  There are numerous scenarios in which populations of cells migrate in crowded
environments. Typical examples include wound healing, cancer growth and embryo
development. In these crowded environments cells are able to interact with each
other in a variety of ways. These include excluded volume interactions,
adhesion, repulsion, cell signalling, pushing and pulling. One popular way to
understand the behaviour of a group of interacting cells is through an
agent-based model (ABM). A typical aim of modellers using such represtations is
to elucidate how the microscopic interactions at the cell-level impact on the
macroscopic behaviour of the population. The complex cell-cell interactions
listed above have also been incorporated into such models; all apart from
cell-cell pulling. In this paper we consider this under-represented cell-cell
interaction, in which an active cell is able to `pull' a nearby neighbour as it
moves. We incorporate a variety of potential cell-cell pulling mechanisms into
on- and off-lattice agent-based volume exclusion models of cell movement. For
each of these agent-based models we derive a continuum partial differential
equation which describes the evolution of the cells at a population-level. We
study the agreement between the ABMs and the continuum, population-based
models, and compare and contrast a range of ABMs (accounting for the different
pulling mechanisms) with each other. We find generally good agreement between
the ABMs and the corresponding continuum models that worsens as the agent-based
models become more complex. Interestingly, we observe that the partial
differential equations that we derive differ significantly, depending on
whether they were derived from on- or off-lattice ABMs of pulling. This hints
that it is important employ the appropriate ABM when representing pulling
cell-cell interactions.
