Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues.

The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to continuum methods based on partial differential equations, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for noncrystalline materials, it may still be used as a first-order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to two-dimensional cellular-scale models by assessing the mechanical behavior of model biological tissues, including crystalline (honeycomb) and noncrystalline reference states. The numerical procedure involves applying an affine deformation to the boundary cells and computing the quasistatic position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For center-based cell models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based cell models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete and continuous modeling, adaptation of atom-to-continuum techniques to biological tissues, and model classification

Some Temporal Factors Effecting Shuttle Sidman Avoidance Performance in Rats

A paper presented at the Kentucky Academy of Science at Northern Kentucky University by Francis H. Osborne and Howard Chandler in November of 1979 on the effects of variables on avoidance efficiency in a modified shuttle Sidman-avoidance task

Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues

The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to PDE-based continuum methods, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for non-crystalline materials, it may still be used as a first order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to 2-D cellular-scale models by assessing the mechanical behaviour of model biological tissues, including crystalline (honeycomb) and non-crystalline reference states. The numerical procedure consists in precribing an affine deformation on the boundary cells and computing the position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For centre-based models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete/continuous modelling, adaptation of atom-to-continuum (AtC) techniques to biological tissues and model classification

Solute transport within porous biofilms: diffusion or dispersion?

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behaviour by controllling nutrient supply, evacuation of waste products and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilmscale. We show that solute transport may be described via two coupled partial differential equations for the averaged concentrations, or telegrapher’s equations. These models are particularly relevant for chemical species, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterised by a second-order tensor whose components depend on: (1) the topology of the channels’ network; (2) the solute’s diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion-dominated, this analysis shows that dispersion effects may significantly contribute to transport

Cell morphology drives spatial patterning in microbial communities

The clearest phenotypic characteristic of microbial cells is their shape, but we do not understand how cell shape affects the dense communities, known as biofilms, where many microbes live. Here, we use individual-based modeling to systematically vary cell shape and study its impact in simulated communities. We compete cells with different cell morphologies under a range of conditions and ask how shape affects the patterning and evolutionary fitness of cells within a community. Our models predict that cell shape will strongly influence the fate of a cell lineage: we describe a mechanism through which coccal (round) cells rise to the upper surface of a community, leading to a strong spatial structuring that can be critical for fitness. We test our predictions experimentally using strains of Escherichia coli that grow at a similar rate but differ in cell shape due to single amino acid changes in the actin homolog MreB. As predicted by our model, cell types strongly sort by shape, with round cells at the top of the colony and rod cells dominating the basal surface and edges. Our work suggests that cell morphology has a strong impact within microbial communities and may offer new ways to engineer the structure of synthetic communities

Hydrodynamic dispersion within porous biofilms

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport

A parallel implementation of an off-lattice individual-based model of multicellular populations

As computational models of multicellular populations include ever more detailed descriptions of biophysical and biochemical processes, the computational cost of simulating such models limits their ability to generate novel scientific hypotheses and testable predictions. While developments in microchip technology continue to increase the power of individual processors, parallel computing offers an immediate increase in available processing power. To make full use of parallel computing technology, it is necessary to develop specialised algorithms. To this end, we present a parallel algorithm for a class of off-lattice individual-based models of multicellular populations. The algorithm divides the spatial domain between computing processes and comprises communication routines that ensure the model is correctly simulated on multiple processors. The parallel algorithm is shown to accurately reproduce the results of a deterministic simulation performed using a pre-existing serial implementation. We test the scaling of computation time, memory use and load balancing as more processes are used to simulate a cell population of fixed size. We find approximate linear scaling of both speed-up and memory consumption on up to 32 processor cores. Dynamic load balancing is shown to provide speed-up for non-regular spatial distributions of cells in the case of a growing population

The dose makes the poison: have “field realistic” rates of exposure of bees to neonicotinoid insecticides been overestimated in laboratory studies?

Recent laboratory based studies have demonstrated adverse sub-lethal effects of neonicotinoid insecticides on honey bees and bumble bees, and these studies have been influential in leading to a European Union moratorium on the use of three neonicotinoids, clothianidin, imidacloprid, and thiamethoxam on “bee attractive” crops. Yet so far, these same effects have not been observed in field studies. Here we review the three key dosage factors (concentration, duration and choice) relevant to field conditions, and conclude that these have probably been over estimated in many laboratory based studies

An integrative computational model for intestinal tissue renewal

Objectives\ud \ud The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation.\ud \ud Methods\ud \ud At the subcellular level, deterministic models characterise molecular networks, such as cell-cycle control and Wnt signalling. The output of these models determines the behaviour of each epithelial cell in response to intra-, inter- and extracellular cues. The modular nature of the model enables us to easily modify individual assumptions and analyse their effects on the system as a whole.\ud \ud Results\ud \ud We perform virtual microdissection and labelling-index experiments, evaluate the impact of various model extensions, obtain new insight into clonal expansion in the crypt, and compare our predictions with recent mitochondrial DNA mutation data. \ud \ud Conclusions\ud \ud We demonstrate that relaxing the assumption that stem-cell positions are fixed enables clonal expansion and niche succession to occur. We also predict that the presence of extracellular factors near the base of the crypt alone suffices to explain the observed spatial variation in nuclear beta-catenin levels along the crypt axis

A process-based model of conifer forest structure and function with special emphasis on leaf lifespan

We describe the University of Sheffield Conifer Model (USCM), a process-based approach for simulating conifer forest carbon, nitrogen, and water fluxes by up-scaling widely applicable relationships between leaf lifespan and function. The USCM is designed to predict and analyze the biogeochemistry and biophysics of conifer forests that dominated the ice-free high-latitude regions under the high pCO2 “greenhouse” world 290–50 Myr ago. It will be of use in future research investigating controls on the contrasting distribution of ancient evergreen and deciduous forests between hemispheres, and their differential feedbacks on polar climate through the exchange of energy and materials with the atmosphere. Emphasis is placed on leaf lifespan because this trait can be determined from the anatomical characteristics of fossil conifer woods and influences a range of ecosystem processes. Extensive testing of simulated net primary production and partitioning, leaf area index, evapotranspiration, nitrogen uptake, and land surface energy partitioning showed close agreement with observations from sites across a wide climatic gradient. This indicates the generic utility of our model, and adequate representation of the key processes involved in forest function using only information on leaf lifespan, climate, and soils