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ABSTRACT: We extend recent studies of the minimal energy packings of short flexible polymers with hard-core-like repulsions and short-range attractions to include bond-angle interactions with the aim of describing the collapsed conformations of "colloidal" polymers. We find that flexible tangent sticky-hard-sphere (t-SHS) packings provide a useful perturbative basis for analyzing polymer packings with nonzero bending stiffness only for small ratios of the stiffnesses for the bond-angle (k(b)) and pair (k(c)) interactions, i.e., k(b) (crit)/k(c)≲0.01 for N < 10 monomers, and the critical ratio decreases with N. Below k(b) (crit), angular interactions give rise to an exponential (in N) increase in the number of distinct angular energies arising from the diversity of covalent backbone paths through t-SHS packings. As k(b) increases above k(b) (crit), the low-lying energy landscape changes dramatically as finite bending stiffness alters the structure of the polymer packings. This study lays the groundwork for exact-enumeration studies of the collapsed states of t-SHS-like models with larger bending stiffness.
The Journal of chemical physics 02/2013; 138(5):054905. · 3.09 Impact Factor
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ABSTRACT: We perform numerical simulations of athermal repulsive frictionless disks and
spheres in two and three spatial dimensions undergoing cyclic quasi-static
simple shear to investigate particle-scale reversible motion. We identify three
classes of steady-state dynamics as a function of packing fraction \phi and
maximum strain amplitude per cycle \gamma_{\rm max}. Point-reversible states,
where particles do not collide and exactly retrace their intra-cycle
trajectories, occur at low \phi and \gamma_{\rm max}. Particles in
loop-reversible states undergo numerous collisions and execute complex
trajectories, but return to their initial positions at the end of each cycle.
Loop-reversible dynamics represents a novel form of self-organization that
enables reliable preparation of configurations with specified structural and
mechanical properties over a broad range of \phi from contact percolation to
jamming onset at \phi_J. For sufficiently large \phi and \gamma_{\rm max},
systems display irreversible dynamics with nonzero self-diffusion.
01/2013;
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ABSTRACT: Intrinsically disordered proteins (IDPs) are increasingly recognized for their important roles in a range of biological contexts, both in normal physiological function and in a variety of devastating human diseases. However, their structural characterization by traditional biophysical methods, for the purposes of understanding their function and dysfunction, has proved challenging. Here, we investigate the model IDPs α-Synuclein (αS) and tau, that are involved in major neurodegenerative conditions including Parkinson's and Alzheimer's diseases, using excluded volume Monte Carlo simulations constrained by pairwise distance distributions from single-molecule fluorescence measurements. Using this, to our knowledge, novel approach we find that a relatively small number of intermolecular distance constraints are sufficient to accurately determine the dimensions and polymer conformational statistics of αS and tau in solution. Moreover, this method can detect local changes in αS and tau conformations that correlate with enhanced aggregation. Constrained Monte Carlo simulations produce ensembles that are in excellent agreement both with experimental measurements on αS and tau and with all-atom, explicit solvent molecular dynamics simulations of αS, with much lower configurational sampling requirements and computational expense.
Biophysical Journal 11/2012; 103(9):1940-9. · 3.65 Impact Factor
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ABSTRACT: Intrinsically disordered proteins (IDPs) do not possess well-defined three-dimensional structures in solution under physiological conditions. We develop all-atom, united-atom, and coarse-grained Langevin dynamics simulations for the IDP α-synuclein that include geometric, attractive hydrophobic, and screened electrostatic interactions and are calibrated to the inter-residue separations measured in recent single-molecule fluorescence energy transfer (smFRET) experiments. We find that α-synuclein is disordered, with conformational statistics that are intermediate between random walk and collapsed globule behavior. An advantage of calibrated molecular simulations over constraint methods is that physical forces act on all residues, not only on residue pairs that are monitored experimentally, and these simulations can be used to study oligomerization and aggregation of multiple α-synuclein proteins that may precede amyloid formation.
