  Effective treatments that prevent or reduce drug relapse vulnerability should
be developed to relieve the high burden of drug addiction to society. This will
only be possible by enhancing the understanding of the molecular mechanisms
underlying the neurobiology of addiction. Recent experimental data have shown
that dendritic spines, small protrusions from the dendrites that receive input
from excitatory neurons, from spiny neurons in the nucleus accumbens exhibit
morphological changes during drug exposure and withdrawal. Moreover, these
changes relate to the characteristic drug-seeking behavior of addiction.
However, due to the complexity of the dendritic spines, we do not yet fully
understand the processes underlying their structural changes in response to
different inputs. We propose that biophysical models can enhance the current
understanding of these processes by incorporating different, and sometimes,
discrepant experimental data to identify the shared underlying mechanisms and
generate experimentally testable hypotheses. This review aims to give an
up-to-date report on biophysical models of dendritic spines, focusing on those
models that describe their shape changes, which are well-known to relate to
learning and memory. Moreover, it examines how these models can enhance our
understanding of the effect of the drugs and the synaptic changes during
disease progression.
