A molecular network that produces spontaneous oscillations in excitable cells of Dictyostelium

Current reversal in polar flock at order-disorder interface

We studied a system of polar self-propelled particles (SPPs) on a thin rectangular channel designed into three regions of order-disorder-order. The division of the three regions is made on the basis of the noise SPPs experience in the respective regions. The noise in the two wide regions is chosen lower than the critical noise of order-disorder transition and noise in the middle region or interface is higher than the critical noise. This makes the geometry of the system analogous to the Josephson junction (JJ) in solid-state physics. Keeping all other parameters fixed, we study the properties of the moving SPPs in the bulk as well as along the interface for different widths of the junction. On increasing interface width, the system shows an order-to-disorder transition from coherent moving SPPs in the whole system to the interrupted current for large interface width. Surprisingly, inside the interface, we observed the current reversal for intermediate widths of the interface. Such current reversal is due to the strong randomness present inside the interface, which makes the wall of the interface reflecting. Hence, our study gives new interesting collective properties of SPPs at the interface which can be useful to design switching devices using active agents.

Ordering kinetics in the active model B

We undertake a detailed numerical study of the Active Model B proposed by Wittkowski et al., [Nature Commun. 5, 4351 (2014)]2041-172310.1038/ncomms5351. We find that the introduction of activity has a drastic effect on the ordering kinetics. First, the domain growth law shows a crossover from the usual Lifshitz-Slyozov growth law for phase separation (L∼t^{1/3}, where t is the time) to a novel growth law (L∼t^{1/4}) at late times. Second, the equal-time correlation function of the density field exhibits dynamical scaling for a given activity strength λ, but the scaling function depends on λ.

Self-Organizing Microdroplet Protocells Displaying Light-Driven Oscillatory and Morphological Evolution

The development of synthetic systems that enable the sustained active self-assembly of molecular blocks to mimic the complexity and dynamic behavior of living systems is of great interest in elucidating the origins of life, understanding the basic principles behind biological organization, and designing active materials. However, it remains a challenge to construct microsystems with dynamic behaviors and functions that are connected to molecular self-assembly processes driven by external energy. Here, an active self-assembly of microdroplet protocells with dynamic structure and high structural complexity through living radical polymerization under constant energy flux is reported. The active microdroplet protocells exhibit nonlinear behaviors including oscillatory growth and shrinkage. This relies on the transient stabilization of molecular assembly, which can channel the inflow of energy through noncovalent interactions of pure synthetic components. The intercommunication of microdroplet protocells through stochastic fusion leads to the formation of a variety of dynamic and higher-order biomimetic microstructures. This work constitutes an important step toward the realization of autonomous and dynamic microsystems and active materials with life-like properties.

Synthesis of the Dynamical Properties of Feedback Loops in Bio-Pathways

Feedback loops regulate various biological functions such as oscillations, bistability, and robustness. They play a significant role in developmental signalling and failure of feedback can lead to disease. Systematic analysis of feedback loops could be useful in understanding their properties and biological effects. We propose here a method to automatically analyze feedback loops in bio-pathways and synthesize temporal logic properties which describe their dynamics. Starting with an ordinary differential equations (ODEs) based model of a bio-pathway, for a chosen feedback loop present in the pathway, we use a convolutional neural network to classify the behaviours of the key components of the feedback according to templates specified in bounded linear temporal logic (BLTL). Once a template has been identified, we instantiate the symbolic variables appearing in the template and synthesize properties using a parameter estimation procedure based on sequential hypothesis testing. We have applied this framework to a number of bio-pathway models and validated that the synthesized properties faithfully describe the behaviours of the feedback loops.

Speed inhomogeneity accelerates information transfer in polar flock

A collection of self-propelled particles (SPPs) shows coherent motion and exhibits a true long-range-ordered state in two dimensions. Various studies show that the presence of spatial inhomogeneities can destroy the usual long-range ordering in the system. However, the effects of inhomogeneity due to the intrinsic properties of the particles are barely addressed. In this paper we consider a collection of polar SPPs moving at inhomogeneous speed (IS) on a two-dimensional substrate, which can arise due to varying physical strengths of the individual particles. To our surprise, the IS not only preserves the usual long-range ordering present in homogeneous speed models but also induces faster ordering in the system. Furthermore, the response of the flock to an external perturbation is also faster, compared to the Vicsek-like model systems, due to the frequent update of neighbors of each SPP in the presence of the IS. Therefore, our study shows that an IS can promote information transfer in a moving flock.

Constructing and Analyzing Computational Models of Cell Signaling with BioModelAnalyzer

BioModelAnalyzer (BMA) is an open-source graphical tool for the development of executable models of protein and gene networks within cells. Based upon the Qualitative Networks formalism, the user can rapidly construct large networks, either manually or by connecting motifs selected from a built-in library. After the appropriate functions for each variable are defined, the user has access to three analysis engines to test the model. In addition to standard simulation tools, BMA includes an interface to the stability-testing algorithm and to a graphical Linear Temporal Logic (LTL) editor and analysis tool. Alongside this, we have developed a novel ChatBot to aid users constructing LTL queries and to explain the interface and run through tutorials. Here we present worked examples of model construction and testing via the interface. As an initial example, we discuss fate decisions in Dictyostelium discoidum and cAMP signaling. We go on to describe the workflow leading to the construction of a published model of the germline of C. elegans. Finally, we demonstrate how to construct simple models from the built-in network motif library. © 2020 by John Wiley & Sons, Inc. Basic Protocol 1: Modeling the signaling network of Dictyostelium discoidum Basic Protocol 2: Modeling the germline progression of Caenorhabditis elegans Basic Protocol 3: Constructing a model of the cell cycle using motifs.

Reachability Analysis Using Message Passing over Tree Decompositions

In this paper, we study efficient approaches to reachability analysis for discrete-time nonlinear dynamical systems when the dependencies among the variables of the system have low treewidth. Reachability analysis over nonlinear dynamical systems asks if a given set of target states can be reached, starting from an initial set of states. This is solved by computing conservative over approximations of the reachable set using abstract domains to represent these approximations. However, most approaches must tradeoff the level of conservatism against the cost of performing analysis, especially when the number of system variables increases. This makes reachability analysis challenging for nonlinear systems with a large number of state variables. Our approach works by constructing a dependency graph among the variables of the system. The tree decomposition of this graph builds a tree wherein each node of the tree is labeled with subsets of the state variables of the system. Furthermore, the tree decomposition satisfies important structural properties. Using the tree decomposition, our approach abstracts a set of states of the high dimensional system into a tree of sets of lower dimensional projections of this state. We derive various properties of this abstract domain, including conditions under which the original high dimensional set can be fully recovered from its low dimensional projections. Next, we use ideas from message passing developed originally for belief propagation over Bayesian networks to perform reachability analysis over the full state space in an efficient manner. We illustrate our approach on some interesting nonlinear systems with low treewidth to demonstrate the advantages of our approach.

