Swelling behavior and structural characteristics of wheat gluten polypeptide films

Wheat gluten films were subjected to controlled thermomechanical treatments to increase the percentage of aggregated sodium dodecyl sulfate (SDS)-insoluble gluten protein, the aggregation reaction being disulfide bonding. The rheological properties of the films were measured under immersion in water, where wheat gluten films are stable and show only slight swelling. The equilibrium swelling of the gluten films in water decreased with the increase of the percentage of SDS-insoluble protein aggregates, and the frequency the independent shear modulus increased sharply with increasing percentage of SDS-insoluble aggregates. Both findings confirm that disulfide bonding between gluten proteins is the predominant cross-linking reaction in the system. A relationship between shear modulus and aggregated protein compatible with a power law (of exponent 3) suggests the existence of a protein network at a molecular scale. However, the classical Flory-Rehner model failed to describe the relationship between the plateau modulus and the gluten volume fraction (a very drastic increase, compatible with a power law of an exponent of about 14). This result shows that gluten cannot be described as an entangled polymer network. The interpretation of both relationships is a network of mesoscale particles which in turn have a fractal inner structure (with a fractal dimension close to 3).     

Cell wall elasticity: I. A critique of the bulk elastic modulus approach and an analysis using polymer elastic principles

The traditional bulk elastic modulus approach to plant cell pressure-volume relations is inconsistent with its definition. The relationship between the bulk modulus and Young's modulus that forms the basis of their usual application to cell pressure-volume properties is demonstrated to be physically meaningless. The bulk modulus describes stress/strain relations of solid, homogeneous bodies undergoing small deformations, whereas the plant cell is best described as a thin-shelled, fluid-filled structure with a polymer base. Because cell walls possess a polymer structure, an alternative method of mechanical analysis is presented using polymer elasticity principles. This initial study presents the groundwork of polymer mechanics as would be applied to cell walls and discusses how the matrix and microfibrillar network induce nonlinear stress/strain relationships in the cell wall in response to turgor pressure. In subsequent studies, these concepts will be expanded to include anisotropic expansion as regulated by the microfibrillar network.     

Uncovering Patterns of Inter-Urban Trip and Spatial Interaction from Social Media Check-In Data

The article revisits spatial interaction and distance decay from the perspective of human mobility patterns and spatially-embedded networks based on an empirical data set. We extract nationwide inter-urban movements in China from a check-in data set that covers half a million individuals within 370 cities to analyze the underlying patterns of trips and spatial interactions. By fitting the gravity model, we find that the observed spatial interactions are governed by a power law distance decay effect. The obtained gravity model also closely reproduces the exponential trip displacement distribution. The movement of an individual, however, may not obey the same distance decay effect, leading to an ecological fallacy. We also construct a spatial network where the edge weights denote the interaction strengths. The communities detected from the network are spatially cohesive and roughly consistent with province boundaries. We attribute this pattern to different distance decay parameters between intra-province and inter-province trips.     

Modeling the Rheological Properties of Fats: A Perspective and Recent Advances

The elastic modulus of colloidal fat crystal networks scales with the volume fraction of solids in a power–law fashion. To explain and predict how the elastic properties of these networks change with their volume fraction of solids, several physical models have been proposed. In this review, the chronology of the development of structural–mechanical models to explain the elasticity of fats is reviewed, leading to the development of the fractal model. In the fractal model, the fractal-like behavior of fat crystal networks, which can be considered fractal gels of polycrystals in oil, or colloidal crystals, is used to explain the power–law scaling behavior of the shear elastic modulus to the volume fraction of solids. Lately, however, many experimental results and simulation studies suggest that the stress distribution within networks can be dramatically heterogeneous, which means that a small part of the network carries most of the stress. This concept was introduced into a modified fractal model by deriving an expression for the effective volume fraction of stress-carrying solids. The modified fractal model fits the experimental data well and successfully explains the sometimes observed non-linear log–log behavior between the shear elastic modulus and the volume fraction of solids.     

Physical characteristics of calcium induced κ- carrageenan networks

The presence of an optimum counter-ion concentration in calcium-induced κ-carrageenan gels at low polymer concentrations of 5 and 10 g/l is observed. At approximately the stoicheometric molar ratio of 1 calcium per carrageenan sulphate, a gel with high elastic modulus, high optical clarity and fine network structure is observed. On further increase of counter-ion concentration beyond this optimum, elastic modulus decreases significantly associated with sharp increase in the gels turbidity together with a network characterised with coarse and large-pore mesh.

The quite complete characterisation of the various gel networks both mechanically by ways of oscillatory and static rheology and optically by turbidimetry and cryo-SEM shows that the extensive structural charge neutralisation of the polysaccharide by divalent calcium ions is responsible for a marked aggregation of the polymer strands reminiscent of precipitation. At lower counter-ion to polymer ratios, onset of gelation might prevent such phase separation.     

