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Fibrous networks constructed from high aspect ratio protein building blocks are ubiquitous in nature. Despite this ubiquity, the functional advantage of such building blocks over globular proteins is not understood. To answer this question, we engineered hydrogel network building blocks with varying numbers of protein L domains to control the aspect ratio. The mechanical and structural properties of photochemically crosslinked protein L networks were then characterised using shear rheology and small angle neutron scattering. We show that aspect ratio is a crucial property that defines network architecture and mechanics, by shifting the formation from translationally diffusion dominated to rotationally diffusion dominated. Additionally, we demonstrate that a similar transition is observed in the model living system: fibrin blood clot networks. The functional advantages of this transition are increased mechanical strength and the rapid assembly of homogenous networks above a critical protein concentration, crucial for in vivo biological processes such as blood clotting. In addition, manipulating aspect ratio also provides a parameter in the design of future bio-mimetic and bio-inspired materials., (© 2023. Springer Nature Limited.)

Mechanically bonded fabrics account for a significant portion of nonwoven products, and serve many niche areas of nonwoven manufacturing. Such fabrics are characterized by layers of disordered fibrous webs, but we lack an understanding of how such microstructures determine bulk material response. Here we numerically determine the linear shear response of needle-punched fabrics modeled as cross-linked sheets of two-dimensional (2D) Mikado networks. We systematically vary the intra-sheet fiber density, inter-sheet separation distance, and direction of shear, and quantify the macroscopic shear modulus alongside the degree of affinity and energy partition. For shear parallel to the sheets, the response is dominated by intrasheet fibers and follows known trends for 2D Mikado networks. By contrast, shears perpendicular to the sheets induce a softer response dominated by either intrasheet or intersheet fibers depending on a quadratic relation between sheet separation and fiber density. These basic trends are reproduced and elucidated by a simple scaling argument that we provide. We discuss the implications of our findings in the context of real nonwoven fabrics.

Hydrogels constructed from folded protein domains are of increasing interest as resilient and responsive biomaterials, but their optimization for applications requires time-consuming and costly molecular design. Here, we explore a complementary approach to control their properties by examining the influence of crosslinking rate on the structure and viscoelastic response of a model hydrogel constructed from photochemically crosslinked bovine serum albumin (BSA). Gelation is observed to follow a heterogeneous nucleation pathway in which BSA monomers crosslink into compact nuclei that grow into fractal percolated networks. Both the viscoelastic response probed by shear rheology and the nanostructure probed by small-angle X-ray scattering (SAXS) are shown to depend on the photochemical crosslinking reaction rate, with increased reaction rates corresponding to higher viscoelastic moduli, lower fractal dimension, and higher fractal cluster size. Reaction rate-dependent changes are shown to be consistent with a transition between diffusion- and rate-limited assembly, and the corresponding changes to viscoelastic response are proposed to arise from the presence of nonfractal depletion regions, as confirmed by SAXS. This controllable nanostructure and viscoelasticity constitute a potential route for the precise control of hydrogel properties, without the need for molecular modification.

Measurement of a tissue-specific electrical resistance may offer a discriminatory metric for evaluation of tissue health during cancer surgery. With a move toward minimally-invasive procedures, applicable contact sensing modalities must be scalable, fast and robust. A passive resistance characterisation method utilising a biogalvanic cell as an intrinsic power source has been proposed as a potentially suitable solution. Previous work has evaluated this system with results showing effective discrimination of tissue type and damage (through electroporation). However, aspects of the biogalvanic cell have been found to influence the characterisation performance, and are not currently accounted for within the system model. In particular, the electrode and salt-bridge resistance are not independently determined, leading to over-predictions of tissue resistivity. This paper describes a more comprehensive model and characterisation scheme, with electrode parameters and salt-bridge resistivity being evaluated independently. In a generalised form, the presented model illustrates how the relative resistive contributions from the electrodes and medium relate to the existing characterisation method efficacy. We also describe experiments with physiologically relevant salt solutions (1.71, 17.1, 154 mM), used for validation and comparison. The presented model shows improved performance over the current biogalvanic measurement technique at the median conductivity. Both the proposed and extant system models become unable to predict conductivity accurately at high conductivity due to the dominance of the electrodes. The characterisation techniques have also been applied to data collected on freshly excised human colon tissue (healthy and cancerous). The findings suggest that the resistance of the cell under the test conditions is electrode dominated, leading to erroneous tissue resistance determination. Measurement optimisation strategies and the surgical applicability of the biogalvanic technique are discussed in light of these findings.

