WO2015042025A1

WO2015042025A1 - Centrifugal force quartz crystal microbalance

Info

Publication number: WO2015042025A1
Application number: PCT/US2014/055806
Authority: WO
Inventors: Aaron WEBSTER; Frank Vollmer; Yuki Sato
Original assignee: President And Fellows Of Harvard College
Priority date: 2013-09-18
Filing date: 2014-09-16
Publication date: 2015-03-26

Abstract

A system and method include applying a sample to a sensing surface, causing the sensing surface to oscillate, applying force normal t the sensing surface, and measuring oscillation of the sensing surface while applying the force. The system includes a sensing platform having a sensing surface configured to couple with a sample and oscillate in a shear mode.

Description

Centrifugal Force Quartz Crystal Microbalance Related Application

[0001] This application claims priority to United States Provisional

Application Serial Number 61/879,443, filed September 18, 2013, which is incorporated herein by reference. Background

[0002] The quartz crystal microbalance (QCM) has seen increasing prominence as a simple, cost effective, and highly versatile mechanical biosensing platform. Since its introduction by Sauerbrey in 1959 as a sub- monolayer thin-film mass sensor in the gas phase, the understanding and real- world utility of these piezoelectric devices has been repeatedly enhanced to study phenomena such as viscoelastic films in the liquid phase, contact mechanics, and complex samples of biopolymers and biomacromolecules.

[0003] On a fundamental level, a quartz crystal microbalance is simply an extremely responsive inertial mass sensor. When an external load couples to the resonance of the crystal, the hybrid system takes on a new resonance condition. The magnitude and sign of the changes in frequency and bandwidth are related to the inertial properties of the load and the rigidity of its coupling.

Summary

[0004] A method includes applying a sample to a sensing surface, causing the sensing surface to oscillate, applying force normal to the sensing surface, and measuring oscillation of the sensing surface while applying the force.

[0005] A system includes a sensing platform having a sensing surface configured to couple with a sample and oscillate in a shear mode. A force applying mechanism is coupled to the sensing platform to apply force normal to the sensing surface. A circuit is coupled to the sensing platform to detect a frequency of oscillation of the sensing surface responsive to the sample and normal force. [0006] A system includes a sensing platform having a sensing surface configured to couple with a sample and oscillate in a shear mode, the sensing platform configured to couple to a force applying mechanism to apply force normal to the sensing surface. A circuit is coupled to the sensing platform to detect a frequency of oscillation of the sensing surface responsive to the sample and normal force.

[0007] A method for determining the size and number of particles includes acquiring a response of a centrifugal force quartz crystal microbalance (CF-QCM) exposed to a sample containing particles by varying centrifugal force normal to a sensing surface supporting the sample, measuring change in CF- QCM frequency and line width as a function of centrifugal force, and extracting particle size and number of particles from zero crossings in a parametric plot of frequency and linewidth measurements.

[0008] A method for determining the viscoelasticity of a material includes acquiring a response of a centrifugal force quartz crystal microbalance (CF-QCM) exposed to a viscoelastic sample by varying centrifugal force normal to a sensing surface supporting the sample, measuring changes in CF-QCM frequency and linewidth as function of the centrifugal force, and determining storage and loss modulus by fitting a theoretical model to line width versus centrifugal force and frequency versus centrifugal force traces.

Brief Description of the Drawings

[0009] FIG. 1 is a block diagram representation of an example centrifugal force quartz crystal microbalance (CF-QCM) sensor system according to an example embodiment.

[0010] FIG. 2 is a graph illustrating a frequency response for free particles utilizing the system of FIG. 1 according to an example embodiment.

[0011] FIGs. 3A, 3B, 3C, 3D, 3E, and 3F illustrate frequency shift versus g-force for various sample according to an example embodiment.

[0012] FIG. 4 is a plot of the simulated response in frequency and bandwidth for a 10 μιη particle according to an example embodiment.

[0013] FIG. 5 illustrates a method for sizing micron-sized particles according to an example embodiment. [0014] FIGs. 6A, 6B, and 6C illustrate a finite element simulation of normalized frequency and bandwidth difference for different particles according to an example embodiment.

[0015] FIG. 7 is a block schematic diagram of a computer system 700 to execute one or more algorithms or communicate with electronics driving and monitoring a sensing surface according to an example embodiment.

Detailed Description

[0016] In the following description, reference is made to the

accompanying drawings that form a part hereof, and in which is shown by way of illustration specific embodiments which may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, and it is to be understood that other embodiments may be utilized and that structural, logical and electrical changes may be made without departing from the scope of the present invention. The following description of example embodiments is, therefore, not to be taken in a limited sense, and the scope of the present invention is defined by the appended claims.

[0017] The functions or algorithms described herein may be

implemented in software or a combination of software and human implemented procedures in one embodiment. The software may consist of computer executable instructions stored on computer readable media such as memory or other type of storage devices. Further, such functions correspond to modules, which are software, hardware, firmware or any combination thereof. Multiple functions may be performed in one or more modules as desired, and the embodiments described are merely examples. The software may be executed on a digital signal processor, ASIC, microprocessor, or other type of processor operating on a computer system, such as a personal computer, server or other computer system.

[0018] A new sensing platform, a centrifugal force quartz crystal microbalance (CF-QCM) has been developed and its behavior studied under different load situations. By applying forces to the platform, such as centrifugal force, the coupling of the load to the microbalance surface can be non- destructively modified. While a centrifuge with a swinging bucket is described as providing the force, various other embodiments may use different mechanisms to apply force, such as a centrifuge not utilizing a swinging bucket, or devices that accelerate or decelerate the platform along a rail or on the end of a driven cantilever provided measurements may be obtained during such accelerations.

