A Numerical Study on the Effect of Particle Surface Coverage on the Quartz Crystal Microbalance Response

Quartz Crystal Microbalance Frequency Response to Discrete Adsorbates in Liquids

Quartz crystal microbalance with dissipation monitoring (QCM-D) has become a major tool enabling accurate investigation of the adsorption kinetics of nanometric objects such as DNA fragments, polypeptides, proteins, viruses, liposomes, polymer, and metal nanoparticles. However, in liquids, a quantitative analysis of the experimental results is often intricate because of the complex interplay of hydrodynamic and adhesion forces varying with the physicochemical properties of adsorbates and functionalized QCM-D sensors. In the present paper, we dissect the role of hydrodynamics for the analytically tractable case of stiff contact, whereas the adsorbed rigid particles oscillate with the resonator without rotation. Under the assumption of the low surface coverage, we theoretically study the excess shear force exerted on the resonator, which has two contributions: (i) the fluid-mediated force due to flow disturbance created by the particle and (ii) the force exerted on the particle by the fluid and transmitted to the sensor via contact. The theoretical analysis enables an accurate interpretation of the QCM-D impedance measurements. It is demonstrated inter alia that for particles of the size comparable with protein molecules, the hydrodynamic force dominates over the inertial force and that the apparent mass derived from QCM independently of the overtone is about 10 times the Sauerbrey (inertial) mass. The theoretical results show excellent agreement with the results of experiments and advanced numerical simulations for a wide range of particle sizes and oscillation frequencies.

Acoustic detection of a mutation-specific Ligase Chain Reaction based on liposome amplification

Single nucleotide variants (SNVs) play a crucial role in understanding genetic diseases, cancer development, and personalized medicine. However, existing ligase-based amplification and detection techniques, such as Rolling Circle Amplification and Ligase Detection Reaction, suffer from low efficiency and difficulties in product detection. To address these limitations, we propose a novel approach that combines Ligase Chain Reaction (LCR) with acoustic detection using highly dissipative liposomes. In our study, we are using LCR combined with biotin- and cholesterol-tagged primers to produce amplicons also modified at each end with a biotin and cholesterol molecule. We then apply the LCR mix without any purification directly on a neutravidin modified QCM device Au-surface, where the produced amplicons can bind specifically through the biotin end. To improve sensitivity, we finally introduce liposomes as signal enhancers. For demonstration, we used the detection of the BRAF V600E point mutation versus the wild-type allele, achieving an impressive detection limit of 220 aM of the mutant target in the presence of the same amount of the wild type. Finally, we combined the assay with a microfluidic fluidized bed DNA extraction technology, offering the potential for semi-automated detection of SNVs in patients' crude samples. Overall, our LCR/acoustic method outperforms other LCR-based approaches and surface ligation biosensing techniques in terms of detection efficiency and time. It effectively overcomes challenges related to DNA detection, making it applicable in diverse fields, including genetic disease and pathogen detection.

Anisotropic Particle Deposition Kinetics from Quartz Crystal Microbalance Measurements: Beyond the Sphere Paradigm

Deposition kinetics of polymer particles characterized by a prolate spheroid shape on gold sensors modified by the adsorption of poly(allylamine) was investigated using a quartz crystal microbalance and atomic force microscopy. Reference measurements were also performed for polymer particles of a spherical shape and the same diameter as the spheroid shorter axis. Primarily, the frequency and dissipation shifts for various overtones were measured as a function of time. These kinetic data were transformed into the dependence of the complex impedance, scaled up by the inertia impedance, upon the particle size to the hydrodynamic boundary layer ratio. The results obtained for low particle coverage were interpolated, which enabled the derivation of Sauerbrey-like equations, yielding the real particle coverage using the experimental frequency or dissipation (bandwidth) shifts. Experiments carried out for a long deposition time confirmed that, for spheroids, the imaginary and real impedance components were equal to each other for all overtones and for a large range of particle coverage. This result was explained in terms of a hydrodynamic, lubrication-like contact of particles with the sensor, enabling their sliding motion. In contrast, the experimental data obtained for spheres, where the impedance ratio was a complicated function of overtones and particle coverage, showed that the contact was rather stiff, preventing their motion over the sensor. It was concluded that results obtained in this work can be exploited as useful reference systems for a quantitative interpretation of bioparticle, especially bacteria, deposition kinetics on macroion-modified surfaces.

