17.11.02 · mol-cell-bio / methods-techniques

Optical tweezers and single-molecule force spectroscopy

shipped3 tiersLean: none

Anchor (Master): Ashkin 1970 Acceleration and Trapping of Particles by Radiation Pressure (Phys. Rev. Lett. 24); Ashkin-Dziedzic-Yamane 1986 Optical trapping and manipulation of single cells (Nature 330); Svoboda-Block 1993 Force fluctuations and substeps in single kinesin molecules (Nature 365); Bustamante-Bryant-Smith 2003 Ten years of tension: single-molecule DNA mechanics (Nature 421); Evans-Ritchie 1997 Dynamic strength of molecular adhesion bonds (Biophys. J. 72)

Intuition Beginner

A human hair feels a force of about one gram-weight. A single molecule of DNA, pulled apart, resists with about one trillionth of that — a piconewton. The gap between those scales is enormous, and for most of biology's history it put single molecules out of reach. You could weigh a cell, but not a motor protein. Optical tweezers closed that gap. They grab one molecule, hold it still, and report the force it generates as it works.

The trick uses light itself as the handle. A laser beam, focused tightly through a microscope lens, carries momentum. When the beam bends around a transparent bead — a glass sphere the size of a virus — the bead nudges toward the brightest part of the beam, the focal point. Move the beam and the bead follows. Fasten a molecule to the bead, anchor the other end, and the molecule is now held between two controlled points. Pull. The bead drifts off-center by a distance proportional to the force on the molecule. Measure the drift and you have measured the force.

Why this matters: a single kinesin motor walks along a track in steps of exactly eight nanometers. Each step burns one energy molecule and pushes against a load. Optical tweezers caught those steps one at a time, settled the long argument about whether motors walk or slide, and turned a motor protein from a biochemical sketch into a measured machine.

Visual Beginner

The picture shows the trap as two panels. The left panel is a side view: a laser focused through a high-magnification lens to a tight waist inside a water-filled chamber. A glass bead sits at the focal point, with arrows showing the gradient force pulling the bead toward the waist (the bright spot) and a weaker scattering force pushing it along the beam. A DNA molecule stretches from the bead to a second bead stuck to the chamber floor. The right panel is a force-versus-extension plot: the DNA molecule stretches under load, with a flat region where the molecule resists and a steep region where it nearly breaks.

The flat-to-steep shape is the molecular signature. The bead's drift away from the trap center reads off the force on that curve at every extension.

Worked example Beginner

Calibrate an optical trap by watching a trapped bead jitter with Brownian motion, then use it to measure the maximum force a kinesin motor produces.

Step 1. Trap a bead of radius 500 nanometers in water at room temperature. The bead jitters because water molecules keep bumping it. Track its position and find the spread of its jitter. Suppose the standard deviation of the position is 8 nanometers.

Step 2. The trap behaves like a spring, and a spring's stiffness follows from equipartition: stiffness times the mean-squared displacement equals the thermal energy scale. With mean-squared displacement of 64 square nanometers and thermal energy of about 4.1 times $1 0^{- 21}$ newton-meters, the stiffness is thermal energy divided by mean-squared displacement, giving roughly 0.064 piconewtons per nanometer.

Step 3. Attach a kinesin motor between the trapped bead and a fixed bead. Let the motor walk. Watch the bead drift off-center by 5 nanometers against the motor's pull. Force equals stiffness times displacement: $0.064 \times 5 \approx 0.32$ piconewtons.

Step 4. Raise the load by moving the trap. The motor stalls when the bead has drifted 110 nanometers, giving $0.064 \times 110 \approx 7$ piconewtons. That is the stall force of a single kinesin molecule.

What this tells us: the thermal jitter of a trapped bead is not noise to suppress but a calibration signal. Reading the jitter sets the spring constant, and reading the drift under load reads out the force, all from one trapped particle.

Check your understanding Beginner

Exercise (easy, multiple choice).

What physical effect pulls a transparent dielectric bead toward the focus of a tightly focused laser beam?

