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Register a new userA stochastic model for wound healing
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We present a discrete stochastic model which represents many of the salient features of the biological process of wound healing. The model describes fronts of cells invading a wound. We have numerical results in one and two dimensions. In one dimension we can give analytic results for the front speed as a power series expansion in a parameter, p, that gives the relative size of proliferation and diffusion processes for the invading cells. In two dimensions the model becomes the Eden model for p near 1. In both one and two dimensions for small p, front propagation for this model should approach that of the Fisher-Kolmogorov equation. However, as in other cases, this discrete model approaches Fisher-Kolmogorov behavior slowly.
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We present a stochastic model which describes fronts of cells invading a wound. In the model cells can move, proliferate, and experience cell-cell adhesion. We find several qualitatively different regimes of front motion and analyze the transitions between them. Above a critical value of adhesion and for small proliferation large isolated clusters are formed ahead of the front. This is mapped onto the well-known ferromagnetic phase transition in the Ising model. For large adhesion, and larger proliferation the clusters become connected (at some fixed time). For adhesion below the critical value the results are similar to our previous work which neglected adhesion. The results are compared with experiments, and possible directions of future work are proposed.
The mechanisms underlying collective migration, or the coordinated movement of a population of cells, are not well understood despite its ubiquitous nature. As a means to investigate collective migration, we consider a wound healing scenario in which a population of cells fills in the empty space left from a scratch wound. Here we present a simplified mathematical model that uses reaction-diffusion equations to model collective migration during wound healing with an emphasis on cell movement and its response to both cell signaling and cell-cell adhesion. We use the model to investigate the effect of the MAPK signaling cascade on cell-cell adhesion during wound healing after EGF treatment. Our results suggest that activation of the MAPK signaling cascade stimulates collective migration through increases in the pulling strength of leader cells. We further use the model to suggest that treating a cell population with EGF converts the time to wound closure (as function of wound area) from parabolic to linear.
We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al., IMA J. Math. App. Med., 17, 2000. In this work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime: we construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.
The phenotypic plasticity of cancer cells has received special attention in recent years. Even though related models have been widely studied in terms of mathematical properties, a thorough statistical analysis on parameter estimation and model selection is still very lacking. In this study, we present a Bayesian approach on the relative frequencies of cancer stem cells (CSCs). Both Gibbs sampling and Metropolis-Hastings (MH) algorithm are used to perform point and interval estimations of cell-state transition rates between CSCs and non-CSCs. Extensive simulations demonstrate the validity of our model and algorithm. By applying this method to a published data on SW620 colon cancer cell line, the model selection favors the phenotypic plasticity model, relative to conventional hierarchical model of cancer cells. Moreover, it is found that the initial state of CSCs after cell sorting significantly influences the occurrence of phenotypic plasticity.
Next generation wound care technology capable of diagnosing wound parameters, promoting healthy cell growth and reducing pathogenic infections noninvasively will provide patients with an improved standard of care and an accelerated wound repair. Temperature is one of the indicating biomarkers specific to chronic wounds. This work reports a hybrid, multifunctional optical platform: nanodiamond-silk membranes as bioinspired dressings capable of temperature sensing and wound healing. The hybrid was fabricated through electrospinning and formed sub-micron fibrous membranes with high porosity. The silk fibres are capable of compensating for the lack of extracellular matrix at the wound site, supporting the wound healing. The negatively charged nitrogen vacancy (NV-) color centres in nanodiamonds (NDs) exhibit optically detected magnetic resonance (ODMR) properties and act as fluorescent nanoscale thermometers, capable of sensing temperature variations associated to the presence of infection or inflammation in a wound, without physically removing the dressing. Our results show that the presence of NDs in the hybrid ND-silk membranes improve the thermal stability of silk fibres. The NV- color centres in NDs embedded in silk fibres exhibit well-retained fluorescent and ODMR. Using the NV- centres as fluorescent nanoscale thermometers, we achieved temperature sensing at a range of temperatures, including the biologically relevant temperature window, on cell-cultured ND-silk membranes. Enhancement in the temperature sensitivity of the NV- centres was observed for the hybrids. The membranes were further tested in vivo in a murine wound healing model and demonstrated biocompatibility and equivalent wound closure rates as the control wounds. Additionally, the hybrid ND-silk membranes showed selective antifouling and biocidal propensity toward Gram-negative Pseudomonas aeruginosa and Escherichia coli.
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