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Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in contrast, are scale-free cascades of neural activity, often considered as evidence of brain tuning to criticality. While models have been developed to account for oscillations or avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically, or intractable to infer from data rigorously. Here we propose a non-equilibrium feedback-driven Ising like class of neural networks that simultaneously and quantitatively captures scale-free avalanches and scale-specific oscillations. In the most simple yet fully microscopic model version we can analytically compute the phase diagram and make direct contact with human brain resting-state activity recordings via tractable inference of the model's two essential parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor oscillations and collective behaviors of nearly-synchronous extreme events on multiple sensors, to neuronal avalanches unfolding over multiple sensors across multiple time bins. Importantly, the inferred parameters correlate with model-independent signatures of "closeness to criticality", indicating that the coexistence of scale-specific (neural oscillations) and scale-free (neuronal avalanches) dynamics in brain activity occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations., Comment: 29 pages, 20 figures

We experimentally investigate the role of illumination on the collective dynamics of a large school (ca. 50 individuals) of Hemigrammus rhodostomus. The structure of the group, defined using two order parameters, is quantified while progressively altering the visual range of the fish through controlled cycles of ambient light intensity. We show that, at low light levels, the individuals within the group are unable to form a cohesive group, while at higher illuminance the degree of alignment of the school correlates with the light intensity. When increasing the illuminance, the school structure is successively characterized by a polarized state followed by a highly regular and stable rotational configuration (milling). Our study shows that vision is necessary to achieve cohesive collective motion for free swimming fish schools, while the short-range lateral line sensing is insufficient in this situation. The present experiment therefore provides new insights into the interaction mechanisms that govern the emergence and intensity of collective motion in biological systems.

We report a new approach to controllable thermal stimulation of a single living cell and its compartments. The technique is based on the use of a single polycrystalline diamond particle containing silicon-vacancy (SiV) color centers. Due to the presence of amorphous carbon at its intercrystalline boundaries, such a particle is an efficient light absorber and becomes a local heat source when illuminated by a laser. Furthermore, the temperature of such a local heater is tracked by the spectral shift of the zero-phonon line of SiV centers. Thus, the diamond particle acts simultaneously as a heater and a thermometer. In the current work, we demonstrate the ability of such a Diamond Heater-Thermometer (DHT) to locally alter the temperature, one of the numerous parameters that play a decisive role for the living organisms at the nanoscale. In particular, we show that the local heating of 11–12 °C relative to the ambient temperature (22 °C) next to individual HeLa cells and neurons, isolated from the mouse hippocampus, leads to a change in the intracellular distribution of the concentration of free calcium ions. For individual HeLa cells, a long-term (about 30 s) increase in the integral intensity of Fluo-4 NW fluorescence by about three times is observed, which characterizes an increase in the [Ca2+]cyt concentration of free calcium in the cytoplasm. Heating near mouse hippocampal neurons also caused a calcium surge—an increase in the intensity of Fluo-4 NW fluorescence by 30% and a duration of ~ 0.4 ms.

The spatial organization of cell membrane glycoproteins and glycolipids is critical for mediating the binding of ligands, receptors, and macromolecules on the plasma membrane. However, we currently do not have the methods to quantify the spatial heterogeneities of macromolecular crowding on live cell surfaces. In this work, we combine experiment and simulation to report crowding heterogeneities on reconstituted membranes and live cell membranes with nanometer spatial resolution. By quantifying the effective binding affinity of IgG monoclonal antibodies to engineered antigen sensors, we discovered sharp gradients in crowding within a few nanometers of the crowded membrane surface. Our measurements on human cancer cells support the hypothesis that raft-like membrane domains exclude bulky membrane proteins and glycoproteins. Our facile and high-throughput method to quantify spatial crowding heterogeneities on live cell membranes may facilitate monoclonal antibody design and provide a mechanistic understanding of plasma membrane biophysical organization., 31 pages, 4 figures. See Supporting Information in Ancillary files (1 appendix, 3 movies)

Biological events are often initiated when a random "searcher" finds a "target," which is called a first passage time (FPT). In some biological systems involving multiple searchers, an important timescale is the time it takes the slowest searcher(s) to find a target. For example, of the hundreds of thousands of primordial follicles in a woman's ovarian reserve, it is the slowest to leave that trigger the onset of menopause. Such slowest FPTs may also contribute to the reliability of cell signaling pathways and influence the ability of a cell to locate an external stimulus. In this paper, we use extreme value theory and asymptotic analysis to obtain rigorous approximations to the full probability distribution and moments of slowest FPTs. Though the results are proven in the limit of many searchers, numerical simulations reveal that the approximations are accurate for any number of searchers in typical scenarios of interest. We apply these general mathematical results to models of ovarian aging and menopause timing, which reveals the role of slowest FPTs for understanding redundancy in biological systems. We also apply the theory to several popular models of stochastic search, including search by diffusive, subdiffusive, and mortal searchers., Comment: 55 pages, 7 figures

The catalytic reaction system (CRS) formalism by Hordijk and Steel is a versatile method to model autocatalytic biochemical reaction networks. It is particularly suited, and has been widely used, to study self-sustainment and self-generation properties. Its distinguishing feature is the explicit assignment of a catalytic function to chemicals that are part of the system. In this work, it is shown that the subsequent and simultaneous catalytic functions gives rise to an algebraic structure of a semigroup with the additional compatible operation of idempotent addition and a partial order. The aim of this article is to demonstrate that such semigroup models are a natural setup to describe and analyze self-sustaining CRS. The basic algebraic properties of the models are established and the notion of the function of any set of chemicals on the whole CRS is made precise. This leads to a natural discrete dynamics on the network, which results from iteratively considering the self-action on a set of chemicals by its own function. The fixed points of this dynamics are proven to correspond to self-sustaining sets of chemicals, which are functionally closed. Finally, as the main application, a theorem on the maximal self-sustaining set and a structure theorem on the lattice of functionally closed self-sustaining sets of chemicals are proven., Comment: 28 pages, 5 figures

Multicellular organisms exhibit a high degree of structural organization with specific cell types always occurring in characteristic locations. The conventional framework for describing the emergence of such consistent spatial patterns is provided by Wolpert's "French flag" paradigm. According to this view, intra-cellular genetic regulatory mechanisms use positional information provided by morphogen concentration gradients to differentially express distinct fates, resulting in a characteristic pattern of differentiated cells. However, recent experiments have shown that suppression of inter-cellular interactions can alter these spatial patterns, suggesting that cell fates are not exclusively determined by the regulation of gene expression by local morphogen concentration. Using an explicit model where adjacent cells communicate by Notch signaling, we provide a mechanistic description of how contact-mediated interactions allow information from the cellular environment to be incorporated into cell fate decisions. Viewing cellular differentiation in terms of trajectories along an epigenetic landscape (as first enunciated by Waddington), our results suggest that the contours of the landscape are moulded differently in a cell position-dependent manner, not only by the global signal provided by the morphogen but also by the local environment via cell-cell interactions. We show that our results are robust with respect to different choices of coupling between the inter-cellular signaling apparatus and the intra-cellular gene regulatory dynamics. Indeed, we show that the broad features can be observed even in abstract spin models. Our work reconciles interaction-mediated self-organized pattern formation with boundary-organized mechanisms involving signals that break symmetry., 10 pages, 6 figures