Biomimetic hydrogels based on natural polymers are a promising class of biomaterial, mimicking the natural extra-cellular matrix of biological tissues and providing cues for cell attachment, proliferation, and differentiation. With a view to providing an upstream method to guide subsequent experimental design, the aim of this study was to introduce a mathematical model that described the rheological properties of a hydrogel system based on covalently cross-linked collagen triple helices. In light of their organization, such gels exhibit limited collagen bundling that cannot be described by existing fibril network models. The model presented here treats collagen triple helices as discrete semiflexible polymers, permits full access to metrics for network microstructure, and should provide a comprehensive understanding of the parameter space associated with the development of such multifunctional materials. Triple helical hydrogel networks were experimentally obtained via the reaction of type I collagen with both aromatic and aliphatic diacids. The complex modulus G * was found from rheological testing in linear shear and quantitatively compared to model predictions. In silico data from the computational model successfully described the experimental trends in hydrogel storage modulus with either (i) the concentration of collagen triple helices during the cross-linking reaction or (ii) the type of cross-linking segment introduced in resulting hydrogel networks. This approach may pave the way to a step change in the rational design of biomimetic triple helical collagen systems with controlled multifunctionality.

Disordered fibre networks are ubiquitous in nature and have a wide range of industrial applications as novel biomaterials. Predicting their viscoelastic response is straightforward for affine deformations that are uniform over all length scales, but when affinity fails, as has been observed experimentally, modelling becomes challenging. Here we present a numerical methodology, related to an existing framework for amorphous packings, to predict the steady-state viscoelastic spectra and degree of affinity for disordered fibre networks driven at arbitrary frequencies. Applying this method to a peptide gel model reveals a monotonic increase of the shear modulus as the soft, non-affine normal modes are successively suppressed as the driving frequency increases. In addition to being dominated by fibril bending, these low frequency network modes are also shown to be delocalised. The presented methodology provides insights into the importance of non-affinity in the viscoelastic response of peptide gels, and is easily extendible to all types of fibre networks.

Peptide hydrogels have important applications as biomaterials and in nanotechnology, but utilization often depends on their mechanical properties for which we currently have no predictive capability. Here we use a peptide model to simulate the formation of percolating amyloid fibril networks and couple these to the elastic network theory to determine their mechanical properties. We find that the time variation of network length scales can be collapsed onto master curves by using a time scaling function that depends on the peptide interaction anisotropy. The same scaling applies to network mechanics, revealing a nonmonotonic dependence of the shear modulus with time. Our structure-function relationship between the peptide building blocks, network morphology, and network mechanical properties can aid in the design of amyloid fibril networks with tailored mechanical properties.

