Migration Model Research Articles

Implementation of actin polymerization and depolymerization in a two-dimensional cell migration model and its implications on mammalian cell morphology and velocity

Cell migration, a pivotal process in wound healing, immune response, and even cancer metastasis, manifests through intricate interplay between morphology, speed, and cytoskeletal dynamics. Mathematical modeling emerges as a powerful tool to dissect these complex interactions. This work presents a two-dimensional immersed boundary model for mammalian cell migration, incorporating both filamentous actin (F-actin) and monomeric actin (G-actin) to explicitly capture polymerization and depolymerization. This model builds upon our previous one-dimensional efforts, now enabling us to explore the impact of G-actin on not just cell velocity but also morphology. We compare predictions from both models, revealing that while the one-dimensional model captures core dynamics along the cell’s axis, the two-dimensional model excels in portraying cell shape evolution and transverse variations in actin concentration and velocity. Our findings highlight the crucial role of including G-actin in shaping cell morphology. Actin velocity aligned with migration direction elongates the cell, while velocity normal to the membrane promotes spreading. Importantly, the model establishes a link between these microscopic aspects and macroscopic observables like cell shape, offering a deeper understanding of cell migration dynamics. This work not only provides a more comprehensive picture of cell migration but also paves the way for future studies exploring the interplay of actin dynamics, cell morphology, and biophysical parameters in diverse biological contexts.

Research and application of migration and plugging mechanism of temporary plugging balls in multicluster fracturing of horizontal wells

Plugging and diverting stimulation technology using temporary plugging balls (PDSTB) in horizontal wells is one of the effective measures to enhance production in heterogeneous carbonate reservoirs. However, the migration and plugging mechanism of temporary plugging balls in horizontal wells remain unclear, leading to suboptimal field application. Based on the Lagrangian method, the migration and plugging models of temporary plugging balls were established. The study investigated the migration and plugging mechanism of temporary plugging balls. It analyzed the effects of parameters such as displacement on the plugging efficiency. The results show that the flow field in the perforation section is significantly affected by the displacement. Temporary plugging balls show three states of plugging: one ball plugging one shot-hole, multiple balls plugging one shot-hole, and balls remaining in the wellbore. The plugging efficiency initially increases, and then, decreases with the increase in displacement and the ball diameter. The plugging efficiency initially increases, and then, stabilizes with the increase in the viscosity of the carrying fluid and the usage ratio of balls. Plugging efficiency decreases with increasing density of balls. The greater the pressure difference at the outlet of the perforation section, the higher the plugging efficiency in the advantageous inlet section. Based on these results, the field construction of Well M was guided. The gas production was 142.66 × 104 m3/d after stimulation, and the production increase was significant. This study provides a theoretical basis for optimizing and designing the parameters of PDSTB in carbonate long horizontal wells.

Triple junction benchmark for multiphase-field models combining capillary and bulk driving forces

Abstract A benchmark problem is formulated which is well suited for the validation of mesoscopic phase-field models for grain-boundary migration in polycrystals. First, an analytical steady-state solution of the sharp moving boundary problem is derived for a symmetric lamellar structure, which is valid for arbitrary bulk driving forces and triple junction angles. Characteristic quantities are identified to reduce the parameter space which in turn allows a systematic comparison of simulations and analytical results. Various multiphase-field (MPF) formulations are compared which approximate the sharp interface problem in terms of a diffuse regularization. An interfacial thickness convergence study reveals that the model error is largely dependent on the ratio of bulk to interfacial stabilizing force as well as the underlying model formulation. An additional grid convergence study highlights the efficiency of a more advanced discretization scheme. The results can be used to guide the selection of appropriate models and to estimate the interface thickness and spatial resolution required to achieve a given accuracy target. The post-processing framework consists of a fully automated determination of well-defined metrics from the phase field simulation data, eliminating human bias and facilitating reproducibility. The corresponding code is made openly available to assist the materials science and engineering community in validating MPF, multi-order parameter and similar model developments. We believe that this work provides a reliable benchmark procedure to better understand the potentials and limitations of current multiphase-field models as well as alternative approaches.

