A 1D model of leukocyte adhesion coupling bond dynamics with blood velocity

A general numerical model of leukocyte adhesion in microchannels

Leukocyte adhesion on the vascular endothelium plays an important role in human immune system and reflects the physiological condition of a human body. In this paper, a generally implementable dynamic adhesion model based on the length limit of microvilli was developed to explore the behavior of a suspended leukocyte's adhesion process under microchannel shear flow. Simulations showed that the whole adhesion process can be divided into cell sedimentation, preliminary adhesion and stable dynamic adhesion stages. The cell tumbling kinetics, cell deformation, cell adhesion area and adhesion force were studied under the conditions of various bond strength, cell membrane surface tension, inlet flow velocity and cytoplasmic viscosity. Results showed that the bond strength affects the cell tumbling behaviors differently by changing the adhesion force. The cell with lower membrane surface tension induces a larger adhesion area, and eventually results in a greater adhesion and a lower cell tumbling velocity. The flow velocity changes cell velocity through the flow viscous force during the whole adhesion process. The cytoplasmic viscosity affects adhesion mainly in the preliminary adhesion stage by changing the cell deformation rate but has slight effect on the stabilized dynamic adhesion on cells. This study provides a simple theoretical basis to further clarify the mechanism of cell behaviors under stress and adhesion and becomes one of the prerequisites for study of tissue inflammation, wound healing, and disease treatments.

The nanocaterpillar's random walk: diffusion with ligand-receptor contacts

Particles with ligand-receptor contacts bind and unbind fluctuating "legs" to surfaces, whose fluctuations cause the particle to diffuse. Quantifying the diffusion of such "nanoscale caterpillars" is a challenge, since binding events often occur on very short time and length scales. Here we derive an analytical formula, validated by simulations, for the long time translational diffusion coefficient of an overdamped nanocaterpillar, under a range of modeling assumptions. We demonstrate that the effective diffusion coefficient, which depends on the microscopic parameters governing the legs, can be orders of magnitude smaller than the background diffusion coefficient. Furthermore it varies rapidly with temperature, and reproduces the striking variations seen in existing data and our own measurements of the diffusion of DNA-coated colloids. Our model gives insight into the mechanism of motion, and allows us to ask: when does a nanocaterpillar prefer to move by sliding, where one leg is always linked to the surface, and when does it prefer to move by hopping, which requires all legs to unbind simultaneously? We compare a range of systems (viruses, molecular motors, white blood cells, protein cargos in the nuclear pore complex, bacteria such as Escherichia coli, and DNA-coated colloids) and present guidelines to control the mode of motion for materials design.

Analysis of Perturbed Volterra Integral Equations on Time Scales

This paper describes the effect of perturbation of the kernel on the solutions of linear Volterra integral equations on time scales and proposes a new perspective for the stability analysis of numerical methods.

A stochastic model for cell adhesion to the vascular wall

Cell dynamics in the vicinity of the vascular wall involves several factors of mechanical or biochemical origins. It is driven by the competition between the drag force of the blood flow and the resistive force generated by the bonds created between the circulating cell and the endothelial wall. Here, we propose a minimal mathematical model for the adhesive interaction between a circulating cell and the blood vessel wall in shear flow when the cell shape is neglected. The bond dynamics in cell adhesion is modeled as a nonlinear Markovian Jump process that takes into account the growth of adhesion complexes. Performing scaling limits in the spirit of Joffe and Metivier (Adv Appl Probab 18(1):20, 1986), Ethier and Kurtz (Markov processes: characterization and convergence, Wiley, New York, 2009), we obtain deterministic and stochastic continuous models, whose analysis allow to identify a threshold shear velocity associated with the transition from cell rolling and firm adhesion. We also give an estimation of the mean stopping time of the cell resulting from this dynamics. We believe these results can have strong implications for the understanding of major biological phenomena such as cell immunity and metastatic development.