Search

We recently described a paradigm for engineering bacterial adaptation using plasmids coupled to the same origin of replication. In this study, we use plasmid coupling to generate spatially separated and phenotypically distinct populations in response to heterogeneous environments. Using a custom microfluidic device, we continuously tracked engineered populations along induced gradients, enabling an in-depth analysis of the spatiotemporal dynamics of plasmid coupling. Our observations reveal a pronounced phenotypic separation within 4 h exposure to an opposing gradient of AHL and arabinose. Additionally, by modulating the burden strength balance between coupled plasmids, we demonstrate the inherent limitations and tunability of this system. Intriguingly, phenotypic separation persists for an extended time, hinting at a biophysical spatial retention mechanism reminiscent of natural speciation processes. Complementing our experimental data, mathematical models provide invaluable insights into the underlying mechanisms and guide optimization of plasmid coupling for prospective applications of environmental copy number adaptation engineering across separated domains.

Diverse interactions among species within bacterial colonies lead to intricate spatiotemporal dynamics, which can affect their growth and survival. Here, we describe the emergence of complex structures in a colony grown from mixtures of motile and non-motile bacterial species on a soft agar surface. Time-lapse imaging shows that non-motile bacteria 'hitchhike' on the motile bacteria as the latter migrate outward. The non-motile bacteria accumulate at the boundary of the colony and trigger an instability that leaves behind striking flower-like patterns. The mechanism of the front instability governing this pattern formation is elucidated by a mathematical model for the frictional motion of the colony interface, with friction depending on the local concentration of the non-motile species. A more elaborate two-dimensional phase-field model that explicitly accounts for the interplay between growth, mechanical stress from the motile species, and friction provided by the non-motile species, fully reproduces the observed flower-like patterns., Competing Interests: LX, YC, RC, WR, JH, LT No competing interests declared, (© 2020, Xiong et al.)

Advances in synthetic biology have led to an arsenal of proof-of-principle bacterial circuits that can be leveraged for applications ranging from therapeutics to bioproduction. A unifying challenge for most applications is the presence of selective pressures that lead to high mutation rates for engineered bacteria. A common strategy is to develop cloning technologies aimed at increasing the fixation time for deleterious mutations in single cells. We adopt a complementary approach that is guided by ecological interactions, whereby cyclical population control is engineered to stabilize the functionality of intracellular gene circuits. Three strains of Escherichia coli were designed such that each strain could kill or be killed by one of the other two strains. The resulting "rock-paper-scissors" dynamic demonstrates rapid cycling of strains in microfluidic devices and leads to an increase in the stability of gene circuit functionality in cell culture., (Copyright © 2019 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

Bacteria in nature live in complex communities with multiple cell types and spatially-dependent interactions. Studying cells in well-mixed environments such as shaking culture tubes or flasks cannot capture these spatial dynamics, but cells growing in full-fledged biofilms are difficult to observe in real time. We present here a protocol for observing time-resolved, multi-species interactions at single-cell resolution. The protocol involves growing bacterial cells in a near monolayer in a microfluidic device. As a demonstration, we describe in particular observing the dynamic interactions between E. coli and Acinetobacter baylyi. In this case, the protocol is capable of observing both contact-dependent lysis of E. coli by A. baylyi via the Type VI Secretion System (T6SS) and subsequent functional horizontal gene transfer (HGT) of genes from E. coli to A. baylyi ., Competing Interests: Competing interests The authors declare no conflicts of interest.

Cell-free gene expression systems are emerging as an important platform for a diverse range of synthetic biology and biotechnology applications, including production of robust field-ready biosensors. Here, we combine programmed cellular autolysis with a freeze-thaw or freeze-dry cycle to create a practical, reproducible, and a labor- and cost-effective approach for rapid production of bacterial lysates for cell-free gene expression. Using this method, robust and highly active bacterial cell lysates can be produced without specialized equipment at a wide range of scales, making cell-free gene expression easily and broadly accessible. Moreover, live autolysis strain can be freeze-dried directly and subsequently lysed upon rehydration to produce active lysate. We demonstrate the utility of autolysates for synthetic biology by regulating protein production and degradation, implementing quorum sensing, and showing quantitative protection of linear DNA templates by GamS protein. To allow versatile and sensitive β-galactosidase (LacZ) based readout we produce autolysates with no detectable background LacZ activity and use them to produce sensitive mercury(II) biosensors with LacZ-mediated colorimetric and fluorescent outputs. The autolysis approach can facilitate wider adoption of cell-free technology for cell-free gene expression as well as other synthetic biology and biotechnology applications, such as metabolic engineering, natural product biosynthesis, or proteomics.