Solution of the problem with a small parameter in suspension filtration in a porous medium

Relevance. The necessity to calculate the changes in filtration properties during injection of suspensions for subsequent forecasting of technological parameters of wells. This calculation is complicated by the presence of different-scale effects, since the penetration depth of dispersed particles is orders of magnitude smaller than the characteristic dimensions of the formation. These effects have not been studied in detail before. Aim. To analyze the effect of a small parameter on the behavior of flow characteristics using a mathematical model of suspension filtration in a porous medium. Objects. Colmatation coefficient, filtration coefficient, distribution of concentration of dispersed particles in the formation, porosity, mathematical model of deep-bed suspension migration into a porous medium. Methods. Numerical modeling, explicit finite-difference scheme, solution of a problem with a small parameter, introduction of dimensionless parameters, method of characteristics. Results and conclusions. It is shown that the processes of conformance control and colmatation of a porous medium are described within the framework of a unified system of equations of deep-bed suspension migration into a porous medium. It is identified that the concentration of retained particles is a small parameter that allows reducing the complete system of equations of deep-bed suspension migration into a porous medium to a simplified form, in which the solution can be obtained analytically using the method of characteristics. The authors compared the solutions of the complete and simplified systems of equations of deep-bed suspension migration into a porous medium, indicating their compliance with an error of less than 4 %. They obtained the distributions of the concentration of dispersed particles and porosity in the reservoir during colmatation, showing that over time the colmatation front propagates at a constant rate. It is shown that the colmatation coefficient is a small parameter that significantly determines the nature of oil displacement by water, and a decrease in the colmatation coefficient leads to a decrease in the rate of colmatation and the appearance and growth of the size of the stabilized zone near the displacement front.

Modeling Population Mobility Flows: A Hybrid Approach Integrating a Gravity Model and Machine Learning

Population mobility between cities significantly affects traffic congestion, disease spread, and societal well-being. As globalization and urbanization accelerate, understanding the dynamics of population mobility becomes increasingly important. Traditional population migration models reveal the factors influencing migration, while machine learning methods provide effective tools for creating data-driven models to handle the nonlinear relationships between origin and destination characteristics and migration. To deepen the understanding of population mobility issues, this study presents GraviGBM, an expandable population mobility simulation model that combines the gravity model with machine learning, significantly enhancing simulation accuracy. By employing SHAPs (SHapley Additive exPlanations), we interpret the modeling results and explore the relationship between urban characteristics and population migration. Additionally, this study includes a case analysis of COVID-19, extending the model’s application during public health emergencies and evaluating the contribution of model variables in this context. The results show that GraviGBM performs exceptionally well in simulating inter-city population migration, with an RMSE of 4.28, far lower than the RMSE of the gravity model (45.32). This research indicates that distance emerged as the primary factor affecting mobility before the pandemic, with economic factors and population also playing significant roles. During the pandemic, distance remained dominant, but the significance of short distances gained importance. Pandemic-related indicators became prominent, while economics, population density, and transportation substantially lost their influence. A city-to-city flow analysis shows that when population sizes are comparable, economic factors prevail, but when economic profiles match, living conditions dictate migration. During the pandemic, residents from hard-hit areas moved to more distant cities, seeking normalcy. This research offers a comprehensive perspective on population mobility, yielding valuable insights for future urban planning, pandemic response, and decision-making processes.

Investigating immersion and migration decisions for agent-based modelling: Acautionary tale.

