Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles.

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.

Transmission Dynamics of Tuberculosis with Age-specific Disease Progression.

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.

Modeling COVID-19 Transmission Dynamics With Self-Learning Population Behavioral Change.

Many regions observed recurrent outbreaks of COVID-19 cases after relaxing social distancing measures. It suggests that maintaining sufficient social distancing is important for limiting the spread of COVID-19. The change of population behavior responding to the social distancing measures becomes an important factor for the pandemic prediction. In this paper, we develop a SEAIR model for studying the dynamics of COVID-19 transmission with population behavioral change. In our model, the population is divided into several groups with their own social behavior in response to the delayed information about the number of the infected population. The transmission rate depends on the behavioral changes of all the population groups, forming a feedback loop to affect the COVID-19 dynamics. Based on the data of Hong Kong, our simulations demonstrate how the perceived cost after infection and the information delay affect the level and the time period of the COVID-19 waves.

Correction to 'Modelling stem cell ageing: a multi-compartment continuum approach'.

[This corrects the article DOI: 10.1098/rsos.191848.].

Modelling stem cell ageing: a multi-compartment continuum approach.

Stem cells are important to generate all specialized tissues at an early life stage, and in some systems, they also have repair functions to replenish the adult tissues. Repeated cell divisions lead to the accumulation of molecular damage in stem cells, which are commonly recognized as drivers of ageing. In this paper, a novel model is proposed to integrate stem cell proliferation and differentiation with damage accumulation in the stem cell ageing process. A system of two structured PDEs is used to model the population densities of stem cells (including all multiple progenitors) and terminally differentiated (TD) cells. In this system, cell cycle progression and damage accumulation are modelled by continuous dynamics, and damage segregation between daughter cells is considered at each division. Analysis and numerical simulations are conducted to study the steady-state populations and stem cell damage distributions under different damage segregation strategies. Our simulations suggest that equal distribution of the damaging substance between stem cells in a symmetric renewal and less damage retention in stem cells in the asymmetric division are favourable strategies, which reduce the death rate of the stem cells and increase the TD cell populations. Moreover, asymmetric damage segregation in stem cells leads to less concentrated damage distribution in the stem cell population, which may be more robust to the stochastic changes in the damage. The feedback regulation from stem cells can reduce oscillations and population overshoot in the process, and improve the fitness of stem cells by increasing the percentage of cells with less damage in the stem cell population.

Combined control evaluation for Neospora caninum infection in dairy: Economic point of view coupled with population dynamics.

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.

Temporal regulation of cell polarity via the interaction of the Ras GTPase Rsr1 and the scaffold protein Bem1.

The Cdc42 guanosine triphosphatase (GTPase) plays a central role in polarity development in species ranging from yeast to humans. In budding yeast, a specific growth site is selected in the G1 phase. Rsr1, a Ras GTPase, interacts with Cdc42 and its associated proteins to promote polarized growth at the proper bud site. Yet how Rsr1 regulates cell polarization is not fully understood. Here, we show that Rsr1-GDP interacts with the scaffold protein Bem1 in early G1, likely hindering the role of Bem1 in Cdc42 polarization and polarized secretion. Consistent with these in vivo observations, mathematical modeling predicts that Bem1 is unable to promote Cdc42 polarization in early G1 in the presence of Rsr1-GDP. We find that a part of the Bem1 Phox homology domain, which overlaps with a region interacting with the exocyst component Exo70, is necessary for the association of Bem1 with Rsr1-GDP. Overexpression of the GDP-locked Rsr1 interferes with Bem1-dependent Exo70 polarization. We thus propose that Rsr1 functions in spatial and temporal regulation of polarity establishment by associating with distinct polarity factors in its GTP- and GDP-bound states.

Analysis of spontaneous emergence of cell polarity with delayed negative feedback.