Predicting structural and energetic properties of a molecular system is one of the fundamental tasks in molecular simulations, and it has applications in chemistry, biology, and medicine. In the past decade, the advent of machine learning algorithms had an impact on molecular simulations for various tasks, including property prediction of atomistic systems. In this paper, we propose a novel methodology for transferring knowledge obtained from simple molecular systems to a more complex one, endowed with a significantly larger number of atoms and degrees of freedom. In particular, we focus on the classification of high and low free-energy conformations. Our approach relies on utilizing (i) a novel hypergraph representation of molecules, encoding all relevant information for characterizing multi-atom interactions for a given conformation, and (ii) novel message passing and pooling layers for processing and making free-energy predictions on such hypergraph-structured data. Despite the complexity of the problem, our results show a remarkable Area Under the Curve of 0.92 for transfer learning from tri-alanine to the deca-alanine system. Moreover, we show that the same transfer learning approach can also be used in an unsupervised way to group chemically related secondary structures of deca-alanine in clusters having similar free-energy values. Our study represents a proof of concept that reliable transfer learning models for molecular systems can be designed, paving the way to unexplored routes in prediction of structural and energetic properties of biologically relevant systems.

The oxidative damage of DNA is a compelling issue in molecular biophysics as it plays a vital role in the epigenetic control of gene expression and is believed to be associated with mutagenesis, carcinogenesis, and ageing. To understand the microscopic structural changes in physical properties of DNA and the resulting influence on its function due to oxidative damage of its nucleotide bases, we have conducted all-atom molecular dynamic simulations of double-stranded DNA (dsDNA) with its guanine bases being oxidized. The guanine bases are more prone to oxidative damage due to the lowest value of redox potential among all nucleobases. We have analyzed the local as well as global mechanical properties of native and oxidized dsDNA and explained those results by microscopic structural parameters and thermodynamic calculations. Our results show that the oxidative damage of dsDNA does not deform the Watson-Crick geometry; instead, the oxidized DNA structures are found to be better stabilized through electrostatic interactions. Moreover, oxidative damage changes the mechanical, helical, and groove parameters of dsDNA. The persistence length, stretch modulus, and torsional stiffness are found to be 48.87 nm, 1239.26 pN, and 477.30 pN.nm^2, respectively, for native dsDNA, and these values are 61.31 nm, 659.91 pN, and 407.79 pN.nm^2, respectively, when all the guanine bases of the dsDNA are oxidized. Compared to the global mechanical properties, the changes in helical and groove properties are found to be more prominent, concentrated locally at the oxidation sites, and causing the transition of the backbone conformations from BI to BII at the regions of oxidative damage.

Every organism has a size that is convenient for its function. Not only multicellular organisms but also uni-cellular organisms and even subcellular structures have convenient sizes. Flagella of eukaryotic cells are long dynamic cell protrusions. Because of their simple linear geometry, these cell appendages have been popular system for experimental investigation of the mechanisms of size control of organelles of eukaryotic cells. In the past most of the attention have been focussed on mono-flagellates and bi-flagellates. By extending our earlier model of bi-flagellates, here we develop a theoretical model for flagellar length control in {\it Giardia} which is an octo-flagellate. It has four pairs of flagella of four different lengths. Analyzing our model we predict the different sizes of the four pairs of flagella . This analysis not only provide insight into the physical origins of the different lengths but the predicted lengths are also consistent with the experimental data., Final version; Accepted for Publication in "Indian Journal of Physics", a pioneering journal founded by Sir C.V. Raman in 1926

Recovering molecular information remains a grand challenge in the widely used holographic and computational imaging technologies. To address this challenge, we developed a computational mid-infrared photothermal microscope, termed Bond-selective Intensity Diffraction Tomography (BS-IDT). Based on a low-cost brightfield microscope with an add-on pulsed light source, BS-IDT recovers both infrared spectra and bond-selective 3D refractive index maps from intensity-only measurements. High-fidelity infrared fingerprint spectra extraction is validated. Volumetric chemical imaging of biological cells is demonstrated at a speed of ~20 s per volume, with a lateral and axial resolution of ~350 nm and ~1.1 µm, respectively. BS-IDT’s application potential is investigated by chemically quantifying lipids stored in cancer cells and volumetric chemical imaging on Caenorhabditis elegans with a large field of view (~100 µm x 100 µm).

High traffic touch surfaces such as doorknobs, countertops, and handrails can be transmission points for the spread of pathogens, emphasizing the need to develop materials that actively self-sanitize. Metals are frequently used for these surfaces due to their durability, but many metals also possess antimicrobial properties which function through a variety of mechanisms. This work investigates metallic alloys comprised of several bioactive metals with the target of achieving broad-spectrum, rapid bioactivity through synergistic activity. An entropy-motivated stabilization paradigm is proposed to prepare scalable alloys of copper, silver, nickel and cobalt. Using combinatorial sputtering, thin-film alloys were prepared on 100 mm wafers with 50% compositional grading of each element across the wafer. The films were then annealed and investigated for alloy stability. Bioactivity testing was performed on both the as-grown alloys and the annealed films using four microorganisms -- Phi6, MS2, Bacillus subtilis and Escherichia coli -- as surrogates for human viral and bacterial pathogens. Testing showed that after 30 s of contact with some of the test alloys, Phi6, an enveloped, single-stranded RNA bacteriophage that serves as a SARS-CoV 2 surrogate, was reduced up to 6.9 orders of magnitude (>99.9999%). Additionally, the non-enveloped, double-stranded DNA bacteriophage MS2, and the Gram-negative E. coli and Gram-positive B. subtilis bacterial strains showed a 5.0, 6.4, and 5.7 log reduction in activity after 30, 20 and 10 minutes, respectively. Bioactivity in the alloy samples showed a strong dependence on the composition, with the log reduction scaling directly with the Cu content. Concentration of Cu by phase separation after annealing improved activity in some of the samples. The results motivate a variety of themes which can be leveraged to design ideal bioactive surfaces., 15 pages, 6 figures

