How domain growth is implemented determines the long-term behavior of a cell population through its effect on spatial correlations

AbstractDomain growth plays an important role in many biological systems, and so the inclusion of domain growth in models of these biological systems is important to understanding how these biological systems function. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations in a continuum approximation of a lattice-based model of cell motility and proliferation. We show that, depending on the way in which domain growth is implemented, different steady-state densities are predicted for an agent population. Furthermore, we demonstrate that the way in which domain growth is implemented can result in the evolution of the agent density depending on the size of the domain. Continuum approximations that ignore spatial correlations cannot capture these behaviours, while those that account for spatial correlations do. These results will be of interest to researchers in developmental biology, as they suggest that the nature of domain growth can determine the characteristics of cell populations.

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Long-term culture of a cell population from Siberian sturgeon (Acipenser baerii) head kidney

Fish Physiology and Biochemistry ◽

10.1007/s10695-007-9196-8 ◽

2008 ◽

Vol 34 (4) ◽

pp. 367-372 ◽

Cited By ~ 11

Author(s):

P. Ciba ◽

S. Schicktanz ◽

E. Anders ◽

E. Siegl ◽

A. Stielow ◽

...

Keyword(s):

Cell Population ◽

Head Kidney ◽

Siberian Sturgeon ◽

Acipenser Baerii ◽

Long Term Culture ◽

A Cell

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A Stochastic Model for Virus Growth in a Cell Population

Journal of Applied Probability ◽

10.1239/jap/1409932661 ◽

2014 ◽

Vol 51 (3) ◽

pp. 599-612 ◽

Cited By ~ 1

Author(s):

J. E. Björnberg ◽

T. Britton ◽

E. I. Broman ◽

E. Natan

Keyword(s):

Stochastic Model ◽

Host Cell ◽

Cell Population ◽

Branching Process ◽

Virus Population ◽

Virus Growth ◽

Optimal Balance ◽

Large Numbers ◽

A Cell

In this work we introduce a stochastic model for the spread of a virus in a cell population where the virus has two ways of spreading: either by allowing its host cell to live and duplicate, or by multiplying in large numbers within the host cell, causing the host cell to burst and thereby let the virus enter new uninfected cells. The model is a kind of interacting Markov branching process. We focus in particular on the probability that the virus population survives and how this depends on a certain parameter λ which quantifies the ‘aggressiveness’ of the virus. Our main goal is to determine the optimal balance between aggressive growth and long-term success. Our analysis shows that the optimal strategy of the virus (in terms of survival) is obtained when the virus has no effect on the host cell's life cycle, corresponding to λ = 0. This is in agreement with experimental data about real viruses.

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Variable species densities are induced by volume exclusion interactions upon domain growth

10.1101/061341 ◽

2016 ◽

Author(s):

Robert J. H. Ross ◽

C. A. Yates ◽

R. E. Baker

Keyword(s):

Embryonic Development ◽

Domain Growth ◽

Cell Populations ◽

Spatial Correlations ◽

Variable Species ◽

Multiple Species ◽

Spatially Varying ◽

The Way

AbstractIn this work we study the effect of domain growth on spatial correlations in agent populations containing multiple species. This is important as heterogenous cell populations are ubiquitous during the embryonic development of many species. We have previously shown that the long term behaviour of an agent population depends on the way in which domain growth is implemented. We extend this work to show that, depending on the way in which domain growth is implemented, different species dominate in multispecies simulations. Continuum approximations of the lattice-based model that ignore spatial correlations cannot capture this behaviour, while those that explicitly account for spatial correlations can. The results presented here show that the precise mechanism of domain growth can determine the long term behaviour of multispecies populations, and in certain circumstances, establish spatially varying species densities.

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A Stochastic Model for Virus Growth in a Cell Population

Journal of Applied Probability ◽

10.1017/s0021900200011542 ◽

2014 ◽

Vol 51 (03) ◽

pp. 599-612

Author(s):

J. E. Björnberg ◽

T. Britton ◽

E. I. Broman ◽

E. Natan

Keyword(s):

Stochastic Model ◽

Host Cell ◽

Cell Population ◽

Branching Process ◽

Virus Population ◽

Virus Growth ◽

Optimal Balance ◽

Large Numbers ◽

A Cell

In this work we introduce a stochastic model for the spread of a virus in a cell population where the virus has two ways of spreading: either by allowing its host cell to live and duplicate, or by multiplying in large numbers within the host cell, causing the host cell to burst and thereby let the virus enter new uninfected cells. The model is a kind of interacting Markov branching process. We focus in particular on the probability that the virus population survives and how this depends on a certain parameter λ which quantifies the ‘aggressiveness’ of the virus. Our main goal is to determine the optimal balance between aggressive growth and long-term success. Our analysis shows that the optimal strategy of the virus (in terms of survival) is obtained when the virus has no effect on the host cell's life cycle, corresponding to λ = 0. This is in agreement with experimental data about real viruses.

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Faculty Opinions recommendation of The CD8+ T cell population elicited by recombinant adenovirus displays a novel partially exhausted phenotype associated with prolonged antigen presentation that nonetheless provides long-term immunity.

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.1029949.349422 ◽

2005 ◽

Author(s):

Allan Zajac

Keyword(s):

T Cell ◽

Antigen Presentation ◽

Cell Population ◽

Recombinant Adenovirus ◽

Cd8 T Cell

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Effects of acute seizures on cell proliferation, synaptic plasticity and long-term behavior in adult zebrafish

Brain Research ◽

10.1016/j.brainres.2021.147334 ◽

2021 ◽

Vol 1756 ◽

pp. 147334

Author(s):

Charles Budaszewski Pinto ◽

Natividade de Sá Couto-Pereira ◽

Felipe Kawa Odorcyk ◽

Kamila Cagliari Zenki ◽

Carla Dalmaz ◽

...

Keyword(s):

Cell Proliferation ◽

Synaptic Plasticity ◽

Adult Zebrafish ◽

Acute Seizures ◽

Long Term Behavior

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Using Generalized Cell Mapping to Approximate Invariant Measures on Compact Manifolds

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127497001667 ◽

1997 ◽

Vol 07 (11) ◽

pp. 2487-2499 ◽

Cited By ~ 10

Author(s):

Rabbijah Guder ◽

Edwin Kreuzer

Keyword(s):

Dynamical Systems ◽

Invariant Measures ◽

Nonlinear Dynamical Systems ◽

Powerful Method ◽

Cell Mapping ◽

Generalized Cell Mapping ◽

Nonlinear Dynamical ◽

Long Term Behavior ◽

Mapping Theory

In order to predict the long term behavior of nonlinear dynamical systems the generalized cell mapping is an efficient and powerful method for numerical analysis. For this reason it is of interest to know under what circumstances dynamical quantities of the generalized cell mapping (like persistent groups, stationary densities, …) reflect the dynamics of the system (attractors, invariant measures, …). In this article we develop such connections between the generalized cell mapping theory and the theory of nonlinear dynamical systems. We prove that the generalized cell mapping is a discretization of the Frobenius–Perron operator. By applying the results obtained for the Frobenius–Perron operator to the generalized cell mapping we outline for some classes of transformations that the stationary densities of the generalized cell mapping converges to an invariant measure of the system. Furthermore, we discuss what kind of measures and attractors can be approximated by this method.

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