Linear Array Of Cells Research Articles

Local accumulation time for diffusion in cells with gap junction coupling.

In this paper we analyze the relaxation to steady state of intracellular diffusion in a pair of cells with gap-junction coupling. Gap junctions are prevalent in most animal organs and tissues, providing a direct diffusion pathway for both electrical and chemical communication between cells. Most analytical models of gap junctions focus on the steady-state diffusive flux and the associated effective diffusivity. Here we investigate the relaxation to steady state in terms of the so-called local accumulation time. The latter is commonly used to estimate the time to form a protein concentration gradient during morphogenesis. The basic idea is to treat the fractional deviation from the steady-state concentration as a cumulative distribution for the local accumulation time. One of the useful features of the local accumulation time is that it takes into account the fact that different spatial regions can relax at different rates. We consider both static and dynamic gap junction models. The former treats the gap junction as a resistive channel with effective permeability μ, whereas the latter represents the gap junction as a stochastic gate that randomly switches between an open and closed state. The local accumulation time is calculated by solving the diffusion equationin Laplace space and then taking the small-s limit. We show that the accumulation time is a monotonically increasing function of spatial position, with a jump discontinuity at the gap junction. This discontinuity vanishes in the limit μ→∞ for a static junction and β→0 for a stochastically gated junction, where β is the rate at which the gate closes. Finally, our results are generalized to the case of a linear array of cells with nearest-neighbor gap junction coupling.

Roles of basal keratinocytes in actinotrichia formation

The embryonic fins and the tip of adult fins of teleost fish are supported by rows of straight, unmineralized fibrils called actinotrichia. The proximal ends of the actinotrichia are bundled and the mineralized bones called lepidotrichia are made along them. Since malformation in actinotrichia causes wavy fin bones, the correct configuration of actinotrichia is essential for the correct construction of the fin shape. Past studies suggested that two types of cells, basal keratinocytes, and mesenchymal cells involve in the formation of actinotrichia. However, the mechanism how these cells contribute is unknown. In this study, we elucidated the role of basal keratinocytes in actinotrichia formation. First, we developed the imaging tool that specifically visualizes the basal keratinocytes and actinotrichia. Then, we established the in vitro culture method of the basal keratinocytes and found that the keratinocytes developed fine needle-like structures in it. The TEM image of them showed the specific shadow pattern of actinotrichia, indicating that the fine needle-like structures are the newly made actinotrichia. Finally, we cultured the basal keratinocytes with mature actinotrichia and observed that the basal keratinocytes actively holded actinotrichia with their membrane, and often generated a linear array of cells holding a single actinotrichium. This behavior suggested a mechanism with which long actinotrichia are made by relatively small cells. Our results clarified the role of basal keratinocyte and provided a novel insight into understanding the mechanism of actinotrichia formation.

Pore diameter dependence of catalytic activity: p-nitrobenzaldehyde conversion to an aldol product in amine-functionalized mesoporous silica.

The reaction yield for conversion of p-nitrobenzaldehyde (PNB) to an aldol product in amine-functionalized mesoporous silica nanoparticles (MSN) exhibits a 20-fold enhancement for a modest increase in pore diameter, d. This enhanced catalytic activity is shown to reflect a strong increase in the "passing propensity," P, of reactant and product species inside the pores. We find that P ≈ 0, corresponding to single-file diffusion, applies for the smallest d which still significantly exceeds the linear dimensions of PNB and the aldol product. However, in this regime of narrow pores, these elongated species must align with each other and with the pore axis in order to pass. Thus, P reflects both translational and rotational diffusion. Langevin simulation accounting for these features is used to determine P versus d. The results are also augmented by analytic theory for small and large d where simulation is inefficient. The connection with the catalytic activity and yield is achieved by the incorporation of results for P into a multi-scale modeling framework. Specifically, we apply a spatially coarse-grained (CG) stochastic model for the overall catalytic reaction-diffusion process in MSN. Pores are treated as linear arrays of cells from the ends of which species adsorb and desorb, and between which species hop and exchange, with the exchange rate reflecting P. CG model predictions including yield are assessed by Kinetic Monte Carlo simulation.