Ongoing Processes in a Fitness Network Model under Restricted Resources

In real networks, the resources that make up the nodes and edges are finite. This constraint poses a serious problem for network modeling, namely, the compatibility between robustness and efficiency. However, these concepts are generally in conflict with each other. In this study, we propose a new fitness-driven network model for finite resources. In our model, each individual has its own fitness, which it tries to increase. The main assumption in fitness-driven networks is that incomplete estimation of fitness results in a dynamical growing network. By taking into account these internal dynamics, nodes and edges emerge as a result of exchanges between finite resources. We show that our network model exhibits exponential distributions in the in- and out-degree distributions and a power law distribution of edge weights. Furthermore, our network model resolves the trade-off relationship between robustness and efficiency. Our result suggests that growing and anti-growing networks are the result of resolving the trade-off problem itself.     

Effect of cytoskeletal elastic properties on the mechanoelectrical transduction in excitable cells

This paper addresses the possible mechanism of stretch on cell electrochemical potential change, based on the physicochemical properties of cytoskeletal network. Synthetic polyelectrolyte gel was used as an experimental model of the cytoskeleton. Gel samples with different density of network cross linking were studied. Triangular axial deformations of samples were applied. Simultaneously, the electrochemical (Donnan) potential of the gel was measured between a micropipette electrode pinned into the swollen gel, and a reference electrode in the outer solution. We found that axial deformation shifts the gel potential toward depolarization. The extent of gel depolarization showed a close negative correlation with the Young modulus of the gel. We suggest that the underlying mechanism is likely to be a universal process of counterion adsorption on charged polymer filaments due to the decrease of distance between polymer filaments owing to gel elongation.     

Rheological and structural properties of aqueous alginate during gelation via the Ugi multicomponent condensation reaction

Turbidity, structure, and rheological features during gelation via the Ugi multicomponent condensation reaction of semidilute solutions of alginate have been investigated at different polymer and cross-linker concentrations and reaction temperatures. The gelation time of the system decreased with increasing polymer and cross-linker concentrations, and a temperature rise resulted in a faster gelation. At the gel point, a power law frequency dependence of the dynamic storage modulus (G' proportional, variant omega(n)(')) and loss modulus (G' ' proportional, variant omega(n)(' ')) was observed for all gelling systems with n' = n' ' = n. By varying the cross-linker density at a fixed polymer concentration (2.2 wt %), the power law exponent is consistent with that predicted (0.7) from the percolation model. The value of n decreases with increasing polymer concentration, whereas higher temperatures give rise to higher values of n. The elastic properties of the gels continue to grow over a long time in the postgel region, and at later stages in the gelation process, a solidlike response is observed. The turbidity of the gelling system increases as the gel evolves, and this effect is more pronounced at higher cross-linker concentration. The small-angle neutron scattering results reveal large-scale inhomogeneities of the gels, and this effect is enhanced as the cross-linker density increases. The structural, turbidity, and rheological features were found to change over an extended time after the formation of the incipient gel. It was demonstrated that temperature, polymer, and cross-linker concentrations could be utilized to tune the physical properties of the Ugi gels such as structure, transparency, and viscoelasticity.     

Computer simulation of a model network for the erythrocyte cytoskeleton.

The geometry and mechanical properties of the human erythrocyte membrane cytoskeleton are investigated by a computer simulation in which the cytoskeleton is represented by a network of polymer chains. Four elastic moduli as well as the area and thickness are predicted for the chain network as a function of temperature and the number of segments in each chain. Comparisons are made with mean field arguments to examine the importance of steric interactions in determining network properties. Applied to the red blood cell, the simulation predicts that in the bilayer plane the membrane cytoskeleton has a shear modulus of 10 +/- 2 x 10(-6) J/m2 and an areal compression modulus of 17 +/- 2 x 10(-6) J/m2. The volume compression modulus and the transverse Young's modulus of the cytoskeleton are predicted to be 1.2 +/- 0.1 x 10(3) J/m3 and 2.0 +/- 0.1 x 10(3) J/m3, respectively. Elements of the cytoskeleton are predicted to have a mean displacement from the bilayer plane of 15 nm. The simulation agrees with some, but not all, of the shear modulus measurements. The other predicted moduli have not been measured.     

An elastic network model based on the structure of the red blood cell membrane skeleton.

