Inkjet printing of silver nanowire networks

The development of printed electronics will require the ability to deposit a wide range of nanomaterials using printing techniques. Here we demonstrate the controlled deposition of networks of silver nanowires in well-defined patterns by inkjet printing from an optimized isopropyl alcohol-diethylene glycol dispersion. We find that great care must be taken while producing the ink and during solvent evaporation. The resultant networks have good electrical properties, displaying sheet resistances as low as 8 Ω/□ and conductivities as high as 10(5) S/m. Such optimized performances were achieved for line widths of 1-10 mm and network thicknesses of 0.5-2 μm deposited from ∼10-20 passes while using processing temperatures of no more than 110 °C. Thin networks are semitransparent with dc to optical conductivity ratios of ∼40.

Percolating transport and the conductive scaling relationship in lamellar block copolymers under confinement

The topology and transport behavior of the lamellar morphology self-assembled by block copolymers in thin films are shown to depend on the length scale over which they are characterized and can be described by percolation in a network under confinement. Gold nanowires replicating the lamellar morphology were fabricated via self-assembled poly(styrene-block-methyl methacrylate) thin films and a lift-off pattern transfer process. The lamellar morphology exhibits long-range connectivity (macroscopic scale); however, characterization of electrical conduction over confined areas (5-500 μm) demonstrates a discrete probability of disconnection that arises due to the underlying network structure and a lack of self-similarity at these microscale dimensions. In particular, it is proved that the lamellar network morphology under confinement has a conductance that is nonlinear with channel length or width. The experimental results are discussed in terms of percolation theory, and a simple, two-dimensional Monte Carlo model is shown to predict the key trends in the network topology and conductance in lamellar block copolymers, including the dependencies on composition, extent of spatial confinement, and confinement geometry. These results highlight the need to exquisitely control or engineer the self-assembled nanostructured pathways formed by block copolymers to ensure consistent device performance for any application that depends upon percolating material, ionic, or electrical transport, especially when confined in any dimension. It is also concluded that the two most promising approaches for enhancing conductivity in block copolymer materials may be achieved either at the limits of (1) perfectly oriented, single-crystalline or (2) high defect density, polycrystalline microphase separated morphologies and that nanostructured systems with intermediate defect densities would be detrimental to transport in confined systems.

Technical aspects on production of fluid extract from Brosimum gaudichaudii Trécul roots

Instruction:

Despite the increased use of Brosimum gaudichaudii roots as raw material on medicine to treatment of vitiligo, there are not studies that showing the impact of unit operations on the quality and standardized of the extract of B. gaudichaudii. The quality of the herbal extract is essential to ensure the safety and efficacy of pharmaceutical product. Due the medical and commercial importance, this study aimed to evaluate the impact of the extraction method (ultrasound or percolation) on the quality of herbal extract and optimize the extraction of psoralen and 8-methoxypsoralen (8-MOP) from B. gaudichaudii.

Materials and Methods:

The extraction recovery was evaluate by high-performance liquid chromatography (C8 reverse phase column and acetonitrile: Water 45:55 and flow rate 0.6 mL/min). The extraction was performed by ultrasound-assisted extraction (UEA) or percolation using a Box-Behnken design.

Results:

From both chemical markers (psoralen and bergapten), the optimal conditions for the UEA were an extraction time of 25 min, the mean particle size of 100 μm, and an ethanol: Water ratio of 55:45 (v/v).

Conclusion:

The extraction by percolation revealed that ethanol 55% was more efficient than ethanol 80% to extract psoralen and bergapten.

Terahertz-field-induced nonlinear electron delocalization in Au nanostructures

Improved control over the electromagnetic properties of metal nanostructures is indispensable for the development of next-generation integrated nanocircuits and plasmonic devices. The use of terahertz (THz)-field-induced nonlinearity is a promising approach to controlling local electromagnetic properties. Here, we demonstrate how intense THz electric fields can be used to modulate electron delocalization in percolated gold (Au) nanostructures on a picosecond time scale. We prepared both isolated and percolated Au nanostructures deposited on high resistivity Si(100) substrates. With increasing the applied THz electric fields, large opacity in the THz transmission spectra takes place in the percolated nanostructures; the maximum THz-field-induced transmittance difference, 50% more, is reached just above the percolation threshold thickness. Fitting the experimental data to a Drude-Smith model, we found furthermore that the localization parameter and the damping constant strongly depend on the applied THz-field strength. These results show that ultrafast nonlinear electron delocalization proceeds via strong electric field of THz pulses; the intense THz electric field modulates the backscattering rate of localized electrons and induces electron tunneling between Au nanostructures across the narrow insulating bridges without any material breakdown.

