Using biological metrics to score and evaluate sites: a nearest-neighbour reference condition approach

1. Reference (i.e. least or minimally impaired) sites can provide important information about the expected range of biological metrics and can be used to establish impairment or non‐impairment of a test site. A problem with using reference data is that biological metrics are affected by natural conditions. We present an approach that uses local information to adjust for natural conditions and a method for statistically evaluating condition at a test site using biological metrics. 2. Our method consists of four steps: selection of a distance measure to find neighbours of a test site, selecting natural variables to measure the distance, selection of the number of neighbours and calculating a scored metric. 3. We use a simulated example to illustrate when the nearest‐neighbour approach improves classification of sites as reference or not reference. 4. Using a set of data from the Mid‐Atlantic Highlands, we show that the nearest‐neighbour method improved on the ability of a regression approach to correctly classify test sites known to be from a non‐reference group without affecting the ability to correctly classify test sites known to be from the reference group.     

Nearest-neighbour interactions in species-rich shrublands: the roles of abundance, spatial patterns and resources

We explored pairwise nearest‐neighbour interactions in four species‐rich shrubland plant communities, asking the question: how often is an individual of species j the nearest‐neighbour of species i? In the observed data and null models, less than 35% of the maximum possible number of nearest‐neighbour species pairs was present, and at three of the four sites the number of observed nearest‐neighbour pairs were significantly less than those occurring in simulated null communities. Many of the missing pairs included woody shrubs whose absence might be interpreted as evidence of site‐specific competition between larger growth forms for soil resources or space. Less than 5% of the pairs of species that occurred did so at frequencies different from that expected under random mixing, and many of these pairs were conspecific. Of the heterospecific pairs whose frequency differed significantly from random mixing there was a weak bias towards pairs occurring at higher rather than lower frequencies than expected. There was no evidence for asymmetry (interaction of species j with species i but not the reverse) in the frequency of species pairs. Nearest‐neighbour relationships are species‐specific rather than between plant functional types. The four sites form a soil nutrient and water availability gradient, and, according to the stress gradient hypothesis, positive species interactions should be most prevalent at the most stressful sites. However, we found the opposite: the site with the highest availability of resources had both proportionally the most heterospecific pairs, and the most conspecific and heterospecific species pairs with frequencies departing significantly from that expected under random mixing.     

Oscillations and patterns in spatially discrete models for developmental intercellular signalling

We extend previous models for nearest neighbour ligand-receptor binding to include both lateral induction and inhibition of ligand and receptor production, and different geometries (strings of cells and hexagonal arrays, in addition to square arrays). We demonstrate the possibility of lateral inhibition giving patterns with a characteristic length scale of many cell diameters, when receptor production is included. In contrast, lateral induction combined with inhibition of receptor synthesis cannot give rise to a patterning instability under any circumstances. Interesting new dynamics include the analytical prediction and consequent numerical observation of spatiotemporal oscillations, this depends crucially on the production terms and on the relationship between the decay rates of ligand and free receptor. Our approach allows for a detailed comparison with the model for Delta-Notch interactions of Collier et al. [4], and we find that a formal reduction may be made only when the ligand receptor binding kinetics are very slow. Without such very slow receptor kinetics, spatial pattern formation via lateral inhibition in hexagonal cellular arrays requires significant activation of receptor production, a feature that is not apparent from previous analyses.Send offprint requests to:Markus R. Owen     

An information-theoretic characterization of the optimal gradient sensing response of cells

Many cellular systems rely on the ability to interpret spatial heterogeneities in chemoattractant concentration to direct cell migration. The accuracy of this process is limited by stochastic fluctuations in the concentration of the external signal and in the internal signaling components. Here we use information theory to determine the optimal scheme to detect the location of an external chemoattractant source in the presence of noise. We compute the minimum amount of mutual information needed between the chemoattractant gradient and the internal signal to achieve a prespecified chemotactic accuracy. We show that more accurate chemotaxis requires greater mutual information. We also demonstrate that a priori information can improve chemotaxis efficiency. We compare the optimal signaling schemes with existing experimental measurements and models of eukaryotic gradient sensing. Remarkably, there is good quantitative agreement between the optimal response when no a priori assumption is made about the location of the existing source, and the observed experimental response of unpolarized Dictyostelium discoideum cells. In contrast, the measured response of polarized D. discoideum cells matches closely the optimal scheme, assuming prior knowledge of the external gradient-for example, through prolonged chemotaxis in a given direction. Our results demonstrate that different observed classes of responses in cells (polarized and unpolarized) are optimal under varying information assumptions.     