Despite great advances in explaining synaptic plasticity and neuron function, a complete understanding of the brain's learning algorithms is still missing. Artificial neural networks provide a powerful learning paradigm through the backpropagation algorithm which modifies synaptic weights by using feedback connections. Backpropagation requires extensive communication of information back through the layers of a network. This has been argued to be biologically implausible and it is not clear whether backpropagation can be realized in the brain. Here we suggest that biophotons guided by axons provide a potential channel for backward transmission of information in the brain. Biophotons have been experimentally shown to be produced in the brain, yet their purpose is not understood. We propose that biophotons can propagate from each post-synaptic neuron to its pre-synaptic one to carry the required information backward. To reflect the stochastic character of biophoton emissions, our model includes the stochastic backward transmission of teaching signals. We demonstrate that a three-layered network of neurons can learn the MNIST handwritten digit classification task using our proposed backpropagation-like algorithm with stochastic photonic feedback. We model realistic restrictions and show that our system still learns the task for low rates of biophoton emission, information-limited (one bit per photon) backward transmission, and in the presence of noise photons. Our results suggest a new functionality for biophotons and provide an alternate mechanism for backward transmission in the brain., 14 pages, 4 figures

Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g., trapping interactions or the viscoelasticity of the environment. However, sometimes systems dynamics are erroneously claimed to be anomalous, despite the fact that the true motion is Brownian -- or vice versa. This ambiguity in establishing whether the dynamics as normal or anomalous can have far-reaching consequences, e.g., in predictions for reaction- or relaxation-laws. Demonstrating that a system exhibits normal- or anomalous-diffusion is highly desirable for a vast host of applications. Here, we present a criterion for anomalous-diffusion based on the method of power-spectral analysis of single trajectories. The robustness of this criterion is studied for trajectories of fractional-Brownian-motion, a ubiquitous stochastic process for the description of anomalous-diffusion, in the presence of two types of measurement errors. In particular, we find that our criterion is very robust for subdiffusion. Various tests on surrogate data in absence or presence of additional positional noise demonstrate the efficacy of this method in practical contexts. Finally, we provide a proof-of-concept based on diverse experiments exhibiting both normal and anomalous-diffusion., Comment: 13 pages, 6 figures, RevTeX

Controlling the activity of proteins with azobenzene photoswitches is a potent tool for manipulating their biological function. With the help of light, one can change e.g. binding affinities, control allostery or temper with complex biological processes. Additionally, due to their intrinsically fast photoisomerisation, azobenzene photoswitches can serve as triggers to initiate out-of-equilibrium processes. Such switching of the activity, therefore, initiates a cascade of conformational events, which can only be accessed with time-resolved methods. In this Review, we will show how combining the potency of azobenzene photoswitching with transient spectroscopic techniques helps to disclose the order of events and provide an experimental observation of biomolecular interactions in real-time. This will ultimately help us to understand how proteins accommodate, adapt and readjust their structure to answer an incoming signal and it will complete our knowledge of the dynamical character of proteins.

We present an approach to studying and predicting the spatio-temporal progression of infectious diseases. We treat the problem by adopting a partial differential equation (PDE) version of the Susceptible, Infected, Recovered, Deceased (SIRD) compartmental model of epidemiology, which is achieved by replacing compartmental populations by their densities. Building on our recent work (Computat Mech 66:1177, 2020), we replace our earlier use of global polynomial basis functions with those having local support, as epitomized in the finite element method, for the spatial representation of the SIRD parameters. The time dependence is treated by inferring constant parameters over time intervals that coincide with the time step in semi-discrete numerical implementations. In combination, this amounts to a scheme of field inversion of the SIRD parameters over each time step. Applied to data over ten months of 2020 for the pandemic in the US state of Michigan and to all of Mexico, our system inference via field inversion infers spatio-temporally varying PDE SIRD parameters that replicate the progression of the pandemic with high accuracy. It also produces accurate predictions, when compared against data, for a three week period into 2021. Of note is the insight that is suggested on the spatio-temporal variation of infection, recovery and death rates, as well as patterns of the population's mobility revealed by diffusivities of the compartments. Supplementary information The online version contains supplementary material available at 10.1007/s11831-021-09643-1.

von Willebrand Factor is a mechano-sensitive protein circulating in blood that mediates platelet adhesion to subendothelial collagen and platelet aggregation at high shear rates. Its hemostatic function and thrombogenic effect, as well as susceptibility to enzymatic cleavage, are regulated by a conformational change from a collapsed globular state to a stretched state. Therefore, it is essential to account for the conformation of the vWF multimers when modeling vWF-mediated thrombosis or vWF degradation. We introduce a continuum model of vWF unfolding that is developed within the framework of our multi-constituent model of platelet-mediated thrombosis. The model considers two interconvertible vWF species corresponding to the collapsed and stretched conformational states. vWF unfolding takes place via two regimes: tumbling in simple shear and strong unfolding in flows with dominant extensional component. These two regimes were demonstrated in a Couette flow between parallel plates and an extensional flow in a cross-slot geometry. The vWF unfolding model was then verified in several microfluidic systems designed for inducing high-shear vWF-mediated thrombosis and screening for von Willebrand Disease. The model predicted high concentration of stretched vWF in key regions where occlusive thrombosis was observed experimentally. Strong unfolding caused by the extensional flow was limited to the center axis or middle plane of the channels, whereas vWF unfolding near the channel walls relied upon the shear tumbling mechanism. The continuum model of vWF unfolding presented in this work can be employed in numerical simulations of vWF-mediated thrombosis or vWF degradation in complex geometries. However, extending the model to 3-D arbitrary flows and turbulent flows will pose considerable challenges.

Actin and spectrin are important constituents of axonal cytoskeleton. Periodic actin and spectrin structures are found in dendrites, initial segment of axon, and main axon. Actin and spectrin periodicity has been hypothesized to be manipulating the axon stability and mechanical behavior. Several experimental and computational studies have been performed focusing on the mechanical behavior of actin, spectrin, and actin and spectrin network. However, most of the actin studies focus on typical long F actin and do not provide quantitative comparison between the mechanical behavior of short and long actin filaments. Also, most of the spectrin studies focus on erythrocytic spectrin and do not shed light on the behavior of structurally different axonal spectrin. Only a few studies have highlighted forced unfolding of axonal spectrin which are relevant to brain injury scenario. A comprehensive, strain rate dependent mechanical study is still absent in the literature. Moreover, the current opinions regarding periodic actin and spectrin network structure in axon are disputed due to conflicting results on actin ring organization as argued by recent superresolution microscopy studies. This review summarizes the ongoing limitations in this regard and provides insights on possible approaches to address them. This study will invoke further investigation into relevant high strain rate response of actin, spectrin, and actin and spectrin network shedding light into brain pathology scenario such as traumatic brain injury., Comment: Submitted to Multiscale Science and Engineering Journal

Aggregation of chemotactic bacteria under a unimodal distribution of chemical cues was investigated by Monte Carlo simulation and asymptotic analysis based on a kinetic transport equation, which considers an internal adaptation dynamics as well as a finite tumbling duration. It was found that there exist two different regimes of the adaptation time, between which the effect of the adaptation time on the aggregation behavior is reversed; that is, when the adaptation time is as small as the running duration, the aggregation becomes increasingly steeper as the adaptation time increases, while, when the adaptation time is as large as the diffusion time of the population density, the aggregation becomes more diffusive as the adaptation time increases. Moreover, notably, the aggregation profile becomes bimodal (volcano) at the large adaptation-time regime while it is always unimodal at the small adaptation-time regime. The volcano effect occurs in such a way that the population of tumbling cells considerably decreases in a diffusion layer which is created near the peak of the external chemical cues due to the coupling of diffusion and internal adaptation of the bacteria. Two different continuum-limit models are derived by the asymptotic analysis according to the scaling of the adaptation time; that is, at the small adaptation-time regime, the Keller-Segel model while, at the large adaptation-time regime, an extension of KS model, which involves both the internal variable and the tumbling duration. Importantly, either of the models can accurately reproduce the MC results at each adaptation-time regime, involving the volcano effect. Thus, we conclude that the coupling of diffusion, adaptation, and finite tumbling duration is crucial for the volcano effect.