Coverage Effects in Quartz Crystal Microbalance Measurements with Suspended and Adsorbed Nanoparticles

Quartz crystal microbalance (QCM) biosensors often deal with nanoparticles suspended in the solvent at tens of nanometers above the resonator while being linked to some molecular receptor (DNA, antibody, etc.). This work presents a numerical analysis based on the immersed boundary method for the flow and QCM impedance created by an ensemble of spherical particles of radius R at varying surface coverage Θ and particle-surface gap distance Δ. The trends for the frequency Δf and dissipation ΔD shifts against Θ and Δ are shown to be determined by modifications in the structure of the perturbative flow created by the analytes. Simulations are in good agreement with a relatively large experimental database collected from the literature. Qualitative differences between the adsorbed (Δ ≈ 0) and suspended states (Δ > 0) are highlighted. In the case of adsorbed particles, deviations from the linear scaling Δf ∝ Θ are observed above Θ > 0.05 and largely depend on the specific analyte-substrate combination. Moreover, in general, ΔD(Θ) is not monotonous and usually presents a maximum around Θ ∼ 0.2. In the case of suspended analytes, the agreement with the numerical results is quantitative, indicating that the predicted scalings are universal and determined by hydrodynamics. Up to high coverage, the suspended particles present Δf ∼ Θ and ΔD ∼ Θβ, where β ≈ 0.85 is not largely dependent on R. The present findings should help forecast molecular configurations from QCM signals and have implications on QCM analyses, e.g., in the case of suspended ligands (Δf ∝ Θ), it is safe to use Δf to build Langmuir isotherms and estimate equilibrium constants. Open questions on the transition from the suspended-to-adsorbed state are discussed.

Quartz crystal microbalance in soft and biological interfaces

Applications of quartz crystal microbalance with dissipation to studying soft and biological interfaces are reviewed. The focus is primarily on data analysis through viscoelastic modeling and a model-free approach focusing on the acoustic ratio. Current challenges and future research and development directions are discussed.

Particle Adsorption Using a Quartz Crystal Microbalance with Dissipation by Applying a Kelvin-Voigt-Based Viscoelastic Model and the Gauss-Newton Method

The use of a quartz crystal microbalance with dissipation (QCM-D) to study the adsorption of particles larger than 100 nm, such as liposomes, viruses, and nano/micro-plastics, remains challenging owing to the lack of appropriate models for data evaluation. This study presents a method for quantifying the adsorption of negatively charged polystyrene latex (100 nm-1 μm) at the solid-liquid interface. The validity of a viscoelastic model based on Kelvin-Voigt theory was assessed, and the model was used to evaluate particle adsorption data obtained from QCM-D measurements. The Gauss-Newton method was used to fit the data; the values obtained were larger than results from atomic force microscopy, indicating that the viscoelastic model combined with the Gauss-Newton method can quantify the adsorption of large polystyrene particles and the surrounding water around them. We suggested that QCM-D, in combination with an appropriate viscoelastic model, is applicable to estimate adsorption at the solid-liquid interface even for soft particles larger than 1 μm, which are out of the range of applications to the hydrodynamics model. Furthermore, we successfully showed that the recorded dissipation reflects the viscoelastic properties of the layer. The viscoelastic model allowed quantification of the rheological properties of the layer. The ratio of the viscous and elastic contributions was characterized by using loss tangent (tan δ) values that were extracted from the experimental data by applying the viscoelastic model. These values were lower for the adsorption of the negatively charged polystyrene particles on a positive surface than on a negative surface. This suggests that tan δ reflects the strength of the contact between the particle and substrate.

