Response Of Such Networks Research Articles

Gupta Transform Approach to the Series RL and RC Networks with Steady Excitation Sources

The analysis of electric networks circuits is an essential course in engineering. The response of such networks is usually obtained by mathematical approaches such as Laplace Transform, Calculus Approach, Convolution Theorem Approach, Residue Theorem Approach. This paper presents a new integral transform called Gupta Transform for obtaining the complete response of the series RL and RC networks circuits with a steady voltage source. The response obtained will provide electric current or charge flowing through series RL and RC networks circuits with a steady voltage source. In this paper, the response of the series RL and RC networks circuits with steady excitation source is provided as a demonstration of the application of the new integral transform called Gupta Transform.

Revealing structure-function relationships in functional flow networks via persistent homology

This work showcases an approach to characterizing structure-function relationships in complex networks in the context of flow networks tuned to perform specific functions. The authors find that the response of such networks encodes hidden topological features---sectors of uniform pressure---that are not apparent in the underlying network architectures, providing a universal topological description for all networks that perform these types of functions.

Cross-linked biopolymer networks with active motors: Mechanical response and intra-network transport

Cross-linked biopolymer networks are widespread in the cytoskeleton of cells and biological gels, which are responsible for maintaining the structural integrity of the cells/materials as well as generating forces to drive cellular movement. Microscopically, these networks are composed of randomly distributed semi-flexible filaments along with the associated cross-linking and motor proteins that are under constant external and internal stresses. In the present study, we developed a computational model based on Langevin dynamics to examine the mechanical response of such networks where the bending and stretching of individual biopolymers, deformation and breakage of cross-linkers and the active role of molecular motors have all been considered. It was found that pronounced strain stiffening took place with increasing imposed shear deformation. However, such stiffening effect under shear was attenuated by the successive rupture of cross-linkers. Interestingly, the appearance of motor-induced contractile forces within the networks significantly increased their apparent modulus in the entropy-dominated regime (i.e., at small strains). In addition, considerable bundling and re-alignment of filaments were also observed under the contraction by motor proteins, in agreement with experimental observations. Finally, the fluctuating forces generated by active motors were found to contribute to the enhanced diffusion of nanometer-sized particles within the network.

Supersoft and Hyperelastic Polymer Networks with Brushlike Strands

Using a combination of the scaling analysis and molecular dynamics simulations, we study relationship between mechanical properties of networks of graft polymers and their molecular architecture. The elastic response of such networks can be described by replacing the brushlike strands with wormlike strands characterized by the effective Kuhn length which is controlled by the degree of polymerization of the side chains nsc and their grafting density 1/ng. In the framework of this approach we have established relationships between the network structural shear modulus G, strands extension ratio β, and architectural triplet [nsc, ng, nx], where nx is the degree of polymerization of the backbone strand between cross-links. Analysis of the simulation data shows that G could increase with β (G ∝ β), which reflects the “golden rule” of elastomers: softer materials are more deformable. However, networks of graft polymers can also break this rule and demonstrate an increase of the modulus G with decreasing extensio...

Topology effects on nonaffine behavior of semiflexible fiber networks.

Filamentous semiflexible networks define the mechanical and physical properties of many materials such as cytoskeleton. In the absence of a distinct unit cell, the Mikado fiber network model is commonly used algorithm for representing the microstructure of these networks in numerical models. Nevertheless, certain types of filamentous structures such as collagenous tissues, at early stages of their development, are assembled by growth of individual fibers from random nucleation sites. In this work, we develop a computational model to investigate the mechanical response of such networks by characterizing their nonaffine behavior. We show that the deformation of these networks is nonaffine at all length scales. Furthermore, similar to Mikado networks, the degree of nonaffinity in these structures decreases with increasing the probing length scale, the network fiber density, and/or the bending stiffness of constituting filaments. Nevertheless, despite the lower coordination number of these networks, their deformation field is more affine than that of the Mikado networks with the same fiber density and fiber mechanical properties.

Nonequilibrium dynamics of probe filaments in actin-myosin networks.

