A fascinating and much studied biological behavior involves the motion signatures of neutrophils (a type of white blood cell) over the endothelial lining of venules, following an injury which activates the inflammation cascade and causes the vessel surface to become sticky. Then, as a result of transient bond formation and breaking between sialyl-lewisx groups on the neutrophils and selectins on the endothelium, neutrophils roll over the interior surface of the vessel, causing them to move more slowly than they would in flow, not engaged with the surface. Once moving slowly, integrins engage, causing the neutrophils to stop altogether (achieve firm arrest), after which point they migrate into tissue to fight infection. This behavior has been reproduced in vitro employing selectin-functionalized microparticles and a surface of appropriate complimentary, a model which relies on biomolecules. In this talk, we reproduce rolling and arrest behavior in a simple non-biological model which allows us to more systematically probe fundamental variables which govern the problem: Density of surface functional groups, their arrangement in the plane of a surface, their binding strength, the role of the repulsive background field. We report the domains of rolling in the form of multi-variable phase-space maps and discuss two related but distinctly separate ways of describing the behavior: The forming and breaking of stochastic bonds versus particle motion in a complex surface field of colloidal forces.