Corey S. O'Hern

Random Packings of Frictionless Particles

We conduct numerical simulations of random packings of frictionless particles at T = 0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing fractions narrows, and its peak approaches random close packing as the system size increases. For packing fractions within the peak, there is no self-averaging, leading to exponential decay of the interparticle force distribution.

Biomimetic Isotropic Nanostructures for Structural Coloration

The self-assembly of films that mimic color-producing nanostructures in bird feathers is described. These structures are isotropic and have a characteristic length-scale comparable to the wavelength of visible light. Structural colors are produced when wavelength-independent scattering is suppressed by limiting the optical path length through geometry or absorption.

Force Distributions near Jamming and Glass Transitions

We calculate the distribution of interparticle normal forces P(F) near the glass and jamming transitions in model supercooled liquids and foams, respectively. P(F) develops a peak that appears near the glass or jamming transitions, whose height increases with decreasing temperature, decreasing shear stress and increasing packing density. A similar shape of P(F) was observed in experiments on static granular packings. We propose that the appearance of this peak signals the development of a yield stress. The sensitivity of the peak to temperature, shear stress, and density lends credence to the recently proposed generalized jamming phase diagram.

Effective Temperatures of a Driven System Near Jamming

Fluctuations in a model of a sheared, zero-temperature foam are studied numerically. Five different quantities that independently reduce to the true temperature in an equilibrium thermal system are calculated. One of the quantities is calculated up to an unknown coefficient. The other four quantities have the same value and all five have the same shear-rate dependence. These results imply that statistical mechanics is useful for the system even though it is far from thermal equilibrium.

Direct determination of DNA twist-stretch coupling

The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent experiments with torsionally constrained single molecules give the first direct measurement of this important material parameter. We extract its value from a recent experiment of Strick et al. (Science, 271 (1996) 1835) and find agreement with an independent experimental estimate recently given by Marko. We also present a very simple microscopic theory predicting a value comparable to the one observed.

Revisiting the Ramachandran plot from a new angle

The pioneering work of Ramachandran and colleagues emphasized the dominance of steric constraints in specifying the structure of polypeptides. The ubiquitous Ramachandran plot of backbone dihedral angles (ϕ and ψ) defined the allowed regions of conformational space. These predictions were subsequently confirmed in proteins of known structure. Ramachandran and colleagues also investigated the influence of the backbone angle τ on the distribution of allowed ϕ/ψ combinations. The “bridge region” (ϕ ≤ 0° and −20° ≤ ψ ≤ 40°) was predicted to be particularly sensitive to the value of τ. Here we present an analysis of the distribution of ϕ/ψ angles in 850 non‐homologous proteins whose structures are known to a resolution of 1.7 Å or less and sidechain B‐factor less than 30 Å2. We show that the distribution of ϕ/ψ angles for all 87,000 residues in these proteins shows the same dependence on τ as predicted by Ramachandran and colleagues. Our results are important because they make clear that steric constraints alone are sufficient to explain the backbone dihedral angle distributions observed in proteins. Contrary to recent suggestions, no additional energetic contributions, such as hydrogen bonding, need be invoked.

Random close packing revisited: Ways to pack frictionless disks

We create collectively jammed (CJ) packings of 50-50 bidisperse mixtures of smooth disks in two dimensions (2D) using an algorithm in which we successively compress or expand soft particles and minimize the total energy at each step until the particles are just at contact. We focus on small systems in 2D and thus are able to find nearly all of the collectively jammed states at each system size. We decompose the probability P(phi) for obtaining a collectively jammed state at a particular packing fraction phi into two composite functions: (1) the density of CJ packing fractions rho(phi), which only depends on geometry, and (2) the frequency distribution beta(phi), which depends on the particular algorithm used to create them. We find that the function rho(phi) is sharply peaked and that beta(phi) depends exponentially on phi. We predict that in the infinite-system-size limit the behavior of P(phi) in these systems is controlled by the density of CJ packing fractions--not the frequency distribution. These results suggest that the location of the peak in P(phi) when N --> infinity can be used as a protocol-independent definition of random close packing.