The Life Cycle of Dictyostelium discoideum Is Accelerated via MAP Kinase Cascade by a Culture Extract Produced by a Synthetic Microbial Consortium

A cellular slime mold, Dictyostelium discoideum, is an amoeboid organism that has a unique life cycle consisting of distinctly separated vegetative and developmental phases. Thus, this organism presents a rare opportunity in which to examine the effects of bioactive substances on separate cellular activities. In this research, we investigated the effect of a culture extract, termed EMXG, produced by a synthetic microbial consortium. EMXG promoted proliferative response of amoeba cells. It further accelerated the developmental phase, leading to the preferred fruiting body formation from fewer cells. Furthermore, EMXG modulated biological rhythm of this organism, that is, interval of oscillation of cAMP level observed in suspension starvation was significantly shortened. Concomitantly, the level of ERKB, a MAP kinase, was found to oscillate in a similar fashion to that of cAMP. Additionally, ErkB-deficient mutant amoeboid cells did not respond to proliferative stimulation by EMXG. These lines of evidence point to a likelihood that MAP kinase cascade is involved and further that ErkB could be the molecular target of EMXG.

Proteomic and Transcriptomic Profiling Identifies Early Developmentally Regulated Proteins in Dictyostelium Discoideum

Cyclic AMP acts as a secondary messenger involving different cellular functions in eukaryotes. Here, proteomic and transcriptomic profiling has been combined to identify novel early developmentally regulated proteins in eukaryote cells. These proteomic and transcriptomic experiments were performed in Dictyostelium discoideum given the unique advantages that this organism offers as a eukaryotic model for cell motility and as a nonmammalian model of human disease. By comparing whole-cell proteome analysis of developed (cAMP-pulsed) wild-type AX2 cells and an independent transcriptomic analysis of developed wild-type AX4 cells, our results show that up to 70% of the identified proteins overlap in the two independent studies. Among them, we have found 26 proteins previously related to cAMP signaling and identified 110 novel proteins involved in calcium signaling, adhesion, actin cytoskeleton, the ubiquitin-proteasome pathway, metabolism, and proteins that previously lacked any annotation. Our study validates previous findings, mostly for the canonical cAMP-pathway, and also generates further insight into the complexity of the transcriptomic changes during early development. This article also compares proteomic data between parental and cells lacking glkA, a GSK-3 kinase implicated in substrate adhesion and chemotaxis in Dictyostelium. This analysis reveals a set of proteins that show differences in expression in the two strains as well as overlapping protein level changes independent of GlkA.

Self-Driven Phase Transitions Drive Myxococcus xanthus Fruiting Body Formation

Combining high-resolution single cell tracking experiments with numerical simulations, we show that starvation-induced fruiting body formation in Myxococcus xanthus is a phase separation driven by cells that tune their motility over time. The phase separation can be understood in terms of cell density and a dimensionless Péclet number that captures cell motility through speed and reversal frequency. Our work suggests that M. xanthus takes advantage of a self-driven nonequilibrium phase transition that can be controlled at the single cell level.

Biological Oscillators in Nanonetworks-Opportunities and Challenges

One of the major issues in molecular communication-based nanonetworks is the provision and maintenance of a common time knowledge. To stay true to the definition of molecular communication, biological oscillators are the potential solutions to achieve that goal as they generate oscillations through periodic fluctuations in the concentrations of molecules. Through the lens of a communication systems engineer, the scope of this survey is to explicitly classify, for the first time, existing biological oscillators based on whether they are found in nature or not, to discuss, in a tutorial fashion, the main principles that govern the oscillations in each oscillator, and to analyze oscillator parameters that are most relevant to communication engineer researchers. In addition, the survey highlights and addresses the key open research issues pertaining to several physical aspects of the oscillators and the adoption and implementation of the oscillators to nanonetworks. Moreover, key research directions are discussed.

The Dictyostelium GSK3 kinase GlkA coordinates signal relay and chemotaxis in response to growth conditions

GSK3 plays a central role in orchestrating key biological signaling pathways, including cell migration. Here, we identify GlkA as a GSK3 family kinase with functions that overlap with and are distinct from those of GskA. We show that GlkA, as previously shown for GskA, regulates the cell's cytoskeleton through MyoII assembly and control of Ras and Rap1 function, leading to aberrant cell migration. However, there are both qualitative and quantitative differences in the regulation of Ras and Rap1 and their downstream effectors, including PKB, PKBR1, and PI3K, with glkA^- cells exhibiting a more severe chemotaxis phenotype than gskA^- cells. Unexpectedly, the severe glkA^- phenotypes, but not those of gskA^-, are only exhibited when cells are grown attached to a substratum but not in suspension, suggesting that GlkA functions as a key kinase of cell attachment signaling. Using proteomic iTRAQ analysis we show that there are quantitative differences in the pattern of protein expression depending on the growth conditions in wild-type cells. We find that GlkA expression affects the cell's proteome during vegetative growth and development, with many of these changes depending on whether the cells are grown attached to a substratum or in suspension. These changes include key cytoskeletal and signaling proteins known to be essential for proper chemotaxis and signal relay during the aggregation stage of Dictyostelium development.

G-Protein Dependent Signal Transduction and Ubiquitination in Dictyostelium

Signal transduction through G-protein-coupled receptors (GPCRs) is central for the regulation of virtually all cellular functions, and it has been widely implicated in human diseases. These receptors activate a common molecular switch that is represented by the heterotrimeric G-protein generating a number of second messengers (cAMP, cGMP, DAG, IP3, Ca²⁺ etc.), leading to a plethora of diverse cellular responses. Spatiotemporal regulation of signals generated by a given GPCR is crucial for proper signalling and is accomplished by a series of biochemical modifications. Over the past few years, it has become evident that many signalling proteins also undergo ubiquitination, a posttranslational modification that typically leads to protein degradation, but also mediates processes such as protein-protein interaction and protein subcellular localization. The social amoeba Dictyostelium discoideum has proven to be an excellent model to investigate signal transduction triggered by GPCR activation, as cAMP signalling via GPCR is a major regulator of chemotaxis, cell differentiation, and multicellular morphogenesis. Ubiquitin ligases have been recently involved in these processes. In the present review, we will summarize the most significant pathways activated upon GPCRs stimulation and discuss the role played by ubiquitination in Dictyostelium cells.

