Dynamical model for the full stretching curve of DNA

Multiplateau Force-Extension Curves of Long Double-Stranded DNA Molecules

When highly stretched, double-stranded DNA exhibits a plateau region in its force-extension curve. Using a bead-spring coarse-grained dynamic model based on a nonconvex potential, we predict that a long double-stranded DNA fragment made of several consecutive segments with substantially different plateau force values for each segment will exhibit multiple distinct plateau regions in the force-extension curve under physiologically relevant solvent conditions. For example, a long composite double-stranded (ds) DNA fragment consisting of two equal-length segments characterized by two different plateau force values, such as the poly(dA-dT)-poly(dG-dC) fragment, is predicted to exhibit two distinct plateau regions in its force-extension curve; a long composite dsDNA fragment consisting of three segments having three different plateau force values is predicted to have three distinct plateau regions. The formation of mixed states of slightly and highly stretched DNA, coexisting with macroscopically distinct phases of uniformly stretched DNA is also predicted. When one of the segments overstretches, the extensions of the segments can differ drastically. For example, for the poly(dA-dT)-poly(dG-dC) composite fragment, in the middle of the first plateau, 96.7% of the total extension of the fragment (relative to L x /L 0 ≈ 1.0) comes from the poly(dA-dT) segment, while only 3.3% of it comes from the poly(dG-dC) segment. The order of the segments has little effect on the force-extension curve or the distribution of conformational states. We speculate that the distinct structural states of stretched double-stranded DNA may have functional importance. For example, these states may modulate, in a sequence-dependent manner, the rate of double-stranded DNA processing by key cellular machines.

Multi-plateau force-extension curves of long double-stranded DNA molecules

When highly stretched, double-stranded DNA exhibits a plateau region in its force-extension curve. Using a bead-spring coarse-grained dynamic model based on a non-convex potential, we predict that a long double-stranded DNA fragment made of several consecutive segments with substantially different plateau force values for each segment will exhibit multiple distinct plateau regions in the force-extension curve under physiologically relevant solvent conditions. For example, a long composite double-stranded (ds) DNA fragment consisting of two equal-length segments characterized by two different plateau force values, such as the poly(dA-dT)-poly(dG-dC) fragment, is predicted to exhibit two distinct plateau regions in its force-extension curve; a long composite dsDNA fragment consisting of three segments having three different plateau force values is predicted to have three distinct plateau regions. The formation of mixed states of slightly and highly stretched DNA, co-existing with macroscopically distinct phases of uniformly stretched DNA is also predicted. When one of the segments overstretches, the extensions of the segments can differ drastically. For example, for the poly(dA-dT)-poly(dG-dC) composite fragment, in the middle of the first plateau, 96.7 % of the total extension of the fragment (relative toL x / L 0 ≈ 1.0 ) comes from the poly(dA-dT) segment, while only 3.3 % of it comes from the poly(dG-dC) segment. The order of the segments has little effect on the force-extension curve or the distribution of conformational states. We speculate that the distinct structural states of stretched double-stranded DNA may have functional importance. For example, these states may modulate, in a sequence-dependent manner, the rate of double-stranded DNA processing by key cellular machines.

Stretching of Long Double-Stranded DNA and RNA Described by the Same Approach

We propose an approach to help interpret polymer force-extension curves that exhibit plateau regimes. When coupled to a bead-spring dynamic model, the approach accurately reproduces a variety of experimental force-extension curves of long double-stranded DNA and RNA, including torsionally constrained and unconstrained DNA and negatively supercoiled DNA. A key feature of the model is a specific nonconvex energy function of the spring. We provide an algorithm to obtain the five required parameters of the model from experimental force-extension curves. The applicability of the approach to the force-extension curves of double-stranded (ds) DNA of variable GC content as well as to a DNA/RNA hybrid structure is explored and confirmed. We use the approach to explain counterintuitive sequence-dependent trends and make predictions. In the plateau region of the force-extension curves, our molecular dynamics simulations show that the polymer separates into a mix of weakly and strongly stretched states without forming macroscopically distinct phases. The distribution of these states is predicted to depend on the sequence.