[0019] The use of force on the platform allows for the interrogation of complex samples and analysis of their dynamic responses while substantially increasing the sensitivity of the platform. The platform may be used for studies of micro/nano contact mechanics of free particles, beads attached to the surface with oligonucleotides, and particles tethered by lambda phage DNAs to the sensor surface. By reversing the configuration and pulling on the beads tethered to the surface with lambda DNAs via centrifugal force, the sensing platform may also be used for probing DNA kinetics. The CF-QCM sensing that utilizes not only the measurement but also the tuning of contact stiffness has potential applications in highly sensitive single molecule measurements as well as the investigations of mechanical and thermodynamic properties of viruses, bacteria, and cells.

[0020] On a fundamental level, a quartz crystal microbalance is simply an extremely responsive inertial mass sensor. When an external load couples to the resonance of the crystal, a hybrid system is formed. The hybrid system takes on a new resonance condition. The magnitude and sign of the changes in frequency and bandwidth are related to the inertial properties of the load and the rigidity of its coupling.

[0021] Traditional QCM experiments have thus far relied on monitoring the system's resonance while the inertial properties and rigidity of the load's coupling are taken as a fixed parameter (or statistical distribution) under assay. With this approach, one is only able to obtain discrete values for shifts in frequency and bandwidth in an otherwise continuous space. However, there is evidence that accelerations as small as 1 g have a measurable effect on the response of the QCM under load. This has been observed for pure Newtonian liquids, DNA, as well as for force-based techniques involving nanoindenters or atomic force microscope (AFM) probe tips. All of these responses have been found to be significant compared to the baseline acceleration sensitivity of the QCM itself. [0022] Realizing potential of such an approach, a new type of instrument has been developed which uses a quartz crystal microbalance as a direct mechanical transducer for the response of biomolecules in an accelerating local reference frame provided by a centrifuge. This concept enables direct introduction of controlled pico- to nanoscale forces to a sample in the liquid phase, which can be monitored in situ and in real time.

[0023] By applying centrifugal forces to a sample, it is possible to repeatedly and non-destructively interrogate its mechanical properties in situ and in real time. Various embodiments illustrate use of the instruments for interrogating the properties of micron-sized particles, viscoelastic monolayers of DNA, and particles tethered to the quartz crystal microbalance surface by DNA. For certain types of samples on quartz crystal microbalances, application of variable centrifugal force in pico- to nanoscale ranges both enhances sensitivity and reveals additional mechanical, viscoelastic, and conformal properties.

[0024] FIG. 1 is a block diagram representation of an example system

100 including a QCM 110 that is supported by a bucket 1 15 of a swinging bucket centrifuge 120. The bucket 1 15 is supported via pivot points 122 of an arm 125 that is couple to a rotating axis of the centrifuge 120.

[0025] A driver and electronics 130 is coupled to the QCM 1 10 via a tether 135. Electronics 130 may perform data acquistion electrically through the tether 135 and a centrally mounted slip ring 140, or alternatively via a wireless transponder 145, which may be coupled to the QCM in the bucket 1 15. A crystal of the QCM 100 is illustrated in both a loading configuration at 150 and an unloading configuration 155. The crystal 110 itself is mounted in a holder radially by its edges such that the centrifugal force F_c is always normal to the surface of the crystal. The horizontal arrows shown in crystal 1 10 indicate the motion of the QCM's transverse shear mode. On the sensing side of the crystal is a 125 μϊ_^ volume PDMS/glass cell containing the sample 160. The non-sensing side of the crystal remains in air and may include electrodes 170 to drive the crystal and sense oscillation of the crystal 110.

[0026] When in operation, the crystal and cell are mounted in either the loading configuration 150, where the centrifugal force is in to the sensing side or, by mounting it upside down, in the unloading configuration 155, where the force is away from the sensing side. [0027] When spinning, centrifugal force (F_c) is applied to the crystal 1 10.

The force is orthogonal to a sensing surface of the sensing platform, and may be applied via other movement of the platform, such as acceleration along a line orthogonal to the sensing surface. In one embodiment, the crystal 110 includes a sensing surface that is driven to oscillate in plane in a shear mode at a resonant frequency. Samples may be provided to the sensing surface of the crystal 110 by micro or nano fluidics 180 in various embodiments, and the sensing surface may be in contact with liquid used to deliver the sample while it oscillates. The sample is shown as a chamber filled with liquid containing at least one particle attached to the sensing surface.

[0028] The ACM crystal itself is mounted radially by its edges such that the centrifugal force is normal to the surface of the crystal. The sensing side of the crystal may include a microliter volume PDMS/glass cell containing a sample under investigation. The non-sensing side of the crystal may remain in air.

[0029] FIG. 2 is a graph 200 illustrating a frequency response 210 for free particles 215 as the centrifuge is spun up to 90g. In one embodiment, free 1 μιη streptavidin coated polystyrene particles in water are introduced into the sample cell. When the cell is rotated to the loading configuration 220 under the influence of gravity alone, the particles fall toward the sensing surface and a positive shift in the QCM's frequency signal is observed. When the cell is then rotated 180 degrees to the unloading configuration, the particles fall off and the frequency response returns to its original state. Again the cell is rotated 180 degrees to the loading configuration at 230 and the positive frequency shift is observed. As the centrifuge spins up towards 90 g beginning at 235, the particles are "pressed" towards the QCM surface and a four fold increase in the frequency shift is observed at 240 when force of 90g is reached. The centrifuge then spins down and the baseline frequency shift under gravity alone is recovered at 245.

