  Background: For faithful chromosome segregation during cell division, correct
attachments must be established between sister chromosomes and microtubules
from opposite spindle poles through kinetochores (chromosome bi-orientation).
Incorrect attachments of kinetochore microtubules (kMTs) lead to chromosome
mis-segregation and aneuploidy, which is often associated with developmental
abnormalities such as Down syndrome and diseases including cancer. The
interaction between kinetochores and microtubules is highly dynamic with
frequent attachments and detachments. However, it remains unclear how
chromosome bi-orientation is achieved with such accuracy in such a dynamic
process.
  Results: To gain new insight into this essential process, we have developed a
simple mathematical model of kinetochore-microtubule interactions during cell
division in general, i.e. both mitosis and meiosis. Firstly, the model reveals
that the balance between attachment and detachment probabilities of kMTs is
crucial for correct chromosome bi-orientation. With the right balance,
incorrect attachments are resolved spontaneously into correct bi-oriented
conformations while an imbalance leads to persistent errors. In addition, the
model explains why errors are more commonly found in the first meiotic division
(meiosis I) than in mitosis and how a faulty conformation can evade the spindle
assembly checkpoint, which may lead to a chromosome loss.
  Conclusions: The proposed model, despite its simplicity, helps us understand
one of the primary causes of chromosomal instability - aberrant
kinetochore-microtubule interactions. The model reveals that chromosome
bi-orientation is a probabilistic self-organization, rather than a
sophisticated process of error detection and correction.
