Single molecule manipulation using multiple atomic force microscopes

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Single molecule manipulation using multiple
atomic force microscopes

• Presenter Matt Clark
• Advisor Dr. Mark Paul
• Department of Mechanical Engineering

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Methods of single molecule manipulation

• Mechanical Transducers
• Scanning force microscopy cantilevers
  commercially available. Frange 10-11 10-7 N
• Microneedles higher force sensitivity, but less
  standardized than SFM. Frange 10-12 10-10
  N
• External Fields less resolute displacements
• Flow field complex calibration. Frange 10-13
  10-9 N
• Magnetic field magnetic force must be measured
  indirectly. Frange 10-14 10-11
  N
• Photon field can damage samples. Frange
  10-13 10-10 N
• Bustamante, et. al. Grabbing the cat by the
  tail manipulating molecules one by one.
  Nature. Nov. 2000. p130.

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Microscopy Cantilevers

• Operate in H20 (ideal)
• Commercially available
• Tip radius 10nm
• Micro and nano scale
• probes available
• The probes can be constructed on site in any
  number of geometries and sizes (lt 100nm).
• Rectangular or trapezoidal cross-section
• Rectangular or triangular planform
• High spatial resolution.
• Widely used, standardized calibration.
• http//stm2.nrl.navy.mil/how-afm/how-afm.html

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Atomic Force Microscopy

• Uses tip deflection( vertical or torsional ),
  applied force, or constant oscillations to
  measure surface properties
• Topography
• Elasticity
• Roughness
• For a probe that is a rectangular cantilevered
  beam
• composed of silicon ( E 1.74 1011 N/m2, ?c
  997 kg/m3 ).
• Length L, thickness h, width w, Mass moment about
  the width I, spring constant k, resonant
  frequency ?0. C1 is the constant for the first
  cantilever mode.

w h3
----
I
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System Modeling

• Cantilevered beam in fluid can be modeled as a
  simple harmonic oscillator.
• mf is the effective mass of the beam in fluid, ?f
  is the fluidic damping, and the right hand side
  is the stochastic forcing of the fluid.
• Predict motion of single microscopy probe
• beam theory
• fluctuation dissipation theorem
• modeling of the stochastic equations of the beam
  immersed in fluid.
• Verify numerical simulations using system model.

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Fluctuation-Dissipation Theorem

• Proposed by Einstein in 1905.
• States that the way a system absorbs energy is
  directly related to the way it dissipates energy.
• F(t) kbT D(t)
• kb 1.38 10-23 J/K is Boltzmanns constant and T
  is the absolute temperature
• Normalize motion by the external forcing.
• By applying this theorem it is possible to derive
  the motion of a stochastically forced beam from
  its deterministic motion.

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Importance of single molecule analysis

• Gives better understanding of macromolecule
  properties
• Molecule walkers nanometer scale transport
  mechanisms
• Assembly line microtubule manipulation
• Nanometer scale system construction

http//www.imb-jena.de/kboehm/Kinesin.html
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Kinesin base molecular motors

• 50 nm initial length
• Undergoes conformational change upon reaction
  with ATP
• Protein folds back on itself temporarily
• Changes the effective spring constant
• Change is short term relative to event frequency

Force Scale pN Conformation Time Scale ms
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Correlated measurement system

• Most microscopy probes can not resolve to the
  needed force scale.
• Correlated measurements lower the noise floor.
• Measure using two AFM cantilevers
• Motion of one beam causes hydrodynamic
  interaction with the other beam.
• A satisfactory system minimizes the effect one
  probe has on the other.
• Once correlations (ltx1(0)x1(t)gt, ltx1(0)x2(t)gt)
  for the two beams are known, information about
  macromolecular samples can be derived.
• Gives better force resolution than a single
  cantilever.

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Predicting system measurement realms

• Run numerical simulations of two cantilevers in
  fluid (see below).
• Compare results with single cantilever data and
  modeling.
• Derive system force and time scales
• Force sensitivity comes from the maximum spatial
  correlation.
• F11 k ltx1(0)x1(t)gt1/2 F12 k
  ltx1(0)x2(t)gt1/2
• Time scale comes from the frequency at which the
  correlations exist ( G11(?), G12(?) ).

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Two probes (L197?m, h2?m, w29?m) give the
noise spectrum shown. ? 25 kHz, giving a time
scale of 0.04 ms.
Not to scale
However, the force sensitivity for beams of this
size is on the order of nano-Newtons. Therefore
it is necessary to use smaller probes in order to
measure protein dynamics.
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Summary
The analysis of individual macromolecules helps
to give insight into their properties and
operation. We propose a method for manipulating
single macromolecules using current technology.
The use of atomic force microscopy probes allows
for less expensive experiments with easier
calibration. In order to obtain the force
resolutions necessary, a correlated measurement
system will be used. The force sensitivity and
time scales for a system can be predicted
theoretically before they are tested in the
laboratory. Once a suitable system for measuring
the dynamics of kinesin based macromolecules has
been found, the setup will be constructed by a
partner group at the California Institute of
Technology in order to test its performance.
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Conclusions
A process has been determined for the theoretical
verification of measurement systems. Using this
procedure, the expected force sensitivity and
time scale for a basic system has been found.
This basic system does not resolve forces as
small as those required. However, using the same
process other setups can be analyzed until a
suitable system is found for the measurement
realm of interest. Once a suitable system has
been found, verified, and tested, this process
can be repeated for any macromolecular
measurement regime desired.