Horizontal gene transfer (HGT) plays a major role in the spread of antibiotic resistance. Of particular concern are Acinetobacter baumannii bacteria, which recently emerged as global pathogens, with nosocomial mortality rates reaching 19-54% (Centers for Disease Control and Prevention, 2013; Joly Guillou, 2005; Talbot et al., 2006). Acinetobacter gains antibiotic resistance remarkably rapidly (Antunes et al., 2014; Joly Guillou, 2005), with multi drug-resistance (MDR) rates exceeding 60% (Antunes et al., 2014; Centers for Disease Control and Prevention, 2013). Despite growing concern (Centers for Disease Control and Prevention, 2013; Talbot et al., 2006), the mechanisms underlying this extensive HGT remain poorly understood (Adams et al., 2008; Fournier et al., 2006; Imperi et al., 2011; Ramirez et al., 2010; Wilharm et al., 2013). Here, we show bacterial predation by Acinetobacter baylyi increases cross-species HGT by orders of magnitude, and we observe predator cells functionally acquiring adaptive resistance genes from adjacent prey. We then develop a population-dynamic model quantifying killing and HGT on solid surfaces. We show DNA released via cell lysis is readily available for HGT and may be partially protected from the environment, describe the effects of cell density, and evaluate potential environmental inhibitors. These findings establish a framework for understanding, quantifying, and combating HGT within the microbiome and the emergence of MDR super-bugs.

Bacteria residing within biofilm communities can coordinate their behavior through cell-to-cell signaling. However, it remains unclear if these signals can also influence the behavior of distant cells that are not part of the community. Using a microfluidic approach, we find that potassium ion channel-mediated electrical signaling generated by a Bacillus subtilis biofilm can attract distant cells. Integration of experiments and mathematical modeling indicates that extracellular potassium emitted from the biofilm alters the membrane potential of distant cells, thereby directing their motility. This electrically mediated attraction appears to be a generic mechanism that enables cross-species interactions, as Pseudomonas aeruginosa cells also become attracted to the electrical signal released by the B. subtilis biofilm. Cells within a biofilm community can thus not only coordinate their own behavior but also influence the behavior of diverse bacteria at a distance through long-range electrical signaling. PAPERCLIP., (Copyright © 2017 Elsevier Inc. All rights reserved.)

CRISPR-Cas9 has recently emerged as a promising system for multiplexed genome editing as well as epigenome and transcriptome perturbation. Due to its specificity, ease of use and highly modular programmable nature, it has been widely adopted for a variety of applications such as genome editing, transcriptional inhibition and activation, genetic screening, DNA localization imaging, and many more. In this review, we will discuss non-editing applications of CRISPR-Cas9 for transcriptome perturbation, metabolic engineering, and synthetic biology., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

The Turing instability was proposed more than six decades ago as a mechanism leading to spatial patterning, but it has yet to be exploited in a synthetic biology setting. Here we characterize the Turing instability in a specific gene circuit that can be implemented in vitro or in populations of clonal cells producing short-range activator N-Acyl homoserine lactone (AHL) and long-range inhibitor hydrogen peroxide (H2O2) gas. Slowing the production rate of the AHL-degrading enzyme, AiiA, generates stable fixed states, limit cycle oscillations and Turing patterns. Further tuning of signaling parameters determines local robustness and controls the range of unstable wavenumbers in the patterning regime. These findings provide a roadmap for optimizing spatial patterns of gene expression based on familiar quorum and gas sensitive E. coli promoters. The circuit design and predictions may be useful for (re)programming spatial dynamics in synthetic and natural gene expression systems.