[0030] Traditional QCM experiments assume that the inertial properties and rigidity of the sample's coupling are taken as a fixed parameter (or statistical distribution) under assay. With traditional approaches however, one is only able to obtain discrete values in an otherwise continuous parameter space. Hybrid- QCM experiments involving nanoindenters or AFM probe tips have shown intriguing behavior when force is applied to a sample in a QCM measurement. There have also been reports that accelerations as small as 1 g have a measurable effect on a QCM's response for viscoelastic monolayers such as DNA, and even for pure Newtonian liquids. All of these responses have been found to be significant compared to the baseline acceleration sensitivity of the QCM itself. With the integration of a centrifuge to a standard QCM, one can observe these effects under enhanced g-forces and make endpoint measurements (measurements taken after the addition of a sample) in the sample's parameter space continuously and repeatedly.

[0031] To demonstrate this, six different samples have been investigated in the CF-QCM under variable accelerations from approximately 1 g to 90 g. These samples were chosen to be examples of the breadth of load situations accessible with our technique. They are:

A. air

B. deionized water

C. free particles in water

D. paramagnetic particles attached to the sensor via short oligonucleotides.

E. 48 kbp lambda phage DNAs attached to the gold electrode

F. polystyrene particles tethered to the sensor via 48 kbp lambda phage DNAs.

[0032] In one embodiment, the QCM driver circuit 130 outputs

Butterworth van Dyke (BvD) equivalent relative frequency Af (in hertz) and motional resistance R (in ohms). R is approximately related to the bandwidth Γ (half width at half maximum of the frequency response) by Γ = R/(4nL), where L = 40 mH is the motional inductance of the BvD equivalent circuit. For this relationship the small load approximation is assumed to be Af I f_F « 1 , where is the fundamental frequency. An assumption is made that AR is an approximate, and indirect, measure of the bandwidth ΔΓ (in hertz). In addition ΔΓ is an equivalent representation of the "dissipation", D, used in QCM-D devices by D = 2AT/fi.

[0033] The system's response was first tested in air, shown as frequency shift versus g-force in FIG. 3A. The base acceleration sensitivity (change in frequency versus change in g-force) of AT cut quartz normal to the plane of the crystal has a reported value of AflAg = 2.188(6) x 10^"2 Hz/g. System 100 shows similar behavior: Af/Ag = 2.682(23) x 10^~2 Hz/g in the loading configuration. The signs of Af/Ag are found to be opposite in the loading and unloading

configurations. The bandwidth or motional resistance dependence of a QCM under acceleration is AY/Ag = 9.203(171) x 10^"4 Hz/g.

[0034] Next, deionized water was used as a control sample for measurement in the liquid phase, shown as frequency shift versus g-force in FIG.3B. The initial shift in frequency and bandwidth is in agreement with what is obtained the Kanazawa-Gordon relations for water (p=\ g cm^"3 and η =1 mPa s): Af= -714 Hz and R = 359 Ω, which are close to the measured values of Af= - 716Hz and R = 357Ω. The response under centrifugal load was found to be linear and smaller than that of air: Af/Ag = 1.357(24) x 10^~2 Hz/g and AT/Ag = 2.865(73) x 10^~3 Hz/g. Acceleration dependent forces in the liquid phase are not necessarily commensurate with those in the gas phase, but as the effects are small compared to experiments with actual loads, they are treated as baselines to be subtracted.

[0035] Utilizing the flexibility that the system 100 provides in modifying the coupling between the load and the sensor surface, we have applied the technique to the study of discrete micron sized particles. As first referenced in FIG. 2, the frequency and bandwidth shifts of free particles in the liquid phase as a function of g-force is shown in FIG.3C. Here, streptavidin coated polystyrene particles, mean diameter d = 1.07 μιη, are placed in the sample volume with a surface density of N_L = 1.58 x 10¹¹ particles/m² and the signal is observed in both the loading and unloading configurations. The particles did not exhibit adhesion to either the unmodified gold electrode or the glass/PDMS cell surrounding it; in the unloading configuration, the particles quickly drifted away from the sensing area and a signal identical to water was observed. In the loading configuration, a large positive shift in Af and ΔΓ was observed, consistent with previously observed responses for weakly coupled particles in this size range.

[0036] The initial shift under 1 g was found to be Af= 2.2 Hz and ΔΓ = 7.5 Hz. At the maximum acceleration of 90 g the signal increases to Af= 16.5Hz and ΔΓ = 37Hz. This also represents a sensitivity enhancement in the minimum resolvable surface density of the particles. The scaling of Af and ΔΓ with increasing centrifugal load is nonlinear in the applied load, implying non- Hertzian behavior.

[0037] The same experiment was also carried out with 2, 6, 15, and 25 μιη polystyrene particles. The loading curves all followed the same trend, but the relative shifts in Af and ΔΓ differed based on particle size.

[0038] In contrast to the situation of free particles, the behavior of the

CF-QCM in a regime where particles are rigidly coupled to the sensor by attaching 2 μιη (mean diameter d = 1.89 μιη) streptavidin coated paramagnetic particles modified with biotinylated 25 mer oligos to complimentary strands conjugated to the QCM gold surface via thiol bonds is shown as frequency shift versus g-force in FIG.3D. Note that, Af and ΔΓ are both negative and decrease with centrifugal force in the loading orientation. When spinning with the oligo attached particles, the presence of the particle may not be sensed directly but rather the conformational state of the oligonucleotide layer may be sensed. Such an acceleration effect has been observed before, but only within the 2 g orientation difference of gravity. When the oligo layer is under centrifugal load, it compresses, causing the density-viscosity product to increase. This behavior is consistent with the behavior of DNA observed on QCMs under the influence of gravity alone.