Modulation of cyclic nucleotide-mediated cellular signaling and gene expression using photoactivated adenylyl cyclase as an optogenetic tool

Cyclic nucleotide signaling pathway plays a significant role in various biological processes such as cell growth, transcription, inflammation, in microbial pathogenesis, etc. Modulation of cyclic nucleotide levels by optogenetic tools has overcome certain limitations of studying transduction cascade by pharmacological agents and has allowed several ways to modulate biological processes in a spatiotemporal manner. Here, we have shown the optogenetic modulation of the cyclooxygenase 2 (Cox-2) gene expression and their downstream effector molecule (PGE₂) in HEK-293T cells and the development process of Dictyostelium discoideum via modulating the cyclic nucleotide (cAMP) signaling pathway utilizing photoactivated adenylyl cyclases (PACs) as an optogenetic tool. Light-induced activation of PACs in HEK-293T cells increases the cAMP level that leads to activation of cAMP response element-binding protein (CREB) transcription factor and further upregulates downstream Cox-2 gene expression and their downstream effector molecule prostaglandin E2. In D. discoideum, the light-regulated increase in cAMP level affects the starvation-induced developmental process. These PACs could modulate the cAMP levels in a light-dependent manner and have a potential to control gene expression and their downstream effector molecules with varying magnitude. It would enable one to utilize PAC as a tool to decipher cyclic nucleotide mediated signaling pathway regulations and their mechanism.

Phenotypic Evolution With and Beyond Genome Evolution

DNA does not make phenotypes on its own. In this volume entitled "Genes and Phenotypic Evolution," the present review draws the attention on the process of phenotype construction-including development of multicellular organisms-and the multiple interactions and feedbacks between DNA, organism, and environment at various levels and timescales in the evolutionary process. First, during the construction of an individual's phenotype, DNA is recruited as a template for building blocks within the cellular context and may in addition be involved in dynamical feedback loops that depend on the environmental and organismal context. Second, in the production of phenotypic variation among individuals, stochastic, environmental, genetic, and parental sources of variation act jointly. While in controlled laboratory settings, various genetic and environmental factors can be tested one at a time or in various combinations, they cannot be separated in natural populations because the environment is not controlled and the genotype can rarely be replicated. Third, along generations, genotype and environment each have specific properties concerning the origin of their variation, the hereditary transmission of this variation, and the evolutionary feedbacks. Natural selection acts as a feedback from phenotype and environment to genotype. This review integrates recent results and concrete examples that illustrate these three points. Although some themes are shared with recent calls and claims to a new conceptual framework in evolutionary biology, the viewpoint presented here only means to add flesh to the standard evolutionary synthesis.

Inverse problem studies of biochemical systems with structure identification of S-systems by embedding training functions in a genetic algorithm

An efficient inverse problem approach for parameter estimation, state and structure identification from dynamic data by embedding training functions in a genetic algorithm methodology (ETFGA) is proposed for nonlinear dynamical biosystems using S-system canonical models. Use of multiple shooting and decomposition approach as training functions has been shown for handling of noisy datasets and computational efficiency in studying the inverse problem. The advantages of the methodology are brought out systematically by studying it for three biochemical model systems of interest. By studying a small-scale gene regulatory system described by a S-system model, the first example demonstrates the use of ETFGA for the multifold aims of the inverse problem. The estimation of a large number of parameters with simultaneous state and network identification is shown by training a generalized S-system canonical model with noisy datasets. The results of this study bring out the superior performance of ETFGA on comparison with other metaheuristic approaches. The second example studies the regulation of cAMP oscillations in Dictyostelium cells now assuming limited availability of noisy data. Here, flexibility of the approach to incorporate partial system information in the identification process is shown and its effect on accuracy and predictive ability of the estimated model are studied. The third example studies the phenomenological toy model of the regulation of circadian oscillations in Drosophila that follows rate laws different from S-system power-law. For the limited noisy data, using a priori information about properties of the system, we could estimate an alternate S-system model that showed robust oscillatory behavior with predictive abilities.

Marching along to an Offbeat Drum: Entrainment of Synthetic Gene Oscillators by a Noisy Stimulus

Modulation of biological oscillations by stimuli lies at the root of many phenomena, including maintenance of circadian rhythms, propagation of neural signals, and somitogenesis. While it is well established that regular periodic modulation can entrain an oscillator, an aperiodic (noisy) modulation can also robustly entrain oscillations. This latter scenario may describe, for instance, the effect of irregular weather patterns on circadian rhythms, or why irregular neural stimuli can still reliably transmit information. A synthetic gene oscillator approach has already proven to be useful in understanding the entrainment of biological oscillators by periodic signaling, mimicking the entrainment of a number of noisy oscillating systems. We similarly seek to use synthetic biology as a platform to understand how aperiodic signals can strongly correlate the behavior of cells. This study should lead to a deeper understanding of how fluctuations in our environment and even within our body may promote substantial synchrony among our cells. Specifically, we investigate experimentally and theoretically the entrainment of a synthetic gene oscillator in E. coli by a noisy stimulus. This phenomenon was experimentally studied and verified by a combination of microfluidics and microscopy using the real synthetic circuit. Stochastic simulation of an associated model further supports that the synthetic gene oscillator can be strongly entrained by aperiodic signals, especially telegraph noise. Finally, widespread applicability of aperiodic entrainment beyond the synthetic gene oscillator is supported by results derived from both a model for a natural oscillator in D. discoideum and a model for predator-prey oscillations.

Excitable waves and direction-sensing in Dictyostelium discoideum: steps towards a chemotaxis model

In recent years, there have been significant advances in our understanding of the mechanisms underlying chemically directed motility by eukaryotic cells such as Dictyostelium. In particular, the local excitation and global inhibition (LEGI) model has proven capable of providing a framework for quantitatively explaining many experiments that present Dictyostelium cells with tailored chemical stimuli and monitor their subsequent polarization. In their natural setting, cells generate their own directional signals via the detection and secretion of cyclic adenosine monophosphate (cAMP). Here, we couple the LEGI approach to an excitable medium model of the cAMP wave-field that is propagated by the cells and investigate the possibility for this class of models to enable accurate chemotaxis to the cAMP waveforms expected in vivo. Our results indicate that the ultra-sensitive version of the model does an excellent job in providing natural wave rectification, thereby providing a compelling solution to the 'back-of-the-wave paradox' during cellular aggregation.

