Secreted,receptor-associated bone morphogenetic protein regulators reduce stochastic noise intrinsic to many extracellular morphogen distributions

Morphogens are secreted molecules that specify cell-fate organization in developing tissues. Patterns of gene expression or signalling immediately downstream of many morphogens such as the bone morphogenetic protein (BMP) decapentaplegic (Dpp) are highly reproducible and robust to perturbations. This contrasts starkly with our expectation of a noisy interpretation that would arise out of the experimentally determined low concentration (approximately picomolar) range of Dpp activity, tight receptor binding and very slow kinetic rates. To investigate mechanisms by which the intrinsic noise can be attenuated in Dpp signalling, we focus on a class of secreted proteins that bind to Dpp in the extracellular environment and play an active role in regulating Dpp/receptor interactions. We developed a stochastic model of Dpp signalling in Drosophila melanogaster and used the model to quantify the extent that stochastic fluctuations would lead to errors in spatial patterning and extended the model to investigate how a surface-associated BMP-binding protein (SBP) such as Crossveinless-2 (Cv-2) may buffer out signalling noise. In the presence of SBPs, fluctuations in the level of ligand-bound receptor can be reduced by more than twofold depending on parameter values for the intermediate transition states. Regulation of receptor–ligand interactions by SBPs may also increase the frequency of stochastic fluctuations providing a separation of timescales between high-frequency receptor equilibration and slower morphogen patterning. High-frequency noise generated by SBP regulation is easily attenuated by the intracellular network creating a system that imitates the performance of a simple low-pass filter common in audio and communication applications. Together, these data indicate that one of the benefits of receptor–ligand regulation by secreted non-receptors may be greater reliability of morphogen patterning mechanisms.     

The interplay of cell–cell and cell–substrate adhesion in collective cell migration

Collective cell migration often involves notable cell–cell and cell–substrate adhesions and highly coordinated motion of touching cells. We focus on the interplay between cell–substrate adhesion and cell–cell adhesion. We show that the loss of cell-surface contact does not significantly alter the dynamic pattern of protrusions and retractions of fast migrating amoeboid cells (Dictyostelium discoideum), but significantly changes their ability to adhere to other cells. Analysis of the dynamics of cell shapes reveals that cells that are adherent to a surface may coordinate their motion with neighbouring cells through protrusion waves that travel across cell–cell contacts. However, while shape waves exist if cells are detached from surfaces, they do not couple cell to cell. In addition, our investigation of actin polymerization indicates that loss of cell-surface adhesion changes actin polymerization at cell–cell contacts. To further investigate cell–cell/cell–substrate interactions, we used optical micromanipulation to form cell–substrate contact at controlled locations. We find that both cell-shape dynamics and cytoskeletal activity respond rapidly to the formation of cell–substrate contact.     

Stochastic modelling for gradient sensing by chemotactic cells

Chemotaxis, the process by which cells move toward attractant molecules, operates in a range of biological processes including immunity, neuronal patterning, and morphogenesis. Dictyostelium discoideum cells display a strong chemotactic response to cyclic adenosine 3′,5′-monophosphate (cAMP), which binds to a cell surface receptor. Each Dictyostelium has ca. 80000 cAMP receptors, and can transduce shallow spatial chemoattractant gradients into strongly localized intracellular responses in spite of large statistical fluctuation of receptor occupancy even in the case of very low cAMP concentration. In this study, we develop a stochastic model for gradient sensing by chemotactic cells. We simulate the binding of cAMP molecules to receptors by a Monte-Carlo method in order to account for statistical fluctuation of receptor occupancy and treat intracellular signal processing by a diffusion–translocation model, which includes the production of second-messenger molecules and positive feedback mechanisms mediated by effector molecules. Our simulation results show that the fluctuation of second-messenger concentration is much smaller than that of receptor occupancy, and that a shallow chemoattractant gradient are transduced into a large second-messenger concentration gradient through nonlinear signal amplification.     

How receptor diffusion influences gradient sensing

Chemotaxis, or directed motion in chemical gradients, is critical for various biological processes. Many eukaryotic cells perform spatial sensing, i.e. they detect gradients by comparing spatial differences in binding occupancy of chemosensory receptors across their membrane. In many theoretical models of spatial sensing, it is assumed, for the sake of simplicity, that the receptors concerned do not move. However, in reality, receptors undergo diverse modes of diffusion, and can traverse considerable distances in the time it takes such cells to turn in an external gradient. This sets a physical limit on the accuracy of spatial sensing, which we explore using a model in which receptors diffuse freely over the membrane. We find that the Fisher information carried in binding and unbinding events decreases monotonically with the diffusion constant of the receptors.     