There is a growing interest in measuring the cell wall mechanical property at different locations in single walled cells. We present an inference scheme that maps relative surface elastic modulus distributions along the cell wall based on tracking the location of material marker points along the turgid and relaxed cell wall outline. A primary scheme provides a step-function inference of surface elastic moduli by computing the tensions and elastic stretches between material marker points. We perform stability analysis for the primary scheme against perturbations on the marker-point locations, which may occur due to image acquisition and processing from experiments. The perturbation analysis shows that the primary scheme is more stable to noise when the spacing between the marker points is coarser, and has been confirmed by the numerical experiments where we apply the primary scheme to synthetic cell outlines from simulations of hyper-elastic membrane deformation with random noise on the marker-point locations. To improve the spatial resolution of elastic modulus distribution of the primary scheme with noise, we propose two optimization schemes that convert the step-function inferences of elastic moduli into smooth-curve inferences. The first scheme infers a canonical elastic modulus distribution based on marker-point locations from multiple cell samples of the same cell type. The second scheme is a simplified cost-effective version that infers the elastic moduli based on marker-point locations from a single cell. The numerical experiments show that the first scheme significantly improves the inference precision for the underlying canonical elastic modulus distributions and can even capture some degree of nonlinearity when the underlying elastic modulus gradients are nonlinear. The second cost-effective scheme can predict the trend of the elastic modulus gradients consistently., 25 pages, 7 figures

We investigate dynamical changes and its corresponding phase space complexity in a stochastic red blood cell system. The system is obtained by incorporating power noise with the associated sinusoidal flow. Both chaotic and non-chaotic dynamics of sinusoidal flow in red blood cell are identified by 0-1 test. Furthermore, dynamical complexity of the sinusoidal flow in the system is investigated by heterogeneous recurrence based entropy. The numerical simulation is performed to quantify the existence of chaotic dynamics and complexity for the sinusoidal blood flow., 10 pages

Gene expression via transcription-translation is the most fundamental reaction to sustain biological systems, and complex reactions such as this one occur in a small compartment of living cells. There is increasing evidence that t physical effects, such as molecular crowding or excluded volume effects of transcriptional-translational machinery, affect the yield of reaction products. On the other hand, transcriptional feedback that controls gene expression during mRNA synthesis is also a vital mechanism that regulates protein synthesis in cells. However, the excluded volume effect of spatial constraints on feedback regulation is not well understood. Here, we study the confinement effect on transcriptional autoregulatory feedbacks of gene expression reactions using a theoretical model. The excluded volume effects between molecules and the membrane interface suppress the gene expression in a small cell-sized compartment. We find that negative feedback regulation at the transcription step mitigates this size-induced gene repression and alters the scaling relation of gene expression level on compartment volume, approaching the regular scaling relation without the steric effect. This recovery of regular size-scaling of gene expression does not appear in positive feedback regulation, suggesting that negative autoregulatory feedback is crucial for maintaining reaction products constant regardless of compartment size in heterogeneous cell populations., 7 pages, 5 figures

In social networks, users often engage with like-minded peers. This selective exposure to opinions might result in echo chambers, i.e., political fragmentation and social polarization of user interactions. When echo chambers form, opinions have a bimodal distribution with two peaks on opposite sides. In certain issues, where either extreme positions contain a degree of misinformation, neutral consensus is preferable for promoting discourse. In this paper, we use an opinion dynamics model that naturally forms echo chambers in order to find a feedback mechanism that bridges these communities and leads to a neutral consensus. We introduce random dynamical nudge (RDN), which presents each agent with input from a random selection of other agents' opinions and does not require surveillance of every person's opinions. Our computational results in two different models suggest that the RDN leads to a unimodal distribution of opinions centered around the neutral consensus. Furthermore, the RDN is effective both for preventing the formation of echo chambers and also for depolarizing existing echo chambers. Due to the simple and robust nature of the RDN, social media networks might be able to implement a version of this self-feedback mechanism, when appropriate, to prevent the segregation of online communities on complex social issues., 24 pages, 6 Figs

We provide an analytic derivation of the bifurcation conditions for localized bulging in an inflated hyperelastic tube of arbitrary wall thickness and axisymmetric necking in a hyperelastic sheet under equibiaxial stretching. It has previously been shown numerically that the bifurcation condition for the former problem is equivalent to the vanishing of the Jacobian determinant of the internal pressure $P$ and resultant axial force $N$, with each of them viewed as a function of the azimuthal stretch on the inner surface and the axial stretch. This equivalence is established here analytically. For the latter problem for which it has recently been shown that the bifurcation condition is not given by a Jacobian determinant equal to zero, we explain why this is the case and provide an alternative interpretation., 16 pages, 1 figure; revised version, to appear in ZAMP

It is hypothesised that the avian compass relies on spin dynamics in a recombining radical pair. Quantum coherence has been suggested as a resource to this process that nature may utilise to achieve increased compass sensitivity. To date, the true functional role of coherence in these natural systems has remained speculative, lacking insights from sufficiently complex models. Here, we investigate realistically large radical pair models with up to 21 nuclear spins, inspired by the putative magnetosensory protein cryptochrome. By varying relative radical orientations, we reveal correlations of several coherence measures with compass fidelity. Whilst electronic coherence is found to be an ineffective predictor of compass sensitivity, a robust correlation of compass sensitivity and a global coherence measure is established. The results demonstrate the importance of realistic models, and appropriate choice of coherence measure, in elucidating the quantum nature of the avian compass., 10 pages, 4 figures