Function of metabolic and organelle networks in crowded and organized media

(Macro)molecular crowding and the ability of the ubiquitous cytoskeleton to dynamically polymerize–depolymerize are prevalent cytoplasmic conditions in prokaryotic and eukaryotic cells. Protein interactions, enzymatic or signaling reactions - single, sequential or in complexes - whole metabolic pathways and organelles can be affected by crowding, the type and polymeric status of cytoskeletal proteins (e.g., tubulin, actin), and their imparted organization. The self-organizing capability of the cytoskeleton can orchestrate metabolic fluxes through entire pathways while its fractal organization can frame the scaling of activities in several levels of organization. The intracellular environment dynamics (e.g., biochemical reactions) is dominated by the orderly cytoskeleton and the intrinsic randomness of molecular crowding. Existing evidence underscores the inherent capacity of intracellular organization to generate emergent global behavior. Yet unknown is the relative impact on cell function provided by organelle or functional compartmentation based on transient proteins association driven by weak interactions (quinary structures) under specific environmental challenges or functional conditions (e.g., hypoxia, division, differentiation). We propose a qualitative, integrated structural–functional model of cytoplasmic organization based on a modified version of the Sierspinsky–Menger–Mandelbrot sponge, a 3D representation of a percolation cluster, and examine its capacity to accommodate established experimental facts.

Designing new lithium-excess cathode materials from percolation theory: nanohighways in Li(x)Ni(2-4x/3)Sb(x/3)O2

Increasing lithium content is shown to be a successful strategy for designing new cathode materials. In layered Li(x)Ni(2-4x/3)Sb(x/3)O2 (x = 1.00-1.15), lithium excess improves both discharge capacity and capacity retention at 1C. Structural studies reveal a complex nanostructure pattern of Li-Sb and Ni-Sb ordering where the interface between these domains forms the correct local configuration for good lithium mobility. The <1 nm Li-Sb stripe domains and their interfaces thereby effectively act as nanohighways for lithium diffusion.

Percolation transition in dynamical traffic network with evolving critical bottlenecks

A critical phenomenon is an intrinsic feature of traffic dynamics, during which transition between isolated local flows and global flows occurs. However, very little attention has been given to the question of how the local flows in the roads are organized collectively into a global city flow. Here we characterize this organization process of traffic as "traffic percolation," where the giant cluster of local flows disintegrates when the second largest cluster reaches its maximum. We find in real-time data of city road traffic that global traffic is dynamically composed of clusters of local flows, which are connected by bottleneck links. This organization evolves during a day with different bottleneck links appearing in different hours, but similar in the same hours in different days. A small improvement of critical bottleneck roads is found to benefit significantly the global traffic, providing a method to improve city traffic with low cost. Our results may provide insights on the relation between traffic dynamics and percolation, which can be useful for efficient transportation, epidemic control, and emergency evacuation.

Phase Behavior and Percolation Properties of the Patchy Colloidal Fluids in the Random Porous Media

The lack of a simple analytical description of the hard-sphere fluid in a matrix with hard-core obstacles is limiting progress in the development of thermodynamic perturbation theories for the fluid in random porous media. We propose a simple and highly accurate analytical scheme, which allows us to calculate thermodynamic and percolation properties of a network-forming fluid confined in the random porous media, represented by the hard-sphere fluid and overlapping hard-sphere matrices, respectively. Our scheme is based on the combination of scaled-particle theory, Wertheim's thermodynamic perturbation theory for associating fluids and extension of the Flory-Stockmayer theory for percolation. The liquid-gas phase diagram and percolation threshold line for several versions of the patchy colloidal fluid model confined in a random porous media are calculated and discussed. The method presented enables calculation of the thermodynamic and percolation properties of a large variety of polymerizing and network-forming fluids confined in random porous media.

