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Polymers (Basel) 2021 Jul 1;13(13). Epub 2021 Jul 1.

Department of Physics & Astronomy, University of California, Los Angeles, CA 90095, USA.

We examine the nonequilibrium production of topological defects-braids-in semiflexible filament bundles under cycles of compression and tension. During these cycles, the period of compression facilitates the thermally activated pair production of braid/anti-braid pairs, which then may separate when the bundle is under tension. As a result, appropriately tuned alternating periods of compression and extension should lead to the proliferation of braid defects in a bundle so that the linear density of these pairs far exceeds that expected in the thermal equilibrium. Secondly, we examine the slow extension of braided bundles under tension, showing that their end-to-end length creeps nonmonotonically under a fixed force due to braid deformation and the motion of the braid pair along the bundle. We conclude with a few speculations regarding experiments on semiflexible filament bundles and their networks.

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http://dx.doi.org/10.3390/polym13132195 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8271738 | PMC |

July 2021

Proc Natl Acad Sci U S A 2021 Jul;118(29)

Department of Biomedical Engineering, University of Minnesota, Twin Cities, Minneapolis, MN 55455;

Despite the ubiquitous importance of cell contact guidance, the signal-inducing contact guidance of mammalian cells in an aligned fibril network has defied elucidation. This is due to multiple interdependent signals that an aligned fibril network presents to cells, including, at least, anisotropy of adhesion, porosity, and mechanical resistance. By forming aligned fibrin gels with the same alignment strength, but cross-linked to different extents, the anisotropic mechanical resistance hypothesis of contact guidance was tested for human dermal fibroblasts. The cross-linking was shown to increase the mechanical resistance anisotropy, without detectable change in network microstructure and without change in cell adhesion to the cross-linked fibrin gel. This methodology thus isolated anisotropic mechanical resistance as a variable for fixed anisotropy of adhesion and porosity. The mechanical resistance anisotropy |*| - |*| increased over fourfold in terms of the Fourier magnitudes of microbead displacement |*| and |*| at the drive frequency with respect to alignment direction obtained by optical forces in active microrheology. Cells were found to exhibit stronger contact guidance in the cross-linked gels possessing greater mechanical resistance anisotropy: the cell anisotropy index based on the tensor of cell orientation, which has a range 0 to 1, increased by 18% with the fourfold increase in mechanical resistance anisotropy. We also show that modulation of adhesion via function-blocking antibodies can modulate the guidance response, suggesting a concomitant role of cell adhesion. These results indicate that fibroblasts can exhibit contact guidance in aligned fibril networks by sensing anisotropy of network mechanical resistance.

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http://dx.doi.org/10.1073/pnas.2024942118 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8307272 | PMC |

July 2021

Phys Rev E 2021 May;103(5-1):053002

Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA.

We consider the propagation of flexural waves across a nearly flat, thin membrane, whose stress-free state is curved. The stress-free configuration is specified by a quenched height field, whose Fourier components are drawn from a Gaussian distribution with power-law variance. Gaussian curvature couples the in-plane stretching to out-of-plane bending. Integrating out the faster stretching modes yields a wave equation for undulations in the presence of an effective random potential, determined purely by geometry. We show that at long times and lengths, the undulation intensity obeys a diffusion equation. The diffusion coefficient is found to be frequency dependent and sensitive to the quenched height field distribution. Finally, we consider the effect of coherent backscattering corrections, yielding a weak localization correction that decreases the diffusion coefficient proportional to the logarithm of the system size, and induces a localization transition at large amplitude of the quenched height field. The localization transition is confirmed via a self-consistent extension to the strong disorder regime.

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http://dx.doi.org/10.1103/PhysRevE.103.053002 | DOI Listing |

May 2021

Proc Natl Acad Sci U S A 2021 Apr;118(15)

Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1596.

Bundles of stiff filaments are ubiquitous in the living world, found both in the cytoskeleton and in the extracellular medium. These bundles are typically held together by smaller cross-linking molecules. We demonstrate, analytically, numerically, and experimentally, that such bundles can be kinked, that is, have localized regions of high curvature that are long-lived metastable states. We propose three possible mechanisms of kink stabilization: a difference in trapped length of the filament segments between two cross-links, a dislocation where the endpoint of a filament occurs within the bundle, and the braiding of the filaments in the bundle. At a high concentration of cross-links, the last two effects lead to the topologically protected kinked states. Finally, we explore, numerically and analytically, the transition of the metastable kinked state to the stable straight bundle.