We propose and study models of two distributed synthetic gene circuits, toggle-switch and oscillator, each split between two cell strains and coupled via quorum-sensing signals. The distributed toggle switch relies on mutual repression of the two strains, and oscillator is comprised of two strains, one of which acts as an activator for another that in turn acts as a repressor. Distributed toggle switch can exhibit mobile fronts, switching the system from the weaker to the stronger spatially homogeneous state. The circuit can also act as a biosensor, with the switching front dynamics determined by the properties of an external signal. Distributed oscillator system displays another biosensor functionality: oscillations emerge once a small amount of one cell strain appears amid the other, present in abundance. Distribution of synthetic gene circuits among multiple strains allows one to reduce crosstalk among different parts of the overall system and also decrease the energetic burden of the synthetic circuit per cell, which may allow for enhanced functionality and viability of engineered cells.

The progress in development of synthetic gene circuits has been hindered by the limited repertoire of available transcription factors. Recently, it has been greatly expanded using the CRISPR/Cas9 system. However, this system is limited by its imperfect DNA sequence specificity, leading to potential crosstalk with host genome or circuit components. Furthermore, CRISPR/Cas9-mediated gene regulation is context dependent, affecting the modularity of Cas9-based transcription factors. In this paper we address the problems of specificity and modularity by developing a computational approach for selecting Cas9/gRNA transcription factor/promoter pairs that are maximally orthogonal to each other as well as to the host genome and synthetic circuit components. We validate the method by designing and experimentally testing four orthogonal promoter/repressor pairs in the context of a strong promoter PL from phage lambda. We demonstrate that these promoters can be interfaced by constructing double and triple inverter circuits. To address the problem of modularity we propose and experimentally validate a scheme to predictably incorporate orthogonal CRISPR/Cas9 regulation into a large class of natural promoters.

For practical construction of complex synthetic genetic networks able to perform elaborate functions it is important to have a pool of relatively simple modules with different functionality which can be compounded together. To complement engineering of very different existing synthetic genetic devices such as switches, oscillators or logical gates, we propose and develop here a design of synthetic multi-input classifier based on a recently introduced distributed classifier concept. A heterogeneous population of cells acts as a single classifier, whose output is obtained by summarizing the outputs of individual cells. The learning ability is achieved by pruning the population, instead of tuning parameters of an individual cell. The present paper is focused on evaluating two possible schemes of multi-input gene classifier circuits. We demonstrate their suitability for implementing a multi-input distributed classifier capable of separating data which are inseparable for single-input classifiers, and characterize performance of the classifiers by analytical and numerical results. The simpler scheme implements a linear classifier in a single cell and is targeted at separable classification problems with simple class borders. A hard learning strategy is used to train a distributed classifier by removing from the population any cell answering incorrectly to at least one training example. The other scheme implements a circuit with a bell-shaped response in a single cell to allow potentially arbitrary shape of the classification border in the input space of a distributed classifier. Inseparable classification problems are addressed using soft learning strategy, characterized by probabilistic decision to keep or discard a cell at each training iteration. We expect that our classifier design contributes to the development of robust and predictable synthetic biosensors, which have the potential to affect applications in a lot of fields, including that of medicine and industry.

We describe a conceptual design of a distributed classifier formed by a population of genetically engineered microbial cells. The central idea is to create a complex classifier from a population of weak or simple classifiers. We create a master population of cells with randomized synthetic biosensor circuits that have a broad range of sensitivities toward chemical signals of interest that form the input vectors subject to classification. The randomized sensitivities are achieved by constructing a library of synthetic gene circuits with randomized control sequences (e.g., ribosome-binding sites) in the front element. The training procedure consists in reshaping of the master population in such a way that it collectively responds to the "positive" patterns of input signals by producing above-threshold output (e.g., fluorescent signal), and below-threshold output in case of the "negative" patterns. The population reshaping is achieved by presenting sequential examples and pruning the population using either graded selection/counterselection or by fluorescence-activated cell sorting (FACS). We demonstrate the feasibility of experimental implementation of such system computationally using a realistic model of the synthetic sensing gene circuits.

