3,724 research outputs found
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
On the Nature and Shape of Tubulin Trails: Implications on Microtubule Self-Organization
Microtubules, major elements of the cell skeleton are, most of the time, well
organized in vivo, but they can also show self-organizing behaviors in time
and/or space in purified solutions in vitro. Theoretical studies and models
based on the concepts of collective dynamics in complex systems,
reaction-diffusion processes and emergent phenomena were proposed to explain
some of these behaviors. In the particular case of microtubule spatial
self-organization, it has been advanced that microtubules could behave like
ants, self-organizing by 'talking to each other' by way of hypothetic (because
never observed) concentrated chemical trails of tubulin that are expected to be
released by their disassembling ends. Deterministic models based on this idea
yielded indeed like-looking spatio-temporal self-organizing behaviors.
Nevertheless the question remains of whether microscopic tubulin trails
produced by individual or bundles of several microtubules are intense enough to
allow microtubule self-organization at a macroscopic level. In the present
work, by simulating the diffusion of tubulin in microtubule solutions at the
microscopic scale, we measure the shape and intensity of tubulin trails and
discuss about the assumption of microtubule self-organization due to the
production of chemical trails by disassembling microtubules. We show that the
tubulin trails produced by individual microtubules or small microtubule arrays
are very weak and not elongated even at very high reactive rates. Although the
variations of concentration due to such trails are not significant compared to
natural fluctuations of the concentration of tubuline in the chemical
environment, the study shows that heterogeneities of biochemical composition
can form due to microtubule disassembly. They could become significant when
produced by numerous microtubule ends located in the same place. Their possible
formation could play a role in certain conditions of reaction. In particular,
it gives a mesoscopic basis to explain the collective dynamics observed in
excitable microtubule solutions showing the propagation of concentration waves
of microtubules at the millimeter scale, although we doubt that individual
microtubules or bundles can behave like molecular ants
Individual-based and continuum models of phenotypically heterogeneous growing cell populations
T.L. gratefully acknowledges support from the MIUR grant âDipartimenti di Eccellenza 2018-2022â (Project no. E11G18000350001). F.R.M. gratefully acknowledges support from the RSE Saltire Early Career Fellowship âMultiscale mathematical modelling of spatial eco-evolutionary cancer dynamicsâ (Fellowship No. 1879).Existing comparative studies between individual-based models of growing cell populations and their continuum counterparts have mainly been focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However, significant intercellular phenotypic variability is commonly observed in cellular systems. In light of these considerations, we develop here an individual-based model for the growth of phenotypically heterogeneous cell populations. In this model, the phenotypic state of each cell is described by a structuring variable that captures intercellular variability in cell proliferation and migration rates. The model tracks the spatial evolutionary dynamics of single cells, which undergo pressure-dependent proliferation, heritable phenotypic changes and directional movement in response to pressure differentials. We formally show that the continuum limit of this model comprises a non-local partial differential equation for the cell population density function, which generalises earlier models of growing cell populations. We report on the results of numerical simulations of the individual-based model which illustrate how proliferation-migration tradeoffs shaping the evolutionary dynamics of single cells can lead to the formation, at the population level, of travelling waves whereby highly-mobile cells locally dominate at the invasive front, while more-proliferative cells are found at the rear. Moreover, we demonstrate that there is an excellent quantitative agreement between these results and the results of numerical simulations and formal travelling-wave analysis of the continuum model, when sufficiently large cell numbers are considered. We also provide numerical evidence of scenarios in which the predictions of the two models may differ due to demographic stochasticity, which cannot be captured by the continuum model. This indicates the importance of integrating individual-based and continuum approaches when modelling the growth of phenotypically heterogeneous cell populations.Publisher PDFPeer reviewe