Effect of water sorption on the electronic conductivity of porous polymer electrolyte membrane fuel cell catalyst layers

A method is described for measuring the effective electronic conductivity of porous fuel cell catalyst layers (CLs) as a function of relative humidity (RH). Four formulations of CLs with different carbon black (CB) contents and ionomer equivalent weights (EWs) were tested. The van der Pauw method was used to measure the sheet resistance (RS), which increased with RH for all samples. The increase was attributed to ionomer swelling upon water uptake, which affects the connectivity of CB aggregates. Greater increases in RS were observed for samples with lower EW, which uptake more water on a mass basis per mass ionomer. Transient RS measurements were taken during absorption and desorption, and the resistance kinetics were fit using a double exponential decay model. No hysteresis was observed, and the absorption and desorption kinetics were virtually symmetric. Thickness measurements were attempted at different RHs, but no discernible changes were observed. This finding led to the conclusion that the conducting Pt/C volume fraction does not change with RH, which suggests that effective medium theory models that depend on volume fraction alone cannot explain the reduction in conductivity with RH. The merits of percolation-based models were discussed. Optical micrographs revealed an extensive network of "mud cracks" in some samples. The influence of water sorption on CL conductivity is primarily explained by ionomer swelling, and its effects on the quantity and quality of interaggregate contacts were discussed.

Effect of percolation on the capacitance of supercapacitor electrodes prepared from composites of manganese dioxide nanoplatelets and carbon nanotubes

Here we demonstrate significant improvements in the performance of supercapacitor electrodes based on 2D MnO2 nanoplatelets by the addition of carbon nanotubes. Electrodes based on MnO2 nanoplatelets do not display high areal capacitance because the electrical properties of such films are poor, limiting the transport of charge between redox sites and the external circuit. In addition, the mechanical strength is low, limiting the achievable electrode thickness, even in the presence of binders. By adding carbon nanotubes to the MnO2-based electrodes, we have increased the conductivity by up to 8 orders of magnitude, in line with percolation theory. The nanotube network facilitates charge transport, resulting in large increases in capacitance, especially at high rates, around 1 V/s. The increase in MnO2 specific capacitance scaled with nanotube content in a manner fully consistent with percolation theory. Importantly, the mechanical robustness was significantly enhanced, allowing the fabrication of electrodes that were 10 times thicker than could be achieved in MnO2-only films. This resulted in composite films with areal capacitances up to 40 times higher than could be achieved with MnO2-only electrodes.

Carbon Nanofibers and Their Composites: A Review of Synthesizing, Properties and Applications

Carbon nanofiber (CNF), as one of the most important members of carbon fibers, has been investigated in both fundamental scientific research and practical applications. CNF composites are able to be applied as promising materials in many fields, such as electrical devices, electrode materials for batteries and supercapacitors and as sensors. In these applications, the electrical conductivity is always the first priority need to be considered. In fact, the electrical property of CNF composites largely counts on the dispersion and percolation status of CNFs in matrix materials. In this review, the electrical transport phenomenon of CNF composites is systematically summarized based on percolation theory. The effects of the aspect ratio, percolation backbone structure and fractal characteristics of CNFs and the non-universality of the percolation critical exponents on the electrical properties are systematically reviewed. Apart from the electrical property, the thermal conductivity and mechanical properties of CNF composites are briefly reviewed, as well. In addition, the preparation methods of CNFs, including catalytic chemical vapor deposition growth and electrospinning, and the preparation methods of CNF composites, including the melt mixing and solution process, are briefly introduced. Finally, their applications as sensors and electrode materials are described in this review article.

Two exactly soluble models of rigidity percolation

We summarize results for two exactly soluble classes of bond-diluted models for rigidity percolation, which can serve as a benchmark for numerical and approximate methods. For bond dilution problems involving rigidity, the number of floppy modes F plays the role of a free energy. Both models involve pathological lattices with two-dimensional vector displacements. The first model involves hierarchical lattices where renormalization group calculations can be used to give exact solutions. Algebraic scaling transformations produce a transition of the second order, with an unstable critical point and associated scaling laws at a mean coordination <r>=4.41, which is above the 'mean field' value <r>=4 predicted by Maxwell constraint counting. The order parameter exponent associated with the spanning rigid cluster geometry is β=0.0775 and that associated with the divergence of the correlation length and the anomalous lattice dimension d is dν=3.533. The second model involves Bethe lattices where the rigidity transition is massively first order by a mean coordination <r>=3.94 slightly below that predicted by Maxwell constraint counting. We show how a Maxwell equal area construction can be used to locate the first-order transition and how this result agrees with simulation results on larger random-bond lattices using the pebble game algorithm.

A photochromic diode with a continuum of intermediate states: towards high density multilevel storage

A continuum of intermediate states (current levels) is demonstrated for an organic diode utilizing a photochromic (dithienylethene) switching layer. Specific intermediate states can be attained by controlling the fraction of closed isomer (X) in the transduction layer, affording a novel methodology for multilevel storage applications. The analog response of the device is discussed in terms of the concentration and morphology of closed dithienylethene isomer, which can be accessed via optical and electrical switching reactions.