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http://dx.doi.org/10.1073/pnas.2024362118 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8053966 | PMC |

April 2021

Phys Rev E 2021 Jan;103(1-1):013002

Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA.

The mechanics of lower dimensional elastic structures depends strongly on the geometry of their stress-free state. Elastic deformations separate into in-plane stretching and lower energy out-of-plane bending deformations. For elastic structures with a curved stress-free state, these two elastic modes are coupled within linear elasticity. We investigate the effect of that curvature-induced coupling on wave propagation in lower dimensional elastic structures, focusing on the simplest example-a curved elastic rod in two dimensions. We focus only on the geometry-induced coupling between bending and longitudinal (in-plane) strain that is common to both rods in two dimensions and to elastic shells. We find that the dispersion relation of the waves becomes gapped in the presence of finite curvature; bending modes are absent below a frequency proportional to the curvature of the rod. By studying the scattering of undulatory waves off regions of uniform curvature, we find that undulatory waves with frequencies in the gap associated with the curved region tunnel through that curved region via conversion into compression waves. These results should be directly applicable to the spectrum and spatial distribution of phonon modes in a number of curved rod-like elastic solids, including carbon nanotubes and biopolymer filaments.

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http://dx.doi.org/10.1103/PhysRevE.103.013002 | DOI Listing |

January 2021

Phys Rev E 2020 Dec;102(6-1):062406

Department of Physics and Astronomy, UCLA, Los Angeles, California 90095, USA.

We study the dynamics of a single semiflexible filament coupled to a Hookean spring at its boundary. The spring produces a fluctuating tensile force on the filament, the value of which depends on the filament's instantaneous end-to-end length. The spring thereby introduces a nonlinearity, which mixes the undulatory normal modes of the filament and changes their dynamics. We study these dynamics using the Martin-Siggia-Rose-Janssen-De Dominicis formalism, and compute the time-dependent correlation functions of transverse undulations and of the filament's end-to-end distance. The relaxational dynamics of the modes below a characteristic wavelength sqrt[κ/τ_{R}], set by the filament's bending modulus κ and spring-renormalized tension τ_{R}, are changed by the boundary spring. This occurs near the crossover frequency between tension- and bending-dominated modes of the system. The boundary spring can be used to represent the linear elastic compliance of the rest of the filament network to which the filament is cross linked. As a result, we predict that this nonlinear effect will be observable in the dynamical correlations of constituent filaments of networks and in the networks' collective shear response. The system's dynamic shear modulus is predicted to exhibit the well-known crossover with increasing frequency from ω^{1/2} to ω^{3/4}, but the inclusion of the network's compliance in the analysis of the individual filament dynamics shifts this transition to a higher frequency.

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http://dx.doi.org/10.1103/PhysRevE.102.062406 | DOI Listing |

December 2020

Soft Matter 2020 Dec 24. Epub 2020 Dec 24.

Department of Physics & Astronomy, University of California, Los Angeles, 90095, USA. and Department of Chemistry & Biochemistry, University of California, Los Angeles, 90095, USA and Department of Computational Medicine, University of California, Los Angeles, 90095, USA.

We consider the propagation of tension along specific filaments of a semiflexible filament network in response to the application of a point force using a combination of numerical simulations and analytic theory. We find the distribution of force within the network is highly heterogeneous, with a small number of fibers supporting a significant fraction of the applied load over distances of multiple mesh sizes surrounding the point of force application. We suggest that these structures may be thought of as tensile force chains, whose structure we explore via simulation. We develop self-consistent calculations of the point-force response function and introduce a transfer matrix approach to explore the decay of tension (into bending) energy and the branching of tensile force chains in the network.

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http://dx.doi.org/10.1039/d0sm01177k | DOI Listing |

December 2020

Phys Rev E 2020 Jun;101(6-1):062307

Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA.