Actin flow and talin dynamics govern rigidity sensing in actin–integrin linkage through talin extension

At cell–substrate adhesion sites, the linkage between actin filaments and integrin is regulated by mechanical stiffness of the substrate. Of potential molecular regulators, the linker proteins talin and vinculin are of particular interest because mechanical extension of talin induces vinculin binding with talin, which reinforces the actin–integrin linkage. For understanding the molecular and biophysical mechanism of rigidity sensing at cell–substrate adhesion sites, we constructed a simple physical model to examine a role of talin extension in the stiffness-dependent regulation of actin–integrin linkage. We show that talin molecules linking between retrograding actin filaments and substrate-bound integrin are extended in a manner dependent on substrate stiffness. The model predicts that, in adhesion complexes containing ≈30 talin links, talin is extended enough for vinculin binding when the substrate is stiffer than 1 kPa. The lifetime of talin links needs to be 2–5 s to achieve an appropriate response of talin extension against substrate stiffness. Furthermore, changes in actin velocity drastically shift the range of substrate stiffness that induces talin–vinculin binding. Our results suggest that talin extension is a key step in sensing and responding to substrate stiffness at cell adhesion sites.     

Measurements of the wall shear stress distribution in the outflow tract of an embryonic chicken heart

In order to study the role of blood–tissue interaction in the developing chicken embryo heart, detailed information about the haemodynamic forces is needed. In this study, we present the first in vivo measurements of the three-dimensional distribution of wall shear stress (WSS) in the outflow tract (OFT) of an embryonic chicken heart. The data are obtained in a two-step process: first, the three-dimensional flow fields are measured during the cardiac cycle using scanning microscopic particle image velocimetry; second, the location of the wall and the WSS are determined by post-processing flow velocity data (finding velocity gradients at locations where the flow approaches zero). The results are a three-dimensional reconstruction of the geometry, with a spatial resolution of 15–20 µm, and provides detailed information about the WSS in the OFT. The most significant error is the location of the wall, which results in an estimate of the uncertainty in the WSS values of 20 per cent.     

Critical roles for EGFR and EGFR–HER2 clusters in EGF binding of SW620 human carcinoma cells

Epidermal growth factor (EGF) signalling regulates normal epithelial and other cell growth, with EGF receptor (EGFR) overexpression reported in many cancers. However, the role of EGFR clusters in cancer and their dependence on EGF binding is unclear. We present novel single-molecule total internal reflection fluorescence microscopy of (i) EGF and EGFR in living cancer cells, (ii) the action of anti-cancer drugs that separately target EGFR and human EGFR2 (HER2) on these cells and (iii) EGFR–HER2 interactions. We selected human epithelial SW620 carcinoma cells for their low level of native EGFR expression, for stable transfection with fluorescent protein labelled EGFR, and imaged these using single-molecule localization microscopy to quantify receptor architectures and dynamics upon EGF binding. Prior to EGF binding, we observe pre-formed EGFR clusters. Unexpectedly, clusters likely contain both EGFR and HER2, consistent with co-diffusion of EGFR and HER2 observed in a different model CHO-K1 cell line, whose stoichiometry increases following EGF binding. We observe a mean EGFR : EGF stoichiometry of approximately 4 : 1 for plasma membrane-colocalized EGFR–EGF that we can explain using novel time-dependent kinetics modelling, indicating preferential ligand binding to monomers. Our results may inform future cancer drug developments.     

Disease control across urban–rural gradients

Controlling the regional re-emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) after its initial spread in ever-changing personal contact networks and disease landscapes is a challenging task. In a landscape context, contact opportunities within and between populations are changing rapidly as lockdown measures are relaxed and a number of social activities re-activated. Using an individual-based metapopulation model, we explored the efficacy of different control strategies across an urban–rural gradient in Wales, UK. Our model shows that isolation of symptomatic cases or regional lockdowns in response to local outbreaks have limited efficacy unless the overall transmission rate is kept persistently low. Additional isolation of non-symptomatic infected individuals, who may be detected by effective test-and-trace strategies, is pivotal to reducing the overall epidemic size over a wider range of transmission scenarios. We define an ‘urban–rural gradient in epidemic size'' as a correlation between regional epidemic size and connectivity within the region, with more highly connected urban populations experiencing relatively larger outbreaks. For interventions focused on regional lockdowns, the strength of such gradients in epidemic size increased with higher travel frequencies, indicating a reduced efficacy of the control measure in the urban regions under these conditions. When both non-symptomatic and symptomatic individuals are isolated or regional lockdown strategies are enforced, we further found the strongest urban–rural epidemic gradients at high transmission rates. This effect was reversed for strategies targeted at symptomatic individuals only. Our results emphasize the importance of test-and-trace strategies and maintaining low transmission rates for efficiently controlling SARS-CoV-2 spread, both at landscape scale and in urban areas.     