The Invading Anchor Cell Induces Lateral Membrane Constriction during Vulval Lumen Morphogenesis in C. elegans

During epithelial tube morphogenesis, linear arrays of cells are converted into tubular structures through actomyosin-generated intracellular forces that induce tissue invagination and lumen formation. We have investigated lumen morphogenesis in the C.elegans vulva. The first discernible event initiating lumen formation is the apical constriction of the two innermost primary cells (VulF). The VulF cells thereafter constrict their lateral membranes along the apicobasal axis to extend the lumen dorsally. Lateral, but not apical, VulF constriction requires the prior invasion of the anchor cell (AC). The invading AC extends actin-rich protrusions toward VulF, resulting in the formation of a direct AC-VulF interface. The recruitment of the F-BAR-domain protein TOCA-1 to the AC-VulF interface induces the accumulation of force-generating actomyosin, causing a switch from apical to lateral membrane constriction and the dorsal extension of the lumen. Invasive cells may induce shape changes in adjacent cells to penetrate their target tissues.

Monodisperse hard rods in external potentials.

We consider linear arrays of cells of volume V(c) populated by monodisperse rods of size σV(c),σ=1,2,..., subject to hardcore exclusion interaction. Each rod experiences a position-dependent external potential. In one application we also examine effects of contact forces between rods. We employ two distinct methods of exact analysis with complementary strengths and different limits of spatial resolution to calculate profiles of pressure and density on mesoscopic and microscopic length scales at thermal equilibrium. One method uses density functionals and the other statistically interacting vacancy particles. The applications worked out include gravity, power-law traps, and hard walls. We identify oscillations in the profiles on a microscopic length scale and show how they are systematically averaged out on a well-defined mesoscopic length scale to establish full consistency between the two approaches. The continuum limit, realized as V(c)→0,σ→∞ at nonzero and finite σV(c), connects our highest-resolution results with known exact results for monodisperse rods in a continuum. We also compare the pressure profiles obtained from density functionals with the average microscopic pressure profiles derived from the pair distribution function.

Hiding the squid: patterns in artificial cephalopod skin.

Cephalopods employ their chromomorphic skins for rapid and versatile active camouflage and signalling effects. This is achieved using dense networks of pigmented, muscle-driven chromatophore cells which are neurally stimulated to actuate and affect local skin colouring. This allows cephalopods to adopt numerous dynamic and complex skin patterns, most commonly used to blend into the environment or to communicate with other animals. Our ultimate goal is to create an artificial skin that can mimic such pattern generation techniques, and that could produce a host of novel and compliant devices such as cloaking suits and dynamic illuminated clothing. This paper presents the design, mathematical modelling and analysis of a dynamic biomimetic pattern generation system using bioinspired artificial chromatophores. The artificial skin is made from electroactive dielectric elastomer: a soft, planar-actuating smart material that we show can be effective at mimicking the actuation of biological chromatophores. The proposed system achieves dynamic pattern generation by imposing simple local rules into the artificial chromatophore cells so that they can sense their surroundings in order to manipulate their actuation. By modelling sets of artificial chromatophores in linear arrays of cells, we explore the capability of the system to generate a variety of dynamic pattern types. We show that it is possible to mimic patterning seen in cephalopods, such as the passing cloud display, and other complex dynamic patterning.