Mechanical Cell–Cell Communication in Fibrous Networks: The Importance of Network Geometry

Cells contracting in extracellular matrix (ECM) can transmit stress over long distances, communicating their position and orientation to cells many tens of micrometres away. Such phenomena are not observed when cells are seeded on substrates with linear elastic properties, such as polyacrylamide (PA) gel. The ability for fibrous substrates to support far reaching stress and strain fields has implications for many physiological processes, while the mechanical properties of ECM are central to several pathological processes, including tumour invasion and fibrosis. Theoretical models have investigated the properties of ECM in a variety of network geometries. However, the effects of network architecture on mechanical cell–cell communication have received little attention. This work investigates the effects of geometry on network mechanics, and thus the ability for cells to communicate mechanically through different networks. Cell-derived displacement fields are quantified for various network geometries while controlling for network topology, cross-link density and micromechanical properties. We find that the heterogeneity of response, fibre alignment, and substrate displacement fields are sensitive to network choice. Further, we show that certain geometries support mechanical communication over longer distances than others. As such, we predict that the choice of network geometry is important in fundamental modelling of cell–cell interactions in fibrous substrates, as well as in experimental settings, where mechanical signalling at the cellular scale plays an important role. This work thus informs the construction of theoretical models for substrate mechanics and experimental explorations of mechanical cell–cell communication.     

Flow and Diffusion in Channel-Guided Cell Migration

Collective migration of mechanically coupled cell layers is a notable feature of wound healing, embryonic development, and cancer progression. In confluent epithelial sheets, the dynamics have been found to be highly heterogeneous, exhibiting spontaneous formation of swirls, long-range correlations, and glass-like dynamic arrest as a function of cell density. In contrast, the flow-like properties of one-sided cell-sheet expansion in confining geometries are not well understood. Here, we studied the short- and long-term flow of Madin-Darby canine kidney (MDCK) cells as they moved through microchannels. Using single-cell tracking and particle image velocimetry (PIV), we found that a defined averaged stationary cell current emerged that exhibited a velocity gradient in the direction of migration and a plug-flow-like profile across the advancing sheet. The observed flow velocity can be decomposed into a constant term of directed cell migration and a diffusion-like contribution that increases with density gradient. The diffusive component is consistent with the cell-density profile and front propagation speed predicted by the Fisher-Kolmogorov equation. To connect diffusion-mediated transport to underlying cellular motility, we studied single-cell trajectories and occurrence of vorticity. We discovered that the directed large-scale cell flow altered fluctuations in cellular motion at short length scales: vorticity maps showed a reduced frequency of swirl formation in channel flow compared with resting sheets of equal cell density. Furthermore, under flow, single-cell trajectories showed persistent long-range, random-walk behavior superimposed on drift, whereas cells in resting tissue did not show significant displacements with respect to neighboring cells. Our work thus suggests that active cell migration manifests itself in an underlying, spatially uniform drift as well as in randomized bursts of short-range correlated motion that lead to a diffusion-mediated transport.     

Flow and Diffusion in Channel-Guided Cell Migration

Collective migration of mechanically coupled cell layers is a notable feature of wound healing, embryonic development, and cancer progression. In confluent epithelial sheets, the dynamics have been found to be highly heterogeneous, exhibiting spontaneous formation of swirls, long-range correlations, and glass-like dynamic arrest as a function of cell density. In contrast, the flow-like properties of one-sided cell-sheet expansion in confining geometries are not well understood. Here, we studied the short- and long-term flow of Madin-Darby canine kidney (MDCK) cells as they moved through microchannels. Using single-cell tracking and particle image velocimetry (PIV), we found that a defined averaged stationary cell current emerged that exhibited a velocity gradient in the direction of migration and a plug-flow-like profile across the advancing sheet. The observed flow velocity can be decomposed into a constant term of directed cell migration and a diffusion-like contribution that increases with density gradient. The diffusive component is consistent with the cell-density profile and front propagation speed predicted by the Fisher-Kolmogorov equation. To connect diffusion-mediated transport to underlying cellular motility, we studied single-cell trajectories and occurrence of vorticity. We discovered that the directed large-scale cell flow altered fluctuations in cellular motion at short length scales: vorticity maps showed a reduced frequency of swirl formation in channel flow compared with resting sheets of equal cell density. Furthermore, under flow, single-cell trajectories showed persistent long-range, random-walk behavior superimposed on drift, whereas cells in resting tissue did not show significant displacements with respect to neighboring cells. Our work thus suggests that active cell migration manifests itself in an underlying, spatially uniform drift as well as in randomized bursts of short-range correlated motion that lead to a diffusion-mediated transport.     

