Modelling the creation of friends and foes groups in small real social networks

Although friendship networks have been extensively studied, few models and studies are available to understand the reciprocity of friendship and foes. Here a model is presented to explain the directed friendship and foes network formation observed in experiments of Mexican and Hungarian schools. Within the presented model, each agent has a private opinion and a public one that shares to the group. There are two kinds of interactions between agents. The first kind represent interactions with the neighbors while the other represents the attitude of an agent to the overall public available information. Links between agents evolve as a combination of the public and private information available. Friendship is defined using a fitness function according to the strength of the agent's bonds, clustering coefficient, betweenness centrality and degree. Enmity is defined as very negative links. The model allows us to reproduce the distribution of mentions for friends and foes observed in the experiments, as well as the topology of the directed networks.

Socio-economic pandemic modelling: case of Spain

A global disaster, such as the recent Covid-19 pandemic, affects every aspect of our lives and there is a need to investigate these highly complex phenomena if one aims to diminish their impact in the health of the population, as well as their socio-economic stability. In this paper we present an attempt to understand the role of the governmental authorities and the response of the rest of the population facing such emergencies. We present a mathematical model that takes into account the epidemiological features of the pandemic and also the actions of people responding to it, focusing only on three aspects of the system, namely, the fear of catching this serious disease, the impact on the economic activities and the compliance of the people to the mitigating measures adopted by the authorities. We apply the model to the specific case of Spain, since there are accurate data available about these three features. We focused on tourism as an example of the economic activity, since this sector of economy is one of the most likely to be affected by the restrictions imposed by the authorities, and because it represents an important part of Spanish economy. The results of numerical calculations agree with the empirical data in such a way that we can acquire a better insight of the different processes at play in such a complex situation, and also in other different circumstances.

Forecasting virus outbreaks with social media data via neural ordinary differential equations

During the Covid-19 pandemic, real-time social media data could in principle be used as an early predictor of a new epidemic wave. This possibility is examined here by employing a neural ordinary differential equation (neural ODE) trained to forecast viral outbreaks in a specific geographic region. It learns from multivariate time series of signals derived from a novel set of large online polls regarding COVID-19 symptoms. Once trained, the neural ODE can capture the dynamics of interconnected local signals and effectively estimate the number of new infections up to two months in advance. In addition, it may predict the future consequences of changes in the number of infected at a certain period, which might be related with the flow of individuals entering or exiting a region. This study provides persuasive evidence for the predictive ability of widely disseminated social media surveys for public health applications.

Vesicle formation induced by thermal fluctuations

The process of fission and vesicle formation depends on the geometry of the membrane that will split. For instance, a flat surface finds it difficult to form vesicles because of the lack of curved regions where to start the process. Here we show that vesicle formation can be promoted by temperature, by using a membrane phase field model with Gaussian curvature. We find a phase transition between fluctuating and vesiculation phases that depends on temperature, spontaneous curvature, and the ratio between bending and Gaussian moduli. We analysed the energy dynamical behaviour of these processes and found that the main driving ingredient is the Gaussian energy term, although the curvature energy term usually helps with the process as well. We also found that the chemical potential can be used to investigate the temperature of the system. Finally we address how temperature changes the condition for spontaneous vesiculation for all geometries, making it happen in a wider range of values of the Gaussian modulus.

Dynamical shapes of droplets of cyclodextrin-surfactant solutions

We present a series of experiments with droplets of aqueous cyclodextrin-surfactant solutions, in which the volume is reduced after the equilibrium spherical shape is reached. The final shape of the drop after this perturbation is found to be dependent on the concentration of inclusion complexes in the bulk of the solution. These inclusion complexes are formed by two cyclodextrin molecules and one surfactat molecule. We propose a model to describe these dynamical processes. Dipole–dipole interactions on the surface of the drop trigger a competition between water surface tension and dipole–dipole interaction energies. The results of the model reproduce the spherical and rod-like shapes found in the experiments.