Stochasticity inherent to biochemical reactions (intrinsic noise) and variability in cellular states (extrinsic noise) degrade information transmitted through signaling networks. We analyzed the ability of temporal signal modulation--that is, dynamics--to reduce noise-induced information loss. In the extracellular signal-regulated kinase (ERK), calcium (Ca(2+)), and nuclear factor kappa-B (NF-κB) pathways, response dynamics resulted in significantly greater information transmission capacities compared to nondynamic responses. Theoretical analysis demonstrated that signaling dynamics has a key role in overcoming extrinsic noise. Experimental measurements of information transmission in the ERK network under varying signal-to-noise levels confirmed our predictions and showed that signaling dynamics mitigate, and can potentially eliminate, extrinsic noise-induced information loss. By curbing the information-degrading effects of cell-to-cell variability, dynamic responses substantially increase the accuracy of biochemical signaling networks., (Copyright © 2014, American Association for the Advancement of Science.)

Motivated by applications in biological systems, we show for certain multiclass queueing networks that time-dependent distributions for the multiclass queue-lengths can have a factorized form which reduces the problem of computing such distributions to a similar problem for related single-class queueing networks. We give an example of the application of this result to an enzymatic processing network.

Biological clocks are self-sustained oscillators that adjust their phase to the daily environmental cycles in a process known as entrainment. Molecular dissection and mathematical modeling of biological oscillators have progressed quite far, but quantitative insights on the entrainment of clocks are relatively sparse. We simultaneously tracked the phases of hundreds of synthetic genetic oscillators relative to a common external stimulus to map the entrainment regions predicted by a detailed model of the clock. Synthetic oscillators were frequency-locked in wide intervals of the external period and showed higher-order resonance. Computational simulations indicated that natural oscillators may contain a positive-feedback loop to robustly adapt to environmental cycles.

Cells organize in complex three-dimensional patterns by interacting with proteins along with the surrounding extracellular matrix. This organization provides the mechanical and chemical cues that ultimately influence a cell's differentiation and function. Here, we computationally investigate the pattern formation process of vascular mesenchymal cells arising from their interaction with Bone Morphogenic Protein-2 (BMP-2) and its inhibitor, Matrix Gla Protein (MGP). Using a first-principles approach, we derive a reaction-diffusion model based on the biochemical interactions of BMP-2, MGP and cells. Simulations of the model exhibit a wide variety of three-dimensional patterns not observed in a two-dimensional analysis. We demonstrate the emergence of three types of patterns: spheres, tubes, and sheets, and show that the patterns can be tuned by modifying parameters in the model such as the degradation rates of proteins and chemotactic coefficient of cells. Our model may be useful for improved engineering of three-dimensional tissue structures as well as for understanding three dimensional microenvironments in developmental processes.

The engineering of genetic circuits with predictive functionality in living cells represents a defining focus of the expanding field of synthetic biology. This focus was elegantly set in motion a decade ago with the design and construction of a genetic toggle switch and an oscillator, with subsequent highlights that have included circuits capable of pattern generation, noise shaping, edge detection and event counting. Here we describe an engineered gene network with global intercellular coupling that is capable of generating synchronized oscillations in a growing population of cells. Using microfluidic devices tailored for cellular populations at differing length scales, we investigate the collective synchronization properties along with spatiotemporal waves occurring at millimetre scales. We use computational modelling to describe quantitatively the observed dependence of the period and amplitude of the bulk oscillations on the flow rate. The synchronized genetic clock sets the stage for the use of microbes in the creation of a macroscopic biosensor with an oscillatory output. Furthermore, it provides a specific model system for the generation of a mechanistic description of emergent coordinated behaviour at the colony level.

