Bioassays based on molecular nanomechanics

Disease Markers 18 (2002) 167–174 167IOS Press

Bioassays based on molecular nanomechanics

Arun MajumdarNanoengineering Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA94720, USATel.: +1 510 643 8199; Fax: +1 510 642 6163; E-mail: [email protected]

Abstract. Recent experiments have shown that when specific biomolecular interactions are confined to one surface of a microcan-tilever beam, changes in intermolecular nanomechanical forces provide sufficient differential torque to bend the cantilever beam.This has been used to detect single base pair mismatches during DNA hybridization, as well as prostate specific antigen (PSA) atconcentrations and conditions that are clinically relevant for prostate cancer diagnosis. Since cantilever motion originates fromfree energy change induced by specific biomolecular binding, this technique is now offering a common platform for label-freequantitative analysis of protein-protein binding, DNA hybridization DNA-protein interactions, and in general receptor-ligandinteractions. Current work is focused on developing “universal microarrays” of microcantilever beams for high-throughputmultiplexed bioassays.

Keywords: Molecular nanomechanics, microcantilever beams, bioassay, universal microarrays

1. Introduction

It is now fairly well recognized that for diagnosis,monitoring, prognosis, and molecular classification ofcomplex diseases such as cancer, it is necessary to gen-erate molecular profiles and patterns by quantitativelydetecting large numbers of biomolecules from serumor tissue samples. To facilitate this, it is necessaryto develop high-throughput techniques that can detecta wide variety of molecules. For genetic analysis,DNA microarrays have revolutionized the way genesand gene expressions can be analyzed in a multiplexedmanner. Microarray analysis, however, provides onlya glimpse of a small but important fraction of the com-plex molecular machinery involved in a cell. Devel-opment of high-throughput techniques that can iden-tify and quantitate proteins and their various modifi-cations and specific interactions has remained a chal-lenge. The most widely used techniques, which includetwo-dimensional gel electrophoresis and mass spec-troscopy, can identify and quantitate individual pro-teins, but are far from capturing the subtleties of pro-teins and their complex interactions with various othermolecules. What would be ideal are techniques thatare sufficiently robust and universal that can detect sub-

tle changes in molecular configurations and specificmolecular interactions. It is, therefore, important toask the question: What is common between all specificbiomolecular interactions?

It must be recognized that all biomolecular reactionsare thermodynamically driven by reduction of free en-ergy of the system. In addition, the reduction of freeenergy for specific reactions must be much larger thanthat for non-specific interactions, since otherwise non-specific reactions would prevail and the complexity ofmolecular interactions within a cell, which relies ofspecificity, would be lost. It is, therefore, worth askingthe question: Can the free energy change of biomolec-ular reactions be detected?

It is important to note that thermodynamics is thelanguage common between various physical phenom-ena that involve exchange of energy and entropy: me-chanics, electricity, magnetism, etc. Hence, if thefree energy reduction in biomolecular reactions can betranslated into another form, it could provide a wayfor detecting the reaction. Recent experiments haveshown that when specific biomolecular reactions oc-cur on one surface of a “diving board” shaped mi-crocantilever beam (see Fig. 1), the cantilever beambends [1–3]. The cantilever motion is thought to orig-inate from changes in intermolecular nanomechanical

ISSN 0278-0240/02/$8.00 2002 – IOS Press. All rights reserved

168 A. Majumdar / Bioassays based on molecular nanomechanics

Deflection, h

Probe Molecule

Gold

Silicon Nitride Microcantilever Glass

Glass

Target Binding

- +

Target Molecule

Fig. 1. Specific biomolecular interactions between target andprobe molecules alters the intermolecular interactions within aself-assembled monolayer on one side of a cantilever beam. This canproduce a sufficiently large torque to bend the cantilever beam andgenerate motion.

forces, which arise due changes in molecular configura-tions or charges that are induced by the reactions. Fromthe view point of thermodynamics, the reaction on onesurface changes its surface free energy density or sur-face tension, which produces a differential torque thatbends the cantilever. This is an example where the freeenergy reduction of biomolecular interactions can betranslated into increase of mechanical free energyof thecantilever beam. What is critical, however, is the factthat this technique can be used to detect biomolecularreactions under conditions and at levels that are clini-cally important, examples of which are described in thenext section. In addition, because free energy reductionis the driving force for all biomolecular reactions, thiscould be a universal technique for bioassays. Finally,because microcantilever beams are readily amenable tomicroarray formation, one could envision multiplexedbioassays for high-throughput analysis.

