scholarly journals Spatial moment description of birth-death-movement processes incorporating the effects of crowding and obstacles

2018 ◽  
Author(s):  
Anudeep Surendran ◽  
Michael J. Plank ◽  
Matthew J. Simpson
Keyword(s):  
Spatial Structure ◽  
Cell Biology ◽  
Mean Field ◽  
Population Level ◽  
Individual Level ◽  
Spatial Moment ◽  
Motile Cells ◽  
Stationary Obstacles ◽  
Birth Death

AbstractBirth-death-movement processes, modulated by interactions between individuals, are fundamental to many cell biology processes. A key feature of the movement of cells within in vivo environments are the interactions between motile cells and stationary obstacles. Here we propose a multi-species model of individual-level motility, proliferation and death. This model is a spatial birth-death-movement stochastic process, a class of individual-based model (IBM) that is amenable to mathematical analysis. We present the IBM in a general multi-species framework, and then focus on the case of a population of motile, proliferative agents in an environment populated by stationary, non-proliferative obstacles. To analyse the IBM, we derive a system of spatial moment equations governing the evolution of the density of agents and the density of pairs of agents. This approach avoids making the usual mean-field assumption so that our models can be used to study the formation of spatial structure, such as clustering and aggregation, and to understand how spatial structure influences population-level outcomes. Overall the spatial moment model provides a reasonably accurate prediction of the system dynamics, including important effects such as how varying the properties of the obstacles leads to different spatial patterns in the population of agents.

scholarly journals Spatial moment dynamics for collective cell movement incorporating a neighbour-dependent directional bias

2015 ◽  
Vol 12 (106) ◽  
pp. 20150228 ◽  
Author(s):  
Rachelle N. Binny ◽  
Michael J. Plank ◽  
Alex James
Keyword(s):  
Spatial Structure ◽  
Mean Field ◽  
Cell Movement ◽  
Population Level ◽  
Average Density ◽  
Small Scale ◽  
Directional Bias ◽  
Field Approach ◽  
Spatial Moment ◽  
Migrating Cells

The ability of cells to undergo collective movement plays a fundamental role in tissue repair, development and cancer. Interactions occurring at the level of individual cells may lead to the development of spatial structure which will affect the dynamics of migrating cells at a population level. Models that try to predict population-level behaviour often take a mean-field approach, which assumes that individuals interact with one another in proportion to their average density and ignores the presence of any small-scale spatial structure. In this work, we develop a lattice-free individual-based model (IBM) that uses random walk theory to model the stochastic interactions occurring at the scale of individual migrating cells. We incorporate a mechanism for local directional bias such that an individual's direction of movement is dependent on the degree of cell crowding in its neighbourhood. As an alternative to the mean-field approach, we also employ spatial moment theory to develop a population-level model which accounts for spatial structure and predicts how these individual-level interactions propagate to the scale of the whole population. The IBM is used to derive an equation for dynamics of the second spatial moment (the average density of pairs of cells) which incorporates the neighbour-dependent directional bias, and we solve this numerically for a spatially homogeneous case.

scholarly journals Population dynamics with spatial structure and an Allee effect

2020 ◽  
Author(s):  
Anudeep Surendran ◽  
Michael Plank ◽  
Matthew Simpson
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Short Range ◽  
Allee Effect ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Continuum Approximation ◽  
Spatial Moment ◽  
Mean Field Models ◽  
The Mean

AbstractAllee effects describe populations in which long-term survival is only possible if the population density is above some threshold level. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to population extinction, whereas initial densities above the threshold eventually asymptote to some positive carrying capacity density. Mean field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as short-range competition and dispersal. The influence of such non mean-field effects has not been studied in the presence of an Allee effect. To address this we develop an individual-based model (IBM) that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework accurately recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure that mean-field models neglect. For example, we show that there are cases where the mean-field model predicts extinction but the population actually survives and vice versa. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

scholarly journals Spatial structure arising from chase-escape interactions with crowding

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Anudeep Surendran ◽  
Michael J. Plank ◽  
Matthew J. Simpson
Keyword(s):  
Spatial Structure ◽  
Cell Biology ◽  
Scale Up ◽  
Interaction Strength ◽  
Distinct Species ◽  
Interspecies Interactions ◽  
Individual Based Model ◽  
Directional Bias ◽  
Spatial Moments ◽  
Individual Level

