Finite-strain elasticity theory and liquid-liquid phase separation in compressible gels.

The theory of finite-strain elasticity is applied to the phenomenon of cavitation observed in polymer gels following liquid-liquid phase separation of the solvent, which opens a fascinating window on the role of finite-strain elasticity theory in soft materials in general. We show that compressibility effects strongly enhance cavitation in simple materials that obey neo-Hookean elasticity. On the other hand, cavitation phenomena in gels of flexible polymers in a binary solvent that phase separates are surprisingly similar to those of incompressible materials. We find that, as a function of the interfacial energy between the two solvent components, there is a sharp transition between cavitation and classical nucleation and growth. Next, biopolymer gels are characterized by strain hardening and even very low levels of strain hardening turn out to suppress cavitation in polymer gels that obey Flory-Huggins theory in the absence of strain hardening. Our results indicate that cavitation is, in essence, not possible for polymer networks that show strain hardening.

Search and Rescue in California: The Need for a Centralized Reporting System.

INTRODUCTION: There is no published information on the epidemiology of wilderness rescues in California outside of national parks. The objective of this study was to investigate the epidemiology of wilderness search and rescue (SAR) missions in California and identify risk factors for individuals requiring rescue due to accidental injury, illness, or navigation errors in the California wilderness. METHODS: A retrospective review of SAR missions in California from 2018 to 2020 was conducted. This was done from a database of information collected by the California Office of Emergency Services and the Mountain Rescue Association from SAR teams, who submitted voluntarily. The subject demographics, activity, location, and outcomes of each mission were analyzed. RESULTS: Eighty percent of the initial data were excluded because of incomplete or inaccurate data. Seven hundred forty-eight SAR missions involving 952 subjects were included in the study. The demographics, activities, and injuries of our population were consistent with those reported from other epidemiological SAR studies, and there were significant differences in outcomes based on the subject's activity. For example, water activities were highly correlated with a fatal outcome. CONCLUSIONS: The final data show interesting trends, but it is difficult to draw firm conclusions because so much of the initial data had to be excluded. A uniform system for reporting SAR missions in California may be helpful for further research, which may aid both SAR teams and the recreational public in understanding risk factors. A proposed SAR form for easy entry is included in the discussion section.

Microcircuit Synchronization and Heavy-Tailed Synaptic Weight Distribution Augment preBötzinger Complex Bursting Dynamics.

The preBötzinger Complex (preBötC) encodes inspiratory time as rhythmic bursts of activity underlying each breath. Spike synchronization throughout a sparsely connected preBötC microcircuit initiates bursts that ultimately drive the inspiratory motor patterns. Using minimal microcircuit models to explore burst initiation dynamics, we examined the variability in probability and latency to burst following exogenous stimulation of a small subset of neurons, mimicking experiments. Among various physiologically plausible graphs of 1000 excitatory neurons constructed using experimentally determined synaptic and connectivity parameters, directed Erdos-Rényi graphs with a broad (lognormal) distribution of synaptic weights best captured the experimentally observed dynamics. preBötC synchronization leading to bursts was regulated by the efferent connectivity of spiking neurons that are optimally tuned to amplify modest preinspiratory activity through input convergence. Using graph-theoretic and machine learning-based analyses, we found that input convergence of efferent connectivity at the next-nearest neighbor order was a strong predictor of incipient synchronization. Our analyses revealed a crucial role of synaptic heterogeneity in imparting exceptionally robust yet flexible preBötC attractor dynamics. Given the pervasiveness of lognormally distributed synaptic strengths throughout the nervous system, we postulate that these mechanisms represent a ubiquitous template for temporal processing and decision-making computational motifs.SIGNIFICANCE STATEMENT Mammalian breathing is robust, virtually continuous throughout life, yet is inherently labile: to adapt to rapid metabolic shifts (e.g., fleeing a predator or chasing prey); for airway reflexes; and to enable nonventilatory behaviors (e.g., vocalization, breathholding, laughing). Canonical theoretical frameworks-based on pacemakers and intrinsic bursting-cannot account for the observed robustness and flexibility of the preBötzinger Complex rhythm. Experiments reveal that network synchronization is the key to initiate inspiratory bursts in each breathing cycle. We investigated preBötC synchronization dynamics using network models constructed with experimentally determined neuronal and synaptic parameters. We discovered that a fat-tailed (non-Gaussian) synaptic weight distribution-a manifestation of synaptic heterogeneity-augments neuronal synchronization and attractor dynamics in this vital rhythmogenic network, contributing to its extraordinary reliability and responsiveness.

