  We discuss the Lattice Boltzmann-Particle Dynamics (LBPD) multiscale paradigm
for the simulation of complex states of flowing matter at the interface between
Physics, Chemistry and Biology. In particular, we describe current large-scale
LBPD simulations of biopolymer translocation across cellular membranes,
molecular transport in ion channels and amyloid aggregation in cells. We also
provide prospects for future LBPD explorations in the direction of cellular
organization, the direct simulation of full biological organelles, all the way
to up to physiological scales of potential relevance to future
precision-medicine applications, such as the accurate description of
homeostatic processes. It is argued that, with the advent of Exascale
computing, the mesoscale physics approach advocated in this paper, may come to
age in the next decade and open up new exciting perspectives for physics-based
computational medicine.