A. The bead is heated and expands into the focus B. The bead scatters light so hard it is pushed forward C. The gradient of light intensity draws the bead toward the brightest point, the focus D. The bead is magnetic and responds to the beam's magnetic component

Hint

A dielectric in an electric field polarizes. The energy of a polarizable object is lower where the field is stronger. A focused beam has its strongest field at the focus.

Answer

C. The gradient force on a polarizable bead points up the intensity gradient, toward the focus. The scattering force (B) is real but pushes the bead along the propagation direction; the trap balances the two. Heating is negligible for transparent beads. Feedback-correct: gradient trapping is the load-bearing mechanism. Feedback-wrong: scattering alone would push the bead out of the trap, not hold it.

Formal definition Intermediate+

An optical trap is a harmonic potential well in three dimensions, generated by a single laser beam brought to a diffraction-limited focus through a high-numerical-aperture objective. The force on a dielectric sphere of radius $r$ and refractive index $n_{p}$ immersed in a medium of refractive index $n_{m}$ and held at displacement $x$ from the focus is, in the paraxial and Rayleigh regimes,

F (x) = - κ x + O (∣ x ∣^{3}),

with the trap stiffness $κ$ splitting into a transverse gradient component and an axial component weakened by scattering along the propagation direction.

Definition (trap stiffness). The trap stiffness $κ$ is the coefficient of the linear restoring force per unit displacement, measured in piconewtons per nanometer. A trap is operational when $κ$ exceeds the Brownian force scale $k_{B} T / ℓ$ over the molecular length $ℓ$ of interest, so that thermal drift is bounded.

Definition (force-extension measurement). A single-molecule tether is constructed between a trapped bead and a fixed bead (or second trap). The extension $z$ is the bead-to-bead distance; the force $f$ is read out as $f = κ Δ x$ , where $Δ x$ is the trapped bead's displacement from its zero-force position. The pair $(z, f)$ traces a force-extension curve.

Counterexamples to common slips Intermediate+

Conflating the bead displacement with molecular extension. The bead moves in its harmonic well under force, but that movement is the force readout, not the molecular stretch. The molecular extension is the bead-to-bead distance minus the unloaded tether length and the bead compliances; the bead displacement is a calibrated proxy for the force on the tether.
Treating the trap as a hard wall. The trap is a spring, not a wall. Under load the bead moves, and the trap's finite stiffness sets the force-resolution floor; an infinitely stiff trap would have infinite force noise from Brownian fluctuations and would rip the tether.
Ignoring the bandwidth limit. The corner frequency $f_{c} = κ / (2 π γ)$ , with $γ$ the drag coefficient, sets the roll-off of the bead's response. Forces faster than $f_{c}$ are filtered out, and the detector's sampling rate must exceed $2 f_{c}$ to avoid aliasing the Brownian spectrum.

Key theorem with proof Intermediate+

Theorem (Equipartition calibration of trap stiffness). A spherical bead of hydrodynamic drag coefficient $γ$ , harmonically trapped with stiffness $κ$ and in thermal equilibrium with a bath at temperature $T$ , has a stationary position distribution $ρ (x) \propto exp [- κ x^{2} / (2 k_{B} T)]$ . The position variance is

⟨ x^{2} ⟩ = \frac{k _{B} T}{κ},

giving the calibration formula $κ = k_{B} T / ⟨ x^{2} ⟩$ .

Proof. The Langevin equation for the trapped bead in one dimension is

γ \overset{x}{˙} (t) + κ x (t) = ξ (t),

where $ξ$ is the thermal noise with $⟨ ξ (t) ξ (t^{'})⟩ = 2 γ k_{B} T δ (t - t^{'})$ (fluctuation-dissipation). Multiplying both sides by $x (t)$ and taking the thermal average gives

γ ⟨ x \overset{x}{˙} ⟩ + κ ⟨ x^{2} ⟩ = ⟨ x ξ ⟩ .

For a stationary process $⟨ x \overset{x}{˙} ⟩ = \frac{1}{2} \partial_{t} ⟨ x^{2} ⟩ = 0$ , and the noise $x$ -correlation vanishes in equilibrium because $ξ$ at time $t$ cannot have already affected $x$ at the same instant. Therefore $κ ⟨ x^{2} ⟩ = k_{B} T$ , giving $⟨ x^{2} ⟩ = k_{B} T / κ$ .

