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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. [ABSTRACT FROM AUTHOR]

Competing populations within an ecosystem often release chemicals during the interactions and diffusion processes. These chemicals can have diverse effects on competitors, ranging from inhibition to stimulation of species' growth. This work constructs a competition model that incorporates stimulatory substances, spatial effects, and multiple time lags to investigate the combined impact of these phenomena on competitors' growth. When the stimulation rate from the produced chemicals falls within a suitable threshold interval, all species within the system can coexist. Under the species' coexistence, their diffusive phenomenon leads to a spatially heterogeneous distribution, resulting in patchy structures (Turing patterns) within their habitat. As the parameter values exceed their thresholds, species begin to exhibit spatially periodic oscillations (spatial Hopf bifurcation). The presence of multiple delays and competitors' diffusion contributes to spatially complex and heterogeneous behaviors (Turing–Hopf bifurcation). The results help us understand the underlying mechanisms behind these heterogeneous behaviors and enable us to mitigate their negative impact on species' growth and harvest. Numerical simulations are used to measure the dynamics of competitors under different parameter conditions. [ABSTRACT FROM AUTHOR]

Abstract 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. Highlights • 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. [ABSTRACT FROM AUTHOR]

Budding yeast, which undergoes polarized growth during budding and mating, has been a useful model system to study cell polarization. Bud sites are selected differently in haploid and diploid yeast cells: haploid cells bud in an axial manner, while diploid cells bud in a bipolar manner. While previous studies have been focused on the molecular details of the bud site selection and polarity establishment, not much is known about how different budding patterns give rise to different functions at the population level. In this paper, we develop a two-dimensional agent-based model to study budding yeast colonies with cell-type specific biological processes, such as budding, mating, mating type switch, consumption of nutrients, and cell death. The model demonstrates that the axial budding pattern enhances mating probability at an early stage and the bipolar budding pattern improves colony development under nutrient limitation. Our results suggest that the frequency of mating type switch might control the trade-off between diploidization and inbreeding. The effect of cellular aging is also studied through our model. Based on the simulations, colonies initiated by an aged haploid cell show declined mating probability at an early stage and recover as the rejuvenated offsprings become the majority. Colonies initiated with aged diploid cells do not show disadvantage in colony expansion possibly due to the fact that young cells contribute the most to colony expansion. [ABSTRACT FROM AUTHOR]

Populations diffuse in the spatial domain for better habitat and compete for enriching resources for survival and evolution. Some behaviors or chemicals from the species' competitive interactions will occur and have feedback to affect their growth. In this work, we construct a competitive system with diffusion and stimulatory chemicals to investigate the dynamics of competitive species. We first study the existence of the positive steady-state and obtain the related conditions. Furthermore, we analyze the effect of diffusion and stimulating substances on the dynamics of the species concentration. Without diffusion effect, the stimulatory chemicals will contribute to the oscillation of the species concentration if the production rate of the chemicals is greater than the critical value. The diffusion phenomenon in the system causes Turing instability, leading to the non-homogeneous spatial distribution of the species concentration. Finally, several numerical examples are provided to validate the theoretical conclusions in this work. [ABSTRACT FROM AUTHOR]

Crohn’s Disease (CD) results from inappropriate response toward commensal flora. Earlier studies described CD as a Th1 mediated disease. Current models view both phenotypes as a continuum of various permutations between Th1, Th2 and Th17 pathways compounded by a range of Treg disfunctions. In the present paper, we develop a mathematical model, by a system of differential equations, which describe the dynamic relations among these T cells and their cytokines. The model identities four groups of CD patients according to up/down regulation of Th1 and Th2. The model simulations show that immunosuppression by TNF-α blockage benefits the group with Th1High/Th2Low while, by contrast, the group with Th1Low/Th2High will benefit from immune activation. [ABSTRACT FROM AUTHOR]

Cdc42 plays a central role in establishing polarity in yeast and animals, yet how polarization of Cdc42 is achieved in response to spatial cues is poorly understood. Using live-cell imaging, we found distinct dynamics of Cdc42 polarization in haploid budding yeast in correlation with two temporal steps of the G1 phase. The position at which the Cdc42-GTP cluster develops changes rapidly around the division site during the first step but becomes stabilized in the second step, suggesting that an axis of polarized growth is determined in mid G1. Cdc42 polarization in the first step and its proper positioning depend on Rsr1 and its GTPase-activating protein (GAP) Bud2. Interestingly, Rga1, a Cdc42 GAP, exhibits transient localization to a site near the bud neck and to the division site during cytokinesis and G1, and this temporal change of Rga1 distribution is necessary for determination of a proper growth site. Mathematical modeling suggests that a proper axis of Cdc42 polarization in haploid cells might be established through a biphasic mechanism involving sequential positive feedback and transient negative feedback. [ABSTRACT FROM AUTHOR]