[0039] Moving from particles to viscoelastic monolayers is shown as frequency shift versus g-force FIG. 3E, 48 kbp lambda phage DNA in STE buffer were attached to the gold sensor electrode via a complimentary thiolated oligo. Previous studies have shown that, through the use of dissipation monitoring, QCMs are sensitive to not only the adsorbed mass and viscosity, but the physical conformal state ("shape") of DNAs hybridized to the sensor surface. In the experiment, even though the force on the lambda DNAs is on the order of femtonewtons, a strong linear decrease (ΔΓ = -2.9120(95) Hz/g) was observed in the bandwidth as function of g-force, indicating an increase in viscoelastic loss. However, under larger g- forces the sign of Af reverses. The origin of this effect may indicate a nonlinear viscoelastic compliance under load. The unloading configuration sees a smaller negative response in ΔΓ with little effect on Af.

[0040] A salt buffer may be used in experiments involving DNA. There are several studies regarding the effects of various electrolytic buffer solutions and their concentrations on QCM measurements, including reports of an immersion angle (and therefore gravity) dependence. These reports suggest this effect may be related to the behavior of the interfacial layer and ion transport in monovalent electrolytic solutions in accelerating frames. A significant contribution in the unloading configuration for STE buffer alone (Af= -

0.3260(29) Hz/g, and ΔΓ nonlinear) was observed, and subsequently "screened" by the presence of both oligos and lambda DNAs, making the effect negligible in the current set of experiments.

[0041] With the sensitivity to both particles and monolayers, the system 100 may also be used to investigate beads tethered by lambda DNA as a transduction mechanism to investigate its kinetics. One such example is shown in FIG.3F. Streptavidin coated polystyrene particles with a mean diameter of 24.8 μιη were tethered to the CF-QCM by means of a 48 kbp lambda phage DNA. Experiments were done in STE buffer whose density reduced the maximum force the bead could exert to about 40 pN which, according to the worm-like chain model, should almost fully extend the lambda DNA to a length of 16 μιη.

[0042] Preliminary quantitative measurements in this load situation reveal that as the tethered bead extends the DNA under centrifugal force, Af increases and ΔΓ decreases. In the case where the DNAs are trapped and pushed between the bead and the surface, both Af and ΔΓ increase. Signs of the shifts in this scenario have been confirmed with 10 μιη and 6 μιη paramagnetic particles, using a magnet to either pull or push the particles toward or away from the sensor surface. This behavior is distinct from either the case of lambda DNA or free particles alone.

[0043] At F_c = 40 pN, the frequency shift indicates an effective decrease in the density -viscosity product of 10 % or about 1.5 pg. For the surface densities involved (NL = 3.25 x 10⁷particles/m²), the equivalent interfacial mass lost for a fully extended lambda DNA predicted by the worm-like chain model are in the picogram range and cannot account for the more than 10⁶ signal difference shown here. If indeed the response is due to lambda DNA extension, future experiments involving high frequency, large centrifugal force CF-QCMs could easily detect the kinetics of a single tether. [0044] Table 1 illustrates a normalized frequency and bandwidth shifts in

Hz m² at 1 and 90 g for various particle sizes in water. The quoted diameter d is the mean diameter and the superscripts p represents polystyrene particles and m represents magnetite coated polystyrene.

Afi_. /N_h Af : /S_L Af_:.r ?S:_ Δ1½/¾.

1 .07' 1 ,6 I K- 1 1. 1 6.98: 1 I -10

i:-\ I I 7. SO: i-10 JA i -10

5,86 "^: 4 JI k- S J.l >!:> 8 3.43. 5-10 3.41f -10

ISi L .:< >is-07 8 3.8). • J^'¾* §.¾S;lt^;

24. (r BSj lii-07 ; . ^*;.¾ ;: .! 7 ^;-07 -07

TABLE 1

Finite Element Modeling

[0045] To elucidate QCM behavior for samples with discrete particles, 2D finite element simulations were performed based on steady state solutions to the incompressible Navier-Stokes equations. The simulation setup as depicted in FIG. 4 at 400. Particles 410, 415, 420 are represented as spheres (or rather cylinders, in 2D) which are moved towards a tangentially oscillating boundary at the bottom of the computational domain, representing the QCM surface. At 410, the sphere is not in contact with the boundary, while 415 and 420 illustrate successively stronger contact with the boundary. Periodic conditions are imposed on the left and right boundaries such that the ratio of the domain width to the particle size determines the surface coverage and thus NL. As the particle intersects the oscillating boundary it is truncated; this truncation is identified with a finite contact radius r_c in terms of contact mechanics.

[0046] A plot of the simulated response in frequency and bandwidth for a

10 μιη particle is depicted in FIG.4. The spheres were modeled as polystyrene with density p = 1.06 gem^"3, shear modulus

= 1.3 GPa, and loss tangent tan δ= 0.001. The spheres are in water with density 1.0 g cm^"3 and viscosity 1.0 mPa s. The shifts in Af and ΔΓ are plotted as a function of a dimensionless contact surface density A_c, defined as the contact area of the sample per unit area on the oscillating boundary.

[0047] The behavior of the simulation closely matches experimental observations. As the sphere approaches and makes (weak) contact with the oscillating boundary, a positive shift in both frequency and bandwidth is observed. As the contact radius increases, the sphere becomes more strongly coupled to the boundary. The amount of energy dissipated into the particle increases until ΔΓ reaches a maximum and Af experiences a zero crossing. The limiting case sees a rigid attachment and the common negative frequency shift proportional to mass adsorption takes hold.