Physical Review E 10/2012; 86(4-1):041910. · 2.26 Impact Factor
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ABSTRACT: We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in two dimensions that interact via purely repulsive contact forces. We measure the structural relaxation times obtained from the long-time α decay of the self part of the intermediate scattering function for the translational and rotational degrees of freedom (DOF) as a function of packing fraction φ, temperature T, and aspect ratio α. We are able to collapse the packing-fraction and temperature-dependent structural relaxation times for disks, and dimers and ellipses over a wide range of α, onto a universal scaling function F_{±}(|φ-φ_{0}|,T,α), which is similar to that employed in previous studies of dense liquids composed of purely repulsive spherical particles in three dimensions. F_{±} for both the translational and rotational DOF are characterized by the α-dependent scaling exponents μ and δ and packing fraction φ_{0}(α) that signals the crossover in the scaling form F_{±} from hard-particle dynamics to super-Arrhenius behavior for each aspect ratio. We find that the fragility of structural relaxation at φ_{0}, m(φ_{0}), decreases monotonically with increasing aspect ratio for both ellipses and dimers. For α>α_{p}, where α_{p} is the location of the peak in the packing fraction φ_{J} at jamming onset, the rotational DOF are strongly coupled to the translational DOF, and the dynamic scaling exponents and φ_{0} are similar for the rotational and translational DOF. For 1<α<α_{p}, the translational DOF become frozen at higher temperatures than the rotational DOF, and φ_{0} for the rotational degrees of freedom increases above φ_{J}. Moreover, the results for the slow dynamics of dense liquids composed of dimer- and ellipse-shaped particles are qualitatively the same, despite the fact that zero-temperature static packings of dimers are isostatic, while static packings of ellipses are hypostatic. Thus, zero-temperature contact counting arguments do not apply to structural relaxation of dense liquids of anisotropic particles near the glass transition.
Physical Review E 10/2012; 86(4-1):041303. · 2.26 Impact Factor
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ABSTRACT: We perform extensive molecular dynamics simulations of dense liquids composed
of bidisperse dimer- and ellipse-shaped particles in 2D that interact via
repulsive contact forces. We measure the structural relaxation times obtained
from the long-time decay of the self-part of the intermediate scattering
function for the translational and rotational degrees of freedom (DOF) as a
function of packing fraction \phi, temperature T, and aspect ratio \alpha. We
are able to collapse the \phi and T-dependent structural relaxation times for
disks, and dimers and ellipses over a wide range of \alpha, onto a universal
scaling function {\cal F}_{\pm}(|\phi-\phi_0|,T,\alpha), which is similar to
that employed in previous studies of dense liquids composed of purely repulsive
spherical particles in 3D. {\cal F_{\pm}} for both the translational and
rotational DOF are characterized by the \alpha-dependent scaling exponents \mu
and \delta and packing fraction \phi_0(\alpha) that signals the crossover in
the scaling form {\cal F}_{\pm} from hard-particle dynamics to super-Arrhenius
behavior for each aspect ratio. We find that the fragility at \phi_0,
m(\phi_0), decreases monotonically with increasing aspect ratio for both
ellipses and dimers. Moreover, the results for the slow dynamics of dense
liquids composed of dimer- and ellipse-shaped particles are qualitatively the
same, despite the fact that zero-temperature static packings of dimers are
isostatic, while static packings of ellipses are hypostatic.
06/2012;
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ABSTRACT: The energy functions used to predict protein structures typically include both molecular-mechanics and knowledge-based terms. In contrast, our approach is to develop robust physics- and geometry-based methods. Here, we investigate to what extent simple hard-sphere models can be used to predict side-chain conformations. The distributions of the side-chain dihedral angle χ(1) of Val and Thr in proteins of known structure show distinctive features: Val side chains predominantly adopt χ(1) = 180°, whereas Thr side chains typically adopt χ(1) = 60° and 300° (i.e., χ(1) = ±60° or g- and g(+) configurations). Several hypotheses have been proposed to explain these differences, including interresidue steric clashes and hydrogen-bonding interactions. In contrast, we show that the observed side-chain dihedral angle distributions for both Val and Thr can be explained using only local steric interactions in a dipeptide mimetic. Our results emphasize the power of simple physical approaches and their importance for future advances in protein engineering and design.