Cell polarization, in which intracellular substances are asymmetrically distributed, enables cells to carry out specialized functions. While cell polarity is often induced by intracellular or extracellular spatial cues, spontaneous polarization (the so-called symmetry breaking) may also occur in the absence of spatial cues. Many computational models have been used to investigate the mechanisms of symmetry breaking, and it was proved that spontaneous polarization occurs when the lateral diffusion of inactive signaling molecules is much faster than that of active signaling molecules. This conclusion leaves an important question of how, as observed in many biological systems, cell polarity emerges when active and inactive membrane-bound molecules diffuse at similar rates while cycling between cytoplasm and membrane takes place. The recent studies of Rätz and Röger showed that, when the cytosolic and membrane diffusion are very different, spontaneous polarization is possible even if the membrane-bound species diffuse at the same rate. In this paper, we formulate a two-equation non-local reaction-diffusion model with general forms of positive feedback. We apply Turing stability analysis to identify parameter conditions for achieving cell polarization. Our results show that spontaneous polarization can be achieved within some parameter ranges even when active and inactive signaling molecules diffuse at similar rates. In addition, different forms of positive feedback are explored to show that a non-local molecule-mediated feedback is important for sharping the localization as well as giving rise to fast dynamics to achieve robust polarization. [ABSTRACT FROM AUTHOR]

Gut mucosal homeostasis depends on complex interactions among the microbiota, the intestinal epithelium, and the gut associated immune system. A breakdown in some of these interactions may precipitate inflammation. Inflammatory bowel diseases, Crohn’s disease, and ulcerative colitis are chronic inflammatory disorders of the gastrointestinal tract. The initial stages of disease are marked by an abnormally high level of pro-inflammatory helper T cells, Th1. In later stages, Th2 helper cells may dominate while the Th1 response may dampen. The interaction among the T cells includes the regulatory T cells (Treg). The present paper develops a mathematical model by a system of differential equations with terms nonlocal in the space spanned by the concentrations of cytokines that represents the interaction among T cells through a cytokine signaling network. The model demonstrates how the abnormal levels of T cells observed in inflammatory bowel diseases can arise from abnormal regulation of Th1 and Th2 cells by Treg cells. [ABSTRACT FROM AUTHOR]

Cell polarization occurs along a single axis that is generally determined by a spatial cue. Cells of the budding yeast exhibit a characteristic pattern of budding, which depends on cell-type-specific cortical markers, reflecting a genetic programming for the site of cell polarization. The Cdc42 GTPase plays a key role in cell polarization in various cell types. Although previous studies in budding yeast suggested positive feedback loops whereby Cdc42 becomes polarized, these mechanisms do not include spatial cues, neglecting the normal patterns of budding. Here we combine live-cell imaging and mathematical modeling to understand how diploid daughter cells establish polarity preferentially at the pole distal to the previous division site. Live-cell imaging shows that daughter cells of diploids exhibit dynamic polarization of Cdc42-GTP, which localizes to the bud tip until the M phase, to the division site at cytokinesis, and then to the distal pole in the next G1 phase. The strong bias toward distal budding of daughter cells requires the distal-pole tag Bud8 and Rga1, a GTPase activating protein for Cdc42, which inhibits budding at the cytokinesis site. Unexpectedly, we also find that over 50% of daughter cells lacking Rga1 exhibit persistent Cdc42-GTP polarization at the bud tip and the distal pole, revealing an additional role of Rga1 in spatiotemporal regulation of Cdc42 and thus in the pattern of polarized growth. Mathematical modeling indeed reveals robust Cdc42-GTP clustering at the distal pole in diploid daughter cells despite random perturbation of the landmark cues. Moreover, modeling predicts different dynamics of Cdc42-GTP polarization when the landmark level and the initial level of Cdc42-GTP at the division site are perturbed by noise added in the model. [ABSTRACT FROM AUTHOR]

