A bulk-surface moving-mesh finite element method for modelling cell migration pathways
Bibliographic record
Abstract
Abstract 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 properties and biochemical processes. It is a multistep process essential for mammalian organisms and is closely linked to development, cancer invasion and metastasis formation, wound healing, immune response, tissue differentiation and regeneration, and inflammation. 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. Here, we present a computational framework coupling mechanical properties with biochemical processes to model two–dimensional cell migration by considering membrane and cytosolic activities that may be triggered by external cues. Our computational approach shows that the numerical implementation of the mechanobiochemical model is able to deal with fundamental characteristics such as: (i) membrane polarisation, (ii) cytosolic polarisation, and (iii) actin-dependent protrusions. This approach can be generalised to deal with single cell migration through complex non-isotropic environments, both in 2- and 3-dimensions. Author summary When a single or group of cells follow directed movement in response to either chemical and/or mechanical cues, this process is known as cell migration. It is essential for many biological processes such as immune response, embryogenesis, gastrulation, wound repair, cancer metastasis, tumour invasion, inflammation and tissue homeostasis. However, aberrant or defects in cell migration lead to various abnormalities and life-threatening medical conditions [1–4]. Increasing our knowledge on cell migration can help abate the spread of highly malignant cancer cells, reduce the invasion of white cells in the inflammatory process, enhance the healing of wounds and reduce congenital defects in brain development that lead to mental disorders. In this study, we present a computational framework that allows us to couple mechanical properties with biochemical signalling processes to study long time behaviour of single cell migration (either directed or random). The novelty is that the evolution law for the velocity (also known as the flow or material velocity) is described by a biomechanical force balance model posed inside the cell and this in turn is driven by the actomyosin spatiotemporal model (following the classical theory of reaction-diffusion) which is responsible for force generation as described in many experimental works [2, 5, 8, 10, 11]. Hence, our modelling approach is based on a new mathematical formalism of bulk-surface partial differential equations coupled with a novel adaptive moving-mesh finite element method to allow for significant cell deformations during migration. The approach set premises to study cell migration through complex non-isotropic environments, thereby giving biologists a predictive tool for modelling cell migration.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".