We develop a geometric approach to understand the mechanics of perforated thin elastic sheets, using the method of strain-dependent image elastic charges. This technique recognizes the buckling response of a hole under an external load as a geometrically tuned mechanism of stress relief. We use a diagonally pulled square paper frame as a model system to quantitatively test and validate our approach. Specifically, we compare nonlinear force-extension curves and global displacement fields in theory and experiment. We find a strong softening of the force response accompanied by curvature localization at the inner corners of the buckled frame. Counterintuitively, though in complete agreement with our theory, for a range of intermediate hole sizes, wider frames are found to buckle more easily than narrower ones. Upon extending these ideas to many holes, we demonstrate that interacting elastic image charges can provide a useful kirigami design principle to selectively relax stresses in elastic materials.

The highly strained conformation in dense molecular bottlebrushes (DB) has profound effects on the dynamics of these type of macromolecules. Understanding of such effects in both their linear and nonlinear viscoelastic responses is crucial for their design and processing. The nonlinear response of poly(1-octadecene), a highly entangled $\alpha$-olefin DB with linear side chains sixteen carbons long, is studied here and compared to the nonlinear response of a linear polyolefin (polypropylene) with equivalent linear viscoelastic response. We found that the DB shows remarkably larger extensional strain hardening (SH) and extensibility than the linear polyolefin. The strong SH is attributed to a strain-induced increase in friction drag between adjacent chains resulting from side-chain interdigitation and alignment perpendicular to the flow. The higher extensibility of DBs compared to linear counterparts has been predicted previously [Daniel et al., Nat. Mater. 15, 183 (2015)] and confirmed here for the first time in DB melts.

Even though the persistence length $L_P$ of double-stranded DNA plays a pivotal role in cell biology and nanotechnologies, its dependence on ionic strength $I$ lacks a consensual description. Using a high-throughput single-molecule technique and statistical physics modeling, we measure $L_P$ in the presence of monovalent (${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$) and divalent (${\mathrm{Mg}}^{2+}$, ${\mathrm{Ca}}^{2+}$) metallic and alkyl ammonium ions, over a large range $0.5\mathrm{mM}\le I\le 5\mathrm{M}$. We show that linear Debye-Hückel-type theories do not describe even part of these data. By contrast, the Netz-Orland and Trizac-Shen formulas, two approximate theories including nonlinear electrostatic effects and the finite DNA radius, fit our data with divalent and monovalent ions, respectively, over the whole $I$ range. Furthermore, the metallic ion type does not influence $L_P(I)$, in contrast to alkyl ammonium monovalent ions at high $I$.

Stereociliary imprints in the tectorial membrane (TM) have been taken as evidence that outer hair cells are sensitive to shearing displacements of the TM, which plays a key role in shaping cochlear sensitivity and frequency selectivity via resonance and traveling wave mechanisms. However, the TM is highly hydrated (97% water by weight), suggesting that the TM may be flexible even at the level of single hair cells. Here we show that nanoscale oscillatory displacements of microscale spherical probes in contact with the TM are resisted by frequency-dependent forces that are in phase with TM displacement at low and high frequencies, but are in phase with TM velocity at transition frequencies. The phase lead can be as much as a quarter of a cycle, thereby contributing to frequency selectivity and stability of cochlear amplification.

In forced wetting, a rapidly moving surface drags with it a thin layer of trailing fluid as it is plunged into a second fluid bath. Using high-speed interferometry, we find characteristic structure in the thickness of this layer with multiple thin flat triangular structures separated by much thicker regions. These features, depending on liquid viscosity and penetration velocity, are robust and occur in both wetting and dewetting geometries. Their presence clearly shows the importance of motion in the transverse direction. We present a model using the assumption that the velocity profile is robust to thickness fluctuations that gives a good estimate of the gap thickness in the thin regions.

Evolution is essential for shaping the biological functions. Darwin proposed the selection as the driving force for evolution upon mutations. While mutations are clear, the quantification of the selection force is still challenging. In this study, we identified and quantified both thermodynamic stability and kinetic accessibility as the selection forces for protein evolution. The protein evolution can be viewed and quantified as a trajectory moving along a superfunneled energy landscape with a line attractor at the bottom. The resulting evolved sequences and structures show strong protein characteristics including the hydrophobic core, high designability, and fast folding. The evolution principle uncovered here is validated on real proteins and sheds light on the protein design.

Continuous attractor neural networks generate a set of smoothly connected attractor states. In memory systems of the brain, these attractor states may represent continuous pieces of information such as spatial locations and head directions of animals. However, during the replay of previous experiences, hippocampal neurons show a discontinuous sequence in which discrete transitions of the neural state are phase locked with the slow-gamma ($\sim 30–50\mathrm{Hz}$) oscillation. Here, we explore the underlying mechanisms of the discontinuous sequence generation. We find that a continuous attractor neural network has several phases depending on the interactions between external input and local inhibitory feedback. The discrete-attractor-like behavior naturally emerges in one of these phases without any discreteness assumption. We propose that the dynamics of continuous attractor neural networks is the key to generate discontinuous state changes phase locked to the brain rhythm.

Organisms that exploit different environments may experience a stochastic delay in adjusting their fitness when they switch habitats. We study two such organisms whose fitness is determined by the species composition of the local environment, as they interact through a public good. We show that a delay in the fitness adjustment can lead to the coexistence of the two species in a metapopulation, although the faster-growing species always wins in well-mixed competition experiments. Coexistence is favored over wide parameter ranges and is independent of spatial clustering. It arises when species are heterogeneous in their fitness and can keep each other balanced.