Membrane rigidity regulates E. coli proliferation rates

Combining single cell experiments, population dynamics and theoretical methods of membrane mechanics, we put forward that the rate of cell proliferation in E. coli colonies can be regulated by modifiers of the mechanical properties of the bacterial membrane. Bacterial proliferation was modelled as mediated by cell division through a membrane constriction divisome based on FtsZ, a mechanically competent protein at elastic interaction against membrane rigidity. Using membrane fluctuation spectroscopy in the single cells, we revealed either membrane stiffening when considering hydrophobic long chain fatty substances, or membrane softening if short-chained hydrophilic molecules are used. Membrane stiffeners caused hindered growth under normal division in the microbial cultures, as expected for membrane rigidification. Membrane softeners, however, altered regular cell division causing persistent microbes that abnormally grow as long filamentous cells proliferating apparently faster. We invoke the concept of effective growth rate under the assumption of a heterogeneous population structure composed by distinguishable individuals with different FtsZ-content leading the possible forms of cell proliferation, from regular division in two normal daughters to continuous growing filamentation and budding. The results settle altogether into a master plot that captures a universal scaling between membrane rigidity and the divisional instability mediated by FtsZ at the onset of membrane constriction.

A model for social spreading of Covid-19: Cases of Mexico, Finland and Iceland

The shocking severity of the Covid-19 pandemic has woken up an unprecedented interest and accelerated effort of the scientific community to model and forecast epidemic spreading to find ways to control it regionally and between regions. Here we present a model that in addition to describing the dynamics of epidemic spreading with the traditional compartmental approach takes into account the social behaviour of the population distributed over a geographical region. The region to be modelled is defined as a two-dimensional grid of cells, in which each cell is weighted with the population density. In each cell a compartmental SEIRS system of delay difference equations is used to simulate the local dynamics of the disease. The infections between cells are modelled by a network of connections, which could be terrestrial, between neighbouring cells, or long range, between cities by air, road or train traffic. In addition, since people make trips without apparent reason, noise is considered to account for them to carry contagion between two randomly chosen distant cells. Hence, there is a clear separation of the parameters related to the biological characteristics of the disease from the ones that represent the spatial spread of infections due to social behaviour. We demonstrate that these parameters provide sufficient information to trace the evolution of the pandemic in different situations. In order to show the predictive power of this kind of approach we have chosen three, in a number of ways different countries, Mexico, Finland and Iceland, in which the pandemics have followed different dynamic paths. Furthermore we find that our model seems quite capable of reproducing the path of the pandemic for months with few initial data. Unlike similar models, our model shows the emergence of multiple waves in the case when the disease becomes endemic.

Detecting infected asymptomatic cases in a stochastic model for spread of Covid-19: the case of Argentina

We have studied the dynamic evolution of the Covid-19 pandemic in Argentina. The marked heterogeneity in population density and the very extensive geography of the country becomes a challenge itself. Standard compartment models fail when they are implemented in the Argentina case. We extended a previous successful model to describe the geographical spread of the AH1N1 influenza epidemic of 2009 in two essential ways: we added a stochastic local mobility mechanism, and we introduced a new compartment in order to take into account the isolation of infected asymptomatic detected people. Two fundamental parameters drive the dynamics: the time elapsed between contagious and isolation of infected individuals ([Formula: see text]) and the ratio of people isolated over the total infected ones (p). The evolution is more sensitive to the [Formula: see text]parameter. The model not only reproduces the real data but also predicts the second wave before the former vanishes. This effect is intrinsic of extensive countries with heterogeneous population density and interconnection.The model presented has proven to be a reliable predictor of the effects of public policies as, for instance, the unavoidable vaccination campaigns starting at present in the world an particularly in Argentina.

Dipole-dipole interactions control the interfacial rheological response of cyclodextrin/surfactant solutions

A recent surface rheological study has shown that aqueous solutions of α-cyclodextrin (αCD) with anionic surfactants (S) display a remarkable viscoelasticity at the liquid/air interface, which has not been observed in similar systems. The dilatational modulus is various orders of magnitude larger than those for the binary mixtures αCD + water and S + water. The rheological response has been qualitatively related to the bulk distribution of species, the 2 : 1 inclusion complexes (αCD2 : S) playing a fundamental role. In this work, we have developed a model that considers dipole-dipole interactions between 2 : 1 inclusion complexes ordered on the liquid/air interface. When the model is applied to the specific experimental conditions, the dependencies on concentration and temperature of the dilatational modulus and the surface tension were found to be in excellent agreement with the data, indicating clearly that dipole-dipole interactions determine and control the rheological behavior of the interface.