Some Exact and Asymptotic Solutions to Single Server Models of Dynamic Storage

We consider models of queue storage, where items arrive accordingly to a Poisson process of rate λ and each item takes up one cell in a linear array of cells, which are numbered {1, 2, 3,…}. The arriving item is placed in the lowest numbered available cell. The total service rate provided to the items is the constant μ (with ρ = λ/μ), but service may be provided simultaneously to more than one item. If there are 𝒩 items stored and each is serviced at the rate μ/𝒩, this corresponds to processor-sharing (PS). We analyze several models of this type, which have been shown to provide bounds on the PS model. We shall assume that (1) the server works only on the leftmost item, (2) on the two rightmost items, or (3) on all items by the PS discipline, but with a departure of the rightmost item causing a rearrangement of the items within the cells, so that the wasted space remains unchanged. The set of occupied cells at any time is {i 1, i 2,…, i 𝒩} where i 1 < i 2 < … <i 𝒩 and we are interested in the wasted space (W = i 𝒩 − 𝒩), the maximum occupied cell (i 𝒩), and the joint distribution of W and 𝒩. We study these exactly and asymptotically, especially in the heavy traffic limit where ρ ↑ 1.

Adaptive Limited Feedback for Sum-Rate Maximizing Beamforming in Cooperative Multicell Systems

Base station cooperation improves the sum-rates that can be achieved in cellular systems. Conventional cooperation techniques require sharing large amounts of information over finite-capacity backhaul links and assume that base stations have full channel state information (CSI) of all the active users in the system. In this paper, a new limited feedback strategy is proposed for multicell beamforming where cooperation is restricted to sharing only the CSI of active users among base stations. The system setup considered is a linear array of cells based on the “soft hand-off model,” where each cell contains single-antenna users and multi-antenna base stations. Beamforming vectors are designed using a generalized eigenvector approach to maximize the sum-rate in a single-interferer scenario, at high signal to noise ratio. Users are assumed to feedback quantized CSI of the desired and interfering channels using a finite-bandwidth feedback link. An upper bound on the mean loss in sum rate due to random vector quantization is derived. A new feedback-bit allocation strategy, to partition the available bits between the desired and interfering channels, is developed to reduce the mean loss in sum-rate due to quantization for the soft hand-off model. The proposed feedback-bit partitioning algorithm is shown, using simulations, to yield sum-rates close to the those obtained using full CSI at base station.

Is there a significant transmural gradient in repolarization time in the intact heart?

Is there a significant transmural gradient in repolarization time in the intact heart?

Monocytes and Macrophages Form Branched Cell Columns in Matrigel: Implications for a Role in Neovascularization

Linear arrays of cells, or cell columns, have been observed in the extracellular matrix prior to neovascularization, but their nature and significance remains elusive. Based on the emerging evidence implicating a role for monocytes and macrophages (MC/MPH) in vasculogenesis, we hypothesized that MC/MPH also can form linear or branched columns, facilitating the co-migration and the spatial arrangement of other cell types. To test this hypothesis, we studied the distribution of MC/MPH effected by chemotactic migration in novel in vitro and in vivo models of development. We induced transversal and lateral migration of THP-1 monocytoid cells in Matrigel in vitro. The effect of this process on co-localization of other micro-objects was assessed using erythrocytes and micron-sized plastic beads. In vivo, we analyzed MC/MPH infiltration in subcutaneously implanted Matrigel plugs containing angiogenic factors and across a microporous filter comprising the wall of a chamber filled with Matrigel, also placed subcutaneously in mice. In vitro, we found that migrating THP-1 cells induced the lasting degradation of Matrigel and produced cell columns, a process amplified by monocyte chemoattractant protein-1 (MCP-1). We also report the co-localization of erythrocytes with THP-1 cells in cell columns. Endothelium-free tunnels containing MC/MPH, neutrophils, or erythrocytes were also observed in the Matrigel-filled chambers. In free subcutaneous Matrigel plugs, we found MC/MPH-based columns harboring isolated Tie-2+ cells (a marker of endothelial progenitor phenotype), as well as fibroblasts, dendritic cells, and adypocytes. Many of these cell columns displayed conspicuous branching. Our data demonstrate formation of branched MC/MPH cell columns in vitro and in vivo, a previously unrecognized pattern of penetration of extracellular matrices by inflammatory cells. Thus, monocytes and macrophages influence the distribution of neovessels as well as their branching points. These cells are the "architects of development," assisting organogenesis, tumorigenesis, and wound healing by patterning the tissular space.