Modeling positive regulatory feedbacks in cell-cell interactions

Our current understanding of molecular mechanisms of cellular regulation still does not support quantitative predictions of the overall growth kinetics of normal or malignant tissues. However, discernment of the role of growth-factor mediated cell-cell communication in tissue kinetics is possible by the use of simple mathematical models. Here we discuss the design and use of mathematical models in quantifying the contribution of autocrine and paracrine (i.e., humoral) interactions to the kinetics of tissue growth. We present models that include a humorally mediated regulatory feedback among cells built into phenomenological mathematical models of growth. Application of these models to data exemplifies the finite contributions of positive feedback in cell-cell interactions to the overall tissue growth. In addition, we propose a perturbation approach to allow separation of cell-cell interactions dependent on the perturbing agent (such as hormone antagonists in hormone-dependent tissues) from cell-cell interactions independent of it.     

Contact response of cells can mediate morphogenetic pattern formation

Theories of morphogenetic pattern formation have included Turing's chemical prepatterns, mechanochemical interactions, cell sorting, and other mechanisms involving guided motion or signalling of cells. Many of these theories presuppose long-range cellular communication or other controls such as chemical concentration fields. However, the possibility that direct interactions between cells can lead to order and structure has not been seriously investigated in mathematical models. In this paper we consider this possibility, with emphasis on cells that reorient and align with each other when they come into contact. We show that such contact responses can account for the formation of multicellular patterns called parallel arrays. These patterns typically occur in tissue cultures of fibroblasts, and consist of clusters of cells sharing a common axis of orientation. Using predictions of a mathematical model and computer simulations of cell motion and interactions we show that contact responses alone, in the absence of other global controls, can promote the formation of these patterns. We suggest other situations in which patterns may result from direct cellular communication. Previous theories of morphogenesis are briefly reviewed and compared with this proposed mechanism.     

When are cellular oscillators sufficient for sequential segmentation?

Sequential segmentation during embryogenesis involves the generation of a repeated pattern along the embryo, which is concurrently undergoing axial elongation by cell division. Most mathematical models of sequential segmentation involve inherent cellular oscillators, acting as a segmentation clock. The cellular oscillation is assumed to be governed by the cell's physiological age or by its interaction with an external morphogen gradient. Here, we address the issue of when cellular oscillators alone are sufficient for predicting segmentation, and when a morphogen gradient is required. The key to resolving this issue lies in how cells determine positional information in the model - this is directly related to the distribution of cell divisions responsible for axial elongation. Mathematical models demonstrate that if axial elongation occurs through cell divisions restricted to the posterior end of the unsegmented region, a cell can obtain its positional information from its physiological age, and therefore cellular oscillators will suffice. Alternatively, if axial elongation occurs through cell divisions distributed throughout the unsegmented region, then positional information can be obtained through another mechanism, such as a morphogen gradient. Two alternative ways to establish a morphogen gradient in tissue with distributed cell divisions are presented - one with diffusion and the other without diffusion. Our model produces segment polarity and a distribution of segment size from the anterior-to-posterior ends, as observed in some systems. Furthermore, the model predicts segment deletions when there is an interruption in cell division, just as seen in heat shock experiments, as well as the growth and final shrinkage of the presomitic mesoderm during somitogenesis.     

Intercellular water exchanges trigger soliton-like waves in multicellular systems

Oscillations and waves are ubiquitous in living cellular systems. Generations of these spatiotemporal patterns are generally attributed to some mechanochemical feedbacks. Here, we treat cells as open systems, i.e., water and ions can pass through the cell membrane passively or actively, and reveal a new origin of wave generation. We show that osmotic shocks above a shock threshold will trigger self-sustained cell oscillations and result in long-range waves propagating without decrement, a phenomenon that is analogous to the excitable medium. The traveling wave propagates along the intercellular osmotic pressure gradient, and its wave speed scales with the magnitude of intercellular water flows. Furthermore, we also find that the traveling wave exhibits several hallmarks of solitary waves. Together, our findings predict a new mechanism of wave generation in living multicellular systems. The ubiquity of intercellular water exchanges implies that this mechanism may be relevant to a broad class of systems.     