[0048] There are two aspects of the simulation that deserve additional consideration: (1) positive shifts in Af and ΔΓ begin before physical contact with the oscillating boundary and (2) for smaller particles ΔΓ > Af while for larger particles Af > AY. The experiment shows the same behavior, as evidenced in TABLE 1. However, the procedure of truncation and its interpretation as finite contact radius in the framework of contact mechanics utilized here on discrete objects are more accurate for larger particles (10 μιη, as shown in FIG. 4) than smaller ones. It is known in the context of DVLO theory that a micron-sized polystyrene sphere in water near a similarly charged gold surface will experience a repulsive force due to electro-static double-layer effects. The balance between this and the gravitational force determines the height at which the particle will be at equilibrium above the surface. For the relevant material parameters, even at 90 g, the smaller 1 and 2 μιη particles never make contact with the surface, but "hover" at separations of approximately 0.3 μιη to 0.15 μιη. At nonzero separations the sphere-surface coupling, being mediated by a viscous liquid, may be dominated by loss, hence ΔΓ > Af. On the other hand, larger particles (~ 10 μιη and above) with significant mass may overcome the double-layer forces and make contact with the QCM through a finite contact radius. In this case the coupling losses decrease and Af > AT.

Mechanical Model

[0049] Without mention of the actual physics of the coupling, it is observed that the finite element simulation, as well as the experimental data, follow a simple mechanical model based on coupled oscillators. The

arrangement of this mass-spring-dashpot mechanical model is shown in FIG. 4 at 425. Here, the resonance of the quartz crystal = k_q I m_q is coupled to a sample load with mass «L though a parallel spring and dashpot (Voigt model). Note that _L is not an actual spring; it is simply a coupling strength between two oscillators. The same is true for _L- «L is an actual mass, though in this model it represents a Sauerbrey mass uncorrected for viscoelastic properties.

[0050] Using the small load approximation, the response of the system as a function of its coupling _L can be expressed as:

where Z_q is the acoustic impedance of AT cut quartz,^ is the fundamental frequency of the resonator, and NL is a surface density (number per unit area) for discrete loads. EQN. 1 as a function of reproduces the response of the finite element simulation in FIG. 4, which is a function of contact surface density A_c (or in un-normalized terms the contact radius r_c). A best-fit comparison to the finite element simulation is shown as points in conjunction with the simulation in FIG.4.

[0051] The mechanical model has two important limits as a function of the contact stiffness, k known as strong and weak coupling. These limits occur to the left and right of a zero crossing in Af at k_zc = co_q ²m_h .

Δ/ + ΪΔΓ N k\ / , , 2

-!— =— ^ weak, *_L « m_Lfi£ (2) fy ω^πΖ^ V i

Δ/ + ΪΔΓ -N_Lm_Lco_{q 2}\

= — - strong, k_L » m_La)_q (3) fy Zq

where we have made the approximation that ξι_^ « [36]

[0052] Strong coupling is identified with mass loading (Sauerbrey behavior) and a negative frequency shift linearly proportional ί¾. This behavior is the one which is most commonly associated with QCM measurements.

Physically this situation is identified with a coupling rigid enough such that the particle takes part in the oscillation of the QCM. In the opposite limit is weak coupling, also called inertial loading, and is identified by a positive frequency shift independent of the mass and linearly proportional to k^. Here, the coupling is sufficiently weak such that the particle remains at rest in the laboratory frame. It is "clamped" by its own inertia.

[0053] Experiments with nano-indentation probes operating on QCMs in the gas phase, where micron sized spherical tips are pressed against the sensor surface, have observed the same positive frequency shift as a function of applied force, which is identified with the lateral (sphere-plate) Hertzian spring constant. Similar behavior may be observed in the liquid phase: the centrifugal load will primarily act on k^.

[0054] Certain sample parameters may be extracted using this model.

The response of the QCM for different load situations under centrifugal force exhibits a rich and complex set of behavior.

[0055] The coupled oscillator model (EQN. 1), when analyzed for samples of free particles, enables the use of QCMs to determine the size of large micron-sized particles in the liquid phase. In one embodiment, the size of nanometer-sized particles which lie within the QCM's shear acoustic wave may be determined. A plot of Af verses ΔΓ in EQN. 1 as a parametric function of , results in points that lie on a circle with radius r^. The physical mechanism modifying ]¾ is removed from the problem. Fitting a circle to the experimentally observed Δ/-ΔΓ data (plotted parametrically as a function of g- force), allows extrapolation of the behavior in the strong coupling regime by finding the point at which ΔΓ = 0 and Af< 0. Knowing Af, EQN. 3 can then be inverted to solve for either number density or particle size/mass. An example of this procedure is shown in FIG. 5 at 500, using the same data for 1 μιη particles shown in FIG. 1 and 3A-3F. Inset is a table 510 for the same predictions done for particles with known diameter d_actual = 1, 2, 15, and 25 pm. In all cases the surface density was known and the diameter d_predicted was derived from the mass «L, found by inverting EQN. 3. The results are surprisingly accurate despite the exploratory nature of the system's construction, which illustrates the robustness of this unique methodology that CF-QCM provides. It should also be mentioned that with knowledge of the way in which the g-force modifies the frequency zero crossing at k_zc = co_q ²m_L can be used to determine the mass «L without knowledge of the number density N_L.

[0056] In further embodiments, the CF-QCM technique may be used to detect different viscoelastic properties of discrete samples. While the mechanical properties seen in biomaterials spans an enormous range, three general categories were used to highlight interesting sensor responses. In FIGs. 6A, 6B, and 6C samples include cells 610, agarose microparticles 620, and protein microcrystals 630 respectively. Each sample may be treated in the finite element simulation as a discrete sphere, with complex shear modulus G_L = G'_L +G'f, where G'_L is the storage modulus related to elasticity, and GL is the loss modulus related to viscosity. G_L is related to viscosity r by r = GJii O_q). The shifts in frequency Af and bandwidth ΔΓ are again plotted as a function of the dimensionless contact surface density A_c. A fictitious negative A_c is identified with a finite separation distance from the simulated QCM surface 630. In all cases the coverage ratio was 50 %, and furthermore, it is assumed that centrifugal force will act to "push" the sample into the QCM surface 630, increasing A_c and thus the rigidity of its contact with the QCM.