Microvascular invasion during endochondral ossification in experimental fractures in rats

In this study morphologic techniques have been used to detail the angiogenic response that accompanies endochondral fracture healing in a clinically relevant, reproducible rat model. In this displaced fracture, the gap fills with cartilage that later is replaced by bone, via endochondral ossification. A transient periosteal circulation, followed by a permanent medullary circulation accompany this progression. From 2 to 6 weeks, vessels grow out from the periosteal tissue and give rise to vascular buds, which abut directly onto the avascular zone corresponding to the fracture defect. From 3 weeks onwards, a second wave of vessels grows out from the marrow to the cartilage-filled fracture defect, terminating as vascular buds and loops lined by endothelial and perivascular cells. The loops and buds stain strongly for laminin but transmission electron microscopy does not demonstrate an identifiable basement membrane, pointing to a region of active extracellular matrix turnover. These vessels are intimately associated with osteoblasts and newly formed woven bone forming finger-like composite structures that protrude into the mineralized cartilage matrix with which they form a clearly demarcated interface. Invading vessels and woven bone successively replace the cartilage matrix to mediate repair. Both the vascular structures and progression of endochondral ossification observed, closely resemble those described in the normal epiphyseal growth plate, indicating that the fundamental processes are similar. However, there is a difference in the spatial orientation of cells such that the healing front in the fracture model is relatively disorganized, compared to the orderly linear array of cells at the epiphyseal growth plate.

Modeling tight junction dynamics and oscillations.

Tight junction (TJ) permeability responds to changes of extracellular Ca2+ concentration. This can be gauged through changes of the transepithelial electrical conductance (G) determined in the absence of apical Na+. The early events of TJ dynamics were evaluated by the fast Ca2+ switch assay (FCSA) (Lacaz-Vieira, 2000), which consists of opening the TJs by removing basal calcium (Ca2+ bl) and closing by returning Ca2+ bl to normal values. Oscillations of TJ permeability were observed when Ca2+ bl is removed in the presence of apical calcium (Ca2+ ap) and were interpreted as resulting from oscillations of a feedback control loop which involves: (a) a sensor (the Ca2+ binding sites of zonula adhaerens), (b) a control unit (the cell signaling machinery), and (c) an effector (the TJs). A mathematical model to explain the dynamical behavior of the TJs and oscillations was developed. The extracellular route (ER), which comprises the paracellular space in series with the submucosal interstitial fluid, was modeled as a continuous aqueous medium having the TJ as a controlled barrier located at its apical end. The ER was approximated as a linear array of cells. The most apical cell is separated from the apical solution by the TJ and this cell bears the Ca2+ binding sites of zonula adhaerens that control the TJs. According to the model, the control unit receives information from the Ca2+ binding sites and delivers a signal that regulates the TJ barrier. Ca2+ moves along the ER according to one-dimensional diffusion following Fick's second law. Across the TJ, Ca2+ diffusion follows Fick's first law. Our first approach was to simulate the experimental results in a semiquantitative way. The model tested against experiment results performed in the frog urinary bladder adequately predicts the responses obtained in different experimental conditions, such as: (a) TJ opening and closing in a FCSA, (b) opening by the presence of apical Ca2+ and attainment of a new steady-state, (c) the escape phase which follows the halt of TJ opening induced by apical Ca2+, (d) the oscillations of TJ permeability, and (e) the effect of Ca2+ ap concentration on the frequency of oscillations.