OCT4 expression in human embryonic stem cells: spatio-temporal dynamics and fate transitions

The improved in vitro regulation of human embryonic stem cell (hESC) pluripotency and differentiation trajectories is required for their promising clinical applications. The temporal and spatial quantification of the molecular interactions controlling pluripotency is also necessary for the development of successful mathematical and computational models. Here we use time-lapse experimental data of OCT4-mCherry fluorescence intensity to quantify the temporal and spatial dynamics of the pluripotency transcription factor OCT4 in a growing hESC colony in the presence and absence of BMP4. We characterise the internal self-regulation of OCT4 using the Hurst exponent and autocorrelation analysis, quantify the intra-cellular fluctuations and consider the diffusive nature of OCT4 evolution for individual cells and pairs of their descendants. We find that OCT4 abundance in the daughter cells fluctuates sub-diffusively, showing anti-persistent self-regulation. We obtain the stationary probability distributions governing hESC transitions amongst the different cell states and establish the times at which pro-fate cells (which later give rise to pluripotent or differentiated cells) cluster in the colony. By quantifying the similarities between the OCT4 expression amongst neighbouring cells, we show that hESCs express similar OCT4 to cells within their local neighbourhood within the first two days of the experiment and before BMP4 treatment. Our framework allows us to quantify the relevant properties of proliferating hESC colonies and the procedure is widely applicable to other transcription factors and cell populations.

Behavioral role of PACAP signaling reflects its selective distribution in glutamatergic and GABAergic neuronal subpopulations

The neuropeptide PACAP, acting as a co-transmitter, increases neuronal excitability, which may enhance anxiety and arousal associated with threat conveyed by multiple sensory modalities. The distribution of neurons expressing PACAP and its receptor, PAC1, throughout the mouse nervous system was determined, in register with expression of glutamatergic and GABAergic neuronal markers, to develop a coherent chemoanatomical picture of PACAP role in brain motor responses to sensory input. A circuit role for PACAP was tested by observing Fos activation of brain neurons after olfactory threat cue in wild-type and PACAP knockout mice. Neuronal activation and behavioral response, were blunted in PACAP knock-out mice, accompanied by sharply downregulated vesicular transporter expression in both GABAergic and glutamatergic neurons expressing PACAP and its receptor. This report signals a new perspective on the role of neuropeptide signaling in supporting excitatory and inhibitory neurotransmission in the nervous system within functionally coherent polysynaptic circuits.

Dynamics of hierarchical weighted networks of van der Pol oscillators

We investigate the dynamics of regular fractal-like networks of hierarchically coupled van der Pol oscillators. The hierarchy is imposed in terms of the coupling strengths or link weights. We study the low frequency modes, as well as frequency and phase synchronization, in the network by a process of repeated coarse-graining of oscillator units. At any given stage of this process, we sum over the signals from the oscillator units of a clique to obtain a new oscillating unit. The frequencies and the phases for the coarse-grained oscillators are found to progressively synchronize with the number of coarse-graining steps. Furthermore, the characteristic frequency is found to decrease and finally stabilize to a value that can be tuned via the parameters of the system. We compare our numerical results with those of an approximate analytic solution and find good qualitative agreement. Our study on this idealized model shows how oscillations with a precise frequency can be obtained in systems with heterogeneous couplings. It also demonstrates the effect of imposing a hierarchy in terms of link weights instead of one that is solely topological, where the connectivity between oscillators would be the determining factor, as is usually the case.

Universal model for the skin colouration patterns of neotropical catfishes of the genus Pseudoplatystoma

Fish skin colouration has been widely studied because it involves a variety of processes that are important to the broad field of the developmental biology. Mathematical modelling of fish skin patterning first predicted the existence of morphogens and helped to elucidate the mechanisms of pattern formation. The catfishes of the genus Pseudoplatystoma offer a good biological study model, since its species exhibit the most spectacular and amazing variations of colour patterns on the skin. They present labyrinths, closed loops (or cells), alternate spots and stripes, only spots and combinations of these. We have extended a well known mathematical model to study the skin of Pseudoplatystoma. The basic model is a two component, non-linear reaction diffusion system that presents a richness of bifurcations. The extended model assumes that there are two interacting cell/tissue layers in which morphogens diffuse and interact giving rise to the skin colouration pattern. We have found that by varying only two parameters we are able to accurately reproduce the distinct patterns found in all species of Pseudoplatystoma. The histological analysis of skin samples of two species of this genus, with different patterns, revealed differences on the disposition of the colouration cells that are consistent with our theoretical predictions.