Active translocation of a semiflexible polymer assisted by an ATP-based molecular motor

In this work we study the assisted translocation of a polymer across a membrane nanopore, inside which a molecular motor exerts a force fuelled by the hydrolysis of ATP molecules. In our model the motor switches to its active state for a fixed amount of time, while it waits for an ATP molecule which triggers the motor, during an exponentially distributed time lapse. The polymer is modelled as a beads-springs chain with both excluded volume and bending contributions, and moves in a stochastic three dimensional environment modelled with a Langevin dynamics at a fixed temperature. The resulting dynamics shows a Michaelis-Menten translocation velocity that depends on the chain flexibility. The scaling behavior of the mean translocation time with the polymer length for different bending values is also investigated.

Active polymer translocation in the three-dimensional domain

In this work we study the translocation process of a polymer through a nanochannel where a time dependent force is acting. Two conceptually different types of driving are used: a deterministic sinusoidal one and a random telegraph noise force. The mean translocation time presents interesting resonant minima as a function of the frequency of the external driving. For the computed sizes, the translocation time scales with the polymer length according to a power law with the same exponent for almost all the frequencies of the two driving forces. The dependence of the translocation time with the polymer rigidity, which accounts for the persistence length of the molecule, shows a different low frequency dependence for the two drivings.

Equilibrium and kinetics of DNA overstretching modeled with a quartic energy landscape

It is well known that the dsDNA molecule undergoes a phase transition from B-DNA into an overstretched state at high forces. For some time, the structure of the overstretched state remained unknown and highly debated, but recent advances in experimental techniques have presented evidence of more than one possible phase (or even a mixed phase) depending on ionic conditions, temperature, and basepair sequence. Here, we present a theoretical model to study the overstretching transition with the possibility that the overstretched state is a mixture of two phases: a structure with portions of inner strand separation (melted or M-DNA), and an extended phase that retains the basepair structure (S-DNA). We model the double-stranded DNA as a chain composed of n segments of length l, where the transition is studied by means of a Landau quartic potential with statistical fluctuations. The length l is a measure of cooperativity of the transition and is key to characterizing the overstretched phase. By analyzing the different values of l corresponding to a wide spectrum of experiments, we find that for a range of temperatures and ionic conditions, the overstretched form is likely to be a mix of M-DNA and S-DNA. For a transition close to a pure S-DNA state, where the change in extension is close to 1.7 times the original B-DNA length, we find l ? 25 basepairs regardless of temperature and ionic concentration. Our model is fully analytical, yet it accurately reproduces the force-extension curves, as well as the transient kinetic behavior, seen in DNA overstretching experiments.

Cavity approach for modeling and fitting polymer stretching

The mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly studied force-elongation relation is typically hard. Here we draw from techniques developed in the context of disordered systems to solve models for single and double-stranded DNA stretching in the limit of a long polymeric chain. Since we directly derive the marginals for the molecule local orientation, our approach allows us to readily calculate the experimental elongation as well as other observables at wish. As an example, we evaluate the correlation length as a function of the stretching force. Furthermore, we are able to fit successfully our solution to real experimental data. Although the model is admittedly phenomenological, our findings are very sound. For single-stranded DNA our solution yields the correct (monomer) scale and yet, more importantly, the right persistence length of the molecule. In the double-stranded case, our model reproduces the well-known overstretching transition and correctly captures the ratio between native DNA and overstretched DNA. Also in this case the model yields a persistence length in good agreement with consensus, and it gives interesting insights into the bending stiffness of the native and overstretched molecule, respectively.

Coarse-grained simulations of DNA overstretching

We use a recently developed coarse-grained model to simulate the overstretching of duplex DNA. Overstretching at 23 °C occurs at 74 pN in the model, about 6-7 pN higher than the experimental value at equivalent salt conditions. Furthermore, the model reproduces the temperature dependence of the overstretching force well. The mechanism of overstretching is always force-induced melting by unpeeling from the free ends. That we never see S-DNA (overstretched duplex DNA), even though there is clear experimental evidence for this mode of overstretching under certain conditions, suggests that S-DNA is not simply an unstacked but hydrogen-bonded duplex, but instead probably has a more exotic structure.