategies on the binding ability of an immobilized aptamer to its target cell. Because atomic force spectroscopy (AFM) could not only be suitable for the investigation of living cell under physiological conditions but also obtains information reflecting the intrinsic properties of individuals, the effect of immobilization strategies on the interaction of aptamer/human hepatocarcinoma cell Bel‐7404 was successively evaluated using AFM here. Two different immobilization methods, including polyethylene glycol immobilization method and glutaraldehyde immobilization method were used, and the factors, such as aptamer orientation, oligodeoxythymidine spacers and dodecyl spacers, were investigated. Binding events measured by AFM showed that a similar unbinding force was obtained regardless of the change of the aptamer orientation, the immobilization method, and spacers, implying that the biophysical characteristics of the aptamer at the molecular level remain undisturbed. However, it showed that the immobilization orientation, immobilization method, and spacers could alter the binding probability of aptamer/Bel‐7404 cell. Presumably, these factors may affect the accessibility of the aptamer toward its target cell. These results may provide valuable information for aptamer sensor platforms including ultrasensitive biosensor design. Copyright © 2015 John Wiley & Sons, Ltd.     

A glucose oxidase electrode based on polypyrrole with polyanion/PEG/enzyme conjugate dopant

This study investigated a new glucose sensor prepared by electrochemical polymerization of pyrrole with polyanion/poly(ethylene glycol) (PEG)/glucose oxidase (GOD) conjugate dopants. GOD was coupled to a strong polyanion, poly(2-acrylamido-2-methylpropane sulfonic acid) (AMPS) via PEG spacer to effectively and reproducibly immobilize GOD within a polypyrrole matrix onto a Pt electrode surface. PEGs with four different chain lengths (1000, 2000, 3000, and 4000) were used as spacers to study the spacer length effect on enzyme immobilization and electrode function. After conjugation, more than 90% of the GOD bioactivity was preserved and the bioactivity of the conjugated GOD increased with longer PEG spacers. The resulting polyanion/PEG/GOD conjugate was used as a dopant for electropolymerizing pyrrole. The activity of the immobilized enzyme on the electrode ranged from 119 to 209 mU cm(-2) and the bioactivity increased with the use of longer PEG spacers. The amperometric response of the enzyme electrode was linear up to 20 mM glucose concentration with a sensitivity ranging from 180 to 270 nA mM(-1) cm(-2). The kinetic parameters Michaelis-Menten constant (K(M)(app)) and maximum current density (j(max)) depended on the amount of active enzyme, level of substrate diffusion, and PEG spacer length. An increase in the electrical charge passed during polymerization (thus, increasing polypyrrole thickness) to 255 mC cm(-2) increased the sensitivity of the enzyme electrode because of the greater amount of incorporated enzyme. However, although the amount of incorporated GOD continued to increase when the charge increased above 255 mC cm(-2), the sensitivity began to decline gradually. The condition for preparing the enzyme electrode was optimized at 800 mV potential with a dopant concentration of 1 mg ml(-1).     

Simultaneous height and adhesion imaging of antibody-antigen interactions by atomic force microscopy.

Specific molecular recognition events, detected by atomic force microscopy (AFM), so far lack the detailed topographical information that is usually observed in AFM. We have modified our AFM such that, in combination with a recently developed method to measure antibody-antigen recognition on the single molecular level (Hinterdorfer, P., W. Baumgartner, H. J. Gruber, K. Schilcher, and H. Schindler, Proc. Natl. Acad. Sci. USA 93:3477-3481 (1996)), it allows imaging of a submonolayer of intercellular adhesion molecule-1 (ICAM-1) in adhesion mode. We demonstrate that for the first time the resolution of the topographical image in adhesion mode is only limited by tip convolution and thus comparable to tapping mode images. This is demonstrated by imaging of individual ICAM-1 antigens in both the tapping mode and the adhesion mode. The contrast in the adhesion image that was measured simultaneously with the topography is caused by recognition between individual antibody-antigen pairs. By comparing the high-resolution height image with the adhesion image, it is possible to show that specific molecular recognition is highly correlated with topography. The stability of the improved microscope enabled imaging with forces as low as 100 pN and ultrafast scan speed of 22 force curves per second. The analysis of force curves showed that reproducible unbinding events on subsequent scan lines could be measured.     

Direct force measurements of the streptavidin-biotin interaction

The interaction between streptavidin and its ligand, biotin, were studied by direct force measurements. The complimentary approaches of surface force apparatus (SFA) and atomic force microscopy (AFM) were used to elucidate both long-range and short-range adhesive interactions of the streptavidin biotin interaction. The high spatial resolution of the SFA provided a detailed profile of the intersurface forces of apposing surfaces functionalized with streptavidin and biotin. Measurements obtained by the SFA corresponded to long and intermediate-range forces that are important in determining ligand receptor association. AFM was used to measure the unbinding force of individual streptavidin biotin complexes. These measurements revealed the short-range interactions (i.e. hydrophobic and hydrogen bonding forces) that stabilize the intermolecular bond.     