Stigmergic algorithms for multiple minimalistic robots on an RFID floor

Stigmergy is a powerful principle in nature, which has been shown to have interesting applications to robotic systems. By leveraging the ability to store information in the environment, robots with minimal sensing, memory, and computational capabilities can solve complex problems like global path planning. In this paper, we discuss the use of stigmergy in minimalist multi-robot systems, in which robots do not need to use any internal model, long-range sensing, or position awareness. We illustrate our discussion with three case studies: building a globally optimal navigation map, building a gradient map of a sensed feature, and updating the above maps dynamically. All case studies have been implemented in a real environment with multiple ePuck robots, using a floor with 1,500 embedded radio frequency identification tags as the stigmergic medium. Results collected from tens of hours of real experiments and thousands of simulated runs demonstrate the effectiveness of our approach.     

Mathematical and computational analysis of adaptation via feedback inhibition in signal transduction pathways

We perform a systematic analysis of mechanisms of feedback regulation that underlie short-term adaptation in intracellular signaling systems. Upon receiving an external cue, these systems generate a transient response that quickly returns to basal levels even if the stimulus persists. Signaling pathways capable of short-term adaptation are found in systems as diverse as the high osmolarity response of yeast, gradient sensing in Dictyostelium, and the cytokine response in vertebrates. Using mathematical analysis and computational experiments, we compare different feedback architectures in terms of response amplitude and duration, ability to adapt, and response to variable stimulus levels. Our analysis reveals three important features of these systems: 1), multiple step signaling cascades improve sensitivity to low doses by an effect distinct from signal amplification; 2), some feedback architectures act as signal transducers converting stimulus strength into response duration; and 3), feedback deactivation acts as a dose-dependent switch between transient and sustained responses. Finally, we present characteristic features for each form of feedback regulation that can aid in their identification.     

Three-Dimensional (3D) cell culture monitoring: Opportunities and challenges for impedance spectroscopy

Three-dimensional (3D) cell culture has developed rapidly over the past 5–10 years with the goal of better replicating human physiology and tissue complexity in the laboratory. Quantifying cellular responses is fundamental in understanding how cells and tissues respond during their growth cycle and in response to external stimuli. There is a need to develop and validate tools that can give insight into cell number, viability, and distribution in real-time, nondestructively and without the use of stains or other labelling processes. Impedance spectroscopy can address all of these challenges and is currently used both commercially and in academic laboratories to measure cellular processes in 2D cell culture systems. However, its use in 3D cultures is not straight forward due to the complexity of the electrical circuit model of 3D tissues. In addition, there are challenges in the design and integration of electrodes within 3D cell culture systems. Researchers have used a range of strategies to implement impedance spectroscopy in 3D systems. This review examines electrode design, integration, and outcomes of a range of impedance spectroscopy studies and multiparametric systems relevant to 3D cell cultures. While these systems provide whole culture data, impedance tomography approaches have shown how this technique can be used to achieve spatial resolution. This review demonstrates how impedance spectroscopy and tomography can be used to provide real-time sensing in 3D cell cultures, but challenges remain in integrating electrodes without affecting cell culture functionality. If these challenges can be addressed and more realistic electrical models for 3D tissues developed, the implementation of impedance-based systems will be able to provide real-time, quantitative tracking of 3D cell culture systems.     

Information transmission in microbial and fungal communication: from classical to quantum

Microbes have their own communication systems. Secretion and reception of chemical signaling molecules and ion-channels mediated electrical signaling mechanism are yet observed two special ways of information transmission in microbial community. In this article, we address the aspects of various crucial machineries which set the backbone of microbial cell-to-cell communication process such as quorum sensing mechanism (bacterial and fungal), quorum sensing regulated biofilm formation, gene expression, virulence, swarming, quorum quenching, role of noise in quorum sensing, mathematical models (therapy model, evolutionary model, molecular mechanism model and many more), synthetic bacterial communication, bacterial ion-channels, bacterial nanowires and electrical communication. In particular, we highlight bacterial collective behavior with classical and quantum mechanical approaches (including quantum information). Moreover, we shed a new light to introduce the concept of quantum synthetic biology and possible cellular quantum Turing test.     

Island chain models and gradient systems

A range of island chain models in the literature are gradient systems. This implies that the asymptotic dynamics of such models is trivial: all solutions tend to stationary points. Results for one-dimensional island chains are extended to habitats with more complicated geometries and to models with competitive species.     