Abstract Movement of individuals, mediated by localised interactions, plays a key role in numerous processes including cell biology and ecology. In this work, we investigate an individual-based model accounting for various intraspecies and interspecies interactions in a community consisting of two distinct species. In this framework we consider one species to be chasers and the other species to be escapees, and we focus on chase-escape dynamics where the chasers are biased to move towards the escapees, and the escapees are biased to move away from the chasers. This framework allows us to explore how individual-level directional interactions scale up to influence spatial structure at the macroscale. To focus exclusively on the role of motility and directional bias in determining spatial structure, we consider conservative communities where the number of individuals in each species remains constant. To provide additional information about the individual-based model, we also present a mathematically tractable deterministic approximation based on describing the evolution of the spatial moments. We explore how different features of interactions including interaction strength, spatial extent of interaction, and relative density of species influence the formation of the macroscale spatial patterns.

scholarly journals Sources of variability in cytosolic calcium transients triggered by stimulation of homogeneous uro-epithelial cell monolayers

2015 ◽  
Vol 12 (105) ◽  
pp. 20141403 ◽  
Author(s):  
Peter A. Appleby ◽  
Saqib Shabir ◽  
Jennifer Southgate ◽  
Dawn Walker
Keyword(s):  
Cell Biology ◽  
Mean Field ◽  
Population Level ◽  
Cytosolic Calcium ◽  
Calcium Transients ◽  
Local Context ◽  
Epithelial Tissue ◽  
Specific Cell ◽  
Cell Responses ◽  
Context Specific

Epithelial tissue structure is the emergent outcome of the interactions between large numbers of individual cells. Experimental cell biology offers an important tool to unravel these complex interactions, but current methods of analysis tend to be limited to mean field approaches or representation by selected subsets of cells. This may result in bias towards cells that respond in a particular way and/or neglect local, context-specific cell responses. Here, an automated algorithm was applied to examine in detail the individual calcium transients evoked in genetically homogeneous, but asynchronous populations of cultured non-immortalized normal human urothelial cells when subjected to either the global application of an external agonist or a localized scratch wound. The recorded calcium transients were classified automatically according to a set of defined metrics and distinct sub-populations of cells that responded in qualitatively different ways were observed. The nature of this variability in the homogeneous cell population was apportioned to two sources: intrinsic variation in individual cell responses and extrinsic variability due to context-specific factors of the environment, such as spatial heterogeneity. Statistically significant variation in the features of the calcium transients evoked by scratch wounding according to proximity to the wound edge was identified. The manifestation of distinct sub-populations of cells is considered central to the coordination of population-level response resulting in wound closure.

scholarly journals Population dynamics with spatial structure and an Allee effect

2020 ◽  
Vol 476 (2242) ◽  
pp. 20200501
Author(s):  
Anudeep Surendran ◽  
Michael J. Plank ◽  
Matthew J. Simpson
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Short Range ◽  
Allee Effect ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Continuum Approximation ◽  
Spatial Moment ◽  
Mean Field Models ◽  
The Mean

Population dynamics including a strong Allee effect describe the situation where long-term population survival or extinction depends on the initial population density. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to extinction, whereas initial densities above the threshold lead to survival. Mean-field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as competition and dispersal. The influence of non-mean-field effects has not been studied in the presence of an Allee effect. To address this, we develop an individual-based model that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure neglected by mean-field models. For example, there are cases where the mean-field model predicts extinction but the population actually survives. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

scholarly journals Spatial structure arising from chase-escape interactions with crowding

2018 ◽  
Author(s):  
Anudeep Surendran ◽  
Michael J Plank ◽  
Matthew J Simpson
Keyword(s):  
Spatial Structure ◽  
Cell Biology ◽  
Scale Up ◽  
Interaction Strength ◽  
Distinct Species ◽  
Interspecies Interactions ◽  
Individual Based Model ◽  
Directional Bias ◽  
Spatial Moments ◽  
Individual Level

ABSTRACTMovement of individuals, mediated by localised interactions, plays a key role in numerous processes including cell biology and ecology. In this work, we investigate an individual-based model accounting for various intraspecies and interspecies interactions in a community consisting of two distinct species. In this framework we consider one species to be chasers and the other species to be escapees, and we focus on chase-escape dynamics where the chasers are biased to move towards the escapees, and the escapees are biased to move away from the chasers. This framework allows us to explore how individual-level directional interactions scale up to influence spatial structure at the macroscale. To focus exclusively on the role of motility and directional bias in determining spatial structure, we consider conservative communities where the number of individuals in each species remains constant. To provide additional information about the individual-based model, we also present a mathematically tractable deterministic approximation based on describing the evolution of the spatial moments. We explore how different features of interactions including interaction strength, spatial extent of interaction, and relative density of species influence the formation of the macroscale spatial patterns.

