  Polymer composites are ideal candidates for next generation biomimetic soft
materials because of their exquisite bottom-up designability. However, the
richness of behaviours comes at a price: the need for precise and extensive
characterisation of material properties over a highly-dimensional parameter
space, as well as a quantitative understanding of the physical principles
underlying desirable features. Here we couple large-scale Molecular Dynamics
simulations with optical tweezers microrheology to characterise the
viscoelastic response of DNA-actin composites. We discover that the previously
observed non-monotonic stress-stiffening of these composites is robust, yet
tunable, in a broad range of the parameter space that spans two orders of
magnitude in DNA length. Importantly, we discover that the most pronounced
stiffening is achieved when the species are maximally coupled, i.e. have
similar number of entanglements, and not when the number of entanglements per
DNA chain is largest. We further report novel dynamical oscillations of the
microstructure of the composites, alternating between mixed and bundled phases,
opening the door to future investigations. The generic nature of our system
renders our results applicable to the behaviour of a broad class of polymer
composites.