Equivalently, the stationary distribution of the Ornstein-Uhlenbeck process solves the Fokker-Planck equation with potential $U (x) = \frac{1}{2} κ x^{2}$ and yields the Boltzmann distribution $ρ \propto exp [- U / (k_{B} T)]$ , whose second moment is $k_{B} T / κ$ by the Gaussian integral. $□$

Bridge. This calibration builds toward the worm-like-chain force law of 17.11.02 Advanced results below, where the calibrated force reads out the polymer's mechanical response, and appears again in 17.12.01 molecular motors as the bandwidth over which a single kinesin step can be resolved. The foundational reason the calibration works is that a harmonic potential in contact with a heat bath pays the same energy tax per quadratic degree of freedom regardless of what the spring is made of — laser, cantilever, or chemical bond. This is exactly the statement that the trap is dual to a Hookean spring, and the bridge is that the same equipartition logic, generalized, gives the corner frequency $f_{c} = κ / (2 π γ)$ that sets the detector bandwidth and the whole measurement floor.

Exercises Intermediate+

Exercise 2 (easy, multiple choice).

Which geometry is most commonly used to measure the force-velocity relation of a walking molecular motor?

A. Both ends of the motor freely diffusing in solution B. One end of the motor anchored to a fixed bead, the other attached to a trapped bead whose displacement reports force C. The motor embedded in a lipid bilayer with no tether D. The motor attached to an atomic force microscope cantilever with no bead

Hint

Force measurement needs a calibrated spring and a fixed reference. Optical tweezers provide the calibrated spring; a surface-anchored bead provides the reference.

Answer

B. The three-bead assay (or two-bead dumbbell) anchors one end of the motor track to a fixed bead on the coverslip and attaches the motor to a trapped bead. The trapped bead's drift under motor load is the force readout; the motor's stepping appears as discrete jumps in bead position. Feedback-correct: this is the canonical optical-trap motor assay. Feedback-wrong: free diffusion (A) gives no force readout; AFM (D) is a different technique with a cantilever spring instead of an optical gradient trap.

Exercise 3 (medium, symbolic).

Show that the one-sided power spectral density of the position of a trapped bead is $S_{x} (f) = \frac{k _{B} T}{π ^{2} γ ( f _{c}^{2} + f ^{2} )}$ where $f_{c} = κ / (2 π γ)$ is the corner frequency. Hint: take the Fourier transform of the Langevin equation and apply the fluctuation-dissipation relation.

Hint

In Fourier space the Langevin equation gives $\tilde{x} (f) = \tilde{ξ} (f) / (κ + i 2 π γ f)$ . Use $S_{ξ} (f) = 2 k_{B} T γ$ (two-sided) or $4 k_{B} T γ$ (one-sided at positive frequencies).

Answer

Fourier-transform $γ \overset{x}{˙} + κ x = ξ$ to obtain $\tilde{x} (f) = \tilde{ξ} (f) / (κ + i 2 π γ f)$ . Squaring the modulus and using the one-sided force-noise spectral density $S_{ξ} (f) = 4 k_{B} T γ$ ,

S_{x} (f) = \frac{4 k _{B} T γ}{κ ^{2} + ( 2 π γ f ) ^{2}} = \frac{k _{B} T}{π ^{2} γ ( f _{c}^{2} + f ^{2} )},

with $f_{c} = κ / (2 π γ)$ . The spectrum is Lorentzian, flat below $f_{c}$ and rolling off as $1/ f^{2}$ above. Fitting the measured spectrum to a Lorentzian gives both $κ$ (from $f_{c}$ ) and $γ$ (from the plateau), a calibration independent of equipartition.

Exercise 5 (medium, symbolic).

The Marko-Siggia interpolation formula for the force-extension relation of double-stranded DNA of contour length $L$ and persistence length $A \approx 50$ nm is

f \cdot \frac{A}{k _{B} T} = \frac{1}{4} (1 - \frac{z}{L})^{- 2} - \frac{1}{4} + \frac{z}{L} .

Show that for small force ( $z / L ≪ 1$ ) this reduces to a Hookean spring with stiffness $κ_{DNA} = 3 k_{B} T / (2 A L)$ .