The goal of this paper is to review the past researchin this field and provide a look at the near future. Sec-tion 2 describes past single-cantilever experiments onDNA hybridization and single base pair mismatch de-tection, as well as on quantitative detection of prostatespecific antigen (PSA). Section 3 describes our efforton microarray development. Section 4 concludes withsome noteworthy points that emphasize the technolog-ical relevance of this technique.

2. Single cantilever experiments

In this section, past experiments [1–7] using singlecantilever analysis are described. The set-up for theseexperiments is quite common, and hence description ofonly one type of set up, the one used in our laboratory,is provided.

2.1. Experimental set-up

Figure 2 shows the experimental setup. It consistedof a transparent fluid cell within which a gold-coatedsilicon nitride (Au/SiNx) cantilever was mounted. Thecantilevers used were 200–600µm long, 0.5µm thick,and 20–40µm wide. The fluid cell formed a liquidreservoir about 100µl in volume that was connectedto an inlet and an outlet fluid port. To detect can-tilever deflections, a low-power (≈ 1 mW) laser beamwas reflected off the cantilever and was focused onto aposition-sensitive diode (PSD). Such a set up is com-monly used in atomic force microscopes. To elimi-nate thermomechanical motion of the Au-SiNx bimate-rial cantilever due to temperature fluctuations, the glassslide and the fluid cell were mounted on thermoelectriccoolers such that the temperature of the fluid cell couldbe controlled to 25± 0.05◦C. The experiment startedby first placing a Au/SiNx cantilever in a fluid cell andthen injecting a solution of sodium phosphate buffer(PB) at pH∼ 7.0 (always with the same pH but maybedifferent ion concentration for different experiments)into the cell. The cantilever was equilibrated in the PBbuffer until a stable base line was obtained. The nextstep was to immobilize the probe molecules, whichwere resuspended in the same PB buffer used to equi-librate the cantilever, on the cantilever surface. Afterthe immobilization was completed (typically about twohours at room temperature), the fluid cell was washedthoroughly with the PB buffer to be used for hybridiza-tion. Then the cantilever was equilibrated in the samePB buffer (as that to be used for hybridization) againuntil a stable baseline was obtained. Finally, injec-tion of a solution of target molecules (resuspended inthe same PB buffer) followed. The cantilever motionwas optically monitored at both the immobilization andprobe-target binding steps. For each experiment, a newcantilever was used. The error induced by variations inthe geometry of the cantilever (length, width and thick-ness) and the position of the focused laser spot at theend of the cantilever was found to be within± 5–10%.

Fritz et al. [3] monitored the motion of two can-tilevers simultaneously, one functionalized with probebiomolecules and other without any biomolecules.They then obtained the difference signal in orderto eliminate thermomechanical motion and cantileverdrift, and capture only the motion induced by biomolec-ular reactions. This is a better approach for measure-ments as long as the drift and the thermomechanicalresponse of the two cantilevers are the same.

A. Majumdar / Bioassays based on molecular nanomechanics 169

LiquidOutput

PositionSensitiveDetector Laser

O-ring

Glass Slide

TemperatureSensor

Fluid Cell

ThermoelectricCooler

Heat Sink

MicromechanicalCantilever

LiquidInput

LiquidOutput

PositionSensitiveDetector Laser

O-ring

Glass Slide

TemperatureSensor

Fluid Cell

ThermoelectricCooler

Heat Sink

MicromechanicalCantilever

LiquidInput

Fig. 2. Schematic diagram of the experimental setup showing a fluid cell within which a microcantilever beam was mounted. The scanningelectron micrograph on the right shows the geometry of a Au-coated silicon nitride cantilever beam that was 200µm long, 0.5µm thick, and witheach leg 40µm wide. To measure the cantilever deflection, a laser was reflected off the back of the cantilever and focused onto a position-sensitivedetector. The reagents were injected into the fluid cell using the liquid ports. The fluid cell was mounted on a temperature controlled glass slide.

Fig. 3. Changes in Au-Si cantilever deflection due to hybridizationof a probe ssDNA (50 ng/µl or 8 µM concentration) in the distal endwith complementary target ssDNA of different lengths – 20 nt, 15 nt,10 nt, and 9 nt (40 ng/µl or 3–6µM concentration). Also shown isthe absence of cantilever deflection for a non-complementary targetssDNA. The data clearly suggests that differences in nanomechanicalmotion due to one nucleotide difference in length can be observed.