Agent-based modelling provides an appealing methodological choice for simulating human behaviour and decisions. The currently dominant approaches based on static transition rates or unverified assumptions are restrictive, and could be enhanced with insights from cognitive experiments on actual decision making. Here, one common concern is that standard surveys or experiments may lack ecological validity, limiting the extent to which research findings can be generalised to real-life settings. For complex, highly emotive decision-making scenarios, such as those related to irregular migration, the typically used short, methodical survey questions may not appropriately map onto complex real-world decisions of interest. Immersive contexts may offer more accurate representations of reality, potentially enhancing the usefulness of experimental information in multi-disciplinary modelling endeavours. This preregistered study, aimed directly at examining the effect of immersion on risk-taking in the context of migration decisions, and indirectly at informing a multi-disciplinary construction of an agent-based model of migration, presents a choice-based interactive fiction game in which players make migration decisions to advance through a story. (N = 1000 Prolific users) took part in one of four experimental conditions, three involving different renditions of the game attempting to create immersion, with the last condition presenting the decisions in standard survey format. Although addressing the lack of ecological validity in survey data is important for improving agent-based modelling methodology, the experimental design used to tackle this issue, while responding directly to modelling needs, proved too complex. The created experimental conditions ended up too distinct from each other, involving stimuli that differed in quantity and content. This introduced several unintended and uncontrolled confounds, making it impossible to meaningfully interpret the results of this experiment on its own. Our results act as a cautionary tale for agent-based modellers, highlighting that the modelling needs should not override the principles of experimental design, and provide motivation for more rigorous research on this topic.

Agricultural carbon emissions in China: measurement, spatiotemporal evolution, and influencing factors analysis

IntroductionThe agricultural sector is the second largest emitter of greenhouse gases, accounting for 23% of global anthropogenic carbon emissions. Analysis of the basic state of carbon emissions from China's agriculture is helpful to achieve carbon reduction targets.MethodsAgricultural carbon emissions were calculated using the emission factor method, based on data from the China Rural Statistical Yearbook and various provincial statistical yearbooks. To analyze spatial patterns, the standard deviation ellipse method and the center of gravity migration model were employed, uncovering the migration path of agricultural carbon emissions. Regional disparities and the driving factors of agricultural carbon emissions were further examined using the Theil index and the Logarithmic Mean Divisia Index (LMDI) model.ResultsThe analysis indicated that the emissions center has gradually shifted towards the central and western regions, reflecting changes in agricultural production activity areas. Intraregional differences are the primary contributors to the imbalance in agricultural carbon emissions, with pronounced disparities in grain production and consumption balance regions. Key influencing factors include agricultural production efficiency, adjustments in agricultural industrial structure, economic structure and output, and urbanization levels. The economic output effect and urbanization effect are identified as the main drivers of increased carbon emissions, while declining production efficiency has hindered emission reduction efforts.ConclusionThe findings provide valuable insights for regional management and policymaking in China's agricultural sector, highlighting the need to enhance production efficiency and optimize agricultural structure to reduce emissions.

Exploring the Temporal, Spatial and Characteristic Trends and Key Influencing Factors of Tianjin’s Industrial Heritage

Tianjin is currently in the phase of urban stock renewal, yet its industrial heritage encounters significant challenges, including constrained spatial development, a misalignment between industrial progress and the reuse of industrial heritage, and an understated cultural representation. This study utilized geospatial analysis methods, including kernel density analysis, standard deviation ellipse analysis, and gravity migration model analysis, to elucidate the distribution characteristics of Tianjin’s industrial heritage across temporal, spatial, and typological dimensions. Moreover, a geographic detector was employed to assess the impact of various factors on the development of Tianjin’s industrial heritage, ultimately elucidating the correlations between existing challenges and objective patterns. The conclusion of this paper presents three strategic approaches for the renewal of industrial heritage, emphasizing historical culture, environmental space, and sustainable development. These strategies are designed to provide a solid research foundation for protecting and revitalizing Tianjin’s industrial heritage resources.