Active dynamic processes of cells are largely driven by the cytoskeleton, a complex and adaptable semiflexible polymer network, motorized by mechanoenzymes. Small dimensions, confined geometries, and hierarchical structures make it challenging to probe dynamics and mechanical response of such networks. Embedded semiflexible probe polymers can serve as nonperturbing multiscale probes to detect force distributions in active polymer networks. We show here that motor-induced forces transmitted to the probe polymers are reflected in nonequilibrium bending dynamics, which we analyze in terms of spatial eigenmodes of an elastic beam under steady-state conditions. We demonstrate how these active forces induce correlations among the mode amplitudes, which furthermore break time-reversal symmetry. This leads to a breaking of detailed balance in this mode space. We derive analytical predictions for the magnitude of resulting probability currents in mode space in the white-noise limit of motor activity. We relate the structure of these currents to the spatial profile of motor-induced forces along the probe polymers and provide a general relation for observable currents on two-dimensional hyperplanes.

Critical behaviour in the nonlinear elastic response of hydrogels.

In this paper we study the elastic response of synthetic hydrogels to an applied shear stress. The hydrogels studied here have previously been shown to mimic the behaviour of biopolymer networks when they are sufficiently far above the gel point. We show that near the gel point they exhibit an elastic response that is consistent with the predicted critical behaviour of networks near or below the isostatic point of marginal stability. This point separates rigid and floppy states, distinguished by the presence or absence of finite linear elastic moduli. Recent theoretical work has also focused on the response of such networks to finite or large deformations, both near and below the isostatic point. Despite this interest, experimental evidence for the existence of criticality in such networks has been lacking. Using computer simulations, we identify critical signatures in the mechanical response of sub-isostatic networks as a function of applied shear stress. We also present experimental evidence consistent with these predictions. Furthermore, our results show the existence of two distinct critical regimes, one of which arises from the nonlinear stretch response of semi-flexible polymers.

Characterization and synthesis of Rayleigh damped elastodynamic networks

We consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (also known as Rayleigh or proportional damping). We give here a characterization of the frequency response of such networks. We also answer the synthesis question for such networks, i.e., how to construct a Rayleigh damped elastodynamic network with a given frequency response. Our analysis shows that not all damped elastodynamic networks can be realized when the proportionality constants between the damping matrix and the mass and stiffness matrices are fixed.

A combined finite element-Langevin dynamics (FEM-LD) approach for analyzing the mechanical response of bio-polymer networks

A Langevin dynamics based formulation is proposed to describe the shape fluctuations of biopolymer filaments. We derive a set of stochastic partial differential equations (SPDEs) to describe the temporal evolution of the shape of semiflexible filaments and show that the solutions of these equations reduce to predictions from classical modal analysis. A finite element formulation to solve these SPDEs is also developed where, besides entropy, the finite deformation of the filaments has been taken into account. The validity of the proposed finite element-Langevin dynamics (FEM-LD) approach is verified by comparing the simulation results with a variety of theoretical predictions. The method is then applied to study the mechanical behavior of randomly cross-linked F-actin networks. We find that as deformation progresses, the response of such networks undergoes transitions from being entropy dominated to being governed by filament bending and then, eventually, to being dictated by filament stretching. The levels of macroscopic stress at which these transitions take place were found to be around 1% and 10%, respectively, of the initial bulk modulus of the network, in agreement with recent experimental observations.

Nonlinear effective-medium theory of disordered spring networks

Disordered soft materials, such as fibrous networks in biological contexts, exhibit a nonlinear elastic response. We study such nonlinear behavior with a minimal model for networks on lattice geometries with simple Hookian elements with disordered spring constant. By developing a mean-field approach to calculate the differential elastic bulk modulus for the macroscopic network response of such networks under large isotropic deformations, we provide insight into the origins of the strain stiffening and softening behavior of these systems. We find that the nonlinear mechanics depends only weakly on the lattice geometry and is governed by the average network connectivity. In particular, the nonlinear response is controlled by the isostatic connectivity, which depends strongly on the applied strain. Our predictions for the strain dependence of the isostatic point as well as the strain-dependent differential bulk modulus agree well with numerical results in both two and three dimensions. In addition, by using a mapping between the disordered network and a regular network with random forces, we calculate the nonaffine fluctuations of the deformation field and compare them to the numerical results. Finally, we discuss the limitations and implications of the developed theory.

