We show all-optical switching of an input infrared laser beam at 1310 nm by controlling the photoinduced retinal isomerization to tune the resonances in a silica microsphere coated with three bacteriorhodopsin (BR) protein monolayers. The all-optical tunable resonant coupler re-routes the infrared beam between two tapered fibers in 50 μs using a low power (<200 μW) green (532 nm) and blue (405 nm) pump beams. The basic switching configuration has been used to design all-optical computing circuits, namely, half and full adder/subtractor, de-multiplexer, multiplexer, and an arithmetic unit. The design requires 2n-1 switches to realize n bit computation. The designs combine the exceptional sensitivities of BR and high-Q microcavities and the versatile tree architecture for realizing low power circuits and networks (approximately mW power budget). The combined advantages of high Q-factor, tunability, compactness, and low power control signals, with the flexibility of cascading switches to form circuits, and reversibility and reconfigurability to realize arithmetic and logic functions, makes the designs promising for practical applications. The designs are general and can be implemented (i) in both fiber-optic and integrated optic formats, (ii) with any other coated photosensitive material, or (iii) any externally controlled microresonator switch.