Dynamic cluster field modeling of collective chemotaxis

Collective migration of eukaryotic cells is often guided by chemotaxis, and is critical in several biological processes, such as cancer metastasis, wound healing, and embryogenesis. Understanding collective chemotaxis has challenged experimental, theoretical and computational scientists because cells can sense very small chemoattractant gradients that are tightly controlled by cell-cell interactions and the regulation of the chemoattractant distribution by the cells. Computational models of collective cell migration that offer a high-fidelity resolution of the cell motion and chemoattractant dynamics in the extracellular space have been limited to a small number of cells. Here, we present Dynamic cluster field modeling (DCF), a novel computational method that enables simulations of collective chemotaxis of cellular systems with O(1000)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(1000)$$\\end{document} cells and high-resolution transport dynamics of the chemoattractant in the time-evolving extracellular space. We illustrate the efficiency and predictive capabilities of our approach by comparing our numerical simulations with experiments in multiple scenarios that involve chemoattractant secretion and uptake by the migrating cells, cell migration in confined spaces, regulation of the attractant distribution by cell motion, and interactions of the chemoattractant with an enzyme. The proposed algorithm opens new opportunities to address outstanding problems that involve collective cell migration in the central nervous system, immune response and cancer metastasis.

Analyzing the Spatiotemporal Dynamics of Drought in Shaanxi Province

Drought, as a natural disaster with wide-ranging impacts and long duration, has an adverse effect on the global economy and ecosystems. In this paper, four remote sensing drought indices, namely the Crop Water Stress Index (CWSI), Vegetation Supply Water Index (VSWI), Temperature Vegetation Dryness Index (TVDI), and Normalized Difference Water Index (NDWI), are selected for drought analysis. The correlation analysis is carried out with the self-calibrated Palmer Drought Severity Index (sc-PDSI), and based on the optimal index (CWSI), the spatiotemporal characteristics of drought in Shaanxi Province from 2001 to 2021 were studied by SEN trend analysis, Mann–Kendall test, and a center of gravity migration model. The results show that (1) the CWSI performs best in drought monitoring in Shaanxi Province and is suitable for drought studies in this region. (2) Drought in Shaanxi Province shows a decreasing trend from 2001 to 2021; the main manifestation of this phenomenon is the decrease in the occurrence of severe drought, with severe drought covering less than 10% of the area in 2010 and subsequent years. The most severely affected regions in the province are the northern Loess Plateau region and Guanzhong Plain region. In terms of the overall trend, only 0.21% of the area shows an increase in drought, primarily concentrated in the Guanzhong Plain region and the outskirts of the Qinling–Bashan mountainous region. (3) Drought conditions are generally improving, with the droughts’ center of gravity moving northeastward at a rate of 3.31 km per year. The results of this paper can provide a theoretical basis and a practical reference for drought control and decision-making in Shaanxi Province.

VERMEER FCM: A tool integrating exposure and hazard modelling for chemicals migrating from food contact materials

A new tool, VERMEER FCM, was developed to support the risk assessment of single organic chemicals migrating from plastic food contact materials (FCM). The freely available tool is integrated into MERLIN-Expo and has been designed in line with Regulation (EU) No 10/2011 for plastic FCM. Overall, the tool consists of three modules that allow (i) to model the migration of chemicals into food, (ii) to predict toxicological endpoints relevant to risk assessment of FCM chemicals, and (iii) to automatically check whether the chemical of interest is included in Regulation (EU) No 10/2011. To apply the VERMEER FCM tool, users need to provide information regarding the chemical(s) of interest, the FCM, the food and other parameters (e.g. contact time and temperature). The three modules can be run either separately or in combination. Migration is predicted by a recently developed migration model, whereas hazard predictions for genotoxicity, subchronic toxicity, reproductive and developmental toxicity and carcinogenicity are provided by QSAR models selected from the publicly available VEGA HUB. The major novelty of the tool is that it combines information on hazard and exposure (i.e. migration) with regulatory information. Several case studies were performed to demonstrate the application of the tool.

