Stochastic gene expression in regulatory networks is conventionally modelled via the chemical master equation (CME). As explicit solutions to the CME, in the form of so-called propagators, are ...oftentimes not readily available, various approximations have been proposed. A recently developed analytical method is based on a separation of time scales that assumes significant differences in the lifetimes of mRNA and protein in the network, allowing for the efficient approximation of propagators from asymptotic expansions for the corresponding generating functions. Here, we showcase the applicability of that method to simulated data from a ‘telegraph’ model for gene expression that is extended with an autoregulatory mechanism. We demonstrate that the resulting approximate propagators can be applied successfully for parameter inference in the non-regulated model; moreover, we show that, in the extended autoregulated model, autoactivation or autorepression may be refuted under certain assumptions on the model parameters. These results indicate that our approach may allow for successful parameter inference and model identification from longitudinal single cell data.
Mixed-mode oscillations (MMOs) are complex oscillatory patterns in which large-amplitude oscillations (LAOs) of relaxation type alternate with small-amplitude oscillations (SAOs). MMOs are found in ...singularly perturbed systems of ordinary differential equations of slow-fast type, and are typically related to the presence of so-called folded singularities and the corresponding canard trajectories in such systems. Here, we introduce a canonical family of three-dimensional slow-fast systems that exhibit MMOs which are induced by relaxation-type dynamics, and which are hence based on a “jump mechanism”, rather than on a more standard canard mechanism. In particular, we establish a correspondence between that family and a class of associated one-dimensional piecewise affine maps (PAMs) which exhibit MMOs with the same signature. Finally, we give a preliminary classification of admissible mixed-mode signatures, verifying results of (Rajpathak, Pillai, and Bandyopahdyay (2012) 29) in the process, and we illustrate our findings with numerical examples.
We study a singularly perturbed model for a cyclic adenosine monophosphate (cAMP) signalling system that controls aggregation of the amoeboid microorganism Dictyostelium discoideum. The model, which ...is based on a classical model due to Martiel and Goldbeter 16, takes the form of a planar system of ordinary differential equations with two singular perturbation parameters which manifest very differently: while one parameter encodes the separation of scales between the slow and fast variables, the other induces a non-uniformity in the corresponding vector field in the singular limit. We apply geometric singular perturbation theory and the desingularisation technique known as “blow-up” to construct a family of attracting, periodic (relaxation-type) orbits; in the process, we elucidate the novel singular structure of the model, and we describe in detail the resulting oscillatory dynamics.
Yogurt represent one of the oldest fermented foods containing viable lactic acid bacteria and many bioactive compounds that could exhibit beneficial effects on human health and train our immune ...system to better respond to invading pathogens. Streptococcus thermophilus and Lactobacillus delbrueckii ssp. bulgaricus are commonly used for yogurt preparation under controlled temperature and environmental conditions. In this study, we investigated probiotic features of S. thermophilus BGKMJ1-36 and L. bulgaricus BGVLJ1-21 strains isolated from artisanal sour milk and yogurt by using Caenorhabditis elegans as an in vivo model system. Further, we evaluated content of total fat, saturated fatty acids, proteins, and lactose, as well as vitamins and AA of yogurt prepared from above-mentioned starter cultures during 21 d of storage at 4°C to get insights of final product stability. We showed that S. thermophilus BGKMJ1-36 and L. bulgaricus BGVLJ1-21 strains applied in combination upregulated the expression of autophagy-related genes in C. elegans. Beside autophagy, we observed activation of TIR-1-dependent transcription of lysozyme-like antimicrobial genes involved in the immune defense of C. elegans. Upregulation of these genes strongly correlates with an increase in the longevity of the worms fed with yogurt culture bacteria. Further, we showed that yogurt prepared with S. thermophilus BGKMJ1-36 and L. bulgaricus BGVLJ1-21, as a final product, is rich with vitamin B2 and dominant AA known by their prolongevity properties. Taken together, our study pointed to the beneficial features of the tested starter cultures and yogurt and highlighted their potential to be used as a fermented food with added-value properties.
