Super-Resolution Genome Mapping in Silicon Nanochannels.

Optical genome mapping in nanochannels is a powerful genetic analysis method, complementary to deoxyribonucleic acid (DNA) sequencing. The method is based on detecting a pattern of fluorescent labels attached along individual DNA molecules. When such molecules are extended in nanochannels, the labels create a fluorescent genetic barcode that is used for mapping the DNA molecule to its genomic locus and identifying large-scale variation from the genome reference. Mapping resolution is currently limited by two main factors: the optical diffraction limit and the thermal fluctuations of DNA molecules suspended in the nanochannels. Here, we utilize single-molecule tracking and super-resolution localization in order to improve the mapping accuracy and resolving power of this genome mapping technique and achieve a 15-fold increase in resolving power compared to currently practiced methods. We took advantage of a naturally occurring genetic repeat array and labeled each repeat with custom-designed Trolox conjugated fluorophores for enhanced photostability. This model system allowed us to acquire extremely long image sequences of the equally spaced fluorescent markers along DNA molecules, enabling detailed characterization of nanoconfined DNA dynamics and quantitative comparison to the Odijk theory for confined polymer chains. We present a simple method to overcome the thermal fluctuations in the nanochannels and exploit single-step photobleaching to resolve subdiffraction spaced fluorescent markers along fluctuating DNA molecules with ∼100 bp resolution. In addition, we show how time-averaging over just ∼50 frames of 40 ms enhances mapping accuracy, improves mapping P-value scores by 3 orders of magnitude compared to nonaveraged alignment, and provides a significant advantage for analyzing structural variations between DNA molecules with similar sequence composition.

Buckling of an elastic rod embedded on an elastomeric matrix: planar vs. non-planar configurations.

We investigate the buckling of a slender rod embedded in a soft elastomeric matrix through a combination of experiments, numerics and theory. Depending on the control parameters, both planar wavy (2D) or non-planar coiled (3D) configurations are observed in the post-buckling regime. Our analytical and numerical results indicate that the rod buckles into 2D configurations when the compression forces associated to the two lowest critical modes are well separated. In contrast, 3D coiled configurations occur when the two buckling modes are triggered at onset, nearly simultaneously. We show that the separation between these two lowest critical forces can be controlled by tuning the ratio between the stiffness of the matrix and the bending stiffness of the rod, thereby allowing for specific buckling configurations to be target by design.

Structural transition from helices to hemihelices.

Helices are amongst the most common structures in nature and in some cases, such as tethered plant tendrils, a more complex but related shape, the hemihelix forms. In its simplest form it consists of two helices of opposite chirality joined by a perversion. A recent, simple experiment using elastomer strips reveals that hemihelices with multiple reversals of chirality can also occur, a richness not anticipated by existing analyses. Here, we show through analysis and experiments that the transition from a helical to a hemihelical shape, as well as the number of perversions, depends on the height to width ratio of the strip's cross-section. Our findings provides the basis for the deterministic manufacture of a variety of complex three-dimensional shapes from flat strips.

Differential contributions of conformation extension and domain unfolding to properties of fibronectin nanotextiles.

Fibronectin (FN) textiles are built as nanometer-thick fabrics. When uniaxially loaded, these fabrics exhibit a distinct threshold between elastic and plastic deformation with increasing stretch. Fabric mechanics are modeled using an eight-chain network and two-state model, revealing that elastic properties of FN depend on conformational extension of the protein and that plastic deformation depends on domain unfolding. Our results suggest how the molecular architecture of a molecule can be exploited for designer mechanical properties of a bulk material.

Fluctuating elastic filaments under distributed loads.

Filaments under distributed loads are common in biological systems. In this paper, we study the thermo-mechanical properties of an extensible thermally fluctuating elastic filament under distributed forces. The ground state of the filament is solved first, followed by an investigation of the thermal fluctuations around the ground state. We first consider a special case where the tangential component of the distributed force tau is uniform along the filament. For the force-extension relation in this case, we show that the filament is equivalent to one under end-to-end applied force F = tauL0/2 where L0 is the length of the filament. To study the thermal fluctuations under more general distributed loadings, the filament is first discretized into segments, and its energy is approximated up to quadratic order. Then the partition function of the discretized filament, or chain, is evaluated using multi-dimensional Gaussian integrals, from which free energy and other properties of the filament are derived. We show that a filament under distributed loads suffers larger thermal fluctuations than one with the end loads of the same magnitude. We also show that our results for a discretized filament agree with continuum theory for a continuous rod. Finally, we give some applications of our ideas to the stretching and fluctuation of DNA in non-uniform microfluidic channels.

Entropically driven motion of polymers in nonuniform nanochannels.

In nanofluidic devices, nonuniform confinement induces an entropic force that automatically drives biopolymers toward less-confined regions to gain entropy. To understand this phenomenon, we first analyze the diffusion of an entropy-driven particle system. The derived Fokker-Planck equation reveals an effective driving force as the negative gradient of the free energy. The derivation also shows that both the diffusion constant and drag coefficient are location dependent on an arbitrary free-energy landscape. As an application, DNA motion and deformation in nonuniform channels are investigated. Typical solutions reveal large gradients of stress on the polymer where the channel width changes rapidly. Migration of DNA in several nonuniform channels is discussed.

Transition between two regimes describing internal fluctuation of DNA in a nanochannel.

We measure the thermal fluctuation of the internal segments of a piece of DNA confined in a nanochannel about 50-100 nm wide. This local thermodynamic property is key to accurate measurement of distances in genomic analysis. For DNA in ~100 nm channels, we observe a critical length scale ~10 m for the mean extension of internal segments, below which the de Gennes' theory describes the fluctuations with no fitting parameters, and above which the fluctuation data falls into Odijk's deflection theory regime. By analyzing the probability distributions of the extensions of the internal segments, we infer that folded structures of length 150-250 nm, separated by ~10 m exist in the confined DNA during the transition between the two regimes. For ~50 nm channels we find that the fluctuation is significantly reduced since the Odijk regime appears earlier. This is critical for genomic analysis. We further propose a more detailed theory based on small fluctuations and incorporating the effects of confinement to explicitly calculate the statistical properties of the internal fluctuations. Our theory is applicable to polymers with heterogeneous mechanical properties confined in non-uniform channels. We show that existing theories for the end-to-end extension/fluctuation of polymers can be used to study the internal fluctuations only when the contour length of the polymer is many times larger than its persistence length. Finally, our results suggest that introducing nicks in the DNA will not change its fluctuation behavior when the nick density is below 1 nick per kbp DNA.

Mechanics of forced unfolding of proteins.

We describe and solve a two-state kinetic model for the forced unfolding of proteins. The protein oligomer is modeled as a heterogeneous, freely jointed chain with two possible values of Kuhn length and contour length representing its folded and unfolded configurations. We obtain analytical solutions for the force-extension response of the protein oligomer for different types of loading conditions. We fit the analytical solutions for constant-velocity pulling to the force-extension data for ubiquitin and fibrinogen and obtain model parameters, such as Kuhn lengths and kinetic coefficients, for both proteins. We then predict their response under a linearly increasing force and find that our solutions for ubiquitin are consistent with a different set of experiments. Our calculations suggest that the refolding rate of proteins at low forces is several orders larger than the unfolding rate, and neglecting it can lead to lower predictions for the unfolding force, especially at high stretching velocities. By accounting for the refolding of proteins we obtain a critical force below which equilibrium is biased in favor of the folded state. Our calculations also suggest new methods to determine the distance of the transition state from the energy wells representing the folded and unfolded states of a protein.