We explore the firing-rate model of excitatory neurons with dendritic adaptation (the Feldman-Del Negro model [J. L. Feldman and C. A. Del Negro, Nat. Rev. Neurosci. 7, 232 (2006)10.1038/nrn1871; D. J. Schwab et al., Phys. Rev. E 82, 051911 (2010)10.1103/PhysRevE.82.051911] interacting on a fixed, directed Erdős-Rényi network. This model is applied to the dynamics of the pre-Bötzinger complex, the mammalian central pattern generator with N∼10^{3} neurons, which produces a collective metronomic signal that times inspiration. In the all-to-all coupled variant of the model, there is spontaneous symmetry breaking in which some fraction of the neurons becomes stuck in a high-firing-rate state, while others become quiescent. This separation into firing and nonfiring clusters persists into more sparsely connected networks. In these sparser networks, the clustering is influenced by k cores of the underlying network. The model has a number of features of the dynamical phase diagram that violate the predictions of mean-field analysis. In particular, we observe in the simulated networks that stable oscillations do not persist in the high-sensitivity limit, in contradiction to the predictions of mean-field theory. Moreover, we observe that the oscillations in these sparse networks are remarkably robust in response to killing neurons, surviving until only approximately 20% of the network remains. This robustness is consistent with experiment.

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http://dx.doi.org/10.1103/PhysRevE.101.062307 | DOI Listing |

June 2020

Phys Rev E 2020 Jan;101(1-1):012408

Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA.

We examine the equilibrium fluctuation spectrum of a semiflexible filament segment in a network. The effect of this cross linking is to modify the mechanical boundary conditions at the end of the filament. We consider the effect of both tensile stress in the network and its elastic compliance. Most significantly, the network's compliance introduces a nonlinear term into the filament Hamiltonian even in the small-bending approximation. We analyze the effect of this nonlinearity upon the filament's fluctuation profile. We also find that there are three principal fluctuation regimes dominated by one of the following: (i) network tension, (ii) filament bending stiffness, or (iii) network compliance. This work provides the theoretical framework necessary to analyze activity microrheology, which uses the observed filament fluctuations as a noninvasive probe of tension in the network.

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http://dx.doi.org/10.1103/PhysRevE.101.012408 | DOI Listing |

January 2020

Phys Rev E 2019 Jun;99(6-1):062124

Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA.

We study the change in the size and shape of the mean limit cycle of a stochastically driven nonlinear oscillator as a function of noise amplitude. Such dynamics occur in a variety of nonequilibrium systems, including the spontaneous oscillations of hair cells of the inner ear. The noise-induced distortion of the limit cycle generically leads to its rounding through the elimination of sharp (high-curvature) features through a process we call corner cutting. We provide a criterion that may be used to identify limit cycle regions most susceptible to such noise-induced distortions. By using this criterion, one may obtain more meaningful parametric fits of nonlinear dynamical models from noisy experimental data, such as those coming from spontaneously oscillating hair cells.

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http://dx.doi.org/10.1103/PhysRevE.99.062124 | DOI Listing |

June 2019

Phys Rev E 2019 Apr;99(4-1):042501

Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA.

Motivated by the observation of the storage of excess elastic free energy, prestress, in cross-linked semiflexible networks, we consider the problem of the conformational statistics of a single semiflexible polymer in a quenched random potential. The random potential, which represents the effect of cross-linking to other filaments, is assumed to have a finite correlation length ξ and mean strength V_{0}. We examine statistical distribution of curvature in filament with thermal persistence length ℓ_{P} and length L_{0} in the limit in which ℓ_{P}≫L_{0}. We compare our theoretical predictions to finite-element Brownian dynamics simulations. Finally, we comment on the validity of replica field techniques in addressing these questions.

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http://dx.doi.org/10.1103/PhysRevE.99.042501 | DOI Listing |

April 2019

J Biophotonics 2019 03 7;12(3):e201800182. Epub 2018 Nov 7.

Quantitative Light Imaging Laboratory, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois.