QCM-D Investigations of Anisotropic Particle Deposition Kinetics: Evidences of the Hydrodynamic Slip Mechanisms

Deposition kinetics of positively charged polymer microparticles, characterized by prolate spheroid shape, at silica and gold sensors was investigated using the quartz microbalance (QCM) technique. Reference measurements were also performed for positively charged polymer particles of spherical shape and the same mass as the spheroids. Primarily, the frequency and bandwidth shifts for various overtones were measured as a function of time. It is shown that the ratio of these signals is close to unity for all overtones. These results were converted to the dependence of the frequency shift on the particle coverage, directly determined by atomic force microscopy and theoretically interpreted in terms of the hydrodynamic model. A quantitative agreement with experiments was attained considering particle slip relative to the ambient oscillating flow. In contrast, the theoretical results pertinent to the rigid contact model proved inadequate. The particle deposition kinetics derived from the QCM method was compared with theoretical modeling performed according to the random sequential adsorption approach. This allowed to assess the feasibility of the QCM technique to furnish proper deposition kinetics for anisotropic particles. It is argued that the hydrodynamic slip effect should be considered in the interpretation of QCM kinetic results acquired for bioparticles, especially viruses.

Nanoparticle and bioparticle deposition kinetics

Mechanisms and kinetic of particle deposition at solid surfaces leading to the formation of self-assembled layers of controlled structure and density were reviewed. In the first part theoretical aspects were briefly discussed, comprising limiting analytical solutions for the linear transport under flow and diffusion. Methods of the deposition kinetics analysis for non-linear regimes affected by surface blocking were also considered. Characteristic monolayer formation times under diffusion and flow for the nanoparticle size range were calculated. In the second part illustrative experimental results obtained for micro- and nanoparticles were discussed. Deposition at planar substrates was analyzed with emphasis focused on the stability of layers and the release kinetics of silver particles. Applicability of the quartz microbalance measurements (QCM) for quantitative studies of nanoparticle deposition kinetic was also discussed. Except for noble metal and polymer particles, representative results for virus deposition at abiotic surfaces were analyzed. Final part of the review was devoted to nanoparticle corona formation at polymer carrier particles investigated by combination of the concentration depletion, AFM, SEM and the in situ electrokinetic method. It is argued that the results obtained for colloid particles can be used as reliable reference systems for interpretation of protein and other bioparticle deposition, confirming the thesis that simple is universal.

Acoustic Array Biochip Combined with Allele-Specific PCR for Multiple Cancer Mutation Analysis in Tissue and Liquid Biopsy

Regular screening of point mutations is of importance to cancer management and treatment selection. Although techniques like next-generation sequencing and digital polymerase chain reaction (PCR) are available, these are lacking in speed, simplicity, and cost-effectiveness. The development of alternative methods that can detect the extremely low concentrations of the target mutation in a fast and cost-effective way presents an analytical and technological challenge. Here, an approach is presented where for the first time an allele-specific PCR (AS-PCR) is combined with a newly developed high fundamental frequency quartz crystal microbalance array as biosensor for the amplification and detection, respectively, of cancer point mutations. Increased sensitivity, compared to fluorescence detection of the AS-PCR amplicons, is achieved through energy dissipation measurement of acoustically "lossy" liposomes binding to surface-anchored dsDNA targets. The method, applied to the screening of BRAF V600E and KRAS G12D mutations in spiked-in samples, was shown to be able to detect 1 mutant copy of genomic DNA in an excess of 10⁴ wild-type molecules, that is, with a mutant allele frequency (MAF) of 0.01%. Moreover, validation of tissue and plasma samples obtained from melanoma, colorectal, and lung cancer patients showed excellent agreement with Sanger sequencing and ddPCR; remarkably, the efficiency of this AS-PCR/acoustic methodology to detect mutations in real samples was demonstrated to be below 1% MAF. The combined high sensitivity and technology-readiness level of the methodology, together with the ability for multiple sample analysis (24 array biochip), cost-effectiveness, and compatibility with routine workflow, make this approach a promising tool for implementation in clinical oncology labs for tissue and liquid biopsy.