Genetic control of morphogenesis in Dictyostelium

Cells grow, move, expand, shrink and die in the process of generating the characteristic shapes of organisms. Although the structures generated during development of the social amoeba Dictyostelium discoideum look nothing like the structures seen in metazoan embryogenesis, some of the morphogenetic processes used in their making are surprisingly similar. Recent advances in understanding the molecular basis for directed cell migration, cell type specific sorting, differential adhesion, secretion of matrix components, pattern formation, regulation and terminal differentiation are reviewed. Genes involved in Dictyostelium aggregation, slug formation, and culmination of fruiting bodies are discussed.

Modeling oscillations and spiral waves in Dictyostelium populations

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales-from biochemical networks within individual cells to spatially structured cellular populations. Here we present a family of "multiscale" models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cyclic adenosine monophosphate (cAMP) used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various preprocessing modules. We use this family of models to study spatially unstructured populations of "fixed" cells by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then briefly discuss an extension of our model that includes spatial structure and show how this naturally gives rise to spiral waves. Our models exhibit a wide range of novel phenomena. including a density-dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

Leaps and lulls in the developmental transcriptome of Dictyostelium discoideum

BACKGROUND

Development of the soil amoeba Dictyostelium discoideum is triggered by starvation. When placed on a solid substrate, the starving solitary amoebae cease growth, communicate via extracellular cAMP, aggregate by tens of thousands and develop into multicellular organisms. Early phases of the developmental program are often studied in cells starved in suspension while cAMP is provided exogenously. Previous studies revealed massive shifts in the transcriptome under both developmental conditions and a close relationship between gene expression and morphogenesis, but were limited by the sampling frequency and the resolution of the methods.

RESULTS

Here, we combine the superior depth and specificity of RNA-seq-based analysis of mRNA abundance with high frequency sampling during filter development and cAMP pulsing in suspension. We found that the developmental transcriptome exhibits mostly gradual changes interspersed by a few instances of large shifts. For each time point we treated the entire transcriptome as single phenotype, and were able to characterize development as groups of similar time points separated by gaps. The grouped time points represented gradual changes in mRNA abundance, or molecular phenotype, and the gaps represented times during which many genes are differentially expressed rapidly, and thus the phenotype changes dramatically. Comparing developmental experiments revealed that gene expression in filter developed cells lagged behind those treated with exogenous cAMP in suspension. The high sampling frequency revealed many genes whose regulation is reproducibly more complex than indicated by previous studies. Gene Ontology enrichment analysis suggested that the transition to multicellularity coincided with rapid accumulation of transcripts associated with DNA processes and mitosis. Later development included the up-regulation of organic signaling molecules and co-factor biosynthesis. Our analysis also demonstrated a high level of synchrony among the developing structures throughout development.

CONCLUSIONS

Our data describe D. discoideum development as a series of coordinated cellular and multicellular activities. Coordination occurred within fields of aggregating cells and among multicellular bodies, such as mounds or migratory slugs that experience both cell-cell contact and various soluble signaling regimes. These time courses, sampled at the highest temporal resolution to date in this system, provide a comprehensive resource for studies of developmental gene expression.

From intracellular signaling to population oscillations: bridging size- and time-scales in collective behavior

Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems, we know that behavioral changes in the individual constituents of a collectively behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here, we apply such an approach to the emergence of collective oscillations in cellular populations of the social amoeba Dictyostelium discoideum. Through direct tests of our model with quantitative in vivo measurements of single-cell and population signaling dynamics, we show how a simple model can effectively describe a complex molecular signaling network at multiple size and temporal scales. The model predicts novel noise-driven single-cell and population-level signaling phenomena that we then experimentally observe. Our results suggest that like physical systems, collective behavior in biology may be universal and described using simple mathematical models.

Flow-driven waves and phase-locked self-organization in quasi-one-dimensional colonies of Dictyostelium discoideum

We report experiments on flow-driven waves in a microfluidic channel containing the signaling slime mold Dictyostelium discoideum. The observed cyclic adenosine monophosphate (cAMP) wave trains developed spontaneously in the presence of flow and propagated with the velocity proportional to the imposed flow velocity. The period of the wave trains was independent of the flow velocity. Perturbations of flow-driven waves via external periodic pulses of the signaling agent cAMP induced 1∶1, 2∶1, 3∶1, and 1∶2 frequency responses, reminiscent of Arnold tongues in forced oscillatory systems. We expect our observations to be generic to active media governed by reaction-diffusion-advection dynamics, where spatially bound autocatalytic processes occur under flow conditions.

Cell signaling during development of Dictyostelium

Continuous communication between cells is necessary for development of any multicellular organism and depends on the recognition of secreted signals. A wide range of molecules including proteins, peptides, amino acids, nucleic acids, steroids and polylketides are used as intercellular signals in plants and animals. They are also used for communication in the social ameba Dictyostelium discoideum when the solitary cells aggregate to form multicellular structures. Many of the signals are recognized by surface receptors that are seven-transmembrane proteins coupled to trimeric G proteins, which pass the signal on to components within the cytoplasm. Dictyostelium cells have to judge when sufficient cell density has been reached to warrant transition from growth to differentiation. They have to recognize when exogenous nutrients become limiting, and then synchronously initiate development. A few hours later they signal each other with pulses of cAMP that regulate gene expression as well as direct chemotactic aggregation. They then have to recognize kinship and only continue developing when they are surrounded by close kin. Thereafter, the cells diverge into two specialized cell types, prespore and prestalk cells, that continue to signal each other in complex ways to form well proportioned fruiting bodies. In this way they can proceed through the stages of a dependent sequence in an orderly manner without cells being left out or directed down the wrong path.