Films of Carbon Nanomaterials for Transparent Conductors

The demand for transparent conductors is expected to grow rapidly as electronic devices, such as touch screens, displays, solid state lighting and photovoltaics become ubiquitous in our lives. Doped metal oxides, especially indium tin oxide, are the commonly used materials for transparent conductors. As there are some drawbacks to this class of materials, exploration of alternative materials has been conducted. There is an interest in films of carbon nanomaterials such as, carbon nanotubes and graphene as they exhibit outstanding properties. This article reviews the synthesis and assembly of these films and their post-treatment. These processes determine the film performance and understanding of this platform will be useful for future work to improve the film performance.

Low percolation threshold of graphene/polymer composites prepared by solvothermal reduction of graphene oxide in the polymer solution

Graphene/polyvinylidene fluoride (PVDF) composites were prepared using in-situ solvothermal reduction of graphene oxide in the PVDF solution. The electrical conductivity of the composites was greatly improved by doping with graphene sheets. The percolation threshold of such composite was determined to be 0.31 vol.%, being much smaller than that of the composites prepared via blending reduced graphene sheets with polymer matrix. This is attributed to the large aspect ratio of the SRG sheets and their uniform dispersion in the polymer matrix. The dielectric constant of PVDF showed a marked increase from 7 to about 105 with only 0.5 vol.% loading of SRG content. Like the other conductor-insulator systems, the AC conductivity of the system also obeyed the universal dynamic response. In addition, the SRG/PVDF composite shows a much stronger nonlinear conduction behavior than carbon nanotube/nanofiber based polymer composite, owing to intense Zener tunneling between the SRG sheets. The strong electrical nonlinearity provides further support for a homogeneous dispersion of SRG sheets in the polymer matrix.

Intracellular calcium signals display an avalanche-like behavior over multiple lengthscales

Many natural phenomena display “self-organized criticality” (SOC), (Bak et al., 1987). This refers to spatially extended systems for which patterns of activity characterized by different lengthscales can occur with a probability density that follows a power law with pattern size. Differently from power laws at phase transitions, systems displaying SOC do not need the tuning of an external parameter. Here we analyze intracellular calcium (Ca²⁺) signals, a key component of the signaling toolkit of almost any cell type. Ca²⁺ signals can either be spatially restricted (local) or propagate throughout the cell (global). Different models have suggested that the transition from local to global signals is similar to that of directed percolation. Directed percolation has been associated, in turn, to the appearance of SOC. In this paper we discuss these issues within the framework of simple models of Ca²⁺ signal propagation. We also analyze the size distribution of local signals (“puffs”) observed in immature Xenopus Laevis oocytes. The puff amplitude distribution obtained from observed local signals is not Gaussian with a noticeable fraction of large size events. The experimental distribution of puff areas in the spatio-temporal record of the image has a long tail that is approximately log-normal. The distribution can also be fitted with a power law relationship albeit with a smaller goodness of fit. The power law behavior is encountered within a simple model that includes some coupling among individual signals for a wide range of parameter values. An analysis of the model shows that a global elevation of the Ca²⁺ concentration plays a major role in determining whether the puff size distribution is long-tailed or not. This suggests that Ca²⁺-clearing from the cytosol is key to determine whether IP₃-mediated Ca²⁺ signals can display a SOC-like behavior or not.

Physiological Intracellular Crowdedness is Defined by the Perimeter-to-Area Ratio of Sub-Cellular Compartments

The intracellular environment is known to be a crowded and inhomogeneous space. Such an in vivo environment differs from a well-diluted, homogeneous environment for biochemical reactions. However, the effects of both crowdedness and the inhomogeneity of environment on the behavior of a mobile particle have not yet been investigated sufficiently. As described in this paper, we constructed artificial reaction spaces with fractal models, which are assumed to be non-reactive solid obstacles in a reaction space with crevices that function as operating ranges for mobile particles threading the space. Because of the homogeneity of the structures of artificial reaction spaces, the models succeeded in reproducing the physiological fractal dimension of solid structures with a smaller number of non-reactive obstacles than in the physiological condition. This incomplete compatibility was mitigated when we chose a suitable condition of a perimeter-to-area ratio of the operating range to our model. Our results also show that a simulation space is partitioned into convenient reaction compartments as an in vivo environment with the exact amount of solid structures estimated from TEM images. The characteristics of these compartments engender larger mean square displacement of a mobile particle than that of particles in smaller compartments. Subsequently, the particles start to show confined particle-like behavior. These results are compatible with our previously presented results, which predicted that a physiological environment would produce quick response and slow exhaustion reactions.

