Philip C Nelson

Theory of high-force DNA stretching and overstretching

Single-molecule experiments on single- and double-stranded DNA have sparked a renewed interest in the force versus extension of polymers. The extensible freely jointed chain (FJC) model is frequently invoked to explain the observed behavior of single-stranded DNA, but this model does not satisfactorily describe recent high-force stretching data. We instead propose a model (the discrete persistent chain) that borrows features from both the FJC and the wormlike chain, and show that it resembles the data more closely. We find that most of the high-force behavior previously attributed to stretch elasticity is really a feature of the corrected entropic elasticity; the true stretch compliance of single-stranded DNA is several times smaller than that found by previous authors. Next we elaborate our model to allow coexistence of two conformational states of DNA, each with its own stretch and bend elastic constants. Our model is computationally simple and gives an excellent fit through the entire overstretching transition of nicked, double-stranded DNA. The fit gives the first value for the bend stiffness of the overstretched state. In particular, we find the effective bend stiffness for DNA in this state to be about 12 nm k(B)T, a value quite different from either the B-form or single-stranded DNA.

Bosonization on higher genus Riemann surfaces

We prove the equivalence between certain fermionic and bosonic theories in two spacetime dimensions. The theories have fields of arbitrary spin on compact surfaces with any number of handles. Global considerations require that we add new topological terms to the bosonic action. The proof that our prescription is correct relies on methods of complex algebraic geometry.

Exact theory of kinkable elastic polymers

The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection angles, many rod systems exhibit a high-curvature softening. The signature behavior of these rod systems is a kinking transition in which the bending is localized. Recent DNA cyclization experiments by Cloutier and Widom have offered evidence that the linear-elastic bending theory fails to describe the high-curvature mechanics of DNA. Motivated by this recent experimental work, we develop a simple and exact theory of the statistical mechanics of linear-elastic polymer chains that can undergo a kinking transition. We characterize the kinking behavior with a single parameter and show that the resulting theory reproduces both the low-curvature linear-elastic behavior which is already well described by the worm-like chain model, as well as the high-curvature softening observed in recent cyclization experiments.

An Off-Shell Propagator for String Theory

Abstract The Polyakov integral with boundaries can be used to provide a propagator for the second-quantized bosonic string. This propagator makes sense off-shell. For special initial and final states we compute it explicitly in the tree approximation, where it reduces to the correct sum of field theoretic particle propagators.

Measure for moduli The Polyakov string has no nonlocal anomalies

Abstract The functional measure of the bosonic Polyakov string contains nonlocal determinantal factors which seem to spoil its gauge invariances even in the critical dimension. We show that in fact both conformal invariance and reparameterization invariance are maintained for every world-sheet topology.

Entropic Elasticity of Twist-Storing Polymers

We investigate the statistical mechanics of a torsionally constrained polymer. The polymer is modeled as a fluctuating rod with bend stiffness AkBT and twist stiffness CkBT. In such a model, thermal bend fluctuations couple geometrically to an applied torque through the relation Lk = Tw + Wr. We explore this coupling and find agreement between the predictions of our model and recent experimental results on single λ-DNA molecules. This analysis affords an experimental determination of the microscopic twist stiffness (averaged over a helix repeat). Quantitative agreement between theory and experiment is obtained using C = 109 nm (i.e., twist rigidity CkBT = 4.5 × 10-19 erg cm). The theory further predicts a thermal reduction of the effective twist rigidity induced by bend fluctuations. Finally, we find a small reflection of molecular chirality in the experimental data and interpret it in terms of a twist−stretch coupling of the DNA duplex.

The role of microtubule movement in bidirectional organelle transport

We study the role of microtubule movement in bidirectional organelle transport in Drosophila S2 cells and show that EGFP-tagged peroxisomes in cells serve as sensitive probes of motor induced, noisy cytoskeletal motions. Multiple peroxisomes move in unison over large time windows and show correlations with microtubule tip positions, indicating rapid microtubule fluctuations in the longitudinal direction. We report the first high-resolution measurement of longitudinal microtubule fluctuations performed by tracing such pairs of co-moving peroxisomes. The resulting picture shows that motor-dependent longitudinal microtubule oscillations contribute significantly to cargo movement along microtubules. Thus, contrary to the conventional view, organelle transport cannot be described solely in terms of cargo movement along stationary microtubule tracks, but instead includes a strong contribution from the movement of the tracks.

Strings and Supermoduli

Abstract Polyakovs prescription for fermionic closed string amplitudes requires that we integrate over gauge-inequivalent geometries on a 2D supermanifold. These inequivalent geometries are parametrized by a finite-dimensional superspace of moduli. This space is described and an integration measure on it is proposed which comesfrom gauge-fixing the heterotic string. The measure thus obtained is free of conformal and Lorentz anomalies and so canbr used to compute invariant string amplitudes.

Dynamic excitations in membranes induced by optical tweezers.

We present the phenomenology of transformations in lipid bilayers that are excited by laser tweezers. A variety of dynamic instabilities and shape transformations are observed, including the pearling instability, expulsion of vesicles, and more exotic ones, such as the formation of passages. Our physical picture of the laser-membrane interaction is based on the generation of tension in the bilayer and loss of surface area. Although tension is the origin of the pearling instability, it does not suffice to explain expulsion of vesicles, where we observe opening of giant pores and creeping motion of bilayers. We present a quantitative theoretical framework to understand most of the observed phenomenology. The main hypothesis is that lipid is pulled into the optical trap by the familiar dielectric effect, is disrupted, and finally is repackaged into an optically unresolvable suspension of colloidal particles. This suspension, in turn, can produce osmotic pressure and depletion forces, driving the observed transformations.

Bosonization in Arbitrary Genus

Abstract The equivalence is proved between fermionic and scalar field theories on Riemann surfaces of arbitrary topology. The effects of global topology include a modification of the bosonic action.