We investigate the effects of a linear cut-off on front propagation in the Nagumo equation at a so-called Maxwell point, where the corresponding front solution in the absence of a cut-off is ...stationary. We show that the correction to the propagation speed induced by the cut-off is positive in this case; moreover, we determine the leading-order asymptotics of that correction in terms of the cut-off parameter, and we calculate explicitly the corresponding coefficient. Our analysis is based on geometric techniques from dynamical systems theory and, in particular, on the method of geometric desingularization (‘blow-up’).
► We study the effects of a linear cut-off on front propagation in the Nagumo equation. ► We show that the correction to the propagation speed due to the cut-off is positive. ► We determine the leading-order asymptotics of that correction. ► We calculate explicitly the corresponding coefficient.
Enterococci have controversial status due to their emerging role in nosocomial infections and transmission of antibiotic resistance genes, while some enterococci strains are used as probiotics for ...humans and animals and starter cultures in dairy industry. In order to improve our understanding of factors involved in the safe use of enterococci as potential probiotics, the antibiotic susceptibility, virulence and probiotic traits of 75 dairy enterococci isolates belonging to
(50),
(15),
(6),
(3), and
(1) were evaluated. The results revealed that ciprofloxacin resistance and biofilm formation are correlated with isolates originated from Golija mountain (Serbia), while gelatinase activity was more common in isolates from Prigorje region (Croatia), pointing to uncontrolled use of antibiotics and anthropogenic impact on dairy products' microbiota in these regions. The virulence genes were sporadically present in 13 selected dairy enterococci isolates. Interestingly, biofilm formation was correlated with higher ability of strains to reduce the adhesion of
and
Enteritidis to HT29-MTX cells. To our knowledge this is the first study reporting the presence of the
gene (previously correlated with pathogenesis) in dairy enterococci isolates, mostly associated with the genes involved in adhesion property. Hence, the results of this study revealed that the virulence genes are sporadically present in dairy isolates and more correlated to adhesion properties and biofilm formation, implicating their role in gut colonization rather than to the virulence traits.
In this study, for the first time, the comprehensive analysis of antiproliferative and antioxidant activities of ramson, followed by the analysis of its associated microbiota and health-promoting ...effects of lactic acid bacteria (LAB), was performed. Ramson (
) is recognized as a medicinal plant with a long history of use in traditional medicine due to its antimicrobial and antioxidant activity. In this study the influence of
gastrointestinal digestion on the cytotoxic activity of
extracts against human malignant cell lines was demonstrated. Seven sulfur compounds, the degradation products of thiosulfinates, including diallyl disulfide were shown to inhibit proliferation of malignant cells by inducing accumulation within G2/M phase as well as to induce apoptosis through activation of caspase-3 and mitochondrial signaling pathway. Further, the
microbiota, particularly LAB with potential probiotic effects, was analyzed by culture-dependent method and culture-independent method denaturing gradient gel electrophoresis (DGGE). The obtained results revealed that the most abundant genera were
,
, and
. The
genus was mainly represented by
The pulsed-field gel electrophoresis (PFGE) analysis revealed the presence of two PFGE pulsotypes. The probiotic potential of the strain
BGSR163 belonging to PFGE pulsotype 1 and the strain
BGSR227 belonging to the PFGE pulsotype 2 was characterized. The results revealed that both strains are safe for human use, successfully survive the simulated gastrointestinal conditions, have potential to transiently colonize the gastrointestinal tract (GIT) and have a protective immunomodulatory effect, inducing the production of proinflammatory cytokine IL17 and regulatory cytokine IL10, while decreasing the production of proinflammatory cytokine IFN-γ. In conclusion, the results of this study suggest that consumption of
might have health-promoting properties, including anticancer effects, while
strains isolated from
leaves could be used as probiotics for human consumption.