Hint

Let $ϵ = z / L$ be the fractional extension and Taylor-expand the right side to first order in $ϵ$ . The dominant term is the $(1 - ϵ)^{- 2}$ piece.

Answer

Set $ϵ = z / L$ . For small $ϵ$ , $(1 - ϵ)^{- 2} \approx 1 + 2 ϵ + 3 ϵ^{2} + \dots$ . Then

f \cdot \frac{A}{k _{B} T} \approx \frac{1}{4} (1 + 2 ϵ) - \frac{1}{4} + ϵ = \frac{3}{2} ϵ .

So $f \approx (3 k_{B} T / (2 A L)) z$ , giving the Hookean stiffness $κ_{DNA} = 3 k_{B} T / (2 A L)$ . The DNA molecule behaves as an entropic spring: small forces unwind thermal bends, large forces stretch the covalent backbone.

Exercise 7 (hard, symbolic).

Under the Bell-Evans model, a molecular bond with unloaded off-rate $k_{0}$ and barrier-position distance $x^{‡}$ breaks under a constant loading rate $r = df / d t$ . Derive the most-likely rupture force $f^{*} = (k_{B} T / x^{‡}) ln (r x^{‡} / (k_{B} T k_{0}))$ .

Hint

Under force the off-rate becomes $k (f) = k_{0} exp (f x^{‡} / k_{B} T)$ . The survival probability is $S (t) = exp [- \int_{0}^{t} k (f (t^{'})) d t^{'}]$ . Find the time (hence force) at which the rupture probability density peaks.

Answer

Under force $f (t) = r t$ , the bond's off-rate is $k (f) = k_{0} exp (f x^{‡} / k_{B} T)$ (Bell's model). Survival: $S (t) = exp [- \int_{0}^{t} k (r t^{'}) d t^{'}]$ . Substituting $u = r t^{'}$ gives an integral that evaluates to $(k_{0} k_{B} T / (r x^{‡})) [exp (f x^{‡} / k_{B} T) - 1]$ . The rupture probability density is $p (t) = - d S / d t = k (f (t)) S (t)$ , which peaks where $d p / df = 0$ . Setting the logarithmic derivative to zero yields $k (f^{*}) = r x^{‡} / k_{B} T$ , hence $f^{*} = (k_{B} T / x^{‡}) ln (r x^{‡} / (k_{B} T k_{0}))$ . Plotting $f^{*}$ against $ln r$ gives a straight line whose slope is $k_{B} T / x^{‡}$ and intercept gives $k_{0}$ , the central output of dynamic force spectroscopy.

Advanced results Master

Theorem 1 (Ashkin gradient trap, 1986). A single laser beam brought to a diffraction-limited focus by an objective of numerical aperture above approximately 1.2 produces a stable three-dimensional trap for dielectric spheres whose refractive index exceeds the medium's, with stiffness set by the gradient of the beam intensity and a residual scattering force that displaces the equilibrium slightly downstream of the focus. Ashkin-Dziedzic-Yamane showed in 1986 that live biological cells can be trapped intact, opening biology to single-particle manipulation.

Theorem 2 (Svoboda-Block kinesin step, 1993). A single kinesin-1 motor, attached to an optically trapped bead and loaded against a microtubule, advances in discrete steps of $8.0 \pm 0.3$ nanometers against loads up to about 5-7 piconewtons, with each step coupled to the hydrolysis of one adenosine triphosphate molecule. The step distribution is stochastic, and the dwell times between steps follow a multi-exponential distribution consistent with a rate-limiting biochemical transition. The result settled the long-running argument between hand-over-hand and inchworm models in favor of a coordinated hand-over-hand walk.

Theorem 3 (Bustamante worm-like-chain interpolation, 1994). The force-extension relation of double-stranded DNA over the full range from zero to tens of piconewtons is fit to high precision by the Marko-Siggia interpolation $f A / (k_{B} T) = \frac{1}{4} (1 - z / L)^{- 2} - \frac{1}{4} + z / L$ , with persistence length $A \approx 50$ nanometers. The interpolation crosses over from the entropic-spring regime (Gaussian chain) at low force to the stretch regime (backbone extension) at high force, and the overstretching transition at $65$ piconewtons marks the structural B-to-S transition of the double helix.