Prediction uncertainty assessment of a systems biology model requires a sample of the full probability distribution of its parameters

Multi-parameter models in systems biology are typically ‘sloppy’: some parameters or combinations of parameters may be hard to estimate from data, whereas others are not. One might expect that parameter uncertainty automatically leads to uncertain predictions, but this is not the case. We illustrate this by showing that the prediction uncertainty of each of six sloppy models varies enormously among different predictions. Statistical approximations of parameter uncertainty may lead to dramatic errors in prediction uncertainty estimation. We argue that prediction uncertainty assessment must therefore be performed on a per-prediction basis using a full computational uncertainty analysis. In practice this is feasible by providing a model with a sample or ensemble representing the distribution of its parameters. Within a Bayesian framework, such a sample may be generated by a Markov Chain Monte Carlo (MCMC) algorithm that infers the parameter distribution based on experimental data. Matlab code for generating the sample (with the Differential Evolution Markov Chain sampler) and the subsequent uncertainty analysis using such a sample, is supplied as Supplemental Information.

Cell-to-cell coordination for the spontaneous cAMP oscillation in Dictyostelium

We propose a new cellular dynamics scheme for the spontaneous cAMP oscillations in Dictyostelium discoideum. Our scheme seamlessly integrates both receptor dynamics and G-protein dynamics into our previously developed cellular dynamics scheme. Extensive computer simulation studies based on our new cellular dynamics scheme were conducted in mutant cells to evaluate the molecular network. The validity of our proposed molecular network as well as the controversial PKA-dependent negative feedback mechanism was supported by our simulation studies. Spontaneous cAMP oscillations were not observed in a single mutant cell. However, multicellular states of various mutant cells consistently initiated spontaneous cAMP oscillations. Therefore, cell-to-cell coordination via the cAMP receptor is essential for the robust initiation of spontaneous cAMP oscillations.

In silico modeling of Itk activation kinetics in thymocytes suggests competing positive and negative IP4 mediated feedbacks increase robustness

The inositol-phosphate messenger inositol(1,3,4,5)tetrakisphosphate (IP₄) is essential for thymocyte positive selection by regulating plasma-membrane association of the protein tyrosine kinase Itk downstream of the T cell receptor (TCR). IP₄ can act as a soluble analog of the phosphoinositide 3-kinase (PI3K) membrane lipid product phosphatidylinositol(3,4,5)trisphosphate (PIP₃). PIP₃ recruits signaling proteins such as Itk to cellular membranes by binding to PH and other domains. In thymocytes, low-dose IP₄ binding to the Itk PH domain surprisingly promoted and high-dose IP₄ inhibited PIP₃ binding of Itk PH domains. However, the mechanisms that underlie the regulation of membrane recruitment of Itk by IP₄ and PIP₃ remain unclear. The distinct Itk PH domain ability to oligomerize is consistent with a cooperative-allosteric mode of IP₄ action. However, other possibilities cannot be ruled out due to difficulties in quantitatively measuring the interactions between Itk, IP₄ and PIP₃, and in generating non-oligomerizing Itk PH domain mutants. This has hindered a full mechanistic understanding of how IP₄ controls Itk function. By combining experimentally measured kinetics of PLCγ1 phosphorylation by Itk with in silico modeling of multiple Itk signaling circuits and a maximum entropy (MaxEnt) based computational approach, we show that those in silico models which are most robust against variations of protein and lipid expression levels and kinetic rates at the single cell level share a cooperative-allosteric mode of Itk regulation by IP₄ involving oligomeric Itk PH domains at the plasma membrane. This identifies MaxEnt as an excellent tool for quantifying robustness for complex TCR signaling circuits and provides testable predictions to further elucidate a controversial mechanism of PIP₃ signaling.

Synchronization of stochastic oscillators in biochemical systems

We investigate the synchronization of stochastic oscillations in biochemical models by calculating the complex coherence function within the linear noise approximation. The method is illustrated on a simple example and then applied to study the synchronization of chemical concentrations in social amoeba. The degree to which variation of rate constants in different cells and the volume of the cells affects synchronization of the oscillations is explored and the phase lag calculated. In all cases the analytical results are shown to be in good agreement with those obtained through numerical simulations.

The NMRA/NMRAL1 homologue PadA modulates the expression of extracellular cAMP relay genes during aggregation in Dictyostelium discoideum

NMRA-like proteins belong to a class of conserved transcriptional regulators that function as direct sensors of the metabolic state of the cell and link basic metabolism to changes in gene expression. PadA was the first NMRA-like protein described in Dictyostelium discoideum and was shown to be necessary for prestalk cell differentiation and correct development. We describe and characterize padA(-) mutant phenotype during the onset of development, which results in the formation of abnormally small territories and impairment of cAMP responses. Transcriptional analysis shows that cAMP-induced gene expression is downregulated in padA(-), particularly the genes that establish the extracellular cAMP relay. The mutant phenotype can be rescued with the constitutive expression of one of these genes, carA, encoding the cAMP receptor. Transcriptional analysis of padA(-)/A15::carA showed that carA maximum mRNA levels were not reached during aggregation. Our data support a regulatory role for PadA on the regulation of extracellular cAMP relay genes during aggregation and suggest that PadA is required to achieve carA full induction.

Chemotaxis of Dictyostelium discoideum: collective oscillation of cellular contacts

Chemotactic responses of Dictyostelium discoideum cells to periodic self-generated signals of extracellular cAMP comprise a large number of intricate morphological changes on different length scales. Here, we scrutinized chemotaxis of single Dictyostelium discoideum cells under conditions of starvation using a variety of optical, electrical and acoustic methods. Amebas were seeded on gold electrodes displaying impedance oscillations that were simultaneously analyzed by optical video microscopy to relate synchronous changes in cell density, morphology, and distance from the surface to the transient impedance signal. We found that starved amebas periodically reduce their overall distance from the surface producing a larger impedance and higher total fluorescence intensity in total internal reflection fluorescence microscopy. Therefore, we propose that the dominant sources of the observed impedance oscillations observed on electric cell-substrate impedance sensing electrodes are periodic changes of the overall cell-substrate distance of a cell. These synchronous changes of the cell-electrode distance were also observed in the oscillating signal of acoustic resonators covered with amebas. We also found that periodic cell-cell aggregation into transient clusters correlates with changes in the cell-substrate distance and might also contribute to the impedance signal. It turned out that cell-cell contacts as well as cell-substrate contacts form synchronously during chemotaxis of Dictyostelium discoideum cells.

The Amoebozoa

The model organism Dictyostelium discoideum is a member of the Amoebozoa, one of the six major -divisions of eukaryotes. Amoebozoa comprise a wide variety of amoeboid and flagellate organisms with single cells measuring from 5 μm to several meters across. They have adopted many different life styles and sexual behaviors and can live in all but the most extreme environments. This chapter provides an overview of Amoebozoan diversity and compares roads towards multicellularity within the Amoebozoa with inventions of multicellularity in other protist divisions. The chapter closes with a scenario for the evolution of Dictyostelid multicellularity from an Amoebozoan stress response.