Successive detection of insulin‐like growth factor‐II bound to receptors on a living cell surface using an AFM

In this study, we have developed a method of mechanical force detection for ligands bound to receptors on a cell surface, both of which are involved in a signal transduction pathway. This pathway is an autocrine pathway, involving the production of insulin‐like growth factor‐II (IGF‐II) and activation of the IGF‐I receptor, involved in myoblast differentiation induced by MyoD in C3H10T1/2 mouse mesenchymal stem cells. Differentiation of C3H10T1/2 was induced with the DNA demethylation agent 5‐azacytidine (5‐aza). The etched AFM tip used in the force detection had a flat surface of which about 10 µm² was in contact with a cell surface. The forces required to rupture the interactions of IGF‐IIs on a cell and anti mouse IGF‐II polyclonal antibody immobilized on an etched AFM tip were measured within 5 days of induction of differentiation. The mean unbinding force for a single paired antibody–ligand on a cell was about 81 pN, which was measured at a force loading rate of about 440 nN/s. The percentage of unbinding forces over 100 pN increased to 32% after 2 days from the addition of 5‐aza to the medium. This method could be used in non‐invasive and successive evaluation of a living cell's behavior. Copyright © 2009 John Wiley & Sons, Ltd.     

Mechanical sensing of the penetration of various nanoneedles into a living cell using atomic force microscopy

Mechanical responses during insertion of a silicon nanoneedle into a living melanocyte were observed by using an atomic force microscope (AFM). In order to study the dependence of the mechanical response on the shape of the nanoneedle, we prepared various shapes of silicon AFM tips by focused-ion beam (FIB) etching. The force curves showed increases up to 0.65-1.9 nN after contact on the cell surface, and then the force dropped corresponding with the penetration of the needle through the cell membrane. The force required for penetration was significantly smaller than that using a normal pyramidal tip. The force curves with a cylindrical tip showed a shorter indenting distance before penetration than that with the cone-shaped tip. It is considered that the information about the geometry of penetrating material leads to the development of more suitable micro- and nano-materials to insert into a living cell for cell surgery.     

Studies on protein-liposome coupling using novel thiol-reactive coupling lipids: influence of spacer length and polarity.

To optimize the preparation of immunoliposomes, we investigated the coupling of thiolated IgG and BSA to liposomes using a novel group of coupling lipids. All lipids consist of cholesterol as membrane anchor and a thiol-reactive maleimide headgroup, linked by a spacer that differs in length and polarity (ethylene glycol, tetraethylene glycol, PEG 400, PEG 1000, dodecyl). In addition, lipids differ in the electrophilicity of the maleimide group (p- or m-maleimidobenzoic ester). In the case of BSA, coupling efficiency strongly depended on the electrophilicity of the maleimide group as well as on the spacer polarity: The less electrophilic meta constitution seems to be an advantage over the p-maleimidobenzoic ester, resulting in higher coupling efficiency. Polar spacers (tetraethylene glycol, 46%) achieved a higher coupling efficiency than a nonpolar spacer with approximately the same length (dodecyl, 15%).When liposomes containing coupling lipids with the spacers tetraethylene glycol, PEG 400, and PEG 1000 were linked to BSA, coupling efficiencies were in a medium range and similar (41-46%) but were lower for the short ethylene glycol spacer (30%). In contrast, for IgG coupling efficiencies correlated with increasing spacer length. Best results were obtained using coupling lipids with a long polar spacer (PEG 1000) (65%), whereas a coupling lipid bearing a short spacer (ethylene glycol) resulted in a low coupling efficiency of 12%.     

FM-AFM constant height imaging and force curves: high resolution study of DNA-tip interactions

Interaction of the atomic force microscopy (AFM) tip with the sample can be invasive for soft samples. Frequency Modulation (FM) AFM is gentler because it allows scanning in the non‐contact regime where only attractive forces exist between the tip and the sample, and there is no sample compression. Recently, FM‐AFM was used to resolve the atomic structure of single molecules of pentacene and of carbon nanotubes. We are testing similar FM‐AFM‐based approaches to study biological samples. We present FM‐AFM experiments on dsDNA deposited on 3‐aminopropyltriethoxysilane modified mica in ultra high vacuum. With flexible samples such as DNA, the substrate flatness is a sub‐molecular resolution limiting factor. Non‐contact topographic images of DNA show variations that have the periodicity of the right handed helix of B‐form DNA – this is an unexpected result as dehydrated DNA is thought to assume the A‐form structure. Frequency shift maps at constant height allow working in the non‐monotonic frequency shift range, show a rich contrast that changes significantly with the tip‐sample separation, and show 0.2 to 0.4 nm size details on DNA. Frequency shift versus distance curves acquired on DNA molecules and converted in force curves show that for small molecules (height < 2.5 nm), there is a contribution to the interaction force from the substrate when the tip is on top of the molecules. Our data shine a new light on dehydrated and adsorbed DNA behavior. They show a longer tip‐sample interaction distance. These experiments may have an impact on nanotechnological DNA applications in non‐physiological environments such as DNA based nanoelectronics and nanotemplating. Copyright © 2012 John Wiley & Sons, Ltd.