Gradients in the developing spinal cord – mitogens join forces with morphogens

Developmental neurobiologists are growing accustomed to discoveries of signaling centers that help pattern the developing nervous system. A signaling center can be the focal source of a morphogen – a diffusible molecule whose concentration gradient across an embryonic field serves to specify different cell fates at different levels, or ‘thresholds’. A fine example is found in ventral spinal cord, where Sonic hedgehog (Shh) is released from the floor plate. Culture experiments confirm that neural progenitors adopt different phenotypes when confronted with different concentrations of Shh. Opposing the action of this ventral signaling center is a similar one at the dorsal midline of the spinal cord, the roof plate. Here we find another classical morphogen family, the bone morphogenetic proteins (BMPs). A recent paper by Megason and McMahon suggests that morphogens are not the only class of signaling molecules secreted by the roof plate: a mitogen gradient could exist alongside the morphogen gradient to coordinate neurogenesis along the dorsal–ventral (D–V) axis of the spinal cord [1xA mitogen gradient of dorsal midline Wnts organizes growth in the CNS. Megason, S.G. and McMahon, A.P. Development. 2002; 129: 2087–2098PubMedSee all References][1].The mitogens in question belong to the Wnt family. Although several Wnts are present in embryonic spinal cord, evidence implicates Wnt1 and Wnt3a in stimulating proliferation and inhibiting differentiation along the D–V axis. Their message levels peak at the roof plate. Abolishing this D–V asymmetry on one side (via unilateral electroporation of expression constructs) caused a drastic increase in cell division at the expense of differentiation. Wnts enhance cell division, at least in part, by upregulating D-type cyclins. It is notable that the D–V sequence of progenitor identities was not altered, as might have been expected had a morphogen gradient been disturbed. By contrast, blocking the Wnt-signaling pathway reduced cell division without promoting premature differentiation, suggesting that there must be something more than a simple Wnt-regulated switch between proliferation and differentiation. In fact, loss-of-function experiments by Muroyama et al. could be interpreted as lowering the dose of a dorsal morphogen in Wnt1;Wnt3a double knockouts: two dorsal cell types were depleted, whereas the next most-ventral cell type was expanded [2xWnt signaling plays an essential role in neuronal specification of the dorsal spinal cord. Muroyama, Y. et al. Genes Dev. 2002; 16: 548–553Crossref | PubMed | Scopus (203)See all References][2]. In other words, these Wnts might be ‘double-dipping’, as both mitogens and morphogens.In the mitogen gradient model, ventral progenitors find themselves ever further from the dorsal growth organizer as the spinal cord enlarges, increasing the likelihood they will drop out of division to differentiate. Megason and McMahon have used computer modeling to explore how such a scenario plays out across a linear array of cells (http://hombiosys.com/downloads/MitogenGradient). They found that the size and shape of the responding tissue are regulated by the slope of the mitogen gradient. The next challenge will be to embellish the model to account for molecules that have both mitogenic and morphogenic activities. What might otherwise be exhausting mental gymnastics could happily be avoided through computational analysis.

