  Here we study a pumping device capable of maintaining a density gradient and
a flux of particles across a membrane. Its driving mechanism is based on the
flashing ratchet effect powered by the random telegraph process in the presence
of thermal fluctuations. Unlike Brownian motors, the concentrations at both
reservoir boundaries need to be implemented as boundary conditions. The
residence transition rates of the dichotomic flashing are related to the
binding and hydrolysis of ATP molecules. The model is exactly solved and
explored. The pump energetics is discussed and the relevant parameter values
are tuned within a biological scale.