Surface-induced aggregation of ferritin. Concentration dependence of adsorption onto a hydrophobic surface

The isotherm of ferritin adsorption onto a hydrophobic surface was studied by transmission electron microscopy. Adsorbed ferritin was found to be distributed in molecular clusters. The adsorption process was diffusion-rate-limited after 20 h adsorption time at bulk concentrations below 1 mg/1. The clusters formed during the diffusion-rate-limited adsorption had a fractal dimension D approximately 1.0 when averaged over all clusters. The pair distribution function g(r) showed an increased probability of finding nearest neighbours at distances less than 30 nm. The surface concentration of adsorbed ferritin was weakly dependent on the bulk concentration of ferritin in the range 10 mg/1-10 g/1 and the average number of nearest neighbour molecules was constant in this concentration range. The mass distribution of adsorbed ferritin c(r) had a fractal dimension D = 1.8 at a bulk concentration of 10 g/l and a surface concentration corresponding to theta = 0.45 +/- 0.05. The pair correlation function g(r) showed decreasing probability of finding nearest neighbour molecules over long distances as in percolating clusters. The results indicate that ferritin adsorbs strongly to the surface at low surface concentrations and weakly at high surface concentrations. The stability of ferritin adsorption was correlated to the average number of nearest neighbour molecules, indicating a possibility that desorption is a critical supramolecular phenomenon.     

Analytical modelling and simulation of gas adsorption effects on graphene nanoribbon electrical properties

Inspired by the realisation of the ability of graphene nanoribbon (GNR) based sensors to detect individual gas molecules, analytical approach based on the nearest neighbour tight-binding approximation is proposed to study the effect of gas adsorption on GNR electrical properties. Numerical calculations indicate that the electrical properties of the GNR are completely dependent on the adsorbed gas. Conductance as one of the most important electrical parameters as a sensing parameter is considered and analytically modelled. Additionally, gas adsorption effect on the conductance variation in the form of current-voltage characteristics is investigated which points out that gas adsorption dramatically influences electrical conductance of the GNR. Furthermore, to support the proposed analytical models, simulation study is carried out to investigate adsorption of O₂ and NH₃ gas molecules on the GNR surface. While, the charge transfer phenomenon that occurred as a result of molecular doping of the GNR is explored and the roll of band structure changes by adsorbents and their effects on the conductance and I-V characteristics of the GNRFET sensor is analysed. The comparison study with adopted experimental results is presented; also the I-V characteristics obtained from analytical modelling compared with the first principle calculations and close agreement is observed.     

A Sub-Cellular Viscoelastic Model for Cell Population Mechanics

Understanding the biomechanical properties and the effect of biomechanical force on epithelial cells is key to understanding how epithelial cells form uniquely shaped structures in two or three-dimensional space. Nevertheless, with the limitations and challenges posed by biological experiments at this scale, it becomes advantageous to use mathematical and ‘in silico’ (computational) models as an alternate solution. This paper introduces a single-cell-based model representing the cross section of a typical tissue. Each cell in this model is an individual unit containing several sub-cellular elements, such as the elastic plasma membrane, enclosed viscoelastic elements that play the role of cytoskeleton, and the viscoelastic elements of the cell nucleus. The cell membrane is divided into segments where each segment (or point) incorporates the cell''s interaction and communication with other cells and its environment. The model is capable of simulating how cells cooperate and contribute to the overall structure and function of a particular tissue; it mimics many aspects of cellular behavior such as cell growth, division, apoptosis and polarization. The model allows for investigation of the biomechanical properties of cells, cell-cell interactions, effect of environment on cellular clusters, and how individual cells work together and contribute to the structure and function of a particular tissue. To evaluate the current approach in modeling different topologies of growing tissues in distinct biochemical conditions of the surrounding media, we model several key cellular phenomena, namely monolayer cell culture, effects of adhesion intensity, growth of epithelial cell through interaction with extra-cellular matrix (ECM), effects of a gap in the ECM, tensegrity and tissue morphogenesis and formation of hollow epithelial acini. The proposed computational model enables one to isolate the effects of biomechanical properties of individual cells and the communication between cells and their microenvironment while simultaneously allowing for the formation of clusters or sheets of cells that act together as one complex tissue.     

Signaling and Mechanical Roles of E-cadherin

Abstract

The epithelium comprises an important tissue that lines the internal and external surfaces of metazoan organs. In order to organize sheets of epithelial cells into three-dimensional tissues, it requires the coordination of basic cellular processes such as polarity, adhesion, growth, and differentiation. Moreover, as a primary barrier to the external environment, epithelial tissues are often subjected to physical forces and damage. This critical barrier function dictates that these fundamental cellular processes are continually operational in order to maintain tissue homeostasis in the face of almost constant trauma and stress. A protein that is largely responsible for the organization and maintenance of epithelial tissues is the transmembrane protein, E-cadherin, found at the surface of epithelial cells. Though originally investigated for its essential role in mediating intercellular cohesion, its impact on a wide array of physiological processes underscores its fundamental contributions to tissue development and its perturbation in a variety of common diseases.