Generation of ECG signals from a reaction-diffusion model spatially discretized

We propose a model to generate electrocardiogram signals based on a discretized reaction-diffusion system to produce a set of three nonlinear oscillators that simulate the main pacemakers in the heart. The model reproduces electrocardiograms from healthy hearts and from patients suffering various well-known rhythm disorders. In particular, it is shown that under ventricular fibrillation, the electrocardiogram signal is chaotic and the transition from sinus rhythm to chaos is consistent with the Ruelle-Takens-Newhouse route to chaos, as experimental studies indicate. The proposed model constitutes a useful tool for research, medical education, and clinical testing purposes. An electronic device based on the model was built for these purposes

A Synaptically Connected Hypothalamic Magnocellular Vasopressin-Locus Coeruleus Neuronal Circuit and Its Plasticity in Response to Emotional and Physiological Stress

The locus coeruleus (LC)-norepinephrine (NE) system modulates a range of salient brain functions, including memory and response to stress. The LC-NE system is regulated by neurochemically diverse inputs, including a range of neuropeptides such as arginine-vasopressin (AVP). Whilst the origins of many of these LC inputs, their synaptic connectivity with LC neurons, and their contribution to LC-mediated brain functions, have been well characterized, this is not the case for the AVP-LC system. Therefore, our aims were to define the types of synapses formed by AVP+ fibers with LC neurons using immunohistochemistry together with confocal and transmission electron microscopy (TEM), the origins of such inputs, using retrograde tracers, and the plasticity of the LC AVP system in response to stress and spatial learning, using the maternal separation (MS) and Morris water maze (MWM) paradigms, respectively, in rat. Confocal microscopy revealed that AVP+ fibers contacting tyrosine hydroxylase (TH)+ LC neurons were also immunopositive for vesicular glutamate transporter 2, a marker of presynaptic glutamatergic axons. TEM confirmed that AVP+ axons formed Gray type I (asymmetric) synapses with TH+ dendrites thus confirming excitatory synaptic connections between these systems. Retrograde tracing revealed that these LC AVP+ fibers originate from hypothalamic vasopressinergic magnocellular neurosecretory neurons (AVPMNNs). MS induced a significant increase in the density of LC AVP+ fibers. Finally, AVPMNN circuit upregulation by water-deprivation improved MWM performance while increased Fos expression was found in LC and efferent regions such as hippocampus and prefrontal cortex, suggesting that AVPMMN projections to LC could integrate homeostatic responses modifying neuroplasticity.

Curvature-driven spatial patterns in growing 3D domains: A mechanochemical model for phyllotaxis

Here we discuss the formation of phyllotactic patterns in the shoot apical meristem (SAM) of plants, where the spatial distribution of the phytohormone auxin determines phyllotaxis in a domain that is growing and changing in time. We assume that the concentration of auxin modifies the mechanical properties of the domain and that the mechanical stress field in the SAM orients the flux of auxin. To study this problem we propose a mechanism for pattern formation in growing domains with variable curvature. The dynamics of chemicals is modeled by a reaction-diffusion system that produces a three dimensional pattern of chemical concentrations that changes the stress field in the domain while growing. The growth process is modeled by a phase-field order parameter which determines the location of the boundaries of the domain. This field is coupled to the chemical concentration through a curvature term that affects the local mechanical stress in the domain. The local stress changes in turn modify the chemical patterns. Our model constitutes a useful and novel approach in theoretical biology, as many developmental processes in organisms seem to be affected by the changes of curvature, size, mechanical stress and other physical aspects. Several patterns seen in many plants are reproduced under certain conditions by our model.

A physico-genetic module for the polarisation of auxin efflux carriers PIN-FORMED (PIN)

Intracellular polarisation of auxin efflux carriers is crucial for understanding how auxin gradients form in plants. The polarisation dynamics of auxin efflux carriers PIN-FORMED (PIN) depends on both biomechanical forces as well as chemical, molecular and genetic factors. Biomechanical forces have shown to affect the localisation of PIN transporters to the plasma membrane. We propose a physico-genetic module of PIN polarisation that integrates biomechanical, molecular, and cellular processes as well as their non-linear interactions. The module was implemented as a discrete Boolean model and then approximated to a continuous dynamic system, in order to explore the relative contribution of the factors mediating PIN polarisation at the scale of single cell. Our models recovered qualitative behaviours that have been experimentally observed and enable us to predict that, in the context of PIN polarisation, the effects of the mechanical forces can predominate over the activity of molecular factors such as the GTPase ROP6 and the ROP-INTERACTIVE CRIB MOTIF-CONTAINING PROTEIN RIC1.