Biophysical Journal 05/2012; 102(10):2345-52. · 3.65 Impact Factor
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ABSTRACT: We analyze the geometric structure and mechanical stability of a complete set
of isostatic and hyperstatic sphere packings obtained via exact enumeration.
The number of nonisomorphic isostatic packings grows exponentially with the
number of spheres $N$, and their diversity of structure and symmetry increases
with increasing $N$ and decreases with increasing hyperstaticity $H \equiv N_c
- N_{ISO}$, where $N_c$ is the number of pair contacts and $N_{ISO} = 3N-6$.
Maximally contacting packings are in general neither the densest nor the most
symmetric. Analyses of local structure show that the fraction $f$ of nuclei
with order compatible with the bulk (RHCP) crystal decreases sharply with
increasing $N$ due to a high propensity for stacking faults, 5- and near-5-fold
symmetric structures, and other motifs that preclude RHCP order. While $f$
increases with increasing $H$, a significant fraction of hyperstatic nuclei for
$N$ as small as 11 retain non-RHCP structure. Classical theories of nucleation
that consider only spherical nuclei, or only nuclei with the same ordering as
the bulk crystal, cannot capture such effects. Our results provide an
explanation for the failure of classical nucleation theory for hard-sphere
systems of $N\lesssim 10$ particles; we argue that in this size regime, it is
essential to consider nuclei of unconstrained geometry. Our results are also
applicable to understanding kinetic arrest and jamming in systems that interact
via hard-core-like repulsive and short-ranged attractive interactions.
02/2012;
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ABSTRACT: We numerically investigate the mechanical properties of static packings of
ellipsoidal particles in 2D and 3D over a range of aspect ratio and compression
$\Delta \phi$. While amorphous packings of spherical particles at jamming onset
($\Delta \phi=0$) are isostatic and possess the minimum contact number $z_{\rm
iso}$ required for them to be collectively jammed, amorphous packings of
ellipsoidal particles generally possess fewer contacts than expected for
collective jamming ($z < z_{\rm iso}$) from naive counting arguments, which
assume that all contacts give rise to linearly independent constraints on
interparticle separations. To understand this behavior, we decompose the
dynamical matrix $M=H-S$ for static packings of ellipsoidal particles into two
important components: the stiffness $H$ and stress $S$ matrices. We find that
the stiffness matrix possesses $N(z_{\rm iso} - z)$ eigenmodes ${\hat e}_0$
with zero eigenvalues even at finite compression, where $N$ is the number of
particles. In addition, these modes ${\hat e}_0$ are nearly eigenvectors of the
dynamical matrix with eigenvalues that scale as $\Delta \phi$, and thus finite
compression stabilizes packings of ellipsoidal particles. At jamming onset, the
harmonic response of static packings of ellipsoidal particles vanishes, and the
total potential energy scales as $\delta^4$ for perturbations by amplitude
$\delta$ along these `quartic' modes, ${\hat e}_0$. These findings illustrate
the significant differences between static packings of spherical and
ellipsoidal particles.
01/2012;
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Protein Science 08/2011; · 2.80 Impact Factor
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ABSTRACT: We describe the self-assembly of nonspherical particles into crystals with novel structure and optical properties combining a partial photonic band gap with birefringence that can be modulated by an external field or quenched by solvent evaporation. Specifically, we study symmetric optical-scale polymer dumbbells with an aspect ratio of 1.58. Hard particles with this geometry have been predicted to crystallize in equilibrium at high concentrations. However, unlike spherical particles, which readily crystallize in the bulk, previous experiments have shown that these dumbbells crystallize only under strong confinement. Here, we demonstrate the use of an external electric field to align and assemble the dumbbells to make a birefringent suspension with structural color. When the electric field is turned off, the dumbbells rapidly lose their orientational order and the color and birefringence quickly go away. In this way, dumbbells combine the structural color of photonic crystals with the field addressability of liquid crystals. In addition, we find that if the solvent is removed in the presence of an electric field, the particles self-assemble into a novel, dense crystalline packing hundreds of particles thick. Analysis of the crystal structure indicates that the dumbbells have a packing fraction of 0.7862, higher than the densest known packings of spheres and ellipsoids. We perform numerical experiments to more generally demonstrate the importance of controlling the orientation of anisotropic particles during a concentration quench to achieve long-range order.