Humans have co-evolved with micro-organisms and have a symbiotic or mutualistic relationship with their resident microbiome. As at other body surfaces, the mouth has a diverse microbiota that grows on oral surfaces as structurally and functionally organised biofilms. The oral microbiota is natural and provides important benefits to the host, including immunological priming, down-regulation of excessive pro-inflammatory responses, regulation of gastrointestinal and cardiovascular systems, and colonisation by exogenous microbes. On occasions, this symbiotic relationship breaks down, and previously minor components of the microbiota outcompete beneficial bacteria, thereby increasing the risk of disease. Antimicrobial agents have been formulated into many oral care products to augment mechanical plaque control. A delicate balance is needed, however, to control the oral microbiota at levels compatible with health, without killing beneficial bacteria and losing the key benefits delivered by these resident microbes. These antimicrobial agents may achieve this by virtue of their recommended twice daily topical use, which results in pharmacokinetic profiles indicating that they are retained in the mouth for relatively long periods at sublethal levels. At these concentrations they are still able to inhibit bacterial traits implicated in disease (e.g. sugar transport/acid production; protease activity) and retard growth without eliminating beneficial species. In silico modelling studies have been performed which support the concept that either reducing the frequency of acid challenge and/or the terminal pH, or by merely slowing bacterial growth, results in maintaining a community of beneficial bacteria under conditions that might otherwise lead to disease (control without killing)., (2015 S. Karger AG, Basel)

The mouth supports a diverse microbiota which provides major benefits to the host. On occasions, this symbiotic relationship breaks down (dysbiosis), and disease can be a consequence. We argue that progress in the control of oral diseases will depend on a paradigm shift away from approaches that have proved successful in medicine for many diseases with a specific microbial aetiology. Factors that drive dysbiosis in the mouth should be identified and, where possible, negated, reduced or removed, while antimicrobial agents delivered by oral care products may function effectively, even at sub-lethal concentrations, by modulating the activity and growth of potentially pathogenic bacteria. In this way, the beneficial activities of the resident oral microbiota will be retained and the risk of dysbiosis occurring will be reduced.

Dental caries or tooth decay is a prevalent global disease whose causative agent is the oral biofilm known as plaque. According to the ecological plaque hypothesis, this biofilm becomes pathogenic when external challenges drive it towards a state with a high proportion of acid-producing bacteria. Determining which factors control biofilm composition is therefore desirable when developing novel clinical treatments to combat caries, but is also challenging due to the system complexity and the existence of multiple bacterial species performing similar functions. Here we employ agent-based mathematical modelling to simulate a biofilm consisting of two competing, distinct types of bacterial populations, each parameterised by their nutrient uptake and aciduricity, periodically subjected to an acid challenge resulting from the metabolism of dietary carbohydrates. It was found that one population was progressively eliminated from the system to give either a benign or a pathogenic biofilm, with a tipping point between these two fates depending on a multiplicity of factors relating to microbial physiology and biofilm geometry. Parameter sensitivity was quantified by individually varying the model parameters against putative experimental measures, suggesting non-lethal interventions that can favourably modulate biofilm composition. We discuss how the same parameter sensitivity data can be used to guide the design of validation experiments, and argue for the benefits of in silico modelling in providing an additional predictive capability upstream from in vitro experiments.

The cytoskeleton is a network of crosslinked, semiflexible filaments, and it has been suggested that it has properties of a glassy state. Here we employ optical-trap-based microrheology to apply forces to a model cytoskeleton and measure the high-bandwidth response at an anterior point. Simulating the highly nonlinear and anisotropic stress-strain propagation assuming affinity, we found that theoretical predictions for the quasistatic response of semiflexible polymers are only realized at high frequencies inaccessible to conventional rheometers. We give a theoretical basis for determining the frequency when both affinity and quasistaticity are valid, and we discuss with experimental evidence that the relaxations at lower frequencies can be characterized by the experimentally obtained nonaffinity parameter.

In the presence of adenosine triphosphate, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modeling can help to quantify the relationship between individual motors plus filaments to organization and dynamics on molecular and supramolecular length scales. Here, we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment, and detachment, including a differential detachment rate from filament ends, reveals a range of nonequilibrium behavior. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles, or layers, whose stability depends on motor speed and differential end detachment. The gross features of the dependence of the observed structures on the motor rate and the filament concentration can be captured by a simple one-filament model. Loosely bound aggregates exhibit superdiffusive mass transport, where filament translocation scales with lag time with nonunique exponents that depend on motor kinetics. An empirical data collapse of filament speed as a function of motor speed and end detachment is found, suggesting a dimensional reduction of the relevant parameter space. We conclude by discussing the perspectives of microscopic modeling in the field of active gels.