Sliding Columnar Phase of DNA-Lipid Complexes

DNA is a remarkable polymer that exhibits a complex phase behavior as a function of packing density, salt concentration, and other variables [1]. It is anionic, giving up positive counterions to solution. Mixtures of DNA and cationic and neutral lipids in water form complexes that facilitate transfection of DNA into living cells and that play an important role in the emerging field of gene therapy [2]. Recent x-ray experiments [3] reveal the structure of these complexes at length scales from 10 to several hundred angstroms, particularly near the isoelectric point where the total charge of counterions given up by the DNA equals that given up by the cationic lipids. The lipids form bilayer membranes that stack in a lamellar structure (Fig. 1). Parallel strands of DNA arrange in 2D smectic structures in the galleries between lipid bilayers. The distance between lipid bilayers is equal to the diameter of a DNA molecule plus a hydration layer. In addition, the distance d between DNA strands increases with increasing concentration of neutral lipids in a manner consistent with counterions being expelled to solution and charge neutrality of the complex being determined only by the DNA and cationic lipids. The best fit to x-ray diffraction data is obtained when some correlation between DNA lattices in different galleries is introduced. We undertake here a theoretical investigation of possible equilibrium phases of these lamellar DNAlipid complexes. We identify a new phase, with a nonvanishing smectic compression modulus B in each gallery, in which there is long-range orientational but not positional correlation between DNA lattices in different galleries. This phase exhibits no restoring force for sliding DNA lattices rigidly relative to each other, but it does exhibit a restoring force preventing their relative rotation. We will refer to it as a sliding columnar phase. It is distinct from both the columnar phase in which the DNA segments form a 2D lattice and the totally decoupled phase in which there is no communication between different DNA lattices. It is similar to the decoupled phase of stacks of tethered membranes [4]. Dislocations can destroy positional correlations within the DNA lattices, melt the sliding columnar phase, and produce a nematic lamellar phase with B › 0. Whether they always melt the phase will be discussed in detail elsewhere [5]. We consider a model in which the DNA strands are confined to galleries between lipid bilayers in a perfect lamellar structure (with layer spacing a) with no dislocations or other defects. We assume the ground state of DNA strands in each gallery n is that favored by electrostatic interactions, i.e., a 2D smectic lattice with layer spacing d › 2pyk0. We take the lipid bilayers to be parallel to the x-z plane and the DNA strands to be aligned, on average, parallel to the x axis as shown in Fig. 1. For the moment, we assume that the lipid bilayers are perfectly flat and do not fluctuate. In this case, long-wavelength properties of the DNA lattice in gallery n are described entirely in terms of displacements u n srd along the z direction, where r › sx, zd is a position in the x-z plane. The LandauGinzburg-Wilson Hamiltonian for the complex is then a sum of independent elastic energies for each gallery and terms coupling displacements and angles in neighboring

Jamming in systems composed of frictionless ellipse-shaped particles.

We study numerically frictionless ellipse packings versus the aspect ratio alpha, and find that the jamming transition is fundamentally different from that for spherical particles. The normal mode spectra possess two gaps and three distinct branches over a range of alpha. The energy from deformations along modes in the lowest-energy branch increases quartically, not quadratically. The quartic modes cause novel power-law scaling of the static shear modulus and their number matches the deviation from isostaticity. These results point to a new critical point at alpha>1 that controls jamming of aspherical particles.

Non-random-coil Behavior as a Consequence of Extensive PPII Structure in the Denatured State

Unfolded proteins may contain a native or nonnative residual structure, which has important implications for the thermodynamics and kinetics of folding, as well as for misfolding and aggregation diseases. However, it has been universally accepted that residual structure should not affect the global size scaling of the denatured chain, which obeys the statistics of random coil polymers. Here we use a single-molecule optical technique--fluorescence correlation spectroscopy--to probe the denatured state of a set of repeat proteins containing an increasing number of identical domains, from 2 to 20. The availability of this set allows us to obtain the scaling law for the unfolded state of these proteins, which turns out to be unusually compact, strongly deviating from random coil statistics. The origin of this unexpected behavior is traced to the presence of an extensive nonnative polyproline II helical structure, which we localize to specific segments of the polypeptide chain. We show that the experimentally observed effects of polyproline II on the size scaling of the denatured state can be well-described by simple polymer models. Our findings suggest a hitherto unforeseen potential of nonnative structure to induce significant compaction of denatured proteins, significantly affecting folding pathways and kinetics.