Spatial and temporal evolution patterns and driving mechanisms of rural settlements: a case study of Xunwu County, Jiangxi Province, China

Urbanization and industrialization have driven rapid socio-economic development, leading to a significant population shift from rural areas to cities. This demographic transition has resulted in substantial changes in rural settlements, presenting considerable challenges for rural revitalization. Given the spatial differentiation, it is crucial to analyze the spatiotemporal evolution patterns and driving mechanisms of rural settlements under various development scenarios and at multiple scales within a county. Such analysis is essential for rational planning and sustainable development. This study analyzes the spatial and temporal evolution patterns and driving mechanisms of rural settlements in Xunwu County, Jiangxi Province, China, using land use dynamics, hot and cold spot analysis, and center of gravity migration models. The Multiscale Geographically Weighted Regression Model (MGWR) is employed to explore their transformation driving mechanisms. The results show that during 2010–2020 in the study area, the total change rate of rural settlements was 39.82%, with a dynamic degree of 2.87%. The average centroid of the settlements is located in Wenfeng Township, gradually migrating southeastward by 3.7 km. Cold spots are shrinking northward, while hotspots are gathering in Chengjiang Town. Socio-economic conditions dominate the evolution of rural clusters in this region, showing obvious spatial heterogeneity. This is followed by locational conditions that are weakening in influence, while the impact of natural geographical conditions exists in the northeast region. The research findings offer a scientifically rigorous and well-founded analysis of the evolution and driving mechanisms of rural settlements. This analysis provides a solid theoretical basis for policy planning in urban-rural integrated development and supports the sustainable growth of rural communities.

Synergistic effect of ceramic filler in polymer salt complex for improved ion dissociation and migration mechanism

Abstract Use of Ceramic filler is one of the most common approaches to improve the conductivity and stability properties of a solid polymer electrolyte (SPE) cum separator. Among them, active fillers like Garnet have been extensively used to enhance the stability and conductivity of SPE. However, SPE suffers from limited ion migration at room temperature acting as a bottleneck for their application in all solid-state batteries. An extensive study on these fillers' role in ion dissociation and migration can be a stepping stone for advanced SPE. In the present work, an FTIR analysis has primarily been used to identify and evaluate cation coordinate site-cation, and ion pair interactions in a Li6.5La3Zr1.75Te0.25O12 loaded polyethylene oxide-LiCF3SO3 matrix with varying ceramic concentrations. Further, the Trukhan model has been used to calculate diffusion coefficient, mobility, and charge carrier density to interpret relaxation parameters, conductivity, and FTIR results in the SPE samples. Finally, an ion migration model has been proposed based on the results obtained in experimental studies.

Forced migration in wartime: decision-making and trajectory

Russia’s full-scale war against Ukraine has caused a new wave of mass forced migrants. We conducted in-depth interviews with Ukrainians forced to relocate to Finland, to understand the differences in their migration decision-making and migration trajectories. The study showed that there are two models of forced migration. The first one is spontaneous and fast, where respondents didn’t consider the positive and negative consequences of migration. The second one includes a longer process of decision-making: respondents considered mainly the characteristics of their household and the conditions in the country of residence. They were motivated by the loss of security in Ukraine, and the inability to find sources of income or provide education for their children. But there were also factors that made decision-making more difficult and longer. Specifically, the need to be separated from the family, the lack of access to information about the support system abroad, and the high risks to life during the journey (caused by the danger of leaving the occupied territory and lack of other trajectories except to go to Finland through Russia).