We present an approximation scheme for deriving reaction rate equations of genetic regulatory networks. This scheme predicts the timescales of transient dynamics of such networks more accurately than does standard quasi-steady state analysis by introducing prefactors to the ODEs that govern the dynamics of the protein concentrations. These prefactors render the ODE systems slower than their quasi-steady state approximation counterparts. We introduce the method by examining a positive feedback gene regulatory network, and show how the transient dynamics of this network are more accurately modeled when the prefactor is included. Next, we examine the repressilator, a genetic oscillator, and show that the period, amplitude, and bifurcation diagram defining the onset of the oscillations are better estimated by the prefactor method. Finally, we examine the consequences of the method to the dynamics of reduced models of the phage lambda switch, and show that the switching times between the two states is slowed by the presence of the prefactor that arises from protein multimerization and DNA binding.

In temporal lobe epilepsy, changes in synaptic and intrinsic properties occur on a background of altered network architecture resulting from cell loss and axonal sprouting. Although modeling studies using idealized networks indicated the general importance of network topology in epilepsy, it is unknown whether structural changes that actually take place during epileptogenesis result in hyperexcitability. To answer this question, we built a 1:1 scale structural model of the rat dentate gyrus from published in vivo and in vitro cell type-specific connectivity data. This virtual dentate gyrus in control condition displayed globally and locally well connected ("small world") architecture. The average number of synapses between any two neurons in this network of over one million cells was less than three, similar to that measured for the orders of magnitude smaller C. elegans nervous system. To study how network architecture changes during epileptogenesis, long-distance projecting hilar cells were gradually removed in the structural model, causing massive reductions in the number of total connections. However, as long as even a few hilar cells survived, global connectivity in the network was effectively maintained and, as a result of the spatially restricted sprouting of granule cell axons, local connectivity increased. Simulations of activity in a functional dentate network model, consisting of over 50,000 multicompartmental single-cell models of major glutamatergic and GABAergic cell types, revealed that the survival of even a small fraction of hilar cells was enough to sustain networkwide hyperexcitability. These data indicate new roles for fractionally surviving long-distance projecting hilar cells observed in specimens from epilepsy patients.

We study the dynamics of an array of Stuart-Landau oscillators with repulsive coupling. Autonomous network with global repulsive coupling settles on one from a continuum of synchronized regimes characterized by zero mean field. Driving this array by an external oscillatory signal produces a nonzero mean field that follows the driving signal even when the oscillators are not locked to the external signal. At sufficiently large amplitude the external signal synchronizes the oscillators and locks the phases of the array oscillations. Application of this system as a beam-forming element of a phase array antenna is considered. The phase dynamics of the oscillator array synchronization is used to reshape the phases of signals received from the phase array antenna and improve its beam pattern characteristics.

Transcriptional regulation in small genetic circuits exhibits large stochastic fluctuations. Recent experiments have shown that a significant fraction of these fluctuations is caused by extrinsic factors. In this paper we review several theoretical and computational approaches to modeling of small genetic circuits driven by extrinsic stochastic processes. We propose a simplified approach to this problem, which can be used in the case when extrinsic fluctuations dominate the stochastic dynamics of the circuit (as appears to be the case in eukaryots). This approach is applied to a model of a single nonregulated gene that is driven by a certain gating process that affects the rate of transcription, and to a simplified version of the galactose utilization circuit in yeast.

We investigate the dynamics in an ensemble of chaotic elements with nondiffusive coupling. First, we analyze the case of global coupling. The type of coupling we consider leads to the suppression of oscillations in the whole ensemble at a high coupling strength. A distinct feature of this transition from high-dimensional chaos at a low coupling strength to the stationary state is that there is no partially ordered phase characterized by a large number of coexisting synchronized clusters. A two-cluster mode emerges abruptly, replacing the asynchronous mode. We focus on the influence of connectivity on the dynamics in the two-cluster modes and their domains of existence. We introduce a parameter that characterizes the connectivity: the range of coupling. Our computational and analytical results indicate that the most significant changes in the dynamics occur in the case of local coupling, when extra connections are added. By contrast, if the range of coupling is high, even substantial changes in this range have a small influence on the dynamics.

A new spread spectrum communication system utilizing chaotic frequency modulation of sinusoidal signals is discussed. A single phase lock loop (PLL) system in the receiver is used both to synchronize the local chaotic oscillator and to recover the information signal. We study the dynamics of the synchronization process, stability of the PLL system, and evaluate the bit-error-rate performance of this chaos-based communication system.