Model of polar auxin transport coupled to mechanical forces retrieves robust morphogenesis along the Arabidopsis root

Stem cells are identical in many scales, they share the same molecular composition, DNA, genes, and genetic networks, yet they should acquire different properties to form a functional tissue. Therefore, they must interact and get some external information from their environment, either spatial (dynamical fields) or temporal (lineage). In this paper we test to what extent coupled chemical and physical fields can underlie the cell's positional information during development. We choose the root apical meristem of Arabidopsis thaliana to model the emergence of cellular patterns. We built a model to study the dynamics and interactions between the cell divisions, the local auxin concentration, and physical elastic fields. Our model recovers important aspects of the self-organized and resilient behavior of the observed cellular patterns in the Arabidopsis root, in particular, the reverse fountain pattern observed in the auxin transport, the PIN-FORMED (protein family of auxin transporters) polarization pattern and the accumulation of auxin near the region of maximum curvature in a bent root. Our model may be extended to predict altered cellular patterns that are expected under various applied auxin treatments or modified physical growth conditions.

Dynamics of deceptive interactions in social networks

In this paper, we examine the role of lies in human social relations by implementing some salient characteristics of deceptive interactions into an opinion formation model, so as to describe the dynamical behaviour of a social network more realistically. In this model, we take into account such basic properties of social networks as the dynamics of the intensity of interactions, the influence of public opinion and the fact that in every human interaction it might be convenient to deceive or withhold information depending on the instantaneous situation of each individual in the network. We find that lies shape the topology of social networks, especially the formation of tightly linked, small communities with loose connections between them. We also find that agents with a larger proportion of deceptive interactions are the ones that connect communities of different opinion, and, in this sense, they have substantial centrality in the network. We then discuss the consequences of these results for the social behaviour of humans and predict the changes that could arise due to a varying tolerance for lies in society.

Thirst Is Associated with Suppression of Habenula Output and Active Stress Coping: Is there a Role for a Non-canonical Vasopressin-Glutamate Pathway?

Water-homeostasis is a fundamental physiological process for terrestrial life. In vertebrates, thirst drives water intake, but the neuronal circuits that connect the physiology of water regulation with emotional context are poorly understood. Vasopressin (VP) is a prominent messenger in this circuit, as well as L-glutamate. We have investigated the role of a VP circuit and interaction between thirst and motivational behaviors evoked by life-threatening stimuli in rats. We demonstrate a direct pathway from hypothalamic paraventricular VP-expressing, glutamatergic magnocellular neurons to the medial division of lateral habenula (LHbM), a region containing GABAergic neurons. In vivo recording and juxtacellular labeling revealed that GABAergic neurons in the LHbM had locally branching axons, and received VP-positive axon terminal contacts on their dendrites. Water deprivation significantly reduced freezing and immobility behaviors evoked by innate fear and behavioral despair, respectively, accompanied by decreased Fos expression in the lateral habenula. Our results reveal a novel VP-expressing hypothalamus to the LHbM circuit that is likely to evoke GABA-mediated inhibition in the LHbM, which promotes escape behavior during stress coping.

Effects of deception in social networks

Honesty plays a crucial role in any situation where organisms exchange information or resources. Dishonesty can thus be expected to have damaging effects on social coherence if agents cannot trust the information or goods they receive. However, a distinction is often drawn between prosocial lies ('white' lies) and antisocial lying (i.e. deception for personal gain), with the former being considered much less destructive than the latter. We use an agent-based model to show that antisocial lying causes social networks to become increasingly fragmented. Antisocial dishonesty thus places strong constraints on the size and cohesion of social communities, providing a major hurdle that organisms have to overcome (e.g. by evolving counter-deception strategies) in order to evolve large, socially cohesive communities. In contrast, white lies can prove to be beneficial in smoothing the flow of interactions and facilitating a larger, more integrated network. Our results demonstrate that these group-level effects can arise as emergent properties of interactions at the dyadic level. The balance between prosocial and antisocial lies may set constraints on the structure of social networks, and hence the shape of society as a whole.

Extra-neurohypophyseal axonal projections from individual vasopressin-containing magnocellular neurons in rat hypothalamus

