  Faithful segregation of genetic material during cell division requires
alignment of chromosomes between two spindle poles and attachment of their
kinetochores to each of the poles. Failure of these complex dynamical processes
leads to chromosomal instability (CIN), a characteristic feature of several
diseases including cancer. While a multitude of biological factors regulating
chromosome congression and bi-orientation have been identified, it is still
unclear how they are integrated so that coherent chromosome motion emerges from
a large collection of random and deterministic processes. Here we address this
issue by a three dimensional computational model of motor-driven chromosome
congression and bi-orientation during mitosis. Our model reveals that
successful cell division requires control of the total number of microtubules:
if this number is too small bi-orientation fails, while if it is too large not
all the chromosomes are able to congress. The optimal number of microtubules
predicted by our model compares well with early observations in mammalian cell
spindles. Our results shed new light on the origin of several pathological
conditions related to chromosomal instability.