The effect of remodelling and contractility of the actin cytoskeleton on the shear resistance of single cells: a computational and experimental investigation

The biomechanisms that govern the response of chondrocytes to mechanical stimuli are poorly understood. In this study, a series of in vitro tests are performed, in which single chondrocytes are subjected to shear deformation by a horizontally moving probe. Dramatically different probe force–indentation curves are obtained for untreated cells and for cells in which the actin cytoskeleton has been disrupted. Untreated cells exhibit a rapid increase in force upon probe contact followed by yielding behaviour. Cells in which the contractile actin cytoskeleton was removed exhibit a linear force–indentation response. In order to investigate the mechanisms underlying this behaviour, a three-dimensional active modelling framework incorporating stress fibre (SF) remodelling and contractility is used to simulate the in vitro tests. Simulations reveal that the characteristic force–indentation curve observed for untreated chondrocytes occurs as a result of two factors: (i) yielding of SFs due to stretching of the cytoplasm near the probe and (ii) dissociation of SFs due to reduced cytoplasm tension at the front of the cell. In contrast, a passive hyperelastic model predicts a linear force–indentation curve similar to that observed for cells in which the actin cytoskeleton has been disrupted. This combined modelling–experimental study offers a novel insight into the role of the active contractility and remodelling of the actin cytoskeleton in the response of chondrocytes to mechanical loading.     

Stochastic modelling for gradient sensing by chemotactic cells

Chemotaxis, the process by which cells move toward attractant molecules, operates in a range of biological processes including immunity, neuronal patterning, and morphogenesis. Dictyostelium discoideum cells display a strong chemotactic response to cyclic adenosine 3^',5^'-monophosphate (cAMP), which binds to a cell surface receptor. Each Dictyostelium has ca. 80000 cAMP receptors, and can transduce shallow spatial chemoattractant gradients into strongly localized intracellular responses in spite of large statistical fluctuation of receptor occupancy even in the case of very low cAMP concentration. In this study, we develop a stochastic model for gradient sensing by chemotactic cells. We simulate the binding of cAMP molecules to receptors by a Monte-Carlo method in order to account for statistical fluctuation of receptor occupancy and treat intracellular signal processing by a diffusion–translocation model, which includes the production of second-messenger molecules and positive feedback mechanisms mediated by effector molecules. Our simulation results show that the fluctuation of second-messenger concentration is much smaller than that of receptor occupancy, and that a shallow chemoattractant gradient are transduced into a large second-messenger concentration gradient through nonlinear signal amplification.     

Demographic buffering: titrating the effects of birth rate and imperfect immunity on epidemic dynamics

Host demography can alter the dynamics of infectious disease. In the case of perfectly immunizing infections, observations of strong sensitivity to demographic variation have been mechanistically explained through analysis of the susceptible–infected–recovered (SIR) model that assumes lifelong immunity following recovery from infection. When imperfect immunity is incorporated into this framework via the susceptible–infected–recovered–susceptible (SIRS) model, with individuals regaining full susceptibility following recovery, we show that rapid loss of immunity is predicted to buffer populations against the effects of demographic change. However, this buffering is contrary to the dependence on demography recently observed for partially immunizing infections such as rotavirus and respiratory syncytial virus. We show that this discrepancy arises from a key simplification embedded in the SIR(S) framework, namely that the potential for differential immune responses to repeat exposures is ignored. We explore the minimum additional immunological information that must be included to reflect the range of observed dependencies on demography. We show that including partial protection and lower transmission following primary infection is sufficient to capture more realistic reduced levels of buffering, in addition to changes in epidemic timing, across a range of partially and fully immunizing infections. Furthermore, our results identify key variables in this relationship, including R₀.     

