Lattice diffusion of a single molecule in solution

Abstract

The ability to trap a single molecule in an electrostatic potential well in solution has opened up new possibilities for the use of molecular electrical charge to study macromolecular conformation and dynamics at the level of the single entity. Here we study the diffusion of a single macromolecule in a two-dimensional lattice of electrostatic traps in solution. We report the ability to measure both the size and effective electrical charge of a macromolecule by observing single-molecule transport trajectories, typically a few seconds in length, using fluorescence microscopy. While, as shown previously, the time spent by the molecule in a trap is a strong function of its effective charge, we demonstrate here that the average travel time between traps in the landscape yields its hydrodynamic radius. Tailoring the pitch of the lattice thus yields two different experimentally measurable time scales that together uniquely determine both the size and charge of the molecule. Since no information is required on the location of the molecule between consecutive departure and arrival events at lattice sites, the technique is ideally suited to measurements on weakly emitting entities such as single molecules.

Entropic Trapping of a Singly Charged Molecule in Solution

“…In the limit of strong electrostatic interactions (e.g., high molecular charge), we have measured molecular residence times in the trap as long as ∼30 min . Residence times can be tuned by the geometry of the trapping nanostructure and salt concentration in solution. ,, …”

“…For an object confined in a potential well in the fluid phase, overdamped diffusive crossing of a barrier is well described by Kramers’ theory in the regime W > 5 k B T , where the average time to escape the potential well is given by . , Here t r is a time scale representing the position relaxation time of the molecule. Brownian dynamics simulations that take into consideration the full 3D morphology of the potential well are used to convert the measured average escape time, t esc , of a trapped molecule to a well depth, W . , (See the Supporting Information for further details.) Since the well depth in turn depends directly on the effective charge of the molecule, q eff , we have previously achieved highly precise measurements (precision ∼1%) of the effective charge of a variety of biomolecules using the escape-time-based measurement approach described above, which we term “escape-time electrometry” (ET e ) .…”

“…For a given value of q eff , the above integrals are all a function of spatial electrical potential, ψ­( x , y , z ) alone, which is readily obtained by solving the nonlinear Poisson–Boltzmann equation in the nanostructure as previously described . We use constant charge boundary conditions on the slit walls that correspond to a value of ψ s = −2.8 k B T / e for the surface potential of the walls, which we have found to hold under our experimental conditions . From eq , we further note that fluctuations render the particle’s mean electrostatic energy, slightly larger than its electrostatic energy at the midplane of the slit, q eff ψ m, r , typically by about 5%.…”

Equilibrium organization, conformation, and dynamics of two polymers under box-like confinement

“…10,11 Embedded nanotopography devices can also serve as useful models to characterize single-molecule transport across free energy landscapes. [12][13][14][15][16][17][18] One notable study using nanofluidics techniques to study the effects of nanoconfinement on polymers was reported recently by Capaldi et al 19 Their experiment employed pneumatic pressure to deflect a thin nitride lid into a nanoslit containing a solution of fluorescently stained λ-DNA chains, forcing the molecules into an array of nanocavities embedded in one surface of the slit. Each cavity had a square cross section of side length 2 µm, was 200 nm deep, and was able to trap up to two λ-DNA chains per cavity.…”

Brownian motion of a charged colloid in restricted confinement

“…Understanding the Brownian motion of colloids under confinement has been a great challenge in recent decades [1]. Such motion is present in the segregation and transport of particles though the bio-cellular membranes [2], in microfluidic devices [3], and in particle trapping and tracking technologies [4,5].…”