Sitagliptin, an anti-diabetic drug, is a dipeptidyl peptidase (DPP)-4/CD26 inhibitor with additional anti-inflammatory and immunomodulatory properties. In this study, we investigated for the first ...time the effect of sitagliptin on the differentiation and functions of human dendritic cells generated from monocytes (MoDCs) for 4 days using the standard GM-CSF/IL-4 procedure. LPS/IFN-γ treatment for an additional 24 h was used for maturation induction of MoDCs. Sitagliptin was added at the highest non-cytotoxic concentration (500 µg/mL) either at the beginning (sita 0d protocol) or after MoDC differentiation (sita 4d protocol). Sitagliptin impaired differentiation and maturation of MoDCs as judged with the lower expression of CD40, CD83, CD86, NLRP3, and HLA-DR, retention of CD14 expression, and inhibited production of IL-β, IL-12p70, IL-23, and IL-27. In contrast, the expression of CD26, tolerogenic DC markers (ILT4 and IDO1), and production of immunoregulatory cytokines (IL-10 and TGF-β) were increased. Generally, the sita 0d protocol was more efficient. Sitagliptin-treated MoDCs were poorer allostimulators of T-cells in MoDC/T-cell co-culture and inhibited Th1 and Th17 but augmented Th2 and Treg responses. Tolerogenic properties of sitagliptin-treated MoDCs were additionally confirmed by an increased frequency of CD4+CD25+CD127- FoxP3+ Tregs and Tr1 cells (CD4+IL-10+FoxP3-) in MoDC/T-cell co-culture. The differentiation of IL-10+ and TGF-β+ Tregs depended on the sitagliptin protocol used. A Western blot analysis showed that sitagliptin inhibited p65 expression of NF-kB and p38MAPK during the maturation of MoDCs. In conclusion, sitagliptin induces differentiation of tolerogenic DCs, and the effect is important when considering sitagliptin for treating autoimmune diseases and allotransplant rejection.
The paper considers utilization of rocket motor propellant grains that consist of two propellants. The idea is to achieve approximately neutral burning using an outer surface inhibited cylindrical ...shape and complex contact surface between propellants. An existing propellant grain with complex geometry has been analytically modeled in terms of determination of evolution of corresponding burning surface areas. The analytical and experimental results? diagrams of this grain have been found to have a saw-tooth shape because of the segments that separate the two propellants, causing potential problems in the burning process during the relatively short active phase, showing an obvious need for further optimization. This has created an opportunity for development of improved propellant grain geometry and corresponding mathematical model for determination of main interior ballistic parameters. Comparison between calculation results based on both models and experimentally determined chamber pressure data shows very good agreement. Therefore, two-component propellant grains have significant application possibilities using the suggested modeling approaches.
Stochastic models for gene expression frequently exhibit dynamics on several different scales. One potential time-scale separation is caused by significant differences in the lifetimes of mRNA and ...protein; the ratio of the two degradation rates gives a natural small parameter in the resulting chemical master equation, allowing for the application of perturbation techniques. Here, we develop a framework for the analysis of a family of ‘fast-slow’ models for gene expression that is based on geometric singular perturbation theory. We illustrate our approach by giving a complete characterisation of a standard two-stage model which assumes transcription, translation, and degradation to be first-order reactions. In particular, we present a systematic expansion procedure for the probability-generating function that can in principle be taken to any order in the perturbation parameter, allowing for an approximation of the corresponding propagator probabilities to that same order. For illustrative purposes, we perform this expansion explicitly to first order, both on the fast and the slow time-scales; then, we combine the resulting asymptotics into a composite fast-slow expansion that is uniformly valid in time. In the process, we extend, and prove rigorously, results previously obtained by Shahrezaei and Swain (Proc Natl Acad Sci USA 105(45):17256–17261,
2008
) and Bokes et al. (J Math Biol 64(5):829–854,
2012
; J Math Biol 65(3):493–520,
2012
). We verify our asymptotics by numerical simulation, and we explore its practical applicability and the effects of a variation in the system parameters and the time-scale separation. Focussing on biologically relevant parameter regimes that induce translational bursting, as well as those in which mRNA is frequently transcribed, we find that the first-order correction can significantly improve the steady-state probability distribution. Similarly, in the time-dependent scenario, inclusion of the first-order fast asymptotics results in a uniform approximation for the propagator probabilities that is superior to the slow dynamics alone. Finally, we discuss the generalisation of our geometric framework to models for regulated gene expression that involve additional stages.
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