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

Using a probabilistic approach to derive a two-phase model of flow-induced cell migration

Interstitial fluid flow is a feature of many solid tumours. In vitro experiments have shown that such fluid flow can direct tumour cell movement upstream or downstream depending on the balance between the competing mechanisms of tensotaxis and autologous chemotaxis. In this work we develop a probabilistic-continuum, two-phase model for cell migration in response to interstitial flow. We use a Fokker-Planck type equation for the cell-velocity probability density function, and model the flow-dependent mechanochemical stimulus as a forcing term which biases cell migration upstream and downstream. Using velocity-space averaging, we reformulate the model as a system of continuum equations for the spatio-temporal evolution of the cell volume fraction and flux, in response to forcing terms which depend on the local direction and magnitude of the mechanochemical cues. We specialise our model to describe a one-dimensional cell layer subject to fluid flow. Using a combination of numerical simulations and asymptotic analysis, we delineate the parameter regime where transitions from downstream to upstream cell migration occur. As has been observed experimentally, the model predicts downstream-oriented, chemotactic migration at low cell volume fractions, and upstream-oriented, tensotactic migration at larger volume fractions. We show that the locus of the critical volume fraction, at which the system transitions from downstream to upstream migration, is dominated by the ratio of the rate of chemokine secretion and advection. Our model predicts that, because the tensotactic stimulus depends strongly on the cell volume fraction, upstream migration occurs only transiently when the cells are initially seeded, and transitions to downstream migration occur at later times due to the dispersive effect of cell diffusion.Comment: 20 pages, 6 figures. Submitted to Biophysical Journa

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

Abnormal morphology biases haematocrit distribution in tumour vasculature and contributes to heterogeneity in tissue oxygenation

Oxygen heterogeneity in solid tumors is recognized as a limiting factor for therapeutic efficacy. This heterogeneity arises from the abnormal vascular structure of the tumor, but the precise mechanisms linking abnormal structure and compromised oxygen transport are only partially understood. In this paper, we investigate the role that red blood cell (RBC) transport plays in establishing oxygen heterogeneity in tumor tissue. We focus on heterogeneity driven by network effects, which are challenging to observe experimentally due to the reduced fields of view typically considered. Motivated by our findings of abnormal vascular patterns linked to deviations from current RBC transport theory, we calculated average vessel lengths L⎯⎯ and diameters d⎯⎯ from tumor allografts of three cancer cell lines and observed a substantial reduction in the ratio λ=L⎯⎯/d⎯⎯ compared to physiological conditions. Mathematical modeling reveals that small values of the ratio λ (i.e., λ<6 ) can bias hematocrit distribution in tumor vascular networks and drive heterogeneous oxygenation of tumor tissue. Finally, we show an increase in the value of λ in tumor vascular networks following treatment with the antiangiogenic cancer agent DC101. Based on our findings, we propose λ as an effective way of monitoring the efficacy of antiangiogenic agents and as a proxy measure of perfusion and oxygenation in tumor tissue undergoing antiangiogenic treatment

Ten Simple Rules for Effective Computational Research

<p>Ten Simple Rules for Effective Computational Research</p

Chaste: an open source C++ library for computational physiology and biology

Chaste - Cancer, Heart And Soft Tissue Environment - is an open source C++ library for the computational simulation of mathematical models developed for physiology and biology. Code development has been driven by two initial applications: cardiac electrophysiology and cancer development. A large number of cardiac electrophysiology studies have been enabled and performed, including high performance computational investigations of defibrillation on realistic human cardiac geometries. New models for the initiation and growth of tumours have been developed. In particular, cell-based simulations have provided novel insight into the role of stem cells in the colorectal crypt. Chaste is constantly evolving and is now being applied to a far wider range of problems. The code provides modules for handling common scientific computing components, such as meshes and solvers for ordinary and partial differential equations (ODEs/PDEs). Re-use of these components avoids the need for researchers to "re-invent the wheel" with each new project, accelerating the rate of progress in new applications. Chaste is developed using industrially-derived techniques, in particular test-driven development, to ensure code quality, re-use and reliability. In this article we provide examples that illustrate the types of problems Chaste can be used to solve, which can be run on a desktop computer. We highlight some scientific studies that have used or are using Chaste, and the insights they have provided. The source code, both for specific releases and the development version, is available to download under an open source Berkeley Software Distribution (BSD) licence at http://www.cs.ox.ac.uk/chaste, together with details of a mailing list and links to documentation and tutorials

Chaste : Cancer, Heart and Soft Tissue Environment

Funding: UK Engineering and Physical Sciences Research Council [grant number EP/N509711/1 (J.K.)].Chaste (Cancer, Heart And Soft Tissue Environment) is an open source simulation package for the numerical solution of mathematical models arising in physiology and biology. To date, Chaste development has been driven primarily by applications that include continuum modelling of cardiac electrophysiology (‘Cardiac Chaste’), discrete cell-based modelling of soft tissues (‘Cell-based Chaste’), and modelling of ventilation in lungs (‘Lung Chaste’). Cardiac Chaste addresses the need for a high-performance, generic, and verified simulation framewor kfor cardiac electrophysiology that is freely available to the scientific community. Cardiac chaste provides a software package capable of realistic heart simulations that is efficient, rigorously tested, and runs on HPC platforms. Cell-based Chaste addresses the need for efficient and verified implementations of cell-based modelling frameworks, providing a set of extensible tools for simulating biological tissues. Computational modelling, along with live imaging techniques, plays an important role in understanding the processes of tissue growth and repair. A wide range of cell-based modelling frameworks have been developed that have each been successfully applied in a range of biological applications. Cell-based Chaste includes implementations of the cellular automaton model, the cellular Potts model, cell-centre models with cell representations as overlapping spheres or Voronoi tessellations, and the vertex model. Lung Chaste addresses the need for a novel, generic and efficient lung modelling software package that is both tested and verified. It aims to couple biophysically-detailed models of airway mechanics with organ-scale ventilation models in a package that is freely available to the scientific community.Publisher PDFPeer reviewe