Characterizing the effects of force fields generated by cells on proliferation, migration and differentiation processes is challenging due to limited availability of nondestructive imaging modalities. Here, we integrate a new real-time traction stress imaging modality, Hilbert phase dynamometry (HPD), with spatial light interference microscopy (SLIM) for simultaneous monitoring of cell growth during differentiation processes. HPD uses holographic principles to extract displacement fields from chemically patterned fluorescent grid on deformable substrates. This is converted into forces by solving an elasticity inverse problem. Since HPD uses the epi-fluorescence channel of an inverted microscope, cellular behavior can be concurrently studied in transmission with SLIM. We studied the differentiation of mesenchymal stem cells (MSCs) and found that cells undergoing osteogenesis and adipogenesis exerted larger and more dynamic stresses than their precursors, with MSCs developing the smallest forces and growth rates. Thus, we develop a powerful means to study mechanotransduction during dynamic processes where the matrix provides context to guide cells toward a physiological or pathological outcome.

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http://dx.doi.org/10.1002/jbio.201800182 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7236521 | PMC |

March 2019

Phys Rev E 2018 Jun;97(6-1):062411

Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA.

We develop a framework for the general interpretation of the stochastic dynamical system near a limit cycle. Such quasiperiodic dynamics are commonly found in a variety of nonequilibrium systems, including the spontaneous oscillations of hair cells of the inner ear. We demonstrate quite generally that in the presence of noise, the phase of the limit cycle oscillator will diffuse, while deviations in the directions locally orthogonal to that limit cycle will display the Lorentzian power spectrum of a damped oscillator. We identify two mechanisms by which these stochastic dynamics can acquire a complex frequency dependence and discuss the deformation of the mean limit cycle as a function of temperature. The theoretical ideas are applied to data obtained from spontaneously oscillating hair cells of the amphibian sacculus.

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http://dx.doi.org/10.1103/PhysRevE.97.062411 | DOI Listing |

June 2018

Soft Matter 2018 Mar;14(11):2052-2058

James Franck Institute, The University of Chicago, Chicago, IL 60637, USA.

Understanding the response of complex materials to external force is central to fields ranging from materials science to biology. Here, we describe a novel type of mechanical adaptation in cross-linked networks of F-actin, a ubiquitous protein found in eukaryotic cells. We show that shear stress changes the network's nonlinear mechanical response even long after that stress is removed. The duration, magnitude and direction of forcing history all change this mechanical response. While the mechanical hysteresis is long-lived, it can be simply erased by force application in the opposite direction. We further show that the observed mechanical adaptation is consistent with stress-dependent changes in the nematic order of the constituent filaments. Thus, this mechanical hysteresis arises from the changes in non-linear response that originates from stress-induced changes to filament orientation. This demonstrates that F-actin networks can exhibit analog read-write mechanical hysteretic properties, which can be used for adaptation to mechanical stimuli.

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http://dx.doi.org/10.1039/c7sm01948c | DOI Listing |

March 2018

Sci Adv 2018 01 12;4(1):e1601453. Epub 2018 Jan 12.

Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA 90095, USA.

We developed membrane voltage nanosensors that are based on inorganic semiconductor nanoparticles. We provide here a feasibility study for their utilization. We use a rationally designed peptide to functionalize the nanosensors, imparting them with the ability to self-insert into a lipid membrane with a desired orientation. Once inserted, these nanosensors could sense membrane potential via the quantum confined Stark effect, with a single-particle sensitivity. With further improvements, these nanosensors could potentially be used for simultaneous recording of action potentials from multiple neurons in a large field of view over a long duration and for recording electrical signals on the nanoscale, such as across one synapse.

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http://dx.doi.org/10.1126/sciadv.1601453 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5770167 | PMC |

January 2018

Soft Matter 2017 Oct;13(38):6730-6742

Department of Chemistry & Biochemistry, University of California, Los Angeles 90095, USA.

Lipid monolayers at the air/water interface are often subject to large mechanical stresses when compressed laterally. For large enough compression they fold in the out-of-plane direction to relax stress. The repetitive folding and unfolding of lung surfactant monolayers during breathing plays a critical role in conserving monolayer material at the air/water interface lining the lung. Although the mechanisms behind the folding have been explored recently, relatively little information exists regarding the implications of folding dynamics on the long-term stability of the monolayer. We address this question by investigating the dynamical effect of folding rate in a lipid monolayer containing nano-particles, using a combination of analytic theory, simulation and experiment. We find that the presence of adsorbed particles are essential for monolayer rupture during unfolding. These particles act as linkers pinning the folds shut. The rate of folding affects reversibility as well. We construct a reversibility phase diagram spanned by the compression period and the size of the adsorbed particles showing the complex interaction of fold morphology, particle diffusion, and linker unbinding that results in reversible or irreversible folding.