Quantitative description of the response of finite size adsorbates on a quartz crystal microbalance in liquids using analytical hydrodynamics

Despite being a fundamental tool in soft matter research and biosensing, quartz crystal microbalance (QCM) analyses of discrete macromolecules in liquids so far lack a firm theoretical basis. Quite often, acoustic signals of discrete particles are qualitatively interpreted using ad hoc frameworks based on effective electrical circuits, effective springs and trapped-solvent models with many fitting parameters. Nevertheless, due to its extreme sensitivity, the QCM technique pledges to become an accurate predictive tool. Using unsteady low Reynolds hydrodynamics we derive analytical expressions for the acoustic impedance of adsorbed discrete spheres. The present approach is successfully validated against 3D simulations and a plethora of experimental results covering more than a decade of research on proteins, viruses, liposomes, and massive nanoparticles, with sizes ranging from a few to hundreds of nanometers. The agreement without fitting parameters indicates that the acoustic response is dominated by the hydrodynamic propagation of the particle surface stress over the resonator. Understanding this leading contribution is a prerequisite for deciphering the secondary contributions arising from the relevant specific molecular and physico-chemical forces.

Soft Viscoelastic Particles in Contact with a Quartz Crystal Microbalance (QCM): A Frequency-Domain Lattice Boltzmann Simulation

Shifts of frequency and bandwidth of a quartz crystal microbalance (QCM) in contact with a structured, viscoelastic sample have been computed with a linearized version of the lattice Boltzmann method (LBM). The algorithm operates in the frequency domain and covers viscoelasticity. The different domains are characterized by different values of the complex viscosity, η, equivalent to different values of the shear modulus, G. Stiff particles are given large |η_Sph|, where |η_Sph| must be less than ∼100 η_bulk with η_bulk the viscosity of the ambient liquid. Critical to the computational efficiency is a match of the LBM populations at the upper boundary of the simulation box to an analytical solution of the Stokes equation in the bulk above the box. The application example is a test of the ΔΓ/(-Δf)-extrapolation scheme, where Δf and ΔΓ are the shifts in resonance frequency and half bandwidth, respectively. For adsorbed particles, plots of ΔΓ/(-Δf) versus - Δf/n (with n the overtone order) show almost straight lines. The extrapolation of these lines to zero yields a frequency shift, which, after conversion to a thickness with the Sauerbrey equation, closely agrees with the height of the particles. Plots of Δf/n and ΔΓ/n versus n look similar to the corresponding plots obtained for viscoelastic films, where the parameters, which would usually be extracted from those plots (apparent mass and apparent compliance), depend on the geometry and the sample's viscoelasticity in a nontrivial way.

Studying Soft Interfaces with Shear Waves: Principles and Applications of the Quartz Crystal Microbalance (QCM)

The response of the quartz crystal microbalance (QCM, also: QCM-D for "QCM with Dissipation monitoring") to loading with a diverse set of samples is reviewed in a consistent frame. After a brief introduction to the advanced QCMs, the governing equation (the small-load approximation) is derived. Planar films and adsorbates are modeled based on the acoustic multilayer formalism. In liquid environments, viscoelastic spectroscopy and high-frequency rheology are possible, even on layers with a thickness in the monolayer range. For particulate samples, the contact stiffness can be derived. Because the stress at the contact is large, the force is not always proportional to the displacement. Nonlinear effects are observed, leading to a dependence of the resonance frequency and the resonance bandwidth on the amplitude of oscillation. Partial slip, in particular, can be studied in detail. Advanced topics include structured samples and the extension of the small-load approximation to its tensorial version.