We investigate the dynamics of a dimer bouncing on a vertically oscillated plate. The dimer, composed of two spheres rigidly connected by a light rod, exhibits several modes depending on initial and driving conditions. The first excited mode has a novel horizontal drift in which one end of the dimer stays on the plate during most of the cycle, while the other end bounces in phase with the plate. The speed and direction of the drift depend on the aspect ratio of the dimer. We employ event-driven simulations based on a detailed treatment of frictional interactions between the dimer and the plate in order to elucidate the nature of the transport mechanism in the drift mode.

We study the dynamics of a repulsively coupled array of phase oscillators. For an array of globally coupled identical oscillators, repulsive coupling results in a family of synchronized regimes characterized by zero mean field. If the number of oscillators is sufficiently large, phase locking among oscillators is destroyed, independently of the coupling strength, when the oscillators' natural frequencies are not the same. In locally coupled networks, however, phase locking occurs even for nonidentical oscillators when the coupling strength is sufficiently strong.

Networks of globally coupled, noise-activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian approximation as well as (2) a dichotomous model. The system demonstrates ordering phase transitions and multistability. That is, for a strong enough feedback it exhibits nontrivial stationary states and oscillatory states whose frequencies depend only on the mean of the time delay distribution function. Other observed dynamical phenomena include coherence resonance and, in the case of nonuniform coupling strengths, amplitude death and chaos. Furthermore, an increase of the stability of the trivial equilibrium with increasing nonuniformity of the time delays is observed.

Recent experimental studies elucidating the importance of noise in gene regulation have ignited widespread interest in Gillespie's stochastic simulation technique for biochemical networks. We formulate modifications to the Gillespie algorithm which are necessary to correctly simulate chemical reactions with time-dependent reaction rates. We concentrate on time dependence of kinetic rates arising from the periodic process of growth and division of the cellular volume, and demonstrate that a careful re-derivation of the Gillespie algorithm is important when all stochastically simulated reactions have rates slower or comparable to the cellular growth rate. For an unregulated single-gene system, we illustrate our findings using recently proposed hybrid simulation techniques, and systematically compare our algorithm with analytic results obtained from the chemical master equation.

The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level, the system undergoes ordering transitions and demonstrates multistability. That is, for a strong enough positive feedback it exhibits a nonzero stationary mean-field,and a variety of stable oscillatory mean-field states are accessible for positive and negative feedback. The regularity of the oscillatory states is maximal for a certain noise level; i.e., the system demonstrates coherence resonance. While away from the transition points the system dynamics is well described by a Gaussian approximation, near the bifurcation points a description in terms of a dichotomous theory is more adequate.

Experiments with a thin gas-fluidized granular layer revealed a sequence of well-defined transitions as the amplitude and frequency of the gas flow modulation are varied. The observed patterns include subharmonic squares and stripes, quasiperiodic and disordered structures. The wavelength of subharmonic patterns increases with the mean flow rate and decreases with the modulation frequency.

The chaotic spike train of a homoclinic dynamical system is self-synchronized by applying a time-delayed correction proportional to the laser output intensity. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long-periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization, displays analogies with neurodynamic events that occur in the buildup of long-term memories.

Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with transition rates depending on the earlier state of the system. Analytical solutions for the autocorrelation function and the power spectrum have been found. The power spectrum has a peak at the frequency corresponding to the inverse delay time, whose amplitude has a maximum at a certain noise level, thus demonstrating coherence resonance. The linear response to the external periodic force also has maxima at the frequencies corresponding to the inverse delay time and its harmonics.

We report a novel morphological transition in a Bacillus subtilis colony initially growing under ambient conditions, after ultraviolet radiation exposure. The bacteria in the central regions of the colonies are observed to migrate towards the colony edge forming a ring during uniform spatial exposure. When the radiation is switched off, the colonies were observed to grow both inward into the evacuated regions as well as outward indicating that the pattern is not formed due to depletion of nutrients at the center of the colony. We also propose a reaction-diffusion model in which waste-limited chemotaxis initiated by the UV radiation leads to the observed phenomenology.