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http://dx.doi.org/10.1039/c6sm01382a | DOI Listing |

October 2017

Proc Natl Acad Sci U S A 2017 03 27;114(11):2865-2870. Epub 2017 Feb 27.

Department of Physics and Astronomy, University of California, Los Angeles, CA 90095.

The thermal fluctuations of membranes and nanoscale shells affect their mechanical characteristics. Whereas these fluctuations are well understood for flat membranes, curved shells show anomalous behavior due to the geometric coupling between in-plane elasticity and out-of-plane bending. Using conventional shallow shell theory in combination with equilibrium statistical physics we theoretically demonstrate that thermalized shells containing regions of negative Gaussian curvature naturally develop anomalously large fluctuations. Moreover, the existence of special curves, "singular lines," leads to a breakdown of linear membrane theory. As a result, these geometric curves effectively partition the cell into regions whose fluctuations are only weakly coupled. We validate these predictions using high-resolution microscopy of human red blood cells (RBCs) as a case study. Our observations show geometry-dependent localization of thermal fluctuations consistent with our theoretical modeling, demonstrating the efficacy in combining shell theory with equilibrium statistical physics for describing the thermalized morphology of cellular membranes.

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http://dx.doi.org/10.1073/pnas.1613204114 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5358351 | PMC |

March 2017

Phys Rev E 2016 Sep 19;94(3-1):032505. Epub 2016 Sep 19.

Department of Physics, UCLA, Los Angeles, California 90095-1596, USA.

Fluctuation-induced interactions are an important organizing principle in a variety of soft matter systems. We investigate the role of fluctuation-based or thermal Casimir interactions between cross linkers in a semiflexible network. One finds that, by integrating out the polymer degrees of freedom, there is an attractive logarithmic potential between nearest-neighbor cross linkers in a bundle, with a significantly weaker next-nearest-neighbor interaction. Here we show that a one-dimensional gas of these strongly interacting linkers in equilibrium with a source of unbound ones admits a discontinuous phase transition between a sparsely and a densely bound bundle. This discontinuous transition induced by the long-ranged nature of the Casimir interaction allows for a similarly abrupt structural transition in semiflexible filament networks between a low cross linker density isotropic phase and a higher cross link density bundle network. We support these calculations with the results of finite element Brownian dynamics simulations of semiflexible filaments and transient cross linkers.

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http://dx.doi.org/10.1103/PhysRevE.94.032505 | DOI Listing |

September 2016

Data Brief 2016 Sep 28;8:506-15. Epub 2016 May 28.

Department of Chemistry & Biochemistry, University of California, Los Angeles, CA 90095, USA; Department of Physics & Astronomy, University of California, Los Angeles, CA 90095, USA; Department of Biomathematics, University of California, Los Angeles, CA 90095, USA; California Nanosystems Institute, University of California, Los Angeles, CA 90095, USA.

We present here the calculation of the mean time to capture of a tethered ligand to the receptor. This calculation is then used to determine the shift in the partitioning between (1) free, (2) singly bound, and (3) doubly bound ligands in chemical equilibrium as a function of the length of the tether. These calculations are used in the research article Fibroblast Growth Factor 2 Dimer with Superagonist in vitro Activity Improves Granulation Tissue Formation During Wound Healing (Decker et al., in press [1]) to explain quantitatively how changes in polymeric linker length in the ligand dimers modifies the efficacy of these molecules relative to that of free ligands.

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http://dx.doi.org/10.1016/j.dib.2016.05.050 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4925454 | PMC |

September 2016

Phys Rev E 2016 Mar 30;93(3):032613. Epub 2016 Mar 30.

Department of Physics and Astronomy, University of California, Irvine, California 92697, USA.

We report on the collapse of bubble rafts under compression in a closed rectangular geometry. A bubble raft is a single layer of bubbles at the air-water interface. A collapse event occurs when bubbles submerge beneath the neighboring bubbles under compression, causing the structure of the bubble raft to go from single-layer to multilayer. We studied the collapse dynamics as a function of compression velocity. At higher compression velocity we observe a more uniform distribution of collapse events, whereas at lower compression velocities the collapse events accumulate at the system boundaries. We propose that this system can be understood in terms of a linear elastic sheet coupled to a local internal (Ising) degree of freedom. The two internal states, which represent one bubble layer versus two, couple to the elasticity of the sheet by locally changing the reference state of the material. By exploring the collapse dynamics of the bubble raft, one may address the basic nonlinear mechanics of a number of complex systems in which elastic stress is coupled to local internal variables.