[0057] As can be seen, the simulated response of the CF-QCM is markedly different in each case. Cells 630, are assigned a shear modulus of G_L = (10 + 50i) kPa and density /¾, equal to the surrounding liquid medium. The high loss modulus and low storage modulus predict the cell will exhibit shifts characteristic of a viscous fluid. Likewise, the simulation shows Af and ΔΓ decrease and increase linearly proportional to the contact parameter, beginning before physical contact occurs. The proportionality is a simple function of the shear modulus and de imation.

(4)

Cells in and of themselves span a large range of viscoelastic properties which have been demonstrated to be predictive for diseases such as cancer [45]. If one knows the way with which A_c is modulated by an applied force (e.g. viscoelastic compliance), linear fitting to the CF-QCM response will recover G_L or p_L.

[0058] Next, FIG. 6B shows the simulated response of agarose microparticles 615 with a complex shear modulus of G_L = (78 + 78i) kPa. Again the density was assumed to be the same as the surrounding medium. Similar to the viscous behavior of cells, ΔΓ decreases linearly with ^_c. In this sample however, an equally large elastic term, G'L, precludes the equally linear decrease in Af seen for cells. Instead, Af increases slightly before contact and decreases slightly. [0059] At the end of the spectrum, FIG.6C are lysozyme microcrystals

620. These microcrystals are "hard", having been assigned a complex shear modulus of G_L = (0.659 + 0.235i) GPa. The response of these is similar to what is experimentally observed with polystyrene microparticles (Gx = 1.3GPa). When the microcrystal enters the acoustic evanescent wave, there is an initial negative shift as the effective viscosity-density product increases. At small contact parameters there is a positive shift in Af and ΔΓ. Increasing the contact parameter, ΔΓ sees a maximum and Af a zero crossing. As the microcrystal becomes strongly coupled to the QCM, the familiar negative Afis recovered which, as in FIG. 4, can be used to determine the particle size or mass.

[0060] Other types of signals from the system 100 may be related to ionic transport, the conformal state of DNA, and nonlinear viscoelastic behavior. Objects such as microparticles attached or tethered to a biopolymer on the QCM surface become inertial transducers through which one can extract mechanical and thermodynamic properties of the macromolecules. Furthermore, the variable force QCM technique is applicable to microscopic biological objects such as viruses, bacteria, and cells where measurements of mechanical properties and their changes have been directly linked to disease.

[0061] The enhanced signal for most samples under centrifugal load points to an interesting avenue of increasing the sensitivity of a state of the art QCM biosensor. The use of commercial centrifuges to provide force will increase the current low-g regimes of 90 g or below. Even with such low-g regimes, Sensitivity increases have been observed corresponding to changes of 10 % in the density -viscosity product for viscoelastic loads, and up to a factor of 10 increase in sensitivity for discrete particles. However, the use of commercial centrifuges may result in further changes and increases. In still further embodiments, other related modalities such as the nanotribological effects of sliding friction may be obtained by orienting the crystal at an angle to the applied centrifugal force, propelling biomolecules across the surface.

[0062] Various results described above and shown in graphs utilized an experimental embodiment, and are not a representation that the same results may be obtained in further embodiments. The experimental embodiment included a 25 mm diameter 5 MHz gold coated crystal in combination with an SRS QCM200 PLL based driver circuit. On the sensing side of the crystal, a 125 μΐ, PDMS/glass cell was used to contain the sample or specimen under

investigation. The cell was made of a thin o-ring of PDMS (Sylgard 184, 10: 1 ratio, cured 20 min at 120°C) OD = 25 mm, ID = 15.5 mm in contact with the sensing side of the crystal and covered with 25 mm round N² 1 coverglass, nominal thickness 0.15 mm. The non-sensing side of the crystal remained in air and was isolated from the body of the centrifuge. The quartz crystals were always cleaned before use by immersion in fresh piranha solution (3 : 1 mixture of 97% H₂S0₄ and 30% ¾(¾) for 5 min and rinsing liberally with pure water.

[0063] Free particles (Spherotech SVP-10-5, SVM-15-10, and SVP-200- 4), of different diameters were prepared by diluting a solution of 30 μΐ_^ particles in 300 μΐ, H₂0. A 125 μΐ, aliquot of the 300 μΐ, volume was then placed in the PDMS cell in contact with the sensing side of the crystal. The sensing area was calculated to be 1.195cm². The particles in solution experience a buoyant force which reduces their apparent mass. The surface density N_L was determined by counting the average number of particles per unit area with a microscope and was found to be within 20 % of the value predicted by the volume concentration.

[0064] For experiments involving oligos, the crystals were first immersed in a 1 μΜ solution of thiolated oligos (5'- ThioMC6-TTT TTT TTT CAC TAA AGT TCT TAC CCA TCG CCC-3 ') in a 1 M potassium phosphate buffer, 0.5 M KH₂P0₄, pH 3.8 for 1 h. Following, immersion in 1 mM 6-

Mercapto-l-hexanol (MCH) was used to block residual reactive sites on the gold electrode. After rinsing, attachment to the prepared particles was done in STE buffer: 1 M NaCl with 10 mM Tris buffer, pH 7.4 and 1 mM EDTA. A complimentary strand (5'-biotin- CT CAC TAT AGG GCG ATG GGT AAG AAC TTT AGT-3 ') was attached to the streptavidin coated particles. The particles were first washed two times by alliquoting a 100 μΕ base solution of particles in 100 μϊ_^ STE buffer, 5000 RPM for 3 min and decanting the supernatant. The particles were resuspended in 20 μΕ of STE buffer and 10 μg of oligos were added. The mixture was incubated 15 min at room temperature under slow vortexing, then washed again and resuspended in 100 μΕ STE buffer. The oligo attached particle suspension was allowed to attach to the gold surface for 15 min before spinning. [0065] Lambda DNAs were prepared by combining 50 μΐ, of lambda

DNA at 500 μg mL^"1, 5.5 μΐ of lOx T4 ligase, and 0.5 μΐ, of diluted 10 μΜ thiolated linker oligonucleotide and heating to 70 C for 5 min. The suspension was left to cool to room temperature as the litigation of the oligos to the DNA COS ends occured. Once the mixture was at room temperature, 15 μΐ, lOx ligase buffer, 127 μΐ, H₂0, and 2 μΐ, T4 DNA ligase was added to the annealed linker. The reaction was allowed to proceed at room temperature for 3 h.

