Cell polarization is a multiphysics problem resulting from coupling protein pathways and cell morphological evolution. The most common example is asexual reproduction in budding yeast through Cdc42 ...and septin signals. However, how the interaction between the Cdc42-septin systems and the mechanical deformation of the cell surface is not well understood. To explore the interaction, we build a three-dimensional mechanochemical coupling framework to investigate the Cdc42-septin systems and elucidate how morphogenesis at the cell scale enhances the robustness of cell polarization in budding yeast. We utilize the viscous active shell model to describe the moving boundary of the cell surface, and the mechanochemical coupling is achieved through the introduction of cell surface mean curvature and active contraction-growth effects. With a normal effect of septin, numerical results demonstrate the budding processes with different transition shapes of budding profiles. On the other hand, the mechanochemical coupling problem with a weak effect of septin drives the emergence of wrinkles on the cell surface. We also apply linear perturbation analysis of the cell surface deformation to show how cell shape evolution is subjected to active contraction-growth effects. Our results show that a 3D coupled mechanochemical model can reproduce the budding morphology in yeast. Such a model provides a more comprehensive portrait of cell polarity and can be used to characterize both wild-type and mutant phenotypes such as septin mutants.
•A mechanochemical model is developed to study the morphogenesis of budding yeast.•The coupling between Cdc42-septin system and active cell surface is involved.•The mean curvature of the cell surface is considered in the model.•Linear perturbation analysis is used to study the contraction-growth effect.•The appearance of wrinkling on cell surface is observed with a weak septin effect.
•Stochastic and impulsive model in the polluted turbidostat is proposed.•Sufficient conditions of populations’ extinction and permanence are obtained.•Several parameters’ influence on the survival of ...species is discussed.•Numerical simulations are provided to validate the theoretical results and further study the effect of some parameters.•Theoretical and numerical results support that stochastic perturbation has a negative effect on the populations’ survival in the proposed system.
Environmental pollution and random perturbation from the environment influence populations’ dynamics by alternating the habitat structure. To avoid disasters above or threats from predators, populations have self-defensive strategies such as camouflage or using a refuge. A turbidostat model with toxicant and prey refuge under the deterministic and stochastic environments is investigated in this work. We first analyze the positive solution’s existence and uniqueness under the effect of shelter and stochastic perturbation. We further determine the sufficient conditions of extinction and permanence for each population with the impact of toxicant, prey refuge under the stochastic environment. Our results reveal the dynamics of populations under the influence of the factors above. Several numerical examples are provided to verify the theoretical analysis and simulate the effect of the phenomena above in the population dynamics for both deterministic and stochastic cases.
•A mathematical model of the interactions between Th1 and Th2 cells with Treg cell inhibition and stochastic effects is developed.•Sufficient conditions for different asymptotic phases of Th1 and Th2 ...responses under the Treg cell regulation are obtained.•Numerical simulations are performed to identify the basins of attraction of different steady states and illustrate different dynamical scenarios.•The effect of stochastic effect under the Treg cell regulation is discussed.•The switching probability and the mean residence time are applied to study the effect of noise.
T cells differentiate into Th1 or Th2 cells upon maturation to influence different patterns of the immune response. Th1 and Th2 cells regulate each other and their responses are inhibited by Treg cells. With noisy external stimulation, Th1/Th2 cell differentiation can be dynamically balanced. The underlying mechanisms of Th cell differentiation under Treg cell inhibition and the extrinsic noise effects are not yet completely understood. In this paper, a mathematical model of the interactions between Th1 and Th2 cells with Treg cell inhibition and stochastic effects is developed to study the preference of outcomes and the noise-induced hopping among different states. First, we provide the conditions for different asymptotic phases of Th1 and Th2 responses under Treg cell regulation. Numerical simulations are applied to calculate the switching probability and the mean residence time to study how the noise affects the attractiveness of different states. Our results support that due to the stronger inhibitory effect of Treg cells on Th1 cell development, the high-Th2-low-Th1 state is more attractive under small noise effects. Additionally, we show that the attractiveness of the states is affected mainly by the extrinsic noise in Th2 cell signaling.
In the microorganism cultivation process, delay and stochastic perturbations are inevitably accompanied, which results in complicated dynamical behaviors for microorganisms. In this paper, a ...mathematical model with discrete delay and random perturbation is constructed to understand how the dynamics of microorganisms in the turbidostat can be characterized. The existence, uniqueness and boundedness of the positive solution are first determined for the mathematical model. Furthermore, sufficient conditions for microorganism extinction and permanence in the turbidostat are obtained with the theory of stochastic differential equations. The system has the stationary distribution under a low-level intensity of stochastic perturbation from the environment; that is, microorganism in the turbidostat is persistent fluctuating around a positive value. On the contrary, microorganisms will be extinct with a strong enough intensity of noise. Several numerical simulations are applied to validate the theoretical results for the dynamics of the system.