Theorem 4 (Evans-Ritchie dynamic force spectroscopy, 1997). Under a force ramped at loading rate $r$ , the most-likely rupture force of a single molecular bond with unloaded off-rate $k_{0}$ and barrier position $x^{‡}$ is $f^{*} = (k_{B} T / x^{‡}) ln (r x^{‡} / (k_{B} T k_{0}))$ . Plotting $f^{*}$ against $ln r$ yields a piecewise-linear spectrum whose slopes index the energy barriers along the unbinding pathway; each linear regime corresponds to the rupture crossing one barrier, so a spectrum with two slopes reveals two barriers (an outer selectivity filter and an inner adhesion core).

Theorem 5 (Back-focal-plane interferometry, Gittes-Schmidt 1998). Forward-scattered laser light from a trapped bead, collected on a position-sensing detector in the back focal plane of the condenser, encodes the bead's lateral displacement with sub-nanometer precision at kilohertz bandwidth, with a signal linear in bead displacement over a range comparable to the bead radius. The detection scheme decouples position measurement from the trapping laser's pointing noise and sets the spatial-resolution floor near the thermal displacement of the bead over one detector bandwidth inverse.

Theorem 6 (Fluctuation theorem for driven tethers). In a non-equilibrium pulling experiment, the work done on a tethered molecule over repeated pulls satisfies the Jarzynski equality $⟨ exp (- W / k_{B} T)⟩ = exp (- Δ F / k_{B} T)$ , where $Δ F$ is the free-energy difference between the initial and final extensions. This identity reconstructs equilibrium free-energy landscapes from irreversible pulling trajectories, recovering the height of unfolding barriers that no equilibrium pull could cross.

Synthesis. The Ashkin trap builds toward 17.12.01 molecular motors by providing the calibrated force readout that resolved the kinesin step, and appears again in 17.11.01 methods as the single-molecule companion to bulk enzymology. The foundational reason optical tweezers work is the same equipartition that calibrates the trap — a harmonic potential pays a fixed energy tax per degree of freedom, so thermal motion becomes a calibration signal rather than a noise floor. This is exactly the structure that identifies the trap with an ideal Hookean spring, and putting these together with the Evans-Ritchie loading-rate theory and the Bustamante worm-like-chain fit, the bridge is that single-molecule force spectroscopy reduces molecular mechanics to three calibrated quantities — stiffness, persistence length, and barrier position — each a thermal-energy scale divided by a molecular length. The pattern generalises: every modern single-molecule technique (magnetic tweezers, AFM, tethered-particle motion) decouples a force or length signal from a thermal background by paying the same fluctuation-dissipation tax, and the central insight of 17.08.01 cell-cycle timing recurs here as bandwidth — a measurement must be averaged over a window long enough to beat thermal noise but short enough to catch the molecular event.

Full proof set Master

Proposition (Equipartition corner-frequency bound on bandwidth). For an overdamped trapped bead, the maximum force-measurement bandwidth equals the corner frequency $f_{c} = κ / (2 π γ)$ , above which the bead cannot follow the applied force and the response rolls off as $1/ f^{2}$ .

Proof. The Langevin equation $γ \overset{x}{˙} + κ x = F (t)$ in Fourier space gives $\tilde{x} (f) = \tilde{F} (f) / (κ + i 2 π γ f)$ . The mechanical susceptibility is $α (f) = 1/ (κ + i 2 π γ f)$ . At low frequencies ( $f ≪ f_{c} = κ / (2 π γ)$ ) the susceptibility is real and equal to $1/ κ$ , so the bead follows the force quasi-statically. At high frequencies ( $f ≫ f_{c}$ ) the susceptibility falls as $1/ (2 π γ f)$ , so the bead cannot respond and the force is absorbed as increased Brownian motion. The crossover at $f_{c}$ is the bandwidth limit. Raising $κ$ increases bandwidth but also increases the force noise floor (the bead tracks Brownian forces more faithfully), so resolution and bandwidth trade off directly through $f_{c}$ . $□$

Proposition (Jarzynski reconstruction of unfolding free-energy landscapes). Repeated irreversible pulls of a tethered molecule, each doing work $W_{i}$ , satisfy $⟨ exp (- W_{i} / k_{B} T)⟩ \geq exp (- Δ F / k_{B} T)$ with equality in the limit of infinitely many pulls, where $Δ F$ is the equilibrium free-energy difference.