Mechanistic Aspects of the Evolution of 3D Cholesterol Crystallites in a Supported Lipid Membrane via a Quartz Crystal Microbalance with Dissipation Monitoring

The irreversible formation of cholesterol monohydrate crystals within biological membranes is the leading cause of various diseases, including atherosclerosis. Understanding the process of cholesterol crystallization is fundamentally important and could also lead to the development of improved therapeutic strategies. This has driven several studies investigating the effect of the environmental parameters on the induction of cholesterol crystallite growth and the structure of the cholesterol crystallites, while the kinetics and mechanistic aspects of the crystallite formation process within lipid membranes remain poorly understood. Herein, we fabricated cholesterol crystallites within a supported lipid bilayer (SLB) by adsorbing a cholesterol-rich bicellar mixture onto a glass and silica surface and investigated the real-time kinetics of cholesterol crystallite nucleation and growth using epifluorescence microscopy and quartz crystal microbalance with dissipation (QCM-D) monitoring. Microscopic imaging showed the evolution of the morphology of cholesterol crystallites from nanorod- and plate-shaped habits during the initial stage to mostly large, micron-sized three-dimensional (3D) plate-shaped crystallites in the end, which was likened to Ostwald ripening. QCM-D kinetics revealed unique signal responses during the later stage of the growth process, characterized by simultaneous positive frequency shifts, nonmonotonous energy dissipation shifts, and significant overtone dependence. Based on the optically observed changes in crystallite morphology, we discussed the physical background of these unique QCM-D signal responses and the mechanistic aspects of Ostwald ripening in this system. Together, our findings revealed mechanistic details of the cholesterol crystallite growth kinetics, which may be useful in biointerfacial sensing and bioanalytical applications.

Nanoparticle and Bioparticle Deposition Kinetics: Quartz Microbalance Measurements

Controlled deposition of nanoparticles and bioparticles is necessary for their separation and purification by chromatography, filtration, food emulsion and foam stabilization, etc. Compared to numerous experimental techniques used to quantify bioparticle deposition kinetics, the quartz crystal microbalance (QCM) method is advantageous because it enables real time measurements under different transport conditions with high precision. Because of its versatility and the deceptive simplicity of measurements, this technique is used in a plethora of investigations involving nanoparticles, macroions, proteins, viruses, bacteria and cells. However, in contrast to the robustness of the measurements, theoretical interpretations of QCM measurements for a particle-like load is complicated because the primary signals (the oscillation frequency and the band width shifts) depend on the force exerted on the sensor rather than on the particle mass. Therefore, it is postulated that a proper interpretation of the QCM data requires a reliable theoretical framework furnishing reference results for well-defined systems. Providing such results is a primary motivation of this work where the kinetics of particle deposition under diffusion and flow conditions is discussed. Expressions for calculating the deposition rates and the maximum coverage are presented. Theoretical results describing the QCM response to a heterogeneous load are discussed, which enables a quantitative interpretation of experimental data obtained for nanoparticles and bioparticles comprising viruses and protein molecules.

Applicability of QCM-D for Quantitative Measurements of Nano- and Microparticle Deposition Kinetics: Theoretical Modeling and Experiments

A new theoretical model is formulated for the quantitative analysis of quartz crystal microbalance (QCM) response for heterogeneous loads consisting of nano- and microparticles. The influence of particle coverage and structure is described using a universal correction function in an ab initio manner. Explicit analytical expressions for the frequency and dissipation shifts are derived for the entire range of particle size under the rigid contact regime. The solvent coupling functions are also calculated to determine the dry coverage using the QCM measurements. These expressions furnish the upper limit of the QCM signal, which can be attained for a sensor providing perfect adhesion of particles. Correction functions accounting for the finite adhesion strength (soft contact regime) are also derived. The theoretical results are confronted with QCM and atomic force microscopy measurements of positively charged polymer particle deposition on silica sensors. The main features of the theoretical model are confirmed, especially the abrupt decrease in the QCM wet mass with the particle coverage and the overtone number. The latter effect is especially pronounced for microparticles under the soft contact regime, where the higher-number overtones produce a negligible QCM signal. These results represent a useful reference data for the interpretation of protein and bioparticles, for example, virus and bacteria attachment processes to various substrates.