The sessile microbial communities known as biofilms exhibit varying architectures as environmental factors are varied, which for immersed biofilms includes the shear rate of the surrounding flow. Here we modify an established agent-based biofilm model to include affine flow and employ it to analyze the growth of surface roughness of single-species, three-dimensional biofilms. We find linear growth laws for surface geometry in both horizontal and vertical directions and measure the thickness of the active surface layer, which is shown to anticorrelate with roughness. Flow is shown to monotonically reduce surface roughness without affecting the thickness of the active layer. We argue that the rapid roughening is due to nonlocal surface interactions mediated by the nutrient field, which are curtailed when advection competes with diffusion. We further argue the need for simplified models to elucidate the underlying mechanisms coupling flow to growth.

Analytical and numerical calculations are presented for the mechanical response of fiber networks in a state of axisymmetric prestress, in the limit where geometric nonlinearities such as fiber rotation are negligible. This allows us to focus on the anisotropy deriving purely from the nonlinear force-extension curves of individual fibers. The number of independent elastic coefficients for isotropic, axisymmetric, and fully anisotropic networks are enumerated before deriving expressions for the response to a locally applied force that can be tested against, e.g., microrheology experiments. Localized forces can generate anisotropy away from the point of application, so numerical integration of nonlinear continuum equations is employed to determine the stress field, and induced mechanical anisotropy, at points located directly behind and in front of a force monopole. Results are presented for the wormlike chain model in normalized forms, allowing them to be easily mapped to a range of systems. Finally, the relevance of these findings to naturally occurring systems and directions for future investigation are discussed.

Background: Robust self-organization of subcellular structures is a key principle governing the dynamics and evolution of cellular life. In fission yeast cells undergoing division, the mitotic spindle spontaneously emerges from the interaction of microtubules, motor proteins and the confining cell walls, and asters and vortices have been observed to self-assemble in quasi-two dimensional microtubule-kinesin assays. There is no clear microscopic picture of the role of the active motors driving this pattern formation, and the relevance of continuum modeling to filament-scale structures remains uncertain., Results: Here we present results of numerical simulations of a discrete filament-motor protein model confined to a pressurised cylindrical box. Stable spindles, nematic configurations, asters and high-density semi-asters spontaneously emerge, the latter pair having also been observed in cytosol confined within emulsion droplets. State diagrams are presented delineating each stationary state as the pressure, motor speed and motor density are varied. We further highlight a parameter regime where vortices form exhibiting collective rotation of all filaments, but have a finite life-time before contracting to a semi-aster. Quantifying the distribution of life-times suggests this contraction is a Poisson process. Equivalent systems with fixed volume exhibit persistent vortices with stochastic switching in the direction of rotation, with switching times obeying similar statistics to contraction times in pressurised systems. Furthermore, we show that increasing the detachment rate of motors from filament plus-ends can both destroy vortices and turn some asters into vortices., Conclusions: We have shown that discrete filament-motor protein models provide new insights into the stationary and dynamical behavior of active gels and subcellular structures, because many phenomena occur on the length-scale of single filaments. Based on our findings, we argue the need for a deeper understanding of the microscopic activities underpinning macroscopic self-organization in active gels and urge further experiments to help bridge these lengths.

Many active materials and biological systems are driven far from equilibrium by embedded agents that spontaneously generate forces and distort the surrounding material. Probing and characterizing these athermal fluctuations are essential to understand the properties and behaviors of such systems. Here we present a mathematical procedure to estimate the local action of force-generating agents from the observed fluctuating displacement fields. The active agents are modeled as oriented force dipoles or isotropic compression foci, and the matrix on which they act is assumed to be either a compressible elastic continuum or a coupled network-solvent system. Correlations at a single point and between points separated by an arbitrary distance are obtained, giving a total of three independent fluctuation modes that can be tested with microrheology experiments. Since oriented dipoles and isotropic compression foci give different contributions to these fluctuation modes, ratiometric analysis allows us characterize the force generators. We also predict and experimentally find a high-frequency ballistic regime, arising from individual force-generating events in the form of the slow buildup of stress followed by rapid but finite decay. Finally, we provide a quantitative statistical model to estimate the mean filament tension from these athermal fluctuations, which leads to stiffening of active networks.

