Single Molecule Manipulation Methods

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Single Molecule Manipulation Methods
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Methods of Single Molecule Manipulation
1873 The Dutch scientist J.D. van der
Waals proposes his theory of
continuity between the gas and liquid
states of matter All properties of matter
depend on the strength and the direction of
the forces that molecules exert on each other

1889 Svante Arrhenius suggests that the rate
of a chemical reaction is determined
by the rate of attainment of a strained, high
energy state or transition state along its
reaction coordinate
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Bulk Methods vs. Single Molecule Methods

• Bulk Methods
• Robust, but afford little control to
  investigate forces developed in
• the course of a chemical reactions.
• Measured properties are time and population
  averages Smooth
• varying. Fluctuations are mostly cancelled
  out.
• Picture An idealized molecule with
  well-defined dynamics
• Population is assumed to be homogeneous
  (unimodal distrib.)

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Bulk Methods vs. Single Molecule Methods

• Single Molecule Methods
• Molecules display a fast, instantaneous
  dynamics
• Behavior appear random and stochastic
• Fluctuations are predominant
• Molecules are seen to co-exist in various
  states. Populations are
• multimodal
• Molecules can be found in states far from the
  mean of the
• population (extreme states)

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Why single Molecule Methods?
The microscopic view matters in describing the
cell interior Many cellular processes, such
as Chromosome replication and segregation DNA
transcription, recombination, and RNA
translation Are often carried out by a few
molecules. Far from displaying smooth dynamics
these process are stochastic in nature.
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Why single Molecule Methods?
One molecule in an E. coli cell (about 1 mm3 in
volume is at a concentration of 1.6 nM.
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Why single Molecule Methods?
The advent of methods of single molecule
manipulation has made it possible, for the first
time to Measure the forces that maintain the
3D structure of macromolecules Characterize the
stress-strain relationships of molecules
Measure the forces generated in chemical
biochemical reactions Investigate
time-averaged and time-dependent fluctuations
Characterize the dynamics of molecular motors
Exert External forces and torques to alter the
extent and fate of chem. Rxns.
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Single Molecule Manipulation Experiments

• Two features distinguish single molecule
  manipulation experiments
• From their bulk counterparts
• The unique role played by forces or torques as
  direct observables
• of the experiment
• The importance of fluctuations
• Together this area of research can be called
• Mechanochemistry

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In Biochemistry.
Mechanochemical processes often involve the
formation or breaking of covalent bonds, but also
of a large number of highly stereo-specific weak
interactions. Processes as diverse as Protein
folding DNA elasticity Protein-induced bending
of DNA The stress-induced catalysis of
enzymes The dynamics of molecular
motors Induced-fit molecular recognition involve
all the generation of stresses and strains along
their reaction coordinates and the formation or
breaking of weak ints.
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Technical Requirements
I) Methods to locate molecules a microscope
that works in liquids

• Optical Fluorescence labelling, Particle
  tagging
• b) Probe Microscopes STM, SFM (AFM), SNOM

