We present a design of the conservative, reversible, and universal all-optical Fredkin logic gate based on a single bacteriorhodopsin (BR)-protein-coated silica microcavity. The switching of a near-IR laser beam at 1310 or 1550 nm by photoactivating a silica microsphere coated with BR monolayers with a low power control signal at 532 nm, in contact between two tapered single-mode fibers, is used as a template for a four-port tunable resonant coupler Fredkin gate. The proposed gate has also been used to design low-power all-optical AND, OR, NOT, XOR, and X-NOR gates and full-adder and demultiplexer/multiplexer circuits. The advantages of high Q-factor, tunability, compactness, low-power control signals, high fan-out, and flexibility of cascading switches in 2-D to 3-D architectures to form circuits, makes the designs promising for practical applications. The proposed design provides a new paradigm for hybrid nanobiophotonic integration for all-optical computing.