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TECHNICAL PAPERS

Dynamic Analysis of a Protein-Ligand Molecular Chain Attached to an Atomic Force Microscope

[+] Author and Article Information
Deman Tang, Earl H. Dowell

Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300

J. Vib. Acoust 126(4), 496-513 (Dec 21, 2004) (18 pages) doi:10.1115/1.1804999 History: Received April 01, 2003; Revised January 01, 2004; Online December 21, 2004
Copyright © 2004 by ASME
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References

Florin,  E. L., Moy,  V. T., and Gaub,  H. E., 1994, “Adhesion Between Individual Ligand Receptor Pairs,” Science, 264, pp. 415–417.
Moy,  V. T., Florin,  E. L., and Gaub,  H. E., 1994, “Intermolecular Forces and Energies Between Ligand and Receptor,” Science, 266, pp. 257–259.
Lee,  G. U., Chrisey,  L. A., and Colton,  R. J., 1994, “Direct Measurement of the Forces Between Complementary Strands of DNA,” Science, 266, pp. 771–773.
Florin,  E. L., Rief,  M., Lehmann,  H., Ludwig,  M., Dornmair,  C., Moy,  V. T., and Gaub,  H. E., 1995, “Sensing Specific Molecular Interactions With the Atomic Force Microscope,” Biosens. Bioelectron., 10, pp. 895–901.
Shapiro,  B. E., and Qian,  Hong, 1997, “A Quantitative Analysis of Single Protein-Ligand Complex Separation With the Atomic Force Microscope,” Biophys. Chem., 67, pp. 211–219.
Grandbois,  M., Beyer,  M., Rief,  M., Clausen-Schaumann,  H., and Gaub,  H. E., 1999, “How Strong Is a Covalent Bond?,” Science, 283, pp. 1727–1730.
Rudd,  R. E., and Broughton,  J. Q., 1999, “Atomistic Simulation of MEMS Resonators Through the Coupling of Length Scales,” J. Model. Simul. Microsyst., 1, p. 29.
Rudd,  R. E., and Broughton,  J. Q., 2000, “Concurrent Coupling of Length Scales in Solid State Systems,” Phys. Status Solidi B, 217(1), pp. 251–281.
Dowell,  E. H., and Tang,  D. M., 2003, “Multiscale, Multiphenomena Modeling and Simulation at the Nanoscale: On Constructing Reduced Order Models for Nonlinear Dynamical Systems With Many Degrees of Freedom,” ASME J. Appl. Mech., 70(3), pp. 328–338.
Haile, J. M., 1992, Molecular Dynamics Simulation, Wiley, New York.
Basso,  M., Giarre,  L., Dahleh,  M., and Mezic,  I., 2000, “Complex Dynamics in a Harmonically Excited Lennard-Jones Oscillator: Microcantilever-Sample Interaction in Scanning Probe Microscopes,” ASME J. Dyn. Syst., Meas., Control, 122, pp. 240–245.
Rong-Fong,  Fung, and Shih-Chien,  Huang, 2001, “Dynamic Modeling and Vibration Analysis of Atomic Force Microscope,” ASME J. Vibr. Acoust., 123, pp. 502–509.

Figures

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Schematic diagram of macromolecular chain model with AFM measurement system
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Nonlinear interatomic force versus the interatomic separation r/σ
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Nondimensional static equilibrium parameter Δ/σ versus base position of tip probe
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Total potential energy versus the interatomic separation r/σ for I=1
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(a) Total potential energy versus the interatomic separation x1/σ,x2/σ, for I=2 and (b) corresponding contour plot
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(a) Total potential energy versus the interatomic separation x99/σ and x100/σ for I=100 and (b) corresponding contour plot
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Time history for A0/σ=0.2,μ=0.01 and I=1
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FFT analysis of both linear and nonlinear responses for A0/σ=0.2,μ=0.01, and I=1
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Dynamic response behavior for A0/σ=0.5,μ=0.1095,x/σ|τ=0=1.2, and I=1
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FFT analysis of the dynamic response for A0/σ=0.5,μ=0.1095,x/σ|τ=0=1.2, and I=1
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RMS response amplitude versus ω/Ω for A0/σ=0.1,L/σ=1.0, and I=1
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Nonlinear and linearized time histories for A0/σ=0.2,μ=0.02,x/σ|τ=0=1.0, and I=2
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Chaotic behavior for A0/σ=2.6,μ=0.45,x1/σ|τ=0=1.0,x2/σ|τ=0=2.0, and I=2
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FFT analysis of the dynamic response for A0/σ=2.6,μ=0.45,x1/σ|τ=0=1.0,x2/σ|τ=0=2.0, and I=2
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RMS response amplitude versus ω/Ω for A0/σ=0.2,L/2σ=1.0, and I=2
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Eigenvalues and eigenmodes for the linearized perturbation system with I=1000 and d=0
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Dynamic responses of the macromolecular chain for A0/σ=0.2 and 4, and μ=0.02
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Rms amplitude of each atom A0/σ=1 and μ=0.01
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Total rms error (linear compared to nonlinear response) versus excitation amplitude A0/σ for different excitation frequency μ=0.01, and 0.02
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Dynamic response of the macromolecular chain using the fully linear reduced-order model with the quasi-static correction (QSC) for A0/σ=1 and μ=0.03
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Total rms error versus total number of eigenmodes retained in the reduced-order model for A0/σ=1 and μ=0.01,0.02,0.03 using the fully linear reduced-order model with quasi-static correction
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Dynamic response of the macromolecular chain using combined linear/nonlinear reduced-order model with the quasi-static correction (QSC) for two nonlinear elements included (mn=2) and A0/σ=1
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Total rms error versus eigenmodes for two nonlinear elements included (mn=2),A0/σ=1 and μ=0.01,0.02,0.03 using the combined linear/nonlinear reduced-order model with quasi-static correction
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Dynamic response of the macromolecular chain using the fully nonlinear reduced order model with the quasi-static correction for A0/σ=1 and μ=0.03
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Total rms error versus total number eigenmodes included for A0/σ=1 and μ=0.01, 0.02 and 0.03 using the full nonlinear reduced-order model based on the quasi-static response correction
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Total rms error of the fully linearized response to the fully nonlinear response versus nondimensional excitation amplitude, A0/σ, for μ=0.03
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Dynamic response of the macromolecular chain using the fully nonlinear reduced order model based on the linearized response correction for A0/σ=2,3,4 and μ=0.03
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Total rms error vs. total number eigenmodes included for μ=0.03 and A0/σ=1,2,3 and A0/σ=4,5 using the full nonlinear reduced order model based on the linearized dynamic response correction (LDRC)
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The percentage of the retained eigenmodes needed to the total (1000) number of modes vs. the excitation amplitude, A0/σ, for a permitted total rms error of 5% and μ=0.03
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Dynamic response of the macromolecular chain using the fully nonlinear reduced order model based on the quasi-static response correction (QSRC) and based on the linearized dynamic response correction (LDRC) for A0/σ=3,μ=0.03 and 10 eigenmodes retained in the calculations
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Computational rms error between the approximate and exact solutions of the nonlinear algebraic equation (51) versus the nondimensional excitation amplitude A0/σ for μ=0.01 and I=1000
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Total rms error versus total number eigenmodes included for A0/σ=1 and μ=0.01 and 0.02 using the combined linear/nonlinear reduced-order model with quasi-static correction

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