[0066] FIG. 7 is a block schematic diagram of a computer system 700 to execute one or more algorithms or communicate with electronics driving and monitoring the sensing surface. In one embodiment, multiple such computer systems are utilized in a distributed network to implement multiple components in a transaction based environment. An object-oriented, service-oriented, or other architecture may be used to implement such functions and communicate between the multiple systems and components. One example computing device in the form of a computer 700, may include a processing unit 702, memory 703, removable storage 710, and non-removable storage 712. Memory 703 may include volatile memory 714 and non-volatile memory 708. Computer 700 may include - or have access to a computing environment that includes - a variety of computer-readable media, such as volatile memory 714 and non-volatile memory 708, removable storage 710 and non-removable storage 712. Computer storage includes random access memory (RAM), read only memory (ROM), erasable programmable read-only memory (EPROM) & electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD ROM), Digital Versatile Disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium capable of storing computer-readable instructions. Computer 700 may include or have access to a computing environment that includes input 706, output 704, and a communication connection 716. The computer may operate in a networked environment using a communication connection to connect to one or more remote computers, such as database servers. The remote computer may include a personal computer (PC), server, router, network PC, a peer device or other common network node, or the like. The communication connection may include a Local Area Network (LAN), a Wide Area Network (WAN) or other networks.

[0067] Computer-readable instructions stored on a computer-readable medium are executable by the processing unit 802 of the computer 800. A hard drive, CD-ROM, and RAM are some examples of articles including a non- transitory computer-readable medium. For example, a computer program 818 capable of providing a generic technique to perform access control check for data access and/or for doing an operation on one of the servers in a component object model (COM) based system may be included on a CD-ROM and loaded from the CD-ROM to a hard drive. The computer-readable instructions allow computer 800 to provide generic access controls in a COM based computer network system having multiple users and servers.

[0068] Examples:

[0069] 1. A device comprising a quartz crystal microbalance (QCM) sensor placed into an accelerating local frame to exert force on the QCM sensor.

[0070] 2. A device according to example 1 wherein the accelerating local frame comprises a centrifugal force machine to provide a variable force, and wherein the QCM is coupled to electronics to measure changes in frequency and linewidth (bandwidth) of the QCM resonance in real time.

[0071] 3. A device according to any of examples 1-2 where the

QCM sensor is connected to an electronic readout device via a slip ring and wire tether.

[0072] 4. A device according to any of examples 1-3 where the

QCM sensor is connected to an electronic readout device via wireless communications.

[0073] 5. A device according to any of examples 1-4 wherein the accelerating local frame comprises centrifugal force machine swinging bucket rotor to support the QCM sensor such that the centrifugal force is normal to the sensor interface.

[0074] 6. A device according to any of examples 1-5 wherein the accelerating local frame comprises centrifugal force machine swinging bucket rotor to support the QCM sensor such the centrifugal force points normal to the sensor interface and the sensor surface is mounted at fixed angle with respect to the bucket. [0075] 7. A device according to any of examples 1-6 and further comprising a microfluidic flow cell coupled to provide a sample to a QCM sensor sample surface.

[0076] 8. A method comprising:

microfluidic loading of a quartz crystal microbalance (QCM) sensor such that biomolecules in a sample interact with a sensor surface in solution; applying increasing and decreasing centrifugal loads to the QCM sensor; measuring of mechanical resonance frequency and linewidth change of the QCM sensor;

applying a mechanical resonator model to extract mechanical parameters of the sensor and of the biomolecule interacting with the sensor surface.

[0077] 9. A method comprising:

binding of biomolecules in a sample to microbeads;

placing the microbeads in contact with a centrifugal force quartz crystal microbalance (CF-QCM)sensor surface;

applying increasing and decreasing centrifugal loads to the sensor; measuring mechanical resonance frequency and linewidth of the sensor under the applied loads; and

applying a mechanical resonator model to extract mechanical parameters of the sensor and of biomolecule interacting with the sensor surface.

[0078] 10. A method comprising

loading a quartz crystal microbalance (QCM) sensor surface with particles in a solution such that the particles can interact with the sensor surface in the solution;

applying increasing and decreasing centrifugal loads to the sensor; measuring mechanical resonance frequency and linewidth change of the sensor in response to the varying loads; and

applying a mechanical resonator model to extract mechanical parameters of the sensor and of the particles interacting with the sensor surface.

[0079] 11. A system comprising:

a sensing platform having a sensing surface configured to couple with a sample and oscillate in a shear mode;

a force applying mechanism coupled to the sensing platform to apply force normal to the sensing surface; and a circuit coupled to the sensing platform to detect a frequency of oscillation of the sensing surface responsive to the sample and normal force.

[0080] 12. The system of example 1 1 wherein the sensing surface comprises gold.

[0081] 13. The system of any of examples 1 1-12 wherein the force applying mechanism comprises a centrifuge.