Reconstructing the flight kinematics of swarming and mating in wild mosquitoes

We describe a novel tracking system for reconstructing three-dimensional tracks of individual mosquitoes in wild swarms and present the results of validating the system by filming swarms and mating events of the malaria mosquito Anopheles gambiae in Mali. The tracking system is designed to address noisy, low frame-rate (25 frames per second) video streams from a stereo camera system. Because flying A. gambiae move at 1–4 m s⁻¹, they appear as faded streaks in the images or sometimes do not appear at all. We provide an adaptive algorithm to search for missing streaks and a likelihood function that uses streak endpoints to extract velocity information. A modified multi-hypothesis tracker probabilistically addresses occlusions and a particle filter estimates the trajectories. The output of the tracking algorithm is a set of track segments with an average length of 0.6–1 s. The segments are verified and combined under human supervision to create individual tracks up to the duration of the video (90 s). We evaluate tracking performance using an established metric for multi-target tracking and validate the accuracy using independent stereo measurements of a single swarm. Three-dimensional reconstructions of A. gambiae swarming and mating events are presented.     

A dose and time response Markov model for the in-host dynamics of infection with intracellular bacteria following inhalation: with application to Francisella tularensis

In a novel approach, the standard birth–death process is extended to incorporate a fundamental mechanism undergone by intracellular bacteria, phagocytosis. The model accounts for stochastic interaction between bacteria and cells of the immune system and heterogeneity in susceptibility to infection of individual hosts within a population. Model output is the dose–response relation and the dose-dependent distribution of time until response, where response is the onset of symptoms. The model is thereafter parametrized with respect to the highly virulent Schu S4 strain of Francisella tularensis, in the first such study to consider a biologically plausible mathematical model for early human infection with this bacterium. Results indicate a median infectious dose of about 23 organisms, which is higher than previously thought, and an average incubation period of between 3 and 7 days depending on dose. The distribution of incubation periods is right-skewed up to about 100 organisms and symmetric for larger doses. Moreover, there are some interesting parallels to the hypotheses of some of the classical dose–response models, such as independent action (single-hit model) and individual effective dose (probit model). The findings of this study support experimental evidence and postulations from other investigations that response is, in fact, influenced by both in-host and between-host variability.     

Flagellar phenotypic plasticity in volvocalean algae correlates with Péclet number

Flagella-generated fluid stirring has been suggested to enhance nutrient uptake for sufficiently large micro-organisms, and to have played a role in evolutionary transitions to multicellularity. A corollary to this predicted size-dependent benefit is a propensity for phenotypic plasticity in the flow-generating mechanism to appear in large species under nutrient deprivation. We examined four species of volvocalean algae whose radii and flow speeds differ greatly, with Péclet numbers (Pe) separated by several orders of magnitude. Populations of unicellular Chlamydomonas reinhardtii and one- to eight-celled Gonium pectorale (Pe ∼ 0.1–1) and multicellular Volvox carteri and Volvox barberi (Pe ∼ 100) were grown in diluted and undiluted media. For C. reinhardtii and G. pectorale, decreasing the nutrient concentration resulted in smaller cells, but had no effect on flagellar length and propulsion force. In contrast, these conditions induced Volvox colonies to grow larger and increase their flagellar length, separating the somatic cells further. Detailed studies on V. carteri found that the opposing effects of increasing beating force and flagellar spacing balance, so the fluid speed across the colony surface remains unchanged between nutrient conditions. These results lend further support to the hypothesized link between the Péclet number, nutrient uptake and the evolution of biological complexity in the Volvocales.     

A stochastic T cell response criterion

The adaptive immune system relies on different cell types to provide fast and coordinated responses, characterized by recognition of pathogenic challenge, extensive cellular proliferation and differentiation, as well as death. T cells are a subset of the adaptive immune cellular pool that recognize immunogenic peptides expressed on the surface of antigen-presenting cells by means of specialized receptors on their membrane. T cell receptor binding to ligand determines T cell responses at different times and locations during the life of a T cell. Current experimental evidence provides support to the following: (i) sufficiently long receptor–ligand engagements are required to initiate the T cell signalling cascade that results in productive signal transduction and (ii) counting devices are at work in T cells to allow signal accumulation, decoding and translation into biological responses. In the light of these results, we explore, with mathematical models, the timescales associated with T cell responses. We consider two different criteria: a stochastic one (the mean time it takes to have had N receptor–ligand complexes bound for at least a dwell time, τ, each) and one based on equilibrium (the time to reach a threshold number N of receptor–ligand complexes). We have applied mathematical models to previous experiments in the context of thymic negative selection and to recent two-dimensional experiments. Our results indicate that the stochastic criterion provides support to the thymic affinity threshold hypothesis, whereas the equilibrium one does not, and agrees with the ligand hierarchy experimentally established for thymic negative selection.     