Gradients in the developing spinal cord – mitogens join forces with morphogens

Developmental neurobiologists are growing accustomed to discoveries of signaling centers that help pattern the developing nervous system. A signaling center can be the focal source of a morphogen – a diffusible molecule whose concentration gradient across an embryonic field serves to specify different cell fates at different levels, or ‘thresholds’. A fine example is found in ventral spinal cord, where Sonic hedgehog (Shh) is released from the floor plate. Culture experiments confirm that neural progenitors adopt different phenotypes when confronted with different concentrations of Shh. Opposing the action of this ventral signaling center is a similar one at the dorsal midline of the spinal cord, the roof plate. Here we find another classical morphogen family, the bone morphogenetic proteins (BMPs). A recent paper by Megason and McMahon suggests that morphogens are not the only class of signaling molecules secreted by the roof plate: a mitogen gradient could exist alongside the morphogen gradient to coordinate neurogenesis along the dorsal–ventral (D–V) axis of the spinal cord [1xA mitogen gradient of dorsal midline Wnts organizes growth in the CNS. Megason, S.G. and McMahon, A.P. Development. 2002; 129: 2087–2098PubMedSee all References[1].The mitogens in question belong to the Wnt family. Although several Wnts are present in embryonic spinal cord, evidence implicates Wnt1 and Wnt3a in stimulating proliferation and inhibiting differentiation along the D–V axis. Their message levels peak at the roof plate. Abolishing this D–V asymmetry on one side (via unilateral electroporation of expression constructs) caused a drastic increase in cell division at the expense of differentiation. Wnts enhance cell division, at least in part, by upregulating D-type cyclins. It is notable that the D–V sequence of progenitor identities was not altered, as this might have been expected had a morphogen gradient been disturbed. By contrast, blocking the Wnt-signaling pathway reduced cell division without promoting premature differentiation, suggesting that there must be something more than a simple Wnt-regulated switch between proliferation and differentiation. In fact, loss-of-function experiments by Muroyama et al. could be interpreted as lowering the dose of a dorsal morphogen in Wnt1;Wnt3a double knockouts: two dorsal cell types were depleted, whereas the next most-ventral cell type was expanded [2xWnt signaling plays an essential role in neuronal specification of the dorsal spinal cord. Muroyama, Y. et al. Genes Dev. 2002; 16: 548–553Crossref | PubMed | Scopus (185)See all References[2]. In other words, these Wnts might be ‘double-dipping’, as both mitogens and morphogens.In the mitogen gradient model, ventral progenitors find themselves ever further from the dorsal growth organizer as the spinal cord enlarges, increasing the likelihood they will drop out of division to differentiate. Megason and McMahon have used computer modeling to explore how such a scenario plays out across a linear array of cells (http://hombiosys.com/downloads/MitogenGradient). They found that the size and shape of the responding tissue are regulated by the slope of the mitogen gradient. The next challenge will be to embellish the model to account for molecules that have both mitogenic and morphogenic activities. What might otherwise be exhausting mental gymnastics could happily be avoided through computational analysis.

Competitive Hebbian learning and the hippocampal place cell system: modeling the interaction of visual and path integration cues.

The hippocampus has long been thought essential for implementing a cognitive map of the environment. However, almost 30 years since place cells were found in rodent hippocampal field CA1, it is still unclear how such an allocentric representation arises from an ego-centrically perceived world. By means of a competitive Hebbian learning rule responsible for coding visual and path integration cues, our model is able to explain the diversity of place cell responses observed in a large set of electrophysiological experiments with a single fixed set of parameters. Experiments included changes observed in place fields due to exploration of a new environment, darkness, retrosplenial cortex inactivation, and removal, rotation, and permutation of landmarks. To code for visual cues for each landmark, we defined two perceptual schemas representing landmark bearing and distance information over a linear array of cells. The information conveyed by the perceptual schemas is further processed through a network of adaptive layers which ultimately modulate the resulting activity of our simulated place cells. In path integration terms, our system is able to dynamically remap a bump of activity coding for the displacement of the animal in relation to an environmental anchor. We hypothesize that path integration information is computed in the rodent posterior parietal cortex and conveyed to the hippocampus where, together with visual information, it modulates place cell activity. The resulting network yields a more direct treatment of partial remapping of place fields than other models. In so doing, it makes new predictions regarding the nature of the interaction between visual and path integration cues during new learning and when the system is challenged with environmental changes.