Diez reglas sencillas para una exitosa colaboración transdisciplinar

El presente artículo es la versión en castellano de la publicación: KNAPP, B.; BARDENET, R.; BERNABEU, M.O.; BORDAS, R.; BRUNA, M.; CALDERHEAD, B. ET AL. (2015) “Ten Simple Rules for a Successful Cross-Disciplinary Collaboration”. PLoS Comput Biol 11(4): e1004214, disponible en: https://doi.org/10.1371/journal.pcbi.1004214. La traducción, autorizada por la entidad editora, ha sido llevada a cabo por Ona Lorda Roure y Leila Adim, colaboradoras del Instituto de Investigación TransJus y supervisada por el Dr. Juli Ponce Solé, Director del TransJus. En la misma se han incluido algunas notas aclaratorias para el lector en español, así como bibliografía complementaria en español.[spa] En el auge de las colaboraciones interdisciplinarias entre los distintos campos científicos, la transdisciplinariedad se presenta como la clave para encontrar soluciones a una variedad de problemas globales. Este trabajo, situado en el marco de la biología informática, se centra en exponer una lista extensa de reglas y consejos útiles para lograr una exitosa sinergia entre los varios colaboradores de un proyecto transdisciplinar. Se trata, de hecho, de una guía que pretende dirigirse tanto a investigadores noveles como a aquellos investigadores consolidados que se adentran en un espacio transdisciplinar por primera vez. En particular, este trabajo expone los beneficios principales de establecer una colaboración transdisciplinar, así como los problemas que de ella puedan surgir.[cat] En l'auge de les col·laboracions interdisciplinàries entre els diferents camps científics, la transdisciplinarietat es presenta com la clau per trobar solucions a una varietat de problemes globals. Aquest treball, situat en el marc de la biologia informàtica, es centra en exposar una llista extensa de regles i consells útils per aconseguir una reeixida sinergia entre els varis col·laboradors d'un projecte transdisciplinar. Es tracta, de fet, d'una guia que pretén dirigir-se tant a recercadors novells com a aquells recercadors consolidats que s'endinsen en un espai transdisciplinar per primera vegada. En particular, aquest treball exposa els beneficis principals d'establir una col·laboració transdisciplinar, així com els problemes que d'ella puguin sorgir.[eng] At a time of increasing interdisciplinary collaboration between different scientific fields, cross-disciplinarity represents a key for finding solutions to a variety of global problems. This work, located within the framework of computer biology, focuses on exposing an extensive list of rules and useful tips to achieve a successful synergy among the various collaborators of a transdisciplinary project. It is, in fact, a guide aimed at addressing both first-time researchers and consolidated researchers who enter a transdisciplinary space for the first time. In particular, this work exposes the main benefits of establishing a cross-disciplinary collaboration, as well as the problems that may arise from it

Comparing individual-based approaches to modelling the self-organization of multicellular tissues.

The coordinated behaviour of populations of cells plays a central role in tissue growth and renewal. Cells react to their microenvironment by modulating processes such as movement, growth and proliferation, and signalling. Alongside experimental studies, computational models offer a useful means by which to investigate these processes. To this end a variety of cell-based modelling approaches have been developed, ranging from lattice-based cellular automata to lattice-free models that treat cells as point-like particles or extended shapes. However, it remains unclear how these approaches compare when applied to the same biological problem, and what differences in behaviour are due to different model assumptions and abstractions. Here, we exploit the availability of an implementation of five popular cell-based modelling approaches within a consistent computational framework, Chaste (http://www.cs.ox.ac.uk/chaste). This framework allows one to easily change constitutive assumptions within these models. In each case we provide full details of all technical aspects of our model implementations. We compare model implementations using four case studies, chosen to reflect the key cellular processes of proliferation, adhesion, and short- and long-range signalling. These case studies demonstrate the applicability of each model and provide a guide for model usage

Bayesian calibration, validation and uncertainty quantification for predictive modelling of tumour growth: a tutorial

In this work we present a pedagogical tumour growth example, in which we apply calibration and validation techniques to an uncertain, Gompertzian model of tumour spheroid growth. The key contribution of this article is the discussion and application of these methods (that are not commonly employed in the field of cancer modelling) in the context of a simple model, whose deterministic analogue is widely known within the community. In the course of the example we calibrate the model against experimental data that is subject to measurement errors, and then validate the resulting uncertain model predictions. We then analyse the sensitivity of the model predictions to the underlying measurement model. Finally, we propose an elementary learning approach for tuning a threshold parameter in the validation procedure in order to maximize predictive accuracy of our validated model