II) Means of manipulating or acting on single
molecules a) Mechanical transducers soft
cantilevers, bendable micropipettes
movable rigid
micropipettes, etc b) External Fields
Electric, magnetic and photon fields III) Methods
of spatial detection a)
diffraction-limited displacement, centroid
displacement b) optical lever detection
c) optical interference
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Methods, Capabilities and Applications
Bustamante et al. Nature Rev. Mol. and Cell
Biol., 1, 130 136 (2000).
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Difficults Inherent to Single Molecule Work
Are all molecules identical? Molecular
behavior depends a) initial conditions b)
effect of boundaries restricted config.
space if Eint kT trapping
effects if Eintgtgt kT conf. changes
Consequences Data tends to
segregate into classes of similar behavior.
Convenient to reduce the of classes by using
more homogeneous initial conditions and
minimizing boundary effects.
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Applications
Bustamante et al. Nature Rev. Mol. and Cell
Biol., 1, 130 136 (2000).
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Applications
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Applications
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Applications
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Time-length and Force Scales of Experiments
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Time Scale
The time scale in single molecule exps. is
typically sub-msec. Thus, cyclic process on the
third level can be resolved, but elementary and
intermediate processes are averaged out.
Events in single molecule manipulation
experiments result form a large number of
stochastic steps that are not directly observable
but that influence the microscopic dynamics of
the overall process. As a result, all processes
can be described as random walks or diffusions in
the parameter space of the system.
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Length Scale
The length scale is set by the type of process
and the size of the molecules under study.
Range Angstroms (Small motions in a
protein) Nanometers (Most processes) Microns
(Stretching of a long DNA)
Single molecule manipulation instruments must
be able to make and /or measure displacements of
nanometers or better. AFM and OT instruments
ßprovide these days Å detection.
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Force Scale
Forces can be Inertial Dissipative
(frictional) Related to a potential of some
sort -On single molecule experiments, inertial
forces are usually negligible compared to
frictional forces The low Reynolds number
regime.
F
Expl For a 1 micron silica bead in water, tacc
is 10-7 s, well below the time res. of most
instruments.
g fric. coeff and m spheres mass
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Range of Forces
Typica forces are in the picoNewtons regime
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Means of Manipulating Single Molecules
External Fields Electric, Magnetic, flow and
photon fields can be used effectively to exert
forces on molecules. Choice depends on -
magnitude of the force desired - degree of
control of force needed
Fields make it possible to act on molecules at a
distance. Can be an advantage or a
disadvantage. Its possible to manipulate many
molecules simultaneously, but their lack of
locality makes them less selective.
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Electric Fields
Most macromolecules are charged in solution
they can be acted on by electric fields. Typical
design
driver electrodes
probe electrodes connected to a high
impedence voltmeter and separated by a
known distance
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Migration DNA Molecules During Gel Electrophoresis
T4 DNA
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Difficulties
Current may cause Heating of the buffer
Polarization of the electrodes due to localized
ion build up Electro-endosmosis (EEO) near
charged surfaces like glass Glass bubbles at the
electrodes Arbitrary fields can be used, as long
as the electrodes are placed close enough that
the potential difference remains below 1 volt,
the dissociation potential for H2O
E-fields are easy to control and measure. But
the forces exerted on molecules are not so easily
determined. Ex DNA in solution
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Non-homogeneous E-fields
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Dielectric objects immersed in liquid, will
develop an induced-dipole moment, P in an
external field E. If the field is inhomogeneous
they will be attracted to the field with a
force
e is the dielectric polarizability of the object
relative to the fluid.
Electro-rotation
As E rotates w/ ang. freq. w P will lag by an
angle Q(w) a torque M P x E
e E2 sinQ(w) will be generated.
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Electro-rotation (cont)
For w in MHz, the applied torque is independent
of orientation since it is averaged out over all
configurations.
Method used by Washizu et al. (IEEE Trans.
Ind. Applications 29 286, 1993) and Berg and
Turner ( Biphys. J. 65 2201, 1993) to rotate
bacterial cells attached by a single flagella to
a glass surface. Applied known torques to follow
the performance by a single flagellum
aiding or opposing this rotation.
Bacterium
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Magnetic Fields
Magnetic fields are easy to generate and to
control. Are ideal to produce small forces fN.

• Method
• tether molecules to magnetic beads
  (commercially available, with a
• ferrite Fe2O3, core)
• expose them to an inhomogeneous magnetic field
• The magnetic force acting on the object is
• Typical force ranges are between 10 fN to 10 pN
  with commercial
• beads and permanent magnets.

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DNA Elasticity
Smith et al. Science (1992)
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DNA Elasticity
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DNA Elasticity
Magnetic beads often contain a preferred
magnetization axis. These beds lock at a fixed
angle with the field. This property can be used
to supercoil by over or undertwisting a single
molecule of DNA Strick et al. (1996).
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Flow Fields
Controlled flows can also be used to exert
forces on molecules or on molecules tethered to
beads. Often the force acting on a molecule can
be directly calculated from the Stokes force
acting on the bead where is the viscosity of
the fluid, r the radius of the bead and v the
flow velocity. This form is often modified
by the hydrodynamic coupling between the bead
and the surfaces of the micro-chamber.
d
r
Lorenz, Handbuch der Physik, 1907
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Experimental Test
Smith et al. Science (1992)
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Optical Tweezers
Beam Axis
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Estimating Forces
1. Assume a linear-spring restoring force 2.
Determine trap stiffness k 3. Measure Dx relative
to trap center
F k Dx
Dx
trap center
bead center
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Measuring forces by analyzing momentum of the
trap beam
F -D dP/dt
(nW/c) sin q
Light ray with power W
(nW/c) (1-cos q)
dP/dt nW/c
q
DdP/dt
input
dP/dt
output
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Force-measuring optical tweezers
liquid
l/4
l/4
OBJ
OBJ
LASER
LASER
DNA
psd
psd
pipette
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DNA Assembly Using a DNA Fishing Line
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Entropic elasticity of flexible molecules
External tension
Force (pN)
dsDNA
Thermal forces
ssDNA
Higher flexibility
Extension (mm)
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Mechanical Transducers
Cantilevers and bendable micropipettes can be
used to exert and measure forces on molecules.
The magnitude of the forces can be
readily obtained from the deflection of the
mecanical transducers, if their force
constants are known.
Typical cantilvers have force constant in the
range of 1 - 0.01 nN/nm while soft, bendable
micropipettes are about typically 100 to
1000 times softer.
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Mechanical Transducers