Defect Production in Compressed Filament Bundles.

We discuss the response of biopolymer filament bundles bound by transient cross-linkers to compressive loading. These systems admit a mechanical instability at stresses typically below that of traditional Euler buckling. In this instability, there is thermally activated pair production of topological defects that generate localized regions of bending-kinks. These kinks shorten the bundle's effective length, thereby reducing the elastic energy of the mechanically loaded structure. This effect is the thermal analog of the Schwinger effect, in which a sufficiently large electric field causes electron-positron pair production. We discuss this analogy and describe the implications of this analysis for the mechanics of biopolymer filament bundles of various types under compression.

Braiding Dynamics in Semiflexible Filament Bundles under Oscillatory Forcing.

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.

Cell contact guidance via sensing anisotropy of network mechanical resistance.

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 |Y*| -1 - |X*| -1 increased over fourfold in terms of the Fourier magnitudes of microbead displacement |X*| and |Y*| at the drive frequency with respect to alignment direction Y 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.

Geometrically induced localization of flexural waves on thin warped physical membranes.

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.

Topological defects produce kinks in biopolymer filament bundles.

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.

Effects of curvature on the propagation of undulatory waves in lower dimensional elastic materials.

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.

Directed force propagation in semiflexible networks.

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.

Dynamical phase separation on rhythmogenic neuronal networks.

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 Erdos-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.

Equilibrium fluctuations of a semiflexible filament cross linked into a network.

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.

Dynamics of undulatory fluctuations of semiflexible filaments in a network.

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.

Noise-induced distortion of the mean limit cycle of nonlinear oscillators.

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.

Parent Intent and Willingness to Immunize Children Against Influenza in the Pediatric Emergency Department.

OBJECTIVES: To determine rates of influenza immunization among children treated in a pediatric emergency department (ED) and to ascertain parent willingness for children to receive influenza vaccine (IV) in the ED. METHODS: Interviews were conducted with parents of children 6 months or older evaluated in the ED for minor illness or injury. Demographic data, IV history, and intent and willingness to receive future IV were recorded during the summer of 2013. Participants were contacted in March 2014 to assess IV status, barriers to obtaining IV, and willingness to obtain IV in the ED. Chart review determined number of patients who were at high risk. RESULTS: Of 457 families approached, 285 (62%) were enrolled. Two hundred forty-two (85%) intended to vaccinate; 83% reported willingness to receive IV at a future ED visit. Common reasons for not receiving IV were concerns about adverse effects (31%) and lack of time or interest (24%). Of the 224 participants (79%) reached in follow-up, 112 (50%) had received IV in the prior season. Among those who did not receive IV, 65 (66%) had intended to vaccinate, and 54 (55%) indicated they would have accepted IV in the ED. Fifty-three (54%) of unvaccinated patients at follow-up had high risk of influenza complications. CONCLUSIONS: Our data support an IV program in the pediatric ED as a means of increasing vaccination rates, particularly among high-risk patients. Parents are often concerned about adverse effects of IV, and providers should target education in this area.

Conformation of a semiflexible filament in a quenched random potential.

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.

Simultaneous cell traction and growth measurements using light.

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.

Nonequilibrium limit-cycle oscillators: Fluctuations in hair bundle dynamics.

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.

Mechanical hysteresis in actin networks.

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.

Membrane insertion of-and membrane potential sensing by-semiconductor voltage nanosensors: Feasibility demonstration.

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.