A finite element network model has been developed to predict the macroscopic elastic shear modulus and the area expansion modulus of the red blood cell (RBC) membrane skeleton on the basis of its microstructure. The topological organization of connections between spectrin molecules is represented by the edges of a random Delaunay triangulation, and the elasticity of an individual spectrin molecule is represented by the spring constant, K, for a linear spring element. The model network is subjected to deformations by prescribing nodal displacements on the boundary. The positions of internal nodes are computed by the finite element program. The average response of the network is used to compute the shear modulus (mu) and area expansion modulus (kappa) for the corresponding effective continuum. For networks with a moderate degree of randomness, this model predicts mu/K = 0.45 and kappa/K = 0.90 in small deformations. These results are consistent with previous computational models and experimental estimates of the ratio mu/kappa. This model also predicts that the elastic moduli vary by 20% or more in networks with varying degrees of randomness. In large deformations, mu increases as a cubic function of the extension ratio lambda 1, with mu/K = 0.62 when lambda 1 = 1.5.     

Dynamic mechanical properties of agarose gels modeled by a fractional derivative model

The complex modulus (E*) and elastic modulus (E') of agarose gels (2% to 4%) are measured with a dynamic mechanical analyzer in frequency sweep shear sandwich mode between 0.1 and 20 Hz. The data showed that E* and E' increase with frequency according to a power law which can be described by a fractional derivative model to characterize the dynamic viscoelasticity of the gel. The functions between the model parameters including storage modulus coefficient (H) and the power law exponent (beta) and the agarose concentration are established. A molecular basis for the application of the fractional derivative model to gel polymers is also discussed. Such an approach can be useful in tissue culture studies employing dynamic pressurization or for validation of magnetic resonance elastography.     

Spectrin properties and the elasticity of the red blood cell membrane skeleton

Two models of spectrin elasticity are developed and compared to experimental measurements of the red blood cell (RBC) membrane shear modulus through the use of an elastic finite element model of the RBC membrane skeleton. The two molecular models of spectrin are: (i) An entropic spring model of spectrin as a flexible chain. This is a model proposed by several previous authors. (ii) An elastic model of a helical coiled-coil which expands by increasing helical pitch. In previous papers, we have computed the relationship between the stiffness of a single spectrin molecule (K) and the shear modulus of a network (μ), and have shown that this behavior is strongly dependent upon network topology. For realistic network models of the RBC membrane skeleton, we equate μ to micropipette measurements of RBCs and predict K for spectrin that is consistent with the coiled-coil molecular model. The value of spectrin stiffness derived from the entropic molecular model would need to be at least 30 times greater to match the experimental results. Thus, the conclusion of this study is that a helical coiled-coil model for spectrin is more realistic than a purely entropic model.     

Modeling bond correlations in denatured proteins and polypeptides

Bond‐orientational correlations for finite‐length homopolypeptides and a selected group of denatured proteins are obtained by numerical simulations using a polypeptide model with a potential of mean force. These correlations characterize the stiffness of the polypeptide backbone and are generally described by either an exponential or a power‐law decay in the asymptotic limit. However, for finite length polypeptides and unfolded proteins the correlations significantly deviate from either single exponential or power‐law behavior. A heuristic model is developed to analyze the correlations of homopolypeptides, which depends on the chain length and the side‐chain properties. The model contains power‐law and multi‐exponential terms, the latter which could be interpreted as local persistence lengths. In the asymptotic limit, the model reduces to the expected power‐law behavior. Simulations of denatured proteins show that the power‐law behavior of the correlations is significantly suppressed and only the multi‐exponential term is needed to model the correlations. In addition, average persistence lengths (ranging from 2.0 to 2.5 nm) are obtained from the correlations by fitting single exponentials and shown to be in general agreement with experiments, which also assume single exponential decay. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 312–323, 2016.     

Scaling analysis of the concentration dependence on elasticity of agarose gel

Since the critical exponent of the elastic modulus is related to the spatial dimension and the critical exponent of the correlation length, depending on the characteristics of elasticity, we experimentally evaluated both the elastic modulus of a sol-gel transition system and also the correlation length. We could determine the correlation length of agarose gel by the dynamic light scattering method; it was well described by the power law as a function of the deviation from the sol-gel transition point. Three scaling laws between the critical exponent of the correlation length (v) and that of the elastic shear modulus (t) were compared, and the critical exponent of the elastic modulus was described by the equation of de Gennes expression (t=1+v(d-2), where d is the spatial dimension). This result suggests that agarose fibers are stiff enough to show scalar elasticity.     