2.2. DNA hybridization

Single stranded DNA (ssDNA) can be immobilizedusing gold-thiol strong binding on one side of a can-tilever by coating that side with gold and using a thiollinker at one end of ssDNA. ssDNA bound to the can-tilever acts as the probe (or receptor) molecule for thetarget complementary strands. After immobilizing theprobe ssDNA, a solution containing complementarytarget ssDNA was injected into the fluid cell at the samePB concentration that was used to immobilize the probessDNA. Figure 3 shows the deflection profiles for the

hybridization reactions where the probe ssDNA was20 nt long and the complementary target ssDNA wereof four different lengths (20 nt, 15 nt, 10 nt and 9 nt) andchosen to be distally complementary [4]. The nanome-chanical signal was sufficiently sensitive to detect sin-gle nucleotide length differences. We have also per-formed hybridization experiments using 30–50 nt longDNA and the results have shown very similar trends.The observation that the cantilever bent upwards in allcases suggests that hybridization relieved the compres-sive stress created during immoblization of thiolatedprobe ssDNA. To confirm that the signals were dueto hybridization, a solution of a non-complementarytarget ssDNA was used and was found to produce nodeflection.

It was found that the amount of deflection during ss-DNA immobilization and DNA hybridization dependedon the ion concentration in the solution. This suggeststhat electrostatic repulsive forces between neighboringDNA molecules must play a role in cantilever motion.Because each nucleotide carries a net negative chargedue to the presence of a phosphate group, one wouldexpect the hybridization to cause even more repulsiondue to the presence of additional negativecharge. How-ever, the data in Fig. 3 clearly indicates that hybridiza-tion always relieved the stress and produced upwardcantilever motion. Therefore, electrostatic or steric re-pulsion alone cannot explain the behavior.

It is well known [8] that end-graftedpolymers, at suf-ficiently high grafting densities, adopt stretched con-formations in order to reduce intersegment interactionsresulting from steric or electrostatic repulsion. Thischain stretching is, however, entropically unfavorable.


Fig. 4. Schematic diagram illustrating the mechanism of motion generation due to DNA immobilization and hybridization. Immobilization ofssDNA on the top surface bends the cantilever down. The persistence length of ssDNA is 7.5µ, and this flexibility provides an entropic drivingforce for forming curved interfaces. Hybridization increases the persistence length to about 50 nm, which significantly reduces the conformationalentropic driving force, thereby reducing the importance of curvature producing an upward cantilever motion.

Time (s)

0 500 1000 1500 2000 2500 3000

Def

lect

ion,

nm

-20

-10

0

10

20

30

40

25 mer, complementary

25 mer, distal mismatch

25 mer, proximal mismatch

25 mer, 1 internal mismatch



Fig. 5. Cantilever deflection for 25 mer thiolated probe ssDNA hybridized with complementary and mismatch target oligonulceotides.

As is well known [9], the entropic penalty can be al-leviated by adsorption onto a convex surface. This isbecause the curvature allows each chain to adopt moreconformations (hence acquiring greater conformationalentropy) as the distance from the surface increases. Atthe ionic strengths of our experiments (0.05–1 M), thepersistence length of ssDNA is 0.75 nm [10], whichcorresponds to approximately two nucleotides. Thus,for sufficiently long ssDNA molecules, the conforma-tional entropy gain by forming a curved interface is sig-nificant. Thus, in addition to electrostatic intersegmentrepulsion, there is an entropic driving force for bendingthe cantilever downwards. These forces are balancedby the strain energy of bending the cantilever, leading to

an equilibrium value of curvature and cantilever deflec-tion. The persistence length of double-stranded DNA(dsDNA) formed after hybridization is 50–80 nm [11].Thus, upon hybridization, the dramatically increasedchain stiffness makes the entropic driving force to forma curved interface unimportant, as illustrated in Fig. 4.Therefore, the cantilever strain energy and interseg-ment repulsion are balanced at a smaller curvature (i.e.smaller deflection).