We develop a continuum description of partially fluidized granular flows. Our theory is based on the hydrodynamic equation for the flow coupled with the order parameter equation, which describes the transition between flowing and static components of the granular system. This theory captures important phenomenology recently observed in experiments with granular flows on rough inclined planes [A. Daerr and S. Douady, Nature (London) 399, 241 (1999)]: layer bistability, and transition from triangular avalanches propagating downhill at small inclination angles to balloon-shaped avalanches also propagating uphill for larger angles.

We study the spreading of calcium-induced calcium release with the stochastic DeYoung-Keizer-model of the inositol 1,4,5-trisphosphate receptor channel. The model shows a transition from isolated release events to steadily propagating waves with increasing IP3 concentration. A state--stochastic backfiring--was found in the regime of steady propagation. The model can be reduced by an adiabatic elimination of the partial differential equation for the Ca(2+) concentration to a lattice of stochastic channel clusters.

We propose a discrete stochastic model for calcium dynamics in living cells. A set of probabilities for the opening/closing of calcium channels is assumed to depend on the calcium concentration. We study this model in one dimension, analytically in the limit of a large number of channels per site N, and numerically for small N. As the number of channels per site is increased, the transition from a nonpropagating region of activity to a propagating one changes from one described by directed percolation to that of deterministic depinning in a spatially discrete system. Also, for a small number of channels a propagating calcium wave can leave behind a novel fluctuation-driven state.

The results of the experimental study of the dynamics of a shallow fluidized bed are reported. The behavior of granular material is controlled by the interplay of two factors--levitation due to the upward airflow, and sliding back due to gravity. Near the threshold of instability, the system shows critical behavior with remarkably long transient dynamics. The experimental observations are compared with a simple cellular automata model.

We develop a continuum description for the axial segregation of granular materials in a long rotating drum based on the dynamics of the thin near-surface granular flow coupled to bulk flow. The equations of motion are reduced to the one-dimensional system for two local variables only, the concentration difference and the dynamic angle of repose, or the average slope of the free surface. The parameters of the system are established from comparison with experimental data. The resulting system describes both initial transient traveling wave dynamics and the formation of quasi-stationary bands of segregated materials. A long-term evolution proceeds through slow logarithmic coarsening of the band structure which is analogous to the spinoidal decomposition described by the Cahn-Hilliard equation.

RNA virus evolution is generally considered to be highly unpredictable, but tests of determinism in the evolution of competing populations during viral infections have not been performed. Here we study the fate of two closely related evolving quasispecies of vesicular stomatitis virus, by determining the relative concentration of a wild-type clone and a surrogate marked virus subclone (MARM-C) upon extensive competitive replication in a constant cell culture environment. A highly predictable nonlinear behaviour of the two competing populations was found. In addition, the presence of critical points, which are defined as points from which viral competitions may follow different trajectories, has been documented. Critical points were reached after nearly constant periods of time. The dynamics of relative fitness values for both competing populations were calculated during the replication passages. Concomitant with expected fitness gain of both competing viral populations (which follow the Red Queen hypothesis) a tendency for the MARM-C to gain less fitness than the wild-type was observed. Although fitness variations were noisy, this tendency was seen in all evolutionary replicas. Thus, despite the stochastic process of mutation that leads to a continuous generation of mutant genomes during RNA virus replication, a nonlinear, nearly deterministic evolutionary behaviour has been observed. It is proposed that such a behaviour is mediated by a low-pass filter (averaging of mutational noise signals) due to competitive selection among variants.

The aggregation stage of the life cycle of Dictyostelium discoideum is governed by the chemotactic response of individual amoebae to excitable waves of cAMP. We modeled this process through a recently introduced hybrid automata-continuum scheme and used computer simulation to unravel the role of specific components of this complex developmental process. Our results indicated an essential role for positive feedback between the cAMP signaling and the expression of the genes encoding the signal transduction and response machinery.