We conduct athermal simulations of freely cooling, viscous soft spheres around the jamming transition density varphi(J) and find evidence for a growing length xi(t) that governs relaxation to mechanical equilibrium. xi(t) is manifest in both the velocity correlation function and the spatial correlations in a scalar measure of local force balance which we define. Data for different densities varphi can be collapsed onto two master curves by scaling xi(t) and t by powers of |varphi-varphi(J)|, indicative of critical scaling. Furthermore, particle transport for varphi>varphi(J) exhibits aging and superdiffusion similar to a range of soft matter experiments, suggesting a common origin. Finally, we explain how xi(t) at late times maps onto known behavior away from varphi(J).

In an attempt to extend the range of model jamming transitions, we simulate systems of athermal particles which attract when slightly overlapping. Following from recent work on purely repulsive systems, dynamics are neglected and relaxation performed via a potential energy minimisation algorithm. Our central finding is of a transition to a low-density tensile solid which is sharp in the limit of infinite system size. The critical density depends on the range of the attractive regime in the pair-potential. Furthermore, solidity is shown to be related to the coordination number of the packing according to the approximate constraint-counting scheme known as Maxwell counting, although more corrections need to be considered than with the repulsive-only case, as explained. We finish by discussing how the numerical difficulties encountered in this work could be overcome in future studies.

Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquid-vapor interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to generate crusts that are thicker near the pinned contact line than the apex. Here we investigate, by nonlinear quasistatic simulation and scaling analysis, the deformation mode and stability properties of elastic caps with a nonuniform thickness profile. By suitably scaling the mean thickness and the contact angle between crust and substrate, we find that data collapse onto a master curve for both buckling pressure and deformation mode, thus allowing us to predict when the deformed shape is a dimple, Mexican hat, and so on. This master curve is parameterized by a dimensionless measure of the nonuniformity of the shell. We also speculate on how overlapping time scales for gelation and deformation may alter our findings.

Previous research on semiflexible polymers including cytoskeletal networks in cells has suggested the existence of distinct regimes of elastic response, in which the strain field is either uniform (affine) or nonuniform (nonaffine) under external stress. Associated with these regimes, it has been further suggested that a mesoscopic length scale emerges, which characterizes the scale for the crossover from nonaffine to affine deformations. Here, we extend these studies by probing the response to localized forces and force dipoles. We show that the previously identified nonaffinity length [D. A. Head, Phys. Rev. E 68, 061907 (2003)] controls the mesoscopic response to point forces and the crossover to continuum elastic behavior at large distances.

A theory for kinetic arrest in isotropic systems of repulsive, radially interacting particles is presented that predicts exponents for the scaling of various macroscopic quantities near the rigidity transition that are in agreement with simulations, including the nontrivial shear exponent. Both statics and dynamics are treated in a simplified, one-particle level description and coupled via the assumption that kinetic arrest occurs on the boundary between mechanically stable and unstable regions of the static parameter diagram. This suggests that the arrested states observed in simulations are at (or near) an elastic buckling transition. Some additional numerical evidence to confirm the scaling of microscopic quantities is also provided.

Semiflexible polymers such as filamentous actin (F-actin) play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominately affine and the filaments stretch and compress; and a second in which bending modes dominate. We identify a dimensionless scalar quantity, being a combination of the material length scales, that specifies to which regime a given network belongs. A scaling argument is presented that approximately agrees with this crossover variable. By a direct geometric measure, we also confirm that the degree of affinity under strain correlates with the distinct elastic regimes. We discuss the implications of our findings and suggest possible directions for future investigations.