We consider the Pavlovian eyeblink conditioning (EBC) via repeated presentation of paired conditioned stimulus (tone) and unconditioned stimulus (airpuff). The influence of various temporal recoding of granule cells on the EBC is investigated in a cerebellar network where the connection probability $p_c$ from Golgi to granule cells is changed. In an optimal case of $p_c^*~(=0.029)$, individual granule cells show various well- and ill-matched firing patterns relative to the unconditioned stimulus. Then, these variously-recoded signals are fed into the Purkinje cells (PCs) through parallel-fibers (PFs). In the case of well-matched PF-PC synapses, their synaptic weights are strongly depressed through strong long-term depression (LTD). On the other hand, practically no LTD occurs for the ill-matched PF-PC synapses. This type of "effective" depression at the PF-PC synapses coordinates firings of PCs effectively, which then make effective inhibitory coordination on cerebellar nucleus neuron [which elicits conditioned response (CR; eyeblink)]. When the learning trial passes a threshold, acquisition of CR begins. In this case, the timing degree ${\cal T}_d$ of CR becomes good due to presence of the ill-matched firing group which plays a role of protection barrier for the timing. With further increase in the trial, strength $\cal S$ of CR (corresponding to the amplitude of eyelid closure) increases due to strong LTD in the well-matched firing group. Thus, with increasing the learning trial, the (overall) learning efficiency degree ${\cal L}_e$ (taking into consideration both timing and strength of CR) for the CR is increased, and eventually it becomes saturated. By changing $p_c$ from $p_c^*$, we also investigate the influence of various temporal recoding on the EBC. It is thus found that, the more various in temporal recoding, the more effective in learning for the Pavlovian EBC., Comment: arXiv admin note: substantial text overlap with arXiv:2003.11325

In the course of various biological processes, specific DNA-binding proteins must efficiently find a particular target sequence/protein or a damaged site on the DNA. DNA-binding proteins perform this task based on diffusion. Nevertheless, investigations over recent decades have found that the diffusion dynamics of DNA-binding proteins are generally complicated and, further, protein specific. In this review, we collect experimental and theoretical studies that quantify the diffusion dynamics of DNA-binding proteins and review them from the viewpoint of diffusion processes.

The intracellular transport process plays an important role in delivering essential materials throughout branched geometries of neurons for their survival and function. Many neurodegenerative diseases have been associated with the disruption of transport. Therefore, it is essential to study how neurons control the transport process to localize materials to necessary locations. Here, we develop a novel optimization model to simulate the traffic regulation mechanism of material transport in complex geometries of neurons. The transport is controlled to avoid traffic jam of materials by minimizing a pre-defined objective function. The optimization subjects to a set of partial differential equation (PDE) constraints that describe the material transport process based on a macroscopic molecular-motor-assisted transport model of intracellular particles. The proposed PDE-constrained optimization model is solved in complex tree structures by using isogeometric analysis (IGA). Different simulation parameters are used to introduce traffic jams and study how neurons handle the transport issue. Specifically, we successfully model and explain the traffic jam caused by reduced number of microtubules (MTs) and MT swirls. In summary, our model effectively simulates the material transport process in healthy neurons and also explains the formation of a traffic jam in abnormal neurons. Our results demonstrate that both geometry and MT structure play important roles in achieving an optimal transport process in neuron.

Stochastic Schr\"odinger equations that govern the dynamics of open quantum systems are given by the equations for signal processing. In particular, the Brownian motion that drives the wave function of the system does not represent noise, but provides purely the arrival of new information. Thus the wave function is guided by the optimal signal detection about the conditions of the environments under noisy observations. This behaviour is similar to biological systems that detect environmental cues, process this information, and adapt to them optimally by minimising uncertainties about the conditions of their environments. It is postulated that information-processing capability is a fundamental law of nature, and hence that models describing open quantum systems can equally be applied to biological systems to model their dynamics. For illustration, simple stochastic models are considered to capture heliotropic and gravitropic motions of plants. The advantage of such dynamical models is that it allows for the quantification of information processed by the plants. By considering the consequence of information erasure, it is argued that biological systems can process environmental signals relatively close to the Landauer limit of computation, and that loss of information must lie at the heart of ageing in biological systems., Comment: 15 pages

Daylight plays a major role in the wake/sleep cycle in humans. Indeed, the wake/sleep system stems from biological systems that follow a circadian rhythm determined by the light/dark alternation. The oscillations can be modeled by the higher order non-linearity van der Pol -type equation driven by a term that mimics the light cycle. In this work noise in the illumination is introduced to investigate its effect on the human circadian cycle. It is found that the presence of noise is detrimental for the sleep/wake rhythm, except for some special values for which it may favor regular oscillations. Depending for system parameters, noise induces regularities, such as stochastic resonance: if the natural light is turned off, it emerges that there is an optimal value of intensity noise which most deteriorates the regularity of the cycle, it is the phenomenon of anti-coherent resonance. Also, the phenomenon of stochastic resonance occurs: in the presence of the drive of natural light, there is an optimal noise intensity which improves the evolution of the wake / sleep system. However, there is a critical value of the noise beyond which the system becomes chaotic; indeed, for sufficiently high noise levels (how high depends upon the parameter of the system), the sleep/wake cycle evolves in a random and unpredictable manner, for whatever parameters of the external light.

Funder: Medical Research Council; doi: http://dx.doi.org/10.13039/501100000265, Funder: Cambridge Vice Chancellor’s Award Fund, Funder: Open Philanthropy/Silicon Valley, Funder: Weston Havens Foundations, Polarization of the mammalian embryo at the right developmental time is critical for its development to term and would be valuable in assessing the potential of human embryos. However, tracking polarization requires invasive fluorescence staining, impermissible in the in vitro fertilization clinic. Here, we report the use of artificial intelligence to detect polarization from unstained time-lapse movies of mouse embryos. We assembled a dataset of bright-field movie frames from 8-cell-stage embryos, side-by-side with corresponding images of fluorescent markers of cell polarization. We then used an ensemble learning model to detect whether any bright-field frame showed an embryo before or after onset of polarization. Our resulting model has an accuracy of 85% for detecting polarization, significantly outperforming human volunteers trained on the same data (61% accuracy). We discovered that our self-learning model focuses upon the angle between cells as one known cue for compaction, which precedes polarization, but it outperforms the use of this cue alone. By compressing three-dimensional time-lapsed image data into two-dimensions, we are able to reduce data to an easily manageable size for deep learning processing. In conclusion, we describe a method for detecting a key developmental feature of embryo development that avoids clinically impermissible fluorescence staining.