ACS Nano 08/2011; 5(8):6695-700. · 10.77 Impact Factor
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ABSTRACT: Many jammed particulate systems, such as granular and colloidal materials, interact via repulsive contact forces. We find that these systems possess no harmonic regime in the large system limit (N→∞) for all compressions Δϕ studied, and at jamming onset Δϕ→0 for all N. We perform fixed energy simulations following perturbations with amplitude δ along eigendirections of the dynamical matrix. The fluctuations abruptly spread to all modes for δ≈δ(c) (where a single contact breaks) in contrast to linear and weakly nonlinear behavior. For δ > δ(c), all discrete modes disappear into a continuous frequency band. <δ(c)> scales with 1/N and Δϕ, which limits harmonic behavior to only overcompressed systems. The density of vibrational modes deviates strongly from that predicted from the dynamical matrix when the system enters the nonharmonic regime, which significantly affects its mechanical and transport properties.
Physical Review Letters 08/2011; 107(7):078301. · 7.37 Impact Factor
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ABSTRACT: We present a systematic study of photonic band gaps (PBGs) in
three-dimensional (3D) photonic amorphous structures (PAS) with short-range
order. From calculations of the density of optical states (DOS) for PAS with
different topologies, we find that tetrahedrally connected dielectric networks
produce the largest isotropic PBGs. Local uniformity and tetrahedral order are
essential to the formation of PBGs in PAS, in addition to short-range geometric
order. This work demonstrates that it is possible to create broad, isotropic
PBGs for vector light fields in 3D PAS without long-range order.
08/2011;
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ABSTRACT: 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 Ų. 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.
Protein Science 07/2011; 20(7):1166-71. · 2.80 Impact Factor
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ABSTRACT: We perform extensive computational studies of two-dimensional static bidisperse disk packings using two distinct packing-generation protocols. The first involves thermally quenching equilibrated liquid configurations to zero temperature over a range of thermal quench rates r and initial packing fractions followed by compression and decompression in small steps to reach packing fractions φ(J) at jamming onset. For the second, we seed the system with initial configurations that promote micro- and macrophase-separated packings followed by compression and decompression to φ(J). Using these protocols, we generate more than 10(4) static packings over a wide range of packing fraction, contact number, and compositional and positional order. We find that disordered, isostatic packings exist over a finite range of packing fractions in the large-system limit. In agreement with previous calculations, the most dilute mechanically stable packings with φ min ≈ 0.84 are obtained for r > r*, where r* is the rate above which φ(J) is insensitive to rate. We further compare the structural and mechanical properties of isostatic versus hyperstatic packings. The structural characterizations include the contact number, several order parameters, and mixing ratios of the large and small particles. We find that the isostatic packings are positionally and compositionally disordered (with only small changes in a number of order parameters), whereas bond-orientational and compositional order increase strongly with contact number for hyperstatic packings. In addition, we calculate the static shear modulus and normal mode frequencies (in the harmonic approximation) of the static packings to understand the extent to which the mechanical properties of disordered, isostatic packings differ from partially ordered packings. We find that the mechanical properties of the packings change continuously as the contact number increases from isostatic to hyperstatic.
Physical Review E 07/2011; 84(1 Pt 1):011305. · 2.26 Impact Factor
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ABSTRACT: We examine nonequilibrium features of collapse behavior in model polymers
with competing crystallization and glass transitions using extensive molecular
dynamics simulations. By comparing to "colloidal" systems with no covalent
bonds but the same non-bonded interactions, we find three principal results:
(i) Tangent-sphere polymers and colloids, in the equilibrium-crystallite phase,
have nearly identical static properties when the temperature T is scaled by the
crystallization temperature T_{cryst}; (ii) Qualitative features of
nonequilibrium relaxation below T_{cryst}, measured by the evolution of local
structural properties (such as the number of contacts) toward equilibrium
crystallites, are the same for polymers and colloids; and (iii) Significant
quantitative differences in rearrangements in polymeric and colloidal
crystallites, in both far-from equilibrium and near-equilibrium systems, can be
understood in terms of chain connectivity. These results have important
implications for understanding slow relaxation processes in collapsed polymers,
partially folded, misfolded, and intrinsically disordered proteins.