Networks of filamentous proteins play a crucial role in cell mechanics. These cytoskeletal networks, together with various cross-linking and other associated proteins largely determine the (visco)elastic response of cells. In this Letter we study a model system of cross-linked, stiff filaments in order to explore the connection between the microstructure under strain and the macroscopic response of cytoskeletal networks. We find two distinct regimes as a function primarily of cross-link density and filament rigidity: one characterized by affine deformation and one by nonaffine deformation. We characterize the crossover between these two.

We numerically investigate the rigidity percolation transition in two-dimensional flexible, random rod networks with freely rotating cross links. Near the transition, networks are dominated by bending modes and the elastic modulii vanish with an exponent f=3.0+/-0.2, in contrast with central force percolation which shares the same geometric exponents. This indicates that universality for geometric quantities does not imply universality for elastic ones. The implications of this result for actin-fiber networks is discussed.

We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress sigma is driven at a constant shear rate gamma; and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(sigma(1)) and a linear decay at rate lambda sigma(2). Here sigma(1,2)(t)= tau(-1)(1,2) integral (t)(0)sigma(t')exp[-(t-t')/tau(1,2)]dt' are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when tau(2)>tau(1) and 0>R'(sigma)>-lambda so that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of the material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case tau(1)-->0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.

The local persistence R(t), defined as the proportion of the system still in its initial state at time t, is measured for the Bak-Sneppen model. For one and two dimensions, it is found that the decay of R(t) depends on one of two classes of initial configuration. For a subcritical initial state, R(t) equivalent to t(-theta), where the persistence exponent theta can be expressed in terms of a known universal exponent. Hence theta is universal. Conversely, starting from a supercritical state, R(t) decays by the anomalous form 1-R(t) equivalent to t(tau(all)) until a finite time t(0), where tau(all) is also a known exponent. Finally, for the high dimensional model R(t) decays exponentially with a nonuniversal decay constant.

We investigate shear thickening and jamming within the framework of a family of spatially homogeneous, scalar rheological models. These are based on the "soft glassy rheology" model of Sollich et al. [Phys. Rev. Lett. 78, 2020 (1997)], but with an effective temperature x that is a decreasing function of either the global stress sigma or the local strain l. For appropriate x=x(sigma), it is shown that the flow curves include a region of negative slope, around which the stress exhibits hysteresis under a cyclically varying imposed strain rate (.)gamma.A subclass of these x(sigma) have flow curves that touch the (.)gamma=0 axis for a finite range of stresses; imposing a stress from this range jams the system, in the sense that the strain gamma creeps only logarithmically with time t, gamma(t) approximately ln t. These same systems may produce a finite asymptotic yield stress under an imposed strain, in a manner that depends on the entire stress history of the sample, a phenomenon we refer to as history-dependent jamming. In contrast, when x=x(l) the flow curves are always monotonic, but we show that some x(l) generate an oscillatory strain response for a range of steady imposed stresses. Similar spontaneous oscillations are observed in a simplified model with fewer degrees of freedom. We discuss this result in relation to the temporal instabilities observed in rheological experiments and stick-slip behavior found in other contexts, and comment on the possible relationship with "delay differential equations" that are known to produce oscillations and chaos.

A model for weakly excited granular media is derived by combining the free volume argument of Nowak et al. [Phys. Rev. E 57, 1971 (1998)] and the phenomenological model for supercooled liquids of Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)]. This is made possible by relating the granular excitation parameter Gamma, defined as the peak acceleration of the driving pulse scaled by gravity, to a temperaturelike parameter eta(Gamma). The resulting master equation is formally identical to that of Bouchaud's trap model for glasses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results are shown to compare favorably with a range of known experimental behavior. This includes the logarithmic densification and power spectrum of fluctuations under constant eta, the annealing curve when eta is varied cyclically in time, and memory effects observed for a discontinuous shift in eta. Finally, we discuss the physical interpretation of the model parameters and suggest further experiments for this class of systems.