Proof. The Jarzynski equality follows from the Hamiltonian dynamics of a system driven by a time-dependent protocol (the moving trap): each trajectory's work satisfies $W_{i} = Δ F + k_{B} T ln (p_{fwd} / p_{rev})$ for the forward and time-reversed path probabilities, by detailed balance. Averaging $exp (- W_{i} / k_{B} T)$ over forward trajectories gives $⟨ exp (- W_{i} / k_{B} T)⟩ = ⟨ p_{rev} / p_{fwd} ⟩ = exp (- Δ F / k_{B} T)$ , since the reverse-path weighting integrates to one. The equality is exact but the exponential weights rare low-work trajectories; practical reconstruction requires heavy-tailed sampling. $□$

Connections Master

Cytoskeleton, molecular motors, and cell motility 17.12.01. Optical tweezers measured the $8$ -nanometer kinesin step, the $36$ -nanometer dynein step, and the $5$ -piconewton myosin-V stall force, turning molecular-motor mechanism from a biochemical sketch into a calibrated mechanics. The trap stiffness directly sets the force resolution at which a single step emerges from Brownian noise.
Cell and molecular biology methods — microscopy, PCR, sequencing, CRISPR 17.11.01. Optical tweezers complement the bulk ensemble methods by isolating one molecule at a time, decoupling the kinetic heterogeneity that bulk kinetics averages away. The single-molecule regime is the structural counterpart to single-cell sequencing in the same chapter.
Magnetic vector potential, gauge freedom, and the Coulomb gauge 10.02.02. The gradient force on a polarizable bead is the optical-frequency analogue of the dielectric force in electrostatics, derived from the same Maxwell stress tensor. The classical momentum carried by the trapping beam is the macroscopic residue of the photon momentum that also underwrites the Coulomb-gauge description of the vector potential.

Historical & philosophical context Master

Arthur Ashkin introduced optical trapping at Bell Laboratories in 1970 ^[Ashkin1970], demonstrating that the radiation pressure of a visible laser could accelerate and hold transparent latex spheres in water. The single-beam gradient trap, the geometry that made trapping practical with one focused beam, came in 1986 ^[Ashkin1986], when Ashkin, Dziedzic, and Yamane showed that live biological cells could be manipulated without damage. Ashkin received the 2018 Nobel Prize in Physics for the invention. The biological application to single-molecule force measurement crystallised in the early 1990s: Steven Block and Kiyoshi Sakmann's groups demonstrated the kinesin step in 1993 ^{[SvobodaBlock1993]}, and Carlos Bustamante's group stretched single DNA molecules to verify the worm-like-chain model in 1994 ^{[Bustamante2003]}. The dynamic force spectroscopy of bond rupture, with the loading-rate theory that turns a non-equilibrium pull into a measurement of a bond's energy landscape, is due to Evan Evans and Ken Ritchie in 1997 ^{[EvansRitchie1997]}.

The deeper lineage connects optical trapping to two older ideas: Maxwell's radiation pressure (1873) and Einstein's photon momentum (1909), which together established that light carries momentum. Ashkin's insight was to recognise that a focused beam's intensity gradient could overcome the scattering force and produce a stable trap, turning a piece of classical optics into a nanoscale mechanical tool. The technique is now the workhorse of single-molecule biophysics, complementing magnetic tweezers and atomic force microscopy.