Biologically, for any organism life does not start at birth but at fertilization of the embryo. Embryonic development is of great importance because it determines congenital anomalies and influences their severity. Whereas there is detailed qualitative knowledge of the successive steps of embryonic development, little is known about their probabilities of success or failure. Embryonic mortality as a function of post fertilization time provides a simple (albeit crude) way to identify major defects. We find that, in line with the few other species for which data are available, the embryonic mortality of zebrafish has a prominent peak shortly after fertilization. This is called the early embryonic mortality (EEM) effect. Although a number of immediate causes of death (e.g. infection, excess of carbon dioxide or of lactic acid, chromosomal defects) can be cited, the common underlying factor remains unknown. After reviewing embryonic mortality data available for chicken and a few other farm animals, we explain that zebrafish are particularly suited for such a study because embryogenesis can be followed from its very beginning and can be observed easily thanks to transparent egg shells. We report the following findings. (i) The mortality peak occurs in the first 15% of the 75-80 hours of embryogenesis and it is about 50 times higher than the low plateau which follows. (ii) The shape of the age-specific death rate is largely independent of the death level. Presently, little is known about the nature of embryonic defects. However, by reviewing two special cases we show that even small initial defects, e.g. spatial cellular asymmetries or irregularities in the timing of development, carry with them lethal effects in later stages of embryogenesis., 25 pages, 11 figures

We present an analytical and numerical investigation of the activity-induced hydrodynamic instabilities in model brain organoids. While several mechanisms have been introduced to explain the experimental observation of surface instabilities in brain organoids, the role of activity has been largely overlooked. Our results show that the active stress generated by the cells can be a, previously overlooked, contributor to the emergence of surface deformations in brain organoids. Supplementary Information The online version supplementary material available at 10.1140/epje/s10189-021-00149-z.

A multiscale mathematical model is presented to describe the de novo granulation and the evolution of multispecies granular biofilms within a continuous reactor. The granule is modelled as a spherical free boundary domain with radial symmetry. The equation which governs the free boundary is derived from global mass balance considerations and takes into account the growth of sessile biomass and the exchange fluxes with the bulk liquid. Starting from a vanishing initial value, the expansion of the free boundary is initiated by the attachment process, which depends on the microbial species concentrations within the bulk liquid and their specific attachment velocity. Nonlinear hyperbolic PDEs model the growth of the sessile microbial species, while quasi-linear parabolic PDEs govern the dynamics of substrates and invading species within the granular biofilm. Nonlinear ODEs govern the evolution of soluble substrates and planktonic biomass within the bulk liquid. The model is applied to an anaerobic granular-based system and solved numerically to test its qualitative behaviour and explore the main aspects of de novo anaerobic granulation: ecology, biomass distribution, relative abundance, dimensional evolution of the granules and soluble substrates and planktonic biomass dynamics within the reactor. The numerical results confirm that the model accurately describes the ecology and the concentrically-layered structure of anaerobic granules observed experimentally, and is able to predict the effects of some significant factors, such as influent wastewater composition, granulation properties of planktonic biomass, biomass density and hydrodynamic and shear stress conditions, on the process performance., Comment: 41 pages, 21 figures, preprint version

Deviations from Brownian motion leading to anomalous diffusion are ubiquitously found in transport dynamics, playing a crucial role in phenomena from quantum physics to life sciences. The detection and characterization of anomalous diffusion from the measurement of an individual trajectory are challenging tasks, which traditionally rely on calculating the mean squared displacement of the trajectory. However, this approach breaks down for cases of important practical interest, e.g., short or noisy trajectories, ensembles of heterogeneous trajectories, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. Aiming to perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams independently applied their own algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, the results revealed clear differences between the various approaches, providing practical advice for users and a benchmark for developers., Comment: 63 pages, 5 main figures, 1 table, 28 supplementary figures. Website: http://www.andi-challenge.org

Motivated by a possible convergence of terrestrial limbless locomotion strategies ultimately determined by interfacial effects, we show how both 3D gait alterations and locomotory adaptations to heterogeneous terrains can be understood through the lens of local friction modulation. Via an effective-friction modeling approach, compounded by 3D simulations, the emergence and disappearance of a range of locomotory behaviors observed in nature is systematically explained in relation to inhabited environments. Our approach also simplifies the treatment of terrain heterogeneity, whereby even solid obstacles may be seen as high friction regions, which we confirm against experiments of snakes ‘diffracting’ while traversing rows of posts, similar to optical waves. We further this optic analogy by illustrating snake refraction, reflection and lens focusing. We use these insights to engineer surface friction patterns and demonstrate passive snake navigation in complex topographies. Overall, our study outlines a unified view that connects active and passive 3D mechanics with heterogeneous interfacial effects to explain a broad set of biological observations, and potentially inspire engineering design., A long puzzle in snake’s locomotion, sidewinding allows them to travel at an angle and reorient in some environments without loss of speed. Here, authors provide a mathematical argument to the evolution of sidewinding gaits and reinforce an analogy between limbless terrestrial locomotion and optics.

Humans communicate using systems of interconnected stimuli or concepts -- from language and music to literature and science -- yet it remains unclear how, if at all, the structure of these networks supports the communication of information. Although information theory provides tools to quantify the information produced by a system, traditional metrics do not account for the inefficient ways that humans process this information. Here we develop an analytical framework to study the information generated by a system as perceived by a human observer. We demonstrate experimentally that this perceived information depends critically on a system's network topology. Applying our framework to several real networks, we find that they communicate a large amount of information (having high entropy) and do so efficiently (maintaining low divergence from human expectations). Moreover, we show that such efficient communication arises in networks that are simultaneously heterogeneous, with high-degree hubs, and clustered, with tightly-connected modules -- the two defining features of hierarchical organization. Together, these results suggest that many communication networks are constrained by the pressures of information transmission, and that these pressures select for specific structural features., 87 pages, 26 figures, 13 tables

Fluorescence is a powerful means to probe information processing in the mammalian brain1. However, neuronal tissues are highly heterogeneous and thus opaque to light. A wide set of non-invasive or invasive techniques for scattered light rejection, optical sectioning or localized excitation have been developed, but non-invasive optical recording of activity through a highly scattering layer beyond the ballistic regime is impossible as yet. Here, we show that functional signals from fluorescent time-varying sources located below a highly scattering bone tissue can be retrieved efficiently by exploiting matrix factorization algorithms to demix this information from temporal sequences of low-contrast fluorescence speckle patterns. By exploiting low-contrast fluctuating speckle patterns from extended fluorescence sources using an advanced signal-processing algorithm, functional signals through highly scattering tissues can be extracted.

