Chemotaxis Term Research Articles

Dynamics of a size-structured predator–prey model with chemotaxis mechanism

This paper is concerned with a size-structured diffusive predator–prey model with chemotaxis mechanism. The existence, linearized stability and monotonicity with respect to the growth rates of boundary steady-state solutions are analyzed. Moreover, the global stability of trivial steady-state solution under certain conditions is proved by constructing Lyapunov functional. We investigate the local and global bifurcations of positive steady-state solutions that emanate from semi-trivial steady-state solutions using Lyapunov–Schmidt reduction and bifurcation techniques when the fertility intensity of a predator or prey is used as a bifurcation parameter. It is shown that the nonlinear nonlocal chemotaxis term can lead to the emergence of Allee effect.

Identification and validation of oxidative stress-related diagnostic markers for recurrent pregnancy loss: insights from machine learning and molecular analysis.

It has been recognized that oxidative stress (OS) is implicated in the etiology of recurrent pregnancy loss (RPL), yet the biomarkers reflecting oxidative stress in association with RPL remain scarce. The dataset GSE165004 was retrieved from the Gene Expression Omnibus (GEO) database. From the GeneCards database, a compendium of 789 genes related to oxidative stress-related genes (OSRGs) was compiled. By intersecting differentially expressed genes (DEGs) in normal and RPL samples with OSRGs, differentially expressed OSRGs (DE-OSRGs) were identified. In addition, four machine learning algorithms were employed for the selection of diagnostic markers for RPL. The Receiver Operating Characteristic (ROC) curves for these genes were generated and a predictive nomogram for the diagnostic markers was established. The functions and pathways associated with the diagnostic markers were elucidated, and the correlations between immune cells and diagnostic markers were examined. Potential therapeutics targeting the diagnostic markers were proposed based on data from the Comparative Toxicogenomics Database and ClinicalTrials.gov. The candidate biomarker genes from the four models were further validated in RPL tissue samples using RT-PCR and immunohistochemistry. A set of 20 DE-OSRGs was identified, with 4 genes (KRAS, C2orf69, CYP17A1, and UCP3) being recognized by machine learning algorithms as diagnostic markers exhibiting robust diagnostic capabilities. The nomogram constructed demonstrated favorable predictive accuracy. Pathways including ribosome, peroxisome, Parkinson's disease, oxidative phosphorylation, Huntington's disease, and Alzheimer's disease were co-enriched by KRAS, C2orf69, and CYP17A1. Cell chemotaxis terms were commonly enriched by all four diagnostic markers. Significant differences in the abundance of five cell types, namely eosinophils, monocytes, natural killer cells, regulatory T cells, and T follicular helper cells, were observed between normal and RPL samples. A total of 180 drugs were predicted to target the diagnostic markers, including C544151, D014635, and CYP17A1. In the validation cohort of RPL patients, the LASSO model demonstrated superiority over other models. The expression levels of KRAS, C2orf69, and CYP17A1 were significantly reduced in RPL, while UCP3 levels were elevated, indicating their suitability as molecular markers for RPL. Four oxidative stress-related diagnostic markers (KRAS, C2orf69, CYP17A1, and UCP3) have been proposed to diagnose and potentially treat RPL.

A chemotaxis model of prey and predator of three species: Existence of unique global solutions

An intraguild predation model consisting of three species with densities s, u1, u2 in R2 is studied. Under certain natural conditions, namely the positivity of the initial values s0,u10 and u20, the solutions exist globally in time in the spaces of Lp∩H1, 1⩽p⩽∞. Our result, avoids the usual modifications on the chemotaxis term ∇⋅[u1∇u2].

Intestinal flora altered and correlated with interleukin-2/4 in patients with primary immune thrombocytopenia

BackgroundLittle is known about the changes and mechanisms of intestinal flora in primary immune thrombocytopenia (ITP) patients.AimTo explore the structural and functional differences of intestinal flora between ITP patients and healthy controls, and clarify the correlation between intestinal flora and Th1/Th2 imbalance.MethodsFeces from ITP patients and healthy controls were studied by 16S rRNA and metagenomic techniques at phylum, genus, species or functional levels. Blood samples were collected for the detection of interleukin −2 (IL-2) and IL-4 concentrations.ResultsThe following changes in ITP patients were found: a decrease of Bacteroidetes phylum, an increase of Proteobacteria phylum and alterations of ten genera and 1045 species. IL-2 and IL-4 were significantly correlated with six and five genera, respectively. Species of C. freundii, C. rodentium, and C. youngae were negatively correlated with bleeding scores, and S. infantis was positively related to platelet counts. Functionally, the intestinal flora of ITP patients changed mainly in terms of motility, chemotaxis, membrane transport, and metabolism.ConclusionThe mechanism underlying functional and structural changes of intestinal flora in ITP patients may be related to inflammation and immunity, providing possibilities of probiotics or fecal transplants for ITP.

