Simulating rolling paths and reorientation behavior of ball-rolling dung beetles

Ball-rolling dung beetles show a remarkable ability to maintain a straight path while rolling dung balls away from a dung pile. Rolling in a straight line is beneficial, as it enables beetles to efficiently escape competition near the dung pile. Research has shown that beetles use the sky to choose and maintain an initial rolling direction, and to reorient (correct their direction) when pushed off their intended course by obstacles or uneven ground. While beetles' mechanisms for navigation are well understood, it remains unclear how beetles regulate the timing of reorientation and under what circumstances reorientation is beneficial. Previous studies have focused only on the observable data from the movement of real dung beetles, in the field and simulated environments. In this paper, we formulate a mathematical model based on a persistent random walk to simulate a dung beetle's movement in a circular arena. We simulate two possible reorientation strategies and analyze the impact when reorientation is not perfect. We show that our model provides an approximation of actual dung ball rolling paths, analyze the benefits of each reorientation technique under varying conditions, and show that when the sky is obscured, rolling without reorientation can be a beetle's optimal strategy.

Interplay Between the Persistent Random Walk and the Contact Inhibition of Locomotion Leads to Collective Cell Behaviors

Cell migration plays an important role in physiology and pathophysiology. It was observed in the experiments that cells, such as fibroblast, leukocytes, and cancer cells, exhibit a wide variety of migratory behaviors, such as persistent random walk, contact inhibition of locomotion, and ordered behaviors. To identify biophysical mechanisms for these cellular behaviors, we developed a rigorous computational model of cell migration on a two-dimensional non-deformable substrate. Cells in the model undergo motion driven by mechanical interactions between cellular protrusions and the substrate via the balance of tensile forces. Properties of dynamic formation of lamellipodia induced the persistent random walk behavior of a migrating cell. When multiple cells are included in the simulation, the model recapitulated the contact inhibition of locomotion between cells at low density without any phenomenological assumptions or momentum transfer. Instead, the model showed that contact inhibition of locomotion can emerge via indirect interactions between the cells through their interactions with the underlying substrate. At high density, contact inhibition of locomotion between numerous cells gave rise to confined motions or ordered behaviors, depending on cell density and how likely lamellipodia turn over due to contact with other cells. Results in our study suggest that various collective migratory behaviors may emerge without more restrictive assumptions or direct cell-to-cell biomechanical interactions.

Cell Migration in 1D and 2D Nanofiber Microenvironments

Understanding how cells migrate in fibrous environments is important in wound healing, immune function, and cancer progression. A key question is how fiber orientation and network geometry influence cell movement. Here we describe a quantitative, modeling-based approach toward identifying the mechanisms by which cells migrate in fibrous geometries having well controlled orientation. Specifically, U251 glioblastoma cells were seeded onto non-electrospinning Spinneret based tunable engineering parameters fiber substrates that consist of networks of suspended 400 nm diameter nanofibers. Cells were classified based on the local fiber geometry and cell migration dynamics observed by light microscopy. Cells were found in three distinct geometries: adhering two a single fiber, adhering to two parallel fibers, and adhering to a network of orthogonal fibers. Cells adhering to a single fiber or two parallel fibers can only move in one dimension along the fiber axis, whereas cells on a network of orthogonal fibers can move in two dimensions. We found that cells move faster and more persistently in 1D geometries than in 2D, with cell migration being faster on parallel fibers than on single fibers. To explain these behaviors mechanistically, we simulated cell migration in the three different geometries using a motor-clutch based model for cell traction forces. Using nearly identical parameter sets for each of the three cases, we found that the simulated cells naturally replicated the reduced migration in 2D relative to 1D geometries. In addition, the modestly faster 1D migration on parallel fibers relative to single fibers was captured using a correspondingly modest increase in the number of clutches to reflect increased surface area of adhesion on parallel fibers. Overall, the integrated modeling and experimental analysis shows that cell migration in response to varying fibrous geometries can be explained by a simple mechanical readout of geometry via a motor-clutch mechanism.