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Register a new userPattern formation of skin cancers: Effects of cancer proliferation and hydrodynamic interactions
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We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional Model H for macrophase separations by considering a logistic growth of cancer cells and also a mechanical friction between dermis and epidermis. Importantly, our model exhibits a microphase separation due to the proliferation of cancer cells. By numerically solving the time evolution equations of the cancer composition and its velocity, we show that the phase separation kinetics strongly depends on the cell proliferation rate as well as on the strength of hydrodynamic interactions. A steady state diagram of cancer patterns is established in terms of these two dynamical parameters and some of the patterns correspond to clinically observed cancer patterns. Furthermore, we examine in detail the time evolution of the average composition of cancer cells and the characteristic length of the microstructures. Our results demonstrate that different sequence of cancer patterns can be obtained by changing the proliferation rate and/or hydrodynamic interactions.
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The influence of hydrodynamic interactions on lane formation of oppositely charged driven colloidal suspensions is investigated using Brownian dynamics computer simulations performed on the Rotne-Prager level of the mobility tensor. Two cases are considered, namely sedimentation and electrophoresis. In the latter case the Oseen contribution to the mobility tensor is screened due to the opposite motion of counterions. The simulation results are compared to that resulting from simple Brownian dynamics where hydrodynamic interactions are neglected. For sedimentation, we find that hydrodynamic interactions strongly disfavor laning. In the steady-state of lanes, a macroscopic phase separation of lanes is observed. This is in marked contrast to the simple Brownian case where a finite size of lanes was obtained in the steady-state. For strong Coulomb interactions between the colloidal particles a lateral square lattice of oppositely driven lanes is stable similar to the simple Brownian dynamics. In an electric field, on the other hand, the behavior is found in qualitative and quantitative accordance with the case of neglected hydrodynamics.
Partial differential equations (PDE) have been widely used to reproduce patterns in nature and to give insight into the mechanism underlying pattern formation. Although many PDE models have been proposed, they rely on the pre-request knowledge of physical laws and symmetries, and developing a model to reproduce a given desired pattern remains difficult. We propose a novel method, referred to as Bayesian modelling of PDE (BM-PDE), to estimate the best PDE for one snapshot of a target pattern under the stationary state. We show the order parameters extracting symmetries of a pattern together with Bayesian modelling successfully estimate parameters as well as the best model to make the target pattern. We apply BM-PDE to nontrivial patterns, such as quasi-crystals, a double gyroid and Frank Kasper structures. Our method works for noisy patterns and the pattern synthesised without the ground truth parameters, which are required for the application toward experimental data.
Transforming growth factor (TGF) $beta$ is known to have properties of both a tumor suppressor and a tumor promoter. While it inhibits cell proliferation, it also increases cell motility and decreases cell--cell adhesion. Coupling mathematical modeling and experiments, we investigate the growth and motility of oncogene--expressing human mammary epithelial cells under exposure to TGF--$beta$. We use a version of the well--known Fisher--Kolmogorov equation, and prescribe a procedure for its parametrization. We quantify the simultaneous effects of TGF--$beta$ to increase the tendency of individual cells and cell clusters to move randomly and to decrease overall population growth. We demonstrate that in experiments with TGF--$beta$ treated cells textit{in vitro}, TGF--$beta$ increases cell motility by a factor of 2 and decreases cell proliferation by a factor of 1/2 in comparison with untreated cells.
We experimentally and theoretically investigate the collective behavior of three colloidal particles that are driven by a constant force along a toroidal trap. Due to hydrodynamic interactions, a characteristic limit cycle is observed. When we additionally apply a periodic sawtooth potential, we find a novel caterpillar-like motional sequence that is dominated by hydrodynamic interactions and promotes the surmounting of potential barriers by the particles.
Some types of bacteria use rotating helical flagella to swim. The motion of such organisms takes place in the regime of low Reynolds numbers where viscous effects dominate and where the dynamics is governed by hydrodynamic interactions. Typically, rotating flagella form bundles, which means that their rotation is synchronized. The aim of this study is to investigate whether hydrodynamic interactions can be at the origin of such a bundling and synchronization. We consider two stiff helices that are modelled by rigidly connected beads, neglecting any elastic deformations. They are driven by constant and equal torques, and they are fixed in space by anchoring their terminal beads in harmonic traps. We observe that, for finite trap strength, hydrodynamic interactions do indeed synchronize the helix rotations. The speed of phase synchronization decreases with increasing trap stiffness. In the limit of infinite trap stiffness, the speed is zero and the helices do not synchronize.
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