Spatiotemporal dynamics of a three-component chemotaxis model for Alopecia Areata

In this paper, we investigate the influence of two indirect chemotaxis terms χ1,χ2 on the spatiotemporal dynamics of a three-component model for Alopecia areata. The stability of the unique positive equilibrium and bifurcations are discussed by choosing the bifurcating parameters χ1,χ2. When χ1=0, χ2 can lead to complex spatial pattern via Turing bifurcation. And fixing χ2 in a certain region, χ1 can lead to spatially nonhomogeneous periodic solutions via Hopf bifurcation. It is shown that there exist a codimension-2 Turing–Turing bifurcation due to the joint effect of χ2 and proliferation rate and Double-Hopf bifurcation due to nonhomogeneous Hopf bifurcations with different modes induced by χ1 and proliferation rate.

Theoretical and numerical analysis of a parabolic system with chemoattraction modeling the growth of glioma cells

In this paper, we consider a two dimensional PDE model describing the proliferation-invasion structure of hypoxic glial cells in the brain, in which the cell movement is determined not only by natural diffusion but also, by the gradient of the concentration of oxygen. This model is given by a second order nonlinear system involving the density of cancer cells and the oxygen concentration, which are coupled by a chemoattraction term, a source of logistic growth, and a reaction term of Michaelis-Menten type. The contribution of this paper is summarized in the following two main aspects: first, we prove the existence and uniqueness of strong solutions; and second, we propose a nonlinear fully discrete finite element (FE) approximation for the model. We prove its well-posedness, some uniform estimates, the positivity for the discrete oxygen concentration and approximated positivity for the discrete tumour cells, which are required in this biological model. The key point to develop the numerical analysis is to control properly the second order nonlinear chemotaxis term as well as to obtain a discrete energy estimate which, in particular, gives a bounded energy; this energy estimate is derived by using a regularization technique. Finally, we present some numerical simulations which allow us to validate the theoretical results obtained.

On an elliptic chemotaxis system with flux limitation and subcritical signal production

In this article we study the existence of solutions of a system of partial differential equations of elliptic type, describing the distribution of a biological species “u” and the density of a chemical stimulus “ψ” in a bounded domain Ω of RN. The equation for u includes a chemotaxis term with nonlinear flux limitation which depends on the exponent p>1.The equation for u is given by −div(M(x)∇u)+u=−χdiv(u|∇ψ|p−2∇ψ)+f(x),where ψ presents a subcritical production term uθ and satisfies the equation −div(M(x)∇ψ)+ψ=uθ.The matrix of coefficients, M, is a known, symmetric and positive defined with coefficients mij∈C1(Ω¯),χ is a given real constant, f is a non-negative function belonging to Lm(Ω), m>max{1,N2}. The production term exponent, θ, is assumed to be positive and fulfills one of the following constrains 1<p<NθNθ−1,1<Nθor max{N,p}<θ+1θ for θ>0.The problem is completed with Dirichlet boundary conditions for u and ψ. The main result of the article includes the existence of positive solutions in H01(Ω)∩L∞(Ω).

A Glioblastoma PDE-ODE model including chemotaxis and vasculature

In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes chemotaxis term directed to vasculature. First, we obtain some a priori estimates for the (possible) solutions of the model. In particular, under some conditions on the parameters, we obtain that the system does not develop blow-up at finite time. In addition, we design a fully discrete finite element scheme for the model which preserves some pointwise estimates of the continuous problem. Later, we make an adimensional study in order to reduce the number of parameters. Finally, we detect the main parameters determining different width of the ring formed by proliferative and necrotic cells and different regular/irregular behaviour of the tumor surface.

Application of reaction-diffusion equations for modeling human and breeding site attraction movement behavior of Aedes aegypti mosquito.