Although this seemed like a plausible explanationearlier [4], further in-depth studies have shown thatthis may not be the complete picture [12]. It has beenfound that osmotic effects (entropic force for the ionssurrounding DNA) are equally important. In fact, be-


Time [min]

0 60 120 180 240

Def

lect

ion

, h [

nm

]

-40

-20

0

20

40

60

80

Injections

[HSA] = 1 mg/ml[fPSA]

6 ng/ml

60 ng/ml

No PSA Ab ([fPSA] = 60 µg/ml)

HP only ([HP] = 1 mg/ml)

No PSA

Fig. 6. Specificity of free PSA (fPSA) detection against a highbackground of human serum proteins, namely, human serum albu-min (HSA) and human plasminogen (HP), both at concentrations of1 mg/ml. The cantilevers used were 200µm long and 0.5µm thickand made of silicon nitride.

cause the distance between neighboring DNA strandsin a self-assembled monolayer is on the order of 3–5 nm, their hydration shells can overlap. Hence, hy-dration forces can become extremely important, andperhaps dominant in generating the nanomechanicalforces. Finally, it was concluded that because hydra-tion, osmotic and conformational entropic forces arehighly non-linear with intermolecular distance, the dis-order in the self-assembly of probe molecules is an im-portant parameter that controls the level of cantileverdeflection. It is clear that although we understand someaspects of the origins of cantilever motion, much re-mains to be learnt.

Figure 5 shows cantilever deflection versus time forDNA hybridization [5], in which the probe ssDNA was25 nt long. Target ssDNA of 25 nt long was used,but in some cases a single base pair mismatch wasintroducedeither in the proximal or distal ends, or in themiddle. It can be seen that single base pair mismatchescan be mechanically distinguished. What is intriguing,however, is the fact that when the target ssDNA lengthis reduced to 10 nt, then introducing a single base pairmismatch moved the cantilever downwards (oppositeto the other cases), while introducing two base pairmismatches produced almost the double the downwardsdeflection. The origins of this are not yet understood.

The fact that single base pair mismatches can be me-chanically detected opens the possibility of analyzingsingle nucleotide polymorphisms (SNPs) that impor-tant not only in detecting diseases for a wide varietyof genomic studies. It is also important to point outthat while DNA microarrays that rely on fluorescent

detection require probe DNAs that are typically 20 merin length, the cantilever based technique might allowdetection of shorter oligonucleotides, which could beimportant in many genomic applications.

2.3. Antigen-antibody reactions

Antigen-antibody binding reactions are a class ofhighly specific protein-protein interactions. When an-tibody molecules were immobilized to one surface ofa cantilever, it has been shown that specific bindingbetween antigens produced cantilever deflection [1–3]. In the last two years, joint work between threelaboratories1 have shown the prostate specific antigen(PSA) can be detected at concentrations and under con-ditions that are clinically relevant [6]. It should benoted that PSA that is detectable in serum has provento be an extremely useful marker for early detection ofprostate cancer and in monitoring patients for diseaseprogression and treatment efficacy.

To detect PSA using cantilevers, a single polyclonalanti-PSA antibody was covalently linked to cantileversurface. The cantilevers used were made of silicon ni-tride (SiNx) with a thin coating of gold (Au) on oneside and with length of 200µm, thickness of 0.5µm,with each leg width of 20µm. A Au film was used toimmobilize the PSA antibody to the cantilever throughthiol chemistry. Figure 6 shows cantilever deflectionas a function of time for different concentration of PSAin a mixture of human serum albumin (HSA) and hu-man plasminogen (HP) as simulated background, eachat a high concentration of 1 mg/ml. Similar resultswere observed against a background of bovine serumalbumin (BSA) at 1 mg/ml. The specificity of PSAdetection was verified by exposing PSA to a cantileverwithout any PSA antibody, where negligible deflectionwas found. When a cantilever functionalized with PSAantibody was exposed to HSA and HP in the absenceof fPSA, no significant cantilever deflection was ob-served. This indicated the high specificity betweenPSA antigen-antibody binding in the background ofHSA and HP.

As the data indicates, it took considerable time forthe deflection to reach steady state. This was largelyattributed to the time required for the PSA molecules todiffuse in a fluid cell. The time could be drastically re-

1Arun Majumdar, Mechanical Engineering Dept., UC Berkeley;Thomas Thundat, Life Sciences Division, Oak Ridge National Lab;Ram Datar and Richard Cote, Dept. of Pathology, U. SouthernCalifornia.


PSA Concentration [ng/ml]10-2 10-1 100 101 102 103 104 105

Ste

ady-

stat

e D

efle

ctio

n, h

s [n

m]

0

50

100

150

200Clinical Threshold ofPSA Concentration(4 ng/ml)

Cantilever: 200 µm long, 0.5 µm thick

Cantilever: 366 µm long,0.65 µm thick

Cantilever:600 µm long, 0.65 µm thick

[BSA] = 1 mg/ml

cPSA

fPSA

fPSAfPSA

Fig. 7. Steady state cantilever deflections as a function of PSA concentrations for three different cantilever geometries. Note that longer cantileversproduce larger deflections for the same PSA concentration, thereby providing higher sensitivity. Using 600µm long and 0.65µm thick siliconnitride cantilevers, it was feasible to detect fPSA concentration of 0.2 ng/ml.

