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.

On Gaussian curvature and membrane fission.

We propose a three-dimensional mathematical model to describe dynamical processes of membrane fission. The model is based on a phase field equation that includes the Gaussian curvature contribution to the bending energy. With the addition of the Gaussian curvature energy term numerical simulations agree with the predictions that tubular shapes can break down into multiple vesicles. A dispersion relation obtained with linear analysis predicts the wavelength of the instability and the number of formed vesicles. Finally, a membrane shape diagram is obtained for the different Gaussian and bending modulus, showing different shape regimes.

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.

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.

Quantification of the morphological characteristics of hESC colonies.

The maintenance of the undifferentiated state in human embryonic stem cells (hESCs) is critical for further application in regenerative medicine, drug testing and studies of fundamental biology. Currently, the selection of the best quality cells and colonies for propagation is typically performed by eye, in terms of the displayed morphological features, such as prominent/abundant nucleoli and a colony with a tightly packed appearance and a well-defined edge. Using image analysis and computational tools, we precisely quantify these properties using phase-contrast images of hESC colonies of different sizes (0.1-1.1 [Formula: see text]) during days 2, 3 and 4 after plating. Our analyses reveal noticeable differences in their structure influenced directly by the colony area [Formula: see text]. Large colonies (A > 0.6 mm2) have cells with smaller nuclei and a short intercellular distance when compared with small colonies (A < 0.2 mm2). The gaps between the cells, which are present in small and medium sized colonies with A ≤ 0.6 mm2, disappear in large colonies (A > 0.6 mm2) due to the proliferation of the cells in the bulk. This increases the colony density and the number of nearest neighbours. We also detect the self-organisation of cells in the colonies where newly divided (smallest) cells cluster together in patches, separated from larger cells at the final stages of the cell cycle. This might influence directly cell-to-cell interactions and the community effects within the colonies since the segregation induced by size differences allows the interchange of neighbours as the cells proliferate and the colony grows. Our findings are relevant to efforts to determine the quality of hESC colonies and establish colony characteristics database.

Coherent directed movement toward food modeled in Trichoplax, a ciliated animal lacking a nervous system.

Trichoplax adhaerens is a small, ciliated marine animal that glides on surfaces grazing upon algae, which it digests externally. It has no muscles or nervous system and only six cell types, all but two of which are embedded in its epithelium. The epithelial cells are joined by apical adherens junctions; neither tight junctions nor gap junctions are present. Monociliated epithelial cells on the lower surface propel gliding. The cilia beat regularly, but asynchronously, and transiently contact the substrate with each stroke. The animal moves in random directions in the absence of food. We show here that it exhibits chemotaxis, moving preferentially toward algae embedded in a disk of agar. We present a mathematical model to explain how coherent, directional movements could arise from the collective actions of a set of ciliated epithelial cells, each independently sensing and responding to a chemoattractant gradient. The model incorporates realistic values for viscoelastic properties of cells and produces coordinated movements and changes in body shape that resemble the actual movements of the animal. The model demonstrates that an animal can move coherently in search of food without any need for chemical signaling between cells and introduces a different approach to modeling behavior in primitive multicellular organisms.

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.

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.

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.