04/2011;
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ABSTRACT: Jammed particulate systems, such as granular media, colloids, and foams,
interact via one-sided forces that are nonzero only when particles overlap. We
find that systems with one-sided repulsive interactions possess no linear
response regime in the large system limit ($N\rightarrow \infty$) for all
pressures $p$ (or compressions $\Delta \phi$), and for all $N$ near jamming
onset $p\rightarrow 0$. We perform simulations on 2D frictionless bidisperse
mechanically stable disk packings over a range of packing fractions $\Delta
\phi = \phi-\phi_J$ above jamming onset $\phi_J$. We apply perturbations with
amplitude $\delta$ to the packings along each eigen-direction from the
dynamical matrix and determine whether the response of the system evolving at
constant energy remains in the original eigenmode of the perturbation. For
$\delta > \delta_c$, which we calculate analytically, a single contact breaks
and fluctuations abruptly spread to all harmonic modes. As $\delta$ increases
further all discrete harmonic modes disappear into a continuous frequency band.
We find that $<\delta_c >\sim \Delta \phi/N^{\lambda}$, where $1 > \lambda >
0.5$, and thus jammed particulate systems are inherently nonharmonic with no
linear vibrational response regime as $N\rightarrow \infty$ over the full range
of $\Delta \phi$, and as $\Delta \phi \rightarrow 0$ at any $N$.
12/2010;
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ABSTRACT: A simple theory for glassy-polymeric mechanical response that accounts for large-scale chain relaxation is presented. It captures the crossover from perfect-plastic response to Gaussian strain hardening as the degree of polymerization N increases, without invoking entanglements. By relating hardening to interactions on the scale of monomers and chain segments, we correctly predict its magnitude. Strain-activated relaxation arising from the need to maintain constant chain contour length reduces the characteristic relaxation time by a factor ~εN during active deformation at strain rate ε. This prediction is consistent with results from recent experiments and simulations, and we suggest how it may be further tested experimentally.
Physical Review E 10/2010; 82(4 Pt 1):041803. · 2.26 Impact Factor
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ABSTRACT: We study numerically the density of optical states (DOS) in two-dimensional photonic structures with short-range positional order, and observe a clear transition from polycrystalline to amorphous photonic systems. In polycrystals, photonic band gaps (PBGs) are formed within individual do- mains, which leads to a depletion of the DOS similar to that in periodic structures. In amorphous photonic media, the domain sizes are too small to form PBGs, thus the depletion of the DOS is weakened significantly. The critical domain size that separates the polycrystalline and amorphous regimes is determined by the attenuation length of Bragg scattering, which depends not only on the degree of positional order but also the refractive index contrast of the photonic material. Even with relatively low refractive index contrast, we find that modest short-range positional order in photonic structures enhances light confinement via collective scattering and interference. Comment: 20 pages, 10 figures
08/2010;
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ABSTRACT: We enumerate all minimal energy packings (MEPs) for small single linear and ring polymers composed of spherical monomers with contact attractions and hard-core repulsions and compare them to corresponding results for monomer packings. We define and identify "dividing surfaces" in polymer packings, which reduce the number of arrangements that satisfy hard-sphere and covalent-bond constraints. Compared to monomer MEPs, polymer MEPs favor intermediate structural symmetry. We also examine the packing-preparation dependence for longer single chains using molecular dynamics simulations. For slow temperature quenches, chains form crystallites with close-packed cores. As the quench rate increases, the core size decreases and the exterior becomes more disordered. By examining the contact number, we connect the suppression of crystallization to the onset of isostaticity in disordered packings.
Physical Review Letters 08/2010; 105(6):068001. · 7.37 Impact Factor