Conventional neuroanatomical, immunohistochemical techniques, and electrophysiological recording, as well as in vitro labeling methods may fail to detect long range extra-neurohypophyseal-projecting axons from vasopressin (AVP)-containing magnocellular neurons (magnocells) in the hypothalamic paraventricular nucleus (PVN). Here, we used in vivo extracellular recording, juxtacellular labeling, post-hoc anatomo-immunohistochemical analysis and camera lucida reconstruction to address this question. We demonstrate that all well-labeled AVP immunopositive neurons inside the PVN possess main axons joining the tract of Greving and multi-axon-like processes, as well as axonal collaterals branching very near to the somata, which project to extra-neurohypophyseal regions. The detected regions in this study include the medial and lateral preoptical area, suprachiasmatic nucleus (SCN), lateral habenula (LHb), medial and central amygdala and the conducting systems, such as stria medullaris, the fornix and the internal capsule. Expression of vesicular glutamate transporter 2 was observed in axon-collaterals. These results, in congruency with several previous reports in the literature, provided unequivocal evidence that AVP magnocells have an uncommon feature of possessing multiple axon-like processes emanating from somata or proximal dendrites. Furthermore, the long-range non-neurohypophyseal projections are more common than an “occasional” phenomenon as previously thought.

Phase-field modelling of the dynamics of Z-ring formation in liposomes: Onset of constriction and coarsening

We propose a model for the dynamics of the formation of rings of FtsZ on tubular liposomes which produce constriction on the corresponding membrane. Our phase-field model is based on a simple bending energy that captures the dynamics of the interplay between the protein and the membrane. The short-time regime is analyzed by a linear dispersion relation, with which we are able to predict the number of rings per unit length on a tubular liposome. We study numerically the long-time dynamics of the system in the non-linear regime where we observe coarsening of Z-rings on tubular liposomes. In particular, our numerical results show that, during the coarsening process, the number of Z-rings decreases as the radius of tubular liposome increases. This is consistent with the experimental observation that the separation between rings is proportional to the radius of the liposome. Our model predicts that the mechanism for the increased rate of coarsening in liposomes of larger radius is a consequence of the increased interface energy.

Cell patterns emerge from coupled chemical and physical fields with cell proliferation dynamics: the Arabidopsis thaliana root as a study system

A central issue in developmental biology is to uncover the mechanisms by which stem cells maintain their capacity to regenerate, yet at the same time produce daughter cells that differentiate and attain their ultimate fate as a functional part of a tissue or an organ. In this paper we propose that, during development, cells within growing organs obtain positional information from a macroscopic physical field that is produced in space while cells are proliferating. This dynamical interaction triggers and responds to chemical and genetic processes that are specific to each biological system. We chose the root apical meristem of Arabidopsis thaliana to develop our dynamical model because this system is well studied at the molecular, genetic and cellular levels and has the key traits of multicellular stem-cell niches. We built a dynamical model that couples fundamental molecular mechanisms of the cell cycle to a tension physical field and to auxin dynamics, both of which are known to play a role in root development. We perform extensive numerical calculations that allow for quantitative comparison with experimental measurements that consider the cellular patterns at the root tip. Our model recovers, as an emergent pattern, the transition from proliferative to transition and elongation domains, characteristic of stem-cell niches in multicellular organisms. In addition, we successfully predict altered cellular patterns that are expected under various applied auxin treatments or modified physical growth conditions. Our modeling platform may be extended to explicitly consider gene regulatory networks or to treat other developmental systems.

The emergence of tumors results from altered cell differentiation and proliferation during organ and tissue development. Understanding how such altered or normal patterns are established is still a challenge. Molecular genetic approaches to understanding pattern formation have searched for key central genetic controllers. However, biological patterns emerge as a consequence of coupled complex genetic and non-genetic sub-systems operating at various spatial and temporal scales and levels of organization. We present a two-dimensional model and simulation benchmark that considers the integrated dynamics of physical and chemical fields that result from cell proliferation. We aim at understanding how the cellular patterns of stem-cell niches emerge. In these, organizer cells with very low rates of proliferation are surrounded by stem cells with slightly higher proliferation rates that transit to a domain of active proliferation and then of elongation and differentiation. We quantified such cellular patterns in the Arabidopsis thaliana root to test our theoretical propositions. The results of our simulations closely mimic observed root cellular patterns, thus providing a proof of principle that coupled physical fields and chemical processes under active cell proliferation give rise to stem-cell patterns. Our framework may be extended to other developmental systems and to consider gene regulatory networks.

Are opinions based on science: modelling social response to scientific facts

As scientists we like to think that modern societies and their members base their views, opinions and behaviour on scientific facts. This is not necessarily the case, even though we are all (over-) exposed to information flow through various channels of media, i.e. newspapers, television, radio, internet, and web. It is thought that this is mainly due to the conflicting information on the mass media and to the individual attitude (formed by cultural, educational and environmental factors), that is, one external factor and another personal factor. In this paper we will investigate the dynamical development of opinion in a small population of agents by means of a computational model of opinion formation in a co-evolving network of socially linked agents. The personal and external factors are taken into account by assigning an individual attitude parameter to each agent, and by subjecting all to an external but homogeneous field to simulate the effect of the media. We then adjust the field strength in the model by using actual data on scientific perception surveys carried out in two different populations, which allow us to compare two different societies. We interpret the model findings with the aid of simple mean field calculations. Our results suggest that scientifically sound concepts are more difficult to acquire than concepts not validated by science, since opposing individuals organize themselves in close communities that prevent opinion consensus.