Network inference via adaptive optimal design

Background

Current research in network reverse engineering for genetic or metabolic networks very often does not include a proper experimental and/or input design. In this paper we address this issue in more detail and suggest a method that includes an iterative design of experiments based, on the most recent data that become available. The presented approach allows a reliable reconstruction of the network and addresses an important issue, i.e., the analysis and the propagation of uncertainties as they exist in both the data and in our own knowledge. These two types of uncertainties have their immediate ramifications for the uncertainties in the parameter estimates and, hence, are taken into account from the very beginning of our experimental design.

Findings

The method is demonstrated for two small networks that include a genetic network for mRNA synthesis and degradation and an oscillatory network describing a molecular network underlying adenosine 3’-5’ cyclic monophosphate (cAMP) as observed in populations of Dyctyostelium cells. In both cases a substantial reduction in parameter uncertainty was observed. Extension to larger scale networks is possible but needs a more rigorous parameter estimation algorithm that includes sparsity as a constraint in the optimization procedure.

Conclusion

We conclude that a careful experiment design very often (but not always) pays off in terms of reliability in the inferred network topology. For large scale networks a better parameter estimation algorithm is required that includes sparsity as an additional constraint. These algorithms are available in the literature and can also be used in an adaptive optimal design setting as demonstrated in this paper.

A molecular network underlying spontaneous cAMP oscillation and synchronization in Dictyostelium

We propose a molecular network, incorporating both adaptation and phosphorylation, to account for the spontaneous cAMP oscillation of Dictyostelium discoideum. We have modified the scheme previously proposed by Loomis and his collaborators so as to include adaptation by the cAMP receptor and such that extracellular cAMP is formed by the secreted intracellular cAMP instead of being directly produced by adenylyl cyclase. Furthermore, our scheme provides better robustness, and can be applied to spontaneous cAMP production by a cluster of cells.

Communicating oscillatory networks: frequency domain analysis

Background

Constructing predictive dynamic models of interacting signalling networks remains one of the great challenges facing systems biology. While detailed dynamical data exists about individual pathways, the task of combining such data without further lengthy experimentation is highly nontrivial. The communicating links between pathways, implicitly assumed to be unimportant and thus excluded, are precisely what become important in the larger system and must be reinstated. To maintain the delicate phase relationships between signals, signalling networks demand accurate dynamical parameters, but parameters optimised in isolation and under varying conditions are unlikely to remain optimal when combined. The computational burden of estimating parameters increases exponentially with increasing system size, so it is crucial to find precise and efficient ways of measuring the behaviour of systems, in order to re-use existing work.

Results

Motivated by the above, we present a new frequency domain-based systematic analysis technique that attempts to address the challenge of network assembly by defining a rigorous means to quantify the behaviour of stochastic systems. As our focus we construct a novel coupled oscillatory model of p53, NF-kB and the mammalian cell cycle, based on recent experimentally verified mathematical models. Informed by online databases of protein networks and interactions, we distilled their key elements into simplified models containing the most significant parts. Having coupled these systems, we constructed stochastic models for use in our frequency domain analysis. We used our new technique to investigate the crosstalk between the components of our model and measure the efficacy of certain network-based heuristic measures.

Conclusions

We find that the interactions between the networks we study are highly complex and not intuitive: (i) points of maximum perturbation do not necessarily correspond to points of maximum proximity to influence; (ii) increased coupling strength does not necessarily increase perturbation; (iii) different perturbations do not necessarily sum and (iv) overall, susceptibility to perturbation is amplitude and frequency dependent and cannot easily be predicted by heuristic measures.

Our methodology is particularly relevant for oscillatory systems, though not limited to these, and is most revealing when applied to the results of stochastic simulation. The technique is able to characterise precisely the distance in behaviour between different models, different systems and different parts within the same system. It can also measure the difference between different simulation algorithms used on the same system and can be used to inform the choice of dynamic parameters. By measuring crosstalk between subsystems it can also indicate mechanisms by which such systems may be controlled in experiments and therapeutics. We have thus found our technique of frequency domain analysis to be a valuable benchmark systems-biological tool.

Collective oscillations in developing cells: insights from simple systems

From hormonal secretion to gene expression, multicellular dynamics are rich in oscillatory regulation. When organized in space and time, periodic cell-cell signaling can give rise to long-range coordination of gene expression and cell movement in tissues. Lack of synchrony of the oscillations on the other hand can serve as a source of initial divergence of cell fate in stem cells. How properties of individual cells can account for collective rhythmic behaviors at the tissue level remains elusive in most cases. Recently, studies in chemical reactions, synthetic gene circuits, yeast and social amoeba Dictyostelium have greatly enhanced our view of collective oscillations in cell populations. From these relatively simple systems, a unified view of how excitable and oscillatory regulations could be tuned and coupled to give rise to tissue-level oscillations is emerging. The review focuses on recent progress in cyclic adenosine monophosphate oscillations in Dictyostelium and highlights similarities and differences with other systems. We will see that the autonomy of single-cell level oscillations and different ways in which cells are coupled influence how group-level information can be encoded in collective oscillations.

Direct biochemical measurements of signal relay during Dictyostelium development

Upon starvation, individual Dictyostelium discoideum cells enter a developmental program that leads to collective migration and the formation of a multicellular organism. The process is mediated by extracellular cAMP binding to the G protein-coupled cAMP receptor 1, which initiates a signaling cascade leading to the activation of adenylyl cyclase A (ACA), the synthesis and secretion of additional cAMP, and an autocrine and paracrine activation loop. The release of cAMP allows neighboring cells to polarize and migrate directionally and form characteristic chains of cells called streams. We now report that cAMP relay can be measured biochemically by assessing ACA, ERK2, and TORC2 activities at successive time points in development after stimulating cells with subsaturating concentrations of cAMP. We also find that the activation profiles of ACA, ERK2, and TORC2 change in the course of development, with later developed cells showing a loss of sensitivity to the relayed signal. We examined mutants in PKA activity that have been associated with precocious development and find that this loss in responsiveness occurs earlier in these mutants. Remarkably, we show that this loss in sensitivity correlates with a switch in migration patterns as cells transition from streams to aggregates. We propose that as cells proceed through development, the cAMP-induced desensitization and down-regulation of cAMP receptor 1 impacts the sensitivities of chemotactic signaling cascades leading to changes in migration patterns.

