Human NK cells differ more in their KIR2DL1-dependent thresholds for HLA-Cw6-mediated inhibition than in their maximal killing capacity

In this study we have addressed the question of how activation and inhibition of human NK cells is regulated by the expression level of MHC class I protein on target cells. Using target cell transfectants sorted to stably express different levels of the MHC class I protein HLA-Cw6, we show that induction of degranulation and that of IFN-γ secretion are not correlated. In contrast, the inhibition of these two processes by MHC class-I occurs at the same level of class I MHC protein. Primary human NK cell clones were found to differ in the amount of target MHC class I protein required for their inhibition, rather than in their maximum killing capacity. Importantly, we show that KIR2DL1 expression determines the thresholds (in terms of MHC I protein levels) required for NK cell inhibition, while the expression of other receptors such as LIR1 is less important. Furthermore, using mathematical models to explore the dynamics of target cell killing, we found that the observed delay in target cell killing is exhibited by a model in which NK cells require some activation or priming, such that each cell can lyse a target cell only after being activated by a first encounter with the same or a different target cell, but not by models which lack this feature.     

Neutral biogeography of phylogenetically structured interaction networks

Little is known about how biogeographic processes affect the dynamics of species interactions in space and time, although it is widely accepted that they drive community assemblage. In functional interactions, such as pollination and seed dispersal, species that share common ancestry tend to retain a common number of interactions and interact with similar sets of species, a pattern more commonly observed for animals than plants. On the one hand, the most coherent explanation for the phylogenetic structure of pollination and seed dispersal networks is that species retain ecological traits over evolution, which would cause the conservation of interaction partners. On the other hand, fundamental processes of biodiversity, such as dispersal and evolutionary rates seem to have important roles shaping the observed phylogenetic structure of mutualistic networks, but no model has been created to study the effect of these processes in the phylogenetic structure of mutualistic interactions. Here, we developed a stochastic simulation model to study the evolution of two interacting groups of species, which evolve independently over the same geographical domain. In our model, individuals of the same interaction group share ecological traits, whereas individuals of different trophic groups are ecologically distinct. We show that even in the absence of ecological differences between individuals, and disregarding any conservation of phenotypical and phenological traits between species, the interplay of dispersal and speciation is still a major driver of complex phylogenetic structure of functional interactions, such as pollination and seed dispersal.     

Relationships between migration rates and landscape resistance assessed using individual-based simulations

Linking landscape effects on gene flow to processes such as dispersal and mating is essential to provide a conceptual foundation for landscape genetics. It is particularly important to determine how classical population genetic models relate to recent individual-based landscape genetic models when assessing individual movement and its influence on population genetic structure. We used classical Wright-Fisher models and spatially explicit, individual-based, landscape genetic models to simulate gene flow via dispersal and mating in a series of landscapes representing two patches of habitat separated by a barrier. We developed a mathematical formula that predicts the relationship between barrier strength (i.e., permeability) and the migration rate (m) across the barrier, thereby linking spatially explicit landscape genetics to classical population genetics theory. We then assessed the reliability of the function by obtaining population genetics parameters (m, F(ST) ) using simulations for both spatially explicit and Wright-Fisher simulation models for a range of gene flow rates. Next, we show that relaxing some of the assumptions of the Wright-Fisher model can substantially change population substructure (i.e., F(ST) ). For example, isolation by distance among individuals on each side of a barrier maintains an F(ST) of ～0.20 regardless of migration rate across the barrier, whereas panmixia on each side of the barrier results in an F(ST) that changes with m as predicted by classical population genetics theory. We suggest that individual-based, spatially explicit modelling provides a general framework to investigate how interactions between movement and landscape resistance drive population genetic patterns and connectivity across complex landscapes.     

Quantitative modeling perspectives on the ErbB system of cell regulatory processes

The complexities of the processes involved in ErbB-mediated regulation of cellular phenotype are broadly appreciated, so much so that it might be reasonably argued that this highly studied system provided significant impetus for the systems perspective on cell signaling processes in general. Recent years have seen major advances in the level of characterization of the ErbB system as well as our ability to make measurements of the system. This new data provides significant new insight, while at the same time creating new challenges for making quantitative statements and predictions with certainty. Here, we discuss recent advances in each of these directions and the interplay between them, with a particular focus on quantitative modeling approaches to interpret data and provide predictive power. Our discussion follows the sequential order of ErbB pathway activation, beginning with considerations of receptor/ligand interactions and dynamics, proceeding to the generation of intracellular signals, and ending with determination of cellular phenotype. As discussed herein, these processes become increasingly difficult to describe or interpret in terms of traditional models, and we review emerging methodologies to address this complexity.     