Flocking analysis and control of a nonlinear collective migration model

Abstract In this paper, we study a nonlinear collective migration model with the Cucker–Smale type weight, the nonlinear velocity coupling and the distributed network. Finite-time flocking tracking can be achieved by the alignment force gathering agents and the tracking force matching target. A trade-off existing between the two forces is established by the tracking strategy that can be viewed as a control. When the strategy is time-invariant, finite-time flocking tracking would occur for any initial state under the long-range weight, only for partial initial state under the short-range weight. An invariant set of the system is proposed and proved to be an attractive domain of the flocking state. Then two time-varying strategies, the average strategy and the maximum strategy, are designed to overcome the constraint of initial state under the short-range weight. The average strategy has to mobilize all agents simultaneously, but only causes once switch. The maximum strategy only mobilizes the agent with the largest velocity deviation, but produces more switches. Several numerical simulations are provided to observe the effects of the time-invariant and time-varying strategies.

Language and education in migration policy: the inter-state model

Regarding the various indications such as social, cultural, political, educational, and labor policies of the host country for family migration, the present study discussed the index of inclusivity in psychosocial and educational immigration policies. The study aimed to propose how social and educational vulnerabilities of migrants should be addressed. To achieve this, the study examined the current status (state) and potential improvements in psychosocial and educational migration policies in terms of inclusivity. A wide range of materials including articles, news reports, journal pieces, legal documents from Europe and North America, specifically the EU, were analyzed to provide a comprehensive view of the subject. The study also utilized Selinker's Interlanguage theory from Second Language Acquisition to compare with migration policy in answering research questions. Through dynamic review, thematic analysis, and qualitative research design, the study concluded that the index of inclusivity is evolving and should be implemented in various aspects of migration policy. As a result, a model for education in migration policy, named "The Inter-state Model," was proposed. This model aims to provide clarity on the role and support of migration policies for migrants, particularly vulnerable populations. / Keywords: moderate inclusive education, transmigration, assimilation, diversity, migration policy, inter- state migration model

Study on failure mechanism of cracked coal rock and law of gas migration

China possesses abundant coal resources and has extensive potential for exploitation. Nevertheless, the coal rock exhibits low strength, and the coal seam fractures due to mining activities, leading to an increased rate of gas emission from the coal seam. This poses significant obstacles to the exploration and development of the coal seam. This paper focuses on studying the failure mechanism of fractured coal rock by conducting uniaxial and triaxial compression experiments on the coal rock found at the Wangpo coal mine site. Simultaneously, in conjunction with the findings from the field experiment, a gas migration model of the mining fracture field is constructed to elucidate the pattern of coal seam gas distribution during mining-induced disturbances. The study structure reveals that coal rock exhibits three distinct failure modes: tensile failure, shear failure, and tension-shear failure. The intricate fissure in the rock layer will intensify the unpredictability of rock collapse patterns. The compressive strength of coal rock diminishes as the confining pressure drops. The coal rock in the working face area will collapse as a result of the lack of confining pressure. In the rock strata above the mining fracture zone, the gas pressure is first higher and then significantly falls with time. After 100 days of ventilation, the low gas pressure area changes little, so to ensure the safety of the project, the ventilation time of the fully mechanized mining surface is at least 100 days. The research results will help to establish the core technology system of coal seam development and improve the competitiveness of coal seam resources in China.

Effect of salt erosion on interfacial adhesion of waste tire crumb rubber-modified asphalt mixtures: A molecular dynamics study

In this study, a wetting and migration model was established using the molecular dynamics simulation method. Through in-depth analysis of parameters such as contact angle, mean square displacement, and work of adhesion, the dynamic wetting and migration characteristics of salt solution were explored, and the damage mechanism of waste tire crumb rubber-modified asphalt mixtures under salt erosion was revealed. The results showed that compared with an aqueous solution, the salt solution was more likely to be adsorbed and dispersed on the asphalt surface. This exacerbated its damage. However, the presence of salt ions reduced the wetting effect of the solution on the aggregate surface and reduced the migration rate of the solution at the asphalt-aggregate interface. Significant diffusion of Na+ and Cl- ions occurs during salt solution migration, while SO42- ions mainly accumulate near the aggregate surface. In addition, salt solution migration alters the distribution of asphalt components. This further affects the interface adhesion effect. The inclusion of crumb rubber can effectively reduce the sensitivity of asphalt to salt solutions and enhance its hydrophobicity. Simultaneously, it enhances the adhesion strength and stability of the asphalt. This effectively obstructs the intrusion of water molecules and salt ions.