[0082] 14. A system comprising:

a sensing platform having a sensing surface configured to couple with a sample and oscillate in a shear mode, the sensing platform configured to couple to a force applying mechanism to apply force normal to the sensing surface; and a circuit coupled to the sensing platform to detect a frequency of oscillation of the sensing surface responsive to the sample and normal force.

[0083] 15. The system of example 14 and further comprising a force applying mechanism coupled to the sensing platform to apply force normal to the sensing surface.

[0084] 16. The system of any of examples 14-15 wherein the sensing surface comprises gold.

[0085] 17. The system of any of examples 14-16 wherein the force applying mechanism comprises a centrifuge.

[0086] 18. The system of any of examples 14-17 wherein the sensing platform comprises a quartz crystal microbalance.

[0087] 19. A method comprising:

applying a sample to a sensing surface;

causing the sensing surface to oscillate;

applying force normal to the sensing surface; and

measuring oscillation of the sensing surface while applying the force.

[0088] 20. The method of example 19 wherein the sample is applied to the sensing surface by microfluidics in a liquid that remains in contact with the sensing surface while the sensing surface oscillates.

[0089] 21. The method of any of examples 19-20 wherein measuring oscillation of the sensing surface comprises measuring a frequency and bandwidth of the oscillation. [0090] 22. The method of any of examples 19-21 wherein the force is varied and the oscillation of the sensing surface is measured at multiple different forces of the varied force.

[0091] 23. A method for determining the size and number of particles, the method comprising:

acquiring a response of a centrifugal force quartz crystal microbalance (CF-QCM) exposed to a sample containing particles by varying centrifugal force normal to a sensing surface supporting the sample;

measuring change in CF-QCM frequency and linewidth as a function of centrifugal force; and

extracting particle size and number of particles from zero crossings in a parametric plot of frequency and linewidth measurements.

[0092] 24. A method for determining the viscoelasticity of a material comprising:

acquiring a response of a centrifugal force quartz crystal microbalance

(CF-QCM) exposed to a viscoelastic sample by varying centrifugal force normal to a sensing surface supporting the sample;

measuring changes in CF-QCM frequency and linewidth as function of the centrifugal force; and

determining storage and loss modulus by fitting a theoretical model to linewidth versus centrifugal force and frequency versus centrifugal force traces.

[0093] Although a few embodiments have been described in detail above, other modifications are possible. For example, the logic flows depicted in the figures do not require the particular order shown, or sequential order, to achieve desirable results. Other steps may be provided, or steps may be eliminated, from the described flows, and other components may be added to, or removed from, the described systems. Other embodiments may be within the scope of the following claims.

Claims

What is claimed is:

1. A device comprising a quartz crystal microbalance (QCM) sensor placed into an accelerating local frame to exert force on the QCM sensor.

2. A device according to claim 1 wherein the accelerating local frame comprises a centrifugal force machine to provide a variable force, and wherein the QCM is coupled to electronics to measure changes in frequency and linewidth (bandwidth) of the QCM resonance in real time.

3. A device according to claim 1 where the QCM sensor is connected to an electronic readout device via a slip ring and wire tether.

4. A device according to claim 1 where the QCM sensor is connected to an electronic readout device via wireless communications.

5. A device according to claim 1 wherein the accelerating local frame comprises centrifugal force machine swinging bucket rotor to support the QCM sensor such that the centrifugal force is normal to the sensor interface.

6. A device according to claim 1 wherein the accelerating local frame comprises centrifugal force machine swinging bucket rotor to support the QCM sensor such the centrifugal force points normal to the sensor interface and the sensor surface is mounted at fixed angle with respect to the bucket.

7. A device according to claim 1 and further comprising a microfluidic flow cell coupled to provide a sample to a QCM sensor sample surface.

8. A method comprising:

microfluidic loading of a quartz crystal microbalance (QCM) sensor such that biomolecules in a sample interact with a sensor surface in solution; applying increasing and decreasing centrifugal loads to the QCM sensor; measuring of mechanical resonance frequency and linewidth change of the QCM sensor; applying a mechanical resonator model to extract mechanical parameters of the sensor and of the biomolecule interacting with the sensor surface.

9. A method comprising:

binding of biomolecules in a sample to microbeads;

10. A method comprising

1 1. A system comprising:

a force applying mechanism coupled to the sensing platform to apply force normal to the sensing surface; and

a circuit coupled to the sensing platform to detect a frequency of oscillation of the sensing surface responsive to the sample and normal force.

12. The system of claim 11 wherein the sensing surface comprises gold.

13. The system of claim 11 wherein the force applying mechanism comprises a centrifuge.

14. A system comprising:

15. The system of claim 14 and further comprising a force applying mechanism coupled to the sensing platform to apply force normal to the sensing surface.

16. The system of claim 14 wherein the sensing surface comprises gold.

17. The system of claim 14 wherein the force applying mechanism comprises a centrifuge.

18. The system of claim 14 wherein the sensing platform comprises a quartz crystal microbalance.

19. A method comprising:

applying a sample to a sensing surface;

causing the sensing surface to oscillate;

applying force normal to the sensing surface; and

measuring oscillation of the sensing surface while applying the force.

20. The method of claim 19 wherein the sample is applied to the sensing surface by microfluidics in a liquid that remains in contact with the sensing surface while the sensing surface oscillates.

21. The method of claim 19 wherein measuring oscillation of the sensing surface comprises measuring a frequency and bandwidth of the oscillation.

22. The method of claim 19 wherein the force is varied and the oscillation of the sensing surface is measured at multiple different forces of the varied force.

23. A method for determining the size and number of particles, the method comprising:

24. A method for determining the viscoelasticity of a material comprising: acquiring a response of a centrifugal force quartz crystal microbalance (CF-QCM) exposed to a viscoelastic sample by varying centrifugal force normal to a sensing surface supporting the sample;