Scanning Tunneling Microscopy and Atomic Force Microscopy of Enzymes and Enzyme Complexes

1990 ◽  
Vol 48 (3) ◽  
pp. 174-175
Author(s):  
Ronald D. Edstrom ◽  
Xiuru Yang ◽  
Mary E. Gurnack ◽  
Marcia A. Miller ◽  
Rui Yang ◽  
...  
Keyword(s):  
Cell Biology ◽  
Inorganic Ions ◽  
Bulk Liquid ◽  
Soluble Form ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Metabolic Channeling ◽  
Simplistic Notion ◽  
Soluble Enzymes

Many of the questions in biochemistry and cell biology are concerned with the relationships of proteins and other macromolecules in complex arrays which are responsible for carrying out metabolic sequences. The simplistic notion that the enzymes we isolate in soluble form from the cytoplasm were also soluble in vivo is being replaced by the concept that these enzymes occur in organized systems within the cell. In this newer view, the cytoplasm is organized and the “soluble enzymes” are in fact fixed in the cellular space and the only soluble components of the cell are small metabolites, inorganic ions etc. Further support for the concept of metabolic organization is provided by the evidence of metabolic channeling. It has been shown that for some metabolic pathways, the intermediates are not in free diffusion equilibrium with the bulk liquid in the cell but are passed along, more or less directly, from one enzyme to the next.

scholarly journals PDE limits of stochastic SIS epidemics on networks

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
F Di Lauro ◽  
J-C Croix ◽  
L Berthouze ◽  
I Z Kiss
Keyword(s):  
Network Inference ◽  
Mean Field ◽  
Population Level ◽  
Death Process ◽  
Disease Dynamics ◽  
Epidemic Outbreak ◽  
Numerical Tests ◽  
Mean Field Models ◽  
Stochastic Epidemic ◽  
Fokker Planck Equations

Abstract Stochastic epidemic models on networks are inherently high-dimensional and the resulting exact models are intractable numerically even for modest network sizes. Mean-field models provide an alternative but can only capture average quantities, thus offering little or no information about variability in the outcome of the exact process. In this article, we conjecture and numerically demonstrate that it is possible to construct partial differential equation (PDE)-limits of the exact stochastic susceptible-infected-susceptible epidemics on Regular, Erdős–Rényi, Barabási–Albert networks and lattices. To do this, we first approximate the exact stochastic process at population level by a Birth-and-Death process (BD) (with a state space of $O(N)$ rather than $O(2^N)$) whose coefficients are determined numerically from Gillespie simulations of the exact epidemic on explicit networks. We numerically demonstrate that the coefficients of the resulting BD process are density-dependent, a crucial condition for the existence of a PDE limit. Extensive numerical tests for Regular, Erdős–Rényi, Barabási–Albert networks and lattices show excellent agreement between the outcome of simulations and the numerical solution of the Fokker–Planck equations. Apart from a significant reduction in dimensionality, the PDE also provides the means to derive the epidemic outbreak threshold linking network and disease dynamics parameters, albeit in an implicit way. Perhaps more importantly, it enables the formulation and numerical evaluation of likelihoods for epidemic and network inference as illustrated in a fully worked out example.

scholarly journals Blood Pressure Trajectories Across the Life Course

2021 ◽  
Vol 34 (3) ◽  
pp. 234-241
Author(s):  
Norrina B Allen ◽  
Sadiya S Khan
Keyword(s):  
Blood Pressure ◽  
Measurement Errors ◽  
Clinical Care ◽  
Population Level ◽  
Cumulative Exposure ◽  
Older Adulthood ◽  
Individual Level ◽  
The Life Course ◽  
Level Group ◽  
Improve Health

Abstract High blood pressure (BP) is a strong modifiable risk factor for cardiovascular disease (CVD). Longitudinal BP patterns themselves may reflect the burden of risk and vascular damage due to prolonged cumulative exposure to high BP levels. Current studies have begun to characterize BP patterns as a trajectory over an individual’s lifetime. These BP trajectories take into account the absolute BP levels as well as the slope of BP changes throughout the lifetime thus incorporating longitudinal BP patterns into a single metric. Methodologic issues that need to be considered when examining BP trajectories include individual-level vs. population-level group-based modeling, use of distinct but complementary BP metrics (systolic, diastolic, mean arterial, mid, and pulse pressure), and potential for measurement errors related to varied settings, devices, and number of readings utilized. There appear to be very specific developmental periods during which divergent BP trajectories may emerge, specifically adolescence, the pregnancy period, and older adulthood. Lifetime BP trajectories are impacted by both individual-level and community-level factors and have been associated with incident hypertension, multimorbidity (CVD, renal disease, cognitive impairment), and overall life expectancy. Key unanswered questions remain around the additive predictive value of BP trajectories, intergenerational contributions to BP patterns (in utero BP exposure), and potential genetic drivers of BP patterns. The next phase in understanding BP trajectories needs to focus on how best to incorporate this knowledge into clinical care to reduce the burden of hypertensive-related outcomes and improve health equity.

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