Brownian motion is widely used as a paradigmatic model of diffusion in equilibrium media throughout the physical, chemical, and biological sciences. However, many real world systems, particularly biological ones, are intrinsically out-of-equilibrium due to the energy-dissipating active processes underlying their mechanical and dynamical features. The diffusion process followed by a passive tracer in prototypical active media such as suspensions of active colloids or swimming microorganisms indeed differs significantly from Brownian motion, manifest in a greatly enhanced diffusion coefficient, non-Gaussian tails of the displacement statistics, and crossover phenomena from non-Gaussian to Gaussian scaling. While such characteristic features have been extensively observed in experiments, there is so far no comprehensive theory explaining how they emerge from the microscopic active dynamics. Here we present a theoretical framework of the enhanced tracer diffusion in an active medium from its microscopic dynamics by coarse-graining the hydrodynamic interactions between the tracer and the active particles as a stochastic process. The tracer is shown to follow a non-Markovian coloured Poisson process that accounts quantitatively for all empirical observations. The theory predicts in particular a long-lived L\'evy flight regime of the tracer motion with a non-monotonic crossover between two different power-law exponents. The duration of this regime can be tuned by the swimmer density, thus suggesting that the optimal foraging strategy of swimming microorganisms might crucially depend on the density in order to exploit the L\'evy flights of nutrients. Our framework provides the first validation of the celebrated L\'evy flight model from a physical microscopic dynamics., Comment: 7 pages, 3 figures

We consider a two-population network consisting of both inhibitory (I) interneurons and excitatory (E) pyramidal cells. This I-E neuronal network has adaptive dynamic I to E and E to I interpopulation synaptic strengths, governed by interpopulation spike-timing-dependent plasticity (STDP). In previous works without STDPs, fast sparsely synchronized rhythms, related to diverse cognitive functions, were found to appear in a range of noise intensityDfor static synaptic strengths. Here, by varyingD, we investigate the effect of interpopulation STDPs on fast sparsely synchronized rhythms that emerge in both the I- and the E-populations. Depending on values ofD, long-term potentiation (LTP) and long-term depression (LTD) for population-averaged values of saturated interpopulation synaptic strengths are found to occur. Then, the degree of fast sparse synchronization varies due to effects of LTP and LTD. In a broad region of intermediateD, the degree of good synchronization (with higher synchronization degree) becomes decreased, while in a region of largeD, the degree of bad synchronization (with lower synchronization degree) gets increased. Consequently, in each I- or E-population, the synchronization degree becomes nearly the same in a wide range ofD(including both the intermediate and the largeDregions). This kind of “equalization effect” is found to occur via cooperative interplay between the average occupation and pacing degrees of spikes (i.e., the average fraction of firing neurons and the average degree of phase coherence between spikes in each synchronized stripe of spikes in the raster plot of spikes) in fast sparsely synchronized rhythms. Finally, emergences of LTP and LTD of interpopulation synaptic strengths (leading to occurrence of equalization effect) are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic spike times.PACS numbers87.19.lw, 87.19.lm, 87.19.lc

Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population genetics. Our governing equations are time-dependent differential equations labeled by a set of genotype frequencies. Our equations are uniquely derived from 4 assumptions within any population: (1) a closed system; (2) average-and-random mating process (mean-field behavior); (3) Mendelian inheritance; (4) exponential growth/death. Although our equations are nonlinear with time-evolutionary dynamics, we have obtained an exact analytic time-dependent solution and an exactly solvable model. From the phenomenological viewpoint, any initial parameter of genotype frequencies of a closed system will eventually approach a stable fixed point. Under time evolution, we show (1) the monotonic behavior of genotype frequencies, (2) any genotype or allele that appears in the population will never become extinct, (3) the Hardy-Weinberg law, and (4) the global stability without chaos in the parameter space. To demonstrate the experimental evidence for our theory, as an example, we show a mapping from the data of blood type genotype frequencies of world ethnic groups to our stable fixed-point solutions. This fixed-point Hardy-Weinberg manifold, attracting any initial point in any Euclidean fiber bounded within the genotype frequency space to the fixed point where this fiber is attached. The stable base manifold and its attached fibers form a fiber bundle, which fills in the whole genotype frequency space completely. We can define the genetic distance of two populations as their geodesic distance on the equilibrium manifold. The modification of our theory under the process of natural selection and mutation is addressed., 32 pages, 15 figures, 6 tables. (Work completed in 2006 and reported in 2014.) See Tables and Figures for a summary of key results, sequel arXiv:1502.07741. Blood type data of world ethnic groups from: http://www.bloodbook.com/world-abo.html and https://www.human-abo.org/. v3: Refinement, to appear on Theory in Biosciences - Springer

Two-dimensional electronic spectra (2DES) provide unique ways to track the energy transfer dynamics in light-harvesting complexes. The interpretation of the peaks and structures found in experimentally recorded 2DES is often not straightforward, since several processes are imaged simultaneously. The choice of specific pulse polarization sequences helps to disentangle the sometimes convoluted spectra, but brings along other disturbances. We show by detailed theoretical calculations how 2DES of the Fenna-Matthews-Olson complex are affected by rotational and conformational disorder of the chromophores., Comment: 8 pages, 4 figures

A study of the induced effect of different types of weak magnetic field exposure on bacterial growth is performed, comparing the relative changes after removal from the magnetic fields. This investigation is relevant to understand the effect of magnetic field exposure on human beings due to electronic devices. For this purpose, we use four species of common bacteria in reference to human health and safety including Escherichia coli, Staphylococcus aureus, Staphylococcus epidermidis, and Pseudomonas aeruginosa. The choice of these four bacteria also allows us to check for effects which rely upon the Gram-staining properties or shapes of bacterial species. These species were initially exposed to static, non-homogeneous and alternating weak magnetic fields, and then they were grown in incubators in the same environment at 37 {\deg}C simultaneously. Comparative measurements of optical density are then used to track the sustained impact on bacterial growth in the experimental samples. Bacteria was first grown in different weak magnetic fields on a plain glass surface both in liquid and solid media. Magnetic field treated bacteria were then transferred into similar test tubes to grow in an incubator concurrently. Bacterial cultures in liquid nutrient broth on plain glass proliferated faster in most species. Different magnetic fields affect the growth pattern of bacteria differently, depending on the bacterial strain. The weak magnetic field seems to decelerate the growth rate, even after the magnetic field is removed. With application of this study, we can potentially investigate the effect of weak field exposures on Eukaryotic cells and gene dynamics., Comment: 12 pages with 12 figures

The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate predictions about the population dynamics and its asymptotic behaviour. In this paper, we develop a rigourous mathematical analysis to study positive and negative effects of increased population density in the classical nonlinear age-structured population model introduced by Gurtin \& MacCamy in the late 1970s. One of our main results expresses the global stability of the system in terms of the newborn function only. We also derive the existence of a threshold population size implying the population extinction, which is well-known in population dynamics as an Allee effect., 20 pages, submitted to J. Math. Sci

At the neuromuscular junction (NMJ), the nicotinic acetylcholine receptor (nAChR) self-associates to give rise to rapid muscle movement. While lipid domains have maintained nAChR aggregates in vitro, their specific roles in nAChR clustering are currently unknown. In the present study, we carried out coarse-grained molecular dynamics simulations (CG-MD) of 1-4 nAChR molecules in two membrane environments: one mixture containing domain-forming, homoacidic lipids, and a second mixture consisting of heteroacidic lipids. Spontaneous dimerization of nAChRs was up to ten times more likely in domain-forming membranes; however, the effect was not significant in four-protein systems, suggesting that lipid domains are less critical to nAChR oligomerization when protein concentration is higher. With regard to lipid preferences, nAChRs consistently partitioned into liquid-disordered domains occupied by the omega-3 ([Formula: see text]-3) fatty acid, docosahexaenoic acid (DHA); enrichment of DHA boundary lipids increased with protein concentration, particularly in homoacidic membranes. This result suggests dimer formation blocks access of saturated chains and cholesterol, but not polyunsaturated chains, to boundary lipid sites.