Abstract: As a result of chronic inflammation of their colon, patients with ulcerative colitis or Crohn''s disease are at risk of developing colon cancer. In this paper, we consider the progression of colitis-associated colon cancer. Unlike normal colon mucosa, the inflammed colon mucosa undergoes genetic mutations, affecting, in particular, tumor suppressors TP53 and adenomatous polyposis coli (APC) gene. We develop a mathematical model that involves these genes, under chronic inflammation, as well as , , MUC1 and MUC2. The model demonstrates that increased level of cells with TP53 mutations results in abnormal growth and proliferation of the epithelium; further increase in the epithelium proliferation results from additional APC mutations. The model may serve as a conceptual framework for further data-based study of the early stage of colon cancer. [Copyright &y& Elsevier]

Abstract: An inhomogeneous steady state pattern of nonlinear reaction–diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction–diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction–diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction–diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction–diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction–diffusion equations in a large parameter space. [Copyright &y& Elsevier]

Summary: Background: How morphogen gradients form has long been a subject of controversy. The strongest support for the view that morphogens do not simply spread by free diffusion has come from a variety of studies of the Decapentaplegic (Dpp) gradient of the Drosophila larval wing disc. Results: In the present study, we initially show how the failure, in such studies, to consider the coupling of transport to receptor-mediated uptake and degradation has led to estimates of transport rates that are orders of magnitude too low, lending unwarranted support to a variety of hypothetical mechanisms, such as “planar transcytosis” and “restricted extracellular diffusion.” Using several independent dynamic methods, we obtain data that are inconsistent with such models and show directly that Dpp transport occurs by simple, rapid diffusion in the extracellular space. We discuss the implications of these findings for other morphogen systems in which complex transport mechanisms have been proposed. Conclusions: We believe that these findings resolve a major, longstanding question about morphogen gradient formation and provide a solid framework for interpreting experimental observations of morphogen gradient dynamics. [ABSTRACT FROM AUTHOR]

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. Author summary: Defective interfering particles (DIPs) are viral mutants in which a crucial part of the particle's genome has been lost. DIPs are not infectious but can still co-infect cells with natural viruses. Such mutations are not uncommon. In fact, it has been found in most classes of viruses, including SARS coronavirus and influenza virus. It gives DIPs a promising future as a medium for disease treatment. However, the mechanism by which DIPs affect virus transmission remains unclear. In this paper, we develop a model to study the interaction between viruses and DIPs within host cells and the role stochastic effects play in virus transmission. Our simulations can capture patchy patterns and other spatial spread features observed in experiments and demonstrate that DIPs can slow down the growth of virus particles and make the spread of viruses more patchy. [ABSTRACT FROM AUTHOR]

Demographic structure and latent phenomenon are two essential factors determining the rate of tuberculosis transmission. However, only a few mathematical models considered age structure coupling with disease stages of infectious individuals. This paper develops a system of delay partial differential equations to model tuberculosis transmission in a heterogeneous population. The system considers demographic structure coupling with the continuous development of disease stage, which is crucial for studying how aging affects tuberculosis dynamics and disease progression. Here, we determine the basic reproduction number, and several numerical simulations are used to investigate the influence of various progression rates on tuberculosis dynamics. Our results support that the aging effect on the disease progression rate contributes to tuberculosis permanence. [ABSTRACT FROM AUTHOR]

• 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. [ABSTRACT FROM AUTHOR]

Development of biomarkers that detect early stage resectable premalignant lesions of colon can provide critical aid in the prevention of colorectal cancer. Recent lines of evidence suggest the utility of mucin expression to predict malignant transformation of colon pre-neoplastic lesions. In this study, we investigated the combined expression of multiple mucins and mucin-associated glycans during the adenoma-carcinoma sequence of colon cancer progression. Further, we evaluated their applicability as markers for differentiating adenomas/adenocarcinomas from hyperplastic polyps. Immunohistochemical analyses performed on colon disease tissue microarrays revealed downregulation of MUC2 and MUC4 expression (p < 0.0001) while MUC1 and MUC5AC expressions were upregulated (p = 0.01) during adenoma-adenocarcinoma progression. Expression of MUC17 was downregulated in inflamed tissues compared to normal tissues, but its increased expression differentiated adenomas (p = 0.0028) and adenocarcinomas (p = 0.025) from inflammation. Glycan epitope-Tn/STn on MUC1 showed higher expression in hyperplastic polyps (p = 0.023), adenomas (p = 0.042) and adenocarcinomas (p = 0.0096) compared to normal tissues. Multivariate regression analyses indicated that a combination of MUC2, MUC5AC, and MUC17 could effectively discriminate adenoma-adenocarcinoma from hyperplastic polyps. Altogether, a combined analysis of altered mucins and mucin-associated glycans is a useful approach to distinguish premalignant/malignant lesions of colon from benign polyps. [ABSTRACT FROM AUTHOR]