BIO-LGCA: A cellular automaton modelling class for analysing collective cell migration

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics—understood as population behaviour arising from the interplay of the constituting discrete cells—can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments.     

Effects of perceptual and movement ranges on joint predator–prey distributions

We developed a spatially‐explicit individual‐based model to study how limited perceptual and movement ranges affect spatial predator–prey interactions. Earlier models of ‘predator–prey space games’ were often developed by modifying ideal free distribution models, which are spatially‐implicit and also assume that individuals are omniscient, although some more recent models have relaxed these assumptions. We found that under some conditions, the spatially‐explicit model generated similar predictions to previous models. However, the model showed that limited range in a spatially‐explicit context generated different predictions when 1) predator density and range are both small, and 2) when the predator movement range varied while the prey range was small. The model suggests that the differences were the result of 1) movement range changing the value of information sources and thus changing the behavior of individual predators and prey and 2) movement range limiting the ability of individuals to exploit the environment.     

Population interaction structure and the coexistence of bacterial strains playing ‘rock–paper–scissors’

The simplest example of non‐transitive competition is the game rock–paper–scissors (RPS), which exhibits characteristic cyclic strategy replacement: paper beats rock, which in turn beats scissors, which in turn beats paper. In addition to its familiar use in understanding human decision‐making, rock–paper–scissors is also played in many biological systems. Among other reasons, this is important because it potentially provides a mechanism whereby species‐ or strain coexistence can occur in the face of intense competition. Kerr et al. (2002, Nature 418: 171–174) use complementary experiments and simulations to show that RPS‐playing toxic, resistant, and susceptible E. coli bacteria can coexist when interactions between the strains are spatially explicit. This raises the question of whether limited interactions associated with space are sufficient to allow strain coexistence, or whether space per se is crucial. I approach this question by extending the Kerr et al. model to include different (aspatial) population network structures with the same degree distributions as corresponding spatial lattice models. I show that the coexistence that occurs for some parameter combinations when simulated bacterial strains compete on lattices is absent when they compete on random regular graphs. Further, considering small‐world networks of intermediate ‘quenched randomness’ between lattices and random regular graphs, I show that only small deviations from pure spatial interactions are sufficient to prevent strain coexistence. These results emphasize the explicit role of space, rather than merely limited interactions, as being decisive in allowing the coexistence of toxic, resistant, and susceptible strains in this model system.     

Relatedness in spatially structured populations with empty sites: An approach based on spatial moment equations

Taking into account the interplay between spatial ecological dynamics and selection is a major challenge in evolutionary ecology. Although inclusive fitness theory has proven to be a very useful tool to unravel the interactions between spatial genetic structuring and selection, applications of the theory usually rely on simplifying demographic assumptions. In this paper, I attempt to bridge the gap between spatial demographic models and kin selection models by providing a method to compute approximations for relatedness coefficients in a spatial model with empty sites. Using spatial moment equations, I provide an approximation of nearest-neighbour relatedness on random regular networks, and show that this approximation performs much better than the ordinary pair approximation. I discuss the connection between the relatedness coefficients I define and those used in population genetics, and sketch some potential extensions of the theory.     

Solvable models of neighbor-dependent substitution processes

We prove that a wide class of Markov models of neighbor-dependent substitution processes on the integer line is solvable. This class contains some models of nucleotidic substitutions recently introduced and studied empirically by molecular biologists. We show that the polynucleotidic frequencies at equilibrium solve some finite-size linear systems. This provides, for the first time up to our knowledge, explicit and algebraic formulas for the stationary frequencies of non-degenerate neighbor-dependent models of DNA substitutions. Furthermore, we show that the dynamics of these stochastic processes and their distribution at equilibrium exhibit some stringent, rather unexpected, independence properties. For example, nucleotidic sites at distance at least three evolve independently, and all the sites, when encoded as purines and pyrimidines, evolve independently.     

From heterogeneous healthcare data to disease-specific biomarker networks: A hierarchical Bayesian network approach

In this work, we introduce an entirely data-driven and automated approach to reveal disease-associated biomarker and risk factor networks from heterogeneous and high-dimensional healthcare data. Our workflow is based on Bayesian networks, which are a popular tool for analyzing the interplay of biomarkers. Usually, data require extensive manual preprocessing and dimension reduction to allow for effective learning of Bayesian networks. For heterogeneous data, this preprocessing is hard to automatize and typically requires domain-specific prior knowledge. We here combine Bayesian network learning with hierarchical variable clustering in order to detect groups of similar features and learn interactions between them entirely automated. We present an optimization algorithm for the adaptive refinement of such group Bayesian networks to account for a specific target variable, like a disease. The combination of Bayesian networks, clustering, and refinement yields low-dimensional but disease-specific interaction networks. These networks provide easily interpretable, yet accurate models of biomarker interdependencies. We test our method extensively on simulated data, as well as on data from the Study of Health in Pomerania (SHIP-TREND), and demonstrate its effectiveness using non-alcoholic fatty liver disease and hypertension as examples. We show that the group network models outperform available biomarker scores, while at the same time, they provide an easily interpretable interaction network.     