• Advantages
• Mechanical transducers act locally and are
  ideal to manipulate
• macromolecules on the small side of the
  spectrum.
• - Because of their dimensions, cantilevers have
  better time response
• than optical tweezers or soft bendable
  micropipettes as indicated by
• their rather high corner frequencies wc
  k/g, where k is the force
• constant of the cantilever and g its friction
  coefficient (see below).
• Disadvantages
• Dificult to calibrate.

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Balancing Signal, Noise and Time Resolution
At temperature T, a linear system, such as a
cantilever experiences a mean square displacement
noise ltDx2gt given by the Equipartition
Theorem Where k is the force constant of the
cantilever and k is Boltzmanns constant.
Correspondingly, its mean quadratic force
fluctuation will be
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Balancing Signal, Noise and Time Resolution
Note that a sort of Uncertainty Thermal
Relation applies for such systems, since the
product of the root mean square fluctuations in
position and force is equal to the thermal
energy Thus, the stiffer the mechanical
transducer, the smaller its position noise and
viceversa. Fluctuations are not spread
uniformly over all frequencies, however. The
spectrum of fluctuations is determined by the
proportionality that exists between the ability
of the linear system to absorb thermal energy and
its ability to dissipate it by friction.
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Balancing Signal, Noise and Time Resolution
This result is embodied in the so-called
Fluctuation-Dissipation Theorem The mean
quadratic displacement of a linear device per
unit frequency at frequency w is

where, as before, g and wc are the friction
coefficient and the corner frequency of the
device. A 1 mm diameter bead in a typical optical
trap has a wc 1000 Hz, whereas that of a 100 mm
long 10 mm wide cantilever is 6000 Hz.
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Balancing Signal, Noise and Time Resolution
Thus, a transducer with higher corner frequency
makes it possible to take more data in the same
amount of time. Moreover, since
Thus, for the same k, the total area under
the power spectrum is the same.
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Balancing Signal, Noise and Time Resolution
Measurements are often performed in a narrow band
(bandwidth B) around the frequency of the signal.
Suppose that the signal to be measured is a
force developed by a molecular motor. The
signal-to-noise in that measurement, for B ltlt wc
is
Thus for the same k and the same B, the
signal- noise ratio of the meas. will be
higher for the transducer having
the higher corner frequency
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Balancing Signal, Noise and Time Resolution
that is, for the one having the smaller friction
coefficient, or, for the one possessing the
smallest dimensions. This is the rationale for
the development of mini-cantilevers, whose
stiffness are comparable to regular
cantilevers, but whose gs are significantly
smaller and their corner frequencies,
correspondingly larger.
Notice also that the S/N ratio is independent of
the stiffness of the transducer as k
decreases, the noise increases exactly as fast
as the signal. Thus a softer transducer does
not provide higher S/N than a stiffer one.
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Balancing Signal, Noise and Time Resolution
Finally, the S/N can be increased by
reducing the bandwidth and therefore the
time-resolution of the measurement, but this
approach is ultimately limited by the
frequency of the biological process.
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Difficulties
Current may cause Heating of the buffer
Polarization of the electrodes due to localized
ion build up Electro-endosmosis (EEO) near
charged surfaces like glass Glass bubbles at the
electrodes Arbitrary fields can be used, as long
as the electrodes are placed close enough that
the potential difference remains below 1 volt,
the dissociation potential for H2O
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Reversible Pulling of P5ab
Handle behavior is well-predicted by
Force (pN)
Bustamante et al., Science 265, 1599 (1994)
Extension (nm)
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Bi-stable Length with Constant-ForceFeedback
Directly observe k1 , k-1, and Keq
as a function of force under exp.
conditions
length
time