Efficient image processing algorithms on the scan line array processor

Develops efficient algorithms for low and intermediate level image processing on the scan line array processor, a SIMD machine consisting of a linear array of cells that processes images in a scan line fashion. For low level processing, the authors present algorithms for block DFT, block DCT, convolution, template matching, shrinking, and expanding which run in real-time. By real-time, the authors mean that, if the required processing is based on neighborhoods of size m/spl times/m, then the output lines are generated at a rate of O(m) operations per line and a latency of O(m) scan lines, which is the best that can be achieved on this model. The authors also develop an algorithm for median filtering which runs in almost real-time at a cost of O(m log m) time per scan line and a latency of [m/2] scan lines. For intermediate level processing, the authors present optimal algorithms for translation, histogram computation, scaling, and rotation. The authors also develop efficient algorithms for labelling the connected components and determining the convex hulls of multiple figures which run in O(n log n) and O(n log/sup 2/n) time, respectively. The latter algorithms are significantly simpler and easier to implement than those already reported in the literature for linear arrays. >

Direct Simulation of Phonon-Mediated Heat Transfer in a Debye Crystal

A direct simulation of phonon-mediated heat transfer is described and preliminary results are reported. The method is derived from past work in simulating gas-dynamic flow and uses a linear array of cells for modeling a one-dimensional heat transfer problem. Central to the development of the technique is the Debye model for heat capacity of a crystal. The energy equation for this type of solid is presented and a phonon frequency distribution is obtained leading to a simulation technique that naturally takes into account changes in heat capacity. Using the linear array of cells, two fundamental problems are investigated. The first deals with the time evolution of the temperature profile in an array of 40 cells where the initial temperature distribution is 300 K, and at time zero the temperature of the first cell is raised to 500 K and maintained at this value. The second problem involves determining the steady-state heat transfer through an array of 20 cells where the two boundary cells are held at 500 K and 300 K. In this latter problem, the phonon mean free path is varied for each run and the results compared to both a continuum and radiation model for the heat transfer. Considering the simplistic approach used in modeling the phonon collisions, the results from both the time evolution problem and the steady energy transfer one are encouragingly close to predictions made with analytical solutions.

Generalized fixed channel assignment in microcellular communication systems

Overlapping coverage areas of nearby base stations arise naturally in cellular communication systems-especially in small-cell, high-capacity microcellular configurations. Because of overlap, users may have access to channels at more than one base station. With an appropriate control strategy, this enhanced access can be used to improve teletraffic performance characteristics. The authors consider a generalized fixed channel assignment scheme with priority for hand-off calls. The scheme systematically accounts for and exploits coverage overlap in its channel assignment strategy. An analytically tractable model is developed for a linear array of cells, such as those that might be used along a highway. The effects of shadow fading are included. Overall performance characteristics that are computed account for both signal availability and channel availability. Blocking probability, forced termination probability, hand-off activity, and carried traffic are determined. >

Lines of interacting quantum-dot cells: A binary wire

The behavior of linear arrays of cells composed of quantum dots is examined. Each cell holds two electrons and interacts Coulombically with neighboring cells. The electrons in the cell tend to align along one of two axes resulting in a cell ‘‘polarization’’ which can be used to encode binary information. The ground-state polarization of a cell is a highly nonlinear function of the polarization of its neighbors. The resulting bistable saturation can be used to transmit binary information along the line of cells, thus forming a binary wire.

Multiple steady states and dissipative structures in a circular and linear array of three cells: Numerical and experimental approaches

The steady-state behavior of a circular and linear array of three cells containing a substrate-inhibited-like kinetics catalyzed by immobilized thylakoids is studied. The photobiochemical reaction used to model the system is based on previous studies concerning a single and a two-cell system. In a general model all the cells in the array are considered to be continuously fed by the substrate and under diffusional relation with each others. Several models are then considered (circular and linear arrangements) depending upon the presence or the absence of these previous characteristics on each cell. The behavior of the various configurations is studied as a function of both the external substrate input concentration a0, and the ratio between the transport terms λ. The results given by bifurcation analysis and limit point continuation allows to determine three domains of stable stationary behavior: I, monostability; II, bistability and multistability; III, multistability and occurrence of dissipative structures. The existence of domain III is strictly dependent on the existence of a topological and functional symmetry in the arrangement. The experimental occurrence of both stable symmetric and asymmetric steady states in a circular and linear array of cells is also illustrated.