Beyond dual-lattice models: Incorporating plant strategies when modeling the interplay between facilitation and competition along environmental severity gradients

We introduce a spatially explicit model that evaluates how the trade-offs between the life strategies of two interacting plant species affect the outcome of their interaction along environmental severity gradients. In our model, we represent the landscape as a two-dimensional lattice, with environmental severity increasing from left to right. Two species with different strategies, a competitor and a stress-tolerant, interact in the lattice. We find that facilitation expands the realized niche of the competitor into harsh environments by suppressing the stress-tolerant species. Most of their coexisting range is dominated by a positive effect of one species on another, with a reciprocal negative effect from the species receiving the benefits on its benefactor (“+, −”), whereas mutualistic (“+, +”) interactions are only found in the harshest part of the environmental gradient. Contrarily as assumed by models commonly used in facilitation research (e.g. dual-lattice models), our results indicate that “+, +” interactions are not dominant, and that their differences with “+, −” interactions along environmental severity gradients depend on the strategies of the interacting species. By integrating the trade-off between competitive ability and stress tolerance, our model provides a new framework to investigate the interplay of facilitative and competitive interactions along environmental gradients and their impacts on processes such as population dynamics and community organization.     

Local Competition and Metapopulation Processes Drive Long-Term Seagrass-Epiphyte Population Dynamics

It is well known that ecological processes such as population regulation and natural enemy interactions potentially occur over a range of spatial scales, and there is a substantial body of literature developing theoretical understanding of the interplay between these processes. However, there are comparatively few studies quantifying the long-term effects of spatial scaling in natural ecosystems. A key challenge is that trophic complexity in real-world biological communities quickly obscures the signal from a focal process. Seagrass meadows provide an excellent opportunity in this respect: in many instances, seagrasses effectively form extensive natural monocultures, in which hypotheses about endogenous dynamics can be formulated and tested. We present amongst the longest unbroken, spatially explict time series of seagrass abundance published to date. Data include annual measures of shoot density, total above-ground abundance, and associated epiphyte cover from five Zostera marina meadows distributed around the Isles of Scilly, UK, from 1996 to 2011. We explore empirical patterns at the local and metapopulation scale using standard time series analysis and develop a simple population dynamic model, testing the hypothesis that both local and metapopulation scale feedback processes are important. We find little evidence of an interaction between scales in seagrass dynamics but that both scales contribute approximately equally to observed local epiphyte abundance. By quantifying the long-term dynamics of seagrass-epiphyte interactions we show how measures of density and extent are both important in establishing baseline information relevant to predicting responses to environmental change and developing management plans. We hope that this study complements existing mechanistic studies of physiology, genetics and productivity in seagrass, whilst highlighting the potential of seagrass as a model ecosystem. More generally, this study provides a rare opportunity to test some of the predictions of ecological theory in a natural ecosystem of global conservation and economic value.     

Epithelial topology

It is universally accepted that genetic control over basic aspects of cell and molecular biology is the primary organizing principle in development and homeostasis of living systems. However, instances do exist where important aspects of biological order arise without explicit genetic instruction, emerging instead from simple physical principles, stochastic processes, or the complex self-organizing interaction between random and seemingly unrelated parts. Being mostly resistant to direct genetic dissection, the analysis of such emergent processes falls into a grey area between mathematics, physics and molecular cell biology and therefore remains very poorly understood. We recently proposed a mathematical model predicting the emergence of a specific non-Gaussian distribution of polygonal cell shapes from the stochastic cell division process in epithelial cell sheets; this cell shape distribution appears to be conserved across a diverse set of animals and plants.1 The use of such topological models to study the process of cellular morphogenesis has a long history, starting almost a century ago, and many insights from those original works influence current experimental studies. Here we review current and past literature on this topic while exploring some new ideas on the origins and implications of topological order in proliferating epithelia.     