Cell polarity refers to spatial di erences in the shape and structure of cells, which leads to the generation of diverse cell types playing di erent roles in biological processes. Cell polarization usually involves the localization of some specific signaling molecules to a proper location of the cell membrane. Recent studies proposed that delayed negative feedback may be important for maintaining the robustness of cell polarization and the observed oscillating behavior of signaling cluster. However, the fundamental mechanisms for achieving cell polarization under negative feedback remain controversial. In this paper, we formulate the cell polarization system as a non-local reaction di usion equation with positive and delayed negative feedback loops. Through the Turing stability analysis, we identify the parameter conditions, including the range of the time delay constant, for achieving cell polarization without any inhomogeneous spatial cues. Also, our numerical results support that by controlling the length of the time delay in negative feedback and the magnitude of positive feedback, the oscillating behavior of signaling cluster can be observed in our simulations.

A modeling study of budding yeast colony formation and its relationship to budding pattern and aging.

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.

Fine-tuning the orientation of the polarity axis by Rga1, a Cdc42 GTPase-activating protein.

In yeast and animal cells, signaling pathways involving small guanosine triphosphatases (GTPases) regulate cell polarization. In budding yeast, selection of a bud site directs polarity establishment and subsequently determines the plane of cell division. Rga1, a Cdc42 GTPase-activating protein, prevents budding within the division site by inhibiting Cdc42 repolarization. A protein complex including Nba1 and Nis1 is involved in preventing rebudding at old division sites, yet how these proteins and Rga1 might function in negative polarity signaling has been elusive. Here we show that Rga1 transiently localizes to the immediately preceding and older division sites by interacting with Nba1 and Nis1. The LIM domains of Rga1 are necessary for its interaction with Nba1, and loss of this interaction results in premature delocalization of Rga1 from the immediately preceding division site and, consequently, abnormal bud-site selection in daughter cells. However, such defects are minor in mother cells of these mutants, likely because the G1 phase is shorter and a new bud site is established prior to delocalization of Rga1. Indeed, our biphasic mathematical model of Cdc42 polarization predicts that premature delocalization of Rga1 leads to more frequent Cdc42 repolarization within the division site when the first temporal step in G1 is assumed to last longer. Spatial distribution of a Cdc42 GAP in coordination with G1 progression may thus be critical for fine-tuning the orientation of the polarity axis in yeast.

Inflammatory Bowel Disease: How Effective Is TNF-α Suppression?

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.

A hybrid continuous-discrete method for stochastic reaction-diffusion processes.

Stochastic fluctuations in reaction-diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method.

Mucins and associated glycan signatures in colon adenoma-carcinoma sequence: Prospective pathological implication(s) for early diagnosis of colon cancer.

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.

Regulation of Cdc42 polarization by the Rsr1 GTPase and Rga1, a Cdc42 GTPase-activating protein, in budding yeast.

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.

Robust and precise morphogen-mediated patterning: trade-offs, constraints and mechanisms.

The patterning of many developing tissues is organized by morphogens. Genetic and environmental perturbations of gene expression, protein synthesis and ligand binding are among the sources of unreliability that limit the accuracy and precision of morphogen-mediated patterning. While it has been found that the robustness of morphogen gradients to the perturbation of morphogen synthesis can be enhanced by particular mechanisms, how such mechanisms affect robustness to other perturbations, such as to receptor synthesis for the same morphogen, has been little explored. Here, we investigate the interplay between the robustness of patterning to the changes in receptor synthesis and morphogen synthesis and to the effects of cell-to-cell variability. Our analysis elucidates the trade-offs and constraints that arise as a result of achieving these three performance objectives simultaneously in the context of simple, steady-state morphogen gradients formed by diffusion and receptor-mediated uptake. Analysis of the interdependence between length scales of patterning and these performance objectives reveals several potential mechanisms for mitigating such trade-offs and constraints. One involves downregulation of receptor synthesis in the morphogen source, while another involves the presence of non-signalling cell-surface morphogen-binding molecules. Both of these mechanisms occur in Drosophila wing discs during their patterning. We computationally elucidate how these mechanisms improve the robustness and precision of morphogen-mediated patterning.

Mathematical analysis of spontaneous emergence of cell polarity.

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.

Mathematical model of the roles of T cells in inflammatory bowel disease.

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.

Polarization of diploid daughter cells directed by spatial cues and GTP hydrolysis of Cdc42 budding yeast.

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.

Mathematical model of colitis-associated colon cancer.

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 NF-κB, ß-catenin, 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.

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems.

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.