Applications of percolation theory to fungal spread with synergy

There is increasing interest in the use of the percolation paradigm to analyse and predict the progress of disease spreading in spatially structured populations of animals and plants. The wider utility of the approach has been limited, however, by several restrictive assumptions, foremost of which is a strict requirement for simple nearest-neighbour transmission, in which the disease history of an individual is influenced only by that of its neighbours. In a recent paper, the percolation paradigm has been generalized to incorporate synergistic interactions in host infectivity and susceptibility, and the impact of these interactions on the invasive dynamics of an epidemic has been demonstrated. In the current paper, we elicit evidence that such synergistic interactions may underlie transmission dynamics in real-world systems by first formulating a model for the spread of a ubiquitous parasitic and saprotrophic fungus through replicated populations of nutrient sites and subsequently fitting and testing the model using data from experimental microcosms. Using Bayesian computational methods for model fitting, we demonstrate that synergistic interactions are necessary to explain the dynamics observed in the replicate experiments. The broader implications of this work in identifying disease-control strategies that deflect epidemics from invasive to non-invasive regimes are discussed.

The conundrum of functional brain networks: small-world efficiency or fractal modularity

The human brain has been studied at multiple scales, from neurons, circuits, areas with well-defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed the problem of the hierarchical organization in the brain through network analysis. Our analysis identified functional brain modules of fractal structure that were inter-connected in a small-world topology. Here, we provide more details on the use of network science tools to elaborate on this behavior. We indicate the importance of using percolation theory to highlight the modular character of the functional brain network. These modules present a fractal, self-similar topology, identified through fractal network methods. When we lower the threshold of correlations to include weaker ties, the network as a whole assumes a small-world character. These weak ties are organized precisely as predicted by theory maximizing information transfer with minimal wiring costs.

Fragmentation: loss of global coherence or breakdown of modularity in functional brain architecture?

Psychiatric illnesses characterized by disorganized cognition, such as schizophrenia, have been described in terms of fragmentation and hence understood as reduction in functional brain connectivity, particularly in prefrontal and parietal areas. However, as graph theory shows, relatively small numbers of nonlocal connections are sufficient to ensure global coherence in the modular small-world network structure of the brain. We reconsider fragmentation in this perspective. Computational studies have shown that for a given level of connectivity in a model of coupled nonlinear oscillators, modular small-world networks evolve from an initially random organization. Here we demonstrate that with decreasing connectivity, the probability of evolving into a modular small-world network breaks down at a critical point, which scales to the percolation function of random networks with a universal exponent of α = 1.17. Thus, according to the model, local modularity systematically breaks down before there is loss of global coherence in network connectivity. We, therefore, propose that fragmentation may involve, at least in its initial stages, the inability of a dynamically evolving network to sustain a modular small-world structure. The result is in a shift in the balance in schizophrenia from local to global functional connectivity.

Far from equilibrium percolation, stochastic and shape resonances in the physics of life

Key physical concepts, relevant for the cross-fertilization between condensed matter physics and the physics of life seen as a collective phenomenon in a system out-of-equilibrium, are discussed. The onset of life can be driven by: (a) the critical fluctuations at the protonic percolation threshold in membrane transport; (b) the stochastic resonance in biological systems, a mechanism that can exploit external and self-generated noise in order to gain efficiency in signal processing; and (c) the shape resonance (or Fano resonance or Feshbach resonance) in the association and dissociation processes of bio-molecules (a quantum mechanism that could play a key role to establish a macroscopic quantum coherence in the cell).