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http://dx.doi.org/10.1103/PhysRevE.93.032613 | DOI Listing |

March 2016

ACS Nano 2016 Mar 25;10(3):3509-17. Epub 2016 Feb 25.

Department of Physics and Astronomy, University of California , Irvine, California 92697, United States.

Passage time through single micropores is an important parameter used to quantify the surface charge and zeta potential of particles. In the resistive-pulse technique, the measured time of pressure- or electric-field-induced translocation is assumed to be direction independent. This assumption is supported by the low velocities of the particles and the supporting fluid such that the transport reversibility known for Stokes flow is expected to apply. In this article, we present examples of micropores in which passage time of ∼400 nm diameter particles becomes direction-dependent; that is, the particles' translocation times from left to right and right to left are different. These pores are characterized by an undulating inner diameter such that at least one wider zone called a cavity separates two narrower regions of different lengths. We propose that the observed direction-dependence of the translocation velocity is caused by an asymmetric efficiency of particle focusing toward the pore axis, which leads to a direction-dependent set of particle trajectories. The reported pores present the simplest system in which time-broken symmetry has been observed. The results are of importance for sensing of particles and molecules by the resistive-pulse technique since pores used for detection are often characterized by finite roughness or noncylindrical shape. This article also points to the role of particle focusing in the magnitude and distribution of the translocation times.

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http://dx.doi.org/10.1021/acsnano.5b07709 | DOI Listing |

March 2016

Biomaterials 2016 Mar 15;81:157-168. Epub 2015 Dec 15.

Department of Chemistry and Biochemistry and California NanoSystems Institute, University of California, Los Angeles, 607 Charles E. Young Drive South, Los Angeles, CA 90095-1569, United States. Electronic address:

Site-specific chemical dimerization of fibroblast growth factor 2 (FGF2) with the optimal linker length resulted in a FGF2 homodimer with improved granulation tissue formation and blood vessel formation at exceptionally low concentrations. Homodimers of FGF2 were synthesized through site-specific linkages to both ends of different molecular weight poly(ethylene glycols) (PEGs). The optimal linker length was determined by screening dimer-induced metabolic activity of human dermal fibroblasts and found to be that closest to the inter-cysteine distance, 70 Å, corresponding to 2 kDa PEG. A straightforward analysis of the kinetics of second ligand binding as a function of tether length showed that, as the polymerization index (the number of monomer repeat units in the polymer, N) of the tether decreases, the mean time for second ligand capture decreases as ∼N(3/2), leading to an enhancement of the number of doubly bound ligands in steady-state for a given (tethered) ligand concentration. FGF2-PEG2k-FGF2 induced greater fibroblast metabolic activity than FGF2 alone, all other dimers, and all monoconjugates, at each concentration tested, with the greatest difference observed at low (0.1 ng/mL) concentration. FGF2-PEG2k-FGF2 further exhibited superior activity compared to FGF2 for both metabolic activity and migration in human umbilical vein endothelial cells, as well as improved angiogenesis in a coculture model in vitro. Efficacy in an in vivo wound healing model was assessed in diabetic mice. FGF2-PEG2k-FGF2 increased granulation tissue and blood vessel density in the wound bed compared to FGF2. The results suggest that this rationally designed construct may be useful for improving the fibroblast matrix formation and angiogenesis in chronic wound healing.

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http://dx.doi.org/10.1016/j.biomaterials.2015.12.003 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4715972 | PMC |

March 2016

Soft Matter 2015 Jun 27;11(24):4899-911. Epub 2015 May 27.

Department of Physics & Astronomy, UCLA, Los Angeles, CA 90005, USA.

