Bidirectional molecular transport shapes cell polarization in a two-dimensional model of eukaryotic chemotaxis

Numerical characterization of regenerative axons growing along a spherical multifunctional scaffold after spinal cord injury

Spinal cord injury (SCI) followed by extensive cell loss, inflammation, and scarring, often permanently damages neurological function. Biomaterial scaffolds are promising but currently have limited applicability in SCI because after entering the scaffold, regenerating axons tend to become trapped and rarelyre-enter the host tissue, the reasons for which remain to be completely explored. Here, we propose a mathematical model and computer simulation for characterizing regenerative axons growing along a scaffold following SCI, and how their growth may be guided. The model assumed a solid, spherical, multifunctional, biomaterial scaffold, that would bridge the rostral and caudal stumps of a completely transected spinal cord in a rat model and would guide the rostral regenerative axons toward the caudal tissue. Other assumptions include the whole scaffold being coated with extracellular matrix components, and the caudal area being additionally seeded with chemoattractants. The chemical factors on and around the scaffold were formulated to several coupled variables, and the parameter values were derived fromexisting experimental data. Special attention was given to the effects of coating strength, seeding location, and seeding density, as well as the ramp slope of the scaffold, on axonal regeneration. In numerical simulations, a slimmer scaffold provided a small slope at the entry "on-ramp" area that improved the success rate of axonal regeneration. If success rates are high, an increased number of regenerative axons traverse through the narrow channels, causing congestion and lowering the growth rate. An increase in the number of severed axons (300-12000) did not significantly affect the growth rate, but it reduced the success rate of axonal regeneration. However, an increase in the seeding densities of the complexes on the whole scaffold, and that in the seeding densities of the chemoattractants on the caudal area, improved both the success and growth rates. However, an increase in the density of thecomplexes on the whole scaffold risks an over-eutrophic surface that harms axonal regeneration.Although theoretical predictions are yet to be validated directly by experiments, this theoretical tool can advance the treatment of SCI, and is also applicable to scaffolds with other architectures.

Mechanochemical modeling of neutrophil migration based on four signaling layers, integrin dynamics, and substrate stiffness

Directional neutrophil migration during human immune responses is a highly coordinated process regulated by both biochemical and biomechanical environments. In this paper, we developed an integrative mathematical model of neutrophil migration using a lattice Boltzmann-particle method built in-house to solve the moving boundary problem with spatiotemporal regulation of biochemical components. The mechanical features of the cell cortex are modeled by a series of spring-connected nodes representing discrete cell-substrate adhesive sites. The intracellular signaling cascades responsible for cytoskeletal remodeling [e.g., small GTPases, phosphoinositide-3-kinase (PI3K), and phosphatase and tensin homolog] are built based on our previous four-layered signaling model centered on the bidirectional molecular transport mechanism and implemented as reaction-diffusion equations. Focal adhesion dynamics are determined by force-dependent integrin-ligand binding kinetics and integrin recycling and are thus integrated with cell motion. Using numerical simulations, the model reproduces the major features of cell migration in response to uniform and gradient biochemical stimuli based on the quantitative spatiotemporal regulation of signaling molecules, which agree with experimental observations. The existence of multiple types of integrins with different binding kinetics could act as an adaptation mechanism for substrate stiffness. Moreover, cells can perform reversal, U-turn, or lock-on behaviors depending on the steepness of the reversal biochemical signals received. Finally, this model is also applied to predict the responses of mutants in which PTEN is overexpressed or disrupted.

Dynamic seesaw model for rapid signaling responses in eukaryotic chemotaxis

Directed movement of eukaryotic cells toward spatiotemporally varied chemotactic stimuli enables rapid intracellular signaling responses. While macroscopic cellular manifestation is shaped by balancing external stimuli strength with finite internal delays, the organizing principles of the underlying molecular mechanisms remain to be clarified. Here, we developed a novel modeling framework based on a simple seesaw mechanism to elucidate how cells repeatedly reverse polarity. As a key feature of the modeling, the bottom module of bidirectional molecular transport is successively controlled by three upstream modules of signal reception, initial signal processing, and Rho GTPase regulation. Our simulations indicated that an isotropic cell is polarized in response to a graded input signal. By applying a reversal gradient to a chemoattractant signal, lamellipod-specific molecules (i.e. PIP₃ and PI3K) disappear, first from the cell front, and then they redistribute at the opposite side, whereas functional molecules at the rear of the cell (i.e. PIP₂ and PTEN) act oppositely. In particular, the model cell exhibits a seesaw-like spatiotemporal pattern for the establishment of front and rear and interconversion, consistent with those related experimental observations. Increasing the switching frequency of the chemotactic gradient causes the cell to stay in a trapped state, further supporting the proposed dynamics of eukaryotic chemotaxis with the underlying cytoskeletal remodeling.