  Dendritic spines, the carriers of long-term memory, occupy a small fraction
of cortical space, and yet they are the major consumers of brain metabolic
energy. What fraction of this energy goes for synaptic plasticity, correlated
with learning and memory? It is estimated here based on neurophysiological and
proteomic data for rat brain that, depending on the level of protein
phosphorylation, the energy cost of synaptic plasticity constitutes a small
fraction of the energy used for fast excitatory synaptic transmission,
typically $4.0-11.2 \%$. Next, this study analyzes a metabolic cost of a new
learning and its memory trace in relation to the cost of prior memories, using
a class of cascade models of synaptic plasticity. It is argued that these
models must contain bidirectional cyclic motifs, related to protein
phosphorylation, to be compatible with basic thermodynamic principles. For most
investigated parameters longer memories generally require proportionally more
energy to store. The exception are the parameters controlling the speed of
molecular transitions (e.g. ATP driven phosphorylation rate), for which memory
lifetime per invested energy can increase progressively for longer memories.
Furthermore, in general, a memory trace decouples dynamically from a
corresponding synaptic metabolic rate such that the energy expended on a new
learning and its memory trace constitutes in most cases only a small fraction
of the baseline energy associated with prior memories. Taken together, these
empirical and theoretical results suggest a metabolic efficiency of
synaptically stored information.