Viscoelastic fluid description of bacterial biofilm material properties

A mathematical model describing the constitutive properties of biofilms is required for predicting biofilm deformation, failure, and detachment in response to mechanical forces. Laboratory observations indicate that biofilms are viscoelastic materials. Likewise, current knowledge of biofilm internal structure suggests modeling biofilms as associated polymer viscoelastic systems. Supporting experimental results and a system of viscoelastic fluid equations with a linear Jeffreys viscoelastic stress-strain law are presented here. This system of equations is based on elements of associated polymer physics and is also consistent with presented and previous experimental results. A number of predictions can be made. One particularly interesting result is the prediction of an elastic relaxation time on the order of a few minutes-biofilm disturbances on shorter time scales produce an elastic response, biofilm disturbances on longer time scales result in viscous flow, i.e., nonreversible biofilm deformation. Although not previously recognized, evidence of this phenomenon is in fact present in recent experimental results.     

Dynamics of Polymer Molecules with Sacrificial Bond and Hidden Length Systems: Towards a Physically-Based Mesoscopic Constitutive Law

We investigate the entropic force-elongation behavior of a polymer chain in the presence of the sacrificial bond and hidden length (SBHL) system observed experimentally in many biomaterials. We show that in most cases the SBHL system leads to a significant increase in toughness. However, the presence of a large number of bonds or relatively strong bonds in the SBHL system can reduce the net gain in toughness. We also incorporate the polymer model into a network of polymers with random properties (e.g., contour length, number and strength of sacrificial bonds, length of hidden loops). This allows us to derive a physically-based mesoscopic force-displacement law that governs the collective behavior.     

In Vivo Determination of Fluctuating Forces during Endosome Trafficking Using a Combination of Active and Passive Microrheology

Background

Regulation of intracellular trafficking is a central issue in cell biology. The forces acting on intracellular vesicles (endosomes) can be assessed in living cells by using a combination of active and passive microrheology.

Methodology/Principal Findings

This dual approach is based on endosome labeling with magnetic nanoparticles. The resulting magnetic endosomes act both as probes that can be manipulated with external magnetic fields to infer the viscoelastic modulus of their surrounding microenvironment, and as biological vehicles that are trafficked along the microtubule network by means of forces generated by molecular motors. The intracellular viscoelastic modulus exhibits power law dependence with frequency, which is microtubule and actin-dependent. The mean square displacements of endosomes do not follow the predictions of the fluctuation-dissipation theorem, which offers evidence for active force generation. Microtubule disruption brings the intracellular medium closer to thermal equilibrium: active forces acting on the endosomes depend on microtubule-associated motors. The power spectra of these active forces, deduced through the use of a generalized Langevin equation, show a power law decrease with frequency and reveal an actin-dependent persistence of the force with time. Experimental spectra have been reproduced by a simple model consisting in a series of force steps power-law distributed in time. This model enlightens the role of the cytoskeleton dependent force exerted on endosomes to perform intracellular trafficking.

Conclusions/Significance

In this work, the influence of cytoskeleton components and molecular motors on intracellular viscoelasticity and transport is addressed. The use of an original probe, the magnetic endosome, allows retrieving the power spectrum of active forces on these organelles thanks to interrelated active and passive measures.Finally a computational model gives estimates of the force itself and hence of the number of the motors pulling on endosomes.     

Quantifying the kinetic parameters of prion replication.

The mechanism of protein-only prion replication is controversial. A detailed mathematical model of prion replication by nucleated polymerisation is developed, and its parameters are estimated from published data. PrP-res decay is around two orders of magnitude slower than PrP-sen decay, a plausible ratio of two parameters estimated from very different experiments. By varying the polymer breakage rate, we reveal that systems of short polymers grow the fastest. Drugs which break polymers could therefore accelerate disease progression. Growth in PrP-res seems slower than growth in infectious titre. This can be explained either by a novel hypothesis concerning inoculum clearance from a newly infected brain, or by the faster growth of compartments containing smaller polymers. The existence of compartments can also explain why prion growth sometimes reaches a plateau. Published kinetic data are all compatible with our mathematical model, so the nucleated polymerisation hypothesis cannot be ruled out on dynamic grounds.     

桤柏混交林密度变化规律的人工神经网络模型研究

本文应用人工神经网络方法建立了桤柏混交林密度变化的神经网络模型,并与传统模型进行了比较,仿真结果表明,人工神经网络模型可适用于桤柏混交林密度变化规律描述,且优于传统模型,从而丰富和发展了森林稀疏规律理论。     

Distribution of end-points of a branching network with decaying branch length

The geometry of the human bronchial tree has been described as a network formed by successive dichotomous branching with constant branching angles and geometrically decaying branch lengths. Models having these properties and with randomly distributed branching planes are constructed. The distribution of the end points of the model networks are described by computing the variance of the distributions in the direction of the axis of the network and in the transverse directions. It is found that, for a given decay ratio, there is a branching angle for which the volume filled by the end points is a maximum. The advantages of the network with the decay ratio and branching angle of the human bronchial tree are discussed.