Free Energy of a Polymer in Slit-like Confinement from the Odijk Regime to the Bulk

Abstract

We directly measure the free energy of confinement for semiflexible polymers from the nanoscale to bulk regimes in slit-like confinement. We use convex lens-induced confinement (CLiC) microscopy of DNA to directly count molecules at equilibrium in a single chamber of smoothly increasing height. Our data, acquired across a continuum of confinement regimes, provide a bridge with which to connect scaling theories established for qualitatively different regimes. We present new experimental data and simulations that connect the Odijk theory describing sub-persistence-length confinement, the interpolation model by Chen and Sullivan extending Odijk to moderate confinement, and the Casassa theory describing the transition from moderate confinement to bulk. Further, this work establishes a robust, quantitative platform for understanding and manipulating biopolymers at the nanoscale, with key applications and insights toward emerging genomic analysis tools.

Evidence for the extended de Gennes regime of a semiflexible polymer in slit confinement

“…We have previously shown [45] that our PERM simulations provide essentially the same confinement free energy for ideal chains as the interpolation formula of Chen and Sullivan [48], the latter obtained from the ground-state approximation in a propagator approach. We have repeated these ideal chain simulations for additional values of H/l p in the context of the present work and again obtained excellent agreement with Chen and Sullivan [48], essentially identical to our previous work [45] and that obtained using a different simulation method [27].…”

“…Reducing the ionic strength does not improve the situation, as the ratio l p /w decreases and ionic strength decreases [53]. Nevertheless, it would be interesting to see if recent experimental methods for experimentally measuring the free energy of confinement for DNA in slits [27, 58] can detect a deviation from the de Gennes regime that would indicate the existence of marginal solution behavior [7, 8]. We are cautiously optimistic, as experiments focused on the variance in DNA extension in a nanochannel [14, 15] have provided clear evidence for the extended de Gennes regime even though the restrictions on channel size noted above for nanoslits also apply in nanochannels [13].…”

“…It is worthwhile to compare the de Gennes and extended de Gennes scaling theories to the theory of Casassa [49], which has been used recently [27] to model the confinement of relatively short DNA molecules. Casassa’s calculation of the confinement free energy [49] is valid for flexible, ideal chains as the confinement passes from H > R g , where the polymer easily fits into the slit but experiences a depletion near the slit walls, to H < R g , where the polymer must adopt a pancake-like configuration to fit inside the slit.…”

“…Rather, the size of a chain in slit confinement is measured by the root-mean-square (RMS) end-to-end distance of the chain. The problem of determining the size of a semiflexible chain in slit confinement has been the subject of extensive experimental work using DNA as a model polymer [19–27], along with concomitant simulations [17, 19, 27–47], and theory [1, 3, 5, 45, 48]. A key conclusion emerging from this body of work is that the scaling law prediction for the RMS size of a chain of length L [1],…”

Standalone interferometry-based calibration of convex lens-induced confinement microscopy with nanoscale accuracy

“…The confinement of individual molecules enabled longer tracking times and the observation of single molecules at higher analyte concentrations (due to the reduced background fluorescence) when compared to other methods such as total internal reflection fluorescence and confocal microscopy, as well as provided an effective nanoslit geometry in which the behavior of particles at various gap heights could be studied. 24 These methods were extended by the Leslie lab, which demonstrated various applications of the CLiC geometry through the determination of free energies of confinement, 25 electric-field assisted free energies within confinement, 26 and DNA hybridization events (determined using Förster Resonance Energy Transfer or FRET). 27 Previous CLiC experiments focused mainly on dynamics within environments with characteristic confinement dimensions in the range of several hundred nm to several μm, where the gap thickness was readily characterized with little ambiguity.…”