Mobility of MenC and PhoU in Live E. Coli: A Single Molecule Tracking Study

Innumerable signal transduction systems have evolved in which an environmental signal is transferred across the cell membrane to the cell interior via a series of protein movements and protein-protein interactions. Knowledge of the diffusion of signalling proteins in these networks and the effects of the presence of their interacting partners is required to understand the dynamics of the signalling response of such networks. Here, we will discuss our recent research using single molecule imaging techniques to determine the mobility of several proteins labelled by the fast folding variant of yellow fluorescent protein, Venus, in live E. coli. Specifically, we have determined the mobility of PhoU, a member of the PhoR-PhoB two-component signalling system and MenC, the o-succinylbenzoyl-CoA synthase, which has been found to interact with PhoU (Y.-J. Hsieh, Y. Yang, and B. L. Wanner, unpublished data). The effect of interactions of these proteins on their mobilities was investigated through monitoring protein diffusion in cells having deletions of the interacting partner genes. Results will be discussed in terms of their implications on the dynamics of signal transduction systems and in comparison to the known mobilities of other proteins and lipids in E. coli and eukaryotic cells.

Topologically invariant macroscopic statistics in balanced networks of conductance-based integrate-and-fire neurons

The relationship between the dynamics of neural networks and their patterns of connectivity is far from clear, despite its importance for understanding functional properties. Here, we have studied sparsely-connected networks of conductance-based integrate-and-fire (IF) neurons with balanced excitatory and inhibitory connections and with finite axonal propagation speed. We focused on the genesis of states with highly irregular spiking activity and synchronous firing patterns at low rates, called slow Synchronous Irregular (SI) states. In such balanced networks, we examined the "macroscopic" properties of the spiking activity, such as ensemble correlations and mean firing rates, for different intracortical connectivity profiles ranging from randomly connected networks to networks with Gaussian-distributed local connectivity. We systematically computed the distance-dependent correlations at the extracellular (spiking) and intracellular (membrane potential) levels between randomly assigned pairs of neurons. The main finding is that such properties, when they are averaged at a macroscopic scale, are invariant with respect to the different connectivity patterns, provided the excitatory-inhibitory balance is the same. In particular, the same correlation structure holds for different connectivity profiles. In addition, we examined the response of such networks to external input, and found that the correlation landscape can be modulated by the mean level of synchrony imposed by the external drive. This modulation was found again to be independent of the external connectivity profile. We conclude that first and second-order "mean-field" statistics of such networks do not depend on the details of the connectivity at a microscopic scale. This study is an encouraging step toward a mean-field description of topological neuronal networks.

Mechanics of Biophysical Networks with Flexible Cross-links

Various mechanical properties and functions of euchariotic cells largely originate from the cytoskeleton. The predominant cytoskeletal constituent is the biopolymer filamentous actin (F-actin). In the presence of various cross-linking proteins, F-actins can comprise two rather different structures: isotropic orthogonal networks or bundled fibers. Actin bundles are formed mostly by short and stiff cross-linking proteins (like α-actinin and scruin), while large and flexible cross-linkers, such as filamin, lead to an orthogonal network. Orthogonal networks can also be formed at lower concentrations of short cross-linking proteins, but rheological experiments of in vitro F-actin networks showed that the mechanical response of such networks is different from that of networks cross-linked with filamin. Moreover, atomic force microscope stretching experiments on filamin demonstrated the possibility of force-induced domain unfolding, characterized by a sawtooth-like pattern in the force-displacement curve.Here we present a 3D discrete model of F-actin networks that extends our previous, rigidly cross-linked network model by incorporating a flexible cross-linking model for human filamin A (hsFLNa). The implemented hsFLNa element has a highly nonlinear response to stretching, incorporating the transition to a softer response that characterizes filamin domain unfolding. Simple shear simulations of F-actin/hsFLNa networks show that the response of such networks is dominated by the behavior of the hsFLNa cross-linkers, while F-actin behaves almost rigid. We observe that force-induced unfolding of the hsFLNa relaxes the stresses in actin filaments, thus allowing for large network strains. By contrast, the shearing of F-actin networks with rigid cross-links leads to a large number of actin filaments stressed well beyond their breaking force. An increase in actin concentration increases the initial shear modulus, while the maximum network stiffening depends on the hsFLNa axial stiffness. The calculated initial modulus of F-actin/hsFLNa networks is found to be comparable with experimental measurements.

Effective Medium Theory of Semiflexible Filamentous Networks

We develop an effective medium approach to the mechanics of disordered, semiflexible polymer networks and study the response of such networks to uniform and nonuniform strain. We identify distinct elastic regimes in which the contributions of either filament bending or stretching to the macroscopic modulus vanish. We also show that our effective medium theory predicts a crossover between affine and nonaffine strain, consistent with both prior numerical studies and scaling theory.