Nonlinear effects on Turing patterns: time oscillations and chaos

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems.

Curvature multiphase field model for phase separation on a membrane

We propose a model to describe the physical mechanisms by which chemical substances separate in the vicinity of a membrane. We assume that the adsorption of the different components of a complex liquid on a membrane is governed by interactions that couple them to the spontaneous curvature of the membrane. This problem is relevant to many fields in science, as cell constriction and division, micelles with cosurfactants, holometamorphosis, and morphogenesis in general.

Phase change in an opinion-dynamics model with separation of time scales

We define an opinion formation model of agents in a one-dimensional ring, where the opinion of an agent evolves due to its interactions with close neighbors and due to its either positive or negative attitude toward the overall mood of all the other agents. While the dynamics of the agent's opinion is described with an appropriate differential equation, from time to time pairs of agents are allowed to change their locations to improve the homogeneity of opinion (or comfort feeling) with respect to their short-range environment. In this way the timescale of transaction dynamics and that of environment update are well separated and controlled by a single parameter. By varying this parameter we discovered a phase change in the number of undecided individuals. This phenomenon arises from the fact that too frequent location exchanges among agents result in frustration in their opinion formation. Our mean field analysis supports this picture.

Analysis of stationary droplets in a generic Turing reaction-diffusion system

Solitonlike structures called "droplets" are found to exist within a paradigm reaction-diffusion model that can be used to describe patterning in a number of biological systems, for example, on the skin of various fish species. They have also been found in many other systems that can be modeled with a complex Ginzburg-Landau system. These droplets can be analyzed in the biological paradigm model because the system has two nonzero stable steady states that are symmetric; however, the asymmetric case is more challenging. We first review the properties of the paradigm system and then extend a recently developed perturbation technique [D. Gomila, J. Opt. B: Quantum Semiclassical Opt. 6, S265 (2004)] to investigate the weakly asymmetric case. We compare the results of our mathematical analysis with numerical simulations and show good agreement in the region where the assumptions hold.

Opinion and community formation in coevolving networks

In human societies, opinion formation is mediated by social interactions, consequently taking place on a network of relationships and at the same time influencing the structure of the network and its evolution. To investigate this coevolution of opinions and social interaction structure, we develop a dynamic agent-based network model by taking into account short range interactions like discussions between individuals, long range interactions like a sense for overall mood modulated by the attitudes of individuals, and external field corresponding to outside influence. Moreover, individual biases can be naturally taken into account. In addition, the model includes the opinion-dependent link-rewiring scheme to describe network topology coevolution with a slower time scale than that of the opinion formation. With this model, comprehensive numerical simulations and mean field calculations have been carried out and they show the importance of the separation between fast and slow time scales resulting in the network to organize as well-connected small communities of agents with the same opinion.

Modeling the skin pattern of fishes

Complicated patterns showing various spatial scales have been obtained in the past by coupling Turing systems in such a way that the scales of the independent systems resonate. This produces superimposed patterns with different length scales. Here we propose a model consisting of two identical reaction-diffusion systems coupled together in such a way that one of them produces a simple Turing pattern of spots or stripes, and the other traveling wave fronts that eventually become stationary. The basic idea is to assume that one of the systems becomes fixed after some time and serves as a source of morphogens for the other system. This mechanism produces patterns very similar to the pigmentation patterns observed in different species of stingrays and other fishes. The biological mechanisms that support the realization of this model are discussed.

Dynamics of reaction-diffusion systems in a subdiffusive regime

In this paper, we examine the dynamics of reaction-diffusion systems with fractional time derivatives. It is shown that in these conditions diffusion is anomalous, in the sense that the mean-square displacement r2 approximately tgamma, where gamma<1, a situation known as subdiffusion. We study the conditions for the appearance of a diffusion-driven instability and show that the restrictive conditions for a Turing instability are relaxed. This implies that systems whose kinetics are not of the activator-inhibitor kind can have a Turing instability and a modulated final state. We demonstrate our results with numerical calculations in two dimensions using a generic Turing model.