We consider a scale-free network of inhibitory Hindmarsh-Rose (HR) bursting neurons, and investigate coupling-induced cluster burst synchronization by varying the average coupling strength $J_0$. For sufficiently small $J_0$, non-cluster desynchronized states exist. However, when passing a critical point $J^*_c~(\simeq 0.16)$, the whole population is segregated into 3 clusters via a constructive role of synaptic inhibition to stimulate dynamical clustering between individual burstings, and thus 3-cluster desynchronized states appear. As $J_0$ is further increased and passes a lower threshold $J^*_l~(\simeq 0.78)$, a transition to 3-cluster burst synchronization occurs due to another constructive role of synaptic inhibition to favor population synchronization. In this case, HR neurons in each cluster exhibit burst synchronization. However, as $J_0$ passes an intermediate threshold $J^*_m~(\simeq 5.2)$, HR neurons begin to make intermittent hoppings between the 3 clusters. Due to the intermittent intercluster hoppings, the 3 clusters are integrated into a single one. In spite of break-up of the 3 clusters, (non-cluster) burst synchronization persists in the whole population, which is well visualized in the raster plot of burst onset times where bursting stripes (composed of burst onset times and indicating burst synchronization) appear successively. With further increase in $J_0$, intercluster hoppings are intensified, and bursting stripes also become smeared more and more due to a destructive role of synaptic inhibition to spoil the burst synchronization. Eventually, when passing a higher threshold $J^*_h~(\simeq 17.8)$ a transition to desynchronization occurs via complete overlap between the bursting stripes. Finally, we also investigate the effects of stochastic noise on both 3-cluster burst synchronization and intercluster hoppings., Comment: arXiv admin note: text overlap with arXiv:1803.07256, arXiv:1708.04543

Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible S, infected I, removed R and dead people D. In order to have a cross validation, a deterministic version of such a model is also devised which is represented by a system of ordinary differential equations with delays. In the second stochastic model two further compartments are added: the class A of asymptomatic individuals and the class L of isolated infected people. Effects such as social distancing measures are easily included and the consequences are analyzed. Numerical solutions are obtained with Monte Carlo simulations. Quantitative predictions are provided which can be useful for the evaluation of political measures, e.g. the obtained results suggest that strategies based on herd immunity are too risky. Finally, the models are calibrated on data referring to the second wave of infection in Italy.

Homeostasis refers to a phenomenon whereby the output $x_o$ of a system is approximately constant on variation of an input $\mathcal{I}$. Homeostasis occurs frequently in biochemical networks and in other networks of interacting elements where mathematical models are based on differential equations associated to the network. These networks can be abstracted as digraphs $\mathcal{G}$ with a distinguished input node $\iota$, a different distinguished output node $o$, and a number of regulatory nodes $\rho_1,\ldots,\rho_n$. In these models the input-output map $x_o(\mathcal{I})$ is defined by a stable equilibrium $X_0$ at $\mathcal{I}_0$. Stability implies that there is a stable equilibrium $X(\mathcal{I})$ for each $\mathcal{I}$ near $\mathcal{I}_0$ and infinitesimal homeostasis occurs at $\mathcal{I}_0$ when $(dx_o/d\mathcal{I})(\mathcal{I}_0) = 0$. We show that there is an $(n+1)\times(n+1)$ homeostasis matrix $H(\mathcal{I})$ for which $dx_o/d\mathcal{I} = 0$ if and only if $\det(H) = 0$. We note that the entries in $H$ are linearized couplings and $\det(H)$ is a homogeneous polynomial of degree $n+1$ in these entries. We use combinatorial matrix theory to factor the polynomial $\det(H)$ and thereby determine a menu of different types of possible homeostasis associated with each digraph $\mathcal{G}$. Specifically, we prove that each factor corresponds to a subnetwork of $\mathcal{G}$. The factors divide into two combinatorially defined classes: structural and appendage. Structural factors correspond to feedforward motifs and appendage factors correspond to feedback motifs. Finally, we discover an algorithm for determining the homeostasis subnetwork motif corresponding to each factor of $\det(H)$ without performing numerical simulations on model equations. The algorithm allows us to classify low degree factors of $\det(H)$., Comment: 45 pages, 7 figures, 2 tables, minor revision

Type 2 diabetes (T2D) is a challenging metabolic disorder characterized by a substantial loss of $$\beta $$ β -cell mass and alteration of $$\beta $$ β -cell function in the islets of Langerhans, disrupting insulin secretion and glucose homeostasis. The mechanisms for deficiency in $$\beta $$ β -cell mass and function during the hyperglycemia development and T2D pathogenesis are complex. To study the relative contribution of $$\beta $$ β -cell mass to $$\beta $$ β -cell function in T2D, we make use of a comprehensive electrophysiological model of human $$\beta $$ β -cell clusters. We find that defect in $$\beta $$ β -cell mass causes a functional decline in single $$\beta $$ β -cell, impairment in intra-islet synchrony, and changes in the form of oscillatory patterns of membrane potential and intracellular $${\text {Ca}}^{2+}$$ Ca 2 + concentration, which can lead to changes in insulin secretion dynamics and in insulin levels. The model demonstrates a good correspondence between suppression of synchronizing electrical activity and published experimental measurements. We then compare the role of gap junction-mediated electrical coupling with both $$\beta $$ β -cell synchronization and metabolic coupling in the behavior of $${\text {Ca}}^{2+}$$ Ca 2 + concentration dynamics within human islets. Our results indicate that inter-$$\beta $$ β -cellular electrical coupling depicts a more important factor in shaping the physiological regulation of islet function and in human T2D. We further predict that varying the whole-cell conductance of delayed rectifier $$\text {K}^{+}$$ K + channels modifies oscillatory activity patterns of $$\beta $$ β -cell population lacking intercellular coupling, which significantly affect $${\text {Ca}}^{2+}$$ Ca 2 + concentration and insulin secretion.

Eukaryotic cells adhere to extracellular matrix during the normal development of the organism, forming static adhesion as well as during cell motility. We study this process by considering a simplified coarse-grained model of a vesicle that has uniform adhesion energy with a flat substrate, mobile curved membrane proteins and active forces. We find that a high concentration of curved proteins alone increases the spreading of the vesicle, by the self-organization of the curved proteins at the high curvature vesicle-substrate contact line, thereby reducing the bending energy penalty at the vesicle rim. This is most significant in the regime of low bare vesicle-substrate adhesion. When these curved proteins induce protrusive forces, representing the actin cytoskeleton, we find efficient spreading, in the form of sheet-like lamellipodia. Finally, the same mechanism of spreading is found to include a minimal set of ingredients needed to give rise to motile phenotypes., 30 pages, 27 figures