We report on a numerical study of polymer network formation of asymmetric biomimetic telechelic polymers with two reactive ends based on a self-assembling collagen, elastin or silk-like polypeptide sequence. The two reactive ends of the polymer can be activated independently using physicochemical triggers such as temperature and pH. We show, using a simple coarse grained model that the order in which this triggering occurs influences the final morphology. For both of collagen-silk and elastin-silk topologies we find that for relatively short connector chains the morphology of the assembly is greatly influenced by the order of the trigger, whereas for longer chains the equilibrium situation is more easily achieved. Moreover, self-assembly is greatly enhanced at moderate collagen interaction strength, due to facilitated binding and unbinding of the peptides. This finding indicates that both the trigger sequence and strength can be used to steer self-assembly in these biomimetic polymer systems.