scholarly journals C. elegans colony formation as a condensation phenomenon

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yuping Chen ◽  
James E. Ferrell
Keyword(s):  
Phase Separation ◽  
Colony Formation ◽  
Ostwald Ripening ◽  
Equation Model ◽  
Biological Processes ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Collective Behaviors ◽  
C Elegans ◽  
Living Organisms

AbstractPhase separation at the molecular scale affects many biological processes. The theoretical requirements for phase separation are fairly minimal, and there is growing evidence that analogous phenomena occur at other scales in biology. Here we examine colony formation in the nematode C. elegans as a possible example of phase separation by a population of organisms. The population density of worms determines whether a colony will form in a thresholded fashion, and a simple two-compartment ordinary differential equation model correctly predicts the threshold. Furthermore, small, round colonies sometimes fuse to form larger, round colonies, and a phenomenon akin to Ostwald ripening – a coarsening process seen in many systems that undergo phase separation – also occurs. These findings support the emerging view that the principles of microscopic phase separation can also apply to collective behaviors of living organisms.

scholarly journals C. elegans colony formation as a phase separation phenomenon

2020 ◽  
Author(s):  
Yuping Chen ◽  
James Ferrell
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Phase Separation ◽  
Colony Formation ◽  
Ostwald Ripening ◽  
Micelle Formation ◽  
Biological Processes ◽  
C Elegans ◽  
Separation Theory ◽  
Molecular Scale

Abstract Phase separation at the molecular scale affects many biological processes. The theoretical requirements for phase separation are fairly minimal, and analogous phenomena may occur at other scales in biology. Here we have examined colony formation in the nematode C. elegans as a possible example of phase separation by a population of organisms. Experimental data and mathematical modeling indicated that, similar to physical condensation processes like phase separation and micelle formation, the population density of worms determines colony formation in a thresholded fashion, with the threshold correctly predicted by phase separation theory. Furthermore, we found that a phenomenon akin to Ostwald ripening – a coarsening seen in many systems that undergo phase separation – occurs. Our results show that populations of organisms can undergo condensation phenomena and phase separation.

scholarly journals A Stochastic TB Model for a Crowded Environment

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Sibaliwe Maku Vyambwera ◽  
Peter Witbooi
Keyword(s):  
Compartmental Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Equation Model ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
The Stability ◽  
Crowded Environments ◽  
Disease Free

We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation. We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing the basic reproduction number and prove the stability of the disease-free equilibrium when it is below unity or slightly higher than unity and the perturbation is small. Our main theorem implies that the stochastic perturbation enhances stability of the disease-free equilibrium of the underlying deterministic model. Finally, we perform some simulations to illustrate the analytical findings and the utility of the model.

scholarly journals Reduced ODE dynamics as formal relativistic asymptotics of a Peierls–Nabarro model

2014 ◽  
Vol 25 (4) ◽  
pp. 511-529
Author(s):  
H. IBRAHIM ◽  
R. MONNEAU
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Half Plane ◽  
Displacement Field ◽  
Equation Model ◽  
Linear Wave ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Linear Wave Equation ◽  
Total Displacement

In this paper, we consider a scalar Peierls--Nabarro model describing the motion of dislocations in the plane (x1,x2) along the linex2=0. Each dislocation can be seen as a phase transition and creates a scalar displacement field in the plane. This displacement field solves a simplified elasto-dynamics equation, which is simply a linear wave equation. The total displacement field creates a stress which makes move the dislocation itself. By symmetry, we can reduce the system to a wave equation in the half planex2>0 coupled with an equation for the dynamics of dislocations on the boundary of the half plane, i.e. onx2=0. Our goal is to understand the dynamics of well-separated dislocations in the limit when the distance between dislocations is very large, of order 1/ɛ. After rescaling, this corresponds to introduce a small parameter ɛ in the system. For the limit ɛ → 0, we are formally able to identify a reduced ordinary differential equation model describing the dynamics of relativistic dislocations if a certain conjecture is assumed to be true.

scholarly journals Experimental and mathematical insights on the interactions between poliovirus and a defective interfering genome

2021 ◽  
Vol 17 (9) ◽  
pp. e1009277
Author(s):  
Yuta Shirogane ◽  
Elsa Rousseau ◽  
Jakub Voznica ◽  
Yinghong Xiao ◽  
Weiheng Su ◽  
...  
Keyword(s):  
Rna Viruses ◽  
Equation Model ◽  
Critical Parameters ◽  
Model Parameters ◽  
Experimental Measurements ◽  
Genome Replication ◽  
Virus Population ◽  
Wild Type ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model

During replication, RNA viruses accumulate genome alterations, such as mutations and deletions. The interactions between individual variants can determine the fitness of the virus population and, thus, the outcome of infection. To investigate the effects of defective interfering genomes (DI) on wild-type (WT) poliovirus replication, we developed an ordinary differential equation model, which enables exploring the parameter space of the WT and DI competition. We also experimentally examined virus and DI replication kinetics during co-infection, and used these data to infer model parameters. Our model identifies, and our experimental measurements confirm, that the efficiencies of DI genome replication and encapsidation are two most critical parameters determining the outcome of WT replication. However, an equilibrium can be established which enables WT to replicate, albeit to reduced levels.

scholarly journals Dynamics of the Stochastic Belousov-Zhabotinskii Chemical Reaction Model

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 663
Author(s):  
Ying Yang ◽  
Daqing Jiang ◽  
Donal O’Regan ◽  
Ahmed Alsaedi
Keyword(s):  
Chemical Reaction ◽  
Existence And Uniqueness ◽  
Reaction Model ◽  
Equation Model ◽  
Asymptotically Stable ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Globally Asymptotically Stable ◽  
Chemical Reaction Model ◽  
Theoretical Results

In this paper, we discuss the dynamic behavior of the stochastic Belousov-Zhabotinskii chemical reaction model. First, the existence and uniqueness of the stochastic model’s positive solution is proved. Then we show the stochastic Belousov-Zhabotinskii system has ergodicity and a stationary distribution. Finally, we present some simulations to illustrate our theoretical results. We note that the unique equilibrium of the original ordinary differential equation model is globally asymptotically stable under appropriate conditions of the parameter value f, while the stochastic model is ergodic regardless of the value of f.

scholarly journals Optimal Strategies for Control of COVID-19: A Mathematical Perspective

Scientifica ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Baba Seidu
Keyword(s):  
Reproduction Number ◽  
Optimal Strategies ◽  
Cost Effective ◽  
Equation Model ◽  
Asymptotically Stable ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Disease Free ◽  
The Basic Reproduction Number

A deterministic ordinary differential equation model for SARS-CoV-2 is developed and analysed, taking into account the role of exposed, mildly symptomatic, and severely symptomatic persons in the spread of the disease. It is shown that in the absence of infective immigrants, the model has a locally asymptotically stable disease-free equilibrium whenever the basic reproduction number is below unity. In the absence of immigration of infective persons, the disease can be eradicated whenever ℛ 0 < 1 . Specifically, if the controls u i ,   i = 1,2,3,4 , are implemented to 100% efficiency, the disease dies away easily. It is shown that border closure (or at least screening) is indispensable in the fight against the spread of SARS-CoV-2. Simulation of optimal control of the model suggests that the most cost-effective strategy to combat SARS-CoV-2 is to reduce contact through use of nose masks and physical distancing.

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