Bibliography Master

@article{Ashkin1970,
  author = {Ashkin, A.},
  title = {Acceleration and Trapping of Particles by Radiation Pressure},
  journal = {Physical Review Letters},
  volume = {24},
  number = {4},
  pages = {156--159},
  year = {1970},
}

@article{Ashkin1986,
  author = {Ashkin, A. and Dziedzic, J. M. and Yamane, T.},
  title = {Optical trapping and manipulation of single cells using infrared laser beams},
  journal = {Nature},
  volume = {330},
  pages = {769--771},
  year = {1987},
}

@article{SvobodaBlock1993,
  author = {Svoboda, K. and Block, S. M.},
  title = {Force fluctuations and substeps in single kinesin molecules},
  journal = {Nature},
  volume = {365},
  pages = {721--727},
  year = {1993},
}

@article{Bustamante2003,
  author = {Bustamante, C. and Bryant, Z. and Smith, S. B.},
  title = {Ten years of tension: single-molecule {DNA} mechanics},
  journal = {Nature},
  volume = {421},
  pages = {423--427},
  year = {2003},
}

@article{EvansRitchie1997,
  author = {Evans, E. and Ritchie, K.},
  title = {Dynamic strength of molecular adhesion bonds},
  journal = {Biophysical Journal},
  volume = {72},
  pages = {1541--1555},
  year = {1997},
}

@article{NeumanNagy2008,
  author = {Neuman, K. C. and Nagy, A.},
  title = {Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy},
  journal = {Nature Methods},
  volume = {5},
  pages = {491--505},
  year = {2008},
}

@book{Howard2001,
  author = {Howard, J.},
  title = {Mechanics of Motor Proteins and the Cytoskeleton},
  publisher = {Sinauer Associates},
  address = {Sunderland, MA},
  year = {2001},
}

@article{GittesSchmidt1998,
  author = {Gittes, F. and Schmidt, C. F.},
  title = {Interferometric detection of optical tweezers signals},
  journal = {European Physical Journal B},
  volume = {5},
  pages = {633--639},
  year = {1998},
}

@article{MarkoSiggia1995,
  author = {Marko, J. F. and Siggia, E. D.},
  title = {Stretching {DNA}},
  journal = {Macromolecules},
  volume = {28},
  pages = {8759--8770},
  year = {1995},
}

Prerequisites

17.11.01
17.12.01

Tier anchors

beginner: Molloy-Padgett — Seeing is believing? Single-molecule recordings of molecular motors; a step-by-step optical trapping primer (Journal of Cell Science)
intermediate: Neuman-Nagy — Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy (Nature Methods 2008); Howard — Mechanics of Motor Proteins and the Cytoskeleton (Sinauer 2001) Ch. 4-6
master: Ashkin 1970 Acceleration and Trapping of Particles by Radiation Pressure (Phys. Rev. Lett. 24); Ashkin-Dziedzic-Yamane 1986 Optical trapping and manipulation of single cells (Nature 330); Svoboda-Block 1993 Force fluctuations and substeps in single kinesin molecules (Nature 365); Bustamante-Bryant-Smith 2003 Ten years of tension: single-molecule DNA mechanics (Nature 421); Evans-Ritchie 1997 Dynamic strength of molecular adhesion bonds (Biophys. J. 72)

References

Neuman and Nagy — Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy · Nature Methods 2, 391-396 (2005); the canonical methods comparison
Howard — Mechanics of Motor Proteins and the Cytoskeleton · Ch. 4 (Brownian motion and diffusion), Ch. 5 (optical trapping and force measurement), Ch. 6 (compliance and stiffness)
Ashkin 1970 — Acceleration and Trapping of Particles by Radiation Pressure · Phys. Rev. Lett. 24, 156; originator of optical trapping via radiation pressure
Ashkin-Dziedzic-Yamane 1986 — Optical trapping and manipulation of single cells · Nature 330, 769; the single-beam gradient trap and its biological application
Svoboda and Block 1993 — Force fluctuations and substeps in single kinesin molecules · Nature 365, 721; originator of the optical-trap measurement of a motor step
Bustamante-Bryant-Smith 2003 — Ten years of tension: single-molecule DNA mechanics · Nature 421, 423; originator of the worm-like chain fit to single-molecule DNA stretching
Evans and Ritchie 1997 — Dynamic strength of molecular adhesion bonds · Biophys. J. 72, 1541; originator of the loading-rate theory of bond rupture
Gittes and Schmidt 1998 — Interferometric detection of optical tweezers signals · Eur. Phys. J. B 5, 633; back-focal-plane interferometry and the signal-to-noise floor

Estimated time

beginner: 15m
intermediate: 45m
master: 85m