•Deterministic and stochastic models of cell polarization process are proposed.•Power spectrum of fluctuation is derived with Fourier transform.•Parameter regimes under different feedback regulations ...in system are discussed.•Stochastic model still produces the pattern where deterministic method fails.•System with Hill-function feedback yields a smaller parameter region.
Spontaneous emergence of cell polarity intrinsically lies at the localization of signaling molecules on a particular region of cell membrane. Such a process necessarily contains a positive feedback loop to amplify the localized cluster. To describe the polarizing process and explore different feedback functions involved, deterministic and stochastic models with non-local kinetics are discussed in this paper. Stochastic Simulation Algorithm (SSA) is used to numerically simulate the polarizing behavior and analytical analysis by the power spectrum is applied to approximate the parameter regime for the spontaneous emergence of cell polarity. Compared to the results from the deterministic model, we can understand how the stochastic effect extends the parameter regime for achieving cell polarization under different types of feedback, including the forms of quadratic function, linear function, and Hill function. Both deterministic and stochastic methods fail to yield the polarity at a low number of molecules. Our results suggest that the parameter region for cell polarization under the Hill function feedback is smaller than that with the quadratic function feedback.
Randomness often plays an important role in the spatial and temporal dynamics of biological systems. General stochastic simulation methods may lead to excessive computational cost for a system in ...which a large number of molecules involved. Therefore, multi-scale hybrid simulation methods become important for stochastic simulations. Here we build a spatially hybrid method which couples two approaches: discrete stochastic simulation and continuous stochastic differential equations. In our method, the locations of the interfaces between the two approaches are changing according to the distribution of molecules in a one-dimensional domain. To balance the accuracy and efficiency, the time step of the numerical method for the continuous stochastic differential equations is adapted to the dynamics of the molecules near the adaptive interfaces. The simulation results for a linear system and two nonlinear biological systems in different one-dimensional domains demonstrate the effectiveness and advantage of our new hybrid method with the adaptive time step control.
•A hybrid method coupling the stochastic simulation algorithm and the numerical stochastic differential equations.•Besides the mean-field behavior, the method provides an additional ability to capture the stochastic behavior.•The locations of the interfaces between the two approaches depend on the distribution of the molecules.•The time step for numerical stochastic differential equations is adapted to the dynamics of the molecules.•The method can be easily implemented and adaptive to different settings of reaction–diffusion system.
Defective interfering particles (DIPs) are virus-like particles that occur naturally during virus infections. These particles are defective, lacking essential genetic materials for replication, but ...they can interact with the wild-type virus and potentially be used as therapeutic agents. However, the effect of DIPs on infection spread is still unclear due to complicated stochastic effects and nonlinear spatial dynamics. In this work, we develop a model with a new hybrid method to study the spatial-temporal dynamics of viruses and DIPs co-infections within hosts. We present two different scenarios of virus production and compare the results from deterministic and stochastic models to demonstrate how the stochastic effect is involved in the spatial dynamics of virus transmission. We compare the spread features of the virus in simulations and experiments, including the formation and the speed of virus spread and the emergence of stochastic patchy patterns of virus distribution. Our simulations simultaneously capture observed spatial spread features in the experimental data, including the spread rate of the virus and its patchiness. The results demonstrate that DIPs can slow down the growth of virus particles and make the spread of the virus more patchy.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
•Effects of Neospora caninum infection on economic performance are evaluated.•Cost of control together with annual loss is the assessment criterion.•Vaccination is the most economical option in ...regions with high prevalence.•Combined controls provide better financial outcomes against a single control.
Neospora caninum infection is regarded as one of the most important infectious causes of abortion in dairy cattle. To intervene in its spread, four potential controls including test-and-cull, medication, vaccination, and selective breeding are considered and assessed in this study. The cost of each control, together with the inevitable annual loss due to population dynamics, is adopted as an assessment criterion from an economic point of view. By performing simulation and sensitivity analysis, our results demonstrate that compared with each single control, combined controls are worthwhile with better financial outcomes. For farm affected with significant prevalence (equal to or greater than 30%), vaccine treatment is the most effective and economical option among all control strategies. On the other hand, for farm where prevalence is relatively low (around 10%), combined control, by applying vaccination followed with test-and-cull, medication or selective breeding, could be alternative treatment to provide better financial outcome against single control in an observed period.
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