  A fundamental function of cortical circuits is the integration of information
from different sources to form a reliable basis for behavior. While animals
behave as if they optimally integrate information according to Bayesian
probability theory, the implementation of the required computations in the
biological substrate remains unclear. We propose a novel, Bayesian view on the
dynamics of conductance-based neurons and synapses which suggests that they are
naturally equipped to optimally perform information integration. In our
approach apical dendrites represent prior expectations over somatic potentials,
while basal dendrites represent likelihoods of somatic potentials. These are
parametrized by local quantities, the effective reversal potentials and
membrane conductances. We formally demonstrate that under these assumptions the
somatic compartment naturally computes the corresponding posterior. We derive a
gradient-based plasticity rule, allowing neurons to learn desired target
distributions and weight synaptic inputs by their relative reliabilities. Our
theory explains various experimental findings on the system and single-cell
level related to multi-sensory integration, which we illustrate with
simulations. Furthermore, we make experimentally testable predictions on
Bayesian dendritic integration and synaptic plasticity.