Biomimetic membrane systems to study cellular organization

During many cellular processes such as cell division, polarization and motility, the plasma membrane does not only represent a passive physical barrier, but also provides a highly dynamic platform for the interplay between lipids, membrane binding proteins and cytoskeletal elements. Even though many regulators of these interactions are known, their mutual interdependence appears to be highly complex and difficult to study in a living cell. Over the past few years, in vitro studies on membrane–cytoskeleton interactions using biomimetic membranes turned out to be extremely helpful to get better mechanistic insight into the dynamics of these processes. In this review, we discuss some of the recent developments using in vitro assays to dissect the role of the players involved: lipids in the membrane, proteins binding to membranes and proteins binding to membrane proteins. We also summarize advantages and disadvantages of supported lipid bilayers as model membrane.     

The common patterns of nature

We typically observe large‐scale outcomes that arise from the interactions of many hidden, small‐scale processes. Examples include age of disease onset, rates of amino acid substitutions and composition of ecological communities. The macroscopic patterns in each problem often vary around a characteristic shape that can be generated by neutral processes. A neutral generative model assumes that each microscopic process follows unbiased or random stochastic fluctuations: random connections of network nodes; amino acid substitutions with no effect on fitness; species that arise or disappear from communities randomly. These neutral generative models often match common patterns of nature. In this paper, I present the theoretical background by which we can understand why these neutral generative models are so successful. I show where the classic patterns come from, such as the Poisson pattern, the normal or Gaussian pattern and many others. Each classic pattern was often discovered by a simple neutral generative model. The neutral patterns share a special characteristic: they describe the patterns of nature that follow from simple constraints on information. For example, any aggregation of processes that preserves information only about the mean and variance attracts to the Gaussian pattern; any aggregation that preserves information only about the mean attracts to the exponential pattern; any aggregation that preserves information only about the geometric mean attracts to the power law pattern. I present a simple and consistent informational framework of the common patterns of nature based on the method of maximum entropy. This framework shows that each neutral generative model is a special case that helps to discover a particular set of informational constraints; those informational constraints define a much wider domain of non‐neutral generative processes that attract to the same neutral pattern.     

The shaping of intrinsic membrane potential oscillations: positive/negative feedback,ionic resonance/amplification,nonlinearities and time scales

The generation of intrinsic subthreshold (membrane potential) oscillations (STOs) in neuronal models requires the interaction between two processes: a relatively fast positive feedback that favors changes in voltage and a slower negative feedback that opposes these changes. These are provided by the so-called resonant and amplifying gating variables associated to the participating ionic currents. We investigate both the biophysical and dynamic mechanisms of generation of STOs and how their attributes (frequency and amplitude) depend on the model parameters for biophysical (conductance-based) models having qualitatively different types of resonant currents (activating and inactivating) and an amplifying current. Combinations of the same types of ionic currents (same models) in different parameter regimes give rise to different types of nonlinearities in the voltage equation: quasi-linear, parabolic-like and cubic-like. On the other hand, combinations of different types of ionic currents (different models) may give rise to the same type of nonlinearities. We examine how the attributes of the resulting STOs depend on the combined effect of these resonant and amplifying ionic processes, operating at different effective time scales, and the various types of nonlinearities. We find that, while some STO properties and attribute dependencies on the model parameters are determined by the specific combinations of ionic currents (biophysical properties), and are different for models with different such combinations, others are determined by the type of nonlinearities and are common for models with different types of ionic currents. Our results highlight the richness of STO behavior in single cells as the result of the various ways in which resonant and amplifying currents interact and affect the generation and termination of STOs as control parameters change. We make predictions that can be tested experimentally and are expected to contribute to the understanding of how rhythmic activity in neuronal networks emerge from the interplay of the intrinsic properties of the participating neurons and the network connectivity.     

Integrating demography,dispersal and interspecific interactions into bird distribution models

Species’ ranges are primarily limited by the physiological (abiotic) tolerance of the species, described by their fundamental niche. Additionally, demographic processes, dispersal, and interspecific interactions with other species are shaping species distributions, resulting in the realised niche. Understanding the complex interplay between these drivers is vital for making robust biodiversity predictions to novel environments. Correlative species distribution models have been widely used to predict biodiversity response but also remain criticised, as they are not able to properly disentangle the abiotic and biotic drivers shaping species’ niches. Recent developments have thus focussed on 1) integrating demography and dispersal into species distribution models, and on 2) integrating interspecific interactions. Here, I review recent demographic and multi‐species modelling approaches and discuss critical aspects of these models that remain underexplored in general and in respect to birds, for example, the complex life histories of birds and other animals as well as the scale dependence of interspecific interactions. I conclude by formulating modelling guidelines for integrating the abiotic and biotic processes that limit species’ ranges, which will help to disentangle the complex roles of demography, dispersal and interspecific interactions in shaping species niches. Throughout, I pinpoint complexities of avian life cycles that are critical for consideration in the models and identify data requirements for operationalizing the different modelling steps.