Evolution of developmental cyclic adenosine monophosphate signaling in the Dictyostelia from an amoebozoan stress response

The Dictyostelid social amoebas represent one of nature's several inventions of multicellularity. Though normally feeding as single cells, nutrient stress triggers the collection of amoebas into colonies that form delicately shaped fruiting structures in which the cells differentiate into spores and up to three cell types to support the spore mass. Cyclic adenosine monophosphate (cAMP) plays a very dominant role in controlling morphogenesis and cell differentiation in the model species Dictyostelium discoideum. As a secreted chemoattractant cAMP coordinates cell movement during aggregation and fruiting body morphogenesis. Secreted cAMP also controls gene expression at different developmental stages, while intracellular cAMP is extensively used to transduce the effect of other stimuli that control the developmental program. In this review, I present an overview of the different roles of cAMP in the model D. discoideum and I summarize studies aimed to resolve how these roles emerged during Dictyostelid evolution.

Evolutionary crossroads in developmental biology: Dictyostelium discoideum

Dictyostelium discoideum belongs to a group of multicellular life forms that can also exist for long periods as single cells. This ability to shift between uni- and multicellularity makes the group ideal for studying the genetic changes that occurred at the crossroads between uni- and multicellular life. In this Primer, I discuss the mechanisms that control multicellular development in Dictyostelium discoideum and reconstruct how some of these mechanisms evolved from a stress response in the unicellular ancestor.

cAMP diffusion in Dictyostelium discoideum: a Green's function method

A Green's function method is developed to approach the spatiotemporal equations describing the cAMP production in Dictyostelium discoideum, markedly reducing numerical calculations times: cAMP concentrations and gradients are calculated just at the amoeba locations. A single set of parameters is capable of reproducing the different observed behaviors, from cAMP synchronization, spiral waves and reaction-diffusion patterns to streaming and mound formation. After aggregation, the emergence of a circular motion of amoebas, breaking the radial cAMP field symmetry, is observed.

Efficient estimation of the robustness region of biological models with oscillatory behavior

Robustness is an essential feature of biological systems, and any mathematical model that describes such a system should reflect this feature. Especially, persistence of oscillatory behavior is an important issue. A benchmark model for this phenomenon is the Laub-Loomis model, a nonlinear model for cAMP oscillations in Dictyostelium discoideum. This model captures the most important features of biomolecular networks oscillating at constant frequencies. Nevertheless, the robustness of its oscillatory behavior is not yet fully understood. Given a system that exhibits oscillating behavior for some set of parameters, the central question of robustness is how far the parameters may be changed, such that the qualitative behavior does not change. The determination of such a “robustness region” in parameter space is an intricate task. If the number of parameters is high, it may be also time consuming. In the literature, several methods are proposed that partially tackle this problem. For example, some methods only detect particular bifurcations, or only find a relatively small box-shaped estimate for an irregularly shaped robustness region. Here, we present an approach that is much more general, and is especially designed to be efficient for systems with a large number of parameters. As an illustration, we apply the method first to a well understood low-dimensional system, the Rosenzweig-MacArthur model. This is a predator-prey model featuring satiation of the predator. It has only two parameters and its bifurcation diagram is available in the literature. We find a good agreement with the existing knowledge about this model. When we apply the new method to the high dimensional Laub-Loomis model, we obtain a much larger robustness region than reported earlier in the literature. This clearly demonstrates the power of our method. From the results, we conclude that the biological system underlying is much more robust than was realized until now.

A cAMP signaling model explains the benefit of maintaining two forms of phosphodiesterase in Dictyostelium

Starving Dictyostelium cells respond chemotactically to cell-generated waves of cyclic adenosine -3',5'- monophosphate (cAMP) that guide cell aggregation toward a signaling center. In this process, a large number of cells are recruited, resulting in the formation of aggregation territories that are essential for fruiting body formation. The enzyme PdsA phosphodiesterase (PDE), a crucial component of the signaling system, breaks down the external cAMP and can be either membrane-bound or secreted. The existence of two such forms is unusual in cell biology, and it remains to be determined why they have both been maintained through evolution. Here, using a model of the cAMP signaling system, I show that colonies can successfully organize into aggregates over a wider range of initial cell densities when both forms of PDE are present in an appropriately tuned ratio than when only a single form is present. The model indicates that membrane-bound PDE maintains aggregation-territory integrity in colonies with high initial cell density, whereas the secreted form is important for wave propagation at low cell densities. Thus, the ultimate retention of both forms can increase territory size. These findings have implications for other excitable media, including Ca(2+) propagation in cardiac cells and propagation of electrical excitation in nerve axons, since these systems have similar features of spatial nonuniform "release" and "degradation" of the relevant signals.

Reverse engineering gene regulatory network from microarray data using linear time-variant model

Background

Gene regulatory network is an abstract mapping of gene regulations in living cells that can help to predict the system behavior of living organisms. Such prediction capability can potentially lead to the development of improved diagnostic tests and therapeutics. DNA microarrays, which measure the expression level of thousands of genes in parallel, constitute the numeric seed for the inference of gene regulatory networks. In this paper, we have proposed a new approach for inferring gene regulatory networks from time-series gene expression data using linear time-variant model. Here, Self-Adaptive Differential Evolution, a versatile and robust Evolutionary Algorithm, is used as the learning paradigm.

Results

To assess the potency of the proposed work, a well known nonlinear synthetic network has been used. The reconstruction method has inferred this synthetic network topology and the associated regulatory parameters with high accuracy from both the noise-free and noisy time-series data. For validation purposes, the proposed approach is also applied to the simulated expression dataset of cAMP oscillations in Dictyostelium discoideum and has proved it's strength in finding the correct regulations. The strength of this work has also been verified by analyzing the real expression dataset of SOS DNA repair system in Escherichia coli and it has succeeded in finding more correct and reasonable regulations as compared to various existing works.

Conclusion

By the proposed approach, the gene interaction networks have been inferred in an efficient manner from both the synthetic, simulated cAMP oscillation expression data and real expression data. The computational time of this approach is also considerably smaller, which makes it to be more suitable for larger network reconstruction. Thus the proposed approach can serve as an initiate for the future researches regarding the associated area.

A method for determining the robustness of bio-molecular oscillator models

Background

Quantifying the robustness of biochemical models is important both for determining the validity of a natural system model and for designing reliable and robust synthetic biochemical networks. Several tools have been proposed in the literature. Unfortunately, multiparameter robustness analysis suffers from computational limitations.