The role of the actomyosin network is investigated in the elongation of C. elegans during embryonic morphogenesis. We present a model of active elongating matter that combines prestress and passive stress in nonlinear elasticity. Using this model we revisit recently published data from laser ablation experiments to account for why cells under contraction can lead to an opening fracture. By taking into account the specific embryo geometry, we obtain quantitative predictions for the contractile forces exerted by the molecular motors myosin II for an elongation up to 70% of the initial length. This study demonstrates the importance of active processes in embryonic morphogenesis and the interplay between geometry and nonlinear mechanics during morphological events. In particular, it outlines the role of each connected layer of the epidermis compressed by an apical extracellular matrix that distributes the stresses during elongation.

Composites of flexible and rigid polymers are ubiquitous in biology and industry alike, yet the physical principles determining their mechanical properties are far from understood. Here, we couple force spectroscopy with large-scale Brownian dynamics simulations to elucidate the unique viscoelastic properties of custom-engineered blends of entangled flexible DNA molecules and semiflexible actin filaments. We show that composites exhibit enhanced stress stiffening and prolonged mechanomemory compared to systems of actin or DNA alone, and that these nonlinear features display a surprising nonmonotonic dependence on the fraction of actin in the composite. Simulations reveal that these counterintuitive results arise from synergistic microscale interactions between the two biopolymers. Namely, DNA entropically drives actin filaments to form bundles that stiffen the network but reduce the entanglement density, while a uniform well-connected actin network is required to reinforce the DNA network against yielding and flow. The competition between bundling and connectivity triggers an unexpected stress response that leads equal mass DNA-actin composites to exhibit the most pronounced stress stiffening and the most long-lived entanglements.

We investigate the nature of long-range density fluctuations in melts of model “soft” polymers, specifically stars and bottlebrushes, over a wide temperature range by molecular dynamics simulation. The cores of the stars and the backbones of bottlebrush polymers are found to have a hyperuniform distribution; i.e., they exhibit anomalously small density fluctuations over a wide temperature range above the glass transition temperature. The hyperuniformity of these substituent polymer subregions is hidden since the fluid as a whole does not exhibit this property. These findings offer a strategy for the practical design of hyperuniform polymeric materials.

We study a network of unidirectionally coupled rotators with independent identically distributed (i.i.d.) frequencies and i.i.d. coupling coefficients. Similar to biological networks, this system can attain an asynchronous state with pronounced temporal autocorrelations of the rotators. We derive differential equations for the self-consistent autocorrelation function that can be solved analytically in limit cases. For more involved scenarios, its numerical solution is confirmed by simulations of networks with Gaussian or sparsely distributed coupling coefficients. The theory is finally generalized for pulse-coupled units and tested on a standard model of computational neuroscience, a recurrent network of sparsely coupled exponential integrate-and-fire neurons.

Vacancies in simple cubic crystals of hard cubes are known to delocalize over one-dimensional chains of several lattice sites. Here, we use computer simulations to examine the structure and dynamics of vacancies in simple cubic crystals formed by hard cubes, right rhombic prisms (slanted cubes), truncated cubes, and particles interacting via a soft isotropic pair potential. We show that these vacancies form a vacancy analog of the crowdion interstitial, generating a strain field which follows a soliton solution of the sine-Gordon equation, and diffusing via a persistent random walk. Surprisingly, we find that the structure of these “voidions” is not significantly affected by changes in density, vacancy concentration, and even particle interaction. We explain this structure quantitatively using a one-dimensional model that includes the free-energy barrier particles have to overcome to slide between lattice sites and the effective pair interaction along this line. We argue that voidions are a robust phenomenon in systems of repulsive particles forming simple cubic crystals.

An increasing number of proteins with intrinsically disordered domains have been shown to phase separate in buffer to form liquidlike phases. These protein condensates serve as simple models for the investigation of the more complex membraneless organelles in cells. To understand the function of such proteins in cells, the material properties of the condensates they form are important. However, these material properties are not well understood. Here, we develop a novel method based on optical traps to study the frequency-dependent rheology and the surface tension of P-granule protein PGL-3 condensates as a function of salt concentration. We find that PGL-3 droplets are predominantly viscous but also exhibit elastic properties. As the salt concentration is reduced, their elastic modulus, viscosity, and surface tension increase. Our findings show that salt concentration has a strong influence on the rheology and dynamics of protein condensates suggesting an important role of electrostatic interactions for their material properties.

We show that the social dynamics responsible for the formation of connected components that appear recurrently in face-to-face interaction networks find a natural explanation in the assumption that the agents of the temporal network reside in a hidden similarity space. Distances between the agents in this space act as similarity forces directing their motion towards other agents in the physical space and determining the duration of their interactions. By contrast, if such forces are ignored in the motion of the agents recurrent components do not form, although other main properties of such networks can still be reproduced.

Manufacturing of plastics is typically performed via flow processing of a molten polymeric fluid. Until recently, conventional knowledge has maintained that the deformation of the constituent molecules under flow is homogeneous and obeys Gaussian statistics. In this study via virtual experimentation, an entangled polyethylene melt subjected to planar elongational flow displays an unanticipated microphase separation into a heterogeneous liquid composed of regions of either highly stretched or tightly coiled macromolecules, thus providing a natural realization of a biphasic coil-stretch transition.

We confine a nematic liquid crystal with homeotropic anchoring to stable toroidal droplets and study how geometry affects the equilibrium director configuration. In contrast to the case of cylindrical confinement, we find that the equilibrium state is chiral—a twisted and escaped radial director configuration. Furthermore, we find that the magnitude of the twist distortion increases as the ratio of the ring radius to the tube radius decreases; we confirm this with computer simulations of optically polarized microscopy textures. In addition, numerical calculations also indicate that the local geometry indeed affects the magnitude of the twist distortion. We further confirm this curvature-induced twisting using bent cylindrical capillaries.