Load Impedance of Immersed Layers on the Quartz Crystal Microbalance: A Comparison with Colloidal Suspensions of Spheres

The analytical theories derived here for the acoustic load impedance measured by a quartz crystal microbalance (QCM), due to the presence of layers of different types (rigid, elastic, and viscous) immersed in a fluid, display generic properties, such as "vanishing mass" and positive frequency shifts, which have been observed in QCM experiments with soft-matter systems. These phenomena seem to contradict the well-known Sauerbrey relation at the heart of many QCM measurements, but here, we show that they arise as a natural consequence of hydrodynamics. We compare our one-dimensional immersed plate theory with three-dimensional simulations of rigid and flexible submicron-sized suspended spheres and with experimental results for adsorbed micron-sized colloids, which yield a "negative acoustic mass". The parallel behavior unveiled indicates that the QCM response is highly sensitive to hydrodynamics, even for adsorbed colloids. Our conclusions call for a revision of existing theories based on adhesion forces and elastic stiffness at contact, which should, in most cases, include hydrodynamics.

cAMP sensitive nanochannels driven by conformational transition of a tripeptide-based smart polymer

Inspired by biological nanochannels, a novel cyclic 3',5'-adenosine monophosphate (cAMP)-regulated artificial nanochannel based on a tripeptide Arg-Thr-Ala (RTA) design is developed. Highly specific binding between the tripeptide and cAMP triggers an obvious conformational transition of a smart polymer chain from a contracted state to a swollen one, which leads to a dynamic modulation of the gating behaviours of the nanochannels.

Interaction between LDL-mimetic liposomes and acid-treated carbon nanotube electrode during Cu2+-mediated oxidation

Oxidation of low-density lipoproteins (LDL) causes atherosclerosis. Detection of oxidation of LDL-mimetic liposomes using an electrode might serve as a convenient tool in the search of antioxidants for the prevention of atherosclerosis. This report proposes a reaction mechanism between LDL-mimetic liposomes and an acid-treated carbon nanotube (CNT) electrode. Oxidation of the liposomes, mediated by Cu²⁺, was monitored by the change in electrode potential, and the fluorescence intensity generated by diphenyl-1-pyrenylphosphine (DPPP) as control. The electrode potential and fluorescence intensity increased concomitantly during oxidation, followed by a gradual decrease. Although the electrical potential peaked faster than the fluorescence intensity, addition of CNT to the DPPP reaction accelerated the latter, suggesting the role of CNT as an accelerator of liposome oxidation. Atomic force microscopy showed increased binding of liposomes to CNT along with liposomal deformation. Further, binding of Cu²⁺ to the liposome-bound CNT surface was observed by quartz crystal microbalance. In conclusion, the interaction of liposomes with Cu²⁺ and CNT surface explains the rapid response of the electrode in liposome oxidation.

Nanoarchitectonic-Based Material Platforms for Environmental and Bioprocessing Applications

The challenges of pollution, environmental science, and energy consumption have become global issues of broad societal importance. In order to address these challenges, novel functional systems and advanced materials are needed to achieve high efficiency, low emission, and environmentally friendly performance. A promising approach involves nanostructure-level controls of functional material design through a novel concept, nanoarchitectonics. In this account article, we summarize nanoarchitectonic approaches to create nanoscale platform structures that are potentially useful for environmentally green and bioprocessing applications. The introduced platforms are roughly classified into (i) membrane platforms and (ii) nanostructured platforms. The examples are discussed together with the relevant chemical processes, environmental sensing, bio-related interaction analyses, materials for environmental remediation, non-precious metal catalysts, and facile separation for biomedical uses.

Modified Sauerbrey equation: a facile method to quantitatively probe the conformation of isolated molecules at solid–liquid interfaces

It is found that a quartz crystal microbalance signal is proportional to the product of mass and intrinsic viscosity of molecules at solid–liquid interfaces, with a constant coefficient. This relationship provides a convenient way to semi-quantitatively probe the conformation of a discrete polymer at solid–liquid interfaces.