This paper shows how biological population dynamic models in the form of coupled reaction-diffusion equations with nonlinear reaction terms can be applied to heterogeneous landscapes. The presented systems of coupled partial differential equations (PDEs) combine the dispersal of disease-vector mosquitoes and the spread of the disease in a human population. Realistic biological dispersal behavior is taken into account by applying chemotaxis terms for the attraction to the human host and the attraction of suitable breeding sites. These terms are capable of generating the complex active movement patterns of mosquitoes along the gradients of the attractants. The nonlinear initial boundary value problems are solved numerically for geometries of heterogeneous landscapes, which have been imported from geographic information system data to construct a general-purpose finite-element solver for systems of coupled PDEs. The method is applied to the dispersal of the dengue disease vector for Aedes aegypti in a small-scale rural setting consisting of small houses and different breeding sites, and to a large-scale section of the suburban zone of a metropolitan area in Vietnam. Numerical simulations illustrate how the setup of model equations and geographic information can be used for the assessment of control measures, including the spraying patterns of pesticides and biological control by inducing male sterility.

Positivity-preserving high-order compact difference method for the Keller-Segel chemotaxis model.

The paper is concerned with development of an accurate and effective positivity-preserving high-order compact difference method for solving the Keller-Segel chemotaxis model, which is a kind of nonlinear parabolic-parabolic system in mathematical biology. Firstly, a stiffly-stable five-step fourth-order fully implicit compact difference scheme is proposed. The new scheme not only has fourth-order accuracy in the spatial direction, but also has fourth-order accuracy in the temporal direction, and the computational strategy for the nonlinear chemotaxis term is provided. Then, a positivity-preserving numerical algorithm is presented, which ensures the non-negativity of cell density at all time without accuracy loss. And a time advancement algorithm is established. Finally, the proposed method is applied to the numerical simulation for chemotaxis phenomena, and the accuracy, stability and positivity-preserving of the new scheme are validated with several numerical examples.

Spatio-Temporal Modeling of Immune Response to SARS-CoV-2 Infection

COVID-19 is a disease occurring as a result of infection by a novel coronavirus called SARS-CoV-2. Since the WHO announced COVID-19 as a global pandemic, mathematical works have taken place to simulate infection scenarios at different scales even though the majority of these models only consider the temporal dynamics of SARS-COV-2. In this paper, we present a new spatio-temporal within-host mathematical model of COVID-19, accounting for the coupled dynamics of healthy cells, infected cells, SARS-CoV-2 molecules, chemokine concentration, effector T cells, regulatory T cells, B-lymphocytes cells and antibodies. We develop a computational framework involving discretisation schemes for diffusion and chemotaxis terms using central differences and midpoint approximations within two dimensional space combined with a predict–evaluate–correct mode for time marching. Then, we numerically investigate the model performance using a list of values simulating the baseline scenario for viral infection at a cellular scale. Moreover, we explore the model sensitivity via applying certain conditions to observe the model validity in a comparison with clinical outcomes collected from recent studies. In this computational investigation, we have a numerical range of 104 to 108 for the viral load peak, which is equivalent to what has been obtained from throat swab samples for many patients.

Pattern formation of reaction-diffusion system with chemotaxis terms.

In this paper, we systematically study two-species reaction-diffusion system with chemotaxis terms. We, first, compare conditions for chemotaxis-driven instability and Turing instability. It follows that conditions for chemotaxis-driven instability are the generalization of conditions for Turing instability without chemotaxis. Most of all, we provide sufficient conditions for chemotaxis-driven instability, which implies that chemotaxis can give rise to pattern formation for the same diffusion coefficients. To support our theoretical analyses, we take the Rosenzweig-MacArthur model as an example to illustrate the influence of parameters on pattern formation. By conditions for chemotaxis-driven instability and numerical simulations, we show parameter spaces of chemotaxis-driven instability (Turing spaces). In addition, we establish the similarity and difference between these Turing spaces. Our numerical simulations validate the dependence of pattern formation on parameters and that unstable parameter spaces induced by chemotaxis can be sufficiently larger than that induced by the reaction-diffusion system without chemotaxis (standard Turing space). Furthermore, we present the pattern formation induced by chemotaxis for Du=Dv. For numerical simulations, we can choose r and β from the Turing spaces to validate previous analysis.

Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis

We consider a system of reaction–diffusion equations including chemotaxis terms and coming out of the modelling of multiple sclerosis. The global existence of strong solutions to this system in any dimension is proved, and it is also shown that the solution is bounded uniformly in time. Finally, a nonlinear stability result is obtained when the chemotaxis term is not too big. We also perform numerical simulations to show the appearance of Turing patterns when the chemotaxis term is large.

Local delivery of FTY720 induces neutrophil activation through chemokine signaling in an oronasal fistula model

PurposeCleft palate repair surgeries lack a regenerative reconstructive option and, in many cases, develop complications including oronasal fistula (ONF). Our group has developed a novel murine phenocopy of ONF to study the oral cavity wound healing program. Using this model, our team previously identified that delivery of FTY720 on a nanofiber scaffold had a unique immunomodulatory effect directing macrophages and monocytes into a pro-regenerative state during ONF healing. Here, the objective of this study was to determine the effects of local biomaterial-based FTY720 delivery in the ONF model on the early bulk gene expression and neutrophil phenotypic response within the regenerating tissue.MethodsUsing a mouse model of ONF formation, a palate defect was created and was treated with FTY720 nanofiber scaffolds or (blank) vehicle control nanofibers. At 1 and 3 days post-implantation, ONF oral mucosal tissue from the defect region was collected for RNA sequencing analysis or flow cytometry. For the RNA-seq expression profiling, intracellular pathways were assessed using the KEGG Pathway database and Gene Ontology (GO) Terms enrichment interactive graph. To assess the effects of FTY720 on different neutrophil subpopulations, flow cytometry data was analyzed using pseudotime analysis based on Spanning-tree Progression Analysis of Density-normalized Events (SPADE).ResultsRNA sequencing analysis of palate mucosa injured tissue identified 669 genes that were differentially expressed (DE) during the first 3 days of ONF wound healing after local delivery of FTY720, including multiple genes in the sphingolipid signaling pathway. Evaluation of the DE genes at the KEGG Pathway database also identified the inflammatory immune response pathways (chemokine signaling, cytokine-cytokine receptor interaction, and leukocyte transendothelial migration), and the Gene Ontology enrichment analysis identified neutrophil chemotaxis and migration terms. SPADE dendrograms of CD11b+Ly6G+ neutrophils at both day 1 and day 3 post-injury showed significantly distinct subpopulations of neutrophils in oral mucosal defect tissue from the FTY720 scaffold treatment group compared to the vehicle control group (blank). Increased expression of CD88 and Vav1, among other genes, were found and staining of the ONF area demonstrated increased VAV1 staining in FTY720‐treated healing oral mucosa.ConclusionTreatment of oral mucosal defects using FTY720 scaffolds is a promising new immunotherapy to improve healing outcomes and reducing ONF formation during cleft palate surgical repair. Local delivery of FTY720 nanofiber scaffolds during ONF healing significantly shifted early gene transcription associated with immune cell recruitment and modulation of the immune microenvironment results in distinct neutrophil subpopulations in the oral mucosal defect tissue that provides a critical shift toward pro-regenerative immune signaling.

Root exudates influence chemotaxis and colonization of diverse plant growth promoting rhizobacteria in the pigeon pea – maize intercropping system

Intercropping, the co-cultivation of two or more plant species in the same field, has several advantages over growing only one plant species, however, the role of plant-microbe interactions in such a setup is poorly understood. To investigate the influence of rhizosphere colonization by plant growth-promoting rhizobacteria (PGPR) in an intercropping system, a model legume-cereal intercropping system involving maize (Zea mays) and pigeon pea (Cajanus cajan) was assessed for colonization using three different bacterial strains Enterobacter sp. C1D, Pseudomonas sp. G22, Rhizobium sp. IC3109. Cross colonization experiments suggested bacterial movement from one plant species to another in the presence/absence of a mesh barrier, implicating the role of intercrop root exudates. In vitro assays and plant inoculation studies displayed that Enterobacter sp. C1D had a preference for monocropped plants while Rhizobium sp. IC3109 to intercropped plants and Pseudomonas sp. G22 was evenly colonized in both conditions. Organic acids like fumarate, malate, and succinate, as analyzed by LC/MS/MS (MRM), were found to be prominent in monocropped plant root exudates, while co-cultivation resulted in a decrease of the exudation of these metabolites. The PGPR strains showed differential behavioral responses in terms of chemotaxis and biofilm formation towards root exudates of intercropped and monocropped plants. Overall, our study provides pieces of evidence that co-cultivation of legume and cereal plants leads to the variation in root exudates and the response of plant beneficial bacteria.