Fading memory and time series prediction in recurrent networks with different forms of plasticity

We investigate how different forms of plasticity shape the dynamics and computational properties of simple recurrent spiking neural networks. In particular, we study the effect of combining two forms of neuronal plasticity: spike timing dependent plasticity (STDP), which changes the synaptic strength, and intrinsic plasticity (IP), which changes the excitability of individual neurons to maintain homeostasis of their activity. We find that the interaction of these forms of plasticity gives rise to interesting network dynamics characterized by a comparatively large number of stable limit cycles. We study the response of such networks to external input and find that they exhibit a fading memory of recent inputs. We then demonstrate that the combination of STDP and IP shapes the network structure and dynamics in ways that allow the discovery of patterns in input time series and lead to good performance in time series prediction. Our results underscore the importance of studying the interaction of different forms of plasticity on network behavior.

Nonlinear mechanics of soft fibrous networks

Mechanical networks of fibres arise on a range of scales in nature and technology, from the cytoskeleton of a cell to blood clots, from textiles and felts to skin and collageneous tissues. Their collective response is dependent on the individual response of the constituent filaments as well as density, topology and order in the network. Here, we use the example of a low-density synthetic felt of athermal filaments to study the generic features of the mechanical response of such networks including strain stiffening and large effective Poisson ratios. A simple microscopic model allows us to explain these features of our observations, and provides us with a baseline framework to understand active biomechanical networks.

The role of interparticle forces in colloidal aggregates: local investigations and modelling of restructuring during filtration

Industrial solid-liquid separation processes, such as pressure filtration or membrane processes, involve the application of pressure to suspensions. In response, some water is extracted, the suspension volume is reduced, and the dispersed aggregates start to form a network. In recent works, we aimed to make a prediction for the response of aggregates to stress which occurs during a filtration. We chose model systems made of aggregated silica nanoparticles. Some of these systems offer a strong resistance to applied stresses, and retain their permeability; others yield and collapse. We used small angle neutron scattering by which we can locally quantify the particle distribution withi the network to determine the processes by which particles reorganise during collapse: we found that reordering processes at the scale of 1 to 10 particle diameters control the course of collapse and the loss of permeability. Finally we constructed a numerical model for describing the processes by which colloidal aggregates are compressed. This model predicts that the response of such networks to pressure follows some scaling laws, which depend only on the elastic vs. dissipative nature of interparticle bonds.

The orientation of flies towards visual patterns: on the search for the underlying functional interactions.

The average optomotor response of insects to a given visual stimulus (measured in open-loop conditions) can be decomposed into a direction sensitive and a direction insensitive component. This decomposition is conceptual and always possible. The direction sensitive optomotor response represents the “classical” optomotor reflex, already studied in previous investigations; the direction insensitive optomotor response is strictly connected to the orientation and tracking behaviour (see the work of Reichardt and coworkers). Thus a characterization of the direction insensitive response is useful in clarifying the nervous mechanisms underlying the orientation behaviour. For this reason we study in this paper the direction insensitive optomotor (torque) response of fixed flying fliesMusca domestica. Periodic gratings, either moving or flickering, represent our main stimulus, since the dependence of the fly response on the spatial wavelength can unravel the presence and properties of the underlying lateral interactions. In this connection an extension of the Volterra series formalism to multi-input (nervous) networks is first outlined in order to connect our (behavioural) input-output data with the interactive structure of the network. A number of results concerning, for instance, the response of such networks to flickered and moving gratings are derived; they are not restricted to our behavioural results and may be relevant in other fields of neuroscience. These theoretical considerations provide the logical framework of our experimental investigation. The main results are: Furthermore the attraction towards a flickered periodic grating shows, as theoretically expected, a wavelength-dependence similar to that of the direction insensitive response, again present only in the lower part of the eye. The interactions which affect the orientation response are selective with respect to the spatiotemporal mapping of the pattern onto the receptor array. It is conjectured that these interactions are the basic mechanisms underlying spontaneous pattern discrimination in flies. Their possible organization is further discussed in terms of our formalism. Moreover our data suggest that two specific nervous circuitries correspond to our conceptual decomposition of the optomotor response.