Fly wing vein patterns have spatial reproducibility of a single cell

Developmental processes in multicellular organisms occur in fluctuating environments and are prone to noise, yet they produce complex patterns with astonishing reproducibility. We measure the left–right and inter-individual precision of bilaterally symmetric fly wings across the natural range of genetic and environmental conditions and find that wing vein patterns are specified with identical spatial precision and are reproducible to within a single-cell width. The early fly embryo operates at a similar degree of reproducibility, suggesting that the overall spatial precision of morphogenesis in Drosophila performs at the single-cell level. Could development be operating at the physical limit of what a biological system can achieve?     

Nonlinear analyte concentration gradients for one-step kinetic analysis employing optical microring resonators

Conventional methods to probe the binding kinetics of macromolecules at biosensor surfaces employ a stepwise titration of analyte concentrations and measure the association and dissociation to the immobilized ligand at each concentration level. It has previously been shown that kinetic rates can be measured in a single step by monitoring binding as the analyte concentration increases over time in a linear gradient. We report here the application of nonlinear analyte concentration gradients for determining kinetic rates and equilibrium binding affinities in a single experiment. A versatile nonlinear gradient maker is presented, which is easily applied to microfluidic systems. Simulations validate that accurate kinetic rates can be extracted for a wide range of association and dissociation rates, gradient slopes, and curvatures, and with models for mass transport. The nonlinear analyte gradient method is demonstrated with a silicon photonic microring resonator platform to measure prostate specific antigen-antibody binding kinetics.     

Novel temperature-responsive polymer brushes with carbohydrate residues facilitate selective adhesion and collection of hepatocytes

Temperature-responsive glycopolymer brushes were designed to investigate the effects of grafting architectures of the copolymers on the selective adhesion and collection of hypatocytes. Homo, random and block sequences of N-isopropylacrylamide and 2-lactobionamidoethyl methacrylate were grafted on glass substrates via surface-initiated atom transfer radical polymerization. The galactose/lactose-specific lectin RCA₁₂₀ and HepG2 cells were used to test for specific recognition of the polymer brushes containing galactose residues over the lower critical solution temperatures (LCSTs). RCA₁₂₀ showed a specific binding to the brush surfaces at 37 °C. These brush surfaces also facilitated the adhesion of HepG2 cells at 37 °C under nonserum conditions, whereas no adhesion was observed for NIH-3T3 fibroblasts. When the temperature was decreased to 25 °C, almost all the HepG2 cells detached from the block copolymer brush, whereas the random copolymer brush did not release the cells. The difference in releasing kinetics of cells from the surfaces with different grafting architectures can be explained by the correlated effects of significant changes in LCST, mobility, hydrophilicity and mechanical properties of the grafted polymer chains. These findings are important for designing ‘on–off’ cell capture/release substrates for various biomedical applications such as selective cell separation.     

Opposite valence social information provided by bio-robotic demonstrators shapes selection processes in the green bottle fly

Social learning represents a high-level complex process to acquire information about the environment, which is increasingly reported in invertebrates. The animal–robot interaction paradigm turned out to be an encouraging strategy to unveil social learning in vertebrates, but it has not been fully exploited in invertebrates. In this study, Lucilia sericata adults were induced to observe bio-robotic conspecific and predator demonstrators to reproduce different flower foraging choices. Can a fly manage two flows of social information with opposite valence? Herein, we attempt a reply. The selection process of L. sericata was affected by social information provided through different bio-robotic demonstrators, by avoiding coloured discs previously visited by a bio-robotic predator and preferring coloured discs previously visited by a bio-robotic conspecific. When both bio-robotic demonstrators visited the same disc, the latency duration increased and the flies significantly tended to avoid this disc. This indicates the complex risk–benefit evaluation process carried out by L. sericata during the acquisition of such social information. Overall, this article provides a unique perspective on the behavioural ecology of social learning in non-social insects; it also highlights the high potential of the animal–robot interaction approach for unveiling the full spectrum of invertebrates'' abilities in using social information.