We examine the bond-breaking dynamics of transiently cross-linked semiflexible networks using a single filament model in which that filament is peeled from an array of cross-linkers. We examine the effect of quenched disorder in the placement of the linkers along the filament and the effect of stochastic bond-breaking (assuming Bell model unbinding kinetics) on the dynamics of filament cross-linker dissociation and the statistics of ripping events. We find that bond forces decay exponentially away from the point of loading and that bond breaking proceeds sequentially down the linker array from the point of loading in a series of stochastic ripping events. We compare these theoretical predictions to the observed trajectories of large beads in a cross-linked microtubule network and identify the observed jumps of the bead with the linker rupture events predicted by the single filament model.

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http://dx.doi.org/10.1039/c5sm00262a | DOI Listing |

June 2015

Phys Rev Lett 2014 Jun 10;112(23):238102. Epub 2014 Jun 10.

Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095-1596, USA and Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA and Department of Biomathematics, UCLA, Los Angeles, California 90095-1596, USA.

We present a theoretical and computational analysis of the rheology of networks made up of bundles of semiflexible filaments bound by transient cross-linkers. Such systems are ubiquitous in the cytoskeleton and can be formed in vitro using filamentous actin and various cross-linkers. We find that their high-frequency rheology is characterized by a scaling behavior that is quite distinct from that of networks of the well-studied single semiflexible filaments. This regime can be understood theoretically in terms of a length-scale-dependent bending modulus for bundles. Next, we observe new dissipative dynamics associated with the shear-induced disruption of the network at intermediate frequencies. Finally, at low frequencies, we encounter a region of non-Newtonian rheology characterized by power-law scaling. This regime is dominated by bundle dissolution and large-scale rearrangements of the network driven by equilibrium thermal fluctuations.

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http://dx.doi.org/10.1103/PhysRevLett.112.238102 | DOI Listing |

June 2014

Phys Rev E Stat Nonlin Soft Matter Phys 2013 Nov 11;88(5):052404. Epub 2013 Nov 11.

Department of Physics, UCLA, Los Angeles, California 90095-1596, USA.

We study elasticity-driven morphological transitions of soft spherical core-shell structures in which the core can be treated as an isotropic elastic continuum and the surface or shell as a tensionless liquid layer, whose elastic response is dominated by bending. To generate the transitions, we consider the case where the surface area of the liquid layer is increased for a fixed amount of interior elastic material. We find that generically there is a critical excess surface area at which the isotropic sphere becomes unstable to buckling. At this point it adopts a lower symmetry wrinkled structure that can be described by a spherical harmonic deformation. We study the dependence of the buckled sphere and critical excess area of the transition on the elastic parameters and size of the system. We also relate our results to recent experiments on the wrinkling of gel-filled vesicles as their interior volume is reduced. The theory may have broader applications to a variety of related structures from the macroscopic to the microscopic, including the wrinkling of dried peas, raisins, as well as the cell nucleus.

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http://dx.doi.org/10.1103/PhysRevE.88.052404 | DOI Listing |

November 2013

Phys Rev Lett 2013 Jul 16;111(3):038101. Epub 2013 Jul 16.

Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095-1596, USA.

We present a theory of flexural wave propagation on elastic shells having nontrivial geometry and develop an analogy to geometric optics. The transport of momentum within the shell itself is anisotropic due to the curvature, and as such complex classical effects such as birefringence are generically found. We determine the equations of reflection and refraction of such waves at boundaries between different local geometries, showing that waves are totally internally reflected, especially at boundaries between regions of positive and negative Gaussian curvature. We verify these effects by using finite element simulations and discuss the ramifications of these effects for the statistical mechanics of thin curved materials.

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http://dx.doi.org/10.1103/PhysRevLett.111.038101 | DOI Listing |

July 2013

Phys Rev Lett 2013 Mar 25;110(13):137802. Epub 2013 Mar 25.

Department of Chemistry & Biochemistry, UCLA, Los Angeles, California 90095-1596, USA.

Microrheological studies of phospholipid monolayers, bilayers, and other Langmuir monolayer systems are traditionally performed by observing the thermal fluctuations of tracers attached to the membrane or interface. Measurements of this type obtain surface moduli that are orders of magnitude different from those obtained using macroscopic or active techniques. These large discrepancies can result from uncertainties in the tracer's coupling to the monolayer or the local disruption of the monolayer by the tracer. To avoid such problems, we perform a microrheological experiment with the tracer particle placed at a known depth beneath the monolayer; this avoids the issues mentioned at the cost of generating a weaker, purely hydrodynamic coupling between the tracer and the monolayer. We calculate the appropriate response functions for this submerged particle microrheology and demonstrate the technique on three model monolayer systems.