Heterogeneity in susceptible-infected-removed (SIR) epidemics on lattices

The percolation paradigm is widely used in spatially explicit epidemic models where disease spreads between neighbouring hosts. It has been successful in identifying epidemic thresholds for invasion, separating non-invasive regimes, where the disease never invades the system, from invasive regimes where the probability of invasion is positive. However, its power is mainly limited to homogeneous systems. When heterogeneity (environmental stochasticity) is introduced, the value of the epidemic threshold is, in general, not predictable without numerical simulations. Here, we analyse the role of heterogeneity in a stochastic susceptible-infected-removed epidemic model on a two-dimensional lattice. In the homogeneous case, equivalent to bond percolation, the probability of invasion is controlled by a single parameter, the transmissibility of the pathogen between neighbouring hosts. In the heterogeneous model, the transmissibility becomes a random variable drawn from a probability distribution. We investigate how heterogeneity in transmissibility influences the value of the invasion threshold, and find that the resilience of the system to invasion can be suitably described by two control parameters, the mean and variance of the transmissibility. We analyse a two-dimensional phase diagram, where the threshold is represented by a phase boundary separating an invasive regime in the high-mean, low-variance region from a non-invasive regime in the low-mean, high-variance region of the parameter space. We thus show that the percolation paradigm can be extended to the heterogeneous case. Our results have practical implications for the analysis of disease control strategies in realistic heterogeneous epidemic systems.

Critical effect of dependency groups on the function of networks

Current network models assume one type of links to define the relations between the network entities. However, many real networks can only be correctly described using two different types of relations. Connectivity links that enable the nodes to function cooperatively as a network and dependency links that bind the failure of one network element to the failure of other network elements. Here we present an analytical framework for studying the robustness of networks that include both connectivity and dependency links. We show that a synergy exists between the failure of connectivity and dependency links that leads to an iterative process of cascading failures that has a devastating effect on the network stability. We present exact analytical results for the dramatic change in the network behavior when introducing dependency links. For a high density of dependency links, the network disintegrates in a form of a first-order phase transition, whereas for a low density of dependency links, the network disintegrates in a second-order transition. Moreover, opposed to networks containing only connectivity links where a broader degree distribution results in a more robust network, when both types of links are present a broad degree distribution leads to higher vulnerability.

Leaders of neuronal cultures in a quorum percolation model

We present a theoretical framework using quorum percolation for describing the initiation of activity in a neural culture. The cultures are modeled as random graphs, whose nodes are excitatory neurons with k_in inputs and k_out outputs, and whose input degrees k_in = k obey given distribution functions p_k. We examine the firing activity of the population of neurons according to their input degree (k) classes and calculate for each class its firing probability Φ_k(t) as a function of t. The probability of a node to fire is found to be determined by its in-degree k, and the first-to-fire neurons are those that have a high k. A small minority of high-k-classes may be called “Leaders,” as they form an interconnected sub-network that consistently fires much before the rest of the culture. Once initiated, the activity spreads from the Leaders to the less connected majority of the culture. We then use the distribution of in-degree of the Leaders to study the growth rate of the number of neurons active in a burst, which was experimentally measured to be initially exponential. We find that this kind of growth rate is best described by a population that has an in-degree distribution that is a Gaussian centered around k = 75 with width σ = 31 for the majority of the neurons, but also has a power law tail with exponent −2 for 10% of the population. Neurons in the tail may have as many as k = 4,700 inputs. We explore and discuss the correspondence between the degree distribution and a dynamic neuronal threshold, showing that from the functional point of view, structure and elementary dynamics are interchangeable. We discuss possible geometric origins of this distribution, and comment on the importance of size, or of having a large number of neurons, in the culture.

Signal percolation through plants and the shape of the calcium signature

Plants respond to almost any kind of external stimulus with transients in their cytoplasmic free calcium concentration ([Ca(2+)](c)). A huge variety of kinetics recorded by optical techniques has been reported in the past. This variety has been credited the specificity needed to explain how information about incoming stimuli is evaluated by the organism and turned into the right physiological responses which provide advantages for survival and reproduction. A physiological response often takes place away from the site of stimulation. This requires cell-to-cell communication. Hence, responding cells are not necessarily directly stimulated but rather receive an indirect stimulus via cell-to-cell communication. It appears unlikely that the '[Ca(2+)](c) signature' in the primarily stimulated cell is conveyed over long distances via cell-to-cell communication from the 'receptor cells' to the 'effector cells'. Here, a novel aspect is highlighted to explain the variety of [Ca(2+)] kinetics seen by integrating methods of [Ca(2+)](c) recording. Plants can generally be seen as cellular automata with specific morphology and capable for cell-to-cell communication. Just a few rules are needed to demonstrate how waves of [Ca(2+)](c)-increases percolate through the organism and thereby deliver a broad variety of 'signatures'. Modelling intercellular signalling may be a possible way to find explanations for different kinds of signal transmission, signal amplification, wave formation, oscillations and stimulus-response coupling. The basic examples presented here show that care has to be taken when interpreting cellular '[Ca(2+)](c) signatures' recorded by optical techniques which integrate over a big number of cells or even whole plants.