Fig. 8. Electron micrographs of two different chips containing arrays of microcantilever beams. In one, the cantilevers have only one arm, whilein the other the cantilevers have two arms. In both cases, a square paddle at the end of the cantilever was used for reflecting light.

duced if the fluid cell is reduced in size (see Section 3).What is important, however, is the observation that thesteady-state deflection depended on the concentrationof PSA in solution. Figure 7 plots the steady-statecantilever deflection as a function of PSA concentra-tion for three different cantilever lengths. It can beobserved that longer cantilevers are more sensitive andproduce larger deflections for the same PSA concen-trations. What is critical is the demonstration that PSAcan be detected at the lowest level of 0.2 ng/ml, whichis comparable to other techniques such as ELISA. It isalso noteworthy that the clinical threshold for detectionof prostate cancer is 4 ng/ml. Wu et al. [6] have providedetailed discussion on the advantages of the cantileverbased technique compared to ELISA.

3. Cantilever microarrays

The experiments in Section 2 clearly demonstratethat nanomechanical detection of biomolecules can bea useful approach for biomolecular analysis. However,all the results so far have been derived from single can-tilever experiments. The true merit of this technologywill be realized if one could develop microcantileverarrays for multiplexed high-throughput bioassays. Ourgroup and those of a few others have started develop-ing microcantilever arrays for this purpose. In this sec-tion, a brief synopsis of our current activity is provided,while a detailed discussion will appear in a separatepublication [13].


Si

Glass/PDMS

Cantilever

Micropipette 100 m

10 m

Si

Glass/PDMS

Cantilever

Micropipette 100 m

10 m

Fig. 9. A schematic of the cantilever and the reaction chamber. A micro reaction chamber is integrated on the chip for each cantilever to allowseparate functionalization. Each chamber has one inlet and one outlet to promote bubble-free filling. (b) SEM pictures of a cantilever and itspaddle. The cantilever has a 200µm× 40µm leg and a 100µm× 100µm paddle for optical readout. The ridge on the paddle provides rigidityto the paddle.

Fig. 10. A schematic of the optical readout system. An expanded laser beam illuminates the microarray. The paddle at the end of a cantileverworks as a mirror to reflect the laser beam. When a cantilever deflects, the paddle changes its angle so the reflected spot shifts on the CCD screen.Two reflection spots are shown.

Figure 8 shows electron micrographs of two dif-ferent chips, each containing an array of microcan-tilevers. Using traditional bulk and surface microma-chining techniques, the array was fabricated on a siliconsubstrate with a glass or a PDMS cover. The microarrayintegrates a reaction chamber with each cantilever to al-low for individual cantilever functionalization specificto the target analyte. The reaction chambers have oneinlet and one outlet to promote chamber filling. Thechambers are made sufficiently small (1µl) such thatdiffusion times of large biopolymers will be on the or-der of a few minutes. Currently, a micropipette is usedto inject fluid into the reaction chamber (Fig. 9). At thefree end of the cantilever, a rigid paddle acts as a mirrorsurface for the optical readout method described later.We have preferred to use PDMS cover instead of a glass

one, since the latter requires a high-temperature bond-ing process that can warp the cantilever while PDMSbonding is a room temperature process. The PDMScover is made of Sylgard� 184 Silicone Elastomer. Itis fabricated using a silicon wafer mold. The cover isthen aligned with the silicon chip to form individualreaction chambers. The microcantilever array is finallysubjected to oxygen plasma to make the PDMS surfacehydrophilic and then immersed and stored in clean DIwater.

Simultaneous detection of deflections of hundredsor thousands of cantilevers with 1–5 nm resolution re-quires thoughtful design. So far we have opted for anoptical technique. If there are N cantilevers, one canuse N sources and 1 detector, 1 source and N detec-tors, or N sources and N detectors. We have selec-


tion the second option, where we use one laser whosebeam is expanded to be incident on the whole microar-ray. Reflection of the laser from the reflector paddle ofeach cantilever is then directed towards a CCD camera,which monitors the laser spots reflected from multiplecantilevers. Figure 10 shows a schematic diagram ofthe optical system. Currently, we are performing mul-tiplexed bioassays using this array system, the resultsof which will be published elsewhere.