Results

A novel method for quantifying the robustness of oscillatory behavior to parameter perturbations is presented in this paper. This method relies on the combination of Hopf bifurcation and Routh-Hurwitz stability criterion, which is widely applied in control system design. The proposed method is employed to calculate the robustness of two oscillating biochemical network models previously analyzed in the literature. The robustness bounds here obtained are tighter than what was previously obtained in the literature for both models.

Conclusion

The method here proposed for quantifying the robustness of biochemical oscillator models is computationally less demanding than similar multiparamter variation techniques available in the literature. It also provides tighter bounds on two models previously analyzed in the literature.

Systematic analysis of synchronized oscillatory neuronal networks reveals an enrichment for coupled direct and indirect feedback motifs

MOTIVATION

Synchronized bursting behavior is a remarkable phenomenon in neural dynamics. So, identification of the underlying functional structure is crucial to understand its regulatory mechanism at a system level. On the other hand, we noted that feedback loops (FBLs) are commonly used basic building blocks in engineering circuit design, especially for synchronization, and they have also been considered as important regulatory network motifs in systems biology. From these motivations, we have investigated the relationship between synchronized bursting behavior and feedback motifs in neural networks.

RESULTS

Through extensive simulations of synthetic spike oscillation models, we found that a particular structure of FBLs, coupled direct and indirect positive feedback loops (PFLs), can induce robust synchronized bursting behaviors. To further investigate this, we have developed a novel FBL identification method based on sampled time-series data and applied it to synchronized spiking records measured from cultured neural networks of rat by using multi-electrode array. As a result, we have identified coupled direct and indirect PFLs.

CONCLUSION

We therefore conclude that coupled direct and indirect PFLs might be an important design principle that causes the synchronized bursting behavior in neuronal networks although an extrapolation of this result to in vivo brain dynamics still remains an unanswered question.

Computational modelling suggests dynamic interactions between Ca2+, IP3 and G protein-coupled modules are key to robust Dictyostelium aggregation

Under conditions of starvation, Dictyostelium cells begin a programme of development during which they aggregate to form a multicellular structure by chemotaxis, guided by propagating waves of cyclic AMP that are relayed robustly from cell to cell. In this paper, we develop and analyse a new model for the intracellular and extracellular cAMP dependent processes that regulate Dictyostelium migration. The model allows, for the first time, a quantitative analysis of the dynamic interactions between calcium, IP(3) and G protein-dependent modules that are shown to be key to the generation of robust cAMP oscillations in Dictyostelium cells. The model provides a mechanistic explanation for the transient increase in cytosolic free Ca(2+) concentration seen in recent experiments with the application of the calmodulin inhibitor calmidazolium (R24571) to Dictyostelium cells, and also allows elucidation of the effects of varying both the conductivity of stretch-activated channels and the concentration of external phosphodiesterase on the oscillatory regime of an individual cell. A rigorous analysis of the robustness of the new model shows that interactions between the different modules significantly reduce the sensitivity of the resulting cAMP oscillations to variations in the kinetics of different Dictyostelium cells, an essential requirement for the generation of the spatially and temporally synchronised chemoattractant cAMP waves that guide Dictyostelium aggregation.

Identification of feedback loops embedded in cellular circuits by investigating non-causal impulse response components

Feedback circuits are crucial dynamic motifs which occur in many biomolecular regulatory networks. They play a pivotal role in the regulation and control of many important cellular processes such as gene transcription, signal transduction, and metabolism. In this study, we develop a novel computationally efficient method to identify feedback loops embedded in intracellular networks, which uses only time-series experimental data and requires no knowledge of the network structure. In the proposed approach, a non-parametric system identification technique, as well as a spectral factor analysis, is applied to derive a graphical criterion based on non-causal components of the system's impulse response. The appearance of non-causal components in the impulse response sequences arising from stochastic output perturbations is shown to imply the presence of underlying feedback connections within a linear network. In order to extend the approach to nonlinear networks, we linearize the intracellular networks about an equilibrium point, and then choose the magnitude of the output perturbations sufficiently small so that the resulting time-series responses remain close to the chosen equilibrium point. In this way, the impulse response sequences of the linearized system can be used to determine the presence or absence of feedback loops in the corresponding nonlinear network. The proposed method utilizes the time profile data from intracellular perturbation experiments and only requires the perturbability of output nodes. Most importantly, the method does not require any a priori knowledge of the system structure. For these reasons, the proposed approach is very well suited to identifying feedback loops in large-scale biomolecular networks. The effectiveness of the proposed method is illustrated via two examples: a synthetic network model with a negative feedback loop and a nonlinear caspase function model of apoptosis with a positive feedback loop.

Consensus of self-driven agents with avoidance of collisions

In recent years, many efforts have been addressed on collision avoidance of collectively moving agents. In this paper, we propose a modified version of the Vicsek model with adaptive speed, which can guarantee the absence of collisions. However, this strategy leads to an aggregated state with slowly moving agents. We therefore further add a certain repulsion, which results in both faster consensus and longer safe distance among agents, and thus provides a powerful mechanism for collective motions in biological and technological multiagent systems.

cAMP oscillations during aggregation of Dictyostelium

For many years it has been known that developing cells of Dictyostelium discoideum show periodic surges as they aggregate. When it was discovered that the cells were responding chemotactically to cAMP gradients produced within the populations, experiments were carried out that demonstrated similar periodic changes in the concentration of extracellular cAMP. Moreover, homogenous populations of developed cells held in suspension could be shown to respond to cAMP by changes in cell shape. Such suspensions showed spontaneous oscillations in light scattering as well as cAMP levels as the result of entrainment of the cells. The molecular components necessary for the pulsatile release of cAMP were uncovered by analyzing the behavior of a large number of strains with defined mutations isolated from saturation mutagenic screens. Subsequent genetic and biochemical studies established the connections between a dozen proteins essential for spontaneous oscillations. Computer simulations of a molecular circuit based on these results showed that it is able to account for the temporal and quantitative aspects of the oscillatory system. The circuit also appears to be coupled to the construction and dismantling of the actin/myosin cortical layer that ensures that pseudopods are restricted to the anterior of cells during chemotaxis and that the cells do not back-track when the natural wave is behind them. Since the same molecular clock controls both signal production and signal response, these behaviors are always kept strictly in phase.