A novel theoretical and experimental approach permits a systems view on stochastic intracellular Ca 2+ signalling
Ca(2+)-Ionen sind ein universeller sekundĂ€rer Botenstoff in eukaryotischen Zellen und ĂŒbertragen Information durch wiederholte, kurzzeitige Erhöhungen der cytosolischen Ca(2+)-Konzentration (Ca(2+) Spikes). Ein bekannter Mechanismus, der solche Ca(2+)-Signale erzeugt, beinhaltet die Freisetzung von Ca(2+)-Ionen aus dem endoplasmatischen Retikulum durch IP3-sensitive KanĂ€le. Puffs sind elementare Ereignisse der Ca(2+)-Freisetzung durch einzelne Cluster von Ca(2+)-KanĂ€len. IntrazellulĂ€re Ca(2+)-Dynamik ist ein stochastisches System, allerdings konnte bisher keine vollstĂ€ndige stochastische Theorie entwickelt werden. Die vorliegende Dissertation formuliert die Theorie mit Hilfe von Interpuffintervallen und PufflĂ€ngen, da diese GröĂen im Gegensatz zu den Eigenschaften der EinzelkanĂ€le direkt messbar sind. Die Theorie reproduziert das typische Spektrum bekannter Ca(2+)-Signale. Die Signalform und das durchschnittliche Interspikeinterval (ISI) hĂ€ngen sensitiv von den genauen Eigenschaften und der rĂ€umlichen Anordnung der Cluster ab. Im Gegensatz dazu hĂ€ngt die Beziehung zwischen Mittelwert und Standardabweichung der ISI weder von den Clustereigenschaften noch von der rĂ€umlichen Anordnung ab, sondern wird lediglich von globalen Feedbackprozessen im Ca(2+)-Signalweg reguliert. Diese Beziehung ist essentiell fĂŒr die Funktion des Signalwegs, da sie trotz der ZufĂ€lligkeit der ISI eine Frequenzkodierung ermöglicht und den maximalen Informationsgehalt der Spikesequenzen bestimmt. Neben der theoretischen Analyse enthĂ€lt die vorliegende Arbeit auch experimentelle Puff- und Spikemessungen an lebenden HEK-Zellen, die wichtige Ergebnisse verifizieren. Insgesamt wird durch die integrierte theoretische und experimentelle Untersuchung auf verschiedenen Stufen molekularer Organisation gezeigt, dass stochastische Ca(2+)-Signale verlĂ€ssliche InformationstrĂ€ger sind, und dass der Mechanismus durch globalen Feedback an die spezifischen Anforderungen eines Signalpfads angepasst werden kann.Ca(2+) is a universal second messenger in eukaryotic cells transmitting information through sequences of concentration spikes. A prominent mechanism to generate these spikes involves Ca(2+) release from the endoplasmic reticulum Ca(2+) store via IP3-sensitive channels. Puffs are elemental events of IP3-induced Ca(2+) release through single clusters of channels. Intracellular Ca(2+) dynamics are a stochastic system, but a complete stochastic theory has not been developed yet. As a new concept, this thesis formulates the theory in terms of interpuff interval and puff duration distributions, since unlike the properties of individual channels, they can be measured in vivo. This leads to a non-Markovian description of system dynamics, for which analytical solutions and efficient stochastic simulation techniques are derived. The theory reproduces the typical spectrum of Ca(2+) signals. Signal form and average interspike interval (ISI) depend sensitively on detailed properties and spatial arrangement of clusters. In difference to that, the relation between the average and the standard deviation of ISIs does not depend on cluster properties and cluster arrangement, and it is robust with respect to cell variability. It can only be regulated by global feedback processes in the Ca(2+) signalling pathway. That relation is essential for pathway function, since it ensures frequency encoding despite the randomness of ISIs and determines the maximal spike train information content. Apart from the theoretical investigation, this thesis verifies key results by live cell imaging of Ca(2+) spikes and puffs in HEK cells. Hence, this work comprises a systems level investigation of Ca(2+) signals, integrating data and theory from different levels of molecular organisation. It demonstrates that stochastic Ca(2+) signals can transmit information reliably, and that the mechanism can be adapted to the specific needs of a pathway by global feedback
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