4. Conclusions

Recent experiments have shown that when specificbiomolecular reactions are confined to one surfaceof a diving-board shaped microcantilever beam, thechanges in intermolecular nanomechanical forces gen-erate sufficient torque to bend the cantilever beam.In this paper, past research on detection of DNA hy-bridization, single base pair mismatch, as well as quan-titation of prostate specific antigen (PSA) is reviewed.The origins of cantilever is discussed and it is suggestedthat since cantilever motion is generated due free en-ergy reduction on the cantilever surface, and becausefree energy reduction is common to all reactions, thistechnique can offer a common platform for label-freedetection of various types of receptor-ligand biomolec-ular binding. It is argued, however, that the true poten-tial of this approach can only be realized through thedevelopment of microcantilever arrays for multiplexedhigh-throughput bioassays. Our initial progress in thisarea is also briefly discussed.

Acknowledgements

This work was supported through grants from theNational Cancer Institute, Department of Energy andDARPA. The author is greatly indebted to his collabora-tors: Thomas Thundat,Karolyn Hansen, and Haifeng Jifrom Oak Ridge National Lab; Ram Datar and RichardCote from University of Southern California; MichaelHagan and Arup Chakraborty from University of Cali-fornia, Berkeley. This work could not have been possi-

ble without the hard work, innovation, and persistenceby the author’s graduate students: Guanghua Wu, MinYue, Srinath Satyanarayana, Daniel Dedrick and HenryLin. The author will always remain grateful for theirtremendous contributions.

References

[1] T. Thundat, P.I. Oden and R.J. Warmack, Microcantilever sen-sors,Microscale Thermophys. Eng. 1 (1997), 185–199.

[2] R. Raiteri, G. Nelles, H.-J. Butt, W. Knoll and P. Skladal,Sensing biological substances based on the bending of micro-fabricated cantilevers,Sens. Actuators B 61 (1999), 213–217.

[3] J. Fritz, M.K. Baller, H.P. Lang, H. Rothuizen, P. Vettiger,E. Meyer, H.J. Guntherodt, Ch. Gerber and J.K. Gimzewski,Translating biomolecular recognition into nanomechanics,Science 288 (2000), 316–318.

[4] G. Wu, H. Ji, K. Hansen, T. Thundat, R. Datar, R. Cote,M.F. Hagan, A.K. Chakraborty and A. Majumdar, Origin ofnanomechanical cantilever motion generated from biomolec-ular interactions,Proceedings of National Academy of Science98 (2001), 1560–1564.

[5] K. Hansen, H. Ji, G. Wu, R. Datar, R. Cote, A. Majumdar andT. Thundat, Cantilever-based optical deflection assay for dis-crimination of DNA single-nucleotide mismatches,AnalyticalChemistry 73 (2001), 1567–1571.

[6] G. Wu, R. Datar, K. Hansen, T. Thundat, R. Cote and A.Majumdar, Bioassay of prostate specific antigen (PSA) usingmicrocantilevers,Nature Biotechnology 19 (2001), 856–860.

[7] G. Wu, Nanomechanical biosensor for high throughput ge-nomic and proteomic analysis, Ph.D. Dissertation, Universityof California, Berkeley, 2001.

[8] S.S. Patel and M. Tirrell, Measurement of forces betweensurfaces in polymer fluids,Ann. Rev. Phys. Chem. 40 (1989),587–635.

[9] C.M. Wijmans and E.B. Zhulina, Polymer brushes at curvedsurfaces,Macromolecules 26 (1993), 7214–7224.

[10] S.B. Smith, Y. Cui and C. Bustamante, Overstretching B-DNA: The elastic response of individual double-stranded andsingle-stranded DNA molecules,Science 271 (1996), 795–799.

[11] C.G. Baumann, S.B. Smith, V.A. Bloomfield and C. Busta-mante, Ionic effects on the elasticity of single DNA molecules,Proc. Natl. Acad. Sci. 94 (1997), 6185–6190.

[12] M.F. Hagan, A. Majumdar and A.K. Chakraborty, Nanome-chanical forces generated by surface grafted DNA,J. Phy.Chem. (in press).

[13] M. Yue, D.E. Dedrick, S. Satyanarayana and A. Majumdar,Microcantilever arrays for multiplexed biomolecular analysis,Proc. ASME IMECE, New Orleans, 2002, in press.

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