Molecular characteristics of dissolved organic matter regulate the binding and migration of tungsten in porous media

Tungsten (W) is an emerging contaminant that poses potential risks to both the environment and human health. While dissolved organic matter (DOM) can significantly influence the W's environmental behavior in natural aquifers, the mechanisms by which DOM's molecular structure and functional group diversity impact W binding and migration remain unclear. Using molecular weight-fractionated soil and sediment DOM (<1 kDa, 1–100 kDa, and 100 kDa–0.45 μm), this study systematically investigated the relationship between DOM molecular characteristics and tungstate (WO42−) binding properties using multiple spectroscopic methods, including FTIR, fluorescence spectroscopy and XPS. The migration behavior of WO42− in porous media was also investigated through quartz sand column experiments. Results revealed that approximately 75 % of W was controlled by DOM, with over 50 % binding to low molecular weight DOM (<1 kDa). Tungsten bound to medium-high molecular weight DOM (1–100 kDa, >100 kDa) showed a greater propensity for retention, with the >100 kDa fractions demonstrating stronger selective binding to W, exhibiting distribution coefficients (Kmd) of 6.11 L/g and 10.69 L/g, respectively. Further analysis indicated that W primarily binds with aromatic rings, phenolic hydroxyls, polysaccharides, and carboxyl groups in DOM, potentially affecting DOM structural stability and consequently influencing W migration characteristics. Free W migration in quartz sand was primarily controlled by Langmuir monolayer adsorption, leading to local enrichment (Da = 6.83, Rd = 86.98). When bound to DOM, W's migration ability significantly increased (Rd = 8–10), with adsorption shifting to a Freundlich multilayer model, primarily controlled by convective transport (Npe = 27–62> > 1.96), while adsorption effects weakened (Da ≈ 1). This study, for the first time, systematically reveals the regulatory mechanisms of DOM molecular characteristics on tungsten's environmental behavior. It offers crucial parameter support for constructing tungsten migration models and provides important guidance for tungsten pollution risk assessment and remediation strategies.

A bulk-surface mechanobiochemical modelling approach for single cell migration in two-space dimensions

In this work, we present a mechanobiochemical model for two-dimensional cell migration which couples mechanical properties of the cell cytosol with biochemical processes taking place near or on the cell plasma membrane. The modelling approach is based on a recently developed mathematical formalism of evolving bulk-surface partial differential equations of reaction–diffusion type. We solve these equations using finite element methods within a moving-mesh framework derived from the weak formulation of the evolving bulk-surface PDEs. In the present work, the cell cytosol interior (bulk) dynamics are coupled to the cell membrane (surface) dynamics through non-homogeneous Dirichlet boundary conditions. The modelling approach exhibits both directed cell migration in response to chemical cues as well as spontaneous migration in the absence of such cues. As a by-product, the approach shows fundamental characteristics associated with single cell migration such as: (i) cytosolic and membrane polarisation, (ii) actin dependent protrusions, and (iii) continuous shape deformation of the cell during migration.Cell migration is an ubiquitous process in life that is mainly triggered by the dynamics of the actin cytoskeleton and therefore is driven by both mechanical and biochemical processes. It is a multistep process essential for mammalian organisms and is closely linked to a vast diversity of processes; from embryonic development to cancer invasion. Experimental, theoretical and computational studies have been key to elucidate the mechanisms underlying cell migration. On one hand, rapid advances in experimental techniques allow for detailed experimental measurements of cell migration pathways, while, on the other, computational approaches allow for the modelling, analysis and understanding of such observations. The bulk-surface mechanobiochemical modelling approach presented in this work, set premises to study single cell migration through complex non-isotropic environments in two- and three-space dimensions.