A parabolic–elliptic chemotaxis system with nonlinear diffusion approached from a Cahn–Hilliard-type system

This paper deals with a parabolic–elliptic chemotaxis system with nonlinear diffusion. It was proved that there exists a solution of a Cahn–Hilliard system as an approximation of a nonlinear diffusion equation by applying an abstract theory by Colli–Visintin (Commun Partial Differ Equ 15:737–756, 1990) for a doubly nonlinear evolution inclusion with some bounded monotone operator and subdifferential operator of a proper lower semicontinuous convex function (cf. Colli–Fukao in J Math Anal Appl 429, 2015:1190–1213). Moreover, Colli–Fukao (J Differ Equ 260:6930–6959, 2016) established existence of solutions to the nonlinear diffusion equation by passing to the limit in the Cahn–Hilliard equation. However, Cahn–Hilliard approaches to chemotaxis systems with nonlinear diffusions seem to be not studied yet. This paper will try to derive existence of solutions to a parabolic–elliptic chemotaxis system with nonlinear diffusion by passing to the limit in a Cahn–Hilliard-type chemotaxis system. Although in this paper, we employ a time discretization scheme to prove existence for the Cahn–Hilliard-type chemotaxis system in reference to Colli–Kurima (Nonlinear Anal 190:111613, 2020), please note that this reference does not deal with chemotaxis terms.

Platelet lysate promotes the healing of long-standing diabetic foot ulcers: A report of two cases and in vitro study

Long-standing foot ulcers present a great challenge in diabetes care. Platelet products have been suggested as a possible therapeutic option. However, nor the effect of an injectable form of platelet lysate on the healing of ulcers nor that on primary cells of the epidermis have been studied. In the current study, we present two cases of an ongoing clinical trial showing the positive effect of autologous platelet lysate injected perilesional. Both clinical cases treated with injections of hPL showed complete healing of previously un-healed within 8 weeks of treatment. Further, we describe the in vitro effect of human platelet lysate (hPL) on primary human epidermal keratinocytes (HEK) in terms of chemotaxis, migration and proliferation. In vitro, HEK showed enhanced chemotaxis towards the hPL compared to keratinocyte-defined media (p < 0.0001). Their migration was also stimulated especially at hPL concentration of 10%V/V (p < 0.0001). In contrast, hPL significantly inhibited HEK proliferation measured through MTT assay (p < 0.0001). In conclusion, the findings presented here provide preliminary evidence of an explanatory mechanism for the effect of hPL on primary keratinocytes and therefore of their potential use in a clinical setting. hPL promotes keratinocyte migration and therefore closure of foot ulcers.

Traveling waves in a chemotaxis model with logistic growth

Traveling wave solutions of a chemotaxis model with a reaction term are studied. We investigate the existence and non-existence of traveling wave solutions in certain ranges of parameters. Particularly for a positive rate of chemical growth, we prove the existence of a heteroclinic orbit by constructing a positively invariant set in the three dimensional space. The monotonicity of traveling waves is also analyzed in terms of chemotaxis, reaction and diffusion parameters. Finally, the traveling wave solutions are shown to be linearly unstable.

Existence for a class of chemotaxis models with fractional diffusion in Besov spaces

In this paper, we are interested in the Cauchy problem for the fractional diffusion equation with a chemotaxis term, which generalizes the Keller-Segel model, for the small enough initial data in critical Besov spaces. Using some estimates of the linear dissipative equation in the frame of mixed time-space spaces, we establish the existence of the solution for such kind of chemotaxis system in $\\mathbb{R}^n$.

On a parabolic–elliptic system with gradient dependent chemotactic coefficient

We consider a second order PDEs system of Parabolic–Elliptic type with chemotactic terms. The system describes the evolution of a biological species “u” moving towards a higher concentration of a chemical stimuli “v” in a bounded and open domain of RN. In the system considered, the chemotaxis sensitivity depends on the gradient of v, i.e., the chemotaxis term has the following expression−div(χu|∇v|p−2∇v), where χ is a positive constant and p satisfiesp∈(1,∞), if N=1 and p∈(1,NN−1), if N≥2. We obtain uniform bounds in L∞(Ω) and the existence of global in time solutions. For the one-dimensional case we prove the existence of infinitely many non-constant steady-states for p∈(1,2) for any χ positive and a given positive mass.