Soliton behaviour in a bistable reaction diffusion model

We analyze a generic reaction-diffusion model that contains the important features of Turing systems and that has been extensively used in the past to model biological interesting patterns. This model presents various fixed points. Analysis of this model has been made in the past only in the case when there is only a single fixed point, and a phase diagram of all the possible instabilities shows that there is a place where a Turing-Hopf bifurcation occurs producing oscillating Turing patterns. In here we focus on the interesting situation of having several fixed points, particularly when one unstable point is in between two equally stable points. We show that the solutions of this bistable system are traveling front waves, or solitons. The predictions and results are tested by performing extensive numerical calculations in one and two dimensions. The dynamics of these solitons is governed by a well defined spatial scale, and collisions and interactions between solitons depend on this scale. In certain regions of parameter space the wave fronts can be stationary, forming a pattern resembling spatial chaos. The patterns in two dimensions are particularly interesting because they can present a coherent dynamics with pseudo spiral rotations that simulate the myocardial beat quite closely. We show that our simple model can produce complicated spatial patterns with many different properties, and could be used in applications in many different fields.

Morphological transitions and bistability in Turing systems

It is well known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures, or their combinations, are observed. In this paper we study transitions between these states in both two and three dimensions. First, we derive the regions of stability for different patterns using nonlinear bifurcation analysis. Then, we apply large scale computer simulations to analyze the pattern selection in a bistable system by studying the effect of parameter selection on morphological clustering and the appearance of topological defects. The method elaborated in this paper presents a probabilistic approach for studying pattern selection in a bistable reaction-diffusion system.

Turing patterns with pentagonal symmetry

We explore numerically the formation of Turing patterns in a confined circular domain with small aspect ratio. Our results show that stable fivefold patterns are formed over a well defined range of disk sizes, offering a possible mechanism for inducing the fivefold symmetry observed in early development of regular echinoids. Using this pattern as a seed, more complex biological structures can be mimicked, such as the pigmentation pattern of sea urchins and the plate arrangements of the calyxes of primitive camerate crinoids.

Turing patterns on a sphere

We address the problem of pattern formation on the surface of a sphere using Turing equations. By considering a generic reaction-diffusion model, we numerically investigate the patterns formed under different conditions on the parameter values. Our results show that a closed surface with curvature, as a sphere, imposes geometrical restrictions on the shape of the pattern. This is important in some biological systems where curvature plays an important role in guiding chemical, biochemical, and embryological processes.

A Two-dimensional Numerical Study of Spatial Pattern Formation in Interacting Turing Systems

For many years Turing systems have been proposed to account for spatial and spatiotemporal pattern formation in chemistry and biology. We extend the study of Turing systems to investigate the rô1e of boundary conditions, domain shape, non-linearities, and coupling of such systems. We show that such modifications lead to a wide variety of patterns that bear a striking resemblance to pigmentation patterns in fish, particularly those involving stripes, spots and transitions between them. Using the Turing system as a metaphor for activator-inhibitor models we conclude that such a mechanism, with the aforementioned modifications, may play a rô1e in fish patterning.

Hierarchically coupled ultradian oscillators generating robust circadian rhythms

Ensembles of mutually coupled ultradian cellular oscillators have been proposed by a number of authors to explain the generation of circadian rhythms in mammals. Most mathematical models using many coupled oscillators predict that the output period should vary as the square root of the number of participating units, thus being inconsistent with the well-established experimental result that ablation of substantial parts of the suprachiasmatic nuclei (SCN), the main circadian pacemaker in mammals, does not eliminate the overt circadian functions, which show no changes in the phases or periods of the rhythms. From these observations, we have developed a theoretical model that exhibits the robustness of the circadian clock to changes in the number of cells in the SCN, and that is readily adaptable to include the successful features of other known models of circadian regulation, such as the phase response curves and light resetting of the phase.

Rhythmic firing patterns in suprachiasmatic nucleus (SCN): the rôle of circuit interactions

The suprachiasmatic nucleus (SCN) is believed to contain the main generator of circadian rhythmicity in mammals. In order to obtain further functional details of this, electrophysiological extracellular measurements in vitro were made. By means of an interspike interval distribution analysis, it is shown that there is a novel kind of neuronal firing pattern: the harmonic pattern. From these observations, we have developed a theoretical model based on possible filtering processes occurring during synaptic transmission. The model suffices to infer that regular ultradian oscillators could be an emergent property of circuit interactions of cells in the suprachiasmatic nucleus.