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http://dx.doi.org/10.1103/PhysRevLett.110.137802 | DOI Listing |

March 2013

Soft Matter 2013 Jan;9(2):383-393

Department of Mechanical Engineering, University of California, Santa Barbara, CA, USA. ; Tel: +805-893-2594;

We determine the time- and force-dependent viscoelastic responses of reconstituted networks of microtubules that have been strongly crosslinked by biotin-streptavidin bonds. To measure the microscale viscoelasticity of such networks, we use a magnetic tweezers device to apply localized forces. At short time scales, the networks respond nonlinearly to applied force, with stiffening at small forces, followed by a reduction in the stiffening response at high forces, which we attribute to the force-induced unbinding of crosslinks. At long time scales, force-induced bond unbinding leads to local network rearrangement and significant bead creep. Interestingly, the network retains its elastic modulus even under conditions of significant plastic flow, suggesting that crosslinker breakage is balanced by the formation of new bonds. To better understand this effect, we developed a finite element model of such a stiff filament network with labile crosslinkers obeying force-dependent Bell model unbinding dynamics. The coexistence of dissipation, due to bond breakage, and the elastic recovery of the network is possible because each filament has many crosslinkers. Recovery can occur as long as a sufficient number of the original crosslinkers are preserved under the loading period. When these remaining original crosslinkers are broken, plastic flow results.

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http://dx.doi.org/10.1039/C2SM26934A | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3618965 | PMC |

January 2013

Phys Rev Lett 2012 Nov 2;109(18):188104. Epub 2012 Nov 2.

Quantitative Light Imaging Laboratory, Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.

Because of its ability to study specifically labeled structures, fluorescence microscopy is the most widely used technique for investigating live cell dynamics and function. Fluorescence correlation spectroscopy is an established method for studying molecular transport and diffusion coefficients at a fixed spatial scale. We propose a new approach, dispersion-relation fluorescence spectroscopy (DFS), to study the transport dynamics over a broad range of spatial and temporal scales. The molecules of interest are labeled with a fluorophore whose motion gives rise to spontaneous fluorescence intensity fluctuations that are analyzed to quantify the governing mass transport dynamics. These data are characterized by the effective dispersion relation. We report on experiments demonstrating that DFS can distinguish diffusive from advection motion in a model system, where we obtain quantitatively accurate values of both diffusivities and advection velocities. Because of its spatially resolved information, DFS can distinguish between directed and diffusive transport in living cells. Our data indicate that the fluorescently labeled actin cytoskeleton exhibits active transport motion along a direction parallel to the fibers and diffusive in the perpendicular direction.

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http://dx.doi.org/10.1103/PhysRevLett.109.188104 | DOI Listing |

November 2012

Phys Rev E Stat Nonlin Soft Matter Phys 2012 May 22;85(5 Pt 1):051915. Epub 2012 May 22.

Department of Chemistry & Biochemistry, University of California, Los Angeles, California 90095, USA.

We develop a continuum elastic approach to examining the bending mechanics of semiflexible filaments with a local internal degree of freedom that couples to the bending modulus. We apply this model to study the nonlinear mechanics of a double-stranded DNA oligomer (shorter than its thermal persistence length) whose free ends are linked by a single-stranded DNA chain. This construct, studied by H. Qu and G. Zocchi [Europhys. Lett. 94, 18003 (2011)], displays nonlinear strain softening associated with the local melting of the double-stranded DNA under applied torque and serves as a model system with which to study the nonlinear elasticity of DNA under large energy deformations. We show that one can account quantitatively for the observed bending mechanics using an augmented wormlike chain model, the helix-coil wormlike chain. We also predict that the highly bent and partially molten dsDNA should exhibit particularly large end-to-end fluctuations associated with the fluctuation of the length of the molten region, and propose appropriate experimental tests. We suggest that the augmented wormlike chain model discussed here is a useful analytic approach to the nonlinear mechanics of DNA or other biopolymer systems.

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http://dx.doi.org/10.1103/PhysRevE.85.051915 | DOI Listing |

May 2012

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